joigus

Ok. Everybody gave such good and precise answers (+1,+1,+1) that I didn't know of anything else to say. Except give the complementary mathematical focus, which is my favourite. Mathematically, a reading scale normally involves something like (at least for most measures within a certain range for both T and X: T=T0+kX Your apparatus is sensitive to X, while your theory connects it to the readings T. One example could be temperature as a function of the position of the mercury column. The zero error would be the error in T0, whether T0 be actually zero or not.

I think something that may help most people reading this post is to provide simple examples of what you mean just after you've introduced some of your definitions. Great philosophers (especially philosophers of science, like, e.g., Bertrand Russell) always set up explanatory examples after an abstract notion was introduced. Examples are like the "laboratory" of philosophy. Help your potential readers know that you mean business. On the whole, I don't think for a second that getting an idea of what a TOE will look like will be helped along by philosophical thinking alone. I'm pessimistic if you want.

👍 I have no doubt you're getting better.

I'd choose good (and generalised) education above a good leader any time. Leaders I see as a necessary evil. Religion is never a good bedfellow of anybody. 😆 It's always worked for itself pretty well, though. Just one more thing. When you say "understandable message", do you mean politics or religion?

Maybe. But I don't think he would be interested in saving the world from a devastating destruction. He seems to be quite happy with us having a fair amount of devastating destructions every now and then. So the thing you suggest sounds to me something like: God: Let's send another devastating destruction and see if this person who doesn't believe in me can thwart me (God whispers the solution to the scientist's ear). Scientist: I don't know who's talking to me, but OK. It's possible. It's certainly compatible with the schizophrenic type that I can see depicted on the Bible. What terrifies me is the kind of psychotic God that our culture seems to have devised. What does it say about us as a species?

Yes, it helps. Thank you. Every bit of information that all of you are giving me helps. People on the spectrum, as well as people who've had experience with it. It's helped me anticipate many things and assess the emotional breakdowns when they've come. In the case of A, only once we've had an emotional breakdown. It was due to an obsessive series of thoughts in relation to something a classmate told him. Today we've had a similar episode, but it's been so much easier to control. Tomorrow he's doing his maths and physics exam. Everything seems to be going very satisfactorily. His family are doing a great work, I must say. I'm amazed that you discovered it so late... I'm sure there are many people out there in their 40's + that weren't properly diagnosed.

So right. So central. +1

I know what you mean. I think that's probably because today, rather than facing a problem of unavailability of information, we're lacking an efficient method to get to the relevant information we need. Our brains evolve far slower than the world of technology. And, as a consequence, connecting the dots is harder than it has ever been. I've learnt that Darwin had had Mendel's paper on his "to do" list, maybe for years. He never got round to it. Imagine how much worse it can be now. Maybe as we speak two people in opposite parts of the world have had ideas that are complementary and would result in a tremendous advance, and they'll never find out for decades just because they don't know how to sort out the information overflow. We may need a new age of search engines based on semantics, rather than the grammatical-lexical search engines we've got today. But that's easier said than done.

Intuition is very dangerous when dealing with QM. How can the Pauli exclusion principle be partially violated? It's a discrete symmetry. As Mordred referred to (+1), particle pairs in QM must be either symmetric or anti-symmetric by exchange of their identity. There's no way to be "a little anti-symmetric." STATE(1,2) = - STATE(2,1) (fermions) If, on the other hand, your assumption is that some particles become symmetric, while others don't, that's not consistent with the principle that particles are indistinguishable from any identical other. We can partially violate C (charge conjugation), P (parity or "inversion of space"), and T (time inversion), but not spin-statistic character. Unless you come up with pretty strong experimental evidence, and then; and that would be most interesting; with a serious alternative to relativistic quantum field theory, because spin-statistics connection is too deeply ingrained in it. The whole machine would go down.

Thanks for sharing. +1. I don't have time now, but I'll get back to you tomorrow, probably.

Suppose you produce yoyos. You make perfect yoyos, but the world no longer is interested, no matter what your passion and ability at making yoyos may be. Who's going to subsidize your yoyo-making? And what for?

The problem with this well-meaning idea is the law of supply and demand.

I also believe in a concept of money that is cyclic. But it's not just spend it; money must be extinguished. It must disappear at a rate that's equated with the rate at which it's issued. The first historical kind of money as unit of exchange is a very clear example of this. If you pump money indefinitely into an economic system, you've got a recipe for inflationary disaster. The modern concept of money is also cyclic. The problem with the present monetary system is not lack of re-cycling; it's that it's the banks who decide who's going to get it and who's not; as well as how much of it is put into circulation. An economic system that's workable, IMO, must define, so to speak, a socialist ground (minimum wealth guaranteed as long as you're healthy and not just a leech) plus a capitalist ceiling (maximum wealth allowed). 1) Everybody must be able to have their basic needs guaranteed 2) Nobody should be able to buy, e.g., all the islands in the Indian Ocean The reason for the first, in my view, is basic human dignity; the reason for the second, if nothing else, is the simple fact that there is a finite number of islands in the Indian Ocean. I know how unpopular this is in some quarters, but any other possibility is simply not sustainable, or ethically acceptable.

Very interesting topic, very interesting comments. Not sure I haven't missed some of the important points. The initial concept of money was far simpler and far less risky than today's. And it was necessary. If I grow beans and you make leather, there should be a way in which you and I agree to exchange our products even if you're not interested in my beans and/or I'm not interested in your leather (see Markus Hanke's point above about "barter-based societies are not good enough"). That's what money originally was invented for. Leather and beans are demanded in sufficient generality so that you and I can produce notes exchangeable for beans or leather for everybody to accept them as payment in any concept. With this old concept, money represents a wealth that has already been produced. But this requires trust (see MigL's point). Then, along came the money lenders in Venice (initially only Jewish families); and later, also Christian families, like the Medici, followed suit. Now it's possible to lend money for an interest. It's also possible to lend money you don't have, because: 1) Not everybody needs all the money at the same time. 2) You can pay with money you don't have, but you think you will have. That complicates things enormously, because value gets entangled with time and predictability. Then, along came the Dutch, who invented the stock market; and followed the British (who sold the idea to everybody else) and invented a concept of money that represents a value that doesn't as yet exist (the wealth will come later). William Paterson invents the Bank of England, and gets us farther and farther into this new concept of money that's entangled with the future and the will to make money from money (see Studiot's point). The last unfortunate development (besides different sophisticated new ways of selling wealth that doesn't yet exist) is the modern banking system. Now, not only unpredictability is entangled every which way. Money is created as pure debt ab initio by banks, which also decide who's going to have it and who isn't. So even the primitive concept of money as a unit of exchange and account for the wealth you have produced has been completely lost. Summarizing: A) Money is based on trust: So, +1. Don't burn your money just yet. People still trust it. +1. Barter alone doesn't cut it. You need a universally accepted unit of exchange and account. +1. Greed. The possession of money leads to trying to find ways to get more money from your money. The people who can't make leather, or grow beans, or do anything real, but crunch numbers. Those are called bankers and investors.

Count me in. In my case it may have been attention deficit. 🤦‍♂️

This is another very good point. On my part, I will brood over it for a while longer, plus go over everybody's comments.

Well, I wouldn't be very good at summing up criteria of philosophical goodness myself, but I cannot deny that there are significant things to be said. Somehow I picture @Eise as the most knowledgeable person I know around here, at least of those I've interacted with. Some of the stickies on the forums rules already cover a number of common fallacies or what an argument in good faith is. Other fallacies could be added, like the argument of authority, or the idola fori (Francis Bacon); that is "many people say or think". If not as explicit prohibitions, at least to make people aware of common sources of error or weak arguments. On the other hand, there are certain philosophical topics that are of interest to science and I think have become universal quality standards for scientific thought: Operationalism (ultimate reference to measurable quantities) Ockam's razor (economy or parsimony of systems of ideas) Falsifiability (K. Popper) --> road to experiments This is a very good point, because if anything, it shows that the distinction is sometimes difficult. I think that dimensions (at least overlapping with @Ghideon, @Mordred) is a concept that generally refers to the ambient space, or space of independent variables, while DOF generally refers to dependent variables that make up the mathematical concept of state, generally a function of the first. So to describe the state of a system you set up a functional dependence Y(t,x), with #DOF = number of independent Y1, Y2,...Yn that you can fix. Any other function of the state would be numerically determined. System, state, variables of state, ambient space I think are the concepts that shape the question. Although there are cases when the distinction can become blurry for several reasons. One of them appears in classical thermodynamics, where the ambient space disappears altogether, and you're left with an implicit relation among the state variables (equation of state): f(P,V,T,n) etc. There you have some kind of cyclicity, in which you can pick any number of these variables to describe the change of the others, and trajectories as abstract (timeless) motions in that surface of state. Then we've got field theory. There the concept of DOF is the set of field variables, so Fa(t,x) would itself be the degree of freedom. A vector field, like the vector potential, mirrors the properties of the ambient space itself, \[A^{\mu}\left(t,x\right)\] but other "internal field variables", like e.g., Yang-Mills fields, have a representation space that is richer. As to GR, you've got the manifold (independent variables) plus a set of fields: g(x), metric; R(x), Riemann; T(x), matter; all of them would add up to the state (dependent variables) as a function of the x's (independent variables). As to classical dynamics, I see the DOFs as the specification of (x1,...,xn,p1,...pn) because, once you fix those, there's nothing else to fix unless you re-define what your system is. But another complication is that there is an existing tradition to call just (x1,...,xn) your DOFs. Then there is @studiot's comments about the equations of constitution. The thing does ring a bell to me, but I don't remember what that is about, so I'd be thankful if he reminded me.

I applaud this idea too. +1 The only thing I find more difficult to establish from a practical POV is the "good" in "good" arguments. You seem to have an idea for when an argument is just too bad quality to be accepted as such... 🤔

Ah. It did ring a bell. +1. I agree. It's a bit outdated maybe, but good stuff.

Glad to be helpful.

I think I can do a little bit more than that. Most, if not all, interesting wave functions in QM have a behaviour that goes to zero as a Gaussian at infinity. If you take a look at most eigenfunctions of "realistic"* Hamiltonians, for example, the harmonic oscillator, hydrogen atom, etc. The all are dominated by exponential damping at infinity. Example: \[\psi\left(x,0\right)=\frac{e^{-x^{2}/2-if\left(x\right)}}{x^{n}}\] Now it's very easy to see that no matter what power of x is integrated against the exponential, the idea works. \[\int_{\mathbb{R}}dx\frac{e^{-x^{2}/2+if\left(x\right)}}{x^{n}}\frac{d}{dx}\left[\frac{e^{-x^{2}/2-if\left(x\right)}}{x^{n}}\right]=\left.\frac{e^{-x^{2}}}{x^{2n}}\right|_{-\infty}^{+\infty}-\int_{\mathbb{R}}dx\frac{d}{dx}\left[\frac{e^{-x^{2}/2+if\left(x\right)}}{x^{n}}\right]\frac{e^{-x^{2}/2-if\left(x\right)}}{x^{n}}\] Watch out for silly mistakes. * Meaning nothing pathological, like Airy functions, or something like that.

Exactly. Under the integral sign, yes. Actually, it's used as a matter of course in all of field theory. Field variables at infinity always go to zero "fast enough", so you can shift the derivative from one factor to the other factor (under the integral sign) by just changing a sign. Sorry. I made a mistake before. The surface term should not be the derivative, but the term that is derived. I've corrected the formula. This is what I wrote: \[\left.\frac{d}{dx}\left(\psi^{*}\psi\right)\right|_{\textrm{infinity}}\] This is what is should be (already corrected in the original post): \[\left.\psi^{*}\psi\right|_{\textrm{infinity}}\]

No, no. Careful. That's not the point. The point is that the integrals, \[\int dx-\left(\frac{\partial\psi^{*}}{\partial x}\psi\right)\] and, \[\int dx\psi^{*}\frac{\partial\psi}{\partial x}\] differ in what is called "a surface term" or "a boundary term". Because in quantum mechanics the boundary is at infinity, they can be identified for all intents and purposes. If you equate one of these integrals to its complex conjugate, what you're saying is that the integral is real. That's not quite so correct. The integrals are equal except terms that vanish at infinity. The point is a bit subtle, but that's the way to read its meaning. Edit: In this case, the surface term is, \[\left.\left(\psi^{*}\psi\right)\right|_{\textrm{infinity}}\]

Consider: \[\int dx\left(-\frac{\partial\psi^{*}}{\partial x}\psi\right)=\int dx\psi^{*}\frac{\partial\psi}{\partial x}\] and what I told you in the other post about fields vanishing fast enough at infinity. You get twice the first integral in 1.30.

It is because you are evaluating the integral at the limits of integration. That's very common in any field theory. The fields are assumed to go to zero fast enough at infinity. In fact, you need that if you want your momentum operator to be Hermitian. If D is any of these differential operators, you need both the i and the vanishing at infinity so that, \[\int d^{3}xF^{*}iD\left(G\right)=\int d^{3}x-\left(DF^{*}\right)iG=\] \[=\int d^{3}x\left(iDF\right)^{*}iG\] I hope that helps. Good question. +1