Poll

pick one, please

math was invented
14 (43.8%)
math was discovered
4 (12.5%)
it's a little bit of both
8 (25%)
don't know
2 (6.3%)
don't care
4 (12.5%)

Total Members Voted: 32

Author Topic: the math poll  (Read 35866 times)

rong

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the math poll
« on: October 10, 2009, 12:34:48 am »
saw this

and decided it was as good an excuse to see what the PD'ers thought about this.

i used to be wholeheartedly convinced that mathematics was always laying around, waiting to be discovered.  nowadays, i'm not so sure.

i'd venture to guess some of you folks have opinions on this and i'd like to hear them.

(if this has been discussed already, i'd appreciate a link to the thread.)
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Kai

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Re: the math poll
« Reply #1 on: October 10, 2009, 01:53:04 am »
saw this

and decided it was as good an excuse to see what the PD'ers thought about this.

i used to be wholeheartedly convinced that mathematics was always laying around, waiting to be discovered.  nowadays, i'm not so sure.

i'd venture to guess some of you folks have opinions on this and i'd like to hear them.

(if this has been discussed already, i'd appreciate a link to the thread.)

What sort of math? I strongly believe that, for example, Newton invented calculus rather than discovering it, but basic addition and subtraction are probably just extentions of our mind's understanding of units and counting.
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Re: the math poll
« Reply #2 on: October 10, 2009, 02:29:59 am »
Math is a language.

Therefore, it was invented.
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Re: the math poll
« Reply #3 on: October 10, 2009, 04:41:37 am »
Mathematical notations and languages were certainly invented by humans. But the relationships they describe were not.

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Re: the math poll
« Reply #4 on: October 10, 2009, 11:06:38 am »
Mathematical notations and languages were certainly invented by humans. But the relationships they describe were not.

Yeah, they were.  Lo5 writ large.

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Re: the math poll
« Reply #5 on: October 10, 2009, 05:30:39 pm »
saw this

and decided it was as good an excuse to see what the PD'ers thought about this.

i used to be wholeheartedly convinced that mathematics was always laying around, waiting to be discovered.  nowadays, i'm not so sure.

i'd venture to guess some of you folks have opinions on this and i'd like to hear them.

(if this has been discussed already, i'd appreciate a link to the thread.)

What sort of math? I strongly believe that, for example, Newton invented calculus rather than discovering it, but basic addition and subtraction are probably just extentions of our mind's understanding of units and counting.

wouldn't you agree, though, that the slope of the equation f(x) = x^2 is 2x whether calculus had been invented or not? 

maybe another way to get at what i am asking is, pi = 3.14159. . . - i don't really think that number was invented.  (although, i heard in chicago, pi is, by law, 3.14).  i would argue that pi was discovered. 

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Re: the math poll
« Reply #6 on: October 10, 2009, 05:46:35 pm »
saw this

and decided it was as good an excuse to see what the PD'ers thought about this.

i used to be wholeheartedly convinced that mathematics was always laying around, waiting to be discovered.  nowadays, i'm not so sure.

i'd venture to guess some of you folks have opinions on this and i'd like to hear them.

(if this has been discussed already, i'd appreciate a link to the thread.)

What sort of math? I strongly believe that, for example, Newton invented calculus rather than discovering it, but basic addition and subtraction are probably just extentions of our mind's understanding of units and counting.

wouldn't you agree, though, that the slope of the equation f(x) = x^2 is 2x whether calculus had been invented or not? 
The function defines the relationship between two things which we identify as measurable units.

maybe another way to get at what i am asking is, pi = 3.14159. . . - i don't really think that number was invented.  (although, i heard in chicago, pi is, by law, 3.14).  i would argue that pi was discovered. 
It's interesting you should mention PI. Does it exist as a measurement, anywhere in the universe? You can't make a "perfect circle" out of any material, much for the same reasons as there is no real answer for where the tip of your finger ends and the rest of the universe begins.

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Re: the math poll
« Reply #7 on: October 10, 2009, 06:42:18 pm »
saw this

and decided it was as good an excuse to see what the PD'ers thought about this.

i used to be wholeheartedly convinced that mathematics was always laying around, waiting to be discovered.  nowadays, i'm not so sure.

i'd venture to guess some of you folks have opinions on this and i'd like to hear them.

(if this has been discussed already, i'd appreciate a link to the thread.)

What sort of math? I strongly believe that, for example, Newton invented calculus rather than discovering it, but basic addition and subtraction are probably just extentions of our mind's understanding of units and counting.

wouldn't you agree, though, that the slope of the equation f(x) = x^2 is 2x whether calculus had been invented or not? 

maybe another way to get at what i am asking is, pi = 3.14159. . . - i don't really think that number was invented.  (although, i heard in chicago, pi is, by law, 3.14).  i would argue that pi was discovered. 



No, the language of math was definitely invented, but they were invented to describe phenomena in the universe in a more precise and quantitative manner, and the relationships between things (which do exist, unless your the sort that wants a barstool), because contrary to what ND Tyson says the universe does not speak in math, it just happens. As roger said, math is a language, a very useful one, but people still had to invent it.

For example, the number pi doesn't exist all by itself. Thats a concept used to describe a relationship we see between the radius of a circle and its circumference, a circle being a plane where all edges are equidistant from the center. It just so happens that that particular relationship is in the universe, and we use pi to describe it, but pi doesn't exist in the same way that the relationship does.

Not even going into bases and all that.
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Re: the math poll
« Reply #8 on: October 10, 2009, 07:03:38 pm »
Mathematical notations and languages were certainly invented by humans. But the relationships they describe were not.

Yeah, they were.  Lo5 writ large.

You sure? How so?

I mean, I can imagine this to be the case, from the point of view that all is Chaos and we separate it into Order and Disorder with our, um, "reality tunnels". You know what I mean. So yeah, the relationships that mathematics describes for us could very well be a result of this, and therefore the Lo5.

However, how can we know for sure? And IMO, there is something about mathematics that reeks as very fundamental to reality, in a way. And really, I wouldn't dare to say what comes first, the Lo5 Chaos=Order+Disorder shtick or Mathematics.

Math is a language.

Therefore, it was invented.

You said this before, I still don't understand. You mean, Math is just a language, and nothing more, right?

Cause then I'm going to need your definition of "language". I have a few, but they won't entirely fit around mathematics.

..

Though thinking some more, I kind of see it, the bit about language describing reality. To ask whether mathematical proofs are invented or discovered, is like asking the same question about poems, or jokes, or puns, right?

I'm still not entirely convinced, because, especially puns, they're not entirely invented, but also discovered. It goes either way, in a creative process* , you know that there are some places you can look that are more likely to contain a good idea, so are the ideas invented or discovered?

It's iffy, and if they are discovered, it means -- blablablabla does it matter anyway.

*involving language, that is. From some musicians on this board (LMNO, RWHN) I get the idea they go in a much more freeflow intuitive manner. Maybe that's something different. Maybe not, I don't have enough experience with making music.



However, an interesting question is, regardless of whether mathematics is something really fundamental in our reality or whether it's just us describing how we observe our reality to work, see they say, "mathematics is the language of nature" or "is the universal language" or something.

So the idea is, if we were to meet a bunch of aliens or their artifacts or such, we would be able to exchange some meaning, or at least recognize mathematical things, their idea of math would be the same as ours.

But if math isn't discovered, but invented, then would that still be so?
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rong

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Re: the math poll
« Reply #9 on: October 10, 2009, 07:10:18 pm »
i think there's some strawmanning going on here.  i'm not interested in whether math is real or not.  i'm trying to decide if it was invented or discovered.

i'm still convinced that PI was discovered - in the sense that someone sat down and said, "hmm - i wonder what the relationship between the radius and circumference of a circle is."  and they discovered it was PI

(i will admit to some strawmanning here too, as i fully realize that PI is not a good representative for all of mathematics)
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rong

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Re: the math poll
« Reply #10 on: October 10, 2009, 07:18:02 pm »
Mathematical notations and languages were certainly invented by humans. But the relationships they describe were not.

Yeah, they were.  Lo5 writ large.

You sure? How so?

I mean, I can imagine this to be the case, from the point of view that all is Chaos and we separate it into Order and Disorder with our, um, "reality tunnels". You know what I mean. So yeah, the relationships that mathematics describes for us could very well be a result of this, and therefore the Lo5.

However, how can we know for sure? And IMO, there is something about mathematics that reeks as very fundamental to reality, in a way. And really, I wouldn't dare to say what comes first, the Lo5 Chaos=Order+Disorder shtick or Mathematics.

Math is a language.

Therefore, it was invented.

You said this before, I still don't understand. You mean, Math is just a language, and nothing more, right?

Cause then I'm going to need your definition of "language". I have a few, but they won't entirely fit around mathematics.

..

Though thinking some more, I kind of see it, the bit about language describing reality. To ask whether mathematical proofs are invented or discovered, is like asking the same question about poems, or jokes, or puns, right?

I'm still not entirely convinced, because, especially puns, they're not entirely invented, but also discovered. It goes either way, in a creative process* , you know that there are some places you can look that are more likely to contain a good idea, so are the ideas invented or discovered?

It's iffy, and if they are discovered, it means -- blablablabla does it matter anyway.

*involving language, that is. From some musicians on this board (LMNO, RWHN) I get the idea they go in a much more freeflow intuitive manner. Maybe that's something different. Maybe not, I don't have enough experience with making music.



However, an interesting question is, regardless of whether mathematics is something really fundamental in our reality or whether it's just us describing how we observe our reality to work, see they say, "mathematics is the language of nature" or "is the universal language" or something.

So the idea is, if we were to meet a bunch of aliens or their artifacts or such, we would be able to exchange some meaning, or at least recognize mathematical things, their idea of math would be the same as ours.

But if math isn't discovered, but invented, then would that still be so?

000 - thanks.  it never occurred to me to take the "language" approach and run with it - into puns and music, etc.

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Re: the math poll
« Reply #11 on: October 11, 2009, 08:11:36 am »


You said this before, I still don't understand. You mean, Math is just a language, and nothing more, right?

Cause then I'm going to need your definition of "language". I have a few, but they won't entirely fit around mathematics.


A means by which to describe and/or communicate a concept.
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Re: the math poll
« Reply #12 on: October 11, 2009, 05:44:07 pm »
To throw my own $.02 - mathematics is a language that allows us to express the relationships between things we call "numbers" in a given system. (Higher mathematics gets a very broad idea of what constitutes a number.)  Mathematics can talk about geometry on a Euclidean plane or one with a non-zero Riemann curvature, arithmetic on a finite, countably infinite, or continuously infinite set of numbers, and any number of classes of relations and functions.  Even if a mathematical system does indeed perfectly describe a system in the "real world," I'd argue for it being "invented," just as I'd argue that representational art was invented rather than discovered.

i think there's some strawmanning going on here.  i'm not interested in whether math is real or not.  i'm trying to decide if it was invented or discovered.

i'm still convinced that PI was discovered - in the sense that someone sat down and said, "hmm - i wonder what the relationship between the radius and circumference of a circle is."  and they discovered it was PI

(i will admit to some strawmanning here too, as i fully realize that PI is not a good representative for all of mathematics)

There is a subtle but significant difference between numbers and mathematics.  Mathematics is a language that deals with numbers, groups of numbers, and their relationships.  Maybe like "nouns" as opposed to "language" ?

wouldn't you agree, though, that the slope of the equation f(x) = x^2 is 2x whether calculus had been invented or not? 

The word "equation" presumes algebra, the word "function" presumes something (don't remember what the most basic field that deals with functions is.  Discrete analysis?) and the word "slope" presumes calculus.  Kind of like asking whether people had constitutional rights before the invention of writing?
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Re: the math poll
« Reply #13 on: October 11, 2009, 06:56:51 pm »
Math "is" an abstracted system that was invented to approximate certain aspects of reality. It usually does a fairly good job, but it is still an imposed pattern laid across Reality.

Pi "is" 3.14 in base 10. And ONLY in base 10.  

In base 13, Pi "is" 3.1AC1049052A2C7.
« Last Edit: October 11, 2009, 07:01:33 pm by LMNO »

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Re: the math poll
« Reply #14 on: October 11, 2009, 07:36:34 pm »
Math "is" an abstracted system that was invented to approximate certain aspects of reality. It usually does a fairly good job, but it is still an imposed pattern laid across Reality.

Pi "is" 3.14 in base 10. And ONLY in base 10.  

In base 13, Pi "is" 3.1AC1049052A2C7.

So then what's the ratio between the square of the radius of a circle and the area enclosed by the circle?
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