Pi, an AMAZING description!!

Ok, I realize it's fiction, I realize it's a TV show, but this was a moment for a very gifted writer and a very gifted actor. It comes from the TV Show "Person of Interest". Finch is posing as a substitute teacher and the everlasting question "When will we ever use this" comes up. He paints an amazing picture involving pi and infinity and relates it in a way that I found truely amazing. I wanted to share it because it really is AWESOME! ...and very accurate as well!!

reply to post by kthxbai


Mind expanding video, but is it true? Math experts, please tell us.

Star and flag and more stars and flags, given to you under the table.

Originally posted by Aleister
reply to post by kthxbai

 

Mind expanding video, but is it true? Math experts, please tell us.

Star and flag and more stars and flags, given to you under the table.

Yes, it's very much true

edited OP to reflect that

reply to post by kthxbai


Worth some thinking time, just to appreciate it. Math wizards also, a question. I've heard that you can't measure a perfect square diagonally, from one corner to another. That each time you try to measure it, say with an infinite ruler, that the measurement will always come out in between two numbers. True? If so, then this relates to the thread and the video.

Yes it is true.

However it is not limited to pi.

This is the same for ANY irrational number, not just pi, e is the same and there are many more.

Pi and Phi, two of my favorite subjects. S & F for a great explanation OP. Professor really gives you a perfect description.

reply to post by Shadowcast


Please correct me if I am wrong but if it never repeats and assuming you assign a letter value to numbers 1-26 how do you get ll and ee and so on? For that matter when is 2425 xy and when is it bdbe?

Originally posted by steppenwolf86
reply to post by Shadowcast

 

Please correct me if I am wrong but if it never repeats and assuming you assign a letter value to numbers 1-26 how do you get ll and ee and so on? For that matter when is 2425 xy and when is it bdbe?

The pattern never repeats.

In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number.

Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational.[1]

When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common.

Perhaps the best-known irrational numbers are: the ratio of a circle's circumference to its diameter π, Euler's number e, the golden ratio φ, and the square root of two √2.

en.wikipedia.org...

reply to post by Aleister


I would say no bc that line has a standard formula to find it. and all the factors that can be input in that formula can be anything, so any number result is possible

I hate maths.

So if it's infinite and contains every other number sequence within it.

I'm left asking, if this is true, then does it only appear to end when we appear to run out of things to count?

Where in PI is 21/12/12 for instance. or 21122012. Or the phone number to nasa? Near the end? It has no end. Middle? Start? Is the start of PI actually the start then, or just where..

I hate maths...

(not denying it, lol, just in case someone asks, but it does my head in)

From wikipedia, "pi":

The digits of π have no apparent pattern and pass tests for statistical randomness including tests for normality; a number of infinite length is called normal when all possible sequences of digits (of any given length) appear equally often. The hypothesis that π is normal has not been proven or disproven. Since the advent of computers, a large number of digits of π have been available on which to perform statistical analysis. Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of π, and found them consistent with normality; for example, the frequency of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found. Despite the fact that π's digits pass statistical tests for randomness, π contains some sequences of digits that may appear non-random to non-mathematicians, such as the Feynman point, which is a sequence of six consecutive 9s that begins at the 762nd decimal place of the decimal representation of π.

"Normality" is the property the teacher is speaking of. While pi seems to be normal in this sense, there is no proof that there is; proof would seem to involve having all the digits of pi available for inspection, and that is plainly impossible.

My favorite story about pi is contained in Sagan's Contact (the book, not the movie). The following constitutes a spoiler, so read no further if you want to try the book out itself. (Pardon, I don't have a copy here, so my telling may be off in details.)

In the story the protagonist is given a hint by an ET (her father, at least in form) that there is a message from the Creator hidden in the expansion of pi. She sets up a program like SETI@Home to work on it. At the end of the book, the computer tells her that when pi is expanded in base 11, some 100,000 digits in, the expansion suddenly breaks into 599 zeros, a 1, and then 597 zeros and three 1s, and proceeds in that fashion of 1s and 0s for 160,000 digits, and then returns to random digits. When plotted on a 400x400 raster, the 1s form a circle on a 0 background. (The idea of using numbers in a rectangular raster to present pictures is used so often earlier in the book that by now, what's happening is obvious even to non-maths.) This is, of course, the source of much wonderment in the last two paragraphs in the book, about a universal Creator who has the power to bend a universal constant to his will.

But (and this isn't from the book) if normalcy for pi is true, then this fictional pattern may mean nothing at all, just the fulfillment of a promise from normalcy. Of course, Sagan was an astronomer, not a mathematician.

Saw the episode and loved the description also, it made things slightly clearer to me. S&F
I also detest math and need help grasping basic concepts of it. Can anyone explain (for a complete math/physics ignoramus like myself) ..How do numbers translate to tangible things? (ie; 'it's in everything') and intagible also, like, sounds, music, colors etc? I'm probably not asking the question right but hopefully someone can interpret what I mean (but don't know what/how to ask-lol) Thx!

Originally posted by Starcrossd
Saw the episode and loved the description also, it made things slightly clearer to me. S&F

I also detest math and need help grasping basic concepts of it. Can anyone explain (for a complete math/physics ignoramus like myself) ..How do numbers translate to tangible things? (ie; 'it's in everything') and intagible also, like, sounds, music, colors etc? I'm probably not asking the question right but hopefully someone can interpret what I mean (but don't know what/how to ask-lol) Thx!

It is both easy and hard to answer that. Mathematics has the property of abstracting, of modeling the world we live in. Why it should do that is a deep philosophical question which I can't even essay, but consider your checkbook register. It uses mathematics (simple, but certainly adequate) to model you're monthly cash flow. Your tax forms model an aspect of your relationship with the sociological institution of the state. Pure math is the domain of a few very talented mathematicians, but all of the rest of us, and even they part of the time, apply math to the world to predict what will happen in the future and where we are going right now. Why does doing that work? I don't know. The only thing I can say is that when it is done properly, it works superbly, and that's both our justification and the best we can expect.

Originally posted by Starcrossd
Saw the episode and loved the description also, it made things slightly clearer to me. S&F

I also detest math and need help grasping basic concepts of it. Can anyone explain (for a complete math/physics ignoramus like myself) ..How do numbers translate to tangible things? (ie; 'it's in everything') and intagible also, like, sounds, music, colors etc? I'm probably not asking the question right but hopefully someone can interpret what I mean (but don't know what/how to ask-lol) Thx!

The irrational number is like infinity. As it cannot repeat its pattern - logically - it must be constantly changing.

Because it is constantly changing, it stands to reason that every possible combination of numbers will contained within an irrational number. So - despite not being able to tell where a particular number will be - the irrational number can be said to contain infinite information though that information(with our current understanding) is essentially useless due to its random nature.

reply to post by puncheex





“In the hour of our Twilight we will be together soon, if we will be anything at all.”

Those numbers only get meaning when we attribute meaning to them. We can not extract new information from it. For example, if you find the string of numbers representing the story of your life, you can not take a look at the subsequent string to know what is going to happen in the future.

In practice, pi is only useful up to a precision of a few decimals. In math its very uncommon to write pi as a decimal number, and whenever pi is for example divided you just write it as a fraction (for example 1/2pi instead of 1.57079632679).

Originally posted by Aleister
reply to post by kthxbai

 

Worth some thinking time, just to appreciate it. Math wizards also, a question. I've heard that you can't measure a perfect square diagonally, from one corner to another. That each time you try to measure it, say with an infinite ruler, that the measurement will always come out in between two numbers. True? If so, then this relates to the thread and the video.

That's true as well. Using the Pythagorean Theorem or the properties of special right triangles, the hypotenuse (diagonal) is the square root of two times the length of a leg (side of the square). The square root of two is an irrational number just as pi is. It never terminates and never repeats, just as pi.

This means you get the same properties he explained while explaining pi

Originally posted by steppenwolf86
reply to post by Shadowcast

 

Please correct me if I am wrong but if it never repeats and assuming you assign a letter value to numbers 1-26 how do you get ll and ee and so on? For that matter when is 2425 xy and when is it bdbe?

It all depends on which way you assign the letters to the numbers and you can assign them in an infinite number of ways