joigus

The whole point of the Stern-Gerlach experiment is to disprove the classical theory of radiation. You get two or more (2S+1), separated, clearly defined spots where the charged particles end up, corresponding to the different values of spin. If the phenomenon could be interpreted classically, you would get a continuous range of arrival positions, which is never the case. That's why the SG experiment is considered to be one --among many-- confimation of quantum dynamics, as opposed to the expectations of classical-field dynamics.

No. If AI were able to "create" a herd of antelope or a coral reef, plus the long-term incremental changes in the fossil record that led to them, I may change my mind. Then we would have gone full circle in the generation of intelligence by intelligence, which is only the first step that it would take to convince me. IOW: Evolution is obvious once you understand its principles and let the facts sink in. And it is impossible to grasp if you have a very concrete, atavistic prejudice that obstructs your understanding, by ignoring the facts and misunderstanding its principles.

I'm rather confused by your use of the term "a number's territory." You obviously mean something you're finding difficult to define --I infer that from your repeated use of quote marks. Can you be more precise? It's obvious there are numbers so big that you would be hard pressed to find anything physical that makes them relevant. Or so I think. Is something like that what you mean?

My pleasure. I don't know how Graham's number is constructed either. A good principle to organise (integer, counting) numbers by scale (in physics) could be perhaps considering this: Small numbers: Number of people in a room (somewhere between 10 and 102=100) Moderately big numbers: Number of atoms in a typical piece of matter (1023) Big numbers: Number of photons in the universe (1090) Really big numbers: Permutations of big numbers or number of ways to re-arrange big numbers: (close to NN/eN) The last one is called Stirling's approximation. It's a way of "taming" really big numbers by avoiding them directly (knowing all their digits) and using instead a ballpark way of dealing with them.

You might be interested in this: https://en.wikipedia.org/wiki/Graham's_number https://en.wikipedia.org/wiki/Large_numbers The thing about these large numbers is not just, of course, how big they are. You could always talk about Graham's number +1, and that would be bigger. It's rather about humongously big numbers that somehow are significant in one part or another of mathematics. Graham's number is really really big in the sense that people seem to be quite uncertain about most of its digits. So in that sense it's very peculiar. Not at all like powers of ten. It's kind of unwieldy in the extreme.

My feelings exactly.

I don't think it's a coincidence. It's obvious that our anatomy seems to favour use of 10-base number system. The Babylonians had a preference for 60-based number system. And the reason is the high number of divisors that 60 has: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30. One problem is that you need sixty symbols or digits, which becomes cumbersome. But still, there are traces of the Babylonian system in our 12-based hour system, as well as in measuring angles.

A good starting point could be, Can you explain in terms as simple as possible how information compression could be relevant to QM?

Yes, but that's on another level. I thought you meant freedom for investors. A regular job is not the market.

I'm afraid 100 % free and 100 % ethical is impossible. The moment you introduce freedom, you also introduce the potential for non-ethical behaviour. It's the law of unintended consequences at work. 100 % free would be like the savanna. 100 % ethical --by regulation-- would stall most enterprising iniciatives. So it's a compromise we must reach. It's always been like that. Would an algorithm be possible to limit the potential damage of guaranteed unethical behaviour? Sure. But I'm afraid people wouldn't like it, plus there's no money in it for algorithm designers. When I say "people wouldn't like it" I mean rather the tens who hold billions than the billions who hold tens.

I'm assuming you're made of matter, so no. I reckon you would have to make an antimatter copy of yourself and send it to an antimatter version of the past environment you would like to be in. Here's the answer, in the form of a well-known poem by physicist Harold P. Furth, A.E.C. stands for "Atomic Energy Comission, and the poem refers to the certainty that any close interaction between matter and anti-matter would end up in a burst of gamma rays. You touch any sizeable amount of antimatter, and you're done.

Agreed. There is such a thing as punctuated evolution, and the concept can be applied to some extent to scientific progress too, I think. Abrupt changes appear out of complex scenarios that could not have been predicted in any analytic way with the tools at hand. AAMOF, they are to be expected somewhere along the way. Alexander Fleming's discovery of penicillin is a perfect example. We are in the middle of a massive data-gathering phase now, measuring things we could barely have dreamt of only decades ago. That's why something new is to be expected. That's also probably why, I think, no continuous model like the law of diminishing returns really applies when it comes to predicting this kind of abrupt changes.

In the words of George Costanza (Season 3, episode 9, The Nose Job), "You can't stop modern science. You can't stop it. You can't stop it. Can't stop science. Can't be stopped. No way, no how, science just marches..."

So do I. There are silent, progressive revolutions, and you understood my point perfectly.

Topological insulators Quantum computing High-precision tests of the standard model (not science-spectacular, but extremely important) Neutrino physics (flavour-changing neutrinos) Observational cosmology (gravitational waves, supermassive BHs, accelerated expansion, exoplanets, etc.) Negative tests of proton decay (negative-result test are extremely important) Non-linear optics And the list goes on... As to other sciences, Ancient DNA Gene therapy Stem-cell therapy Ribozymes Cloning techniques And the list goes on... I think it's the other way around: It's very hard to keep up, really. It's because we're piggybacking on the shoulders of giant breakthroughs that it's so hard to tell how fast we're going --relativistic metaphor-- and even harder to relate the information in order to get a glimpse of any kind of big picture. I think there hasn't been a major change of paradigm, and that's easy to be misinterpreted as no advance. Whether these major advances will coalesce into a paradigm shift is neither certain, nor necessarily the case to be expected.

Maths is the proper language to describe/ascertain uniqueness and/or complexity. What makes you think there is a better language? Approximate calculations without maths? And how would that go?

It is my opinion that words themselves are worthless without the world of meaning behind them. It's what it means what's been, I'm sure, essential in human evolution. Long-distance trade, collaboration, etc. would have been impossible without the phatic function of language. Having others know the communication line is open even if you didn't completely understand the full import that they're trying to get across is a priceless function of language. I learnt that word, as usual, by carefully listening to others. I wouldn't have understood it by just reading a book. Thanks for appreciating...

I personally don't parse every sentence I hear or read through propositional logic. That's all I meant. Language has a phatic function too, you know.

There's nothing wrong with seeing with your mind's eye what your heart feels. It's not science, that's all. And it certainly isn't a scientific speculation.

You have no basis to assert this. All we have is endocasts and certain genetic sequences. How do you know?

Try with different definitions of existence and see if you can make some progress in your understanding. Maybe everything is fleeting, under the proper time perspective. You didn't mention what your definition is, BTW.

You're probably right. We got lost in geometry. I suspect there's something about time that's not entirely geometric. To me, it has the unmistakable flavour of abstract algebra. Suggestions from QFT are clear. Deeply involved in microcausality, operator-ordering questions, and the CPT theorem.

I don't know either.

Why not? Minkowski is R4 with signature (-+++), while R4 with signature (++++) is 4-dimensional Euclidean space. S1xR3 with signature (-+++) would be a Minkowskian cilinder, while with signature (++++) would be Euclidean. Metric signature and topology are quite independent.

What about a 4=1+3 cilinder? A cilinder is flat, it's S1xR3, but it's not R4.