. So, Mark Vernon wants us hard-nosed realists to feel warm and fuzzy. From this BBC post:
A prize-winning quantum physicist says a spiritual reality is veiled from us, and science offers a glimpse behind that veil. So how do scientists investigating the fundamental nature of the universe assess any role of God, asks Mark Vernon.
Before anything, a note on the aforementioned prize winning physicist: It's Bernard d'Espagnat, a French physicist, and more importantly, the prize is The Templeton Prize (aha, that explains it). Firstly, who and what the heck is God. Secondly, what the hell does he mean by 'role of God'. Here's an equivalent restatement without any loss of meaning: So how do scientists investigating the fundamental nature of the universe assess any role of Flying Spaghetti Monster .
Steven Weinberg lays it plain. He says the question is meaningless (I find this assessment the most agreeable). Others are not so clear-minded, especially Brian Swimme who Mark Vernon quotes as saying "the universe is attempting to be felt". Part of the Universe sitting on a sofa is now scratching its head and pondering the meaning of this statement.
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Roger Penrose says:
I'd very much like to hear what these supposed "good grounds" are, because as it stands that last point makes absolutely no sense to me. Rational numbers, indeed all of mathematics, are a quantified expression of the physical things the universe is composed of. No universe means nothing to be quantified, and so the very concept of quantification is meaningless. But I'm no Oxford physicist...
Rational numbers, indeed all of mathematics, are a quantified expression of the physical things the universe is composed of.
-1 is not a quantification of anything that exists.
It is an incredibly tricky concept, since all our language assumes the existence of the universe so it's hard to talk about, but since math is an abstraction without a (necessarily - very hard to talk about this since our brains are things that exist) need for any physical implementation of the things they describe (i.e. I can write and manipulate numbers that are larger than anything that can ever exist) it is possible to consider that the axioms that make 1+1=2 can continue to be true even without a universe.
I'd argue that mathematics does not exist independently - it is a system of ideas and concepts, and as such only exists in the mind. The universe itself doesn't use maths, it simply is what it is. Maths is just part of our attempt to model it.
deatkin: Rational numbers, indeed all of mathematics, are a quantified expression of the physical things the universe is composed of.
This is not the present state of mathematics.
At present (and since the Whitehead to Godel era of the first half of the 20th century), mathematics is a purely philosophical construct, from abstract principles. That these abstractions bear any resemblance to anything related to what we experience (aka, "the universe") is a point somewhere between coincidence and blind assumption, with some hint of "all roads lead to Rome math" destination.
"-1 is not a quantification of anything that exists."
True. Clearly, my comment is in error.
"This is not the present state of mathematics."
Roger Penrose's use of numbers that can be said to describe objects in the universe has led me to take an intellectual shortcut and conceive of the entire discipline of mathematics as such. Even my own academic experience with practicing mathematics, if I had reflected on it, would have prevented me from making this mistake.