Objective reality

Good. Hold that thought. Redefine Pi to be that relationship. Now, is Pi objective and real?

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.

Can you demonstrate that by the scientific method?Irrespective of the language and symbols used, any suitably advanced intelligence will recognise this relationship.

Not by the scientific method Simply by mathematics. Simple, they derive it from mathematics, which is the one example of an objective reality that does not depend upn the scientific method 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.

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.

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.

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.

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?

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?

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!

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

Given the success that approach brought to 20th century physics, I think I'll stick to being "mistaken" 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... Again, I think you are missing the point - it is not the treatment that is elegant but the mathematics that lies behind. 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. 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. 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.

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. 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). 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. 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.

Could be? 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.