Measures idempotent with respect to addition and multiplication.

Question: Does there exist a probability finitely additive measure on $\mathbb N$ which is idempotent with respect to addition and multiplication simultaneously?
It is known (due to Hindman) that there is no ultrafilter that is additively and multiplicatively idempotent. But in the closure of the set of additively idempotent ultrafilters  there are  multiplicatively idempotent ultrafilters.
This question is related to the ones of Justin Moore: Idempotent measures on the free binary system? and Do distinct idempotent measures on finite binary systems have distinct supports?.
There is good background in the first references, but I do repeat some definition...
Consider $l_\infty(\mathbb{N})$ with $\mathbb R$ as a base field. A finitely additive probability measure on $\mathbb{N}$ is $\mu\in l_\infty^*(\mathbb{N})$ which is positive
($\mu(f)\geq 0$ if $f\geq 0$) and $\mu(1)=1$. Denote the set of these measures as $PM(\mathbb{N})$. Let $\star=+$ or $\cdot$. We may define $\star$
on $\mu\in l_\infty^*(\mathbb{N})$ as follows:
$$
\nu\star\mu(f)=\nu_x(\mu_y(f(x\star y))),
$$
where $\mu_y(f(x\star y))$ means that we apply $\mu$ with respect to $y$ for $x$-shifts of $f$, the result is a function of $x$. It looks that the only algebraic property of $+,\cdots$ conserved by this extension is associativity. The set $PM(\mathbb{N})$ is closed
with respect to $\star$. So, in this notation the question is
Does the exist $\mu\in PM(\mathbb{N})$ such that $\mu+\mu=\mu\cdot\mu=\mu$?
Comment: May be I was to quick to post the question. It has the negative answer: $\mathbb{Z}_2$ has no such measure: it has unique idempotent
for $\cdot$: the measure of $1$ is $1$. This is not an idempotent for $+$. The homomorphism $\mathbb{N}\to\mathbb{Z}_2$ solves the problem.

So, why the approach of Hindman was so complicated? Probably he thought about ultrafilters only....
Answer: I decide to repeat my comments to mark this question as answered. It has the negative answer:
If such a measure existed then such a mesure would exist for any homomorphic images of $N$.
But ${\mathbb Z}_2$ does not have such a measure.


What is acid soil?

Question: Everyone talks about acid soil, but what does it mean when someone says my soil is acid?  How does soil get that way?  Is it a good thing?  Is it a bad thing?
Answer: Randy's given a very scientific explanation of the causes and what it means, but in simple terms, it refers to soil ph, which runs on a scale from 0 - 14, the lowest number being highly acidic, and the highest alkaline, and 7 being neutral. If your soil is acidic, then certain plants will do very well in it, things like rhododendrons, pieris, blueberries, most heathers and heaths, but other plants which prefer alkaline soil will do very badly. Japanese Acer (palmatum varieties) is an interesting one - they don't like limey (alkaline) soils, but are perfectly happy in neutral or acid soil conditions. Other Acers, along with many other plants, aren't at all fussy about their ph conditions, although an extreme of 1 or 13 might cause some problems. So the only reason you might want to know your soil ph is to work out what you can grow in it well, or whether you need to make some emendment to it in order to grow a wider range of plants.
There is one plant which is a very useful guide to soil ph without doing a sample ph test - Hydrangea macrophylla hortensia varieties (those with the large, rounded, mophead flowers). Plant a pink one in alkaline soil and the flowers will come out pink - put the same plant in acid soil and the flowers will be blue. Around neutral will give flowers that are mixed between the two colours or a rather faded, unpleasant lilacy shade.
Broader causes of soil ph are the local geology, that is, what kind of bedrock or stone is under the soil, or whether the soil was originally alluvial (such as in old river courses). So, to answer your question fully, acidic soil is neither good nor bad, although you may consider it bad if you want to grow a lime loving plant in acid soil, or the other way around.
You might be interested to know that the ph scale applies to human beings as well - the body expends a lot of effort to keep the blood at 7.39 on the ph scale - illness results very quickly if that alters. Ph of the body, just like soil, changes depending what you put into it regularly, although effecting a permanent change from, say, acid to alkaline in soil is almost impossible.
Comment: Your goal is your goal, Randy, and I respect that. My goal was simply to explain what 'acid soil' meant in regard to growing plants, which is what I've done.
Comment: I've only just realised you asked this question yourself - and then answered it! If I'd noticed that initially, I wouldn't have taken the trouble to give an answer at all.
Comment: I don't think the bedrock plays as much of a role in acidity as weathering from rainfall. There may have been calcareous soils, but if rainfall is high, the weathering would have left the soil acidic. The main cause of soil acidity is rainfall and that idea was the basis for William Albrecht's life's work, see chapter 2 here http://www.soilandhealth.org/01aglibrary/010141.soil.fertility.animal.health/010146.albrecht.animal.health.pdf
Comment: Also, My goal with this Q n A was to show that acid soil is actually depleted soil and to get away from the mainstream idea that acid soil is simply a type of soil that is no better or worse than any other type. Yes, there are plants that have adapted to acid soil, but they are few and won't nourish a hungry population. I think it's important for people to understand that an acid soil is a depleted soil. With the "x ph is good for blueberries and y ph is good for tomatoes" way of thinking, nobody understands that.
Comment: Please take some time to review Albrecht's work and I think you'll understand why my goal is what it is. He was Chairman of the Department of Soils at the University of Missouri, was the foremost authority on the relation of soil fertility to human health and earned four degrees from the University of Illinois. http://en.wikipedia.org/wiki/William_Albrecht He devoted his life to the study of soils and if only people would take time to read what he wrote.
Answer: Let's start with a definition of acid.  An acid is any subtance which can act as a proton donor.  Protons in this case are hydrogen ions (H+).
So, an acid soil would have to be a substance which can donate H+ ions, therefore it is a substance which has lots of H+ ions to give.
Notice that the H+ ion has a positive charge.  Things with positive charges like to stick to things with negative charges.... like clay or humus particles in your soil.  It's like static cling.
A particle of soil can only hold so many things with a positive charge.  Let's call "the things with positive charges" cations (cat-eye-ons).  Cations found stuck to particles of soil include: H+, K+, Ca++, Mg++, Na+, NH4+, Fe++, Mn++, Cu++, Zn++, Al+++ and some other elements and compounds.  Now if a particle can only hold so many of these things with positive charges, and many of them are H+, that must mean that there is less, say, Ca++ (calcium) being stored than what there could be if there wasn't so much H+.

Plants take up cations, which the plant uses for nutrition, by releasing H+ ions from its roots.  One H+ ion may dislodge a potassium (K+) from the clay particle, which the plant can then take up.  But if the soil is so acid that the released H+ simply replaces another H+ on the clay particle, the plant can't get its nutrition.  In this way you can say that acid soil is really malnourishing soil... or depleted soil.  This doesn't seem like a good thing to have.
Unfortunately, it's not that simple.  A slightly acidic soil can prevent potato scab as the bacteria doesn't care much for the acidity.  Slight acidity can also make iron absorption easier.  Soil acidity has been put forth as the reason fusarium fungus isn't found in pine forests.  So, as it turns out, the most nourishing soil isn't the most nourishing soil in most cases:

Very acidic soils, in addition to be non-nourishing, make aluminum and manganese so readily available that they become toxic to plants.
Now that we know what it means to have an acid soil, how does a soil become acidic?
Well, as we can see from the above picture, plant roots give off H+ ions which contribute to acidity.  The decay of organic matter also releases H+ ions, which contributes to acidity.  Rain is also very acidic:

The pH of rain varies, especially due to its origin. On America's East Coast, rain that is derived from the Atlantic Ocean typically has a pH of 5.0-5.6; rain that comes across the continental from the west has a pH of 3.8-4.8; and local thunderstorms can have a pH as low as 2.0. Rain becomes acidic primarily due to the presence of two strong acids, sulfuric acid (H2SO4) and nitric acid (HNO3). Sulfuric acid is derived from natural sources such as volcanoes, and wetlands (sulfate reducing bacteria); and anthropogenic sources such as the combustion of fossil fuels, and mining where H2S is present. Nitric acid is produced by natural sources such as lightning, soil bacteria, and natural fires; while also produced anthropogenically by the combustion of fossil fuels and from power plants.

Not only is rain a source of acid, but the water itself also leaches many of the cations that compete with H+ in the soil solution.

There is a hierarchy in the process of cation exchange on colloids, as they differ in the strength of adsorption by the colloid and hence their ability to replace one another. If present in equal amounts in the soil water solution:
  Al3+ replaces H+ replaces Ca2+ replaces Mg2+ replaces K+ same as NH4+ replaces Na+

http://en.wikipedia.org/wiki/Soil#Cation_and_anion_exchange
We see that Al+++ and H+ replace everything else on the soil particle, which leaves all the nutrients free to be carried away by the rain water.  The result is a soil high in H+ concentration and low in nutrients (Al+++ is not a nutrient, but a toxin that becomes more available to plants in more acidic soils).
The amount of rainfall is the main way soils become acidic.

In high rainfall areas, soils tend to acidity as the basic cations are forced off the soil colloids by the mass action of hydrogen ions from the rain as those attach to the colloids. High rainfall rates can then wash the nutrients out, leaving the soil sterile. Once the colloids are saturated with H+, the addition of any more hydrogen ions or aluminum hydroxyl cations drives the pH even lower (more acidic) as the soil has been left with no buffering capacity. In areas of extreme rainfall and high temperatures, the clay and humus may be washed out, further reducing the buffering capacity of the soil.

http://en.wikipedia.org/wiki/Soil#Soil_reaction_.28pH.29
If you see anything I can add or change, please leave a comment and I'll edit to include.  I put this here as a service to the community so that we all have a clear understanding of what acid soil means and a reference for when explanation is necessary.
Answer: In overly (perhaps) simplified terms every growing media will have a pH (soil, vermiculite, peat whatever your growing media is).  This pH can either be acidic ( below 7 pH) or base (above 7 ph) or roughly neutral (right around 7).
pH has a ton to do with what nutrients in your soil / growing media are available to be used by your plants. You can have extremely rich and fertile soil with a very acidic ( say below a pH of 6 or lower) and have the plants showing signs of nutrient deficiency because the nutrients will be "tied up" in the soil due to the overly acidic pH.
It would behoove you to learn what your plants thrive on best in terms of pH and amend your soil accordingly if needed, after testing.   Or just plant it and keep an eye but having a way to test pH on hand would probably be wise.
pH is weird and kind of complicated but once you have an understanding of what it is, what your local soil is prone to (if that is a factor for you), and how to test and amend soil if need you will be A-ok. For me in Ohio in most cases planting outdoors I have 0 issues with pH unless I'm planting something that has peculiar requirements like blueberries or hydrangea.

What is acid soil?


Mushroom Identificaton(USA)

Question: I need help identifying a perculiar species of mushroom found in my yard today. Color is orange-yellow, around 3-4 inches total radius, its a cluster of tiny to medium mushrooms. They were found near an oak tree. Location is southern Georgia, USa.
Answer: These could be specimens of Omphalotus Illudens based on the orange/yellow color, the time of the year, their association with decaying wood (an oak in this case) and your location (eastern North America)
You can read more about these species in this reference: Messiah College
Comment: You are right about the claimed bioluminescent properties, however this phenomena is not always happening. Apparently some people that study these mushrooms sometimes have to wait hours in the dark to be able to see the glowing and some even say the bioluminescent claims are completely false ( like this reference: [mushroom expert](https://www.mushroomexpert.com/omphalotus_illudens.html) ). I unfortunately lack the expertise to say for sure if they are bioluminescent or not.
Comment: I did some research on Omphalotus Illudens (Jack-o-lanterns) and found that they were bioluminescent. The mushrooms i found are not. Is there a possibility that there is a subspecies of Illundens that are not bioluminescent?
Comment: MikeKatz45, I had cut down a tree about a month ah go, about a foot away from the clusters location. I noticed that the post said "Occurrence on wood substrate: or on the ground from decaying underground roots; ". This somewhat fits in with this type since of the location and the surroundings. Could it be possible that it might actually be it?

Mushroom Identificaton(USA)


Ways to improve shower's water pressure?

Question: I have just moved into a new apartment on the fifth floor of a building and the water pressure is dismal. The sinks I can deal with, but not the shower... are there any hacks you can perform on the shower head itself?
Comment: @Jon Being on-topic on another site doesn't make it off-topic here.
Comment: The very first thing to check is whether you have flow limiters in the shower heads. They often come preinstalled, and are normally very easy to remove by disassembling the head. Results may vary from dramatic improvement to barely noticeable.
Comment: This question appears to be off-topic because it is about Home improvement. This question has been asked on home improvement, a search there will yield high quality answers from experts experienced with your water pressure problem.
Comment: apparently living in the US causes one to have pressure reducing stuff in the shower head. You can take them out. http://diy.stackexchange.com/a/416 (not an answer as I did not try this myself)
Comment: @AngeloFuchs Yes, see Jeff Tucker's _Hack Your Showerhead_ linked in my answer below.
Answer: If you get a narrower head, the water will come out faster, so it will feel like there is higher pressure, even though the water is low in volume. You can even get a head that puts the water out in one narrow stream, which can be quite sharp.
There's nothing you can do to improve the pressure in an apartment complex, other than trying to get your shower at a time when everyone else is not likely to be running water. Showers, dishwashers, and washing machines (not everyone has these last 2) use a lot of water, so 2 running at once will not improve your experience.
Comment: -1 Nope. A narrower head will further decrease the water volume by increasing the resistance to water pressure that is already low. Volume and cross-sectional area (of the tube/pipe/head, etc.) are inversely proportional. The pressure would have to increase for this first statement to be true. It cannot so this is an incorrect solution to the question.
Comment: @Stan a narrower head does decrease volume slightly, while increasing the speed it comes out. And yes, I've tried it
Comment: The question was about pressure, not volume. I better understand your comment.
Answer: Remove flow-rate restrictors in the shower head
You can make sure that there are no water flow rate restrictors  inside the shower head. These can usually be pried out (I've done this on hand-held shower heads, too; see also this video):
 full size image
Or you might need to drill a bigger hole in the water inlet of the shower head (which I've done on larger shower heads).
Remove restrictors in the shower valve / install bigger plumbing
Even if you hack the shower head itself, your flow rate might be limited by the piping / valve of the shower itself (cf. this video).

Also, in the U.S., it's federal law that shower heads must be rated < 2½ gallons per minute! See Jeff Tucker's Hack Your Showerhead: Or How to Get the Government Out of Your Home and article.
Answer: Some shower heads have screen strainers in them, to prevent grit in the pipes from clogging the spray nozzles. unscrew the shower head from the pipe and check for the presence of a clogged screen. it can be unclogged by pushing the grit out of the pores using a needle.
Answer: Use a water heater which has a storage tank that is big enough for your shower needs.
Those storage tanks used to be the rules in the past, so you should be able to find them in many countries.
The life hack solution might be to install a tank or even a tub high enough inside your bathroom that you can run a shower from it, fill it with water to your chosen temperature and run a shower from it.
If just gravity is not enough to get your the required pressure you can think about installing a pump and/or a container under pressure.
Of course, these are solutions for when a change to your shower head does not give the required results.
Comment: This doesn't increase pressure...
Comment: and its also not his choice as he lives in an apartment block
Comment: I do not know about where he lives, but where I live you have to take care of your own hot water, even when you rent an apartment. (Not all over the country but it is the most common.) But you can life hack such a water container.
Comment: his or her profile says he/she lives in new york


convert spotify to mp3

Question: I have an MP3 player that I want to put music from spotify on. What is the best free way to do this?
I've tried Sidify but you can only get 3 mins of each song and it converts into M4A format.
Thanks,
Ceri
Answer: There is no legal way to do this.
There used to be lots of ways. The Spotify internal API uses a websocket to deliver an ogg vorbis stream to the client. Their APIs used to allow you to intercept the raw, uncompressed, interleaved PCM data at CD quality right before it played. It was possible to use this along with libmp3lame to produce good quality mp3s.
But this leak was thoroughly plugged. So much so that I cannot even find the old documentation to show you the methods that were once available. Around 2015 they deprecated a very fun SDK called libspotify (which still worked until about 2018), and the derivative CocoaLibSpotify. For a long time, the ability to intercept the raw PCM data lived on in their mobile SDKs (because it was so cumbersome to abuse).
But, to be clear, doing what you are asking was always against the terms and conditions of all these products. I don't think anyone's going to take the legal risk of providing you with a satisfactory solution on this very public forum, even if they have one.
Answer: XSpotify
XSpotify can do that, it's also open source. If you have a Spotify Premium account, it can download your music in 320 Kbps (160 Kbps in Free account).

I've tried it recently. It extracted the music but the file was corrupt so it did not play for me. And the output format is OGG because that's what Spotify uses.
Sidify
Another option is a commercial program called Sidify.

I used it many times and it works really well but you need to purchase Pro version to record Spotify music.

convert spotify to mp3


Fac input in Blender

Question: I understand fac to represent the percentage of the second shader to be applied. I recall seeing examples where the fac value is set 1.0 and still there a node connected to the first shader input. With fac being 1.0 the first shader input should not be even considered, what is the use of doing this?
Comment: I think this is just to keep the other shader in place (even if not used) without changing the nodes/links configuration
Answer: One of the big uses for this is for keyframing the Fac: value. In Blender, you cannot keyframe Node Tree Connections, so instead, you might have to fake it by keyframing a Fac: value.
Say that you have an animation, and you want your object to be there, be there, be there, and then suddenly be gone. Well, your first try might be having your shader connect to your Material Output and then keyframing a Transparent BSDF jumping to the Material Output connection at some point. That can't happen, though, so you can have your material and the Transparent BSDF fed into a Mix Shader, and keyframe (I while hovering over the Fac:) it to turn from 0.0 to 1.0 at a certain frame.
Answer: If this helps at all, the fac is stored as a raw number value, from 0 to 1. It is not complicated, if you know how to use it. It can be used as a variable in any functions you want to include in your node setup, so long as both the domain and the range (speaking in nerdy terms) are 0 to 1.

Fac input in Blender


Things to consider before Project Initiation

Question: What are the things to consider before project initiation. I believe a lot goes on before the charter can be produced and PMBOk 5 is a bit silent on that point.
Comment: Different organizations will have different processes.  My prior employer has developed at least three pre-initiation stages (Business Case, Statement of Work and Charter).  Another group I worked with refused (with astonishing vehemence) to look at charters at all.  The answer depends on organizational process assets.
Answer: You need to conduct Feasibility study.

Operational feasibility
Economic feasibility
Technical feasibility
Human factors feasibility
Legal/Political feasibility

Usually it is conducted by customer or consultant before hiring PM and Team.
After studies there might be decision to not start a project at all.
If customer gives a green light this study shall be a primary source of data for project charter.
Comment: How does this tie with capability feasibility?
Answer: Yes, quite a bit goes on. Unfortunately, I think a lot of project managers are assigned to projects after pre-project work is done, so are stuck doing piece-work without necessarily having a broader business context... which can lead to bad decision-making down stream.
You should read up on the PRINCE2 standard, they have broken this out into the "Starting Up a Project" phase. Documentation produced and work done during that phase includes:

Project Mandate coming from outside the project which commisions the work and acts as the starting point for all that follows.
Appointment of a PM and project executive which establishes who represents the interests of the business stakeholders and has overall (executive) and day-to-day (PM) authority over the project
Review of previous lessons to avoid repeating mistakes of the past and ensure reproduction of things that worked
ID and appoint project management team to support the executive and PM as you start up the project.
Prepare an outline business case to establish the business value of the project vs expected costs. This will be refined after the project is initiated.
Select approach and assemble the Project Brief to define what the project will produce, how this will be done, which stakeholders need to be considered, what constraints/assumptions you are working under, etc...
Develop an Initiation Plan so that you have a path towards developing a full-on project plan once your project is approved
Approval to Proceed with Initiation from the project board/steering committee
Comment: This still sounds very much like something that happens within a project. What about the points Alexander Averchenko alludes to? It's also assumes that the project management office is the practice that is engaged first and not another practice such as an enterprise architecture one?
Comment: @ Motivated - First of two comments.... All of the feasibility aspects would be incorporated into the outline business case as they all reflect some kind of "cost" as opposed to benefit, IMO they are all integrated (e.g. anything is operationally feasible if you are willing to pay the price to hire new people or whatever to make it so)
Comment: @ Motivated - Second of two comments.... This work all happens prior to monies being released for planning. If you call it part of the project you are welcome to, PRINCE2 nomenclature simply chooses to differentiate them. Your interpretation re. PMO is wrong, first thing to get is a project mandate... which comes from an authority appropriate for your organization, in my experience senior management
Comment: For a business case to signal costs, it has to demonstrate benefits. Without the ability to showcase benefits, why undertake the process of feasibility or viability? While it may be operationally feasible, it may not be economically viable.
Comment: As for your second comment and hence my earlier post is the sequence in which these occur. For example, the business has an idea. To test this idea, it needs to be able to demonstrate both feasibility and viability. Next, is the "mandate" or sign-off. All the subsequent steps are unclear to me since generally in my experience the Enterprise Architecture practice is engaged to look at perform a review of the current state, transition and future state across all areas of the business e.g. business (people, processes, etc), applications, data and technology.
Comment: There is an assessment of sorts from a capability perspective. Now completed there is a map or direction the business needs to take. It is at this stage the PMO is engaged and the practices it performs.


Video Compression

Question: How do you compress a video so that it is a manageable size for protools?  What codec do you recommend and what is a manageable size for LE?  The original video is 360 mb and it is 7min color.  I can't seem to get the right settings in compressor.  Mp4 size only brings it down to 310mb and h.264 brought it up to 1.1gig.
Answer: File size is less of an issue than bit-rate is. People from Avid will tell you to stay away from H.264 with Pro Tools if you can.
As C3Sound mentioned, DV is best (whether you're using NTSC or PAL...). So, use DV NTSC/PAL or DV50 NTSC/PAL as needed. If you have the option 2 Pass VBR will net you a more efficient encode. It takes longer, but it runs smoother.
As I've already mentioned, bit rate/streaming is a big factor. You'll find the video will play back much smoother and cause less strain in your PT session if you have a separate/dedicated video drive. For the best functionality with video, Pro Tools likes 3 drive (OS, Project/Audio, and Video). If you can split out the data onto multiple drives that way, the actual seek time of the drive and the bus speed will be less of an issue.
Comment: Amen on the 3 drive structure. And when working with DV, don't forget to invest in a Firewire DV box like the Canopus ADVC-100 or Sony DVMC DA2. It takes the load of converting the video file off the cpu (and frees up screen real estate). Avid recommends the Canopus but we've got both models working here with no issues.
Comment: @Steve - i've used the canopus in the past (not for a number of years now though), and it was great. you can also use a video i/o card if you want more flexibility for format output...they're just more expensive.
Answer: LE works best with DV-NTSC - if you have some processing power to your comp you can always go H.264 for smaller file size, but sometimes PT can go crazy trying to crank DSP and decompress video at the same time. Only would say use this if you have a quad-core or i7.
H264 shouldnt increase file size. Use Quicktime Pro 7 and make sure everything stays the same with framerate and double check audio isnt being jacked up from 44.1 to 48k or something like that.
Answer: If you're not sending the video out to a Firewire box, photo-jpeg is a nice codec to use - reasonable size, seeks incredibly fast (intraframe) and is very quick to transcode from MP4. I have a habit of running any video I receive through QT Sync, and export to photo-jpeg (Quicktime Movie). H.264 is cpu-intensive and I haven't seen either Pro-Tools or Logic seek accurately within it or any other mpeg-4.. Of course, if you have a firewire box, then DV all the way.
7 min 360mb is just fine. It would be roughly 500mb in high quality Photojpeg. 7 minutes in DV would be way more..
Answer: 360mb for a 7 minute file is pretty small.  Not sure if anything smaller will be good enough quality to do sound design for anything detailed you'd have to see.
I generally use H.264 or a Quicktime .mov.  The trick to a smaller size is the bitrate.  It's a quick calculation to see how big the file will be.  You can also take HD footage and scale it down to a smaller screen resolution.
Who is getting you your video files?  Are you creating the output yourself?  I generally request a .mov from the editor and then go from there.
Answer: I compressed it in compressor with DV/DVCPRO - NTSC, Linear PCM, Timecode and the file is now 2GB.  It is an 8:45 second movie 2 audio channels bitrate total 30,000.  Why is it growing in size when i compress it?  The original file is LinearPCM H.264, bit rate 5700, 374 mb.
Comment: DV has a fixed data rate of ~50000

and you don't need the audio track for PT..

Video Compression


Rate and Distance Question Calc

Question: How do I find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station.
A plane flying horizontally at an altitude of 3 mi and a speed of 460 mi/h passes directly over a radar station
Comment: It looks like the second sentence should precede the first?
Answer: This is a related rates question. The general strategy:

Draw a picture. Invariably useful with these sort of problems. In the picture, label every quantity that is fixed, and every quantity that is changing with a name.
Write down the information you are given. Identify the rates you are told something about, and the rate you want to know something about.
Find an equation that relates the quantities whose rates you are being asked about. A relation among the quantities, not the rates.
Differentiate the equation you found in the previous step; this will give you an equation that relations the quantities and their rates of change.
Plug in all the information you have. Solve for the information you want to know.

Here, after you draw the picture, you'll see that it makes sense to think of the radar station as the origin, and the plane as flying on the line $y=3$. Let $p(t)$ be the horizontal position of the plane at time $t$ (so that the plane will be at the point $(p(t),3)$). Let $D(t)$ be the distance from the plane to the radar station.
You are told how $p(t)$ is changing: that is, you are given information about $\frac{dp}{dt}$. You are being asked about how the Distance is changing; that is, you are being asked to find
$$\frac{dD}{dt}\Bigl|_{D=4}$$
(Actually, it's unclear if you want the derivative when $D$, the straight line from the plane to the radar, is $4$, or if you want it when $p(t)$ is $4$; I think it is the former, though).
So you wan to find some equation that relates $p$ and $D$. After you do that, taking the derivative of the equation with respect to $t$ will give you an equation that relates $p$, $D$, $\frac{dp}{dt}$, and $\frac{dD}{dt}$. You know the value of $\frac{dp}{dt}$, and you know the value of $D$ you want. So you should figure out what $p$ is for that $D$ (if necessary), plug everything in, and solve for $\frac{dD}{dt}$.
Answer: Let $x$ denote the horizontal distance that the plane travels from a point directly overhead. Let $y$ be the slant distance from the radar station to the plane.
By the Pythagorean Theorem, $x^2 + 3^2 = y^2$. Differentiating this leads us to:
$$ 2x \frac{dx}{dt} = 2y\frac{dy}{dt} \tag{1}$$
Note that $\frac{dx}{dt} = 460$ miles per hour.
Simplifying equation (1) and plugging in the value for $\frac{dx}{dt}$ leads us to:
$$460x = y\frac{dy}{dt} \tag{2}$$
When $x = 4, y = \sqrt {25} = 5$ because of the Pythagorean Theorem. So, we now have:
$$460\cdot 4 = 5 \frac{dy}{dt} \tag{3}$$
Thus,
$$\frac{dy}{dt} = 368 \space \text{miles per hour}$$
So, the distance between the plane and the radar station is increasing
at $368$ mph.
Comment: Don't use $=$ when you are approximating. If you are using a decimal approximation of an inexact square root, then use $\approx$; better yet, leave the radical indicated!
Comment: @ArturoMagidin Yeah, you're right.
Comment: It seems I made a mistake by letting $x=3$ instead of $x=4$. The numbers are nice and friendly now - no need for $\approx.$ I think I'm going to take a look at this tomorrow morning when I have a fresh mind to make sure this work is correct. I don't wish to steer the OP down the wrong path.
Answer: More succinctly (and lower sodium too):
Let $x(t) = 4 + 460 t$, $y(t) = 3$. $\delta(t) = \sqrt{x(t)^2+y(t)^2}$.
 We want to compute $\dot{\delta}(0)$.
$\dot{\delta(0)} = \frac{1}{2 \sqrt{x(0)^2+y(0)^2}} (2 x(0) \dot{x}(0)+2 y(0) \dot{y}(0)) = \frac{4 \cdot 460}{\sqrt{4^2+3^2}} = 368.$
Answer: I think Arturo's answer is great and this is merely meant to try to explicitly show some of the point he brings up.
As he mentioned, one of the key points to solving this problem is drawing a picture and writing down the information.

With an image drawn one can begin to notice things which were not necessarily apparent before. The first important piece of information that should be noticed in this case is that $(1)$ the altitude of the plane, $(2)$ the distance along the ground from the radar station to the plane and $(3)$ the direct distance from the radar station and the plane are all related by the Pythagorean theorem i.e. $$x^2+y^2=z^2$$
When dealing with speeds we are always looking at how distances change with respect to time i.e. $$\dfrac{dD}{dt}$$
Where $D$ is distance and $t$ is time. In the current problem all variables $x,y,z$ are distances which are subject to the passing of time. As a result we differentiate both sides with respect to $t$ to understand how these distances vary as time passes. We thus get:
$$\begin{align*}\frac{d}{dt}\left(x^2+y^2\right)&=\frac{d}{dt}\left(z^2\right) \\
\frac{d}{dt}\left(x^2\right)+\frac{d}{dt}\left(y^2\right)&=\frac{d}{dt}\left(z^2\right) \\
2x\frac{dx}{dt}+2y\frac{dy}{dt}&=2z\frac{dz}{dt} \\
x\frac{dx}{dt}+y\frac{dy}{dt}&=z\frac{dz}{dt} \\
\end{align*}$$
Now, we are given the quantities for $x=4$ and $y=3$ at a specific instant. We can also figure out $z$ using the Pythagorean theorem:
$$\begin{align*}z^2&=x^2+y^2& \\
z&=\sqrt{x^2+y^2} \\
z&=\sqrt{4^2+3^2}=5
\end{align*}$$
We also know that the rate that the plane is moving away from the radar station is $460$ mph $\left(\text{aka.} \dfrac{dx}{dt}=460\right)$ and that rate that the altitude is changing is $0$ mph $\left(\dfrac{dy}{dt}=0\right)$. Plugging all of this into our above equation gives:
$$\begin{align*}x\frac{dx}{dt}+y\frac{dy}{dt}&=z\frac{dz}{dt} \\
(4)\frac{dx}{dt}+(3)\frac{dy}{dt}&=(5)\frac{dz}{dt} \\
(4)(460)+(3)(0)&=(5)\frac{dz}{dt} \\
1840&=5\frac{dz}{dt} \\
\frac{dz}{dt}&=368
\end{align*}$$
Note that $\dfrac{dz}{dt}$ is indeed the rate at which the distance between the radar station and the plane is changing and so we have our final answer: $368$ mph.

Rate and Distance Question Calc


Restricting users to certain webpages on IIS server, that uses a CMS to manage webpages/content

Question: I plan on using ExpressionEngine as my CMS on an intranet, IIS server.
The reason I want to use IIS is to take advantage of the ability to restrict certain active-directory groups to certain pages.
For example, only the student group can access intranet/students, and staff can only access intranet/staff
But where my problem comes into play is that ExpressionEngine templating system is a little complex. It is completely database driven, which by default you can only edit the templates within their web based template editor, but there is a setting you can enable to save each template as a flat file, and it will automatically save the template as "nameoftemplate".php, so in my example, it would be news.php
For example, there are template groups, which have templates within them.
For example, the students template group may have 4 or 5 templates, so the URL's to them would be:
http://intranet/students/news
http://intranet/students/calendar
http://intranet/students/forms
http://intranet/students/policies
and the same goes for staff.
As you see, the URL is http://intranet..., that is the URL for being on campus, for accessing the intranet from off-campus, you'd have to type in http://intranet.domain.com/students/
Going back to how the CMS works with templates...
The student news template (http://intranet/students/news) is located at /web/system/templates/students/news.php
On an apache server, I could edit the config to restrict access to a certain active-directory group based on its URL and not the remote path (/web/system/templates/students/news) of the file. You're probably wondering why I just don't go down that path and use that...because it will ask you to log in with your username & password whether you're accessing it from campus (http://intranet/students/news) or off-campus (http://intranet.domain.com/students/news)
I want to be able to let the users on campus view http://intranet/students/news without having to log in, but if they access it from off-campus...then it will ask them to log-in.
They all use IE7 and are use to being able to access their appropriate areas without ever being asked to authenticate, and if they were to be asked now...it would flip their work-lives upside down (yes...it is sad)
This may not be possible, but either way let me know.
Answer: Just make sure that IIS is using NTLM for authentication on the site and IE will log in automatically in your Intranet.  Set NTFS permissions on the folders to implement your security model.  Word of caution, though.  Make sure you don't remove write access to the folders for the account that IIS is running as otherwise your CMS won't be able to write the template files.


Azerbaijan eVisa - Arrival by Train

Question: Does anyone know if it possible to arrive into Azerbaijan by (overnight) train from Georgia with an eVisa? The website for the ASAN visa doesn't mention an arrival restriction, but I have read that there is no one at the border at night to admit you to the country...
Answer: Yes, it is. I have traveled to Azerbaijan last month and met lots of people on my way, who have arrived from Georgia by bus or night train, having eVisa.
Answer: Border checks are total, as almost anywhere except within the Schengen Area.
As such, you will be checked and yes, you can use your e-visa.

Azerbaijan eVisa - Arrival by Train


Other than distance, what other metrics can be used to compare quantum error correcting codes?

Question: Using classical error correction (or channel coding) as a reference, I'd like to be able to compare QECC's from different constructions. Distance is a reasonable measure and you can argue that an $[[n_1,k_1,d_1]]$ is a better code than an $[[n_2,k_2,d_2]]$ if for example $k_1/n_1 = k_2/n_2$ and $d_1>d_2$ (same rate, larger distance); or maybe $d_1 = d_2$ and $k_1/n_1 \gt k_2/n_2$, (same distance, higher rate),or $n_1/k_1=n_2/k_2, d_1=d_2$ and $n_1 \lt n_2$, (same rate and distance, smaller number of physical qubits). However, just like the classical case, I'm sure that distance doesn't tell the whole story. The "channel" (or error model) has to enter the picture as well as the decoding algorithm. Distance can also be difficult to calculate for large $n$. In classical ECC, a plot of BER vs SNR in AWGN channel can quickly tell you if a code/decoder combination gives better performance than another. What would be possible equivalents for QECC? (to simplify things you can ignore decoder complexity as a parameter; you can also limit QECC's to stabilizer codes)
Answer: If you focus solely on stabilizer/additive codes, I believe that the weight of the Paulis in the stabilizer is highly important. The weight of a $n$-qubit Pauli is the number of non-trivial factors in it.
The weight of the correctable errors has a close correspondence with the distance of a code, but the weight of the elements of the stabilizer is also important for the error correction process. In standard error syndrome measurement, a stabilizer generator is measured using an ancilla that is entangled through a 'controlled-generator' gate. The higher the weight of the generator, the harder it is to implement this gate. In current quantum computing architectures, the connectivity between qubits is severely limited (and I think this will always be the case), so measuring a weight-$10$ generator is easier said then done.
For instance, the $5$-qubit 'perfect' code is by no means perfect because the generators are of weight $4$. If you use just $1$ ancilla, that means that this ancilla needs to be connected to all the data qubits.
You can check out the concept of LDPC-codes (Low Density Parity Check) that tries to acknowledge this problem.
Now, by no means this is the only or necessarily most important measure for a code, but I think it is easy to forget about it during theoretical analysis.
Comment: Stabilizer codes can be put in "standard forms" that reduce implementation cost (by one measure or another). The weight of the stabilizers might affect complexity but not performance....I am very familiar with LDPC codes...but my current question is really about code performance and how to measure it to compare. Encoder/decoder complexity is a separate parameter. I would expect there's a trade-off between the two parameters (performance vs complexity) ...
Comment: Thanks for that comment - I meant this answer as a sidenote (and was not aware of your level of familiarity with QECC's). I could have stressed this though.
Answer: So the biggest number used when comparing families of QECCs is the threshold, which is the error rate (generally depolarizing noise or XZ noise, depends on the paper) for which increasing the size (and distance) of the code actually increases performance.
Look at figure 4 in this paper. On the top plot, you can see that above a certain error rate, the extra machinery needed to correct errors is actually not worth it, and smaller codes perform better. However below this threshold, increasing your distance is worthwhile.
Code families (meaning sets of codes that have the same structure, such as surface codes or triangular color codes) are often compared with their threshold. Some, like the Bacon-Shor codes, don't have one at all, and instead have a sweet-spot distance for any given error rate.
Another metric, as mentioned in @JSdj's comment, is the size of the stabilizers. This essentially ends up corresponding to the connectivity required in the quantum hardware to effectively run the code. Codes which require a lot of connectivity often suffer from error propagation issues, since a single component having an error will quickly spread it.
Lastly, when it comes to error models there are a lot of different things to consider. In this paper, we talked about a few ion trap error models, and discussed how their structure interacts with different codes. This paper discusses how important it will be to optimize fault-tolerant protocols to different error models, and shows the sensitivity a codes performance can have to those models.
Comment: Thanks. The plot in figure 4 of the first paper and figure 7 of your paper on 9 qubit code is what I had in mind. The second paper and related video by David Poulin (RIP) https://www.youtube.com/watch?v=Rcnc4cuSytc) are also very relevant. I have some reading up to do but I'd like to be able to generate similar plots for arbitrary codes. I'm not sure how realistic this goal is...I'll ask a followup question about sw tools later.
Comment: Sounds good. David Poulin was an amazing speaker, so that video is definitely a good watch. I think the best place to start would be to look at the initial papers on different codes, and see what specs they list. That should give you a good idea of the kind of things authors think are important to mention in the field!


Two kinds of "borrow"

Question: In Hebrew there is a difference, although often overlooked in spoken Hebrew, between the word "to borrow" for something that is intended to be returned "as is" such as a tool or a vehicle, and the word "to borrow" for something that will not be returned, but an equivalent replacement such as money (the money returned will probably not be the very same coins or bills but different ones carrying the same value).
To my understanding, "borrow" and "lend" don't have that difference in meaning.
Is there any English equivalent?
Comment: Similarly, English has the notion of "bumming" something, like a cigarette.  But, there is no essential notion of repayment.
Comment: @Cerberus Bietsen is just another word for bedelen (begging). As far as I know there is never the intention to re-pay. (for the record: I am Dutch myself.)
Comment: Dutch has *bietsen* as an informal word for "borrowing" something that will be consumed, like a cigarette. There may or may not be a theoretical intention of giving back a (new) cigarette later.
Comment: It's more like taking on "credit" -- you don't return it but compensate for it at a later date (in cash, by default, but sometimes also in kind).
Comment: @Tonny: Yes, but it is in modern Dutch no longer used for begging, but only for "borrowing" cigarettes, don't you agree? Perhaps the intention of repaying is only present in the same sense that you are in a way supposed to buy drinks for everyone in your company later if you accept a round. If someone always bietses your cigarettes, without ever doing anything in return, you may feel slightly cheated.
Comment: @Cerberus Not in my surroundings (Brabant). Here bietsen is most certainly just begging, no intent to repay at all. Even though the thought that it may be re-payed at a later time might still be present in the mind of either party, it is certainly expected that it WON'T be re-payed at all.
Comment: @Tonny: Okay, to me (noordelijke Randstad), it does not mean begging at all (any more?): I had no idea it could even mean that. // So you are saying that, to you, bietsing a cigarette carries less of an expectation of doing something in return for the other party at some point in the theoretical future, maybe, eventually—less so than when you accept a round of beer?
Comment: @Cerberus When it comes to drinks it is an entirely different matter: That is a major social transgression around here. If you accept a round (among friends) you better be prepared to return the favor on the next occasion (not necessarily the same day/event) or you will be out of friends soon. (Of course: If somebody buys a round for an entire bar with many strangers, the strangers don't feel obliged.)
Comment: I think this question might be easier to answer if the asker could add an example of a case where the difference is important: a situation where you want to borrow or lend something and you want to make it clear which sense is meant. The best I can think of is "Can I borrow your lucky penny?" - you'd want to know before answering  if they mean to hold it for luck then return it, or to spend it then repay a different penny. But in this case you'd expect them to return the same penny, since they've specified something and acknowledged that it has value beyond its "fungible" value.
Comment: Thinking about it, I think it's almost always taken on implication, and you can adjust the implication by how specific the question is: If you say yes to "Can I borrow a penny?" you'd expect them to spend it then return a different one, but for "Can I borrow that penny there on the table, the shiny one with the scratch?" you'd expect them to do some trick then return the same coin.
Answer: This is an excellent question.  But, I do not believe that English has a sense of a difference between the two concepts.
Borrow and lend are opposite sides of the same equation.  To lend is to allow someone to borrow.  To borrow is to take someone else's loan.
I think you will have a greater peace with the idea if you think of borrowing money (or other valuable commodity) as being a loan of the fiat value of the money, and not the cash itself.  Hence, you are returning the same item.
Answer: The word you're looking for (though it's an adjective) is fungible. A fungible item is one, such as money, where all versions are treated as identical: if you borrow $10, it's not expected that you somehow return the literal same $10. Non-fungible items are not treated as identical: if you borrow somebody's car, it's expected that you return that exact car, not some similar car or even another car of the same make and model.
While all forms of "borrow", "lend", etc have the same general meaning, you can specify something as being a fungible or non-fungible loan.
Of course, it's even less common in English than Hebrew, so most people other than economists and lawyers won't know what you're talking about.
Answer: Spare.

Sup dude, ya spare a buck?
Comment: `spare` is a fun example because it reverses persons. I don't spare when I ask you something, but I ask you if you can spare it.
Comment: That has no sense of repayment, though.
Comment: I think it depends on social context. If I said that to one of my friends, we know we have a history of give and take. If a guy on the street said that to me, then the sense is different.
Comment: I can accept that.  I just don't know that spare means lend in the same way.  It's really a gift.  That you and your friends repay each other is admirable, but I think it's more of cute thing where you pretend to beg off each other than a term for borrowing . . .  Perhaps I'm wrong.
Comment: For those tempted to downvote this: the second meaning of "to borrow" that's explained in the question above does not match the english version of "to borrow": if anything, it's closer to a loan or an exchange. True, the denotation of spare does not refer to anything resembling repayment, but I can see the connotation of "to spare" implying a repayment in some groups.
Answer: The word "borrow" always implies an intent to return the exact thing borrowed, unless the thing is money or the word is being used sarcastically. Otherwise, something like "trade" or "exchange" would be used.
Comment: I've just moved in next door. Do you think I could borrow a cup of sugar?
Comment: Only if you promise to use a fungible spoon.
Answer: "Reciprocity" is the name of the social system covered by the second instance of Hebrew 'Borrow', and the 'drinks among friends' motif in the comments.
Basically, you exchange items or services without directly counting value but there is expectation of a return exchange at some unspecified future date.  It doesn't even have to be a 1 for 1 exchange...but if someone doesn't reciprocate according to the unwritten rules they will become isolated from the group.
Of course this isn't a term in common use - like most of the steps in a reciprocity relation, the name for this type of transaction isn't mentioned. It might even be termed a gift...but with strings attached.

Two kinds of "borrow"


Can playing blindfold chess be learned or is it a natural skill?

Question: Any blindfold players here? Just wondering if blindfold chess is a skill that can be learned by amateurs like me or a natural skill by chess GM's, IM's, etc.
Answer: In essence, you are asking-

Can memory (or other brain functions) be improved or is it a natural trait?

The answer is yes to both. While it is true that one's memory can be improved, it is also commonly observed that some people are more "gifted" when it comes to memory (and other brain functions) than others.
To play blindfold chess, you need three things -

A decent memory
A good ability to visualize
A decent level of chess playing strength (if you want to play decent chess i.e. or one could simply have a fantastic memory and make legal yet nonsensical moves).

Memory
I never "practiced" blindfold chess to learn it. I simply observed that as soon as my chess level got to FIDE 2000 level (for example), I could easily replay moves in my head and think "blindly". I don't have a great memory. I suppose my memory is average or slightly above average, but chess has surely helped to improve it to some extent.
Visualization
The way I do it is by visualizing a 2D board in my head (like a computer screen). The board doesn't have to be crystal clear (it's often hazy), but as long as you can "see" the pieces in their places, it's fine. I suppose that a chess player's ability to visualize increases the more chess he/she plays. This is normal brain development. The more you exercise a muscle, the better it gets. So I would suggest you practice visualization to get better at it.
Playing Strength
The real point of blind chess is to play chess blindly and yet play it well. So playing strength is indispensable or else there is no point in playing blind chess. If you play blind chess badly, you only prove you have a good memory and visualization power and nothing more. So, as an amateur, I would say your top priority is to improve your playing strength. Work on that and your memory and visualization will automatically improve.
All the best!
Comment: Yes. I think that a 2000 ELO player should be able to play blindfold chess without it being overly difficult for him/her.
Comment: thanks for that inspiring answer. So you mean majority of people with a strength of 2000 ELO, specially the IM's and GM's are capable of doing blindfold chess?

Thanks I'll try to improve my playing strength. Currently I play at 1600 to 1700 level.
Comment: For most I would agree with your Playing Strength section.  However, I'd teach blind chess to those also interested in Discrete Mathematics - specifically Graph Theory, regardless of playing strength or intent to improve.  Although I'm only around a 1500 player, I think this skill has helped me immensely in my studies.
Answer: It is obviously a learned skill. No-one pops into the world after gestating for 9 months able to play blindfold chess!  Just as no-one arrives destined to be an International footballer, genius mathematician or Olympic athlete.
The real question is, is it learned by specifically training to acquire the skills of blindfold chess, or does it develop in some other way?
I am a reasonably strong chess player (and was stronger when I was much younger) but have always been well short of IM or GM strength. Yet I can play blindfold chess with ease. Unfortunately it is not especially strong blindfold chess! It lags about 100 rating points below my OTB rating. The main difference is that although I make fewer gross blunders when playing blindfold I do not find exceptionally strong moves or plans either.
I have never studied specifically for it but I have been able to play blindfold since I passed about 1800 strength.  At least that is when I first tried it, and succeeded. The first hint that I might be able to play blindfold was when I realised that I could follow chess books without a board and pieces. When I got stronger I found that I could play several blindfold games simultaneously, so in my case the ability developed as a side effect of learning to play chess with a board and pieces. I suspect the same is true of most players including all those FMs, IMs and GMs that are much stronger than me.
Isn't this what you would expect? In learning to play chess well we become intimately familiar with the board, with the powers of the pieces, and with the patterns commonly made by tactical operations and by positional features.  We also calculate future positions by imagining sequences of moves and the positions to which they lead.  These are the basic skills of blindfold play, so it is not surprising that the skill can develop naturally alongside increasing chess strength.
This is not to say that you cannot train specifically to play blindfold.  I expect that you can.  But I do not think that is how most chess players gained the skill.
Blindfold chess is  not such an exceptional and amazing mental feat as it is thought to be by people that don't play chess (and by some that do!). I do not know of any strong player that cannot play blindfold. I have challenged some strong players that have never tried to play blindfold to give it a try, and they have always managed it with some ease. What is strong?  Well no-one I know that has achieved a rating of 2100 or more has failed this challenge, and many with lower ratings have managed it.
Comment: One  could add that blindfold is a lot easier to play if you have a familiar position on the (virtual) board. As an example, you could store the information: "fianchettoed  bishop" instead of storing the position of five pieces (e.g. Nf3, Bg2, pawns on f2, g3, h2).
Answer: I learned to play blindfolded chess by practicing it from 2001 to 2005. In my opinion, it is a skill that can be learned, practice will give results.
What I do is to try to visualize the chess board and the pieces on the board at every moment of the game. I have to update it one or more times per second, since it keeps vanishing. It does require considerable effort and you get tired after a single game, even at relatively short time controls.
It might be easier to start off by having an empty chess board in front of you, when training. When practicing, you can ask a friend to play with the board and you sitting with your back to the board, getting and sending your moves verbally. Close your eyes, if you find it helps.
If you find it difficult, then everything is correct :)
There seems to be a nice book out there on the subject:
http://www.blindfoldchess.net/
Perhaps there are more books / articles out there!
Comment: hi sir, thank you for your answer. What should I do if loss the visualization after 6 to 10 moves I always loss or forgot the sequence.
Comment: @LayoutPH keep practicing :)
Comment: +1 for updating one or more times per second. I find my visualization efforts tend to quickly morph or degrade, so more conscious effort at refresh might help, although as you say, tiring.
Answer: As I have said before, this requires physical fitness and strong memory. In order to play blindfolded chess properly you need to master the following:

Having always clear vision of the board.
Properly move and capture pieces.
Properly update the overall position on the board after the move is played.

Now it is time to implement solutions for the above tasks:
1. Having always clear vision of the board.
You must know which squares are light and which are dark. First you must know if the coordinate has odd parity or not. This is important for both letter and number coordinate. You first check the letter's parity, and then you determine the color of the square like below:
1.1 If letter has odd parity and number does not, than it is a light square ( a2, c8, g6... Do you see the pattern now? ).
1.2 If letter and number both have odd parity, than it is a dark square ( a1, c3, g5... Do you see the pattern now? ).
2.1 If letter doesn't have odd parity and number does, than it is a light square ( b3, f5, h7... Do you see the pattern now? ).
2.2 If letter and number don't have odd parity, than it is a dark square ( c1, d4, h8... Do you see the pattern now? ).

2. Properly move and capture pieces.
Here you have *starting square*->it is the square a piece stands on, and the *target square*, the one you wish to move your piece to.
When moving/capturing you change the value of at least one coordinate, be that letter or a number. For example, when you move a rook from h1 to g1 notice that the letter coordinate got decremented by 1. The same goes for number coordinates, when moving a pawn from e2 to e3 notice how number coordinate incremented by 1.
To illustrate this in the most efficient way, I will introduce a special notation that I will explain right now:
We shall adopt the format L[±/+/-]N[±/+/-].
L is the starting letter coordinate and N is the starting number coordinate.
[] store simple adding/subtracting function describing how to calculate the valid coordinate for putting a piece, or be blank in which case the coordinate remains the same.
This function uses symbols ±, +, - for calculation.
The symbol / lists options ( you can always do only one mathematical calculation in the bracket. ) .
For example, rook can move forward or backward so instead of writing  L[+1]N[] or L[-1]L[] it will be shorter to write L[+1/-1]. Then you choose which function to perform, adding or subtracting.
Furthermore, each option for L will have corresponding option for N, meaning that in this example L[-1/+1]N[-1/+1] you either do L[-1]N[-1] or L[+1][+1]. This will all be clearer in practical examples shown below.
Here are the patterns:

Pawn:

When moving a pawn, always increment by one the number coordinate. If testing for capture, replace the starting letter coordinate with its successor or predecessor, else do nothing.
Example:

When you apply this for the diagram above, a pawn on f3 can move to f4 and capture on e4 or g4 and a pawn on b6 can move to b7 and capture on a7 or c7.

Knight:

L[ ±2 / ±1 ]N[ ±1 / ±2 ] for both capture and move.
Example:

In the diagram above knight stands on e4 square. Let us use our pattern to determine on which squares it can stand:
e[ ±2 / ±1 ]4[ ±1 / ±2 ] can have the following results:

First option is e[ ±2 ]4[ ±1 ] :
This means that we can move the knight on e[+2]4[+1] = g5, or e[+2]4[-1] = g3, or e[-2]4[+1] = c5 and finally e[-2]4[-1] = c3.
Second option is e[ ±1 ]4[ ±2 ] :
This means that we can move the knight on e[ +1 ]4[ +2 ] = f6, or e[ +1 ]4[ -2 ] = f2, or e[ -1 ]4[ +2 ] = d6 and finally e[ -1 ]4[ -2 ] = d2.

Bishop:

For the bishop is tough, but I was able to invent a solution that is simple and effective.
You see, we can treat diagonal as an linear function and a bishop as a coordinate on it. After carefully looking on the picture below we can see that diagonal is a part of a square. This is the equation for a linear function with 2 known coordinates:

Where ( x2 , y2 ) is the destination point, and ( x1 , y1 ) is the starting point.
( y2 - y1 ) / ( x2 - x1 ) can only be ±1, since we have a square, which gives us the y2 = y1 ±( x2 - x1 ) equation.
Since we know both the starting square and target square all we have to do is check if the above equation is true and if is then bishop can move/capture on the target square!
We just need slight adjustment since we use letters for x-axis instead of numbers:
Target letter coordinate = Starting letter coordinate ± ( Target number coordinate - Starting number coordinate )
And there it is!
The tricky part is to determine when to choose - and when +. Still there is an easy way:

If your diagonal has direction like blue one in the picture above, you use + else you use - in the equation.
Example:
In the diagram above bishop stands on e4 square. Let us use our equation to determine if it can move to c6 ( here we choose - since the direction of the diagonal is the same as the red one's in the mentioned diagram ): c = e - ( 6 - 4 ) = e - 2 = c which is correct result ( second letter before e is c ).
Now let us test f6 ( here we choose + since the direction of the diagonal would be the same as the blue one's in the mentioned diagram ): f = e + ( 6 - 4 ) = e + 2 = g which is invalid and that is a correct result.
Now let us test b1 ( here we choose + since the direction of the diagonal is the same as the blue one's in the mentioned diagram ): b = e + ( 1 - 4 ) = e - 3 = b which is valid and that is correct result.

Rook:

The target square must have equal letter or number coordinate, in order for a rook to go there.
Example:

For example in the diagram above, rook is on e4 and he can move on any square that has at least one coordinate equal to his start coordinate. Therefore we can see that rook can stand on e8 because that square has the same letter as the starting square, or h4 since the number coordinates are the same.

Queen:

You just have to perform testing the same way you would for bishop or rook:
Either the target square has same letter or number, or must satisfy the equation I gave you for the bishop ( Target letter coordinate = Starting letter coordinate ± ( Target number coordinate - Starting number coordinate ) ).

King:

Two conditions must be fulfilled in order for target square to be valid:

Target square number coordinate - starting square number coordinate must be 1 or -1.
Target letter coordinate must be either successor or predecessor of the starting letter, or equal to it.

Example:

In the diagram above, king is on f3. Let us determine if he can stand on e5:

e is the predecessor of f, which is good so far.
5(target number coordinate) - 3(starting number coordinate) = 2, thus this square is invalid.

Now let us test f2:

f is equal to f, so far so good.
2 - 3 = -1, which is valid result, so yes, king can move there.

3. Properly update the overall position on the board after the move is played.
This is the place where your memory and physical fitness come into play. It will be hard for you to memorize which pieces were exchanged and where each one stand. Especially when you need to calculate lines this can be a cause of many mistakes.
I hope that this answer helps you, sorry for posting late, I have a lot of work to do. These tips are really just a basic math and you really should have no trouble using them successfully. Still if you need help leave a comment.
Good luck and best regards.
Comment: This answer strikes me as absurd. Nobody learns to play blindfold chess like that. Nobody remembers coordinates and does mathematical calculations to find out how to move a piece. If you reach a certain level you just know where any given piece from any given square can move to and you just know which colour any given square has. And you don't remember positions piece by piece, everything is connected and interacting.
Comment: This answer is completely useless. First, it does not answer the question at all. Secondly, the methods shown here are only good for implementing a computer chess program.
Comment: If my opponent tells me "Nd4", I don't memorise these coordinates. Instead I know that there is now a knight on this particular central square. And this fact stays in my mind, not because I learn it by heart, but because I see that it attacks the weak square on c6, it might be sacrificed on e6, it is slightly unstable because of my bishop on g7 and the possibility to play e5 and so forth. I remember the knight on d4 because of its interactions with the other pieces, because of tactical and strategical possibilities. And that's how it works for every halfway decent blindfold player.
Comment: In your answer you completely disengage playing blindfold from the ability to play chess well. Even if some people are capable of remembering all pieces separately and mathematically calculate legal moves - they still wouldn't really play blindfold chess, they would just remember positions and move pieces. That's impressive, but strikes me as pointless. That's like remembering a face by dividing it into pixels and memorising each pixel separately. The human brain doesn't work like that.
Comment: I conccur with what BlindKungFu master posted. A lot of effort was put in this answer but it is a bit absurd. Blndfold play comes very naturally as you play the game and replay chess games from books. You eventually know exactly where all pieces go. When I was learning chess, I was playing a lot of blitzes, and replaying games from Informator. I never even tried to play blindfold then, but I ended up naturally talking about specific positions with other players without a chessboard, it was natural. When I first tried to play blindfold, I could already do bullet 1 minute blindfold easily.
Comment: Hi dude, your answer is excellent specially the patterns if I can only vote for your answer in this question 10times I will do it. :)
Comment: @LayoutPH: Sorry for posting too late, but I was very busy. These tops and tricks look scary "on the paper" but in practice are very easy to implement. Hopefully you will succeed in your goal to learn blindfold chess. Let me know if this answer helped you. Best regards.
Comment: As several others have pointed out, this is an unnecessarily ridiculous answer to a very simple question. And on top of that, this is not how to learn to play blindfold.
Comment: Excellent answer dude
Comment: @BlindKungFuMaster: *Nobody learns to play blindfold chess like that.* I did. *Nobody remembers coordinates* Yes you do, when your opponent tells you where he placed his piece. *If you reach a certain level you just know where any given piece from any given square can move to and you just know which colour any given square has.* How did you play blindfold **before** you have reached that level? *And you don't remember positions piece by piece, everything is connected and interacting.* Unclear what you mean, but I don't care. The most important thing is that this answer solved OP's problem.
Comment: To learn to play blidnfold chess, it is better to check out this question: https://boardgames.stackexchange.com/q/8825/22041. To my surprise, I didn't find this question on chess.se
Comment: The answer is fine, only it's a very good answer to the wrong question
Answer: I just want to share what I am doing now to improve my blindfold chess visualization skill.
I downloaded a dozen of minigames of 10 to 15 moves in PGN format from chessgames.com , then I load it from my chess PGN application from my mobile phone. Then I read the PGN and play it on my mind without browsing it from my PGN reader. As I finished the game from my mind. I verify the position by playing the actual game from my PGN reader. I am using Chess PGN Master available from Iphone and Android.
I feel happy every time I finished a game that matches exactly from the game I visualized.
I think this stepping stone would put me someday from playing blindfold chess.
Answer: the ability to play blindfold chess develops naturally as chess ability improves. By getting better at chess, one gets better at blindfold chess.
Answer: I have a USCF of around 1500 and I can play blind, so if that's what you're looking for it shouldn't be overly difficult.  I did have to push myself a little though.  I want to try multiple boards, we'll see.
Answer: If Marc Lang from germany could play 46 games blindfolded (at once) then there is a chance that you could play one.
http://www.blindfoldchess.net/blog/2011/12/after_64_years_new_world_blindfold_record_set_by_marc_lang_playing_46_games/
Answer: I don't play blindfold but I've been told by people who do that if I want to start learning / training then the place to start is by mentally splitting the board into 4 quarters: a1-4xd1-4, e1-4xh1-4, a5-8xd5-8, e5-8xh5-8. Then picture the pieces in these 4 quarters independently of each other. So, hold in your mind a picture of the first quadrant. Then do the same for the second quadrant, etc. Finally bring the 4 quarters together in your mind.
I've not tried this but it makes sense on the principle of "crawl, walk, run" and is similar to what bridge players do, counting up to 13 in lots of different ways (4xsuits + 4xplayers, etc)
Answer: I am very surprised that in this old thread absolutely no mention is made of visualization. We tend to assume that everyone thinks as we do, but perhaps more or less effectively. This is not true. Some people think visually, others verbally, logically, or kinematically. Those who do visualize vary in accuracy and clarity. See the Wikipedia article on "Visual Thinking". I myself have no power at all to visualize and believed for a long time that the phrase "in the mind's eye" was merely a poetic figure of speech. I have played blindfold, but not well. To become good would be a huge effort.
Long ago, my university team, returning by train from an away match, would divide into two teams and play "blindfold". The player next in line for each team would make the move. Our board two was completely helpless. Some of our lower boards had no difficulty at all.
Comment: +1 from here - I *can* play blindfold but I play rather lousy compared to other players of my club. Interestingly, my memory is very good. It's exactly the visualization department I lack in.
Answer: Blindfold Chess is an ability which can be learned with Practice . Though some People may learn it faster than others but with average Chess intelligence it can be achieved . As like Magnus Carlsen who can play blindfolded with 10 Opponents at a time is something God Gifted but with the Training the Average Player can achieve to play one person blindfolded at one time.
Every Chess Player should try enhancing this Quality because it gradually helps in doing better Chess calculations & Visualizations in Games.
Answer: I play in chess tournaments in Philadelphia and in the U1500 section( i think) is a blind man. He has his own separate room to play in and there are special rules that apply to him. To record the moves he has an audio recording device. He also plays with 2 boards. The main board with the real pieces the opponent plays with and a special board with peg holes for the pieces. On the pieces of the special board are  metal balls on the Black pieces so he can distinguish pieces. He is allowed to touch all the pieces on his board so he can visualize. His opponent has to help him and move his pieces on the main board but he is very independent non the less!
In my mind that is the real blindfolded chess!
Answer: This is a bit late but in case you are still wondering - yes you can. We've been working on our blindfold chess website for the past few months and just released our beta. The entire purpose of the website is for people to learn how to play a full game blindfolded.
We start by running you through basic PGN notation. You can get comfortable with this notation using our minigames. Once you're comfortable with that - you can train your memory using our vision puzzles while also doing 'blindfold' tactics to practice finding optimal sequences in your mind. After that it's just a matter of practicing actual games of chess, which you can do here.
Hopefully this helps you or anyone else looking to learn blindfold chess :)
Comment: Hello, I am interested in learning to play blindfold chess and wanted to try out your website, but the link returns an error 500. Is there any problem with the site, or it's on my side?
Comment: "500 Internal Server Error. Sorry, our fault: internal server error. Head back to our home page."
Answer: This is not a technical answer. Playing blindfold can be practiced and you can gain proficiency upto a level. But beyond that level, as it is with normal chess, you need talent, pure talent.
Answer: Exercises for blindfold chess playing.
IOS/WP app.
https://itunes.apple.com/app/blind-chess-train/id802114888
https://www.microsoft.com/en-us/store/games/blind-chess-train/9wzdncrd2vvn


Problems intalling Elementary OS on a MacBook 4.1

Question: I have a MacBook 4.1 (the black one) and I'm trying to use it again with elementary OS Loki.
I manage to make a USB Bootable, and now i'm trying to install the OS. I want to make Elementary my standalone system. OSX doesn't work that it use to, so I want to remove it.
When boot in Elementary, everithing worlks fine, I can test all the apps and I can install. The installation process is ok.
My problem is when the installation software try to install grub. It simply crash. The problem is that it is not able to install grub.
All the information I have consulted in the internet says that everuthing should work, so i don't understand.
Please can anyone help me?
I'm using the last Loki Build.
Thank you all.
Answer: Finally I manage to install Loki on my Macbook.
I redownload the iso, I reflash the USB on another USB with rufus, and finally it works.
Thanks for the support.


Does creativity decrease when invested in multiple areas?

Question: I'm a math student and I find that coming up with original ideas and being creative is very important in the field. I love math and I'm also a voracious reader and I like to learn about many things including physics, philosophy, history, music, etc. but math is on the top. So I like to think about these areas, however, sometimes I get this worry that because I'm investing my thinking into something other than math that my creative abilities will "run-out" and I won't be able to contribute creative ideas in math . Is there any validity to this idea?
I know my question sounds weird, but it's been bugging me especially that I'm not aware of any research regarding this.
Thanks
Comment: Ah, and I should mention that you should consider writing your question in the abstract (not in the first person). We try to not do "self-help" stuff, more focusing on principles in cognitive psychology that could apply to everyone! See [here](https://cogsci.meta.stackexchange.com/questions/502/why-was-my-self-help-question-closed-as-off-topic) for details.
Comment: Seems similar to this post: https://cogsci.stackexchange.com/questions/17287/are-there-deep-links-between-music-and-the-visual-arts. Perhaps these concepts could give you a start? Typically, I would think the opposite: a fusion of multiple perspectives breeds creativity, not stifles it.
Comment: Thanks for the reference and for letting me know about phrasing the question, I'm new here so I had no idea.
Answer: There are two sources of creativity, the within-domain analogies and the between-domain analogies. Within-domain analogies are less original but more easy to apply and use. Between-domain analogies are far more original but usually need a lot of work to apply them in the target domain. (see this book for more info)

Within-domain analogies may be quite effective in making the resulting design solutions more useful, since the sources may be
industry standards that are effective and tested. But the resulting
solutions are less original.
Between-domain analogy. Random between-domain cues have a positive
affect on originality.

In the community of innovation T-shaped persons are highly valued. These individuals are very specialized in one area (the vertical line of T) and also have a broad but shallow knowledge of many other disciplines (the horizontal line of T).

The vertical bar on the T represents the depth of related skills and
expertise in a single field, whereas the horizontal bar is the ability
to collaborate across disciplines with experts in other areas and to
apply knowledge in areas of expertise other than one's own.

You will not "run-out" of creativity, it is simply a matter of resource allocation. You should spend most of your time at your specialized field, but at the same time you must allocate a significant proportion of your time in other fields like physics, philosophy, history, music, engineering, biology or even to more diverse domains like fishing, sports etc. This way you will create a T-shape knowledge which according to the above references, will make you more creative and more usefull.
Answer: In order to be creative in some areas, you should be bothered by some problems. It is important to have relevant knowledge because creativity in math is not similar to creativity in art, where rules can be broken. Relevant knowledge is essential also because it offers tools. What is relevant is not always easy to identify. Asking related questions might also be good.
It is important, however, to take breaks in dealing with the questions that bother you. It helps to lose the ties that tie you to specific ways of thinking.
Sleeping also contributes because it helps to lose existing ties and build new ties - some of them might be surprising. Dealing with other fields may or may not help directly, depending on how the deep structure of things might be transferred, but the breaks themselves are important, so in general, it is not a bad thing to spread on various different issues, as long as you find the time for the "dry" things.
Comment: Thank you for your response! I'm not fulling understanding the first half of your solution in light of the question: would you be willing to link to any resources supporting your statements?


Firefox Quantum extension that will stop links from opening in new tabs

Question: I'm looking for a Firefox Quantum extension that can prevent links from opening in new tabs.
I was previously using TargetKiller for Firefox but it currently won't work with Quantum. In Chrome, I use Death To _blank. Both of these extensions force all links to open in the current tab instead of a new one by removing the HTML  target attributes: _blank and _new, from all links.
Extensions that use another method are fine as long as they can keep links from opening in new tabs. Allowing additional target attributes to be removed (like TargetKiller) is a good bonus feature, but I'm fine with an extension that just works on _blank and _new.
Descriptions of the two extensions I've used for reference:

TargetKiller

TargetKiller is a small extension for the Firefox web browser. The extension removes the target attribute from links on the fly. You can specify which target attributes should get removed. By default TargetKiller is removing all target attributes which equals to _blank or _new.

Death To _blank

Keeps links from opening new tabs by removing the _blank attribute
Many web page links use the "_blank" target to open in a new tab. This is usually annoying (if I wanted to open a new tab, I would have done so myself!).
Death To _blank removes the "_blank" target from links, causing them to open in the current tab. This script also catches a few other targets (such as "blank" and "_new") that developers use.
Answer: You could certainly do this with a short JavaScript such as
for (var e of document.getElementsByTagName("a"))
    {delete e._blank;
     delete e._new;}

but it might be too slow for pages with lots of links. Try it out.
Answer: You don't need an extension to prevent links from opening in new tabs. This can be done by setting browser.link.open_newwindow to 1 in about:config.
See: https://support.mozilla.org/en-US/questions/1190923


What will happen if one person eats two Devil Fruits?

Question: If a person has already eaten one Devil Fruit, what will happen to him if he eats another Devil Fruit?
Comment: This might answer your question: http://anime.stackexchange.com/questions/9953/is-blackbeard-able-to-absorb-more-than-one-devil-fruit/9962#9962
Comment: @EroSɘnnin Ow, right, I see. It seems I didn't properly read your comment and assumed it was one of those auto-generated duplicate comments. Sorry about that.
Comment: @PeterRaeves lol its okay. I should have made the comment clearer :P
Comment: @EroSɘnnin That is not a duplicate, neither would [this](http://anime.stackexchange.com/q/5261/6166) be. Those two questions ask for Blackbeard and Brook specifically. This questions asks in general and would thus result in a completely different answer, because as we know Blackbeard could *consume* 2 fruits, while most other users could not.
Comment: @PeterRaeves I know that this question isn't a duplicate ( I didn't vote to close it btw). I was suggesting  that [this answer](http://anime.stackexchange.com/questions/9953/can-blackbeard-consume-more-than-one-devil-fruit/9962#9962) contains details regarding this question
Answer:
 Their body would explode without a trace, and they would die...

During the Enies Lobby arc, in chapter 385, we see how Jabra gets scared when seeing the Giraffe Fruit and the Bubble Fruit. He claims that a rumor exists that says that when an ability user comes close to a Devil Fruit, the Devil will come out of the fruit and start fighting with the Devil residing within his body and that would make his body explode. This was immediately countered by Bluenote saying that Grandline scientists have already uncovered that the body would only explode if two fruits are eaten by the same user. Therefore it is believed and apparently proven that eating two Devil Fruits would make a person's body explode.

Later during the Marineford arc, in chapter 577, we have seen an exception to this case. Blackbeard was seen to have two Devil Fruits at the same time. When Whitebeard died, he supposedly extracted the Devil from Whitebeard's body and put it into his own. How Blackbeard was able to extract it and whether his body did not explode due to it being different, due to the Dark Fruit powers or due to a different reason, can be read here.


What is the difference between external and internal-frame packs?

Question: I am starting backpacking and there are both internal and external-frame packs. What is the difference, and is one recommended over the other?
Answer: I've used both kinds of packs.
External frame packs are generally cheaper, can carry more gear, and allow much better ventilation to your back.  In addition to the main compartment and side pockets, most external frame packs also have an area above and below the main compartment where gear can be lashed.
Internal frame packs tend to have larger interior volume, allow more freedom of movement, and (especially in areas prone to thunderstorms) don't have large metallic poles that go above your head.  I've seen a few modern internal frame packs that have air channels for ventilation, I've never tried one, but it looks like it may help to keep things cooler.
Comment: I read https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2763825/ to say that a metallic pole a few inches above your head will not affect your susceptibility to lightning.
Answer: There really isn't much reason to use an external frame backpack, especially if you're looking at modern backpacks. In almost every case, the internal frame is going to be the better option. Internal frame backpacks have a lot of advantages over external frames, they have a smaller profile, and when properly packed keep weight closer to your center of gravity where you want it. They are more form fitting and give you better maneuverability.
The only advantage I can think of for an external frame backpack is that they are often made up of smaller compartments, where as internal frame backpacks tend to have a primary large storage area and you'll have to rely on stuff sacks for organization.
Comment: I disagree...its based on personal choice and price. and packing areas. and usualy internal has ONE BIG place and and multiple smaller pockets. and external have two or three medium sized pockets and not many more then that.

also external are easyer to wash.
Comment: I did mention the different storage areas as one of the only bonus to external frame, however this is no longer a discussion really. Look on any gear site for the number of internal vs external frame backpacks and it's literally 10 internal frame options for every 1 external frame option. There wouldn't be such a discrepancy if external frame packs didn't have so many drawbacks compared to internal frame.
Comment: One other advantage for an external frame pack is that you can hang stuff off of it everywhere. It's not enough advantage for me to give up the additional comfort of an internal frame, though.
Answer: To add to some of the answers already posted:
External: The biggest advantage is how forgiving an external frame pack is. Since the load is hanging on a frame, you can get away with more casual disregard for how you pack the pack, and don't have to worry about the edge of that pot digging in to your shoulder-blades. It can also take a much heavier load more easily - which is why you will often see trail-crew workers hauling heavy and awkward tools with them.
EFs also tend to be more "idiot-proof" with minimal adjustment options to get wrong (or right for that matter) meaning you can "load-and-go" and ride like a Cadillac down the trail.
Internal: Closer to the body, move more with your body, lower center of gravity, narrower profile. Often better when you anticipate scrambling or hiking off trail. They require a bit more attention when packing, and when fitting, but when properly situated can tend to be more a part of you, rather than something on you.
Answer: One possible advantage not yet mentioned for external frame pack is that most are adjustable to fit a wide range of people.  This is useful if you know that the pack is going to be used by several people of different sizes, or if the person is likely to be growing rapidly.  For example my son who was 14 and 4'11" when the pack was purchased then 16 and 6'1" when he went to Philmont
Answer: As a Boy Scout, I prefer the external frame backpack. The internal is more comfortable, but on long hikes, the external is not only practical for more gear, but vents your back so it's not dripping with sweat. I am not as knowledgeable as some on this page, but my strong preference is the external.


Trouble with Android SDK and ADB

Question: I'm trying to load my apk into the SDK and when I type "android-sdk-windows\platform-tools\adb install RaceTones.apk" in the command line, all I get is:
Microsoft Windows XP [Version 5.1.2600]
(C) Copyright 1985-2001 Microsoft Corp.
C:\Documents and Settings\Keith Baldwin>cd c:\
C:>android-sdk-windows\platform-tools\adb install RaceTones.apk
can't find 'RaceTones.apk' to install
I've checked and I do have that apk file in the platform-tools directory. I'm running Windows XP and have the latest SDK. Also, I'm running the emulator as I don't own a Droid device. What am I doing wrong?
Thanks for any and all help!
Answer: adb is looking for the APK in the current directory, from your example, c:\.
So either move the APK to c:\ or change the current directory c:\android-sdk-windows\platform-tools\ and run the adb command again.

Trouble with Android SDK and ADB


Infinite Call History on Android

Question: Do you know any app that can keep more than 500 calls in my Android Call Log?
I currently use apps that backup my log to csv or xls then load the backup file to my PC when needed. I want something that lets me view the full log from my phone without using my PC or a cloud service.
Answer: Since you haven't specified that you want a premium or freeware(now discontinued), I would assume that you are open to both, so you can try Unlimited Call Log By Soft Relay.
Features

Saves and shows all call logs, not just the last 500
Saves and shows all SMS logs
Store both Call and Text Message logs on any Android device
Ultra-fast custom storage, synchronized with Android's stock call log
Groups the log entries by contact, date, or type (incoming, outgoing)
Sortable logs by date, contact, type or duration
Quick searchable history by contact or phone number
"Swipe to call" feature makes Unlimited Call Log the best replacement for Android's stock Call Log App
Two steps deleting ("select one by one" or "select all" plus "delete button") saves time for you
Statistics based on the entire call log or contact's call history
Export call log to CSV/XML file
Dark/light themes supported

Screenshot

Credits: Google PlayStore (Unlimited Call Log Page)
Comment: Unfortunately, this app seems no longer be listed on Google Play (I get a 404 following the link). Do you have a secondary source? Maybe it's in some other repository, like F-Droid? Or is [this app](https://play.google.com/store/apps/details?id=com.softrelay.unlimitedcalllog) its successor?
Comment: @Izzy Thanks for pointing it out, seems like they discontinued the freeware, provided a link for premium now
Comment: Thanks for confirming & updating your answer :)
Comment: The app no longer shows up in the Play Store
Answer: I have not used it myself (I've not that many calls making it worth looking for such an app), but it looks like Spy Call Logs is exactly what you're looking for. It works locally on the device (so no "backup to PC/cloud"), ans seems to have no limit concerning number of records. From its description:

It is very useful application when you want to record more than 500 call logs because default Android Call log stores only 500 call logs data.

How does it meet your requirements:

keep more than 500 calls in my Android Call Log: Yes – as described above.
instant access to all call log entries on my phone: Yes. Including sort (incoming/outgoing/missed), call details (date, time and duration of call), possibility to directly call/message from the logs.

For an alternative, there's also My Call Duration-Unlimited log:

Un-limited call log access - Once you start using this app, your call logs will be remains available inside application. No 500 call logs limits, now access all logs

This app comes with filtering and stats as well, and additionally can be themed (several themes are included with the app). On the downside, it doesn't seem to support direct call/message from the stored logs.

If you've got privacy concerns: Both apps I've mentioned here have access to your call logs and to the Internet, so they theoretically could "spy" on you (which gives the first app's name a quite special meaning). In this case, check the answer of Mr. Alien and follow the link in my comment there: Unlimited Call Log does (currently) not request network access.
(For other call-log related apps, you can also take a look at my listings)
Answer: I recommend BearContact. It has an unlimited call log:
https://play.google.com/store/apps/details?id=com.skzeng.beardialer&hl=en
It is free and reliable.
Answer: IFTTT (If This Then That) is a web-application thats links other web-applications but also offers an IOS and Android phone that lets you link events on your phone to those other web-applications. IFTTT can be easily configed to build a call log on a web-based service such as Google Drive or Google Calendar. This log can then be synced based to your device through the offline capabilities of those apps. You could also sync these automatically to your PC
There are examples on IFTTT that can be found here and include:

Archive your received calls from Android to Google Drive
Log phone calls to Google calendar
Send an E-mail with the call metadata

Lets look at some of the specific requirements of OP as IFTTT isn't perfect but may be useful for other people with a similar question.
In this case, the OP has stated in comments that they specifically aren't interested in cloud-based backup but it is worth considering given IFTTT offers lots of additional possibilities for what can be done with call metadata.
Whether IFTTT meets the requirement of 'Instant Access' depends on what the OP means. If the OP means 'as quickly as possible' then IFTTT isn't suitable as it requires an internet connection and a coordination between several cloud-based services. If the OP is happy with something that is available after a few minutes then IFTTT is definately worth considering.
Note that internet access is only required for IFTTT to execute and update the call log. Depending on the service used, the data should be available offline.
Anecdotally I did read some reviews that said that the first version of the IFTTT Android app was unreliable but I've seen new versions which mention reliability improvements in the version log since then.
Comment: I've read your answer and I don't understand how it answers the question. The question is asking how to keep more logs on the phone, not how to save logs elsewhere. On a related note, your answer doesn't really contain the information that would be useful — the history of IFTTT isn't relevant, but you should explain how to write an IFTTT rule to accomplish what the question is asking for (or as close as can be done with IFTTT).
Comment: @Gilles, thanks for the comment. There was previously a comment discussion with Izzy regarding how I can improve the quality of this answer. That discussion is no longer here unfortunately. I'll make some more edits.
Comment: I've had a quick look at the meta questions for Software Recs and it feels like I should delete my answer given that it doesn't meet all the user requirements. But then it won't be helpful for people searching for similar solutions.

Infinite Call History on Android


Unable to Install and move APK files on SD-card

Question: I have an E-tel(curiosity i110) mobile device running on android 4.42.
I tried to install Apps using APK files to my SD card but i couldn't.
My problem is that I cannot move Apps which already installed to SD-card.
When I check app manger, I seems move to SD card button is fade out.
My question is, why my android OS blocked this feature?
What can i do?
How to select default APK installer as SD card without rooting?
Answer: In your case, if move to SD card option is fade out, then you can't move apps to SD card. The apps installed by user could be moved to SD-card to save internal storage.
There are some system apps which could not be moved to SD-card because OS doesn't allows that.
This may be also app specific, as whatsapp or any game, because block to move their data. Some apps you can move or some you can't.
If it is not possible without rooting, you can go to root your phone and install Link2SD , by which you can create a partition on your SD card and install apps on that.
Comment: Thank you so much VPN. But i can't move Chrome , Hangouts  etc..
Comment: Those are system apps, you can't move them normally. Better is to root your phone and use link2SD, by which you can also remove unwanted system apps.
Comment: Is android OS depend on mobile modal? I mean I assume that there are  tow models of phone which Samsung and HTC that inbuilt same OS assume android 4.42. These OS does contain some differences?
Comment: Yes, Every mobile company place different UI on their mobile phones, also some different features for same android version.
Comment: I understand VPN. But i bought this mobile in last weekend so I have one year warranty with it. If i do that, is it avoid to my warranty?
Comment: Rooting will void warranty
Comment: Then do you have an another way to do this?
Comment: possible there is another way, but I don't have too much research about that, sorry!
Comment: Thanks for you some your helps. If i have another, I'll tell you.