studiot

There I was, browsing for a new telephone. So here is the unexpected humerous example that the elementary AI algorithm offered me Why it thinks that folks frequently buy washing powder and plastic plants along with a telephone I can't imagine. But it is amusing.

Energy doesn't 'go anywhere'. It is converted from one form of energy to another. Have you studied the different forms of energy ? Swansont mentioned using the energy from falling weights, like your ball. It may interest you to know that this was the experiment that kicked off the whole science of energy. So it was a good question of yours. The experiment was carried out by one James Joule, for whom the unit of energy is named. https://resources.pcb.cadence.com/blog/2022-joules-mechanical-equivalent-of-heat-a-conversion-factor We did a simplified experiment like this in school by putting lead shot into the bottom of a tube and turning it upside down over and over again and then measuring the temperature rise in the tube. This was called an experiment to measure the mechanical equivalent of heat.

Noting your comment about attention span here is my short form answer. Matrices refer to when a bunch of things that have some sort of connection between them so that, taken as a whole they form something that is greater than their individual parts. The english word comes from the latin prefix 'matri' which refers to female matters and more particularly the latin word 'matrice' which refers to the womb. In English, the word matrix has been used to indicate this connection in many wide ranging places . For instance in education, matriculation indicates a connection between the subjects studied. Such connections may be shown in a data table, also called a matrix. Many subjects, including formal logic employ data tables. These types of matrix may or may not have a connection to linear algebra. In Materials Science, Chemistry, Engineering and related disciplines a matrix is formed when a large bunch of atoms are connected or linked (by chemical bonds) to form a continuous material. Other terms for this are substrate. An example would be the resin matrix in fibre reinforced plastic. In linear algebra a matrix is a data table in which all the entries are numbers or functions which have definite numerical values. Another word for this is an array of numbers. The connection between these numbers follows the rules of linear algebra.

Thank you for your reply. Note I said formal philosophers. Such as Plato, Kant and Wittgenstein. Archimedes and Bacon stood out because they embraced the formal but went further. By formal I mean those who believe that they can form a worthwhile opinion on anything and everything by sitting in their armchair and pontificating. To my way of thinking this is like taking a blind man to a known beauty spot viewpoint and asking him to describe the scenery. Something (a lot ?) will be missing; something will be wildly wrong in his description.

Perhaps you would like to rephrase this to resolve the apparent contradiction ?

The thing I have against formal philosophers is that they have been debating for thousands of years, yet Philosophy has no developed a growing and increasingly coherent body of a subject. As each generation discards what went before they are no further forward than they were millenia ago. Perhaps this contrast with Science is because Philosophy do not have the reality check of compliance with observational data.

Thanks I lost my last response and further thoughts to mathjax the mangler when I was collecting the OP's further questions to reply to. That is on top of the fact that we had had something of a crisis here, chez moi, and a hectic couple of weeks. I see from your link that PhysicsForums and Stack Exchange are also discussing this problem.

I would help you to think about what is the meaning of momentum. Momentum implies the exertion of a classical force. A simple classical (wave) explanation as to why light exerts a force when it impinges upon a massive body can be had direct from maxwell and the orientation of the E and B fields of the wave. The wave exerts a Lorenz force on the body at it impinges. But force is rate of change of momentum or momentum is the time integral of force.

The smooth change of refractive index condition is exactly what happens in marine acoustics. (It is not the only thing though.) In this context the eiconal equation is discussed chapter 2 page 5 et seq of the book most people refer back to by R J Urick Sound Propagation in the Sea. Originally written in 1979., but is now availble as a free pdf. Alternatively the eiconal equation for optics and many other uses such as the propagation of discontinuities is discussed in Erich Zauderer's book Partial Differential Equations of Applied Mathematics Wiley 1989

Of course there are. I never said the universe or anything else is completely deterministic. These are factual examples not analogies. But not everything in QM is indeterminate. QM expressly says that an electron cannot have a principle quantum number of exactly 2.375. It's not one side or the other ; all or nothing.

Here are two pages from the book by Nobel Physicist Frank Wilczek that may help you. Fundamentals Ten Keys to Reality. His whole theme is to cut down modern Physics, including the maths, to the bare bone essentials, so you might finds lots of useful understandable explanations here. Note here he says that none one really knows why particles have the mass they do and he lists at least three zero mass particles. In the main text he lists mass as on of the three essential characteristics or properties of matter. You will have to read the book to learn what he says about energy. You might be surprised

Nicely put. +1

etc Very patient answers if you ask me. +1 I was waiting till I cooled down to answer to thanks for saving me possible embarrassment. This whole thing sounds more like something EE Doc Smith might have written in the early 1950s

I haven't been able to get to this question yet, with all the chaff. Is prohibition a form of determinism ? It determines what you can't do after all. And QM prohibit an infinity of states to particles, waves and all sorts. Even in Thermodynamics there are prohibitions such as in Caratheodory's version of the second law. Eigenvalues, eigen states and eigenfunctions are all examples of discriminatory determinism, as was H Ford's declaration They can have any color they want so long as it's black. Swansont keeps telling anyone who will listen and many who will not that Science in general and Physics in particular is about models. Ever hypothesis, law, formula and so on needs testing, calibrating, with guaranteed known data and known results, outcomes etc. The only such guaranteed data is in the past.

Obviously they played this game differently in your playgound. This is a ridiculous attempt to contradict by ridicule. "Only some systems exhibit this." I said generally, why repeat it ? "Most systems are chaotic, " Stated without a shred of proof. "Take the state of Earth just after the Theia event. From that state, life is unlikely to form, and if abiogenesis does occur, it will most improbably evolve into anything that would be recognized as a mammal." ditto But here my comment about the compounding probabilities could apply. Also you have again omitted any proof of you modifying adjectives. "You drop successive grains of sand from a fixed point and which way a given grain goes is fairly unpredictable, but the eventual conical hill of sand is very predictable. " You actually agreed. How does that invalidate my point ?

I must point out that the key point of the discussion is about determinism/nondeterminism of the future Interesting point, but don't we use 'hindcasting' to check/test hypotheses ?

Not really since not one of them have achieved their objective. SR is correct within its domain of applicability. Some have tried to extend it beyond that and have found that it does not necessarily work beyond its domain of applicability. This is just plain wrong. A good history of the century of what he calls "The Battle of General Relativity" was written by Professor Ferriera in 2014. Even Einstein himself though one thing, then another then yet another during that time. Lambda, for instance was not originally included. Einstein added it later then withdrew it. But today's (Astro)Physicists have found a f=definited use /reason for it.

This is not a simple standard school problem so it would be helpful to tell us the context in which it set. As said the contact angle at the ceiling must be zero. So you then need a 'hump' shaped line that flattens out to parallel to the horizontal at both sides. As in Fig A. Rotating this line will produce a domed hat like an inverted ww1 or ww2 tommie's hat with a dome and a wide flat brim. This is modelled as in Fig B. You can reduce this to a one dimensional solution by assuming radial symmetry. This would be expected by the action of surface tension. This is shown in Fig C. You have identified the important features of this problem, including the fact that the brim plays a crucial role in maintaining the adhesion since it contains little or no water (weight) but presents an large surface area to the atmousphere to press against. As a first estimate I would suggest that surface tension holds the droplet together but does not hold the droplet against gravity. A more sophisticated model would include the change in surface energy cause by the droplet breaking away, which could be incorporated in the virtual work equation below. Your force balance can be conveniently solved by the theorem of virtual work, either using a differential virtual vertical displacement or a differential virtual increase in the weight of the drop. I don't think Young's formula will help you here, but it was a good idea. The weight of the drop is derivable from the geometry and in particular the surface area. This is then an extremal (maximisation) problem which could be attacked by good old trial and error or by the calculus of variations if you are seeking an analytical solution.

Or they will never complete a game. If you can go back even a short time, then that prior state must be fully determined by the state shortly prior to that, and so on... Hence if we can go back a little and retain determinism, then we can go back all the way to the beginning. Of course there's no evidence of this short term determinism. For one, it presumes a meaningful state of a system, which is a counterfactual, and few interpretations of QM support counterfactuals. I grokked that you didn't grok what I said so I will rephrase it. I meant to clarify what definition of determinism was in play. This asked whether determinism refers to a single event (eg your robots playing RPS) or goes back some indeterminate distance down a causal chain of events. FYI my mathematical comment observes the fact that a chain of probabilities (eg a chain of event each with a probability) does not in general converge to zero but to a definite value and is therefore deterministic, even though we do not know the individual probabilities involved. Probabilities trees are even more complicated.

If that is really your point, why didn't you say so in the first place (first post ?)

You put a lot of effort into this reply to only two participants. So how about you reply to some of the many other participants ? Incidentally I thought this a good point Though what do you mean about it not being an action ? Also have you heard of reflexes and involuntary actions or the many action we carry out all the time without thinking about them at all, such as breathing and walking (can you normally feel the ground when you walk?)

Well why not show it then ? Re this second quote and 'predictability v determinism'. The mathematics of continued products would disagree with you. There are two figures of speech (that I know of) involving elbows in the English language. Both are robust but quite inoffensive. Howevr the German' Lebensraum' has connotations that might offend some members. So I am trying to ignore it.

Interesting question +1 This is also an interesting question +1 I would say the mathematics of continued products.

I look forward to your report. Please note I am not expert in this - it was only a memory from long ago so I was gratified to find out that my memory had not failed me. So I am having to do some fast thinking on the hoof to answer your excellent questions and if you come up with something new I would be glad to hear about it.

How does this affect the issue raised by the thread ?