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47,066 | eastsidegringo | 2007-08-27T17:54:50 | The 3rd Commandment of Supporting Your Family | Draw on the energy of your family or you'll never have enough energy. What's the difference between a workaholic and a supportaholic? For the workaholic there will never be enough work.
| http://tracksuitceo.wordpress.com/2007/08/27/the-3rd-commandment-of-supporting-your-family/ | 4 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,067 | knewjax | 2007-08-27T17:55:16 | Bandsintown at it again | Today Bandsintown launches the first major update to the site since our launch in june. This major update officially launches Bandsintown as a "Social Network"
The updates include the ability to add friends, message, and comment. All users now have profile pages, and an upcoming show widget to be used anywhere they like. We also added a page called Fansintown which displays live music fans in your area. We are still in development and will continually be updating and realeasing new version of the site until the beta version is complete. We are listingin to all our users comments and feedback to help guide our development so please let us know what you think and what you want in a live music community website! thanks again for all the Ycombinator help!<p>Check it out at Bandsintown.com | http://blog.bandsintown.com/ | 7 | 17 | [
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47,072 | kkim | 2007-08-27T18:05:56 | Raganwald on Meanies | http://weblog.raganwald.com/2007/08/off-topic-meanies.html | 14 | 3 | [
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] | null | null | no_error | Off Topic: Meanies! | null | null | (This is a snapshot of my old weblog. New posts and selected republished essays can be found at raganwald.com.)
Off Topic: Meanies!This exchange on comp.compression is like one of those depressing movies where you suddenly realize you don’t like any of the characters.There’s this guy, you think maybe he’s misguided and needs a few pointers to realize he’s trying to create a perpetual motion machine. But no, he turns out to be a complete troll with sock puppets flying in formation.And his interlocutors? Are they patient, nice people pushed over the edge by his behaviour? No, they come across as just plain mean, like a group of nerds in the high school cafeteria laughing at someone because he isn’t as smart as they think they are. Yes, the guy is a troll, but there’s absolutely no need to be so rude to him. Especially when plonk is a key press away.My experience is that rude behaviour is never forced upon people by circumstance. Some people are rude by nature, some people aren’t. Don’t tell me you have to be rude to people like him because of such and such. That’s just rationalization.Argue with idiots, and you become an idiot.The moral of the story is this: do not be lured into taunting or insulting someone on the premise that they are wrong, stupid, or rude themselves. They’re an idiot. Fine. Keep that opinion to yourself. Sharing it with the whole world literally drags you into the muck and reflects very poorly on your character.I am not giving you advice here, I am sharing a painful realization. Looking back on many of my own exchanges, once the heat of the moment passes, I am often dismayed at what I have written, at the tone I have taken, at the sheer meanness of my flames.Learn from my experience: if there is no intellectual benefit to be had from a discussion, walk away.p.s. My comment policy on my blog, as always, is that rudeness to me is always tolerated. Well, I prefer that you not be profane, as a courtesy to other readers, but being mean to me is always acceptable.
| 2024-11-08T17:36:45 | en | train |
|
47,078 | knewjax | 2007-08-27T18:16:40 | Labeling A company as YC rejected? Not OK? | Is this considered unethical or against the hackernews rules?<p>We label Bandsintown as a rejected company to show perseverance and because i think there is an interest in the companies that are applying to YC wether they made it or not. I am curious to how everyone feels on this issue. | 7 | 29 | [
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|
47,079 | kashif | 2007-08-27T18:21:36 | Ask PG: How many submissions yet? | PG, How many applications yet for the next season of YC funding? | 5 | 12 | [
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] | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,084 | transburgh | 2007-08-27T18:33:40 | eBay's Mistakes & What You Can Learn From Them | null | http://www.foundread.com/view/ebays-mistakes-what | 1 | 0 | null | null | null | no_article | null | null | null | null | 2024-11-08T18:00:18 | null | train |
47,085 | transburgh | 2007-08-27T18:34:09 | Why Everyone Hates To Love Technorati But Still Does | null | http://www.webpronews.com/blogtalk/2007/08/27/why-everyone-hates-to-love-technorati-but-still-does | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,091 | luccastera | 2007-08-27T18:45:33 | Google Phone An Attempt To Take On $100 PC? | null | http://gigaom.com/2007/08/27/google-phone-an-attempt-to-take-on-100-pc/ | 5 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,094 | dimida | 2007-08-27T18:49:31 | Brainshark's Software-as-a-Service Presentation Capabilities Ease Communication | null | http://www.cio.com/article/133450/ | 2 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,097 | transburgh | 2007-08-27T18:52:16 | KickApps Gets iPhone-Friendly with Video, Formatting | null | http://www.techcrunch.com/2007/08/27/kickapps-gets-iphone-friendly-with-video-formatting/ | 1 | 0 | null | null | null | no_error | KickApps Gets iPhone-Friendly with Video, Formatting | TechCrunch | 2007-08-27T14:00:39+00:00 | Mark Hendrickson |
KickApps, provider of a platform for building white label social networks, will announce today that it has taken two initiatives to make the social networks hosted on its platform more accessible to iPhone users. First, all videos uploaded to KickApps affiliate networks will be viewable on the iPhone despite the device’s lack of Flash support. Secondly, the company is releasing developer tools that will enable affiliates to format their networks for display on the iPhone.
As of August 24th, KickApps has begun automatically converting uploaded videos to both Flash and QuickTime format. Over the next month or so, the company will also be converting its entire back catalogue of Flash videos to QuickTime. When an iPhone user attempts to view a KickApps-hosted video, he or she will be dished up a QuickTime file, whereas desktop clients will continue to load the standard Flash applet.
While technically speaking this probably wasn’t too hard to pull off, it is a nice gesture by KickApps to potential customers who see the things that other Web 2.0 companies – like Facebook, Meebo, and Netvibes – are doing with the iPhone and want in on the action. As the first white label social networking platform to roll out iPhone features, it also earns the company some bragging rights.
Given that Apple will likely add Flash support to the iPhone before too long, their second announcement about formatting KickApps networks for the iPhone will have longer lasting significance. The company will now allow affiliates to create two CSS files for each of their networks’ pages: one to style the page for a regular browser and one for the iPhone. The appropriate stylesheet will be served after a snippet of JavaScript determines the client’s browsing environment.
KickApps has created a test network (pictured above) at KickFlix.net to demonstrate how formatting and video playback works on the iPhone. While not terribly pretty, this demo lists videos and members in a way that fits nicely into the iPhone’s smaller screen. Unfortunately, the company did not also format the actual video and member pages for the iPhone. This oversight makes me wonder how easy it will actually be for affiliates to create CSS files that make all of their networks’ pages fit the iPhone.
While these offerings feel a bit like KickApps rushed to get them out the door, it’s good to see them taking the lead in the highly congested white label social networking space. Let’s hope that other companies like Ning follow suit.
For more coverage of KickApps, see our recent roundup of do-it-yourself, hosted social networking solutions.
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| 2024-11-08T09:22:35 | en | train |
47,098 | transburgh | 2007-08-27T18:52:55 | Don't Be This Girl | null | http://www.centernetworks.com/dont-be-this-girl | 3 | 15 | [
47229,
47114,
47115
] | null | null | null | null | null | null | null | null | null | train |
47,104 | nostrademons | 2007-08-27T19:01:24 | Computational Capacity of the Universe [PDF] | http://arxiv.org/PS_cache/quant-ph/pdf/0110/0110141v1.pdf | 10 | 2 | [
47106,
47181
] | null | null | null | null | null | null | null | null | null | train |
|
47,121 | paul | 2007-08-27T19:38:39 | Vator.tv - the idea exchange ("venue for innovators to showcase their ideas") | null | http://vator.tv/pitch/show/Vator---the-idea-exchange | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,125 | Laurentvw | 2007-08-27T19:42:55 | How To Write A Press Release For Your Services | http://freelanceswitch.com/finding/how-to-write-a-press-release-for-your-services/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,136 | transburgh | 2007-08-27T20:21:25 | Blogfight: Mark Cuban vs. Fred Wilson, a classic blog battle | null | http://valleywag.com/tech/blogfight/mark-cuban-vs-fred-wilson-a-classic-blog-battle-293833.php | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,147 | vlad | 2007-08-27T20:38:18 | Teenage Girl's MySpace Layouts Worth Millions, Drops Out Of High School | http://www.fastcompany.com/magazine/118/girl-power.html | 88 | 34 | [
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|
47,156 | joshwa | 2007-08-27T21:16:12 | Google's friend-to-friend ad network | null | http://www.roughtype.com/archives/2007/08/googles_friendt.php | 4 | 0 | null | null | null | http_404 | Page not found | ROUGH TYPE | null | null |
This is somewhat embarrassing, isn’t it?
It seems we can’t find what you’re looking for. Perhaps searching can help.
| 2024-11-08T01:11:12 | null | train |
47,158 | joshwa | 2007-08-27T21:17:38 | MySpace reportedly may allow member ads | null | http://money.cnn.com/2007/08/27/technology/myspace_commerce/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,159 | null | 2007-08-27T21:17:50 | null | null | null | null | null | null | [
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47,164 | transburgh | 2007-08-27T21:41:44 | Internet Makes Young People Happy | null | http://www.webpronews.com/topnews/2007/08/27/internet-makes-young-people-happy | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,166 | thinkingserious | 2007-08-27T21:48:29 | What do you install after a Windows re-format? | I have become a minimalist in many ways, so this was a good chance to do some housekeeping and only install the minimums (which ended up being pretty significant). I detailed this process and I am sharing it with you here. It would be interesting to find out what applications you consider essential when doing a complete re-format.
| http://blog.thembid.com/index.php/2007/08/27/what-do-you-install-after-a-windows-re-format/ | 2 | 2 | [
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] | null | null | bot_blocked | Attention Required! | Cloudflare | null | null |
Why have I been blocked?
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| 2024-11-08T14:35:12 | null | train |
47,169 | transburgh | 2007-08-27T21:56:48 | GPhone Rumor "Confirmed"....Again | null | http://www.webpronews.com/topnews/2007/08/27/gphone-rumor-confirmed-again | 6 | 1 | [
47171
] | null | null | null | null | null | null | null | null | null | train |
47,180 | bct | 2007-08-27T22:29:29 | Content-aware image resizing algorithm (watch the linked video, too) | http://www.ultra-premium.com/b/photos/resize.html | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,190 | luccastera | 2007-08-27T22:47:50 | Who Wants to Buy a Virtual World? | null | http://www.techcrunch.com/2007/08/27/who-wants-to-buy-a-virtual-world/ | 2 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,194 | rms | 2007-08-27T22:51:54 | Acer to acquire Gateway, will become #3 in global PC market over Lenovo | http://online.wsj.com/article/SB118820817365109596.html?mod=hpp_us_whats_news | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,195 | dawie | 2007-08-27T22:52:08 | Video: Interview with Jason Fried | http://www.37signals.com/svn/posts/581-crains-chicago-business-interviews-jason | 6 | 2 | [
47226,
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] | null | null | null | null | null | null | null | null | null | train |
|
47,211 | mattjaynes | 2007-08-27T23:44:06 | Great startup opportunity with two former Intuit VP's - RoR | I'll be starting at Scribd next week (woohoo!), but I have been contracting for a great startup in Fremont that needs a replacement for me. The startup is TReX Global (dorky/awesome name I know) that is being self-funded by two former Intuit VP's. The founders are some of the nicest guys I've ever known and that's why I joined them. The product is like an online version of TurboTax, but geared specifically towards Real Estate investors. Both of the founders have been active real estate investors over the years and so are passionate about this market's pain-points they are solving. If you have any interest in that industry, this is an amazing opportunity.<p>They are a Ruby on Rails shop, and the skills they are particularly looking for are super-solid frontend skills (js, css, etc). RoR background is helpful but not required.<p>The pay and options are really great and you'll be working out of a garage, but with a very flexible schedule - telecommuting etc.<p>Let me know if you're interested - just contact me at matt.jaynes on gmail.<p>Thanks!
Matt<p><a href="https://www.trexglobal.com/application" rel="nofollow">https://www.trexglobal.com/application</a> (Product)<p><a href="http://web.intuit.com/about_intuit/executives/pankaj_shukla.html" rel="nofollow">http://web.intuit.com/about_intuit/executives/pankaj_shukla....</a> (Founder - CEO)<p><a href="http://www.linkedin.com/pub/0/881/b09" rel="nofollow">http://www.linkedin.com/pub/0/881/b09</a> (Founder - President) | 2 | 0 | null | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,212 | drm237 | 2007-08-27T23:44:22 | Crucial Steps to Getting Started | Entrepreneurs and startup experts weigh in on what they consider most important when launching a new business | http://www.businessweek.com/smallbiz/content/aug2007/sb20070827_860494.htm | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,218 | limeade | 2007-08-27T23:51:54 | Why does the iPhone have chrome finish, unlike the iPod? | I noticed that it gives the iPhone quite a different aesthetic than the iPod. It makes me associate it with the luxury market, which I think is somewhat unfortunate. | 1 | 0 | null | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,219 | brett | 2007-08-27T23:55:28 | Computer Workstation Ergonomics | http://www.codinghorror.com/blog/archives/000938.html | 4 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,230 | bootload | 2007-08-28T00:26:06 | Why synching sucks | http://www.scripting.com/stories/2007/08/27/whySynchingSucks.html | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,231 | bootload | 2007-08-28T00:26:31 | Google and search | http://192.168.1.20/read/1737 | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,232 | rokhayakebe | 2007-08-28T00:27:27 | do not. I am just letting it out. | O boy. I am not writing for anyone to enjoy or even read this. But this is the only place I am socially active on a daily basis. I kinda feel secure here. Last Tuesday I lost my job ( well I quit, but I did not like it and they were treating me poorly). Wednesday I lost my car. It stopped in the middle of the freeway. I managed to take it home after 3 hours ( the normal ride is about 5 minutes top ). Thursday I lost my phone. If you are addicted to mobile IM and push email, then loosing your phone is like loosing your ability to breath and now you must live with a tube stuck in your throat. Friday I lost my girlfriend. O boy. Now that one hurt. Can you imagine seeing someone leave you when you need them the most. My girlfriend knows me more about me than anyone outside my family. I thought she was sweet. I never thought she really loved me, but we had this rule of "no lie" that made it all smooth. She lied to me. Big time. And to make matters worst, I found she did for a long time. O boy. I am not even mad, but I am hurt and unpleasantly surprised. Saturday and Sunday were tough, but I managed. Today, I found out more lies from her. O boy. And today, the one person I called my best friend let me down. I called him and say I needed his help. O boy. "Hang on" he told me, "You will do fine".
O boy. I keep wishing that I will wake up soon. I wished this is a dream. Somebody wake me up please before it is too late. Wake me up. | 31 | 29 | [
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|
47,235 | Tichy | 2007-08-28T00:30:14 | Is music production comparable to programming? | In software development, I have no problem to envision developing arbitrarily good applications, by building it one building block at a time. On the other hand, the last few days I have listened to extremely good music and I don't see how to ever arrive at that level. Is there a point when one has learned enough basics of music production to be able to produce arbitrarily good music? | null | 14 | 18 | [
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47,236 | dawie | 2007-08-28T00:33:05 | Google Launches Official Facebook App | http://mashable.com/2007/08/27/facebook-google/ | 14 | 3 | [
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|
47,245 | danw | 2007-08-28T00:52:20 | Tip: Block facebook apps with Facebook Profile Cleaner | null | http://tech.karbassi.com/2007/08/27/facebook-profile-cleaner/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,255 | ratsbane | 2007-08-28T01:20:00 | YC application as an exercise to define and focus your startup goals? | null | 2 | 2 | [
47258,
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] | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,257 | charzom | 2007-08-28T01:27:10 | JavaScript Tips for Novices, Acolytes, and Gurus | http://arstechnica.com/journals/linux.ars/2007/08/27/javascript-for-all-ages | 12 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,259 | linsys | 2007-08-28T01:35:39 | Vista & Information Control | null | http://www.pointsboard.net/viewtopic.php?f=40&t=91 | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,260 | linsys | 2007-08-28T01:36:12 | Vista Sucks | http://www.pointsboard.net/viewtopic.php?f=40&t=78 | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,261 | linsys | 2007-08-28T01:36:33 | Why Ubuntu Sucks | http://www.pointsboard.net/viewtopic.php?f=35&t=66 | 1 | 2 | [
47268,
47286
] | null | null | null | null | null | null | null | null | null | train |
|
47,262 | linsys | 2007-08-28T01:36:58 | Linux Media Center Better Then Windows Media Center? | http://www.pointsboard.net/viewtopic.php?f=35&t=84 | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,263 | charzom | 2007-08-28T01:39:24 | A guy who runs his life with index cards | null | http://flickr.com/photos/hawkexpress/sets/72157594200490122/ | 5 | 3 | [
47401,
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47,275 | blored | 2007-08-28T02:22:50 | Are there going to be any changes heading into the Winter '08 program? | Will the median age go up? Will dinners be held on a different night? Did the large batch (19 groups) work out OK? | 6 | 2 | [
47372,
47490
] | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,278 | transburgh | 2007-08-28T02:35:14 | First New Digg Screenshot | null | http://www.centernetworks.com/first-new-digg-screenshot | 3 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,282 | nickb | 2007-08-28T02:37:45 | Getting Git on Mac OS X | http://metastatic.org/text/Concern/2007/08/18/git-package-for-mac-os-x/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,284 | nickb | 2007-08-28T02:40:11 | Performance of anonymous functions in naive Javascript implementations | http://weblog.raganwald.com/2007/08/ruminations-about-performance-of.html | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,285 | nickb | 2007-08-28T02:41:14 | How to speedup your web site | http://www.roscripts.com/How_to_speed_up_your_website-175.html | 2 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,289 | nickb | 2007-08-28T02:58:44 | Are you hosting your blog on Blogger? Read this cautionary tale. | http://munfitnessblog.com/a-new-beginning-for-mun-fitness-blog-a-better-one/ | 4 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,291 | limeade | 2007-08-28T03:00:56 | If we reveal our idea in our YC app and don't accept, would YC possibly recommend it to other, participating teams? | 6 | 7 | [
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] | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
||
47,292 | nickb | 2007-08-28T03:01:06 | Add Cover Flow effect (including reflection) to images on your webpages (JS & canvas hack) | http://www.netzgesta.de/reflex/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,294 | nickb | 2007-08-28T03:03:32 | The Myth of Software Estimation | http://jeffspost.wordpress.com/2007/08/26/the-myth-of-software-estimation/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,297 | jamiequint | 2007-08-28T03:11:30 | Power of the Marginal Video - RailsConf 2006 | I spent the time to find this, so I thought I would share. One of my faves. Enjoy.<p>Link is below (Warning: this is 250+ MB and meant to be downloaded)<p><a href="http://downloads.scribemedia.net/rails2006/04_paul_graham_full.m4v" rel="nofollow">http://downloads.scribemedia.net/rails2006/04_paul_graham_fu...</a> | 1 | 0 | null | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,302 | dawie | 2007-08-28T03:36:13 | 10 Free, Innovative Web Analytics Tools | null | http://www.readwriteweb.com/archives/10_web_analytics_tools_free_innovative.php | 2 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,308 | tel | 2007-08-28T04:11:00 | When do you ignore your users? | Quoted in Getting Real is a passage by Jef Raskin about avoiding "feature blight" (<a href="http://jef.raskincenter.org/unpublished/widgets_of_the_week.html#anchor1152335" rel="nofollow">http://jef.raskincenter.org/unpublished/widgets_of_the_week....</a>). The passage suggests too many features is a bad thing and that the best way to avoid that pitfall is a very real and constricting deadline. My question is that once you've launched and you're able to afford a more liberal deadline, how do you keep feature blight from creeping in?<p>37 Signals was noted here recently for refusing to implement suggestions until there's a critical mass of users looking for them, but is that the "best" way to combat this issue? | 4 | 3 | [
47344
] | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,310 | kyro | 2007-08-28T04:23:36 | How valuable are designers to a startup team? | Compared to the value of having coders on a team, how do designers stack up? Is it common to have a designer on board, or to just a design firm? Also, have the majority of teams accepted to YC had designers on the team, and if not, what have they done? Perhaps pg can best answer that last one.<p>Thanks.
| 17 | 29 | [
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|
47,325 | nivi | 2007-08-28T05:38:53 | Who is YC user PortLAN? -- He is hilarious. | He is funny but he doesn't list contact info: <a href="http://news.ycombinator.com/user?id=portLAN" rel="nofollow">http://news.ycombinator.com/user?id=portLAN</a> | 2 | 0 | [
47369
] | null | true | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,342 | szczupak | 2007-08-28T06:33:19 | Web 2.0 trends; Vint Cerf and the “IPod Moment” | http://www.businesshackers.com/2007/08/28/web-20-trends-vint-cerf-and-the-ipod-moment/ | 2 | 0 | null | null | null | fetch failed | null | null | null | null | 2024-11-08T09:42:33 | null | train |
|
47,345 | toffer | 2007-08-28T06:50:13 | Scott Rosenberg: Web 2.0's five-year development cycle | null | http://www.wordyard.com/2007/08/27/five-years-2/ | 3 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,347 | toffer | 2007-08-28T07:00:56 | Andrew Chen: Are people like lab rats? Using reward schedules to drive engagement | null | http://andrewchen.typepad.com/andrew_chens_blog/2007/08/are-people-like.html | 2 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,348 | rms | 2007-08-28T07:04:31 | Norman Borlaug: the greatest person to ever live? | http://en.wikipedia.org/wiki/Norman_Borlaug | 13 | 14 | [
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|
47,350 | brett | 2007-08-28T07:13:15 | Facebook's platform to reward good, punish bad applications | http://venturebeat.com/2007/08/27/facebooks-platform-to-reward-good-punish-bad-applications/ | 2 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,352 | davidw | 2007-08-28T07:33:06 | Robert Frank talks about economics at Google | http://www.youtube.com/watch?v=QalNVxeIKEE | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,353 | brett | 2007-08-28T07:38:18 | Facebook Takes Further Steps To Curb User Abuse; Change In How Applications Are Measured | http://www.techcrunch.com/2007/08/27/facebook-takes-further-steps-to-curb-user-abuse-change-in-how-applications-are-measured/ | 4 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,356 | brett | 2007-08-28T07:44:29 | Global wheat prices reach record level | null | http://news.bbc.co.uk/2/hi/business/6962211.stm | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,358 | mmpcse | 2007-08-28T08:22:45 | Googles OS Confirmed : Goobuntu A | null | http://hitechstartups.wordpress.com/2007/08/28/googles-os-confirmed-goobuntu/ | 1 | -1 | null | null | true | null | null | null | null | null | null | null | train |
47,359 | macattack | 2007-08-28T08:31:44 | 5000 Web Apps in 333 seconds: simplespark | Simple Spark maintains a list of web apps which recently surpassed 5000 entries. To celebrate, the crammed the logos of the 5000+ web applications they index into a 333-second youtube video (15 logos/second!). How many do you recognize?<p>"Just a few months ago, we launched Simple Spark with 1000 web applications. Today, we're proud to announce that the Simple Spark Catalog has surpassed 5000 fully searchable, summarized, and categorized web apps that are ready for discovery." | http://simplespark.com/blog/announcements/5000-web-apps-in-333-seconds/ | 1 | 0 | null | null | null | http_404 | Page not found – A Simple Spark | null | null |
Oops! That page can’t be found.
It looks like nothing was found at this location. Maybe try one of the links below or a search?
Search for:
| 2024-11-08T05:38:06 | null | train |
47,362 | staunch | 2007-08-28T08:45:24 | Max Levchin at 2006 UIUC Talk "You should start a company right now" (video) | http://video.google.com/videoplay?docid=932124090446967293 | 21 | 3 | [
47396,
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] | null | null | null | null | null | null | null | null | null | train |
|
47,374 | null | 2007-08-28T12:19:50 | null | null | null | null | null | null | [
"true"
] | null | null | null | null | null | null | null | null | train |
47,375 | twism | 2007-08-28T12:20:01 | Is reddit down? | http://www.reddit.com | 16 | 9 | [
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] | null | null | null | null | null | null | null | null | null | train |
|
47,376 | charzom | 2007-08-28T12:20:45 | New hydrogen generating technology "competitive with gasoline" | http://www.physorg.com/news107446364.html | 13 | 4 | [
47437,
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] | null | null | null | null | null | null | null | null | null | train |
|
47,378 | charzom | 2007-08-28T12:24:18 | Big increase in "behaviorally targeted" Internet ads | null | http://investors.com/editorial/IBDArticles.asp?artsec=17&issue=20070823 | 4 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,379 | kkim | 2007-08-28T12:31:32 | How Three Swedish Geeks Became Hollywood's Number One Enemy | http://www.guardian.co.uk/technology/2007/aug/25/piratebay | 15 | 0 | [
47458,
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] | null | null | no_error | Bobbie Johnson interviews the Pirate Bay | 2007-08-25T09:18:35.000Z | Bobbie Johnson | Operating under the sign of a Jolly Roger, The Pirate Bay website hopes to evoke a buccaneer spirit: swashbuckling swordsmen, or perhaps the pirate radio stations of the 1960s. But as the internet's number one destination for illegal downloads, it has raised the hackles of the entertainment industry and elevated its founders to the top of Hollywood's most wanted list.With more than two million visitors every day, The Pirate Bay has become one of the sharpest thorns in the side of the media business. Its controversial success has caused havoc in the music, TV and film industries.Current top downloads include The Bourne Ultimatum, Die Hard 4.0 and Knocked Up — all showing in British cinemas, but available to watch on a computer screen for those willing to take the risk.The three-year campaign to bring down the website is almost an epic of Hollywood proportions, sprinkled with high-flying lawyers and accusations of political extremism. And yet, so far, the chase has failed to bring the pirates down.Despite their high profile, however, the men behind The Pirate Bay are not part of an organised crime syndicate. Instead, they are an unlikely trio of Swedish computer geeks who began their war with the media from a small room in Stockholm.The group, who spoke exclusively to the Guardian, live like students in the suburbs of Sweden's major cities. They wake late and work into the night. The closest thing they have to an official headquarters is a desk on the suburban outskirts of Malmo — and that is simply because it has a working fax machine.But as the most hated men in Hollywood, they said they have become used to the attention. "We get legal threats every day, or we used to," said Peter Sunde, 28, one of the site's main workers. "But we don't have a problem with them — we're just a search engine."Fredrik Neij, a 29-year-old IT consultant, has a more prosaic view: "It's nice to be noticed," he smiled.Chief among those angered by The Pirate Bay's popularity is the Motion Picture Association of America (MPAA), which represents the US film studios. It is waging war against the site, which it claims is costing billions in lost sales.John Malcolm, executive vice-president of the MPAA, has railed against the trio, accusing them of cashing in on illegal activity. "The bottom line is that the operators of The Pirate Bay, and others like them, are criminals who profit handsomely by facilitating the distribution of millions of copyrighted creative works," he said.Mr Sunde insists the site does not profit its founders, and money raised from advertising is used to cover expenses. Instead, he says, the team make their money from a variety of side projects and day jobs.Filesharing and illegal downloading has been a big issue for media companies since the late 1990s. But while pioneering services such as Napster and Kazaa were closed down by the courts, the campaign against The Pirate Bay has failed to make a breakthrough.The crux of the defence is that The Pirate Bay operates like any internet search engine: it points to downloads, rather than hosting any illegal content itself. Under Swedish law this has so far made it immune to prosecution."I don't like the word untouchable, but we feel pretty safe," said Mr Sunde. He thinks that European enmity towards the Bush administration has bolstered support. "The US government is losing popularity every day in Europe, and people don't want to see us give in to them."Their apparent invulnerability to prosecution has made them heroes of the internet piracy movement, but not everybody feels the same way."I certainly don't see them as romantic pirates: it's out and out theft," says John Kennedy, chief executive of the international music industry body IFPI. "It's pure, ruthless greed — or total naivety."But the group's supporters around the world say they are vexed with what they see as the "corruption" of the media industry."This is already happening — you cannot stop it," says Magnus Eriksson of Piratbyran, the Swedish thinktank which helped start the website in 2003. "But the thing is that the people who download the most are also the ones who spend the most on buying media. Media companies already know that they have to change."The pirates suspect the campaign against them is gathering pace. Last year police raided the site and held Gottfried Svartholm, the third member of the group, for questioning. No charges resulted, but the site was offline for two days.Lately critics have focused on potential political links, including one German failed attempt to link the organisation with far-right extremists.More recently Swedish police said they were considering blocking the website because of a tip-off that some pages linked to images of child abuse. This, says Mr Sunde, was just an attempt to smear The Pirate Bay's reputation. "There were three files in question, but it turned out that none of them contained child porn," he said.The group is adamant it is just a search engine, but Mr Kennedy rejects any analogy with traditional internet businesses. "When I sit down with Google they are prepared to talk about copyright issues," he says. "If I thought The Pirate Bay guys were doing something really new and clever, then we'd look at it — but there's no evidence of that."Mr Sunde remains unmoved. He says piracy is a way of life on the internet. "I started off copying disks on my computer when I was eight or nine," he said. "You should never tell people where they can't go or what they can't do."· This article was amended on Monday September 17 2007. We said that The Pirate Bay website keeps an index of torrent files, pointing people in the direction of downloads "whether they are copyrighted or not". We should have said whether or not there are restrictions on their use. | 2024-11-08T00:11:26 | en | train |
|
47,383 | transburgh | 2007-08-28T12:44:36 | Digg Gets A Major Makeover | http://www.techcrunch.com/2007/08/27/digg-gets-a-major-makeover/ | 3 | 2 | [
47470,
47730
] | null | null | null | null | null | null | null | null | null | train |
|
47,384 | drm237 | 2007-08-28T12:45:16 | Start-up tests odds on lotto tickets | A team of four current and former Duke students created a start-up company this summer and their website SeeMeWin.com launched July 14.<p>The project examines how lotteries really work. The company gives people money from advertising revenue to buy lottery tickets and requires scratchers to send in live footage of their shows, as they scratch the cards. | http://media.www.dukechronicle.com/media/storage/paper884/news/2007/08/27/News/StartUp.Tests.Odds.On.Lotto.Tickets-2938375.shtml | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,389 | ivankirigin | 2007-08-28T12:57:52 | Web Innovators Group Event - Sept 10 | null | http://www.webinnovatorsgroup.com/2007/07/23/web-innovators-group-webinno14/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,390 | kkim | 2007-08-28T12:59:50 | What Really Buys Happiness? | http://www.city-journal.org/html/17_3_economic_inequality.html | 9 | 4 | [
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] | null | null | null | null | null | null | null | null | null | train |
|
47,391 | drm237 | 2007-08-28T13:00:30 | The Art of Bootstrapping | Someone once told me that the probability of an entrepreneur getting venture capital is the same as getting struck by lightning while standing at the bottom of a swimming pool on a sunny day. This may be too optimistic. | http://blog.guykawasaki.com/2006/01/the_art_of_boot.html | 7 | 2 | [
47645,
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] | null | null | null | null | null | null | null | null | null | train |
47,400 | luccastera | 2007-08-28T13:15:05 | The Pmarca Guide to Startups, Part 8: Hiring, managing, promoting, and firing executives | http://blog.pmarca.com/2007/08/the-pmarca-guid.html | 24 | 10 | [
47505,
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] | null | null | no_error | Marc Andreessen, Author at Andreessen Horowitz | null | Ben Horowitz, Brad Smith, Marc Andreessen, and Satya Nadella |
More About Marc
Marc Andreessen is a cofounder and general partner at the venture capital firm Andreessen Horowitz. He is an innovator and creator, one of the few to pioneer a software category used by more than a billion people and one of the few to establish multiple billion-dollar companies.
Marc co-created the highly influential Mosaic internet browser and co-founded Netscape, which later sold to AOL for $4.2 billion. He also co-founded Loudcloud, which as Opsware, sold to Hewlett-Packard for $1.6 billion. He later served on the board of Hewlett-Packard from 2008 to 2018.
Marc holds a BS in computer science from the University of Illinois at Urbana-Champaign.
Marc serves on the board of the following Andreessen Horowitz portfolio companies: Applied Intuition, Carta, Coinbase, Dialpad, Flow, Golden, Honor, OpenGov, Samsara, Simple Things, and TipTop Labs. He is also on the board of Meta.
Latest Content
a16z and Microsoft share policy ideas for AI startups so they can thrive, collaborate, and compete.
a16z cofounders Marc Andreessen and Ben Horowitz explore an unusual intersection of AI and crypto: the sudden rise of a bot-beloved memecoin.
In this special episode, Marc and Ben dive deep into the REAL story behind the creation of Netscape—a web browser co-created by Marc that revolutionized the internet and changed the world. As Ben notes at the top, until...
The time has come to stand up for Little Tech. Bad government policies are now the #1 threat to Little Tech. We believe American technology supremacy, and the critical role that Little Tech startups play in ensuring that supremacy, is a first class political issue on par with any other.
In this latest episode on the State of AI, Ben and Marc discuss how small AI startups can compete with Big Tech’s massive compute and data scale advantages, reveal why data is overrated as a sellable asset, and unpack al...
The gaming industry stands as a pioneer of cutting-edge technologies, ushering in innovations like GPUs, virtual and augmented reality, physics engines, and immersive multiplayer experiences.
In this episode, a16z cofounder Marc Andreessen and Andrew Chen, General Partner at a16z Games, dig into why a16z was compelled to establish a dedicated games fund. They explore the origins of tech pessimism, effective engagement with government in tech, its significance for the gaming community, the ongoing AI revolution, and even what Marc himself would build today if he didn't have his hands full.
“If America is going to be America in the next one hundred years, we have to get this right.” - Ben Horowitz
Marc Andreessen and Ben Horowitz discuss the new bestselling book Read Write Own with author Chris Dixon on the web3 with a16z crypto podcast.
"The Ben & Marc Show" features a16z's co-founders Ben Horowitz & Marc Andreessen. In this episode, Marc and Ben continue their in-depth exploration of the current education system. While Part I of their discussion unpacked the crisis facing higher education, Part II presents solutions to overhaul the modern university.
In this one-on-one conversation, Marc and Ben tackle the university system – what has certainly been a hot topic that’s been dominating the news over the past few months. As Marc states at the top of the episode, universities matter tremendously to our world, but they’re currently in a state of crisis.
Marc and Ben are joined by special guest Tony Robbins to discuss new breakthroughs in regenerative medicine, AI, biohacking, gene editing, mindset and why this might be the best time to be alive.
In an article that has sparked widespread conversation across traditional and social media, Marc challenges the pessimistic narrative surrounding technology today, and instead celebrates it as a liberating force that can lead to growth, progress and abundance for all. In this one-on-one conversation based on YOUR questions from X (formerly Twitter), Ben and Marc discuss how technological advancements can improve the quality of human life, uplift marginalized communities, and even encourage us to answer the bigger questions of the universe.
We are told that technology is on the brink of ruining everything. But we are being lied to, and the truth is so much better. Marc Andreessen presents his techno-optimist vision for the future.
TipTop creates tools that reduce the consumer code of owning products. They offer customers a guaranteed buyback price at the time of purchase, so they only pay for the product while they need it.
This week, a16z’s own cofounder Marc Andreessen published a nearly 7,000-word article that aimed to dispel fears over AI's risks to our humanity – both real and imagined. Instead, Marc elaborates on how AI can "make everything we care about better."
In this timely one-on-one conversation with a16z General Partner Martin Casado, Marc discusses how this technology will maximize human potential, why the future of AI should be decided by the free market, and most importantly, why AI won’t destroy the world. In fact, it may save it.
Read Marc’s full article “Why AI Will Save the World” here: https://a16z.com/2023/06/06/ai-will-save-the-world/
There's a full-blown moral panic about AI right now. But the real risk is losing the race to global AI technological superiority.
Back in August, after a16z announced our investment into Adam Neumann’s new company, Flow, it felt like almost everyone – whether it was other VCs, founders, or journalists – had something to say.
But the one person that you didn’t hear from was Adam himself.
In this never-before shared footage from a16z’s American Dynamism Summit in Washington DC, Adam Neumann sits down with Marc Andreessen and David Ulevitch, to discuss the opportunities that have emerged from post-pandemic shifts in both work and home, and what Flow is doing to capitalize.
In this episode, Marc Andreessen and Vijay Pande discuss expert AI and its role in healthcare, bio, and more.
In this episode, Marc Andresseen and Vijay Pande discuss expert AI and its role in healthcare, bio, and more.
Best Clips of 2022
Steph Smith, Das Rush, Steve Wozniak, Chris Power, Ryan Petersen, Marc Andreessen, Balaji Srinivasan, Karen Cheng, Moriba Jah, Alex Fielding, and Neal Stephenson
We’ve had some incredible guests join us on the a16z podcast this year, ranging from moonshot entrepreneurs, to top creators, to some of the most forward thinking technologists – all of which are busy shaping the future right before our eyes…
We have so much more in store for 2023 and cannot wait for you to see who we bring on as guests. But before we turn the page, we wanted to recap some of the most interesting, thought-provoking segments from our 2022 roster. Here are 8 of our favorite clips, covering topics from AI to space to the metaverse… and beyond.
With much coverage of technology lined with pessimism, the a16z Podcast returns to highlight the bright side of technology, alongside the founders building it. But before featuring the solutions in progress, we wanted to explore why building the future is still so important.
And who better to traverse this ground than a16z’s own cofounder Marc Andreessen, who has built and invested in the future time and time again, especially when it wasn't the obvious thing to do.
Together with Marc, this episode explores technology through the lens of history – including the three stages of human psychology as we encounter new technologies, how that process often manifests in regulation, when to change your mind, the Cambrian explosion of opportunity coming from distributed work, the importance of founder-led companies, and perhaps most importantly, we examine why there's still much reason for optimism.
To celebrate the LA community and the city's growth, a16z recently hosted Time to Build: Los Angeles, an event where we invited LA-based investors, founders, and operators from across a diverse range of industries to tal...
An Internet news outlet is asking a lot of people I know, and some I don’t, what I’ve been up to lately. Lord knows what they’ll ultimately publish, so I thought I’d just write this instead.
In this episode from October 2021, Michael Dell, founder and CEO of Dell Technologies and one of the longest serving founder-CEOs in the technology industry, joins a16z general partner Martin Casado, a16z co-founder Marc Andreessen, and host Sonal Choksi on the occasion of Michael’s book, Play Nice to Win: A CEO’s Journey from Founder to Leader.
There are lots of challenges in being public while trying to innovate, and limits to being a private company as well; but it's rare to see a company go public then private then back to public again. As is the case with Dell Technologies, one of the largest tech companies -- which went private 2012-2013 and then also pulled off one of the most epic mergers of all time with Dell + EMC + VMWare 2015-2016 (and which we wrote about here at the time).
Is there a method to the madness? How does one not just start, but keep, and transform, their company and business? Michael, Marc, Martin and Sonal debate these questions, as well as the impact of the cloud wars, how innovation happens when a company is private and when its public (something Michael knows well, having taken Dell public to private to back to public again), whether you can actually play nice to win as a leader, and more.
Our nation has a housing crisis.
In this episode from October 2019, a16z co-founder Marc Andreessen and former a16z podcast showrunner Sonal Choksi bring on MIT economist and bestselling author Andrew McAfee to discuss why the lessons of human growth in times past, from the Industrial Revolution onwards, might not apply to our future. It used to be that the only way for humanity to grow — and progress — was through destroying the environment. But is this interplay between human growth vs. environment really a zero-sum game? Even if it were true in history, is it true today? If capitalism is not responsible for environmental degradation, than who or what is? And where does (and doesn’t) technology come in?
The conversation is based on McAfee’s 2019 book More from Less: The Surprising Story of How We Learned to Prosper Using Fewer Resources -- and What Happens Next, ranging broadly across many areas of growth, from the future of energy and agriculture to the role of capitalism and technology today and tomorrow, from dematerialization to Tesla, Buckminster Fuller, and more.
These are edited highlights from a recent Clubhouse discussion among Hadrian founder and CEO Chris Power, a16z partners Katherine Boyle and Marc Andreessen, and Not Boring newsletter author Packy McCormick. The dialogue...
Marc Andreessen and Sonal interview author, consultant/advisor, and former pro poker player Annie Duke, in one of her first few appearances with us, and in a conversation quite unlike her other conversations. We cover a broad range of topics relevant to both companies and individuals, all about thinking in bets when it comes to innovation in your business or change in your personal life.
Welcome to 16 Minutes, our show on the a16z podcast network where we talk about tech trends that are dominating news headlines, industry buzz, and where we are on the long arc of innovation. Today’s episode actually features a look back at the GameStop saga — the stock market drama that some headlines described as a “David-and-Goliath battle” that “upended Wall Street.”
It's rare to see a company go public then private then back to public again, as Dell Technologies did -- and which also pulled off one of the most epic mergers of all time with Dell + EMC + VMWare. How does one not just start, but keep -- and transform -- a company and business, especially as it adapts to broader, underlying tech platform shifts like demise of PC, end of cloud, cloud wars, and much more? This is really a story about innovation: who decides, who judges, who does it, and where.
We were at an inflection point with the COVID pandemic, between old and new tech, science institutions, public health policy, more. So what can we learn from the past for the future? Former head of the FDA Dr. Scott Gottlieb (author of the upcoming new book, Uncontrolled Spread) shares stories from behind the scenes, debating probing ethical and policy questions with a16z co-founder Marc Andreessen and a16z bio general partners Vineeta Agarwala MD, Phd and Vijay Pande PhD.
On social audio app Clubhouse, Marc Andreessen and Ben Horowitz are hosting a new live show called "One on One with A and Z", where they go deep on questions submitted via Twitter. The show is based in part by a newspaper column that Andy Grove did in the 80s, where readers sent in questions for him to answer in his column.
In this mega-episode of the a16z Podcast, we've combined their first two episodes into almost three hours of discussion and debate about some of the most important topics in entrepreneurship, tech, and culture. Each of these episodes also initially aired on our new show, a16z Live, which captures and share many of the live discussions and events featuring, hosted, or co-hosted by a16z partners (with outside voices too) on Clubhouse and beyond.
For more than 100 years, companies have existed in a binary world, either private or public. Private companies have been highly restricted in how they can raise money, sell stock, provide employee liquidity, and otherwis...
Welcome, Sriram Krishnan, our newest general partner, to Andreessen Horowitz!
If software’s eating the world -- and more specifically, bringing costs down and increasing productivity through entire industries -- why have some industries, like healthcare, been so resistant?
How come things like healthcare, education, and housing get more and more expensive, but things like socks, shoes, and electronics all get cheaper and cheaper? In this episode of Bio Eats World, a16z founder and internet...
In this episode of Bio Eats World, a16z founder and internet pioneer Marc Andreessen and general partner Jorge Conde zoom out to discuss the large scale societal effects of the current pandemic on society, healthcare, bi...
Last year, I wrote about our series B investment in Applied Intuition, which builds simulation software and infrastructure tools to safely test and validate autonomous vehicles at scale. Now, just a little over a year la...
A wide-ranging Q&A all about education, from the purpose, past, and present of education; the economics of education (student loans & the debt crisis, government funding, cost disease, accreditation capture); tradeoffs of "hard" and "soft" degrees; and whether or not to drop out and go straight to field or startup. What's the best advice for students and others contemplating change in their careers... how do you get noticed?
This interview was recorded earlier this year and originally appeared on The Observer Effect; it has only been lightly edited for formatting here.
Marc Andreessen reads out loud IT'S TIME TO BUILD
Every Western institution was unprepared for the coronavirus pandemic, despite many prior warnings. This monumental failure of institutional effectiveness will reverberate for the rest of the decade, but it's not too ear...
Gaming has gone from a niche hobby to a massive global industry across all demographics and well beyond outdated, narrow stereotypes of “gamers”. In fact, games are not even just “games” any longer, but a form of enterta...
Many skeptics thought the internet would never reach mass adoption, but today it’s shaping global culture, is integral to our lives -- and it's just the beginning.
In this conversation from our 2019 innovation summit, Kevin Kelly (Founding Executive Editor, WIRED magazine) and Marc Andreessen sit down to discuss the evolution of technology, key trends, and why they're the most optimistic people in the room.
The creator of hit shows like Grey's Anatomy, Scandal, and others, writer and executive producer Shonda Rhimes shares lessons she's learned about pitching ideas, storytelling, leadership, and scaling a business across mediums.
In this special guest hosted episode -- cross-posted from the new show Starting Greatness (featuring interviews with startup builders before they were successful, hosted by Mike Maples jr) -- Marc Andreessen shares some rare, behind-the-scenes details of his story from 0 to 1... from the University of Illinois and Mosaic to Netscape.
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| 2024-11-08T07:50:38 | en | train |
|
47,402 | jkush | 2007-08-28T13:19:31 | Map of the Internet | http://en.wikipedia.org/wiki/Image:Internet_map_1024.jpg | 1 | 0 | null | null | null | no_error | File:Internet map 1024.jpg - Wikipedia | null | null |
Description
Беларуская (тарашкевіца): Частковая мапа інтэрнэта, заснаваная на дадзеных ад 15 студзеня 2005 г. на opte.org. Кожная лінія намалявана паміж двума вузламі, злучая два IP-адрасы. Даўжыня лініі паказвае часавую затрымку (пінг) паміж двума вузламі. Мапа ўяўляе меньш за 30% сетак клясы C даступных для збора дадзеных у 2005 годзе. Колер лініі адпавядае яе месцазнаходжаньню адпаведна RFC 1918. Выкарыстоўваюцца наступныя колеры:
Тёмна-сініе: net, ca, us
Зялёны: com, org
Чырвоны: mil, gov, edu
Жоўты: jp, cn, tw, au, de us dee auroraaa
Фіялетавы: uk, it, pl, fr
Залаты: br, kr, nl
Белы: невядома
Català: Mapa parcial d'Internet basat en la informació obtinguda pel lloc opte.org el 15 de gener de 2005. Cada línia dibuixada entre dos nodes representa l'enllaç entre dos adreces IP. La longitud de les línies és proporcional al temps d'espera entre els nodes. La imatge representa el 30% de les xarxes tipus C accessibles pel programa de recol·lecció de dades al 2005. El color de les línies correspón a la seva classificació RFC 1918 de la següent manera:
Blau fosc: net, ca, us
Verd: com, org
Vermell: mil, gov, edu
Groc: jp, cn, tw, au, de
Magenta: uk, it, pl, fr
Dorat: br, kr, nl
Blanc: desconegut
Deutsch: Teile einer „Karte“ des Internets, basierend auf Daten von opte.org am 15.1.2005. Jede Linie beschreibt zwei Knotenpunkte, welche zwei IP-Adressen repräsentieren. Die Länge der Linien beschreibt die Verzögerung zwischen den Knotenpunkten. Diese Karte beschreibt weniger als 30% der Klasse-C-Netzwerke, welche Anfang 2005 von dem Datensammelprogramm erreicht werden konnte. Die Linien sind farblich entsprechend der RFC 1918 Addressbereiche gekennzeichnet:
Dunkelblau: net, ca, us
Grün: com, org
Rot: mil, gov, edu
Gelb: jp, cn, tw, au, de
Magenta: uk, it, pl, fr
Gold: br, kr, nl
Weiß: unbekannt
English: Partial map of the Internet based on the January 15, 2005 data found on opte.org. Each line is drawn between two nodes, representing two IP addresses. The length of the lines are indicative of the delay between those two nodes. This graph represents less than 30% of the Class C networks reachable by the data collection program in early 2005. Lines are color-coded according to their corresponding RFC 1918 allocation as follows:
Dark blue: net, ca, us
Green: com, org
Red: mil, gov, edu
Yellow: jp, cn, tw, au, de
Magenta: uk, it, pl, fr
Gold: br, kr, nl
White: unknown
Español: Mapa parcial de Internet basado en la información obtenida del sitio opte.org el 15 de enero de 2005. Cada linea dibujada entre dos nodos representa el enlace entre dos direcciones IP. La longitud de las líneas es proporcional al tiempo de espera entre los nodos. La imagen representa 30% de las redes tipo C accesibles al programa de colección de datos de 2005. El color de las lineas corresponde a su clasificación RFC 1918 de la siguiente manera:
Azul obscuro: net, ca, us
Verde: com, org
Rojo: mil, gov, edu
Amarillo: jp, cn, tw, au, de
Magenta: uk, it, pl, fr
Dorado: br, kr, nl
Blanco: desconocido
Suomi: Osittainen kartta Internetistä perustuen 15. tammikuuta 2005 dataan, löydettävissä osoittesta opte.org. Jokainen viiva on piirretty kahden verkon solmukohdan väliin edustaen kahta IP osoitetta. Viivojen pituuden kuvastavat viivettä näiden kahden solmukohdan välillä. Viivat on värjätty verkkotunnusten mukaan seuraavasti:
Tummansininen: net, ca, us
Vihreä: com, org
Punainen: mil, gov, edu
Keltainen: jp, cn, tw, au, de
Purppura: uk, it, pl, fr
Kultainen: br, kr, nl
Valkoinen: tuntematon
Français : Carte partielle d'Internet, basée sur les données de opte.org du 15 juin 2005. Chaque ligne relie 2 nœuds, représentant 2 adresses IP. La longueur de chaque ligne donne une indication du délai entre les 2 nœuds. Moins de 30 % des réseaux de classe C accessibles par le programme de collecte de données début 2005 sont représentés. Les lignes sont coloriées selon le code de couleur défini par la RFC 1918 :
bleu nuit : net, ca, us ;
vert : com, org ;
rouge : mil, gov, edu ;
jaune : jp, cn, tw, au, de ;
magenta : uk, it, pl, fr ;
or : br, kr, nl ;
blanc : inconnu.
Nederlands: Deelkaart van het internet, gebaseerd op de gegevens die op 15 januari 2005 op opte.org beschikbaar waren. Elk van de lijnen verbindt twee knooppunten, en representeert dus twee IP adressen. De lengtes van de lijnen zijn maatgevend voor de looptijd tussen de twee knooppunten. Deze grafiek vertegenwoordigt nog geen 30% van de klasse C netwerken die vroeg in 2005 voor het data collectie programma bereikbaar waren. De kleurcodering van de lijnen correspondeert op de volgende wijze met hun RFC 1918 toewijzing:
Blauw: net, ca, us
Groen: com, org
Rood: mil, gov, edu
Geel: jp, cn, tw, au, de
Paars: uk, it, pl, fr
Goud: br, kr, nl
Wit: unknown
Polski: Mapa części Internetu oparta o stan z 15 stycznia 2005, dane ze strony opte.org. Każda linia wytyczona jest między dwoma węzłami, reprezentującymi dwa adresy IP. Długość linii wskazuje na opóźnienie między tymi węzłami. Ten wykres reprezentuje niecałe 30% sieci klasy C osiągalnej przez programy zbierające dane na początku 2005 roku. Linie są pokolorowane w zależności od odpowiadającym im alokacjom RFC 1918 w następujący sposób:
Ciemnoniebieski: net, CA, US
Zielony: com, org
Czerwony: mil, gov, edu
Żółty: JP, CN, TW, UA, de
Magenta: uk, it, pl, fr
Złoty: br, kr, nl
Biały: nieznany
Русский: Частичная карта интернета, основанная на данных от 15 января 2005 г. на opte.org. Каждая линия нарисована между двумя узлами, соединяя два IP адреса. Длина линии показывает временную задержку (пинг) между двумя узлами. Карта представляет менее чем 30% сетей класса C доступных сетей для сбора данных в 2005 году. Цвет линии соответствует ее местоположению согласно RFC 1918. Используются следующие цвета:
Темно синий: net, ca, us
Зеленый: com, org
красный: mil, gov, edu
Желтый: jp, cn, tw, au, de
Фиолетовый: uk, it, pl, fr
Золотой: br, kr, nl
Белый: неизвестно
中文：部分互联网地图基于 opte.org 上的2005年1月15日数据。每条线画在两个节点之间，代表两个 IP地址。线的长度表示这两个节点之间的延迟。该图代表了2005年初数据收集程序可到达的Class C网络的不到30%。线条根据其对应的 RFC 1918 编码分配着色，如下所示：
深蓝色：net, ca, us
绿色：com, org
红色：mil, gov, edu
黄色：jp, cn, tw, au, de
洋红色：uk, it, pl, fr
金色：br, kr, nl
白色：未知
| 2024-11-08T05:53:31 | en | train |
|
47,408 | nickb | 2007-08-28T13:30:44 | Who Can Name the Bigger Number? | http://www.scottaaronson.com/writings/bignumbers.html | 8 | 0 | null | null | null | no_error | Who Can Name the Bigger Number? | null | null |
[This essay in Spanish]
[This essay in French]
[This essay in Chinese]
In an old joke, two noblemen vie to name the bigger number. The first, after
ruminating for hours, triumphantly announces "Eighty-three!" The second,
mightily impressed, replies "You win."
A biggest number contest is clearly pointless when the contestants take
turns. But what if the contestants write down their numbers simultaneously,
neither aware of the other�s? To introduce a talk on "Big Numbers," I invite two
audience volunteers to try exactly this. I tell them the rules:
You have fifteen seconds. Using standard math notation, English words, or
both, name a single whole number�not an infinity�on a blank index card. Be
precise enough for any reasonable modern mathematician to determine exactly what
number you�ve named, by consulting only your card and, if necessary, the
published literature.
So contestants can�t say "the number of sand grains in the Sahara," because
sand drifts in and out of the Sahara regularly. Nor can they say "my opponent�s
number plus one," or "the biggest number anyone�s ever thought of plus
one"�again, these are ill-defined, given what our reasonable mathematician has
available. Within the rules, the contestant who names the bigger number
wins.
Are you ready? Get set. Go.
The contest�s results are never quite what I�d hope. Once, a seventh-grade
boy filled his card with a string of successive 9�s. Like many other big-number
tyros, he sought to maximize his number by stuffing a 9 into every place value.
Had he chosen easy-to-write 1�s rather than curvaceous 9�s, his number could
have been millions of times bigger. He still would been decimated, though, by
the girl he was up against, who wrote a string of 9�s followed by the
superscript 999. Aha! An exponential: a number multiplied by itself
999 times. Noticing this innovation, I declared the girl�s victory without
bothering to count the 9�s on the cards.
And yet the girl�s number could have been much bigger still, had she stacked
the mighty exponential more than once. Take , for example. This
behemoth, equal to 9387,420,489, has 369,693,100 digits. By
comparison, the number of elementary particles in the observable universe has a meager 85
digits, give or take. Three 9�s, when stacked exponentially, already lift us
incomprehensibly beyond all the matter we can observe�by a factor of about
10369,693,015. And we�ve said nothing of or
.
Place value, exponentials, stacked exponentials: each can express boundlessly
big numbers, and in this sense they�re all equivalent. But the notational
systems differ dramatically in the numbers they can express concisely.
That�s what the fifteen-second time limit illustrates. It takes the same amount
of time to write 9999, 9999, and �yet the first
number is quotidian, the second astronomical, and the third hyper-mega
astronomical. The key to the biggest number contest is not swift penmanship, but
rather a potent paradigm for concisely capturing the gargantuan.
Such paradigms are historical rarities. We find a flurry in antiquity,
another flurry in the twentieth century, and nothing much in between. But when a
new way to express big numbers concisely does emerge, it�s often a byproduct of
a major scientific revolution: systematized mathematics, formal logic, computer
science. Revolutions this momentous, as any Kuhnian could tell you, only happen
under the right social conditions. Thus is the story of big numbers a story of
human progress.
And herein lies a parallel with another mathematical story. In his remarkable
and underappreciated book A History of π, Petr
Beckmann argues that the ratio of circumference to diameter is "a quaint little
mirror of the history of man." In the rare societies where science and reason
found refuge�the early Athens of Anaxagoras and Hippias, the Alexandria of
Eratosthenes and Euclid, the seventeenth-century England of Newton and
Wallis�mathematicians made tremendous strides in calculating π. In Rome and medieval Europe, by contrast, knowledge of
π stagnated. Crude approximations such as the
Babylonians� 25/8 held sway.
This same pattern holds, I think, for big numbers. Curiosity and openness
lead to fascination with big numbers, and to the buoyant view that no quantity,
whether of the number of stars in the galaxy or the number of possible bridge
hands, is too immense for the mind to enumerate. Conversely, ignorance and
irrationality lead to fatalism concerning big numbers. Historian Ilan Vardi cites the ancient Greek
term sand-hundred,
colloquially meaning zillion; as well as a passage from Pindar�s
Olympic Ode II asserting that "sand escapes counting."
�
But sand doesn�t escape counting, as Archimedes recognized in the third
century B.C. Here�s how he began The Sand-Reckoner, a sort of pop-science
article addressed to the King of Syracuse:
There are some ... who think that the number of the sand is infinite in
multitude ... again there are some who, without regarding it as infinite, yet
think that no number has been named which is great enough to exceed its
multitude ... But I will try to show you [numbers that] exceed not only the
number of the mass of sand equal in magnitude to the earth ... but also that of
a mass equal in magnitude to the universe.
This Archimedes proceeded to do, essentially by using the ancient Greek term
myriad, meaning ten thousand, as a base for exponentials. Adopting a
prescient cosmological model of Aristarchus, in which the "sphere of the fixed
stars" is vastly greater than the sphere in which the Earth revolves around the
sun, Archimedes obtained an upper bound of 1063 on the number of sand
grains needed to fill the universe. (Supposedly 1063 is the biggest
number with a lexicographically standard American name: vigintillion. But
the staid vigintillion had better keep vigil lest it be encroached upon by the
more whimsically-named googol, or 10100, and
googolplex, or .) Vast though it was, of course, 1063
wasn�t to be enshrined as the all-time biggest number. Six centuries later,
Diophantus developed a simpler notation for exponentials, allowing him to
surpass . Then, in the Middle Ages, the rise of Arabic
numerals and place value made it easy to stack exponentials higher still. But
Archimedes� paradigm for expressing big numbers wasn�t fundamentally surpassed
until the twentieth century. And even today, exponentials dominate popular
discussion of the immense.
Consider, for example, the oft-repeated legend of the Grand Vizier in Persia
who invented chess. The King, so the legend goes, was delighted with the new
game, and invited the Vizier to name his own reward. The Vizier replied that,
being a modest man, he desired only one grain of wheat on the first square of a
chessboard, two grains on the second, four on the third, and so on, with twice
as many grains on each square as on the last. The innumerate King agreed, not
realizing that the total number of grains on all 64 squares would be
264-1, or 18.6 quintillion�equivalent to the world�s present wheat
production for 150 years.
Fittingly, this same exponential growth is what makes chess itself so
difficult. There are only about 35 legal choices for each chess move, but the
choices multiply exponentially to yield something like 1050 possible board
positions�too many for even a computer to search exhaustively. That�s why it
took until 1997 for a computer, Deep Blue, to defeat the human world chess
champion. And in Go, which has a 19-by-19 board and over 10150
possible positions, even an amateur human can still rout the world�s top-ranked
computer programs. Exponential growth plagues computers in other guises as well.
The traveling salesman problem asks for the shortest route connecting a set of
cities, given the distances between each pair of cities. The rub is that the
number of possible routes grows exponentially with the number of cities. When
there are, say, a hundred cities, there are about 10158 possible
routes, and, although various shortcuts are possible, no known computer
algorithm is fundamentally better than checking each route one by one. The
traveling salesman problem belongs to a class called NP-complete, which includes
hundreds of other problems of practical interest. (NP stands for the technical
term �Nondeterministic Polynomial-Time.�) It�s known that if there�s an efficient
algorithm for any NP-complete problem, then there are efficient algorithms for
all of them. Here �efficient� means using an amount of time proportional to at
most the problem size raised to some fixed power�for example, the number of
cities cubed. It�s conjectured, however, that no efficient algorithm for
NP-complete problems exists. Proving this conjecture, called P� NP, has been a great unsolved problem of computer science
for thirty years.
Although computers will probably never solve NP-complete problems
efficiently, there�s more hope for another grail of computer science:
replicating human intelligence. The human brain has roughly a hundred billion
neurons linked by a hundred trillion synapses. And though the function of an
individual neuron is only partially understood, it�s thought that each neuron
fires electrical impulses according to relatively simple rules up to a thousand
times each second. So what we have is a highly interconnected computer capable
of maybe 1014 operations per second; by comparison, the world�s
fastest parallel supercomputer, the 9200-Pentium Pro teraflops machine at Sandia
National Labs, can perform 1012 operations per second. Contrary to
popular belief, gray mush is not only hard-wired for intelligence: it surpasses
silicon even in raw computational power. But this is unlikely to remain true for
long. The reason is Moore�s Law, which, in its 1990�s formulation, states that
the amount of information storable on a silicon chip grows exponentially,
doubling roughly once every two years. Moore�s Law will eventually play out, as
microchip components reach the atomic scale and conventional lithography
falters. But radical new technologies, such as optical computers, DNA computers,
or even quantum computers, could conceivably usurp silicon�s place. Exponential
growth in computing power can�t continue forever, but it may continue long
enough for computers�at least in processing power�to surpass human brains.
To prognosticators of artificial intelligence, Moore�s Law is a glorious
herald of exponential growth. But exponentials have a drearier side as well. The
human population recently passed six billion and is doubling about once every
forty years. At this exponential rate, if an average person weighs seventy
kilograms, then by the year 3750 the entire Earth will be composed of human
flesh. But before you invest in deodorant, realize that the population will stop
increasing long before this�either because of famine, epidemic disease, global
warming, mass species extinctions, unbreathable air, or, entering the
speculative realm, birth control. It�s not hard to fathom why physicist Albert
Bartlett asserted "the greatest shortcoming of the human race" to be "our
inability to understand the exponential function." Or why Carl Sagan advised us
to "never underestimate an exponential." In his book Billions &
Billions, Sagan gave some other depressing consequences of exponential
growth. At an inflation rate of five percent a year, a dollar is worth only
thirty-seven cents after twenty years. If a uranium nucleus emits two neutrons,
both of which collide with other uranium nuclei, causing them to emit two
neutrons, and so forth�well, did I mention nuclear holocaust as a possible end
to population growth?
�
Exponentials are familiar, relevant, intimately connected to the physical
world and to human hopes and fears. Using the notational systems I�ll discuss
next, we can concisely name numbers that make exponentials picayune by
comparison, that subjectively speaking exceed as much as the
latter exceeds 9. But these new systems may seem more abstruse than
exponentials. In his essay "On Number Numbness," Douglas Hofstadter leads his
readers to the precipice of these systems, but then avers:
If we were to continue our discussion just one zillisecond longer, we would
find ourselves smack-dab in the middle of the theory of recursive functions and
algorithmic complexity, and that would be too abstract. So let�s drop the topic
right here.
But to drop the topic is to forfeit, not only the biggest number contest, but
any hope of understanding how stronger paradigms lead to vaster numbers. And so
we arrive in the early twentieth century, when a school of mathematicians called
the formalists sought to place all of mathematics on a rigorous axiomatic basis.
A key question for the formalists was what the word �computable� means. That is,
how do we tell whether a sequence of numbers can be listed by a definite,
mechanical procedure? Some mathematicians thought that �computable� coincided
with a technical notion called �primitive recursive.� But in 1928 Wilhelm
Ackermann disproved them by constructing a sequence of numbers that�s clearly
computable, yet grows too quickly to be primitive recursive.
Ackermann�s idea was to create an endless procession of arithmetic
operations, each more powerful than the last. First comes addition. Second comes
multiplication, which we can think of as repeated addition: for example, 5�3 means 5 added to itself 3 times, or 5+5+5 = 15. Third
comes exponentiation, which we can think of as repeated multiplication. Fourth
comes ... what? Well, we have to invent a weird new operation, for repeated
exponentiation. The mathematician Rudy Rucker calls it �tetration.� For example,
�5 tetrated to the 3� means 5 raised to its own power 3 times, or
, a number with 2,185 digits. We can go on. Fifth comes repeated
tetration: shall we call it �pentation�? Sixth comes repeated pentation:
�hexation�? The operations continue infinitely, with each one standing on its
predecessor to peer even higher into the firmament of big numbers.
If each operation were a candy flavor, then the Ackermann sequence would be
the sampler pack, mixing one number of each flavor. First in the sequence is
1+1, or (don�t hold your breath) 2. Second is 2�2, or
4. Third is 3 raised to the 3rd power, or 27. Hey, these numbers
aren�t so big!
Fee. Fi. Fo. Fum.
Fourth is 4 tetrated to the 4, or , which has
10154 digits. If you�re planning to write this number out, better
start now. Fifth is 5 pentated to the 5, or with �5 pentated
to the 4� numerals in the stack. This number is too colossal to describe in any
ordinary terms. And the numbers just get bigger from there.
Wielding the Ackermann sequence, we can clobber unschooled opponents in the
biggest-number contest. But we need to be careful, since there are several
definitions of the Ackermann sequence, not all identical.
Under the fifteen-second time limit, here�s what I might write to avoid
ambiguity:
A(111)�Ackermann seq�A(1)=1+1, A(2)=2�2, A(3)=33,
etc
Recondite as it seems, the Ackermann sequence does have some applications. A
problem in an area called Ramsey theory asks for the minimum dimension of a
hypercube satisfying a certain property. The true dimension is thought to be 6,
but the lowest dimension anyone�s been able is prove is so huge that it can only
be expressed using the same �weird arithmetic� that underlies the Ackermann
sequence. Indeed, the Guinness Book of World Records once listed this
dimension as the biggest number ever used in a mathematical proof. (Another
contender for the title once was Skewes� number, about ,
which arises in the study of how prime numbers are distributed. The famous
mathematician G. H. Hardy quipped that Skewes� was "the largest number which has
ever served any definite purpose in mathematics.") What�s more, Ackermann�s
briskly-rising cavalcade performs an occasional cameo in computer science. For
example, in the analysis of a data structure called �Union-Find,� a term gets
multiplied by the inverse of the Ackermann sequence�meaning, for each whole
number X, the first number N such that the Nth Ackermann number is
bigger than X. The inverse grows as slowly as Ackermann�s original sequence
grows quickly; for all practical purposes, the inverse is at most 4.
�
Ackermann numbers are pretty big, but they�re not yet big enough. The quest
for still bigger numbers takes us back to the formalists. After Ackermann
demonstrated that �primitive recursive� isn�t what we mean by �computable,� the
question still stood: what do we mean by �computable�? In 1936, Alonzo
Church and Alan Turing independently answered this question. While Church
answered using a logical formalism called the lambda calculus, Turing answered
using an idealized computing machine�the Turing machine�that, in essence, is
equivalent to every Compaq, Dell, Macintosh, and Cray in the modern world.
Turing�s paper describing his machine, "On Computable Numbers," is rightly
celebrated as the founding document of computer science.
"Computing," said Turing,
is normally done by writing certain symbols on paper. We may suppose this
paper to be divided into squares like a child�s arithmetic book. In elementary
arithmetic the 2-dimensional character of the paper is sometimes used. But such
use is always avoidable, and I think it will be agreed that the two-dimensional
character of paper is no essential of computation. I assume then that the
computation is carried out on one-dimensional paper, on a tape divided into
squares.
Turing continued to explicate his machine using ingenious reasoning from
first principles. The tape, said Turing, extends infinitely in both directions,
since a theoretical machine ought not be constrained by physical limits on
resources. Furthermore, there�s a symbol written on each square of the tape,
like the �1�s and �0�s in a modern computer�s memory. But how are the symbols
manipulated? Well, there�s a �tape head� moving back and forth along the tape,
examining one square at a time, writing and erasing symbols according to
definite rules. The rules are the tape head�s program: change them, and you
change what the tape head does.
Turing�s august insight was that we can program the tape head to carry out
any computation. Turing machines can add, multiply, extract cube roots,
sort, search, spell-check, parse, play Tic-Tac-Toe, list the Ackermann sequence.
If we represented keyboard input, monitor output, and so forth as symbols on the
tape, we could even run Windows on a Turing machine. But there�s a problem. Set
a tape head loose on a sequence of symbols, and it might stop eventually, or it
might run forever�like the fabled programmer who gets stuck in the shower
because the instructions on the shampoo bottle read "lather, rinse, repeat." If
the machine�s going to run forever, it�d be nice to know this in advance, so
that we don�t spend an eternity waiting for it to finish. But how can we
determine, in a finite amount of time, whether something will go on endlessly?
If you bet a friend that your watch will never stop ticking, when could you
declare victory? But maybe there�s some ingenious program that can examine other
programs and tell us, infallibly, whether they�ll ever stop running. We just
haven�t thought of it yet.
Nope. Turing proved that this problem, called the Halting Problem, is
unsolvable by Turing machines. The proof is a beautiful example of
self-reference. It formalizes an old argument about why you can never have
perfect introspection: because if you could, then you could determine what you
were going to do ten seconds from now, and then do something else. Turing
imagined that there was a special machine that could solve the Halting Problem.
Then he showed how we could have this machine analyze itself, in such a way that
it has to halt if it runs forever, and run forever if it halts. Like a hound
that finally catches its tail and devours itself, the mythical machine vanishes
in a fury of contradiction. (That�s the sort of thing you don�t say in a
research paper.)
�
"Very nice," you say (or perhaps you say, "not nice at all"). "But what does
all this have to do with big numbers?" Aha! The connection wasn�t published
until May of 1962. Then, in the Bell System Technical Journal, nestled
between pragmatically-minded papers on "Multiport Structures" and "Waveguide
Pressure Seals," appeared the modestly titled "On Non-Computable Functions" by
Tibor Rado. In this paper, Rado introduced the biggest numbers anyone had ever
imagined.
His idea was simple. Just as we can classify words by how many letters they
contain, we can classify Turing machines by how many rules they have in the tape
head. Some machines have only one rule, others have two rules, still others have
three rules, and so on. But for each fixed whole number N, just as there are
only finitely many distinct words with N letters, so too are there only finitely many distinct
machines with N rules. Among these machines, some halt and others run forever
when started on a blank tape. Of the ones that halt, asked Rado, what�s the
maximum number of steps that any machine takes before it halts?
(Actually, Rado asked mainly about the maximum number of symbols any machine can
write on the tape before halting. But the maximum number of steps, which Rado
called S(n), has the same basic properties and is easier to reason about.)
Rado called this maximum the Nth "Busy Beaver" number. (Ah yes,
the early 1960�s were a more innocent age.) He visualized each Turing machine as
a beaver bustling busily along the tape, writing and erasing symbols. The
challenge, then, is to find the busiest beaver with exactly N rules,
albeit not an infinitely busy one. We can interpret this challenge as one of
finding the "most complicated" computer program N bits long: the one that does
the most amount of stuff, but not an infinite amount.
Now, suppose we knew the Nth Busy Beaver number, which we�ll call
BB(N). Then we could decide whether any Turing machine with N rules halts on a
blank tape. We�d just have to run the machine: if it halts, fine; but if it
doesn�t halt within BB(N) steps, then we know it never will halt, since
BB(N) is the maximum number of steps it could make before halting. Similarly, if
you knew that all mortals died before age 200, then if Sally lived to be 200,
you could conclude that Sally was immortal. So no Turing machine can list the
Busy Beaver numbers�for if it could, it could solve the Halting Problem, which
we already know is impossible.
But here�s a curious fact. Suppose we could name a number greater than
the Nth Busy Beaver number BB(N). Call this number D for dam, since
like a beaver dam, it�s a roof for the Busy Beaver below. With D in hand,
computing BB(N) itself becomes easy: we just need to simulate all the Turing
machines with N rules. The ones that haven�t halted within D steps�the ones that
bash through the dam�s roof�never will halt. So we can list exactly which
machines halt, and among these, the maximum number of steps that any machine
takes before it halts is BB(N).
Conclusion? The sequence of Busy Beaver numbers, BB(1), BB(2), and so on,
grows faster than any computable sequence. Faster than exponentials,
stacked exponentials, the Ackermann sequence, you name it. Because if a Turing
machine could compute a sequence that grows faster than Busy Beaver, then it
could use that sequence to obtain the D�s�the beaver dams. And with those D�s,
it could list the Busy Beaver numbers, which (sound familiar?) we already know
is impossible. The Busy Beaver sequence is non-computable, solely because it
grows stupendously fast�too fast for any computer to keep up with it, even in
principle.
This means that no computer program could list all the Busy Beavers one by
one. It doesn�t mean that specific Busy Beavers need remain eternally
unknowable. And in fact, pinning them down has been a computer science pastime
ever since Rado published his article. It�s easy to verify that BB(1), the first
Busy Beaver number, is 1. That�s because if a one-rule Turing machine doesn�t
halt after the very first step, it�ll just keep moving along the tape endlessly.
There�s no room for any more complex behavior. With two rules we can do more,
and a little grunt work will ascertain that BB(2) is 6. Six steps. What about
the third Busy Beaver? In 1965 Rado, together with Shen Lin, proved that BB(3)
is 21. The task was an arduous one, requiring human analysis of many machines to
prove that they don�t halt�since, remember, there�s no algorithm for listing the
Busy Beaver numbers. Next, in 1983, Allan Brady proved that BB(4) is 107.
Unimpressed so far? Well, as with the Ackermann sequence, don�t be fooled by the
first few numbers.
In 1984, A.K. Dewdney devoted a Scientific American column to Busy
Beavers, which inspired amateur mathematician George Uhing to build a
special-purpose device for simulating Turing machines. The device, which cost
Uhing less than $100, found a five-rule machine that runs for 2,133,492 steps
before halting�establishing that BB(5) must be at least as high. Then, in 1989,
Heiner Marxen and J�rgen Buntrock discovered that BB(5) is at least 47,176,870.
To this day, BB(5) hasn�t been pinned down precisely, and it could turn out to
be much higher still. As for BB(6), Marxen and Buntrock set another record in
1997 by proving that it�s at least 8,690,333,381,690,951. A formidable
accomplishment, yet Marxen, Buntrock, and the other Busy Beaver hunters are
merely wading along the shores of the unknowable. Humanity may never know the
value of BB(6) for certain, let alone that of BB(7) or any higher number in the
sequence.
Indeed, already the top five and six-rule contenders elude us: we can�t
explain how they �work� in human terms. If creativity imbues their design, it�s
not because humans put it there. One way to understand this is that even small
Turing machines can encode profound mathematical problems. Take Goldbach�s
conjecture, that every even number 4 or higher is a sum of two prime numbers:
10=7+3, 18=13+5. The conjecture has resisted proof since 1742. Yet we could
design a Turing machine with, oh, let�s say 100 rules, that tests each even
number to see whether it�s a sum of two primes, and halts when and if it finds a
counterexample to the conjecture. Then knowing BB(100), we could in principle run
this machine for BB(100) steps, decide whether it halts, and thereby resolve
Goldbach�s conjecture. We need not venture far in the sequence to enter the lair
of basilisks.
But as Rado stressed, even if we can�t list the Busy Beaver numbers, they�re
perfectly well-defined mathematically. If you ever challenge a friend to the
biggest number contest, I suggest you write something like this:
BB(11111)�Busy Beaver shift #�1, 6, 21, etc
If your friend doesn�t know about Turing machines or anything similar, but
only about, say, Ackermann numbers, then you�ll win the contest. You�ll still
win even if you grant your friend a handicap, and allow him the entire lifetime
of the universe to write his number. The key to the biggest number contest is a
potent paradigm, and Turing�s theory of computation is potent indeed.
�
But what if your friend knows about Turing machines as well? Is there a
notational system for big numbers more powerful than even Busy Beavers?
Suppose we could endow a Turing machine with a magical ability to solve the
Halting Problem. What would we get? We�d get a �super Turing machine�: one with
abilities beyond those of any ordinary machine. But now, how hard is it to
decide whether a super machine halts? Hmm. It turns out that not even
super machines can solve this �super Halting Problem�, for the same reason that
ordinary machines can�t solve the ordinary Halting Problem. To solve the Halting
Problem for super machines, we�d need an even more powerful machine: a
�super duper machine.� And to solve the Halting Problem for super duper
machines, we�d need a �super duper pooper machine.� And so on endlessly. This
infinite hierarchy of ever more powerful machines was formalized by the logician
Stephen Kleene in 1943 (although he didn�t use the term �super duper pooper�).
Imagine a novel, which is imbedded in a longer novel, which itself is
imbedded in an even longer novel, and so on ad infinitum. Within each
novel, the characters can debate the literary merits of any of the sub-novels.
But, by analogy with classes of machines that can�t analyze themselves, the
characters can never critique the novel that they themselves are in.
(This, I think, jibes with our ordinary experience of novels.) To fully
understand some reality, we need to go outside of that reality. This is the
essence of Kleene�s hierarchy: that to solve the Halting Problem for some class
of machines, we need a yet more powerful class of machines.
And there�s no escape. Suppose a Turing machine had a magical ability to
solve the Halting Problem, and the super Halting Problem, and the
super duper Halting Problem, and the super duper pooper Halting Problem,
and so on endlessly. Surely this would be the Queen of Turing machines? Not
quite. As soon as we want to decide whether a �Queen of Turing machines� halts,
we need a still more powerful machine: an �Empress of Turing machines.� And
Kleene�s hierarchy continues.
But how�s this relevant to big numbers? Well, each level of Kleene�s
hierarchy generates a faster-growing Busy Beaver sequence than do all the
previous levels. Indeed, each level�s sequence grows so rapidly that it can only
be computed by a higher level. For example, define BB2(N) to be the
maximum number of steps a super machine with N rules can make before halting. If
this super Busy Beaver sequence were computable by super machines, then those
machines could solve the super Halting Problem, which we know is impossible. So
the super Busy Beaver numbers grow too rapidly to be computed, even if we
could compute the ordinary Busy Beaver numbers.
You might think that now, in the biggest-number contest, you could obliterate
even an opponent who uses the Busy Beaver sequence by writing something like
this:
BB2(11111).
But not quite. The problem is that I�ve never seen these "higher-level Busy
Beavers" defined anywhere, probably because, to people who know computability
theory, they�re a fairly obvious extension of the ordinary Busy Beaver numbers.
So our reasonable modern mathematician wouldn�t know what number you were
naming. If you want to use higher-level Busy Beavers in the biggest number
contest, here�s what I suggest. First, publish a paper formalizing the concept
in some obscure, low-prestige journal. Then, during the contest, cite the paper
on your index card.
To exceed higher-level Busy Beavers, we�d presumably need some new
computational model surpassing even Turing machines. I can�t imagine what such a
model would look like. Yet somehow I doubt that the story of notational systems
for big numbers is over. Perhaps someday humans will be able concisely to name
numbers that make Busy Beaver 100 seem as puerile and amusingly small as our
nobleman�s eighty-three. Or if we�ll never name such numbers, perhaps other
civilizations will. Is a biggest number contest afoot throughout the galaxy?
�
You might wonder why we can�t transcend the whole parade of paradigms, and
name numbers by a system that encompasses and surpasses them all. Suppose you
wrote the following in the biggest number contest:
The biggest whole number nameable with 1,000 characters of English
text
Surely this number exists. Using 1,000 characters, we can name only finitely
many numbers, and among these numbers there has to be a biggest. And yet we�ve
made no reference to how the number�s named. The English text could invoke
Ackermann numbers, or Busy Beavers, or higher-level Busy Beavers, or even some
yet more sweeping concept that nobody�s thought of yet. So unless our opponent
uses the same ploy, we�ve got him licked. What a brilliant idea! Why didn�t we
think of this earlier?
Unfortunately it doesn�t work. We might as well have written
One plus the biggest whole number nameable with 1,000 characters of English
text
This number takes at least 1,001 characters to name. Yet we�ve just named it
with only 80 characters! Like a snake that swallows itself whole, our colossal
number dissolves in a tumult of contradiction. What gives?
The paradox I�ve just described was first published by Bertrand Russell, who
attributed it to a librarian named G. G. Berry. The Berry Paradox arises not
from mathematics, but from the ambiguity inherent in the English language.
There�s no surefire way to convert an English phrase into the number it names
(or to decide whether it names a number at all), which is why I invoked a
"reasonable modern mathematician" in the rules for the biggest number contest.
To circumvent the Berry Paradox, we need to name numbers using a precise,
mathematical notational system, such as Turing machines�which is exactly the
idea behind the Busy Beaver sequence. So in short, there�s no wily language
trick by which to surpass Archimedes, Ackermann, Turing, and Rado, no royal road
to big numbers.
You might also wonder why we can�t use infinity in the contest. The answer
is, for the same reason why we can�t use a rocket car in a bike race. Infinity
is fascinating and elegant, but it�s not a whole number. Nor can we �subtract
from infinity� to yield a whole number. Infinity minus 17 is still infinity,
whereas infinity minus infinity is undefined: it could be 0, 38, or even
infinity again. Actually I should speak of infinities, plural. For in the late
nineteenth century, Georg Cantor proved that there are different levels of
infinity: for example, the infinity of points on a line is greater than the
infinity of whole numbers. What�s more, just as there�s no biggest number, so
too is there no biggest infinity. But the quest for big infinities is more
abstruse than the quest for big numbers. And it involves, not a succession of
paradigms, but essentially one: Cantor�s.
�
So here we are, at the frontier of big number knowledge. As Euclid�s disciple
supposedly asked, "what is the use of all this?" We�ve seen that progress
in notational systems for big numbers mirrors progress in broader realms:
mathematics, logic, computer science. And yet, though a mirror reflects reality,
it doesn�t necessarily influence it. Even within mathematics, big numbers are
often considered trivialities, their study an idle amusement with no broader
implications. I want to argue a contrary view: that understanding big numbers is
a key to understanding the world.
Imagine trying to explain the Turing machine to Archimedes. The genius of
Syracuse listens patiently as you discuss the papyrus tape extending infinitely
in both directions, the time steps, states, input and output sequences. At last
he explodes.
"Foolishness!" he declares (or the ancient Greek equivalent). "All you�ve
given me is an elaborate definition, with no value outside of itself."
How do you respond? Archimedes has never heard of computers, those
cantankerous devices that, twenty-three centuries from his time, will transact
the world�s affairs. So you can�t claim practical application. Nor can you
appeal to Hilbert and the formalist program, since Archimedes hasn�t heard of
those either. But then it hits you: the Busy Beaver sequence. You define the
sequence for Archimedes, convince him that BB(1000) is more than his
1063 grains of sand filling the universe, more even than
1063 raised to its own power 1063 times. You defy him to
name a bigger number without invoking Turing machines or some equivalent. And as
he ponders this challenge, the power of the Turing machine concept dawns on him.
Though his intuition may never apprehend the Busy Beaver numbers, his reason
compels him to acknowledge their immensity. Big numbers have a way of imbuing
abstract notions with reality.
Indeed, one could define science as reason�s attempt to compensate for our
inability to perceive big numbers. If we could run at 280,000,000 meters per
second, there�d be no need for a special theory of relativity: it�d be obvious
to everyone that the faster we go, the heavier and squatter we get, and the
faster time elapses in the rest of the world. If we could live for 70,000,000
years, there�d be no theory of evolution, and certainly no creationism:
we could watch speciation and adaptation with our eyes, instead of painstakingly
reconstructing events from fossils and DNA. If we could bake bread at 20,000,000
degrees Kelvin, nuclear fusion would be not the esoteric domain of physicists
but ordinary household knowledge. But we can�t do any of these things, and so we
have science, to deduce about the gargantuan what we, with our infinitesimal
faculties, will never sense. If people fear big numbers, is it any wonder that
they fear science as well and turn for solace to the comforting smallness of
mysticism?
But do people fear big numbers? Certainly they do. I�ve met people who
don�t know the difference between a million and a billion, and don�t care. We
play a lottery with �six ways to win!,� overlooking the twenty million ways to
lose. We yawn at
six billion tons of carbon dioxide released into the atmosphere each year, and
speak of �sustainable development� in the jaws of exponential growth. Such
cases, it seems to me, transcend arithmetical ignorance and represent a basic
unwillingness to grapple with the immense.
Whence the cowering before big numbers, then? Does it have a biological
origin? In 1999, a group led by neuropsychologist
Stanislas Dehaene reported evidence in Science that two separate brain systems contribute
to mathematical thinking. The group trained Russian-English bilinguals to solve
a set of problems, including two-digit addition, base-eight addition, cube
roots, and logarithms. Some subjects were trained in Russian, others in English.
When the subjects were then asked to solve problems approximately�to choose the
closer of two estimates�they performed equally well in both languages. But when
asked to solve problems exactly, they performed better in the language of their
training. What�s more, brain-imaging evidence showed that the subjects� parietal
lobes, involved in spatial reasoning, were more active during approximation
problems; while the left inferior frontal lobes, involved in verbal reasoning,
were more active during exact calculation problems. Studies of patients with
brain lesions paint the same picture: those with parietal lesions sometimes
can�t decide whether 9 is closer to 10 or to 5, but remember the multiplication
table; whereas those with left-hemispheric lesions sometimes can�t decide
whether 2+2 is 3 or 4, but know that the answer is closer to 3 than to 9.
Dehaene et al. conjecture that humans represent numbers in two ways. For
approximate reckoning we use a �mental number line,� which evolved long ago and
which we likely share with other animals. But for exact computation we use
numerical symbols, which evolved recently and which, being language-dependent,
are unique to humans. This hypothesis neatly explains the experiment�s findings:
the reason subjects performed better in the language of their training for exact
computation but not for approximation problems is that the former call upon the
verbally-oriented left inferior frontal lobes, and the latter upon the
spatially-oriented parietal lobes.
If Dehaene et al.�s hypothesis is correct, then which representation do we
use for big numbers? Surely the symbolic one�for nobody�s mental number line
could be long enough to contain , 5 pentated to the 5, or
BB(1000). And here, I suspect, is the problem. When thinking about 3, 4, or 7,
we�re guided by our spatial intuition, honed over millions of years of
perceiving 3 gazelles, 4 mates, 7 members of a hostile clan. But when thinking
about BB(1000), we have only language, that evolutionary neophyte, to rely upon.
The usual neural pathways for representing numbers lead to dead ends. And this,
perhaps, is why people are afraid of big numbers.
Could early intervention mitigate our big number phobia? What if second-grade
math teachers took an hour-long hiatus from stultifying busywork to ask their
students, "How do you name really, really big numbers?" And then told
them about exponentials and stacked exponentials, tetration and the Ackermann
sequence, maybe even Busy Beavers: a cornucopia of numbers vaster than any
they�d ever conceived, and ideas stretching the bounds of their
imaginations.
Who can name the bigger number? Whoever has the deeper paradigm. Are you
ready? Get set. Go.
References
Petr Beckmann, A History of Pi, Golem Press, 1971.
Allan H. Brady, "The Determination of the Value of Rado�s Noncomputable
Function Sigma(k) for Four-State Turing Machines," Mathematics of
Computation, vol. 40, no. 162, April 1983, pp 647-
665.
Gregory J. Chaitin, "The Berry Paradox," Complexity, vol. 1, no. 1,
1995, pp. 26- 30. At http://www.umcs.maine.edu/~chaitin/unm2.html.
A.K. Dewdney, The New Turing Omnibus: 66 Excursions in Computer
Science, W.H. Freeman, 1993.
S. Dehaene and E. Spelke and P. Pinel and R. Stanescu and S. Tsivkin,
"Sources of Mathematical Thinking: Behavioral and Brain-Imaging Evidence,"
Science, vol. 284, no. 5416, May 7, 1999, pp. 970- 974.
Douglas Hofstadter, Metamagical Themas: Questing for the Essence of Mind
and Pattern, Basic Books, 1985. Chapter 6, "On Number Numbness," pp.
115- 135.
Robert Kanigel, The Man Who Knew Infinity: A Life of the Genius
Ramanujan, Washington Square Press, 1991.
Stephen C. Kleene, "Recursive predicates and quantifiers," Transactions of
the American Mathematical Society, vol. 53, 1943, pp. 41- 74.
Donald E. Knuth, Selected Papers on Computer Science, CSLI
Publications, 1996. Chapter 2, "Mathematics and Computer Science: Coping with
Finiteness," pp. 31- 57.
Dexter C. Kozen, Automata and Computability, Springer-Verlag,
1997.
���, The Design and Analysis of Algorithms, Springer-Verlag, 1991.
Shen Lin and Tibor Rado, "Computer studies of Turing machine problems,"
Journal of the Association for Computing Machinery, vol. 12, no. 2, April
1965, pp. 196- 212.
Heiner Marxen, Busy Beaver, at http://www.drb.insel.de/~heiner/BB/.
��� and J�rgen Buntrock, "Attacking the Busy Beaver 5," Bulletin of the
European Association for Theoretical Computer Science, no. 40, February
1990, pp. 247- 251.
Tibor Rado, "On Non-Computable Functions," Bell System Technical
Journal, vol. XLI, no. 2, May 1962, pp. 877-
884.
Rudy Rucker, Infinity and the Mind, Princeton University Press,
1995.
Carl Sagan, Billions & Billions, Random House, 1997.
Michael Somos, "Busy Beaver Turing Machine." At http://grail.cba.csuohio.edu/~somos/bb.html.
Alan Turing, "On computable numbers, with an application to the
Entscheidungsproblem," Proceedings of the London Mathematical Society,
Series 2, vol. 42, pp. 230- 265, 1936. Reprinted in
Martin Davis (ed.), The Undecidable, Raven, 1965.
Ilan Vardi, "Archimedes, the Sand Reckoner," at http://www.ihes.fr/~ilan/sand_reckoner.ps.
Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press,
1999. Entry on "Large Number" at http://www.treasure-troves.com/math/LargeNumber.html.
| 2024-11-08T12:59:17 | en | train |
|
47,411 | nickb | 2007-08-28T13:34:12 | Weighted Slope One in Haskell: collaborative filtering in 29 lines of code | http://www.serpentine.com/blog/2007/08/27/weighted-slope-one-in-haskell-collaborative-filtering-in-29-lines-of-code/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,413 | edu | 2007-08-28T13:34:52 | Heat/power issues at the datacenter make reddit go down. | http://blog.reddit.com/2007/08/reddit-downtime.html | 4 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,415 | jkush | 2007-08-28T13:41:41 | Top 100 "Undiscovered" Web Sites | null | http://www.pcmag.com/slideshow/0,1206,l=213934&s=25234&a=213919,00.asp | 9 | 6 | [
47465,
47611,
47649,
47451
] | null | null | null | null | null | null | null | null | null | train |
47,416 | ivankirigin | 2007-08-28T13:43:08 | Papervision3D: lovely, for a browser | null | http://www.papervision3d.org/ | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,421 | ivankirigin | 2007-08-28T13:56:05 | CSS @ Ten: The Next Big Thing | http://www.alistapart.com/articles/cssatten | 17 | 12 | [
47462,
47545
] | null | null | null | null | null | null | null | null | null | train |
|
47,423 | dawie | 2007-08-28T14:00:46 | Why Apple Can't Stop iPhone Hackers | null | http://www.businessweek.com/technology/content/aug2007/tc20070827_230698.htm | 7 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,425 | transburgh | 2007-08-28T14:02:16 | Oh the Irony | "We expect that advertising funded search engines will be inherently biased towards the advertisers and away from the needs of the consumers." -- Google cofounders Larry Page and Sergey Brin, 1998<p>
<a href="http://infolab.stanford.edu/~backrub/google.html" rel="nofollow">http://infolab.stanford.edu/~backrub/google.html</a>
| 9 | 9 | [
47446,
47426,
47795,
47439,
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] | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,427 | pbnaidu | 2007-08-28T14:13:37 | How do you share YC Winter Program application? | I am in the process of filling the YC 08 winter program application. I have filled the application and I would like my friend (co-founder) to fill some parts and review the application. How do I share the application, do I need to share my user name and password or is there some way to do this?
Thanks in advance and sorry I didn't know where to post this question. | 1 | 4 | [
47443,
47441,
47447
] | null | null | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,428 | abstractbill | 2007-08-28T14:19:53 | jwz: preventing wrist problems | http://www.jwz.org/gruntle/wrists.html | 3 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,432 | abstractbill | 2007-08-28T14:29:11 | Using the Socratic Method to teach binary arithmetic | http://www.garlikov.com/Soc_Meth.html | 7 | 0 | null | null | null | no_error | The Socratic Method | null | Rick Garlikov |
The Socratic Method:
Teaching by Asking Instead
of by Telling
by Rick Garlikov
This work is available here free,
so that
those who cannot afford it can still have access to it, and so that
no one has to pay before they read something that might not be what
they really are seeking. But if, after you have read it, you find it meaningful and helpful
and would like to contribute whatever
easily affordable amount you feel it is worth, please do do. I
will appreciate it. The button to the right will take you to
PayPal where you can make any size donation (of 25 cents or more) you
wish, using either your PayPal account
or a credit card without a PayPal account.
The following is a transcript
of a teaching experiment, using the Socratic method, with a regular third
grade class in a suburban elementary school. I present my perspective and
views on the session, and on the Socratic method as a teaching tool, following
the transcript. The class was conducted on a Friday afternoon beginning
at 1:30, late in May, with about two weeks left in the school year. This
time was purposely chosen as one of the most difficult times to entice
and hold these children's concentration about a somewhat complex intellectual
matter. The point was to demonstrate the power of the Socratic method for
both teaching and also for getting students involved and excited about
the material being taught. There were 22 students in the class. I was told
ahead of time by two different teachers (not the classroom teacher) that
only a couple of students would be able to understand and follow what I
would be presenting. When the class period ended, I and the classroom teacher
believed that at least 19 of the 22 students had fully and excitedly participated
and absorbed the entire material. The three other students' eyes were glazed
over from the very beginning, and they did not seem to be involved in the
class at all. The students' answers below are in capital letters.
The experiment
was to see whether I could teach these students binary arithmetic (arithmetic
using only two numbers, 0 and 1) only by asking them questions.
None of them had been introduced to binary arithmetic before. Though the
ostensible subject matter was binary arithmetic, my primary interest was
to give a demonstration to the teacher of the power and benefit of the
Socratic method where it is applicable. That is my interest here as well.
I chose binary arithmetic as the vehicle for that because it is something
very difficult for children, or anyone, to understand when it is taught
normally; and I believe that a demonstration of a method that can teach
such a difficult subject easily to children and also capture their enthusiasm
about that subject is a very convincing demonstration of the value of the
method. (As you will see below, understanding binary arithmetic is also
about understanding "place-value" in general. For those who seek a much
more detailed explanation about place-value, visit the long paper on The
Concept and Teaching of Place-Value.) This was to be the Socratic method
in what I consider its purest form, where questions (and only questions)
are used to arouse curiosity and at the same time serve as a logical, incremental,
step-wise guide that enables students to figure out about a complex topic
or issue with their own thinking and insights. In a less pure form, which
is normally the way it occurs, students tend to get stuck at some point
and need a teacher's explanation of some aspect, or the teacher gets stuck
and cannot figure out a question that will get the kind of answer or point
desired, or it just becomes more efficient to "tell" what you want to get
across. If "telling" does occur, hopefully by that time, the students have
been aroused by the questions to a state of curious receptivity to absorb
an explanation that might otherwise have been meaningless to them. Many
of the questions are decided before the class; but depending on what answers
are given, some questions have to be thought up extemporaneously. Sometimes
this is very difficult to do, depending on how far from what is anticipated
or expected some of the students' answers are. This particular attempt
went better than my best possible expectation, and I had much higher expectations
than any of the teachers I discussed it with prior to doing it.
I had one prior relationship
with this class. About two weeks earlier I had shown three of the third
grade classes together how to throw a boomerang and had let each student
try it once. They had really enjoyed that. One girl and one boy from the
65 to 70 students had each actually caught their returning boomerang on
their throws. That seemed to add to everyone's enjoyment. I had therefore
already established a certain rapport with the students, rapport being
something that I feel is important for getting them to comfortably and
enthusiastically participate in an intellectually uninhibited manner in
class and without being psychologically paralyzed by fear of "messing up".
When I got to the classroom
for the binary math experiment, students were giving reports on famous
people and were dressed up like the people they were describing. The student
I came in on was reporting on John Glenn, but he had not mentioned the
dramatic and scary problem of that first American trip in orbit. I asked
whether anyone knew what really scary thing had happened on John Glenn's
flight, and whether they knew what the flight was. Many said a trip to
the moon, one thought Mars. I told them it was the first full earth orbit
in space for an American. Then someone remembered hearing about something
wrong with the heat shield, but didn't remember what. By now they were
listening intently. I explained about how a light had come on that indicated
the heat shield was loose or defective and that if so, Glenn would be incinerated
coming back to earth. But he could not stay up there alive forever and
they had nothing to send up to get him with. The engineers finally determined,
or hoped, the problem was not with the heat shield, but with the warning
light. They thought it was what was defective. Glenn came down. The shield
was ok; it had been just the light. They thought that was neat.
"But what I am really here
for today is to try an experiment with you. I am the subject of the experiment,
not you. I want to see whether I can teach you a whole new kind of arithmetic
only by asking you questions. I won't be allowed to tell you anything about
it, just ask you things. When you think you know an answer, just call it
out. You won't need to raise your hands and wait for me to call on you;
that takes too long." [This took them a while to adapt to. They kept raising
their hands; though after a while they simply called out the answers while
raising their hands.] Here we go.
1) "How many is this?" [I held up ten fingers.]
TEN
2) "Who can write that on the board?" [virtually all hands up; I
toss the chalk to one kid and indicate for her to come up and do it]. She
writes
10
3) Who can write ten another way? [They hesitate than some hands
go up. I toss the chalk to another kid.]
| | | | | | | | | |
4) Another way?
| | | | | | | |
5) Another way?
2 x 5 [inspired by the last idea]
6) That's very good, but there are lots of things that equal
ten, right? [student nods agreement], so I'd rather not get into combinations
that equal ten, but just things that represent or sort of mean ten.
That will keep us from having a whole bunch of the same kind of thing.
Anybody else?
TEN
7) One more?
X [Roman
numeral]
8) [I point to the word "ten"]. What is this?
THE WORD TEN
9) What are written words made up of?
LETTERS
10) How many letters are there in the English alphabet?
26
11) How many words can you make out of them?
ZILLIONS
12) [Pointing to the number "10"] What is this way of writing numbers
made up of?
NUMERALS
13) How many numerals are there?
NINE
/ TEN
14) Which, nine or ten?
TEN
15) Starting with zero, what are they? [They call out, I write them
in the following way.]
0
1
2
3
4
5
6
7
8
9
16) How many numbers can you make out of these numerals?
MEGA-ZILLIONS, INFINITE, LOTS
17) How come we have ten numerals? Could it be because we have 10
fingers?
COULD BE
18) What if we were aliens with only two fingers? How many numerals
might we have?
2
19) How many numbers could we write out of 2 numerals?
NOT
MANY /
[one kid:] THERE WOULD BE A PROBLEM
20) What problem?
THEY COULDN'T DO THIS [he holds up seven fingers]
21) [This strikes me as a very quick, intelligent insight I did not
expect so suddenly.] But how can you do fifty five?
[he
flashes five fingers for an instant and then flashes them again]
22) How does someone know that is not ten? [I am not really happy
with my question here but I don't want to get side-tracked by how to logically
try to sign numbers without an established convention. I like that he sees
the problem and has announced it, though he did it with fingers instead
of words, which complicates the issue in a way. When he ponders my question
for a second with a "hmmm", I think he sees
the problem and I move on, saying...]
23) Well, let's see what they could do. Here's the numerals you wrote
down [pointing to the column from 0 to 9] for our ten numerals. If we only
have two numerals and do it like this, what numerals would we have.
0,
1
24) Okay, what can we write as we count? [I write as they
call out answers.]
0
ZERO
1
ONE
[silence]
25) Is that it? What do we do on this planet when we run out of numerals
at 9?
WRITE DOWN "ONE, ZERO"
26) Why?
[almost in unison] I
DON'T KNOW; THAT'S JUST THE WAY YOU WRITE "TEN"
27) You have more than one numeral here and you have already used
these numerals; how can you use them again?
WE PUT THE 1 IN A DIFFERENT COLUMN
28) What do you call that column you put it in?
TENS
29) Why do you call it that?
DON'T KNOW
30) Well, what does this 1 and this 0 mean when written in these
columns?
1 TEN AND NO ONES
31) But why is this a ten? Why is this [pointing] the ten's column?
DON'T KNOW; IT JUST IS!
32) I'll bet there's a reason. What was the first number that needed
a new column for you to be able to write it?
TEN
33) Could that be why it is called the ten's column?! What is the
first number that needs the next column?
100
34) And what column is that?
HUNDREDS
35) After you write 19, what do you have to change to write down
20?
9 to a 0
and 1 to a 2
36) Meaning then 2 tens and no ones, right, because 2 tens are ___?
TWENTY
37) First number that needs a fourth column?
ONE
THOUSAND
38) What column is that?
THOUSANDS
39) Okay, let's go back to our two-fingered aliens arithmetic. We
have
0
zero
1
one.
What would we do to write "two" if we did the same thing we do over
here [tens] to write the next number after you run out of numerals?
START
ANOTHER COLUMN
40) What should we call it?
TWO'S
COLUMN?
41) Right! Because the first number we need it for is ___?
TWO
42) So what do we put in the two's column? How many two's are there
in two?
1
43) And how many one's extra?
ZERO
44) So then two looks like this: [pointing to "10"], right?
RIGHT, BUT THAT SURE LOOKS LIKE TEN.
45) No, only to you guys, because you were taught it wrong [grin]
-- to the aliens it is two. They learn it that way in pre-school just as
you learn to call one, zero [pointing to "10"] "ten". But it's not really
ten, right? It's two -- if you only had two fingers. How long does it take
a little kid in pre-school to learn to read numbers, especially numbers
with more than one numeral or column?
TAKES A WHILE
46) Is there anything obvious about calling "one, zero" "ten" or
do you have to be taught to call it "ten" instead of "one, zero"?
HAVE
TO BE TAUGHT IT
47) Ok, I'm teaching you different. What is "1, 0" here?
TWO
48) Hard to see it that way, though, right?
RIGHT
49) Try to get used to it; the alien children do. What number comes
next?
THREE
50) How do we write it with our numerals?
We need one "TWO" and a "ONE"
[I write down 11 for them] So we have
0
zero
1
one
10
two
11
three
51) Uh oh, now we're out of numerals again. How do we get to four?
START
A NEW COLUMN!
52) Call it what?
THE FOUR'S COLUMN
53) Call it out to me; what do I write?
ONE,
ZERO, ZERO
[I
write "100
four"
under the other numbers]
54) Next?
ONE,
ZERO, ONE
I write "101
five"
55) Now let's add one more to it to get six. But be careful. [I point
to the 1 in the one's column and ask] If we add 1 to 1, we can't write
"2", we can only write zero in this column, so we need to carry ____?
ONE
56) And we get?
ONE, ONE, ZERO
57) Why is this six? What is it made of? [I point to columns, which
I had been labeling at the top with the word "one", "two", and "four" as
they had called out the names of them.]
a "FOUR" and a "TWO"
58) Which is ____?
SIX
59) Next? Seven?
ONE,
ONE, ONE
I write "111
seven"
60) Out of numerals again. Eight?
NEW COLUMN; ONE, ZERO, ZERO, ZERO
I write "1000
eight"
[We do a couple more and I continue to write them one under the other
with the word next to each number, so we have:]
0
zero
1
one
10
two
11
three
100
four
101
five
110
six
111
seven
1000
eight
1001
nine
1010
ten
61) So now, how many numbers do you think you can write with a one
and a zero?
MEGA-ZILLIONS
ALSO/ ALL OF THEM
62) Now, let's look at something. [Point to Roman numeral X that
one kid had written on the board.] Could you easily multiply Roman numerals?
Like MCXVII times LXXV?
NO
63) Let's see what happens if we try to multiply in alien here. Let's
try two times three and you multiply just like you do in tens [in the "traditional"
American style of writing out multiplication].
10
two
x 11 times
three
They call out the "one, zero" for just below the line, and "one,
zero, zero" for just below that and so I write:
10
two
x 11 times
three
10
100
110
64) Ok, look on the list of numbers, up here [pointing to the "chart"
where I have written down the numbers in numeral and word form] what is
110?
SIX
65) And how much is two times three in real life?
SIX
66) So alien arithmetic works just as well as your arithmetic, huh?
LOOKS
LIKE IT
67) Even easier, right, because you just have to multiply or add
zeroes and ones, which is easy, right?
YES!
68) There, now you know how to do it. Of course, until you get used
to reading numbers this way, you need your chart, because it is hard to
read something like "10011001011" in alien, right?
RIGHT
69) So who uses this stuff?
NOBODY/ ALIENS
70) No, I think you guys use this stuff every day. When do you use
it?
NO
WE DON'T
71) Yes you do. Any ideas where?
NO
72) [I walk over to the light switch and, pointing to it, ask:]
What is this?
A SWITCH
73) [I flip it off and on a few times.] How many positions
does it have?
TWO
74) What could you call these positions?
ON
AND OFF/ UP AND DOWN
75) If you were going to give them numbers what would you call them?
ONE
AND TWO/
[one
student] OH!! ZERO
AND ONE!
[other
kids then:] OH, YEAH!
76) You got that right. I am going to end my experiment part here
and just tell you this last part.
Computers and calculators have lots of circuits through essentially
on/off switches, where one way represents 0 and the other way, 1. Electricity
can go through these switches really fast and flip them on or off, depending
on the calculation you are doing. Then, at the end, it translates the strings
of zeroes and ones back into numbers or letters, so we humans, who can't
read long strings of zeroes and ones very well can know what the answers
are.
[at this point one of the kid's in the back yelled out, OH!
NEEEAT!!]
I don't know exactly how these circuits work; so if your teacher
ever gets some electronics engineer to come into talk to you, I want you
to ask him what kind of circuit makes multiplication or alphabetical order,
and so on. And I want you to invite me to sit in on the class with you.
Now, I have to tell you guys, I think you were leading me on about
not knowing any of this stuff. You knew it all before we started, because
I didn't tell you anything about this -- which by the way is called "binary
arithmetic", "bi" meaning two like in "bicycle". I just asked you questions
and you knew all the answers. You've studied this before, haven't you?
NO,
WE HAVEN'T. REALLY.
Then how did you do this? You must be amazing. By the way, some of
you may want to try it with other sets of numerals. You might try three
numerals 0, 1, and 2. Or five numerals. Or you might even try twelve 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, ~, and ^ -- see, you have to make up two new
numerals to do twelve, because we are used to only ten. Then you can check
your system by doing multiplication or addition, etc. Good luck.
After the part about John Glenn, the whole class took only 25 minutes.
Their teacher told me later that after I left the children talked
about it until it was time to go home.
. . . . . . . . . . . . . .
My Views About This Whole Episode
Students do not get bored
or lose concentration if they are actively participating. Almost all of
these children participated the whole time; often calling out in unison
or one after another. If necessary, I could have asked if anyone thought
some answer might be wrong, or if anyone agreed with a particular answer.
You get extra mileage out of a given question that way. I did not have
to do that here. Their answers were almost all immediate and very good.
If necessary, you can also call on particular students; if they don't know,
other students will bail them out. Calling on someone in a non-threatening
way tends to activate others who might otherwise remain silent. That was
not a problem with these kids. Remember, this was not a "gifted" class.
It was a normal suburban third grade of whom two teachers had said only
a few students would be able to understand the ideas.
The topic was "twos",
but I think they learned just as much about the "tens" they had been using
and not really understanding.
This method takes
a lot of energy and concentration when you are doing it fast, the way I
like to do it when beginning a new topic. A teacher cannot do this for
every topic or all day long, at least not the first time one teaches particular
topics this way. It takes a lot of preparation, and a lot of thought. When
it goes well, as this did, it is so exciting for both the students and
the teacher that it is difficult to stay at that peak and pace or to change
gears or topics. When it does not go as well, it is very taxing trying
to figure out what you need to modify or what you need to say. I practiced
this particular sequence of questioning a little bit one time with a first
grade teacher. I found a flaw in my sequence of questions. I had to figure
out how to correct that. I had time to prepare this particular lesson;
I am not a teacher but a volunteer; and I am not a mathematician. I came
to the school just to do this topic that one period.
I did this fast. I personally
like to do new topics fast originally and then re-visit them periodically
at a more leisurely pace as you get to other ideas or circumstances that
apply to, or make use of, them. As you re-visit, you fine tune.
The chief benefits of
this method are that it excites students' curiosity and arouses their thinking,
rather than stifling it. It also makes teaching more interesting, because
most of the time, you learn more from the students -- or by what they make
you think of -- than what you knew going into the class. Each group of
students is just enough different, that it makes it stimulating. It is
a very efficient teaching method, because the first time through tends
to cover the topic very thoroughly, in terms of their understanding it.
It is more efficient for their learning then lecturing to them is, though,
of course, a teacher can lecture in less time.
It gives constant feed-back
and thus allows monitoring of the students' understanding as you go. So
you know what problems and misunderstandings or lack of understandings
you need to address as you are presenting the material. You do not need
to wait to give a quiz or exam; the whole thing is one big quiz as you
go, though a quiz whose point is teaching, not grading. Though, to repeat,
this is teaching by stimulating students' thinking in certain focused areas,
in order to draw ideas out of them; it is not "teaching" by pushing ideas
into students that they may or may not be able to absorb or assimilate.
Further, by quizzing and monitoring their understanding as you go along,
you have the time and opportunity to correct misunderstandings or someone's
being lost at the immediate time, not at the end of six weeks when it is
usually too late to try to "go back" over the material. And in some cases
their ideas will jump ahead to new material so that you can meaningfully
talk about some of it "out of (your!) order" (but in an order relevant
to them). Or you can tell them you will get to exactly that in a little
while, and will answer their question then. Or suggest they might want
to think about it between now and then to see whether they can figure it
out for themselves first. There are all kinds of options, but at least
you know the material is "live" for them, which it is not always when you
are lecturing or just telling them things or they are passively and dutifully
reading or doing worksheets or listening without thinking.
If you can get the right
questions in the right sequence, kids in the whole intellectual spectrum
in a normal class can go at about the same pace without being bored; and
they can "feed off" each others' answers. Gifted kids may have additional
insights they may or may not share at the time, but will tend to reflect
on later. This brings up the issue of teacher expectations. From what I
have read about the supposed sin of tracking, one of the main complaints
is that the students who are not in the "top" group have lower expectations
of themselves and they get teachers who expect little of them, and who
teach them in boring ways because of it. So tracking becomes a self-fulfilling
prophecy about a kid's educability; it becomes dooming. That is a problem,
not with tracking as such, but with teacher expectations of students (and
their ability to teach). These kids were not tracked, and yet they would
never have been exposed to anything like this by most of the teachers in
that school, because most felt the way the two did whose expectations I
reported. Most felt the kids would not be capable enough and certainly
not in the afternoon, on a Friday near the end of the school year yet.
One of the problems with not tracking is that many teachers have almost
as low expectations of, and plans for, students grouped heterogeneously
as they do with non-high-end tracked students. The point is to try to stimulate
and challenge all students as much as possible. The Socratic method is
an excellent way to do that. It works for any topics or any parts of topics
that have any logical natures at all. It does not work for unrelated facts
or for explaining conventions, such as the sounds of letters or the capitals
of states whose capitals are more the result of historical accident than
logical selection.
Of course, you will notice
these questions are very specific, and as logically leading as possible.
That is part of the point of the method. Not just any question will do,
particularly not broad, very open ended questions, like "What is arithmetic?"
or "How would you design an arithmetic with only two numbers?" (or if you
are trying to teach them about why tall trees do not fall over when the
wind blows "what is a tree?"). Students have nothing in particular to focus
on when you ask such questions, and few come up with any sort of interesting
answer.
And it forces the
teacher to think about the logic of a topic, and how to make it most easily
assimilated. In tandem with that, the teacher has to try to understand
at what level the students are, and what prior knowledge they may have
that will help them assimilate what the teacher wants them to learn. It
emphasizes student understanding, rather than teacher presentation; student
intake, interpretation, and "construction", rather than teacher output.
And the point of education is that the students are helped most efficiently
to learn by a teacher, not that a teacher make the finest apparent presentation,
regardless of what students might be learning, or not learning. I was fortunate
in this class that students already understood the difference between numbers
and numerals, or I would have had to teach that by questions also. And
it was an added help that they had already learned Roman numerals. It was
also most fortunate that these students did not take very many, if any,
wrong turns or have any firmly entrenched erroneous ideas that would have
taken much effort to show to be mistaken.
I took a shortcut
in question 15 although I did not have to; but I did it because I thought
their answers to questions 13 and 14 showed an understanding that "0" was
a numeral, and I didn't want to spend time in this particular lesson trying
to get them to see where "0" best fit with regard to order. If they had
said there were only nine numerals and said they were 1-9, then you could
ask how they could write ten numerically using only those nine, and they
would quickly come to see they needed to add "0" to their list of numerals.
These are the four critical
points about the questions: 1) they must be interesting or intriguing to
the students; they must lead by 2) incremental and 3) logical steps (from
the students' prior knowledge or understanding) in order to be readily
answered and, at some point, seen to be evidence toward a conclusion, not
just individual, isolated points; and 4) they must be designed to get the
student to see particular points. You are essentially trying to get students
to use their own logic and therefore see, by their own reflections on your
questions, either the good new ideas or the obviously erroneous ideas that
are the consequences of their established ideas, knowledge, or beliefs.
Therefore you have to know or to be able to find out what the students'
ideas and beliefs are. You cannot ask just any question or start just anywhere.
It is crucial
to understand the difference between "logically" leading questions and
"psychologically" leading questions. Logically leading questions require
understanding of the concepts and principles involved in order to be answered
correctly; psychologically leading questions can be answered by students'
keying in on clues other than the logic of the content. Question 39 above
is psychologically leading, since I did not want to cover in this lesson
the concept of value-representation but just wanted to use "columnar-place"
value, so I psychologically led them into saying "Start another column"
rather than getting them to see the reasoning behind columnar-place as
merely one form of value representation. I wanted them to see how to use
columnar-place value logically without trying here to get them to
totally understand its logic. (A common form of value-representation
that is not "place" value is color value in poker chips, where colors determine
the value of the individual chips in ways similar to how columnar place
does it in writing. For example if white chips are worth "one" unit and
blue chips are worth "ten" units, 4 blue chips and 3 white chips is the
same value as a "4" written in the "tens" column and a "3" written in the
"ones" column for almost the same reasons.)
For the Socratic method
to work as a teaching tool and not just as a magic trick to get kids to
give right answers with no real understanding, it is crucial that the important
questions in the sequence must be logically leading rather than psychologically
leading. There is no magic formula for doing this, but one of the tests
for determining whether you have likely done it is to try to see whether
leaving out some key steps still allows people to give correct answers
to things they are not likely to really understand. Further, in the case
of binary numbers, I found that when you used this sequence of questions
with impatient or math-phobic adults who didn't want to have to think but
just wanted you to "get to the point", they could not correctly answer
very far into even the above sequence. That leads me to believe that answering
most of these questions correctly, requires understandingof the topic rather
than picking up some "external" sorts of clues in order to just guess correctly.
Plus, generally when one uses the Socratic method, it tends to become pretty
clear when people get lost and are either mistaken or just guessing. Their
demeanor tends to change when they are guessing, and they answer with a
questioning tone in their voice. Further, when they are logically understanding
as they go, they tend to say out loud insights they have or reasons they
have for their answers. When they are just guessing, they tend to just
give short answers with almost no comment or enthusiasm. They don't tend
to want to sustain the activity.
Finally, two of the interesting,
perhaps side, benefits of using the Socratic method are that it gives the
students a chance to experience the attendant joy and excitement of discovering
(often complex) ideas on their own. And it gives teachers a chance to learn
how much more inventive and bright a great many more students are than
usually appear to be when they are primarily passive.
[Some additional comments about the Socratic method of teaching are
in a letter, "Using
the Socratic Method".]
[For a more general approach to teaching, of which the Socratic Method
is just one specific
form, see "Teaching
Effectively: Helping Students Absorb and Assimilate Material"]
This work is available here free,
so that
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|
47,436 | transburgh | 2007-08-28T14:40:49 | Google Facebook App Off To Problematic Start | null | http://www.webpronews.com/topnews/2007/08/28/google-facebook-app-off-to-problematic-start | 1 | 0 | null | null | null | null | null | null | null | null | null | null | train |
47,442 | nickb | 2007-08-28T15:18:46 | Crystal Tower, the startup dorm, loses elevator service | http://valleywag.com/tech/breakdowns/crystal-tower-the-startup-dorm-loses-elevator-service-294156.php | 6 | 4 | [
47559,
47680,
47759,
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47477
] | null | null | fetch failed | null | null | null | null | 2024-11-08T09:05:16 | null | train |
|
47,448 | transburgh | 2007-08-28T15:39:55 | Videohybrid 3.0: I Can't Believe This Hasn't Been Banned Yet | http://www.techcrunch.com/2007/08/28/videohybrid-30-i-cant-believe-this-hasnt-been-banned-yet/ | 3 | 0 | null | null | null | no_error | Videohybrid 3.0: I Can't Believe This Hasn't Been Banned Yet | TechCrunch | 2007-08-28T12:59:26+00:00 | Contributor | Videohybrid, a site we first linked to in April as part of a broader post on online video piracy, has relaunched with a new version that is just asking for trouble.
Videohybrid 3.0 marries Q&A functionality with social voting. Users are now able to submit movies, and TV shows they are looking for online, other users who would like to see that video as well vote for the request. Digg style the top requests rise to the top of the list.
Users who respond to video requests earn points that go towards an overall ranking system. Videos are now exclusively embedded on site; unlike Bit Torrent and other services that require downloads Videohybrid is a one stop shop where pirated video can be played immediately on the same page, YouTube style, complete with user commenting and related features. Videohybrid doesn’t offer embedding code for the videos to be displayed elsewhere; from what I can gather the videos are all pulled from other sites, including some well known ones as well: a full rip of the movie Pulp Fiction was being served from Google Video.
There are other sites around operating in the same space; where Videohybrid differs is in its seamless delivery and rather amazing catalog of content. Something this good (from a user perspective, not a legal one) just can’t last. Here’s hoping the two teenagers from Lynbrook High School in San Jose who started the site have it hosted in a country well beyond the reach of the MPAA.
| 2024-11-08T14:51:45 | en | train |
|
47,452 | greendestiny | 2007-08-28T15:45:56 | Don't call me a software engineer | http://greendestinyonyc.blogspot.com/2007/08/why-i-hate-software-engineering.html | 5 | 8 | [
47469,
47537
] | null | null | null | null | null | null | null | null | null | train |
|
47,455 | kkim | 2007-08-28T16:03:44 | Our resistance to an epidemic 3 million years ago may have exposed us to the risk of HIV today | http://www.guardian.co.uk/commentisfree/story/0,,2157399,00.html | 7 | 0 | null | null | null | null | null | null | null | null | null | null | train |
|
47,471 | robg | 2007-08-28T16:28:25 | Feature request: Best list | Pardon me if it already exists, but how about a "best" list for HackerNews?<p>It seems like it would create a nice, evolving library of previous high-ranked posts. | 1 | -1 | null | null | true | invalid_url | null | null | null | null | 2024-11-08T16:37:59 | null | train |
|
47,482 | nickb | 2007-08-28T17:07:01 | The Surprising Truth About Ugly Websites (they perform better) | http://www.sitepronews.com/archives/2006/mar/27prt.html | 18 | 21 | [
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] | null | null | null | null | null | null | null | null | null | train |
|
47,484 | nickb | 2007-08-28T17:13:26 | Controlling Your Visitors Eyes | http://www.site-reference.com/articles/Website-Development/Controlling-Your-Visitors-Eyes.html | 1 | 0 | null | null | null | http_404 | Page Not Found | null | Jayden Gould - | Whether you're looking for a solution to a problem, or just want to learn how to use something new, the website Site-Reference gives you information on all solutions. | 2024-11-07T18:27:07 | null | train |
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