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Wednesday, March 15, 2017

[Math] Is every digit in pi equally likely?

[Math] Is every digit in pi equally likely?


[Math] Is every digit in pi equally likely?

Posted: 14 Mar 2017 11:11 AM PDT

If you were to take pi out to 100,000,000,000 decimal places would there be ~10,000,000,000 0s, 1s, 2s, etc due to the law of large numbers or are some number systemically more common? If so is pi used in random number generating algorithms?

edit: Thank you for all your responces. There happened to be this on r/dataisbeautiful

submitted by /u/LtMelon
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How did we first estimate/calculate the size of and distance to the moon?

Posted: 14 Mar 2017 11:01 AM PDT

Conceptually speaking, what does it mean when you take a number to a power that is not a rational number?

Posted: 14 Mar 2017 09:22 PM PDT

So, my understanding of exponents is basically as follows. Say you have na/b. What this basically means is that you need to do two things to the number n - you need to multiply n by itself a-1 times, and then you need to take the bth root of that result.

So, for example:

  • 32 means 3 * 3 = 9
  • 41/2, or 40.5, means 4, and then you take the square root of 4, which is 2.
  • 53/4 , or 50.75, means 5 * 5 * 5 = 125, and then you take the 4th root of that, which is ~3.3437...

Ok, so that makes sense to me. You can then add on the idea that if either a or b is negative, you just do all of this stuff and then take the reciprocal. And so:

  • 2.5-5/2, or 2.5-2.5, means 2.5 * 2.5 * 2.5 * 2.5 * 2.5 = 97.65625, and then you take the square root of that, which is ~9.882117, and then you take the reciprocal of that, which is ~0.101192

In order to do this, both a and b must be positive integers, because its an iterative process - you can't multiply something by itself 2/3s of a time. But usually you'll be able to express a/b in the form of positive integers.

What doesn't make sense to me is that you can somehow take numbers to the power of things which are not rational (e.g. a/b can't be expressed as a ratio of positive integers) and therefore can't follow this step by step process. I guess there's two different categories here, which are:

  • Exponents which are real but irrational (either transcendental or not). So, for example, how can you take nπ or ne? In these cases, the exponent can't be expressed as a fraction, and so you can't really do the two step process of taking n, multiplying it by itself a-1 times, and then taking the bth root. We can get rough estimates, I suppose (for example, you can use 22/7 or other similar fractions for π), but is that how we actually do this? Or is there some other conceptual way to think about exponents which permit irrational exponents?

  • Exponents which are complex numbers. This is really why I started to think about this entire question, as I was doing some (very basic) learning about the Reimann Zeta function (which I posted about here yesterday and got awesome responses about). That function requires taking numbers to the power of a + bi. And I just don't even know what that means. I know I can type it into google and an answer will spit out, but it just doesn't make conceptual sense to me based on my understanding of what an exponent is.

Any insight would be awesome. Thanks!

Note: I asked this question on /r/AskMath earlier, but didn't get very much of a response and got no answer to the second half of the question. Hoping I might get a better answer here.

submitted by /u/VStarffin
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Was the Velociraptor species as intelligent and clever as the Jurassic Films portrayed them to be?

Posted: 14 Mar 2017 11:42 PM PDT

Wouldn't it be faster to break up and transmit radio signals through space across multiple channels rather than use a single channel?

Posted: 14 Mar 2017 03:53 PM PDT

For example, if you take a picture from the surface of mars and the file size is 4 GB and then you send that picture to earth at 1GB a minute then that takes 4 minutes. If you split the data up into 4 parts of 1GB each and then send those 4 parts simultaneously on 4 different channels then the picture only takes 1 minute to get to earth.

submitted by /u/Azozel
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What are the differences between waves?

Posted: 14 Mar 2017 04:28 PM PDT

I hear sound waves, I see light waves, and I would feel micro waves if they were in a high enough concentration. So what is the difference between then?

submitted by /u/Hiimsimba
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[Physics] How did Balmer arrived at his formula if there was no concept of energy levels or atomic orbitals at his time?

Posted: 15 Mar 2017 04:46 AM PDT

Black hole = magic refrigerator?

Posted: 14 Mar 2017 05:53 PM PDT

Assume I have a large black hole.

And that I have an environment that is extremely hot due to photons flying everywhere.

Let's say I build a giant machine to transfer those photons into the black hole. Not just in the immediate vicinity, but across a vast area.

My question is, is there any limit to how large a machine the hole would be able to cool off by having the material transfer heat into it via radiators or similar. Like, if I built a machine much larger than the actual event horizon that is meant to pass heat into the hole, is there any reason in particular I can't cool the entire machine to the temperature of the hole? Like can I essentially use it as an unlimited thermal wastebin that gets colder and bigger the more heat I throw in it?

submitted by /u/pds314
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Do snow covered mountains still erode?

Posted: 14 Mar 2017 07:21 PM PDT

If the temperature on the mountain never reaches below zero, I figure the only source of erosion is the wind. But when the mountain is covered with snow, does it not act as a barrier between the wind and the mountain?

submitted by /u/itsalilbitlit
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Aren't General Relativity and quantum mechanics just fundamentally, irreconcilably incompatible?

Posted: 15 Mar 2017 01:06 AM PDT

In GR, space and time are facets of a single "thing" and it seems to me that momentum pops out mechanically. There's no inherent limitation on measurement precision built into GR, just like in Newtonian physics.
 

On the other hand, with Heisenbergian inequalities all over the place, we have to choose carefully what we try to measure simultaneously. These limitations on measurement are built right "into the code" of the universe.
 

I just don't see how these theories could ever be unified when they don't even appear to speak the same language. Is there something I'm missing?? (besides, of course, an 8 years in a physics degree program at a university..)

submitted by /u/rpgZenMaster
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Why does a screen recording program not crash when it records itself?

Posted: 14 Mar 2017 07:00 PM PDT

When a screen recording software, such as OBS, records itself, it creates a tunnel effect. If OBS infinitely records itself, why doesn't that make my computer crash/slow down?

submitted by /u/Gifhero
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What does string theory does differently that current theories do not when dealing with singularities?

Posted: 14 Mar 2017 08:27 AM PDT

From what I gather, in string theory we naturally unify QFT and GR, so does it solve the problems that we encounter at a singularity? If so, what explanation does it offer when particles are broken down to their fundamental bits inside a black hole. Please shed light on how our understanding of black holes, and singularities would further if string theory is indeed true?

submitted by /u/elder--wand
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Can a neural network spit bars?

Posted: 14 Mar 2017 03:57 PM PDT

i was watching a video of a neural network learning to speak clearly and my first thought was "when this speaks english perfectly will it be able to rap?" since rap is heavy on the vocabulary it seems fitting to me

to expand on my question, can a neural network rhyme, use word play and make references like a rap song does?

submitted by /u/TubbyMcFuckles
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Why do batteries have a little "nub" on the positive end?

Posted: 14 Mar 2017 11:05 AM PDT

If light was travelling in a 2d circle, would the angular speed of light still be c?

Posted: 14 Mar 2017 07:05 PM PDT

Is it possible for a star of ridiculously high mass and the proper composition to effectively collapse into a black hole so quickly that no supernova is observed outside the event horizon?

Posted: 14 Mar 2017 01:58 PM PDT

I understand (at a very high level) the life processes of a star, balancing gravity's pressure with fusion's outward-pushing energy, until (in some cases) the star begins fusing Iron, which is not an exothermic reaction, and gravity forces the mass of the star together past the Chandrasekhar limit where electron degeneracy pressure can no longer support the growing iron core, and boom. Hopefully I've got that mostly correct within the scope of this question.

I've read that some low-metallicity stars of "only" several dozen solar masses can undergo core collapse and produce a black hole without a supernova - is that effectively what I'm describing in my question text? Or is that happening via some other process?

What about when a really massive star collapses due to photodisintegration? Would that be an example of the text in my question, or is some other process occurring to create a(n) (apparently quite massive) black hole without a supernova in those cases?

Are there any other theoretical cases where a star massive enough to produce a supernova and collapse into a black hole does not actually produce said supernova yet still collapses into a black hole? Or, worded another way (as I hopefully conveyed in the question text), the supernova occurs, but the star is so massive that the event horizon has already formed around the supernova?

Sorry for so many sub-questions, just trying to clarify what I was originally asking and describe what I think I already know.

EDIT: Changed flair to Physics from Astronomy; wasn't sure which applied better.

submitted by /u/FrontColonelShirt
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Why aren't we flung off the surface of the earth if its spinning upwards of 1,000 mph?

Posted: 14 Mar 2017 03:07 PM PDT

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