Ooo-eck. That's my professional commentary.
Rather than saying that the universe is very structured, say that the universe is mostly chaotic and for the most part lacks structure. The reason why we see the structure we do is that scientists act like a sieve and focus only on those phenomena that have structure and are predictable. They do not take into account all phenomena; rather, they select those phenomena they can deal with.
There is an important analogy between physics and mathematics. In both fields, if we do not look at the entirety of a system, but rather look at special subsets of the system, we see more structure. In physics we select certain phenomena (the ones that have a type of symmetry) and ignore the rest. In mathematics we are looking at certain subsets of structures and ignore the rest... we have to give mathematical structure to the world we observe. As physics advances and we try to understand more and more observed physical phenomena, we need larger and larger classes of mathematics. In terms of this function, if we are to enlarge the input of the function, we need to enlarge the output of the function.
When physicists started working with quantum mechanics they realised that the totally ordered real numbers are too restrictive for their needs. They required a number system with fewer axioms. They found the complex numbers.
When Albert Einstein wanted to describe general relativity, he realised that the mathematical structure of Euclidean space with its axiom of flatness (Euclid’s fifth axiom) was too restrictive. He needed curved, non-Euclidian space to describe the spacetime of general relativity.
... Non-Euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.
One possible conclusion would be that if we look at the universe in totality and not bracket any subset of phenomena, the mathematics we would need would have no axioms at all. That is, the universe in totality is devoid of structure and needs no axioms to describe it. Total lawlessness! The mathematics are just plain sets without structure. This would finally eliminate all metaphysics when dealing with the laws of nature and mathematical structure. It is only the way we look at the universe that gives us the illusion of structure.
http://nautil.us/issue/66/clockwork/chaos-makes-the-multiverse-unnecessary-rp
Nah, I'm nowt as educated a man as yerself, so "Ooh-eck" goes roight over my peasant head. But... if this gentleman is correct and hoigher levels of math have fewer axioms, why... ( puffing myself up all proud like, in my wellingtons and carrying my barn shovel ) that renders me fit to opine upon such things, knowing nuttin but a few of Euclid's, now dunnit?
ReplyDeleteThis strikes me as similar to how Buddhists talk about conditioned reality.
ReplyDeleteI don't think there is no structure, we need to revise our axiom of structure in order to improve. Logical/structured/ thinking has its limitations that are most noticeable not in the constrains of the meta-perceptions it introduces, but in its rather flat approach to causality.
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