joigus

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.

Do you mean provide another example of tautology, which we would only escape by proposing further relations in the initial tautology? My example was classical mechanics, which would lead us too far from OP's goal at almost any amount of detail. But I think it's plausible that, if we were to make any progress in the problem of time, new concepts would have to appear, being circular in their initial formulation not constituting a difficulty impossible to overcome. If I were to try, I would take inspiration from similarly groundbreaking advances. In the case of Newton, F=ma seems to be both a definition of both mass and force, which at first sight doesn't look as much of a step towards progress, does it?... Until you formulate a law of force F(x,v), the concept of inertial frame as somewhere far removed from sources of interaction where systems satisfy the 1st law, etc. The problem with time is it's so difficult to conceive of intuitions that would lead the way as, in the case of Newton, isolated systems, force, and mass.

IMO, we shouldn't be too afraid of tautologies, as long as we have an external hypothesis to get us out of it. In fact, if we're ever gonna find a way to understand time, I think it's very likely that we have to do it by formulating some kind of tautology, and then ponder what the external assumption must be if we're to make it into a predicting machine. An outstanding example is Newtonian mechanics. The bare formulation is as tautological as can be. What is force? Mass times acceleration. But hang on. What is mass? Oh, that's easy: It's the ratio between force and acceleration in any direction. We wouldn't get anywhere from just that. But there's a hidden assumption: Whatever we want mass to be, it must be the same in every direction. And then there's the amazingly consequencial assumption that, under different simple circumstances, force depends on position in some particularly simple way. Then we're in business, because we can predict. Something that, with the sheer tautology, was impossible.

It is a scalar field that's needed in inflationary models of cosmology to provide a mechanism for the vacuum to go through different phases of expansion. A scalar field is a field represented by a number at every point of space and every instant of time, so that it doesn't change at all under rotations. In a way, it's very much like the Higgs field. It affords you to "imprint" needed properties on the other fields and space-time itself to account for observed properties that don't quite fit the model without it. It's considered by some to be somewhat ad hoc --convenient, but not very well understood or logically compelling.