SRL Archive - Discussions & Debates

My stupid math teaches say "Math is the language of the universe" and anywhere you where in the universe the logics would be the same…
Did mankind invent math to understand the universe and the nature better or did we discover math?

'We' are Mankind, therefor we did discover maths.

as I understand, most mathematicans say they discover maths rather then invent it.

I would have to agree with Torrent and Yakman on this

Maths is a way to describe the world around us, so it is universal. The concept of "1" would be the same for every intelligent life in the universe - it probably wouldnt be called the same thing but it would represent the same thing. Same as with graphs, calculus, algebra, etc etc.

I disagree with the idea that we discovered maths in the same way that we discovered, say, relativity, or electricity - maths is an abstract concept that describes what we see, whereas relativity and other discoveries are laws/properties of nature (dont get me on semantics, please) that were there the whole time, waiting for us to find them. For example - Newton invented calculus as a way to describe more difficult problems that couldnt be described at the time with the current maths - like motion, for example. Whereas he "discovered" the laws of motion and described/represented them with maths.

You can't really have a strong argument for either of them…

From: newbiezkid
You can't really have a strong argument for either of them…

Then please be so kind as to point out the weaknesses in my arguement, so I can argue with you

It'd be just like someone coming up with a word to describe the color blue. Whether you call it blue, azul, or pink, you're still talking about the same color. You invented the way of expressing the color in words, but not the color itself.

Math is the same way. You can observe things, but there's lots of ways you can write the same thing. Over the last couple thousand years, this is just the best way that we've come up with to write things, with addition, subtraction, multiplication, powers, grouping/parentheses, sums, integrals, unions, etc. You could call math a language if you want.

I don't believe maths is universal. In fact, I don't think any math calculations and equations are valid in all circumstances. There are countless numbers, right? There are also countless calculations/equations you can do with these numbers too. Humankind has revealed only a scratch of all the functions, which to me means that most of the exceptions are yet to be found.
Besides, there are so many flaws in our numeric system. Pi, e (neper) and i (imaginary complex number) are just examples of the things that cannot be presented as a rational number (m/n; m, n {Z}).
Before the 16th century, it was a fact that x² + 1 = 0 has no real solutions. Now we have the imaginary number i (i² = -1) that helps us solve these nonreal equations.
When we now claim that 1 + 1 = 2, can you really be sure that 1+1 is not 3 in some case?

(I heard something like this from someone in these forums)
lim x→∞ ( (3*(1/3))^x) = ?
a) 3*(1/3) = 1
1^x = 1^∞ = 1
Answer: lim x→∞ = 1

b) 1/3 = 0.333…
3*0.333… = 0.999…
0.999^x = 0.999^∞ = 0
Answer: lim x→∞ = 0

What to believe?

(-8)^(1/3)
a)
= ³√(-8) = -2
Answer: -2

b)
=(-8)^(2/6)
= ((-8)²)^(1/6)
= 64^(1/6)
= 2
Answer: 2

What to believe?

Maths is never accurate. It is accurate enough, but never 100%. There are endless solutions.

From: marpis
I don't believe maths is universal. In fact, I don't think any math calculations and equations are valid in all circumstances. There are countless numbers, right? There are also countless calculations/equations you can do with these numbers too. Humankind has revealed only a scratch of all the functions, which to me means that most of the exceptions are yet to be found.
Besides, there are so many flaws in our numeric system. Pi, e (neper) and i (imaginary complex number) are just examples of the things that cannot be presented as a rational number (m/n; m, n {Z}).
Before the 16th century, it was a fact that x² + 1 = 0 has no real solutions. Now we have the imaginary number i (i² = -1) that helps us solve these nonreal equations.
When we now claim that 1 + 1 = 2, can you really be sure that 1+1 is not 3 in some case?

(I heard something like this from someone in these forums)
lim x→∞ ( (3*(1/3))^x) = ?
a) 3*(1/3) = 1
1^x = 1^∞ = 1
Answer: lim x→∞ = 1

b) 1/3 = 0.333…
3*0.333… = 0.999…
0.999^x = 0.999^∞ = 0
Answer: lim x→∞ = 0

What to believe?

(-8)^(1/3)
a)
= ³√(-8) = -2
Answer: -2

b)
=(-8)^(2/6)
= ((-8)²)^(1/6)
= 64^(1/6)
= 2
Answer: 2

What to believe?

Maths is never accurate. It is accurate enough, but never 100%. There are endless solutions.

Irrational numbers arent flaws, theyre like that for a reason - limitations in the way we physically measure things. I'm sure there are flaws in your calculations, I just cant be bothered finding them atm. There are always flaws/incorrect assumptions in things like that (wikipedia math paradoxes, theres a whole lot with explanations on why they arent actually paradoxes).

Before the 16th century, it was a fact that x² + 1 = 0 has no real solutions. Now we have the imaginary number i (i² = -1) that helps us solve these nonreal equations.

That proves that maths is a discovery how? It actually proves that maths is not a discovery, but an invention - the current version of maths in the 16th century just wasnt doing its job for the technology that used it, so someone came up with the concept of imaginary numbers to make it all work.

Humankind has revealed only a scratch of all the functions, which to me means that most of the exceptions are yet to be found.

We havent "revealed" anything, we have invented functions to help us with technology as it progresses. It's not like theres a hidden database somewhere that stores all the maths functions that will ever be invented/used that someone hacks into every few centuries to "discover" a new function/number, and its not like people go digging around in the ground for maths functions in the same way people do to discover dinosaur bones.

Question: On planet azijhoxiahusdjblkzkhx, in galaxy Lolwut, 1000909029109 light years from us, they have a circle too. Because they have intelligent life, they invented the wheel as we did, and then needed some way to measure the circumference of it - do you think the ratio of radius to circumference (pi) would take the same value it does here on earth? Yes, it would, because a circle is a circle regardless of what galaxy/universe youre in. Would euler's number have the same value? Yes, it would. Maths is universal.

Sorry, kind of off topic, but what are your thoughts on the arrow paradox, Marpis or The Claw? :) Or anyone for that matter.

(Also, Zeno's dichotomy paradox. That's more math related, I think. :p)

From quickly reading on wikipedia (its >12am and I'm tired) the arrow paradox seems to just be a play on words to me. Nothing significant, just tricks with language. At any given snapshot of time, everything is stationary, but when compared to a snapshot taken a few instants later, if something is in motion, its position will be different, so motion exists…unless I'm missing the point of the paradox (its late, relax). Like if you paused a movie, you would say nothing was moving, then if you pressed play again, and paused it a few seconds later - nothing is moving again, but things clearly moved over that period of time.

Havent looked up the others yet, will do so tomorrow

The arrow paradox (from what I understand) is if you constantly measure something at any moment, then it's never in motion.

From: marpis

(I heard something like this from someone in these forums)
lim x→∞ ( (3*(1/3))^x) = ?
a) 3*(1/3) = 1
1^x = 1^∞ = 1
Answer: lim x→∞ = 1

b) 1/3 = 0.333…
3*0.333… = 0.999…
0.999^x = 0.999^∞ = 0
Answer: lim x→∞ = 0

What to believe?

(-8)^(1/3)
a)
= ³√(-8) = -2
Answer: -2

b)
=(-8)^(2/6)
= ((-8)²)^(1/6)
= 64^(1/6)
= 2
Answer: 2

What to believe?

0.999… is equivalent to 1, at least according to my calc teacher, textbook, and Wikipedia :p. Also, lim ∑(n from 1 to ∞) 1/n is 0.

With the second one, the answer is actually ±2 but since you added a second solution where there was only one before, you have to manually check both solutions, for which -2 is the only working one.

From: marpis
Maths is never accurate. It is accurate enough, but never 100%. There are endless solutions.

Math is 100% accurate by design, only it's implementations in the real world are not always accurate. You have to understand maths is purely based on Axioms. Since you have to ``accept'' these axioms before even talking about math, it is possibly to define infinite accuracy within these axioms. With these axioms, you can prove theorems, thus expanding the ``rules''.
For limits, there are also certain theorems and axioms that may seem illogical, but they aren't really.

Let's start by taking a look at how Mathematics evolved.
First, we started off with Natural numbers. This allowed us to multiply and add Natural numbers to create new Natural numbers. We couldn't, however, subtract. Then we added the Integers, those allowed us to subtract integers to create new integers. This however, still had restrictions, as we could not divide let's say, four by three. This is why the rational numbers were invented. After these, came the Real numbers, and following those, the complex ones. (Which are used in one of your examples, even though you don't mention them)

You see, the way math works, in it's own world of axioms, you can't prove it wrong, as you first have to accept the axioms.

If you are in a galaxy somewhere far far far from here then even the laws of nature may be different than the ones that we have here on earth. Alpha is changing and therefore the laws of nature is changing.

From: Zyt3x
If you are in a galaxy somewhere far far far from here then even the laws of nature may be different than the ones that we have here on earth. Alpha is changing and therefore the laws of nature is changing.

But that doesn't change maths in it's essence.

From: Wizzup?
But that doesn't change maths in it's essence.

True… Sorry to interrupt.. :P

LOL