Are you recanting your first sentence on this thread where you said that "beauty to be found in mathematics is undeniable"? Evidently so.
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Beauty
- Thread starter Nous
- Start date
And you would say likewise that the fact that there's wide disagreement about how to interpret the quantum wave function and whether it objectively exists shows its subjectivity?
Since Poly isn't here at the moment, I'll jump in with a caution.....
Note that he said "to be found", which can mean mean personal experience.
Eg, to find joy in something means that joy resides in the finder, not in the thing.
Don't read a singular convenient interpretation into ambiguous language.
Note that he said "to be found", which can mean mean personal experience.
Eg, to find joy in something means that joy resides in the finder, not in the thing.
You're using a disagreement about a theory (which is an explanation of a phenomenon).
A preference for one explanation over another can indeed be subjective.
But this is not the same as disagreeing about a measurable intrinsic property of a thing.
How do you define beauty such that it can be objectively measured or otherwise evaluated?
What is your argument that beauty is objectively an intrinsic property of a thing?
Is there anyway to logically claim that what you have said here does not contradict Polymath's sentence that I quoted?
Yes, there is.
No. Math is made up by humans. It is a human form of beauty.
Some physicists claim that the wave function is just a calculational tool that describes "our knowledge" of a system. This is what the wave function is in the Copenhagen Interpretation (et al.). Other physicists say that the wave function is an objective reality that exists not just in the physicist's mind. This is the same distinction people make about the objectivity vs. subjectivity of beauty.
See the features of beauty noted by Aristotle and Bailey and Borwein in the OP. You don't deny that symmetry (e.g., of spheres) exists, do you?
Prove it. ("Prove it" means cite the fact(s), and state the argument.)
So you are disavowing now that beauty is found in mathematics?
That mathematics is made up by humans who then use it as a language to model with universe? We are the ones that choose the rule (axioms). We are the ones that make the models (physics, for example).
No more than I disavow that there is beauty in any other form of art. Math is an art form for mathematicians.
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Symmetries in the real world are all broken: they are not perfect symmetries. Also, not ALL symmetries are beautiful nor is all beauty symmetric. They are different things.
With competing theories of equal predictive value, choosing one over the other involves subjectivity.
When one theory is better, choosing the less useful one is far more subjective.
But you're still not addressing the claim that beauty is a property of the thing,
rather than an experience of the observer.
Rather than facing that wall of text, I'd prefer that
you present your argument....or a summary of theirs.
Koldo
Outstanding Member
"This, of course, doesn't entail that for something to be objective this must be a requirement."
This was part of my last post. The issue still is: How do you substantiate 'beauty' is objective ?
The predictions from using the wave function are objective They are publicly verifiable. The nature of the wave function itself is, at best, undetermined and I don't know many working physicists who consider the wave function to be an objective thing.
In fact, and even setting aside the different interpretations (Copenhagen, Everett, etc), there are multiple ways to describe the exact same physical situation, all of which give *exactly* the same predictions for observables. So, for example, in the Schrodinger formulation, the wave function changes over time and the operators corresponding to observables stay constant, while in the Heisenberg formulation, the wave function stays constant and the operators change over time. And there are intermediate formulations both wave function and operators change over time. That makes a strong case that the wave function itself is not an objective thing.
What do you mean by claiming that you choose the axioms?
Euclid's second axiom is: If equals are added to equals, then the wholes are equal.
Obviously no human chose that axiom to be true. It isn't possible to choose that axiom to be false. Given the antecedent of the sentence, there is no other option to choose for the consequent. So what does your claim mean?
But some examples of symmetry are beautiful?
I wasn't referring to the theory of quauntum mechanics. I referred to the interpretation of the nature of the wave function--whether it is a mere subjective calculational tool or whether it exists objectively. I noted that the fact of these differing interpretations does not mean that the wave function is subjective. The same goes for beauty.
My position on the issue of the objectivity vs. subjectivity of beauty is (as the SEP article primarily discussed) it isn't wholly either. And along with Aristotle, I analogized beauty with the taste of sweetness, which has both objective and subjective components. See the OP.
BTW, did you answer the questions in the OP?
Interpretation is theory.
You don't answer my questions about the objectivity of beauty.
I suggest offering something more positive than mere objection.
What? The Many Worlds Interpretation enatils an objectively real wave function.
What do the "working physicists" you know do with evidence such as:
Quantum mechanics is an outstandingly successful description of nature, underpinning fields from biology through chemistry to physics. At its heart is the quantum wavefunction, the central tool for describing quantum systems. Yet it is still unclear what the wavefunction actually is: does it merely represent our limited knowledge of a system, or is it an element of reality? Recent no-go theorems[11–16] argued that if there was any underlying reality to start with, the wavefunction must be real. However, that conclusion relied on debatable assumptions, without which a partial knowledge interpretation can be maintained to some extent[15, 18]. A different approach is to impose bounds on the degree to which knowledge interpretations can explain quantum phenomena, such as why we cannot perfectly distinguish non-orthogonal quantum states[19–21]. Here we experimentally test this approach with single photons. We find that no knowledge interpretation can fully explain the indistinguishability of non-orthogonal quantum states in three and four dimensions. Assuming that some underlying reality exists, our results strengthen the view that the entire wavefunction should be real. The only alternative is to adopt more unorthodox concepts such as backwards-intime causation, or to completely abandon any notion of objective reality.
https://arxiv.org/pdf/1412.6213.pdf