joigus

The risks of auto correction.

I think this belongs in Spec elation.

Yes, that's one valid way to put it, IMO. In physics there are certain theoretical constructs, like the field, charge, couplings between different fields, etc. Takes considerable time to acquaint yourself with them, but once you do, you're completely won over by their power and generality. You need to let go of the old equipment: push, pull, levers, and so on. You can always go back to them, because sometimes it doesn't help to think about, (eg., an engineering problem) in terms of fields and elementary interactions. So if you're curious about magnetism and the like, you let go of the other stuff. It does no good.

Oh, boy. I'm sorry. I should have read you out. You are much more knowledgeable on this than I am. But your comments reinforce my impression that Gödel's theorem does not provide much in the way of a constructive process, even though the proof itself is constructive. I think what you mean is something like theorems in number theory, propositions on prime numbers, and the like, right? I simply don't know. I've never heard of any of those. That is a very good question. Maybe @wtf has something interesting to say about it.

Cohen's proof that it is undecidable whether there is a cardinality (number of elements) intermediate between that of \( \mathbb{N} \) and that of \( \mathbb{R} \). https://en.wikipedia.org/wiki/Continuum_hypothesis "Undecidable" is perhaps my colourful way of saying it. People seem to prefer the wording:

It's the other way around. We live in a DeSitter universe. So your proposal is against the observations. https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_universe

My condolences, @MigL. I know how hard it is to say goodbye to a friend.

And what is speed? And what is change? Isn't time already implied there?

It's a noble way to end your days in this planet. I can only hope for a dignified final position.

That is trivially true: \[\frac{\triangle Q}{\triangle Q/\triangle t}=\triangle t\] \( \triangle \) meaning "change" and \( Q \) being any physical quantity.

Well, not word by word. I would have probably said "then the one with fewer assumptions is the better one". I'm a stickler for language. Good to see you again, Eise.

This is almost word by word what I wanted to say in answer to,

I remember Sidney Coleman praising this particular moment of Feynman's. How complicated or puzzling a phenomenon is rests on what level of fundamental principles you're allowed to use. It's as @studiot said: The contact force is considered simple by many people, while it's actually a very derived phenomenon in the theory. At some levels, certain simplifications seem to appear, but that's only because we come across emergent levels of simplicity. Same happens with thermodynamics. Internally, it's very complex, but regularities appear. Contact forces, which Feynman mentions there, are an outstanding example.

Well, yes, as @studiot said, that's 'arbitrary', as in, 'those arguments are too arbitrary to be compelling at all' I meant it in a different sense, as in 'to any degree'.

If he was a member of an American religious sect, I'd say he couldn't have been OK. Sorry, I meant Ockhamish. You lot use far too many consonants. Not necessary. What you can do with a "ck", you can do with a "k".

You're becoming less and less Okhamish by the minute. Sorry for being so blunt.

That was my second-favourite one.

The "for the ghost of Hugo Chávez" one was hilarious. 🤣

Just one observation which I hope is relevant to the ongoing discussion: Simple principles can have arbitrarily complicated consequences. The much more "derived" theory is thus expected to be more unwieldy to Ockham-based criteria.

Sorry, I'm not familiar with it. I agree that the OP has a point, even when applied to science. But I still think it all has to do with the scope of what you want to explain, with what we could call first principles vs particular explanatory pathways based on those principles. In the spirit of what @Prometheus says, there are overarching principles (simple), and then there is the implementation of particular scenarios (complicated parametrics). Something like that. I want to make more comments. Perhaps later. I need some sleep. The discussion is tantalizing. I feel a bit behind the game right now. Maybe I'm just tired.

Ockham's-razor rule of thumb rests on two simultaneous optimisation desiderata: 1) Maximum simplicity. 2) Fitness to account for observation. The search for maximum simplicity works under the constriction to fit experimental data. The latter overrides it all. If explanations seem more complicated it's likely because the range of phenomena that we intend to contemplate is widening more than ever before. Further constrictions operate on approximations, ancillary hypothesis, etc., to account for an ever more complicated landscape of phenomenology. I tend to agree with the points as expressed by @CharonY, @Ken Fabian, and @Prometheus even though I cannot be totally sure that we would completely agree with each other in the finer details. Summarising, I think Okham's razor is alive and well, even though it's become subtler and more difficult to apply it.

Yes, I've noticed that. Seems like all of our comments have gone unanswered. I think I've noticed a pattern though. After a couple of posts he even stops addressing the person. I wonder what that means...

I don't know how to interpret the fact that the OP has decided not to address my comments at all.

To add to the panoply of excellent comments by Kino and Markus, you cannot expect an arbitrary linear combination of 4-vectors to be a physically significant 4-vector. Both vectors must be timelike \( \left(u_{\left(i\right)}^{0}\right)^{2}-\boldsymbol{u}_{\left(i\right)}\cdot\boldsymbol{u}_{\left(i\right)}\geq0 \) and orthochronous \( u_{\left(1\right)}^{0},\:u_{\left(2\right)}^{0}>0 \). Also, the resulting 4-vector must be normalised to \( c^2 \). In that sense, when you're working with 4-velocities, you're not working on a plain linear space --Minkowski space--, but in some kind of "unitary quotient of it." This distinction is referred-to in physics by means of the buzzwords "on-shell" and "off-shell." Adding vectors off-shell can lead you to vectors on-shell, and vice versa. This point has arisen before --Ghideon has been particularly persistent. Off the top of my head, you can derive a common (CoM) 4-velocity for 2 material particles moving every which way by calculating the common 4-momentum, and then dividing by \( m_1+m_2 \) --which are relativistic invariants. Another thing you could do is calculate the centre-of-energies motion and then impose that it be normalised as to become a physical 4-vector. One last thing you could do is use Einstein's addition of velocities --which doesn't involve the masses--, to obtain a physical 4-vector, by multiplying by the appropriate observer-dependent factor as to obtain a 4-vector. I don't know. I'm just trying to help you so that your effort is not in vain. So far, it is in vain, simply because you're not distinguishing with any care what's on-shell and what's off-shell.

Thanks for telling us, @studiot. I'm sorry. I'd like to reach out to everybody who has a genuine interest on what all of this (reality) is about, no matter what their background or what their grasp of science is. We as individuals come and go, but the human endeavour to understand the cosmos and ourselves, and how all that we perceive came to be, lives on. My homage to Mike, I will express in the words of Ticho Brahe, as I remember them referred by Carl Sagan --addressed to Johannes Kepler: "Let me not seem to have lived in vain."