Pi, an AMAZING description!!

reply to post by kthxbai


Not entirely true. You can take a square with a diagonal of 1. Of course then the lengths of the legs become irrational. Similarly you can take a circle with a circumvent of 1, resulting in a irrational diameter. Its a matter of perspective.

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!

I guess you could think of it as a cross between "light", "analog" and "digital". Just as the parts, the individual digits, could be isolated in the "digital" sense, there's always a number after it in the "analog" sense. This is in the same manner that light exists or behaves as both a wave and a particle.

Digital is related to decimal equivalents or approximations based on rounding. The fraction and root forms are more accurate or "pure" where the decimal approximations are just really really close. A lot of kids today, just as yesterday, express their "hatred of fractions" but that's where the key is to understanding math. As soon as there is a decimal conversion and a non terminating decimal is presented, the accuracy is affected. Even if it's a decimal that repeats as opposed to an irrational number that doesn't, the accuracy is affected by the rounding and all answers after that are affected. Compounded over time, they can mean a infinitely large error produced by an infinitely small alteration.

Originally posted by -PLB-
reply to post by kthxbai

 

Not entirely true. You can take a square with a diagonal of 1. Of course then the lengths of the legs become irrational. Similarly you can take a circle with a circumvent of 1, resulting in a irrational diameter. Its a matter of perspective.

There is always irrational numbers involved. Since you can never set the legs (sides of the squares) to a definite number, you can never prove it's a perfect square that you are measuring the diagonal of that you profess to be one

Originally posted by puncheex

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.

Yes, what is used by the general population on a daily basis is "arithmetic", it's only a very small subsection of "math" yet we call it math in order to go about our daily lives.
Arithmetic is the most basic form of math, and is the one used by everyone in the world regardless of how novice or advanced they may be. It does lay the foundation. It's the anomolies in arithmetic (that we usually just round off to two decimal places for dollars and cents) that produce the higher mathematical ideas that are then explored.

Originally posted by kthxbai

Originally posted by -PLB-
reply to post by kthxbai

 

Not entirely true. You can take a square with a diagonal of 1. Of course then the lengths of the legs become irrational. Similarly you can take a circle with a circumvent of 1, resulting in a irrational diameter. Its a matter of perspective.

There is always irrational numbers involved. Since you can never set the legs (sides of the squares) to a definite number, you can never prove it's a perfect square that you are measuring the diagonal of that you profess to be one

True, though note that when you are no longer talking about a mathematical model, but about actual existing shapes, lengths represented by a rational number no longer exist anyhow. It will all be an approximation. At the same time you will open a new can of worms involving Planck length and all kind of other quantum mechanical issues such as uncertainty principles.

Originally posted by -PLB-

Originally posted by kthxbai

Originally posted by -PLB-
reply to post by kthxbai

 

Not entirely true. You can take a square with a diagonal of 1. Of course then the lengths of the legs become irrational. Similarly you can take a circle with a circumvent of 1, resulting in a irrational diameter. Its a matter of perspective.

There is always irrational numbers involved. Since you can never set the legs (sides of the squares) to a definite number, you can never prove it's a perfect square that you are measuring the diagonal of that you profess to be one

True, though note that when you are no longer talking about a mathematical model, but about actual existing shapes, lengths represented by a rational number no longer exist anyhow. It will all be an approximation. At the same time you will open a new can of worms involving Planck length and all kind of other quantum mechanical issues such as uncertainty principles.

But due to the non-exact nature, those things cannot be accurately measured with precision. They can only be measured based on the accuracy of the tools we use and the means by which we read those measurements

Originally posted by kthxbai
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!!

edit on 4-1-2013 by kthxbai because: added it was accurate

Wow


Best 2 minutes spent on you tube....ever

16 flags

reply to post by MarioOnTheFly


porntube included

Thanks for the excellent data on the inability to measure the diagonal of a perfect square. So fifty perfect squares laid end to end would make a good coffeetable, but you couldn't measure it! This is a great thread, nice work.

Originally posted by Aleister
Thanks for the excellent data on the inability to measure the diagonal of a perfect square. So fifty perfect squares laid end to end would make a good coffeetable, but you couldn't measure it! This is a great thread, nice work.

nah, you could measure it for all usefull purposes based on the instrument you use in the arithmetic sense. You just can't measure it with absolute accuracy in the mathematical sense

If pi contains everything it contains nothing.

Here is a string which may make this point clearer: just string together every possible sentence in English, first by length and then by alphabetical order. The resulting string contains the answer to every question you could possibly want to ask, but

a) most of what it contains is garbage,

b) you have no way of knowing what is and isn't garbage a priori, and

c) the only way to refer to a part of the string that isn't garbage is to describe its position in the string, and the bits required to do this themselves constitute a (terrible) encoding of the string. So finding this location is exactly as hard as finding the string itself (that is, finding the answer to whatever question you wanted to ask).

Useful communication is useful because of what it does not contain.

Thanks everyone who posted in this thread! I have a tiny bit of understanding, where before, I had no understanding whatsoever. I have always wanted to know about pi, but needed help and all of you contributed to helping me. Thanks so much!

Personally, I prefer 355 divided by 113...

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

Many irrational numbers have patterns. For instance, lets take the hypotenuse of a right triangle with legs of length 1:

√(1² +1²) = √2 = 1.4142135623730950...

The digits here will go on indefinitely in a seemingly random pattern and because of this there is no way to represent the square root of 2 as a whole fraction (repeating or halting). However, there is such a thing as a continued fraction form. In the continued fraction form the √2 is equal to the pattern:

1+(1/2+(1/2+(...)))

One of the things that makes π and e special is that they are transcendental numbers. Numbers that have no repeating continued fraction form. So, for all intents and purposes pi is seemingly patternless as a fraction, other than it being the circumference divided by the diameter of a circle.

A little off topic, was the teacher Ben from Lost?

Originally posted by Razziazoid
If pi contains everything it contains nothing.

Here is a string which may make this point clearer: just string together every possible sentence in English, first by length and then by alphabetical order. The resulting string contains the answer to every question you could possibly want to ask, but

a) most of what it contains is garbage,

b) you have no way of knowing what is and isn't garbage a priori, and

c) the only way to refer to a part of the string that isn't garbage is to describe its position in the string, and the bits required to do this themselves constitute a (terrible) encoding of the string. So finding this location is exactly as hard as finding the string itself (that is, finding the answer to whatever question you wanted to ask).

Useful communication is useful because of what it does not contain.

Of course the null set is a subset of every given set, that was established long, long ago

a. only garbage to the person who is looking for something else. One man's trash is another man's treasure
b. depends on what your'e looking for
c. like finding a needle in a haystack. It may be difficult to find, but it's still there

Originally posted by hypattia
Thanks everyone who posted in this thread! I have a tiny bit of understanding, where before, I had no understanding whatsoever. I have always wanted to know about pi, but needed help and all of you contributed to helping me. Thanks so much!

But.. but... hypatia was one of the very first recorded female mathematicans!!

Originally posted by jhn7537
A little off topic, was the teacher Ben from Lost?

Had to google it because I didn't watch Lost, but yes, the same actor

...actually makes me curious to go back and look at Lost and perhaps watch it after the fact...

Here is an image I came across awhile back that I feel might add to this discussion.



Good insight, is it not?

reply to post by kthxbai


best vid ive seen today...thanks for sharing