The h Bar

Sir Cumference

2:34 AM

Gotta love debugging the test code you're trying to use to debug your program

Novalium Company

7:37 AM

I just realized you can never know the exact diameter of a circle, only an approximation.

John Rennie

Well you could know the diameter exactly, in which case you can never know the circumference exactly.

You're really just saying you can never know the value of pi exactly.

@NovaliumCompany if you're interested there is a proof that pi is irrational, though as I recall it's obscure and complicated.

Novalium Company

I meant that you can't ever know the exact value of pi yeah

How do we know that it's infinite?

John Rennie

Pi is IRRATIONAL: animation of a gorgeous proof

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Novalium Company

oks lemme check

John Rennie

There are actually lots of proofs:

Proof that π is irrational

In the 1760s, Johann Heinrich Lambert proved that the number π (pi) is irrational: that is, it cannot be expressed as a fraction a/b, where a is an integer and b is a non-zero integer. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki. Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. In 1882, Ferdinand von Lindemann proved that π is not just irrational, but transcendental as well. == Lambert... ==

Novalium Company

7:50 AM

"These numbers cannot be written as ratios of integers" - 22/7 ?

John Rennie

22/7 is one of the well known approximations for pi

Novalium Company

gotcha

Sure, pi is irrational, so what?

It still goes to infinity and we still have no proof it goes to infinity. How can anyone know that something is infinite? There may be an end to pi somewhere.

John Rennie

Irrationality means the expansion must be infinite, because if the expansion terminated or started recurring we would be able to write pi as a fraction.

So when you prove pi is irrational you also prove its decimal expansion is infinite.

Novalium Company

Let's get rid of this terminology of irrationality and rationality and definitions and stuff... I'm just asking, if it's infinite, how are you sure? How are you sure that somewhere far far along the line it doesn't stop to a precise definite value?

You can't ever be sure.

Infinity is weird.

John Rennie

You can be sure. If it has a precise value then it must be rational. Since it has been proved to be irrational it cannot have a precise value.

Novalium Company

8:01 AM

You're still constrained by your little definitions you read in a book.

sorry

John Rennie

Rational and irrational are not arbitrary definitions ...

They are fundamental classes of numbers.

It's like saying integer and non-integer are just little definitions I read in a book.

Novalium Company

i'm being a bit rude sorry, i'm just wondering how can anyone be sure that something is infinite. Like... wtf...

For something to be infinite, it means that we don't know it's whole, we can't know it's whole. So how do we know that it doesn't have an end?

Johan Liebert

Better suited discussion for Philosophy.SE!

Novalium Company

I think JohnRennie just gave up on me, but that's fine xD

John Rennie

That's what the proof in that video does. It shows that pi is irrational, and that means it must be infinite.

Suppose pi terminated at the third decimal place i.e. 3.141. Then it could be written as the rational number 3141/1000.

If it terminated at the nth decimal place then it could be written as the rational number 3.141...(nth digit)/10^n

Novalium Company

8:14 AM

I have another theory of equality. Be prepared, this is going down in history. If "a = b", that doesn't mean that "b = a". I know it's counterintuitive but what if "a" is in a superposition of both being equal to b and not being equal to b and the wavefunction drops into two adjacent universes with the corresponding outcomes.

Johan Liebert

In mathematics things are firsts defined and then theorems regarding them are proved (though much more than this is done)

John Rennie

So it it terminates anywhere it can be written as a rational number. Since we have proved it is not a rational number that proves it can never terminate.

Novalium Company

@JohnRennie Got it.

Johan Liebert

A simple proof that $\sqrt 2$ is a non terminating and non recurring number is that to first assume it is a terminating number and then arrive at a contradiction so as to conclude that it indeed is non terminating and non recurring

Novalium Company

@JohnRennie I understand what you're proving with the irrationality thing. I'm just wondering, the definition of infinity states that we can't possibly know the whole thing, so whatever we do, there is always more and more to come, there's always unknown in the number, so how can we be sure that somewhere in that unknown, it doesn't end?

Johan Liebert

8:20 AM

But an interesting thing is that till now we haven't proved if $e+\pi$ is a irrational or a rational number.

John Rennie

@NovaliumCompany pi is a number, and we can know some things about but not others. For example even though we can never know its exact value we can know it is greater than 3 and less than 4.

So the fact that we can never know it exactly doesn't stop us knowing some things about it.

And one of the things we can know is that the decimal expansion never ends.

Novalium Company

Ah... fair enough.

Actually.

You know that it's between 3 and 4 due to the known part of the number. The unknown part of the number can still hide it's end.

Let's just leave it here, shall we? I'm not sure you are enjoying this.

Maybe there are higher things than rationality and the logic our little brains can come up with.

When I create superintelligence, it'll tell me whether pi ends or not. yay

I guess it's a good idea for me to go to China after 19. A lot of AI stuff happening there and that's where I wanna be.

@JohnRennie What do you say about the "a = b" but "b not= a" thingy?

John Rennie

@NovaliumCompany that implies that the equals operator is non-commutative.

Novalium Company

How can anything be equal to anything else?

Like, an apple is never exactly like another apple.

JohnRennie, I'm sorry I'm wasting your time with my BS, I'll just go read my book.

John Rennie

8:35 AM

OK :-)

Slereah

10:15 AM

More importantly

How does one prove that $\pi$ is a number???

lix.polytechnique.fr/Labo/Ilan.Vardi/pi-exists.html

here is one!

JMac

1:02 PM

@JohnRennie physics.stackexchange.com/a/528088/127931 Did you get those diagrams from a textbook, or make them yourself? I don't think I've ever seen a comparison like that, and now I'm kinda questioning why I've never seen it.

Johan Liebert

1:21 PM

@JMac he makes the diagrams himself using Google draw.

John Rennie

1:58 PM

@JMac Google Draw.

One of the students in the JEE chat room asked me about the question, and I had one of those rare light bulb moments. It had never occurred to me before to describe a wheel in those terms but suddenly it seemed obvious

Novalium Company

2:09 PM

@JMac I'm reading Contact now, chapter 8. Books is good enough. Thanks for recommending.

Johan Liebert

2:31 PM

physics.stackexchange.com/help/product-support

This looks like it was designed for Stack Overflow and then Physics.SE was pasted there?

rob

3:23 PM

@JohanLiebert Most or all of /help is the same across the while network.

chandru

3:50 PM

physics.stackexchange.com/q/528049/252528 can somebody take a look at my calculation and tell me whether am going in the right direction?

JMac

@chandru That question isn't really on-topic. It seems to be mostly an engineering question, which are off-topic. It's also a link to a picture of your work, which isn't good. You need to write it down in the actual question body (you can use Mathjax for equations). Also, check my work style questions are off topic, and this appears to be one.

ZeroTheHero

4:05 PM

@chandru yeah a link-only question is terrible.

I mean: please put in some work yourself into getting things in the right format as an inducement for reader to put some work into answering your question.

Even if you were to do so, remember that this is not a site for checking work.

chandru

4:22 PM

ok thank you. Am new to the forum. I tried writing all details in title but it didn't support that many characters.

ZeroTheHero

@chandru you need to use mathjax for this.

chandru

@ZeroTheHero Thank you sir for the information. By the way I didn't intend to compel anyone to check my work. Rather had a genuine doubt whether I could reduce the power by gearbox mechanism for the particular problem. Anyway thanks for the suggestion

ZeroTheHero

@chandru it looks like check-my-work so if it's not this then you might want to edit the question to emphasize how it is not.

baponkar

Hello!

Tell me a good PhD research topic for theoretical quantum mechanics

Novalium Company

What I dislike about the book "Contact" is the political and religious side. The book spends too much time on unnecessary details that in no way contribute to the plot or character development (at least that's how I feel it). It spends too much time exploring the political and religious effects that the "contact" has. I'm not a big fan of that. But still, I'm at page 147, I hope books spends more time on the characters and plot.

chandru

4:34 PM

@ZeroTheHero Yes sir, I deleted the question. I will rewrite it in proper format again. Thank you

ZeroTheHero

Be well.

Novalium Company

5:24 PM

@JMac Gave up Contact. I'll be reading a summary now. 80% of the book is religion and politics, 10% unnecessary details, 5% character development, 5% plot development.

What the f*ck is that?

Carl Sagan - 'A Glorious Dawn' ft Stephen Hawking (Symphony of Science)

►

It's quite nice.

Novalium Company

7:56 PM

I just finished watching the movie Contact. It's amazing. It was everything I wish the book was. The movie is much much better than the book. The problem I have with the book is that it spends too much time on political and religious complications that a potential "we are not alone" scenario comes with. I'm not a big fan of religion nor politics. Anyways, the plot and the characters are just brilliant (although the movie is the one that biased me on that side).

What do you guys think about the book and the movie?

Novalium Company

8:33 PM

@JohnRennie (if you see a random guy named Kapton friending you on goodreads, it's me :P)

Sir Cumference

11:19 PM

@NovaliumCompany Well you can never write pi out finitely in terms of numbers 1-9, as we usually like to do

Though I can give it the symbol $\pi$ and tell you whether it's bigger or smaller than another number, etc.

if "writing in terms of 1-9" is what you consider "knowing the number", then it's true you'll never accomplish that

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