CoxRox asked me to assess the following quote of John Polkinghorne (christian reverend and former particle physicist):

Polkinghorne Wrote:One of the fascinating things about the physical world is that its fundamental structure seems always to be expressed in beautiful mathematics. To me that suggests that there is a Mind behind the structure of the world, and that our minds are somehow attuned to that Mind.

This indeed touches on a subject that interests and puzzles me. Polkinghorne's fascination is akin to the belief that mathematics is the language of nature. This is a view held over the centuries by many prominent scientists and in it most elementary form it asserts that the language of science must necessarily be mathematical. Some even romantically dream of mathematics as something that exists independently of human beings, something that structures our actual physical universe and any possible universe. It should be pointed out however that mathematics is built on formal definitions and these make use of words and symbols that have meaning only in terms of human experience. To state that mathematics is the language of god is pretending to know the mind of god, a rather bold assertion even from a religious viewpoint. All we can say is that mathematics is a formal language developed and understood by humans.

It may be helpful to compare the religious centered view of Polkinghorne on the matter with the science centered view of Einstein. But first some clarification is needed on the religious views of Einstein to place his views in the right context. A popular quote from Einstein on religion is the following:
"I believe in Spinoza's God who reveals Himself in the orderly harmony of what exists, not in a God who concerns himself with fates and actions of human beings." — Albert Einstein
(New York Times, 25 April 1929, p. 60, col. 4. Ronald W. Clark)

Years later he expanded on this in a letter: "I can understand your aversion to the use of the term 'religion' to describe an emotional and psychological attitude which shows itself most clearly in Spinoza," he wrote. "[But] I have not found a better expression than 'religious' for the trust in the rational nature of reality that is, at least to a certain extent, accessible to human reason." So Einstein by using religious terms expresses his unsubstantiated trust in the rational nature of reality. He had found no rational argument to back up the claim that the universe indeed should have a rational nature and the trust on that rational nature he identifies as in essence a leap of faith. And therefore, he concludes, a religious terminology is suited. Notwithstanding this religious terminology Einstein denies any purpose in nature, refutes the idea of a personal god, life after death, the concept of a soul seperate from the body. With Einstein god is the order and lawfulness of the universe itself. This often confuses people.

For me the key point here is that Einstein is very sparse with attributing any characteristics to his 'god'. All he does is identifying the leap of faith which he as a scientist cannot circumvent, i.e. unreasoned trust in the order, lawfullness and rational nature of the cosmos. He (confusingly for many) labels it as a form of religion for which religious terms can and perhaps must be applied. But he does not make any assertions on top of the one he feels he cannot do without. Also it should be noted that this one leap of faith has brought us very spectacular results indeed, and that in itself to me seems enough justification for it.

I suspect that the answer to the question about the relation between mathematics and the universe (famously by Wigner called the unreasonable effectiveness of mathematics) is to be found in the fact that our minds, as a byproduct of necessary adaptation to a a vast range of dynamic situations , have developed rather good pattern recognition faculties. If these faculties are good enough to understand all of it however remains to be seen.

It seems to me, comparing the stances of Polkinghorne and Einstein, the stance of Einstein is the most parsimonious. Polkinghorne adds on top of awe for the order and lawfullness in nature an unreasoned divine purposefull agency and purposeful design, he claims to know the mind of god. I believe these additions to be no more than unsubstantiated leaps of faith.

So are you saying that mathematics is no different to a language, it is purely human made? We choose symbols to depict values etc. 'Language' needs a giver and a receiver in order for it to have a purpose or be understood. We decide what the values are and the meanings, but surely this is not the case with mathematics. Are you saying that pi for example or Einstein's famous equation isn't really out there waiting to be found, rather we have 'created' these equations? Sorry, I'm struggling to convey what I'm thinking. I hope you see where I'm leading...

By the way, have you read much of Kurt Gödel?

CoxRox Wrote:Are you saying that pi for example or Einstein's famous equation isn't really out there waiting to be found, rather we have 'created' these equations?

Humans measured the correlation between diameter and circumference of various circles, and interpreted the data, and then predicted what the circumference of a circle would be if we have a diameter of X. The same is true for surface area. That's how we've arrived at the value of Pi.

Now to say that we created Pi is only half true, we did not create the value of Pi, we measured it. You can measure it time and time again for accuracy. We did create the use of the symbol Pi so we all know what it meant when we see it in an equation.

Einstein's E=mc2 is in fact a culmination of various measurements and hypotheses based on the works of scientists as far back as Newton. Einstein was the first to make the deduction that mass and energy are equivalent. Again using math, he could predict that mass (m) converts in energy (E), should all that mass be converted. And that this formula is accurate we know by its application in atomic weapons.

The point is, we measure, hypothsize, test and predict to see if our hypothesis is correct, whether it is in maths or physics or biology.

(December 29, 2008 at 10:22 am)CoxRox Wrote: So are you saying that mathematics is no different to a language, it is purely human made? We choose symbols to depict values etc. 'Language' needs a giver and a receiver in order for it to have a purpose or be understood. We decide what the values are and the meanings, but surely this is not the case with mathematics. Are you saying that pi for example or Einstein's famous equation isn't really out there waiting to be found, rather we have 'created' these equations? Sorry, I'm struggling to convey what I'm thinking. I hope you see where I'm leading...

CoxRox, I think I see what you mean.

Taking your examples, the value of pi would be the same whether there were humans to measure it or not.
The constant of proportionality between a rest mass and it's associated energy would be proportional to c.c (with the constant of proportionality depending on units of course) irrespective of whether there's any intelligent life to measure it or not. (I assume this is what you mean by Einstein's 'famous' eqn.)

Purple Rabbit, I understand what you mean about mathematics being a formal language. However consider another intelligent species.
Their spoken language may be wildy different to any of those on earth.
However, I think their development of mathematics would be extremely similar. OK, the symbols may vary, and perhaps even a few defintions (0 factorial, square root of -1 etc) may be slightly different. But the syntax would be identical, because they are describing the same universe.

Then the language of their mathematics would be easier to translate than their other spoken languages, provided they are spoken of course, but that would not mean their language is not translatable by definition. It would only be harder.

(December 29, 2008 at 11:26 am)leo-rcc Wrote: Then the language of their mathematics would be easier to translate than their other spoken languages, provided they are spoken of course, but that would not mean their language is not translatable by definition. It would only be harder.

Isn't this getting off track? Language is just the expression of ideas, or 'wills' of the mind. How we convey these messages isn't important, but the messages. Mathematics seems to be 'explaining' things that are already 'out there': laws maybe?

Physics only uses a small percentage of the total mathematics that is available to us. We can use the available mathematics to construct physical worlds which are alien to ours. Furthermore there are indications that mathematics arises from our response to the physical world and thus functions as a natural languages.

For example humans appear to have an innate ability, called subitizing, to count, add, and subtract. It was Kant who observed that our thinking is wired for certain patterns and not for others. Math is based on principles (like symmetry, identity, causality, spatial and temporal dependencies) that are part of our macrolevel experiences. It seems that man is capable of math because the mind of man was organized to recognize patterns, make associations and abstract certain aspect of it. But instead of seeing math as the ultimate language with which to 'read' nature, and in which nature is written, I think it is more like a key for humans to unlock some of the information that is contained in nature. How good this key is to unravel all, at the moment is not quite clear.

I've just come across this article:''Professor wins prize for maths link to God'' http://www.timesonline.co.uk/tol/comment...540989.ece

It's not too long. Here's a small quote from it:

''The work of Professor Heller, above, revolves around the search for a fundamental theory of creation. His research ranges beyond Einstein and into quantum mechanics, cosmology, physics and pure mathematics, including his own version of the Heisenberg equation, below. Although his theories do not prove the existence of God, they may provide circumstantial evidence that He exists.''

Awarded by the Templeton Foundation!!!!

Kind of says it all really doesn't it?

(December 29, 2008 at 11:43 am)Darwinian Wrote: Awarded by the Templeton Foundation!!!!

Kind of says it all really doesn't it?

Forget the award. Is there any 'truth' to it?