Invented or Discovered?
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Agreed. "Mathematics; the study of numbers, shapes and patterns"* plus its notation, (๑ + ๑ = ๒ ) was invented; and, the awareness that one thing plus another thing equals two things was a discovery of that fact, a fact that has been true ever since when, just as E=MC² has been.Bust Nak wrote: ↑Wed Jun 09, 2021 5:42 am [Replying to Miles in post #1]
Mathematics is invented to model the nature of the universe; it is said nature which is discovered. In other words, 1+1=2 is invented; one apple in a basket with another apple makes two apples is discovered.
- Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... hematician)It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it.
One could perhaps describe the situation by saying that God is a mathematician of a very high order, and he used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.
- The Mysterious Universe, p. 134, 1930 ed. Wikiquote, James Jeans ( https://en.wikiquote.org/wiki/James_Jeans )From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
Scratched out by chickens!
As intimated, first you have to present convincing evidence that god exists before any of this matters.elijahpne wrote: ↑Tue Jun 22, 2021 2:42 am [Replying to Miles in post #1]
Remarking on the role of mathematics in nature, P. A. M. Dirac states in Scientific American of May 1963:
- Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... hematician)It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it.
One could perhaps describe the situation by saying that God is a mathematician of a very high order, and he used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.
If God has "used very advanced mathematics in constructing the universe" then we can only discover them not invent them since that event precedes humans by billions of years. God may have used different notations but the essential thing in math are not the notations but the concept - the principles.
I realize, however, that such reasoning would appeal only to those who believe in God. Dirac appeared to be one and so did James Jeans - not sure though.
_________________________
Jeans, James - The Mysterious Universe (1930), p. 134- The Mysterious Universe, p. 134, 1930 ed. Wikiquote, James Jeans ( https://en.wikiquote.org/wiki/James_Jeans )From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
What mathematical discovery would you expect to find if God does not exist?elijahpne wrote: ↑Tue Jun 22, 2021 2:42 am [Replying to Miles in post #1]
Remarking on the role of mathematics in nature, P. A. M. Dirac states in Scientific American of May 1963:
- Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... hematician)It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it.
One could perhaps describe the situation by saying that God is a mathematician of a very high order, and he used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.
If God has "used very advanced mathematics in constructing the universe" then we can only discover them not invent them since that event precedes humans by billions of years. God may have used different notations but the essential thing in math are not the notations but the concept - the principles.
I realize, however, that such reasoning would appeal only to those who believe in God. Dirac appeared to be one and so did James Jeans - not sure though.
_________________________
Jeans, James - The Mysterious Universe (1930), p. 134- The Mysterious Universe, p. 134, 1930 ed. Wikiquote, James Jeans ( https://en.wikiquote.org/wiki/James_Jeans )From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
For Dirac, God is the Mathematician who constructed the fundamental physical laws of the universe through math. The greatest of all mathematicians was there before mankind appeared on the scene. And we can only discover those laws through math because he constructed it in such manner.... fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it.
One could perhaps describe the situation by saying that God is a mathematician of a very high order, and he used very advanced mathematics in constructing the universe. - Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... ematician )
This equation was even voted as the most beautiful equation by a group of physicists and mathematicians in the article You Decide: What is the most beautiful equation? written by Melissa Hogenboom for BBC (http://www.bbc.com/earth/story/20160120 ... er-written)brought together two of the most important ideas in science: quantum mechanics, which describes the behaviour of tiny objects; and Einstein's special theory of relativity, which describes the behaviour of fast-moving objects. As a result, Dirac's equation describes how particles like electrons behave when they travel close to the speed of light.
Perhaps most dramatically, the Dirac equation predicted the existence of antimatter – the mirror image of all known particles. Antimatter was later found to exist in the real world. - The Most Beautiful Equation is ... The Dirac Equation ( http://www.bbc.com/earth/story/20160120 ... c-equation)
Intelligent Design is the best proof for God. For how can fundamental physical laws constructed using math with beauty and great power tell us otherwise!Dirac discovered (italics mine: ) his beautiful equation in 1927, when he was a 25-year-old fellow at St John's college, Cambridge. - Physics + Dirac = poetry https://freerepublic.com/focus/chat/693452/posts
elijahpne wrote: ↑Sun Jun 27, 2021 11:41 pm [Replying to Miles in post #6]
It's staring us in the face!
Intelligent design - that's what is.
Such intelligence is implicit in Paul Dirac's statement mentioned in my first post which I reiterate:
For Dirac, God is the Mathematician who constructed the fundamental physical laws of the universe through math. The greatest of all mathematicians was there before mankind appeared on the scene. And we can only discover those laws through math because he constructed it in such manner.... fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it.
One could perhaps describe the situation by saying that God is a mathematician of a very high order, and he used very advanced mathematics in constructing the universe. - Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... ematician )
And in such a manner - as he described - as a "mathematical theory of great beauty and power"! How?
He had first hand knowledge. In fact he discovered it himself. This equation below - known as the Dirac Equation - has got a lot to do with it:
[
By the way, that equationbrought together two of the most important ideas in science: quantum mechanics, which describes the behaviour of tiny objects; and Einstein's special theory of relativity, which describes the behaviour of fast-moving objects. As a result, Dirac's equation describes how particles like electrons behave when they travel close to the speed of light.
Perhaps most dramatically, the Dirac equation predicted the existence of antimatter – the mirror image of all known particles. Antimatter was later found to exist in the real world. - The Most Beautiful Equation is ... The Dirac Equation ( http://www.bbc.com/earth/story/20160120 ... c-equation)
To whomever scientists - atheist or not - attribute the intelligence they found in the Universe through objective research, study and analysis, the one fact they can't deny is that there is an intelligent designer whether they attribute it to, subjectively, metaphorically: Nature, Chance, Evolution -Dirac did not believe in God. He once said: "God used beautiful mathematics in creating the world," but here he used 'God' as a metaphor for nature.
As to why others would conclude differently, Hoyle remarked:After saying "that biomaterials with their amazing measure of order must be the outcome of intelligent design." Wikipedia adds:
Though Hoyle declared himself an atheist, this apparent suggestion of a guiding hand led him to the conclusion that "a superintellect has monkeyed with physics, as well as with chemistry and biology, and ... there are no blind forces worth speaking about in nature." - Wikipedia, Fred Hoyle https://en.wikipedia.org/wiki/Fred_Hoyle
“Once we see, however, that the probability of life originating at random is so utterly miniscule as to make it absurd, it becomes sensible to think that the favorable properties of physics on which life depends are in every respect deliberate ... . It is therefore almost inevitable that our own measure of intelligence must reflect ... higher intelligences ... even to the limit of God ... such a theory is so obvious that one wonders why it is not widely accepted as being self-evident. The reasons are psychological rather than scientific.”
― Fred Hoyle, Evolution from Space (Evolution From Space Quotes, Evolution from Space Quotes by Fred Hoyle (goodreads.com) https://www.goodreads.com/work/quotes/6 ... reationism
I notice, however, we're already off on a tangent from our original discussion as to whether math is discovered or invented. This discussion about intelligent design probably belongs to another sub-forum."What is chance? Some think in terms of a mathematical probability, such as the chance involved in flipping a coin. However, that is not how many scientists use “chance” regarding the origin of life. The vague word “chance” is used as a substitute for a more precise word such as “cause,” especially when the cause is not known.
“To personify ‘chance’ as if we were talking about a causal agent,” notes biophysicist Donald M. MacKay, “is to make an illegitimate switch from a scientific to a quasi-religious mythological concept.” Similarly, Robert C. Sproul points out: “By calling the unknown cause ‘chance’ for so long, people begin to forget that a substitution was made. . . . The assumption that ‘chance equals an unknown cause’ has come to mean for many that ‘chance equals cause.’”
Thus, if one speaks about life coming about by chance, he is saying that it came about by a causal power that is not known. Could it be that some are virtually spelling “Chance” with a capital letter—in effect saying, Creator? - Evolution - Fact or Fiction by Nicholas Nurston, Chapter 10 (https://books.google.com.ph/books?id=bQ ... se&f=false)