In my previous lecture I showed you scientific inquiry slowly moved from conceptual to mathematical. The origin of this move is Pythagoras, who regarded the universe as mathematical.
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There is mathematics everywhere in science nowadays. Without it there would not be science. We use mathematics, in fact in a rather pragmatic way: it just works.
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But the question “Why is reality mathematical” kept bothering me. Is it the right question or is it just a silly question? I thought: let’s Google “Why is reality mathematical”.
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The result was…on one word……exciting. The question showed to be philosophical gold. I am not the only one who is wondering about it.
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First hit was “Our Mathematical Universe: My Quest for the Ultimate Nature of Reality”, (2014) is a nonfiction book by Swedish-American cosmologist Max Tegmark.
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Written in popular science format, the book interweaves what a New York Times reviewer called "an informative survey of exciting recent developments in astrophysics and quantum theory" with Tegmark's mathematical universe hypothesis, which posits that reality is a mathematical structure.
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This mathematical nature of the universe, Tegmark argues, has important consequences for the way researchers should approach many questions of physics. So the Pythagorean spirit is still alive.
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But some critic already raises the question…..”perhaps the most important question about Tegmark’s claim is, Does it matter, except perhaps to those interested in metaphysics?
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Most of his assertions can’t be tested, and whether you accept them as true or not seems to make no difference to the future development of physics.” — end quote
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At least the question keeps thinkers and scientist still busy. Then take this story:
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When Albert Einstein finally completed his general theory of relativity in 1916, he looked down at the equations and discovered an unexpected message: the universe is expanding.
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Einstein didn't believe the physical universe could shrink or grow, so he ignored what the equations were telling him.
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Thirteen years later, Edwin Hubble found clear evidence of the universe's expansion. Einstein had missed the opportunity to make the most dramatic scientific prediction in history.
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How did Einstein's equations "know" that the universe was expanding when he did not? If mathematics is nothing more than a language we use to describe the world, an invention of the human brain, how can it possibly churn out anything beyond what we put in?
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Then we go to the question: “Does Mathematics Reflect Reality?” on the site www.marxist.com and there we read this answer:
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The content of "pure" mathematics is ultimately derived from the material world. The idea that the truths of mathematics are a special kind of knowledge that is inborn or of divine inspiration does not bear serious examination.
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Mathematics deals with the quantitative relations of the real world. Its so-called axioms only appear to be self-evident to us because they are the product of a long period of observation and experience of reality.
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Unfortunately, this fact seems to be lost on many present-day theoretical mathematicians who delude themselves into thinking that their "pure" subject has nothing to do with the crude world of material things.
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This is a clear example of the negative consequences of carrying the division of labour to the extreme.
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From Pythagoras onwards, the most extravagant claims have been made on behalf of mathematics, which has been portrayed as the queen of the sciences, the magic key opening all doors of the universe.
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Breaking free from all contact with the physical world, mathematics appeared to soar into the heavens, where it acquired a god-like existence, obeying no rule but its own.
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Thus, the great mathematician Henri Poincaré, in the early years of this century, could claim that the laws of science did not relate to the real world at all, but represented arbitrary conventions destined to promote a more convenient and "useful" description of the corresponding phenomena.
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Certain theoretical physicists now openly state that the validity of their mathematical models does not depend upon empirical verification, but on the aesthetic qualities of their equations. End of www.marxist.com
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When sending such a question into the Google Universe and then being rewarded with such an abundance of information is really exciting.
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It is exciting to read, how justified the question is. Is reality mathematical? If so, how can that be the case? How did we discover this? It looks like a miracle.
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Thank you… ^_^
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One concluding message: Next week we’ll make a short Autumnbreak. Thus we’ll also avoid one week of confusion due to asynchronous changing to daylight saving time in the US and Europe….^_^
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