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Author | Topic: Objective reality | |||||||||||||||||||||||||||||||||||||||
cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
The relationship between the circumference and diameter of a circle would continue to exist Good. Hold that thought. Redefine Pi to be that relationship. Now, is Pi objective and real?
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined:
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Assuming that a perfect circle objectively exists In the everyday sense, I would argue that they don't. Does this mean Pi does not exist? Let's take the primes. One is hard-pressed to find the primes on display (although it can be done) in the Universe, yet does that mean that once sentient life is removed, 17 objects could find themselves arranged in a rectangular grid of equally divided columns and rows? What I am trying to show is that there are truths of this reality (any reality?) that are the epitome of objective, and must be recognised as having a level of "existence". I myself go further to suggest that our everyday objective reality is built up of these truths, thus removing any need to consider two types of existence. Edited by cavediver, : No reason given. Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
This is how I see things: Some long-ago hypothesis:-There is a specific and distinct relationship between a circles diameter and it's circumference Some long-ago observations:-Every approximate circle seems to have an extremely similar specific and distinct relationship between it's diameter and it's circumference. -As we create circles closer and closer to "a perfect circle", this value becomes more and more precise Some long-ago conclusions:-This relationship can be represented by a single number, let's call that number "Pi" -"Pi" can be theoretically defined with an idealistic equation, it is correct for every circle we can imagine If that's not the scientific method, then what is? Can you demonstrate that by the scientific method? Irrespective of the language and symbols used, any suitably advanced intelligence will recognise this relationship.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
But I do think that someone can. Not by the scientific method Simply by mathematics.
If you do think it's objective, and you do think that "any suitably advanced intelligence will recognize this relationship"... how will they recognize it unless it is derived (somehow) from observations of reality? Simple, they derive it from mathematics, which is the one example of an objective reality that does not depend upn the scientific method
If it is not derived from observations of reality... how can you be so sure that is, in fact, objective and aliens would recognize it? A valid question - and I would say that you'd just have to appreciate the nature of formal systems to understand. Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
You're all (with the occasional exception of nwr) talking nonsense about math. Again, I'm glad you are here to solve these age old arguments. We really could have done with you in DAMTP - many many hours of arguments over coffee could have been saved. It must be so nice to be so convinced you're right. Have you tried Christianity? It would suit you well.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
Do you have any actual arguments against the point of view that I have expressed? What arguments? That because Pi is not like a tiger, it is obviously not "objective reality", where-as titilation obviously is. Forgive me, but I just prefer to laugh at that rather than argue with it. You seem worringly attached to your beliefs here, hence the justifable comparison with a religious faith. Myself, I'm still on a long journey trying to understand this existence, and I rather debate and argue it with others of similar curiosity. You, in this thread at least, don't fit that bill. Sorry. Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
Well you didn't. Yes, it's strange. From all of Dr A's claims of having shown, demonstrated, and explained, I must be missing half of his posts.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
then that would lead us to also consider the ratio pi as objective, even if we think of numbers as merely useful fictions. I'm interested in this point. Are you treating the ratio Pi as something more "real" other than your fictional numbers, or is it as much a fiction as say the integers?
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
I am distinguishing between ratios and numbers. Yes, that is what I thought. But I can generate the integers in a number of ways that are blatently dimensionless. Topological winding numbers for example. How would you classify these in the sense of our present discussion?
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
how can we know that the integers are a subset of the reals? An excellent question - I think we see clues to an intimate connection in my previously mentioned winding numbers - think of the Cauchy residue formula and the Gauss Bonnet formula. Here the very continuum based geometry forces upon us the integers. But I'm drifting asleep, so this will have to be continued tomorrow. Good night!
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
But what if space and time are actually discrete, which they almost certainly are. Although widely promulgated through popular science, this isn't actually a widely held view of space-time* - at least not in recent years. There is nothing in quantum theory that suggests the discretisation of space-time itself, only restrictions on measurements. And this follows from the discrete nature of particles. But it is the discrete nature of particles that does introduce the integers, through "number" functions, which count properties such as charge and quantity. It is important to distinguish between the classical macro-scale concept of counting of say apples (objects of sufficient similarity at the scale of interest as to belong to the set of objects to be counted) and the quantum concept of "counting" of say the photon number of an n-photon state, which is intimately connected with my previosuly mentioned topological winding. This is a huge, deep, and very interesting topic in its own right, and lies at the heart of my own turn towards a pseudo-Platonism. Perhaps for its own thread? But I am out of time for the moment. * Regge-calculus was one approach to discretised space-time, and elements of it can still be seen in Loop Quantum Gravity
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
Straggler writes: As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant. nwr writes: If physicists believe that, then they are mistaken. Given the success that approach brought to 20th century physics, I think I'll stick to being "mistaken"
One of the things Dirac did, was to use a notion of generalized functions. That's like pointing out Einstein's contribution to refridgeration as a counterexample to the elegance of his work in physics - the delta-function is not exactly amongst Dirac's highest achievements...
Likewise, I suspect that many mathematicians would consider Einstein's treatment of GR as somewhat inelegant. Again, I think you are missing the point - it is not the treatment that is elegant but the mathematics that lies behind.
I am inclined to say that is wrong. It's actually correct. And is precisely how Hilbert beat Einstein to the Field Equations, by jotting down the only possibly action one morning over breakfast.
I look at it as finding a way to modify Newtonian mechanics to incorporate the new assumptions. No, nothing like this at all. Newton plays the role of the desired end-point - as in an r-2 law in the weak field limit - which determines the coupling to the stress-energy tensor. But that is all. For vacuum space-times, Newton is not used at all.
It has always seemed to me that the world (i.e. the universe) is a messy, disorderly place. Then you need to check out QCD, Electro-Weak, and Gravitation more. And remember that today's world is sat at the bottom of a hierarchy of symmetry breaking. You need to get out of the trees to see the real nature of the wood. Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant. As Son Goku mentioned, you have to be clear what is meant here. Actual solutions (things that look like our world) can be exceptionally messy - the elegance is in the top level theory.
Einstein and Dirac spring to mind as two obvious examples of those who have achieved an immense amount with this abstract and highly non-empirical approach. Yes, though the real use of this approach was later with the application of group theory to particle hierarchies, and most successfully (as SG mentioned) with the SU(3) Yang-Mills theory of Quantum Chromodyanamics (QCD).
Is that right? Almost, though Einstein used the requirement that the end theory must reduce to ewton in the weak field limit to produce the correct coupling to the stress-energy tensor. However, that correct coupling is also the most trivial coupling when viewed from the action principle, so even the connection with Newton is not exactly required.
And that is where this more platonic view of reality is derived from. Is that how you see it? Not quite - it certainly speaks to that view, but far more interesting to me is the nature of our fundemental particles and how they are pure group representations.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
Conversely some aspects of empirical reality could be discovered through extrapolation of mathematics Could be?
A mathematical system which is not based on reality could be constructed and which would yield results without a link to physical reality. Or it could yield results with major links to reality - such as with group theory, algebraic topology, the Zeta function, etc... And the converse of course - physics leading to mathematical results that otherwise had no connection reality, such as topological quantum field theory leading to massive simplification in the calculation of Donaldson polynomials.
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