The PokéCommunity Forums [Discussion] Mathematics, discovered or invented?

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#26
July 6th, 2013, 03:06 AM
 Plumpyfoof Join Date: Apr 2011 Location: Melbourne, Australia Age: 20 Gender: Male Nature: Sassy

Quote:
 Originally Posted by Quopol I think whatever in math was right has been discovered and whatever is incorrect in math has been invented... I heard someone mentioned a cube and square. We can find the area and volume of a cube/square by various formulas but the style of those may be different. But it works, so shouldn’t it be true because volume and areas exist in every kind of 2-D and 3-D shapes imaginable?
This entire post.
I've quoted here because I want to point out we were discussing assuming as if it was all correct, but I like your ideas.

The cube/square scenario was describing perspective, so if you look at a cube face on it looks like a square right? But if you have had and can not have any other view of the cube other than face on you would assume it was simply a square and had no evidence to prove otherwise .
#27
July 6th, 2013, 08:42 AM
 Lance Pokémon Champion Join Date: Jul 2009 Location: Blackthorn City Gender: Male Nature: Adamant
Math as a language was invented, but the concepts that language explains existed long before we were able to codify them. It's not like special relativity existed only after Einstein told us all about it. ;p
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#28
July 6th, 2013, 09:37 AM
 gimmepie The Seeker of Pies Join Date: May 2012 Location: Australia Age: 18 Gender: Male Nature: Mild
@Livewire - Exactly! I couldn't have put it better myself.

@Quopol - That is an interesting perspective that has yet to appear and it is indeed well thought out but I must continue to respectfully disagree. The issue with your view isn't correct vs incorrect, it is that it still views mathematics and the principals it describes as the same thing.

Incorrect maths is invented just as you said and pretty much for the reasons you said. I'll give you that one. But correct mathematics was also invented - correct mathematics just means we are using the language of mathematics to accurately describe a discovered principal. In this sense correct mathematics is the equivalent of writing a non-fiction book whilst incorrect mathematics is more like writing a narrative.

It is as Livewire, myself and a few others on here have said. You are all viewing mathematics as though the formula we use to calculate gravity is the same thing as the actual force of gravity.
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#29
July 6th, 2013, 03:31 PM
 Quopol Join Date: Jul 2013
Quote:
 Originally Posted by gimmepie @Livewire - Exactly! I couldn't have put it better myself. @Quopol - That is an interesting perspective that has yet to appear and it is indeed well thought out but I must continue to respectfully disagree. The issue with your view isn't correct vs incorrect, it is that it still views mathematics and the principals it describes as the same thing. Incorrect maths is invented just as you said and pretty much for the reasons you said. I'll give you that one. But correct mathematics was also invented - correct mathematics just means we are using the language of mathematics to accurately describe a discovered principal. In this sense correct mathematics is the equivalent of writing a non-fiction book whilst incorrect mathematics is more like writing a narrative. It is as Livewire, myself and a few others on here have said. You are all viewing mathematics as though the formula we use to calculate gravity is the same thing as the actual force of gravity.
I agree with your idea that we try our best to understand gravity with our formulas, but it doesn't make them equivalent. The formulas aren't what makes math beautiful. It's our world that makes it so.
EDIT: I forgot to mention... Sorry that I sent the wrong message. I agreed with your idea while I was writing my post. I'm not so great at writing and I'm open for constructive criticism. How can I make it so that these kind of incidences don't happen again? Thank you for taking your time to answer my question (if you do so).

Last edited by Quopol; July 6th, 2013 at 03:58 PM.
#30
July 8th, 2013, 06:14 PM
 Arlo Join Date: Dec 2012
I'd say it's fairly obvious that the answer is both, just depending on how one looks at it. I would presume that most "debate" about the issue is a result of equivocal notions of "mathematics."

Mathematics is, at heart, a language used to describe quantities and the relationships between them. That language is man-made - "2" only became "2" when the number was conceived and shared. But the quantity that we represent with the numeral "2" has always existed. We certainly didn't create that. There were 2 planets between the Earth and the Sun LONG before life even appeared on the Earth. The ability of man to conceptualize "2" and create a symbol to represent it had no effect whatsoever on the quantity of planets between the Earth and the Sun. That was a (relatively) fixed aspect of our solar system - we just created a symbol to represent and communicate it.

Similarly, there has ALWAYS been a ratio, and the exact same one, between the radius and the circumference of a circle. We didn't create that - it already existed. We simply discovered it. It's only the language by which it's defined to be 3.14159265... that we created.

And so on. The underlying principles of mathematics are part and parcel of reality. If one starts with a specific quantity of some things and adds some specific amount more of them, one ends up with a specific greater quantity of them. Those quantities would be exactly what they would be and the relationships between them would be exactly what they would be, regardless of whether we had a language with which to describe them or not. The creation of the language didn't create the quantities or alter them - it merely gave us a way to describe them and describe the ways in which the interrelate.
#31
July 15th, 2013, 05:04 AM
 Squirrel This'll be a blast! Community Supporter Join Date: Sep 2011 Location: England Age: 20 Gender: Male Nature: Quirky
Very interesting question!

Quote:
 Originally Posted by Livewire Math as a language was invented, but the concepts that language explains existed long before we were able to codify them. It's not like special relativity existed only after Einstein told us all about it. ;p
This is the perfect answer, I'd say. Mathematics as a language is something that we invented to try to understand our universe in a way that we can manipulate, but the ratios and equations taking place in every day life have always been there. It's entirely possible that our view on the universe (from a mathematical standpoint) is entirely wrong and we've been miscalculating everything (and it's possible that things simply can't be calculated), but given that we're able to understand, evaluate and manipulate the world in the ways that we do, I think it's a safe bet that we've got this down haha. It's interesting to consider an unquantifiable world in which all maths we took to be law is revealed to be false, but from the limited knowledge that we have, it seems likely that'll never happen.

Though 'likely' is a probability, so perhaps we're imagining that too? ;)
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#32
July 25th, 2013, 05:58 AM
 Archer a.k.a: ethan. Community Supporter Join Date: Oct 2006 Location: NSW, Australia Nature: Modest
Maths is a perfect self-contained system. We represent it with an invented language and numeracy system to model things that we perceive and concepts we've invented, but maths itself is not invented.
#33
July 25th, 2013, 06:14 AM
 Omicron boom baby Join Date: Mar 2010 Nature: Modest
Definitely not invented, discovered. Math exists in nature and many examples can be made, like fibonacci's series in plants or nautilus. As Livewire stated above, the way we express math was invented, but math itself was just discovered.
#34
July 25th, 2013, 06:18 AM
 gimmepie The Seeker of Pies Join Date: May 2012 Location: Australia Age: 18 Gender: Male Nature: Mild
The problem with that, as I have said before, is that you are all confusing mathematics with what it describes. Mathematics is a language the patterns and principals that occur naturally throughout the universe were discovered - but mathematics itself is a language just like English or Spanish that we have invented.

What you guys are doing is the same as saying that an apple is the same thing as the word "apple" when in reality one is an object and the other is the word we use to describe that object.
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#35
July 25th, 2013, 06:34 AM
 Archer a.k.a: ethan. Community Supporter Join Date: Oct 2006 Location: NSW, Australia Nature: Modest
Quote:
 Originally Posted by gimmepie What you guys are doing is the same as saying that an apple is the same thing as the word "apple" when in reality one is an object and the other is the word we use to describe that object.
Precisely. The Apple exists and has its properties regardless of whether we choose to describe or label it. The words and labels have been invented, but the reality they describe is discovered.

What do you all think about the notion that maths, being perfect a perfect system (100% consistent, no issues, contradictions, etc) cannot be man-made?
#36
July 25th, 2013, 08:57 AM
 Esper Join Date: Jun 2009 Location: California
It feels like mathematics is something invented because you can do things in math that have no correspondence in the real world. Where do negative numbers exist in nature? Imaginary numbers? (Serious question - I'm not a math person.) Like language, we can create words (and conceptions) of things that don't or can't exist.

Feels to me like mathematics is an interpretation of nature. Nature is discovered, but nature is not math. Math is the language we use to understand nature. In that sense it feelss like it's more communication than anything, a worldview or conception. I think there are several ways of understanding nature, math being just one of them.

Quote:
 Originally Posted by Archer What do you all think about the notion that maths, being perfect a perfect system (100% consistent, no issues, contradictions, etc) cannot be man-made?
I'd say first: Is math perfect? How can we know? Is it complete, growing, changing? Then I'd say: why can't humanity create or conceive of something perfect?
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#37
July 25th, 2013, 09:33 AM
 Overlord Drakow -CONQUERER Join Date: Oct 2007 Location: Hell Nature: Serious
Quote:
 Originally Posted by Scarf It feels like mathematics is something invented because you can do things in math that have no correspondence in the real world. Where do negative numbers exist in nature? Imaginary numbers? (Serious question - I'm not a math person.) Like language, we can create words (and conceptions) of things that don't or can't exist. Imaginary numbers are used a lot in engineering principles and such. I did a course on them in my final year of university but a lot of the stuff I covered escapes me now haha. As for negative numbers, think about opposing forces. So you're driving your car and you have a forward driving force and the backwards force is the resistance. This backwards force can be considered as a negative number to represent a force acting in the opposite direction to the driving force - it all depends on how you choose to label your diagram when you do these kinds of calculations. Feels to me like mathematics is an interpretation of nature. Nature is discovered, but nature is not math. Math is the language we use to understand nature. In that sense it feelss like it's more communication than anything, a worldview or conception. I think there are several ways of understanding nature, math being just one of them.
My response is in red and I agree with what you say in your second paragraph, except for the double s on the word 'feels' :p
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#38
July 26th, 2013, 05:22 PM
 Arlo Join Date: Dec 2012
Quote:
 Originally Posted by gimmepie The problem with that, as I have said before, is that you are all confusing mathematics with what it describes.
Who are you responding to?

I can't see even one post since your last one - not a single one - that doesn't in fact very deliberately and pointedly distinguish between those two things.
#39
July 27th, 2013, 08:23 AM
 gimmepie The Seeker of Pies Join Date: May 2012 Location: Australia Age: 18 Gender: Male Nature: Mild
@Arlo - I was responding to Omicron and Archer, but really it applies to anyone who is trying to say that the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language. They, and everyone else, are of course entitled to their opinions but I, as you may have noticed, disagree to a rather large degree.

Sorry about being unclear as to who that was directed at.
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#40
July 27th, 2013, 01:45 PM
 Arlo Join Date: Dec 2012
Quote:
 Originally Posted by gimmepie @Arlo - I was responding to Omicron and Archer, but really it applies to anyone who is trying to say that the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language. They, and everyone else, are of course entitled to their opinions but I, as you may have noticed, disagree to a rather large degree. Sorry about being unclear as to who that was directed at.
Quote:
 Originally Posted by Archer Maths is a perfect self-contained system. We represent it with an invented language and numeracy system to model things that we perceive and concepts we've invented, but maths itself is not invented.
Quote:
 Originally Posted by Omicron Definitely not invented, discovered. Math exists in nature and many examples can be made, like fibonacci's series in plants or nautilus. As Livewire stated above, the way we express math was invented, but math itself was just discovered.
As I already noted, both of those responses, along with all the other responses at least since your last one, very explicitly point out the distinction between the two things. They very pointedly do NOT claim that "the naturally occurring patterns and "rules" that we describe through mathematics is the same as the language." In fact, at least in the past three weeks or so (I haven't bothered to read back further than that), NOBODY has made that claim.

??
#41
July 27th, 2013, 02:35 PM
 Awkward. #britanna Join Date: May 2012 Age: 17 Gender: Male Nature: Sassy
Math was invented.

You could argue that the world was set up to have math in mind but honestly, that doesn't make sense. Humans didn't know how to explain things so they made up stuff for it. Do you honestly think that the symbol for 8 was passed down from the beginning of time, when there was nothing? No, humans made it up because they wanted to know what "eight" would look like. They also invented "eight", mind you. If math hadn't been invented, I could easily just point to the edge of my laptop and call that an octaganoganatriclogon and everyone would believe me no matter how ridiculous it sounds because it explains something that people otherwise couldn't explain.

Here's a good example: a human measures the distance between two trees and says that it's a yard. People believe it because it explains what the distance between the trees is, thus making the yard measurement permanently written in the human mind. In reality, it's just two trees far apart with an indiscernible distance between them, and it's never really known if it's a yard, an inch, a mile, or if everyone is just crazy for giving a random name to something because they didn't understand it.
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Last edited by Awkward.; July 27th, 2013 at 02:41 PM.