From Closer to Truth: Is mathematics invented or discovered?

_{Denyse O'Leary

January 16, 2021

Intelligent Design, Mathematics}

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Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans-like chisels and hammers and pieces of music? Or is mathematics discovered-always out there, somewhere, like mysterious islands waiting to be found? Featuring interviews with Roger Penrose, Mark Balaguer, Gregory Chaitin, Stephen Wolfram, and Frank Wilczek.

See also: Things exist that are unknowable: A tutorial on Chaitin’s number

Comments

Last post a month ago but the concept of math being invented or discovered came up today by someone associated with ID, William Briggs.
A Simple Proof Mathematics Is Discovered And Not Invented
https://wmbriggs.com/post/34710/jerry_{February 24, 2021
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ET: That doesn’t follow. Try again. Or get an education and come back when you are finished. Well, spell it out for us and make sure your position is clear.JVL_{January 21, 2021
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JVL said:
Ah, but on the other thread you fell on the side of mathematics being abstract and therefore ‘of the mind’ which is saying mathematics is invented.
You're assuming something about what the mental world is here that may not be the case. The argument is that the mental world (or, as other here would say, some of it) is real and that we discover things about it or in it.William J Murray_{January 21, 2021
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JVL:
Ah, but on the other thread you fell on the side of mathematics being abstract and therefore ‘of the mind’ which is saying mathematics is invented.
That doesn't follow. Try again. Or get an education and come back when you are finished.ET_{January 21, 2021
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ET: Definitely discovered. Mathematics was used to intelligently design the universe. That is why the laws that govern nature are so readily described by mathematics. Ah, but on the other thread you fell on the side of mathematics being abstract and therefore 'of the mind' which is saying mathematics is invented. Which is it? Or are you saying mathematics was invented by some supernatural being and is now being discovered by humans?JVL_{January 21, 2021
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Most of mathematics is based on abstractions that do not exist in nature. For example perfect circles don't exist in nature, therefore pi was conceptualized in antiquity based on something that does not exist but yet has many applications in other areas that do exist, in nature such as the propagation of electromagnetism in free space. Even Ohm's law does not exist in nature because perfect resistors do not exist, in nature nor in technology, nor do perfect capacitors nor inductors. Same thing for Hooke's law, because perfectly linear (constant) spring compliance does not exist. Many examples from statistics are illustrations of things that do not exist in nature, but yet are attempts to analyze devices actually operating in nature. For example, in engineering, spectral density S(%omega) is the average of an ensemble of sample functions, each of which is the Fourier transform of a sample from a stationary process. This is a multi-level example, because such ensembles do not exist, they are abstractions for describing the behavior of human devised systems operating in nature. Even as abstractions, application of the concept of 'stationary' can be problematic as an abstraction, because when the lengths of sample functions in the ensemble are short enough, a stationary process begins to take on the properties of a non-stationary process in the analysis. And an even worse problem is that each sample in the ensemble must be extracted from the process by a windowing function (the abstract set of suitable windowing functions is a set of abstractions) which corrupts the spectra from the Fourier transforms. And then of course, the mean of an ensemble of functions does not exist in nature.groovamos_{January 21, 2021
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Definitely discovered. Mathematics was used to intelligently design the universe. That is why the laws that govern nature are so readily described by mathematics.ET_{January 18, 2021
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Viola Lee: I don't think there can be a definitive answer. I fall on the 'discovered' side of the discussion but it doesn't affect the truth of the mathematics we know or how we will go about 'discovering' more.JVL_{January 18, 2021
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I agree. There's a lot of various assumptions about what the words "invented" and "discovered" in this context even mean, which is why most of the people in the video said "some of this, some of that". I don't fault them for not having definitive answers.Viola Lee_{January 17, 2021
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Questions demanding binary answers are inherently unstable.Belfast_{January 17, 2021
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Well, I watched that. Could have been summed up in about 5-10 minutes of reading, which would have been better, but basically went over the options and settled on "some of this, some of that, bit of both"" as the answer, which is what usually happens. Penrose is a strong Platonist. My view is more like Wolfram's and Wilczek's. YMMVViola Lee_{January 17, 2021
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@ 1 hard to describe how you answered that but that was a very impressive reply I have to agreeAaronS1978_{January 17, 2021
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A core of structure and quantity is embedded in the framework for any possible world and awaits discovery.kairosfocus_{January 17, 2021
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Polista's reply is interesting. I don't necessarily agree with everything he said, but I think he's right to question the question.Viola Lee_{January 17, 2021
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Neither. It's not quite the right question. Math and language are not separate. Both are ways of describing and remembering and communicating the current condition and motion of Nature. Both are ways of building an internal picture that can be used as a predictor or comparator. Both have hard-wired sections in our brain, and both are found at every level of every nervous system. All neurons describe and compare and communicate. Every neuron communicates its descriptions as a symbolic code, usually a train of pulses modulated in various ways. (aka music.) So the better question is: Are describing and communicating parts of Nature? Answer: Both are inherent in all life, but not inherent in the inanimate world outside of living things.polistra_{January 17, 2021
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