Is math invented or discovered?
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22-10-2016, 08:40 PM
RE: Is math invented or discovered?
(22-10-2016 04:35 PM)tomilay Wrote:  
(22-10-2016 03:47 PM)Gloucester Wrote:  Hmm, as I think has been said numeric symbols where certainly invented to fill a need as trading got more complex. From that moment it was development, stepwise as realosation and inspiration opened up new conjectures, concepts and avenues over thousands of years.

The real big step after numbers was into abstract maths, not motivated by the physical arts, commercial, military etc, but for the sake of maths and intellect alone.

Bit like the wheel, was it invented as is or did it develop from the roller, the "bobbin" (roller thinned in the middle to miss stones etc), the rolling axle (two "disks" rammed onto a thin branch) then to a fixed axle with rotating discs st the end?

Quite difficult to think of anything that was truly invented, as is, and not a development of or inspired by a simpler, or combination of earlier or simpler, item(s) or idea(s).

True. It happened over an extended period. The abstract math and the like...it is analogous to poetry. Just like language, math can convey imagination and creativity.

Indeed. When I taught high school math and physics, sometimes when solving problems I could see the beauty of it. I see it when working problems in my free time, even now. Turns out that mathematical beauty excites the same regions of the brain that artistic beauty excites. It may take as much time and effort to learn to paint or make some other objet d'art as it does to learn enough mathematics to see the beauty. I know that the mathematics (and physics) that I studied and learned certainly required enough effort. Then again, the realization of a complex design for a mechanical object I've designed provides the same sense of satisfaction and beauty.
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22-10-2016, 10:55 PM (This post was last modified: 22-10-2016 11:04 PM by theBorg.)
RE: Is math invented or discovered?
(20-10-2016 10:54 AM)unknowndevil666 Wrote:  ...... I go a step further and say that the universe is basically mathematical. ......

I see. It is known "TOE". Would you like to discuss with us this:

Mathematical universe hypothesis
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23-10-2016, 02:43 AM
RE: Is math invented or discovered?
(22-10-2016 08:40 PM)Fireball Wrote:  
(22-10-2016 04:35 PM)tomilay Wrote:  True. It happened over an extended period. The abstract math and the like...it is analogous to poetry. Just like language, math can convey imagination and creativity.

Indeed. When I taught high school math and physics, sometimes when solving problems I could see the beauty of it. I see it when working problems in my free time, even now. Turns out that mathematical beauty excites the same regions of the brain that artistic beauty excites. It may take as much time and effort to learn to paint or make some other objet d'art as it does to learn enough mathematics to see the beauty. I know that the mathematics (and physics) that I studied and learned certainly required enough effort. Then again, the realization of a complex design for a mechanical object I've designed provides the same sense of satisfaction and beauty.

Yes the beauty of e=mc^2 and the fact that it took a million years or so's worth of ideas and their development to get to it...

Tomorrow is precious, don't ruin it by fouling up today.
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24-10-2016, 08:50 PM
RE: Is math invented or discovered?
(22-10-2016 10:55 PM)theBorg Wrote:  
(20-10-2016 10:54 AM)unknowndevil666 Wrote:  ...... I go a step further and say that the universe is basically mathematical. ......

I see. It is known "TOE". Would you like to discuss with us this:

Mathematical universe hypothesis

I'm aware of Tegmark's ideas but I haven't read up on them too much, though I intend to.
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24-10-2016, 09:32 PM
RE: Is math invented or discovered?
(21-10-2016 01:19 AM)Gloucester Wrote:  I still contend that accounting systems were the first motivation for a recorded counting system. Once you start something like that . . .

https://en.m.wikipedia.org/wiki/History_...al_systems

Glad you didn't find my response inflammatory, I was feeling bitter and didn't feel like conjuring up a proper response.

I don't contest that us humans created our own mathematical systems and I do find the subject particularly interesting (especially when computer science gets involved). What I question is the so-called "unreasonable effectiveness of mathematics". If mathematics is simply a human creation, especially one initially created to count stuff, how does it then turn out that mathematics can accurately describes the fundamental nature of the universe?

It seems most likely that there is inherently some kind of order that the universe follows that we can observe. Our mathematical systems are developed to try to match that order that we observe, best example being geometry, and by using logic within our systems, we can discover order that does exist in the universe. Where do the first number systems fit into this? The concept of value is the easiest, most fundamental pattern that we observed and were able to work with. Indeed, animals have an intuitive sense of size and number.

I could continue further, but I think it would be better to stop here before treading any deeper into the abstract.
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24-10-2016, 09:51 PM
RE: Is math invented or discovered?
(21-10-2016 12:29 AM)Mathilda Wrote:  You can say the same thing about language. Maths is just a more concise way to describe things. Like logic. Where does Maths end and Logic begin? Is Logic built into the universe? And if so, what form of logic? Predicate calculus? Fuzzy logic? What form of Maths are you talking about? Geometry? Statistics? Calculus? What about computer programming languages?

They're all invented languages and we're inventing new ones to solve new problems.

Like I've said, we create our own mathematical systems like geometry and calculus. But it is in the unexpected use of the systems in understanding reality that implies there is more meaning to be found here than simply calling them useful tools, like a hammer or saw. When I speak of mathematics, I am talking of the order that allows any of our mathematical systems to work. You say that we invent languages to solve new problems, but often problems are solved by languages thought to be purely abstract. The appearance of mathematical concepts in nature suggests that what we call mathematics exists outside of our own invention.

I'm getting tired now and I feel like I'm rambling so I'm going to stop.
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24-10-2016, 09:59 PM
RE: Is math invented or discovered?
(24-10-2016 09:32 PM)unknowndevil666 Wrote:  
(21-10-2016 01:19 AM)Gloucester Wrote:  I still contend that accounting systems were the first motivation for a recorded counting system. Once you start something like that . . .

https://en.m.wikipedia.org/wiki/History_...al_systems

Glad you didn't find my response inflammatory, I was feeling bitter and didn't feel like conjuring up a proper response.

I don't contest that us humans created our own mathematical systems and I do find the subject particularly interesting (especially when computer science gets involved). What I question is the so-called "unreasonable effectiveness of mathematics". If mathematics is simply a human creation, especially one initially created to count stuff, how does it then turn out that mathematics can accurately describes the fundamental nature of the universe?

It seems most likely that there is inherently some kind of order that the universe follows that we can observe. Our mathematical systems are developed to try to match that order that we observe, best example being geometry, and by using logic within our systems, we can discover order that does exist in the universe. Where do the first number systems fit into this? The concept of value is the easiest, most fundamental pattern that we observed and were able to work with. Indeed, animals have an intuitive sense of size and number.

I could continue further, but I think it would be better to stop here before treading any deeper into the abstract.

Bolding mine. Mathematics fits the observations because we make up equations that do that. That's one of the points of using mathematics- to make it describe what is happening! One of my favorite (apocryphal, I'm sure- us physicists learn a ton of math- I myself have 38 units of math in a degree that required 120 semester units for a B Sc in physics- I gradutaed with more units than necessary) stories is the time an experimental physicist went to the math department, trying to figure some reason for the data. The mathematician looked at the graphical data, and said, "Simple, here's an equation that describes this." The physicist looks at the graph, realizes it's upside down, and flips it over. The mathematician says, OK, here is an equation that describes this curve...

FWIW, physicists are providing insights into Number Theory that mathematicians hadn't thought of-

http://empslocal.ex.ac.uk/people/staff/m...rising.htm

See also, Ultraviolet Catastrophe-

https://en.wikipedia.org/wiki/Ultraviolet_catastrophe

Curve fitting FTW!
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25-10-2016, 01:27 AM
RE: Is math invented or discovered?
(24-10-2016 09:51 PM)unknowndevil666 Wrote:  
(21-10-2016 12:29 AM)Mathilda Wrote:  You can say the same thing about language. Maths is just a more concise way to describe things. Like logic. Where does Maths end and Logic begin? Is Logic built into the universe? And if so, what form of logic? Predicate calculus? Fuzzy logic? What form of Maths are you talking about? Geometry? Statistics? Calculus? What about computer programming languages?

They're all invented languages and we're inventing new ones to solve new problems.

Like I've said, we create our own mathematical systems like geometry and calculus. But it is in the unexpected use of the systems in understanding reality that implies there is more meaning to be found here than simply calling them useful tools, like a hammer or saw. When I speak of mathematics, I am talking of the order that allows any of our mathematical systems to work. You say that we invent languages to solve new problems, but often problems are solved by languages thought to be purely abstract. The appearance of mathematical concepts in nature suggests that what we call mathematics exists outside of our own invention.

And what of all the problems that can't be adequately solvdd using any form of known Maths, logic or language? We then create a new language or model to work with that can describe the problem and be manipulated more concisely. It happens all the time.

Saying that Maths exist outside of a concept has no explanatory power. What exactly are these Mathematical laws made from? How do they have the universal effect that they do?
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25-10-2016, 03:44 AM
RE: Is math invented or discovered?
(25-10-2016 01:27 AM)Mathilda Wrote:  
(24-10-2016 09:51 PM)unknowndevil666 Wrote:  Like I've said, we create our own mathematical systems like geometry and calculus. But it is in the unexpected use of the systems in understanding reality that implies there is more meaning to be found here than simply calling them useful tools, like a hammer or saw. When I speak of mathematics, I am talking of the order that allows any of our mathematical systems to work. You say that we invent languages to solve new problems, but often problems are solved by languages thought to be purely abstract. The appearance of mathematical concepts in nature suggests that what we call mathematics exists outside of our own invention.

And what of all the problems that can't be adequately solvdd using any form of known Maths, logic or language? We then create a new language or model to work with that can describe the problem and be manipulated more concisely. It happens all the time.

Saying that Maths exist outside of a concept has no explanatory power. What exactly are these Mathematical laws made from? How do they have the universal effect that they do?

You have gone a way to explain something that my mind cannot quite develop into a neat package. But it goes something like this...

All the maths has actually existed since the Big Bang (at least), e=mc^2 has always been there, just took Albert to recognise it and give it a description that others could also understand.

Yes, it is the language that is most difficult for some and in some cases, such as multi-dimensional space, there seems to be no "lingua franca" translation available for the likes of me!

With regards to curve fitting in data plots: when we got our first PCs at work, with Excell, we started plotting our data there - instead if with paper, pencil and flexi curve (still got the latter, comes in useful in DIY!). Offered a selection of fits for the data, linear, power, log etc, I was told, "Just pick the one that looks best"!

Tomorrow is precious, don't ruin it by fouling up today.
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25-10-2016, 04:23 AM
RE: Is math invented or discovered?
I'm not a physicist or mathematician but I read in Einstein's biography that he had to develop a form of non-Euclidean geometry to describe his general theory of relativity, the Einstein tensor.

That's not to argue that the universe doesn't work in a particular way, but we have to develop a language to describe it. Maybe there was a better way to describe it which someone else might yet devise, who knows?

I can speak as a computer scientist though, CS being an applied form of Maths and logic. I research Artificial Intelligence. I create strong AI. The only natural form that we have of this involves the use of neurons which work in a particularl way. There are good reasons why nature used neurons, but it's very difficult to understand how networks of neurons function and why they work the way the way they do. And consequently, this also means that it's very difficult to actually work with artificial biologically plausible neural networks and get them to do something different, to engineer them.

Instead I describe them using a dynamical systems approach. I did this out of necessity. I devised my own mathematical model that describes how the networks function in a way that allows me to reason about them far more simply and successfully. It abstracts away all the unnecessary detail. In fact I've now spent the last 6 years developing an implementation based on the dynamical systems concept that is more useable than biologically plausible neural networks. Both dynamical systems and neural networks can do exactly the same thing, and just as well as each other it seems, but the former is easier to understand and consequently to play with.
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