joigus

This is what you want: https://en.wikipedia.org/wiki/Logarithmic_differentiation#:~:text=In calculus%2C logarithmic differentiation or,rather than the function itself. Plus changing exponential bases: 2^(-x)=e^(-xln2)

Yes, Pinker's quote is what's in boldface. Pinker's adjectivation is unmistakable. They used atomic randomness as a random-number generator. You read the numbers of decay times and use those numbers as input for another variable that has biological relevance by setting this other variable to take those values. That's what I understand. I hope that helps answer the question, but some feedback would be very useful.

The Road to Reality is a very good book. Any recommendation from Genady is probably worth considering, OTOH. It's not a book to actually learn physics though. It's more of a whirlwind tour of the exciting topics of modern physics. As to popular books with emphasis on experiments, I recommend, Weinberg's The Discovery of Subatomic Particles. Then you can try the Feynman Lectures on Physics. If you want to learn physics in earnest, you probably can't do much better than Landau & Lifshitz's Course of Theoretical Physics. Encyclopedic (10 volumes.) A bit old, but will take you a long way in understanding the deepest principles of physics and how they're applied. There are many other books, I'm sure, and with a more modern focus. A good rule of thumb is: The more unassuming the title is, the more likely it will take you to the nuts and bolts. I think you get the idea. Although we could hardly be more off-topic.

This is no coincidence. The Laplace equation must monitor the spatial/vacuum factor of any physical equation worth its salt, as Einstein observed in his famous popular book on the theory of relativity. Physics does deal with many 3-dimensional problems, of course. When it comes to proposed generalisations of the standard model, it may even consider 26 dimensions. Why do you say that?

Yes, you're right. It's me who brought it up. I forget what it had to do with the primes, though. Or how the question surfaced. I'm no expert on number theory. You may be on to something when you say that differentiable functions of a complex variable may have to do with the prime-counting problem. A function being differentiable in a complex variable z=x+iy is a much more restrictive condition than the corresponding condition on a real-variable function. But in mathematics it's important to define anambiguously your concepts, and the state clearly what your assumptions are, and proving rigorously whatever you say about them. Sorry, I can't contribute much more at this point. I hope that was helpful.

Exactly. God of the gaps is what I meant. Filling in the gaps in your knowledge with answers that are emotionally satisfactory seems to bode well with the needs of a brain that has a frontal cortex as sophisticated as ours, with so many neural connections. And with a FOXP2 gene that accumulates comparatively so many mutations as ours does. The idea is that having a representational scaffolding for all those things we feel unable to solve by reasoning may have some kind of evolutionary advantage. From what I know, paleoanthropologists are toying with this idea. Whether such is the case, or it's simply a spandrel, we may some day learn. It could be just a spandrel that comes with the territory. I watched this talk some time ago. Very interesting. Everything Thomson says is compatible with religion being a psicological spandrel though.

What's the speculation here?

As suggested by other members, gods were invented (not created, I would say) by humans. God is a place holder for everything we don't understand. Patterns can be found in the way different communities of humans fashion their deities. It is no coincidence that monotheisms have been developed by desert peoples. Forest peoples are more prone to animism. The first gods have been identified with powerful animals, ancestors, most basic needs (fertility, good luck,...) Sun and stars. All things that were important to those societies. I think it's a natural byproduct of the activity of a brain that desperately needs to plan ahead. Mind your infinite regressions, BTW: Who created the one who created god? And so on.

I did?

I don't understand what you're getting at. Take, eg., the sentence, ¿i being used as a spanner in the works? What does that mean? The imaginary unit i does not come from a choice, as the vector (0,1) does, for example. Complex numbers are much more constrained than vectors, and obey different definitions. There is no such thing as rotational invariance for complex numbers, for example. Quaternions are very different from complex numbers also. E.g., they're non-commutative. Serious maths are not about "this looks like that" and such. So, while I don't understand what you mean, I see many problems with some of the things you say. Too loose connections in what I can understand from what you say. Harmonic functions are the real and imaginary parts of differentiable functions of a complex variable when expressed in terms of x and y. They're used to represent 2-dimensional problems having to do with the Laplace equation (electrostatics, laminar fluids in absence of eddies, etc.) I don't know what that has to do with the Riemann hypothesis.

Is this homework?

You are conflating several things here that are actually different. Surface of last scattering: The surface in the night sky beyond which we cannot see because at times older than that the universe was opaque to radiation. The distance to us of this layer of the universe changes with time, and is being pushed by expansion towards the kinematical horizon --see below. Kinematical horizon: In a De Sitter universe, every observer has a limit to how far away he can see the galaxies. The distance to us of this layer of the universe is fixed in a universe with a constant rate of expansion, and so doesn't change with time. It doesn't depend on technology either, as it is given by a natural limit. Namely, receding velocities greater than the speed of light don't allow you to see anything there due to redshift. Why the surface of last scattering is "about to disappear" (give or take a couple of billion years) from view in this time of the history of the universe, and whether that is a coincidence, is not known. But it appears to be so.

I bet we haven't heard the end of it.

That's why we have idioms as 'blessing in disguise.'

Define good (vs. bad) use of science. Define making things better. Define what is good. It's clear to me that just good is better than just better. A little better is certainly not as satisfying a lot better. I have clear ideas about "better than nothing". Agreed, but... Are all possible directions equally good?

You're right. There's no conflict. Google search term: God of the gaps.

STUNNED! SENT, TENETS, TENT, STUNT, TUB, BUS, SUB,... 'Cede' is a good one. I see you detected a B boson. Nice one. It opens up many possibilities.

Kronecker delta results, as Swansont said, because of basis being orthogonal. I see you're studying quantum mechanics. The underlying physics of this is: States with different values of an observable must be orthogonal for reasons relating to probability interpretation of quantum mechanics, as products <i|j> are essentially transition amplitudes. Vectors must be normalised, so <i|i>=1 for same i. Orthonormal bases are central to the formalism of quantum mechanics.

You forgot TEST and SET, and also TUT (as term of affection for TutanKhamun). But that's nice. LOL. This is what I do when the lights go out. Warning: I've left some resources untapped. This is a combined exercise in combinatorics as much as in the particle universe.

Only the quarks named as u, d, s, c, t, b are allowed for now. The mandatory language is English Eventually, we will allow the use of bound states of quarks, like p (proton), n (neutron) and any other particles that can be named with a Latin letter, like the electron (e). Here's mine, STUD The next one is pretty obvious. You're allowed to use Shakespearian English, Yorkshire English, Alabama English. Only, please document.

Here's the problem (my emphasis): Now you say (my emphasis): In order to keep an electron on Earth for as long as it takes to send the other one all the way down to M87, you must make it orbit under a field. That's a lot of change in the quantum mechanical phase of the electron. And, further (my emphasis again), This conflicts with previous point that the electron measures up. If they measure anything (any one of them), they're no longer entangled, and their common state is described by a density matrix representing a strict mixed state. But the question whether the gravitational field affects the quantum description and how is outstanding, and I don't know the answer to it, but I'm thinking about a possible gedanken to make an equivalent question without the problems I see. It's questions like this that make me keep coming back to these forums, to the detriment of my activity in other 'more expert-driven' forums. I just would like to emphasize Swansont's particular point that, which I think is essential in all this business.

Mentioned as "base-2" on: https://www.scienceforums.net/search/?q=base-2&quick=1&type=forums_topic As a topic: https://www.scienceforums.net/search/?q=base-2&quick=1&type=forums_topic Mentioned as "binary system" or the like gives similar results. Not exactly. Not all numbers are powers of two, are they? It means all numbers are expanded as combinations of powers of two with multipliers (digits that are only integers less than two). That covers all numbers.

Thanks

Carbon. It takes a hundred suns to die before your magic web extends. But once it does, a world of possibilities is revealed. Your opening act is: "Let there be life". Not quite satisfied with this, you make things that make things that bring about: The hardest substance (diamond) The best lubricant (graphite). The best thermal conductor (graphene). Is there an end to this magic? If the Ancient Greeks had only suspected your capital importance, they would have named a god in your honour. Sorry, I got carried away with carbon love. Here's the news: https://phys.org/news/2022-05-long-hypothesized-material.html?fbclid=IwAR2lCoyyVSC4bkt0XDRGCG9FRV7Y16dM78pO8n4Hq03hv-4QbzeMqIPcFf0

OK. But with that what you're doing is inventing a fancy complex mass m=Re(m)+iIm(m) (a quite esoteric quantity) which is only there to give rise to the 'actual mass', which is its modulus (norm.) You're quite right. You can always declare any positive real quantity as the norm of some other inconsequential complex variable. But Ockam's razor will cut it off.