Mathematics:

For the love of the pursuit of knowledge

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Miles
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Mathematics:

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Post by Miles »

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Invented or Discovered?





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Re: Mathematics:

Post #2

Post by Bust Nak »

[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.

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Re: Mathematics:

Post #3

Post by Miles »

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.
Agreed. "Mathematics; the study of numbers, shapes and patterns"* plus its notation, ( + = ) 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.


* Source: Wikipedia


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Re: Mathematics - Invented or Discovered

Post #4

Post by elijahpne »

[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:
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.
- Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... hematician)

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
From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
- The Mysterious Universe, p. 134, 1930 ed. Wikiquote, James Jeans ( https://en.wikiquote.org/wiki/James_Jeans )
Last edited by elijahpne on Tue Jun 22, 2021 4:20 am, edited 1 time in total.

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Re: Mathematics:

Post #5

Post by JoeyKnothead »

Miles wrote: Tue Jun 08, 2021 4:38 am .


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Invented or Discovered?




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Scratched out by chickens!

Mathematics is using symbols to reflect reality, kinda like how words are symbols used to express thought.
Discovery is finding things that exist.
Invention is using things discovered.

Create that path and engineer a metamorphosis.

- William

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Re: Mathematics - Invented or Discovered

Post #6

Post by Miles »

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:
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.
- Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... hematician)

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
From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
- The Mysterious Universe, p. 134, 1930 ed. Wikiquote, James Jeans ( https://en.wikiquote.org/wiki/James_Jeans )
As intimated, first you have to present convincing evidence that god exists before any of this matters.


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Re: Mathematics - Invented or Discovered

Post #7

Post by bluegreenearth »

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:
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.
- Dirac, God is a Mathematician ( https://reasonandscience.catsboard.com ... hematician)

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
From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
- The Mysterious Universe, p. 134, 1930 ed. Wikiquote, James Jeans ( https://en.wikiquote.org/wiki/James_Jeans )
What mathematical discovery would you expect to find if God does not exist?

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Re: Mathematics - Invented or Discovered

Post #8

Post by elijahpne »

[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:
... 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 )
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.

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:

Image
bbc.com (http://www.bbc.com/earth/story/20160120 ... c-equation)

By the way, that equation
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)
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)

A "mathematical theory of great beauty and power" indeed!

Interestingly, the article Physics + Dirac = poetry said:
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
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!

No other proof is probably greater.
-------------------------------------
Consider the implications of these other quotes as well . . .
Braun, Werner von
Space scientist Dr. Wernher von Braun, in awe of the laws governing the universe, had this to say: “Manned space flight . . . has opened for us thus far only a tiny door for viewing the awesome reaches of space. Our outlook through this peephole at the vast mysteries of the universe only confirms our belief in its creator.” - g99 6/22 pp. 7-8 Did It Just Happen, or Was It Created? ( https://wol.jw.org/en/wol/d/r1/lp-e/101999442#h=28)
Einstein, Albert
I supposed that the notion of a beginning in time annoyed Einstein because of its theological implications. He had well-defined feelings about God but not as the Creator. For Einstein, the existence of God was proved by the laws of nature; that is, that there was order in the universe, and man could discover it. - The Readers Digest, July 1980 p. 51 Have Astronomers Found God? (http://hiebertglobalcenter.org/blog/wp- ... nd-God.pdf)
Einstein, Albert - Unified Field Theory
“The scientist’s religious feelings take the form of rapturous amazement at the harmony of Natural law, which reveals an Intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection.” - Albert Einstein > Quotes > Quotable Quotes (https://www.goodreads.com/quotes/68179- ... -rapturous)
Hoyle, Fred
The “faith” of the famous physicist Fred Hoyle, however, was admittedly shaken later during his life. In the 1980’s, he confessed: “A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.” - g99 6/22 pp. 7-8 Did It Just Happen, or Was It Created? (https://wol.jw.org/en/wol/d/r1/lp-e/101999442#h=20)
Jeans, James - The Mysterious Universe (1930), p. 134
"From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician." - The Mysterious Universe, p. 134, 1930 ed. Wikiquote, James Jeans (
https://en.wikiquote.org/wiki/James_Jeans
)
Rousseau, P - De l’atome a l’etoile (From Atom to Star)
Then what of universal mathematics? All scientists recognize the following fact noted by P. Rousseau in the book De l’atome a l’etoile (From Atom to Star): “Governed by geometry from its smallest to its largest parts, the universe really reveals itself as a mathematical structure.” - g71 8/8 p. 5 The Order in the Universe - from Where does it Come? (https://wol.jw.org/en/wol/d/r1/lp-e/101971560#h=26)

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Re: Mathematics - Invented or Discovered

Post #9

Post by Miles »

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:
... 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 )
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.

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 equation
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)

Interesting that you would quote Dirac as supporting the notion of a god when he was an atheist and would no more credit god than I would credit Donald Trump with bringing peace to Washington, DC on January 6th.

"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.[10]

Werner Heisenberg[11] recollects a friendly conversation among young participants at the 1927 Solvay Conference about Einstein and Planck's views on religion. Wolfgang Pauli, Heisenberg and Dirac took part in it. Dirac's contribution was a poignant and clear criticism of the political manipulation of religion, that was much appreciated for its lucidity by Bohr, when Heisenberg reported it to him later. Among other things, Dirac said: "I cannot understand why we idle discussing religion. If we are honest - and as scientists honesty is our precise duty - we cannot help but admit that any religion is a pack of false statements, deprived of any real foundation. The very idea of God is a product of human imagination. … I do not recognize any religious myth, at least because they contradict one another. …" Heisenberg's view was tolerant. Pauli had kept silent, after some initial remarks, but when finally he was asked for his opinion, jokingly he said: "Well, I'd say that also our friend Dirac has got a religion and the first commandment of this religion is 'God does not exist and Paul Dirac is his prophet.'" Everybody burst into laughter, including Dirac."
source

My emphasis And Dirac speaking:

"I cannot understand why we idle discussing religion. If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way."
source



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Re: Mathematics - Invented or Discovered

Post #10

Post by elijahpne »

[Replying to Miles in post #9]

Miles wrote:
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.
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 -

The eminent scientist, Fred Hoyle, himself an atheist discounted Nature and attributed it directly to "a superintellect". Note what the Wikipedia article about him says:
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
As to why others would conclude differently, Hoyle remarked:
“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

CHANCE AS USED METAPHORICALLY
Something to ponder -
"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)
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.

Good Day!
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2 Cor 10:3-5 For though we walk in the flesh, we do not wage warfare according to what we are in the flesh. For the weapons of our warfare are not fleshly, but powerful by God for overturning strongly entrenched things. For we are overturning reasonings and every lofty thing raised up against the knowledge of God.

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