the math poll

[Triple Zero]

And GA, you can't really measure those formulas, can you?

IMO, all irrational numbers are made-up bullshit. Useful for approximating real things, but don't get it the wrong way around, those numbers are the approximations, a reasonable guess of a real world measurement, assuming ideal conditions. "Ideal conditions" of course means "never gonna happen".

If you're building a square of wood or something and you need to know the length of the diagonal, the square root of two is a real good guess (the best guess, really) of the actual length of the piece of wood you're gonna need. But it's not the length you're gonna end up with, because pieces of wood that are exactly the square root of two times as long as another piece of wood, simply do not exist.

Fractions I have a bit more confidence in, but I'm still suspicious. Natural numbers, however, seem pretty solid so far.

[LMNO]

Pi isn't a metaphor for a relationship - pi is the relationship.  Decimal approximations are an approximation; pi itself is not.

Pi is a relationship of two metaphors. 

[Triple Zero]

Pi isn't a metaphor for a relationship - pi is the relationship.  Decimal approximations are an approximation; pi itself is not.

Pi is a relationship of two metaphors. 

But if you all donate $1 to me, we can get them divorced!

[Cain]

Natural numbers, however, seem pretty solid so far.

BAN GENETICALLY MODIFIED NUMBERS!

[rong]

first off - thanks for everyone's input.  

i think maybe i shouldn't have said anything about Pi - because it kinda got everything off track.

maybe instead i should've said how the hell could e^ix = cos(x) + i sin(x) have been invented?  i'll conced that e^x was invented (even though i don't necessarily think it was) and i'll concede that i, cos and sin were invented, too.  but if all these were invented independently of each other - doesn't that mean that their relationship to each other was discovered?

If you're building a square of wood or something and you need to know the length of the diagonal, the square root of two is a real good guess (the best guess, really) of the actual length of the piece of wood you're gonna need. But it's not the length you're gonna end up with, because pieces of wood that are exactly the square root of two times as long as another piece of wood, simply do not exist.

Fractions I have a bit more confidence in, but I'm still suspicious. Natural numbers, however, seem pretty solid so far.

i think any argument made to say that a piece of wood cannot be of an irrational length can be extended to say that a piece of wood cannot be of any length.

also - that was a really cool bit of info about needing 52 digits of pi to get the size of the visible universe accurate to a proton.  out of curiosity, you wouldn't happen to know how many digits to get the accuracy down to an electron or planck length, would you?

[LMNO]

Well, let's make an analogy:  "Horror" is from the Latin horrre, 'to tremble'.  "Mirth" is from the Middle English myrgth.  Each word was invented independently of each other, over a span of hundreds of years.

So, was "Horrormirth" discovered to describe a particular human situation, or was it invented to do so because the description worked within the language?

[Captain Utopia]

Name one thing it is a genuine measurement of..

I WILL KILL A MOTHERFUCKER

There are plenty of things that are exactly equal to pi.

I meant "genuine" in the sense of "real" - there are no real measurable things which exist in the universe which equal pi, as far as I know.

I just want to mention that the perfect circle does not exist. In order to calculate the ratio of a circle as wide as the currently visible universe, accurate to the proton, you only need Pi up to the 52nd decimal.

That's one of my favourite math facts!

i think any argument made to say that a piece of wood cannot be of an irrational length can be extended to say that a piece of wood cannot be of any length.

I think we can bypass Xeno by asking you how you define length - do you go by the electron cloud orbits at either extent, or the current position of the electrons in their orbits at the given instant of measurement, or...? Is length itself an invention? At best, usable real-world length seems to be definable as a lower and upper bound with an estimated degree of error.

[LMNO]

I just want to mention that the perfect circle does not exist. In order to calculate the ratio of a circle as wide as the currently visible universe, accurate to the proton, you only need Pi up to the 52nd decimal.

That's one of my favourite math facts!

Wouldn't that be considered "science" more than "math"?

[Kai]

Yes. Well, math being a language, therefore technology and science being an investigative method.

[Triple Zero]

I just want to mention that the perfect circle does not exist. In order to calculate the ratio of a circle as wide as the currently visible universe, accurate to the proton, you only need Pi up to the 52nd decimal.

That's one of my favourite math facts!

Wouldn't that be considered "science" more than "math"?

Depends on how you look at it. From the point where the statement says something about Pi, it is about math. From the point where the statement says something about the size of the universe and the amount of precision you need, it is science, or physics .. um wait I am confused, did you mean science? Cause math is a science.

maybe instead i should've said how the hell could e^ix = cos(x) + i sin(x) have been invented?  i'll conced that e^x was invented (even though i don't necessarily think it was) and i'll concede that i, cos and sin were invented, too.  but if all these were invented independently of each other - doesn't that mean that their relationship to each other was discovered?

interesting idea.

I also don't think LMNO's analogy really holds. Combining the words "horror" and "mirth" to "horrormirth" is something different than figuring out that e^{pi * i} + 1 = 0 . Combining "horror" and "mirth" is more like 2 + 3 = 5. The difference is that numbers like 2 and 3 were invented to work for addition, so this is no surprise. In a similar way, words in a language are meant to be concatenated to form new words (regardless of their etymology). The numbers e, pi and i were all invented for entirely unrelated purposes. I realize this might not sound entirely convincing, but there is something special about Euler's formula which makes it different from other mathematical formulas, and that is that it states an Emergent property of mathematics. It is not for nothing that it is claimed he said this formula was proof God exists (not sure if he said it in jest or not--but it is a rather amazing feat where some things appear to click together very unexpectedly).

But then is the question, when is an invention a discovery? If you find a new mersenne prime, did you invent or discover it?

also - that was a really cool bit of info about needing 52 digits of pi to get the size of the visible universe accurate to a proton.  out of curiosity, you wouldn't happen to know how many digits to get the accuracy down to an electron or planck length, would you?

no but I bet that given the proton accuracy requires 52, you should be able to work it out, no?

[LMNO]

Ok, I think I know what's going on here.  Aaaaaaaand it's semantics.  Again.


Some people seem to be using "discover" to describe finding something in the experiential universe that you didn't know was there before: The earth being round, for example.

Some people seem to be using "invent" to describe the creation of the series of rules that govern our attempts to describe the experiential universe, and later to describe artificial or imaginary universes.

Some people are saying that there are relationships and properties of these rules that were not known when the rules were initially created, and are saying they are "discovered", because we didn't know they were there.

Some people are saying that because the rules were invented, then all the relationships and the properties were also "invented".


And now we are using increasingly complex examples in order to either clarify or confuse our arguments.

[Captain Utopia]

I tend to think of Mathematics as an Emergent system - you can invent the rules, but you don't invent the relationships which emerge from the application of those rules.

[LMNO]

But those relationships wouldn't exist without the rules.

[Cain]

Oh I wish IANAR was here.

[The Good Reverend Roger]

But no one here said it was the language of the universe. The post in question was talking about "they say".
Math isn't the language of the universe. Math is the language we use to describe the universe. 

There's a BIP phrase for this, but I absolutely refuse to sully my keyboard by typing it.