Quantum mechanics works perfectly in experiments, but Oxford physicist Tim Palmer argues it rests on a mathematical fiction: irrational numbers like √2 have no basis in physical reality.Paywalled article. No, I do not think he is correct. I am just posting because I think it is amusing.Strip them out, and quantum's strangest mysteries disappear.
Palmer's theory makes a testable prediction: quantum computers will fail beyond 400 qubits, hitting a fundamental limit set by the discrete structure of nature itself.
The coming quantum computing race will determine whether our most successful physical theory contains a basic mistake.
Sunday, August 30, 2026
Palmer says Irrational Numbers Not Real
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Roger,
ReplyDeleteEven pure abstraction has limits.
Just because you can put something on paper syntactically does not mean it's real. It's no different than constructing a grammatically correct sentence about something you made up. You can also write any number divided by zero on paper, nothing is physically stopping you, but it is meaningless and you can't do the calculation.
I would posit that a great deal of physics about so called black holes is in essence meaningless because it keeps insisting you can have any kind of measurable physical phenomena requiring there to be mass at a point (a location of zero size), when it physically can't. There is no way you can calculate a density of zero volume or size, nor can you calculate an instantaneous velocity (velocity at a point), as both require some positive period, or extension of space or time to even have any meaning in reality.
If you are going down that route, no numbers have reality, they are an abstraction from nature that is purely in the mind used to model, so why this argument should be used against irrational numbers specifically I don't know. There is evidence that pi and the golden ratio can be successfully used to model nature.
ReplyDeleteA very wise math teacher once asked me: Have you ever encountered or seen the number '1' in reality. I pointed to the number on a piece of paper.
ReplyDeleteNo. That is the symbol for '1'. It represents the idea or concept for '1'.
I counted a pencil on my desk.
No. That is merely you grouping, like counting sheep, you can count or group the sheep in any way you wish, but that is not the number '1'.
How about computers?
No. Digital computers have no concept of 1, or 0 for that matter, to the machine it is only higher and lower voltage we humans assign to the values of 1 and 0 or on and off. As long as the machine can discern the difference between the higher and lower voltage, it can perform binary logical operations. The machine also has no capacity to evaluate the higher and lower voltage in any way except higher, lower, or similar.
He then tapped my forehead.
"The number one like any abstract idea exists only in the mind. We use it to organize what we see or think about the world and other ideas.'
He also told me the Greeks believed in a dimension or place (the platonic realm) where numbers and geometric shapes actually existed independently, and they somehow seeped into our reality to inform ideas, but that this is at best spiritual mysticism, no different than a belief in any other supernatural religion, not reality. He also admitted most mathematicians believed in it, despite it invalidating the spirit of mathematical proof, in that you are leaving a priori or axiom out of your revealed reasoning in the same way a illusionist doesn't reveal how their illusion actually works.
As for the Golden Ratio, that is a pattern with observe of proportion, which is the relationship of quantity/size in structure. Things are made of stuff, and that stuff can be approximated in quantities. This is a result of actual physical structure in the atoms, and on a higher level, the cells, and how they interact and connect. Some proportions also lend themselves to enduring structure better than others. In this, I think we can see that what we call numbers arises from our desire to observe pattern and keep track of it, so reality informs structure, and our senses, and our brains, and we use concepts to describe it, some of which is what we call numbers and math. I would add that this entire process I describe is a field of philosophy called epistemology, which carefully examines 'how do we know and acquire knowledge?'
Belief in a mathematical realm is very much different from a supernatural religion. Mathematicians have objective ways of determining that a statement is true or false. Religion does not. And it does not invalidate the spirit of mathematical proof. Proof are created for that mathematical realm.
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