Common Lisp: Numbers - <AUTHOR> https://lispcookbook.github.io/cl-cookbook/numbers.html <comment><USER2> The COMPUTABLE-REALS [0] package from the article is interesting because it lets you change the precision even _after_ a computation is "performed". It basically builds up lazy representations of computations that can (internally) recompute to any precision specified. You do all of your arithmetic as normal and only until you need to do something with an actual decimal representation do you "request" it. You grab the actual approximation as a decimal number with the APPROX-R function, which provides as many digits as you please. There is _no_ need to re-run all of your code which produced the (computable) number in the first place to reapproximate at higher precision.

This all directly falls out of a mathematical formalism called "computable real numbers" [1] which are the (countable!) set of real numbers for which an algorithm exists to compute the digits to any desired precision. (Usually binary digits are the standard way to write out the definition of a computable number.)

[0] [https://github.com/stylewarning/computable- reals](https://github.com/stylewarning/computable-reals)

[1] [https://en.m.wikipedia.org/wiki/Computable_number](https://en.m.wikipedia.org/wiki/Computable_number)

<comment><USER3> I don't understand how this is supposed to work. For one thing iterative code wouldn't even do the same number of iterations when you change the desired precision, so merely plugging in higher precision numbers wouldn't give the higher precision approximation you'd be looking for. You'd have to actually re-execute the entire code with higher precision numbers so that intermediate control flow decisions use those numbers instead too, right?

<comment><USER4> Generally, precision is pulled on-demand, as it is needed. If you compare two values as x < y, x and y will be evaluated to higher and higher precision until the answer is unambiguous. This can be an issue if the values are equal, since they often cannot be proven to be equal, so the evaluation may just outright fail to terminate.

<comment><USER3> That doesn't address the situation I outlined?

<comment><USER5> You store the expression. Because that expression is a computable real, you can calculate it to arbitrary precision.

This is quite inefficient for things like summing over a list. Or really, any kind of accumulation.

</comment></comment></comment></comment></comment><comment><USER6> It is worth noting that most scripting languages today are still restricted by 64-bit integers and IEEE floating points limitations.

Python and Ruby are probably the only popular ones that ship by default with unlimited precision integers.

For arbitrary precision reals in Python, there is mpmath [http://mpmath.org/](http://mpmath.org/) . There is also the standard decimal module which "provides support for fast correctly-rounded decimal floating point arithmetic" : [https://docs.python.org/3/library/decimal.html](https://docs.python.org/3/library/decimal.html)

<comment><USER7> For MP work in Python, gmpy2 - [https://pypi.org/project/gmpy2/](https://pypi.org/project/gmpy2/) comes with a much better selection of MP functions, backed by MPFR, MPC.

Also, the buit-in Decimal class is horribly slow by comparison to gmpy2.

<comment><USER8> Purpose of the Decimal module is not really arbitrary precision computation but rather exact computation on decimal numbers wherever it matters (financial arithmetic, etc.). This module should never be used for scientific purposes.

</comment></comment></comment><comment><USER9> I also highly recommend the rtg-math commonlisp library (ql:quickload :rtg- math) [https://github.com/cbaggers/rtg-math](https://github.com/cbaggers/rtg- math)

Incredibly fast with support for quaternions / spherical coordinate systems etc

</comment><comment><USER10> A nice thing about Common Lisp's unlimited precision integer is it made testing a Common Lisp compiler much easier.

One can easily generate random integer-valued lisp forms without having to do much checking that integers are in range. In C or other languages with bounded integer size it's much tougher (see Regehr et al.'s Csmith). It's also tough to reduce a failing test case without introducing bad behavior in C; in Lisp it's straightfoward.</comment>


Ask HN: How to "Understand" Calculus? - <AUTHOR> I am not talking about mugging up formulaes but to understand the fundamentals and what they actually mean? <comment><USER2> first you need to intuit how a cartesian coordinate system works so you understand how a graph works

differential calculus is about rate of change: simplest case means slope or rise over run, practical case means estimating the slope of the portion of a curve.

      This can be a real physical curve or it can be a curve defined by a plot of numeric values on a graph

integral calculus is about estimating the area defined by a curve this is a game of cutting the area up into pieces adding up all the regular pieces and estimating the little pieces that fill in the edges.

FWIW to you here is a wiki link re calculus:

[https://en.wikipedia.org/wiki/Calculus](https://en.wikipedia.org/wiki/Calculus)

and cartesian coordinate:

[https://en.wikipedia.org/wiki/Cartesian_coordinate_system](https://en.wikipedia.org/wiki/Cartesian_coordinate_system)

for cartesian coordinate graphs you should understand euclidian geometry:

[https://en.wikipedia.org/wiki/Euclidean_geometry](https://en.wikipedia.org/wiki/Euclidean_geometry)

and likewise euclidian geometry requires algebra:

[https://en.wikipedia.org/wiki/Algebra](https://en.wikipedia.org/wiki/Algebra)

</comment><comment><USER3> That's an awfully general question. I would expect any high school or 1st year college course or textbook to do a reasonably good job of providing you with the basic intuition behind derivatives and integrals. It would help if you could be more specific about exactly what it is you are trying to understand.</comment>


Iconic Jeans in Movies - <AUTHOR> http://wtfjeans.com/blog/iconic-jeans-in-movies/ Today we don't even notice jeans that actors wear on the big screen. But during the 1950′s you've could been expelled from school, restaurant or theater if you showed up in jeans. Why? Well, everyone wanted to look like James Dean. There are certain movies from the 1950′s onwards that capture what we love the best – Hollywood icons clad in cool denim ;) <comment><USER2> As a techy and denim nerd, having this on hn is awesome.</comment>


ETSI ICT Standards: Lawful Interception - <AUTHOR> https://www.etsi.org/standards#page=1&search=lawful%20interception&title=1&etsiNumber=1&content=1&version=0&onApproval=1&published=1&historical=1&startDate=1988-01-15&endDate=2019-10-29&harmonized=0&keyword=&TB=&stdType=&frequency=&mandate=&collection=&sort=1 <comment><USER2> one could set up a wiki .onion, where users can "be bold" to summarize and go over all ramifications implied or suggested by the standards.</comment>


Deep Space Network Now: Status of communications with our deep space explorers - <AUTHOR> https://eyes.nasa.gov/dsn/ <comment><USER2> The latest episode of the Off-Nominal podcast[1] had a great interview with Shannon Stirone[2] all about DSN. They go into just how critical the infrastructure is, how little support it gets, and just the insane level of planning required for any planetary mission. Definitely worth a listen. See also Stirone's longread[3] about the DSN.

1: [http://offnominal.space/10](http://offnominal.space/10)

2: [https://twitter.com/shannonmstirone](https://twitter.com/shannonmstirone)

3: [https://longreads.com/2018/03/15/welcome-to-the-center-of- th...](https://longreads.com/2018/03/15/welcome-to-the-center-of-the- universe/)

</comment><comment><USER3> The thing I find really impressive is how weak the signals are.

From that page, the downlink from New Horizons is currently 1.89kbps at -143.72 dBm (4.25 x 10-21 kW). That's 0.00000000000000000425 W. Not a lot of signal to work with there, but the DSN is still able to extract a usable carrier. Amazing.

<comment><USER4> The capability to dig such a weak signal out of the noise is, indeed, a remarkable feat. I also think the ability to orient the spacecraft to point the antenna at where the earth is from a distance of a couple billion miles is pretty amazing. Obviously, a signal is going to spread a great deal over those distances but its still important to be close. I'd be curious to know how far off the pointing is from Voyager distance from boresight.

<comment><USER4> Actually, thinking about this, I made a mistake. Voyager isn't pointing its antenna at earth at that instant. It's actually pointing it to where the earth WILL be in 16 to 20 hours. Technically, that is probably no more difficult but my statement is more accurate.

<comment><USER5> Found this saying Voyager has a pointing accuracy of 0.1 degrees: [https://www.quora.com/How-precise-are-spacecrafts-like- New-H...](https://www.quora.com/How-precise-are-spacecrafts-like-New-Horizons- Voyager-I-and-Voyager-II-able-to-point-their-antenna-towards-Earth)

From the distance of Voyager, I doubt it makes any difference where Earth is for pointing the antenna. As in, it is pointing to the same spot no matter the day or season. They probably dial in an inertial coordinate and that is it.

</comment></comment></comment></comment><comment><USER6> Dave Jones of EEVBlog has a nice series of videos talking to Richard Stephenson, Operations Supervisor at the DSN's Canberra site.

How To Contact The Voyager 2 Probe:

Part 1: [https://www.youtube.com/watch?v=FzRP1qdwPKw&list=PLdytWBxFfp...](https://www.youtube.com/watch?v=FzRP1qdwPKw&list=PLdytWBxFfp36NwOTIiidVIrjuJU_UqJ_R&index=3)

Part 2: [https://www.youtube.com/watch?v=1rCrfQUcXDI&list=PLdytWBxFfp...](https://www.youtube.com/watch?v=1rCrfQUcXDI&list=PLdytWBxFfp36NwOTIiidVIrjuJU_UqJ_R&index=2)

Part 3: [https://www.youtube.com/watch?v=sP_hleOXTaU&list=PLdytWBxFfp...](https://www.youtube.com/watch?v=sP_hleOXTaU&list=PLdytWBxFfp36NwOTIiidVIrjuJU_UqJ_R&index=4)

(the playlist is a mess, and videos are unordered)

There are also a couple of Behinde the Scenes videos.

<comment><USER7> I'm about 15 mins into the first video, and I want to buy the camera guy a new taller tripod. I feel like I am a small child having to look up at the speaker.

Getting past that, it's a cool interview. Thanks for these links.

</comment></comment><comment><USER8> From what I can tell, this is an exact replica of what's displayed in the spaceflight operations facility in JPL.

The direction, speed, and density of waves are indicative of the direction, data rate, and data volume of the tx/rx from deep space missions.

</comment><comment><USER9> Recently I read a wonderful review paper about some of the problems engineers faced with early space communication.

It's really amazing how fast things moved back then. From 1954 to 1962 they went from using the moon as a relay satellite to having Telstar in orbit, which was capable of live trans-atlantic TV broadcasts.

The paper was featured on Fermat's Library, it's a great read -> [https://fermatslibrary.com/s/satellite-communication---an- ov...](https://fermatslibrary.com/s/satellite-communication---an-overview-of- the-problems-and-programs)

</comment><comment><USER10> It's neat to look at, for example, Voyager and see the antenna azimuth track in real-time to compensate for Earth rotation.

</comment><comment><USER11> What is the reason that "Wind Speed" is tracked and provided on this website. What does wind speed interact with communication between these antennas and the spacecraft?

<comment><USER12> It's hard to point a big dish accurately if the wind is too strong. They have wind limits above which they stow the dishes (by pointing them straight up to reduce the wind profile).

</comment></comment><comment><USER13> NASA has truly achieved some ridiculous feats. I hope that we see more of this in the future.

<comment><USER14> As they say - where there's a will, and funding for the willing, there's a way.

</comment></comment><comment><USER15> Watching YouTube from the New Horizon space craft would really suck. It's 11.5hr round trip latency and the bandwidth is way worse than dialup!</comment>


Ask HN: What are the easiest ways to earn crypto without investments? - <AUTHOR> I'm constantly asked by non-tech friends how can they earn some bitcoins or altcoins without heavy investment of time or money. What would you recommend? <comment><USER2> Mining bitcoin without specialized hardware is far from profitable (you'll pay 10x+ in electricity what you would buying directly from an exchange).

Altcoins may be profitable, or at least closer to market rates.

Doing work for a company that pays employees in Bitcoin is probably the most straightforward way.

You're going to have to either invest time or money, nobody is giving away free Bitcoins anymore. Some altcoins have giveaways, but I don't think the ones handing out stuff for free are likely to appreciate much.

</comment><comment><USER3> not gonna happen anymore. Unless you want to mine new crypto hopping their value go up.</comment>


Scientists discover first multicellular life that doesn't need oxygen - <AUTHOR> http://www.physorg.com/news189836027.html

<comment><USER2> Totally cool. The headline can act as the tl;dr summary, but basically they found 3 different species in the same family in this weird corner of the Mediterranean. They don't need any oxygen because they have something other than mitochondria in their cells to produce energy.

<comment><USER3> Given their unusual properties I wonder how likely they are to be seeded from 'alien' matter rather than derivatives of known Earth lifeforms.

<comment><USER4> Very unlikely indeed. They are new species but have been classified into previously-known taxonomic groups. They're related to other, perfectly prosaic Earthly animals.

<comment><USER3> Thanks

</comment></comment></comment></comment><comment><USER5> This is exactly the sort of example needed for evolutionists to point to to say "see, it _can_ happen in terrestrial time periods". A puny 50k years, and we appear to have multicellular creatures which evolved to not need oxygen. That's _way_ more than mere adapting, that's a fundamental, radical change.

<comment><USER6> You may be able to impress the undecided by-standers (and that's important). Don't count on winning over anyone who's decided that evolution doesn't fit into their world, at least not with rational arguments.

P.S. This is meant as a comment on the limited reach of arguments in convincing. I don't want to start a discussion on creationism.

</comment></comment><comment><USER7> Mars next?</comment>


Ask HN: How do I grow this? - <AUTHOR> How do I grow this?
I just released a product that helps teams get feedback from real users -- vast, and via video. The product itself seems to be cool once we put it in people's hands, but it's been hard to start conversations. What should I do?
http://sprint.dscout.com <comment><USER2> That landing page doesn't give me any idea in the slightest about what will happen if I click on any of the clickables.

<comment><AUTHOR> Here's the landing page: dscout.com/research/sprint

</comment></comment><comment><USER3> You need a landing page with good marketing copy. I landed at your link and was completely confused.</comment>