Genady

Here are the last two paragraphs in the chapter 14, Wormholes and Time Machines: Hawking suspects that the growing beam of vacuum fluctuations is nature’s way of enforcing chronology protection: Whenever one tries to make a time machine, and no matter what kind of device one uses in one’s attempt (a wormhole, a spinning cylinder, a “cosmic string” or whatever), just before one’s device becomes a time machine, a beam of vacuum fluctuations will circulate through the device and destroy it. Hawking seems ready to bet heavily on this outcome. I am not willing to take the other side in such a bet. I do enjoy making bets with Hawking, but only bets that I have a reasonable chance of winning. My strong gut feeling is that I would lose this one. My own calculations with Kim, and unpublished calculations that Eanna Flanagan (a student of mine) has done more recently, suggest to me that Hawking is likely to be right. Every time machine is likely to self destruct (by means of circulating vacuum fluctuations) at the moment one tries to activate it. However, we cannot know for sure until physicists have fathomed in depth the laws of quantum gravity. Thorne, Kip. Black Holes & Time Warps: Einstein's Outrageous Legacy (Commonwealth Fund Book Program) (p. 521). W. W. Norton & Company.

It is here: Black Holes & Time Warps: Einstein's Outrageous Legacy (Commonwealth Fund Book Program) Reprint, Thorne, Kip, Hawking, Stephen W. - Amazon.com

Oh, well... Just to close the case: In terms of linear algebra, the problem can be expressed as the matrix equation A x = 0 where: x is the vector of x1, x2, ... , x17 A is a 17x17 matrix with 0 along the diagonal, and +1 or –1 at the other positions such that each row has eight +1s and eight –1s 0 is the 17-component zero vector From the equation, x is the null space (the kernel) of A. The problem is to show that for all matrices A satisfying the above, the null space x is: x1 = k x2 = k ··· x16 = k x17 = k where k is an arbitrary value. In other words, null space x has rank 1. For this, rank of A has to be 16. That is, if we take a 16x16 minor matrix of A, its determinant is not 0. So, we take a 16x16 matrix with 0s on diagonal and 1s and -1s everywhere else, and consider its determinant. The determinant is sum of products of all possible combinations of matrix elements, one from each row and from each column, with corresponding coefficients 0, 1 or -1. The combinations that include 0s from the diagonal are 0s and don't contribute to the sum. Each row has 15 non-zeroes. There are 16 rows. So there are 15^16 combinations of 1s or -1s. This is an odd number. For every two rows, 14 non-zero pairs are from a same column. These do not contribute to the determinant because the corresponding coefficient in the determinant formula is 0. There are (14 times a number of pairs of rows) of such combinations, which is an even number. After removing the latter even number from the odd number above (i.e. from 15^16) we are left with some odd number of products that do contribute to the determinant. Each product is equal to either 1 or -1 and contributes with a coefficient of either 1 or -1. Thus the determinant is a sum of odd number of 1s and -1s. Here comes the punch line: No sum of odd number of 1s and -1s makes 0 !!! So, determinant of this 16x16 matrix is not 0. QED.

Yes, quantum computation is based on a different logic. The foundation for it is quantum entanglement, which cannot be implemented using usual logic in principle. Thus, it allows to run completely different kind of algorithms. For some problems these algorithms are orders of magnitude shorter than the ones based on usual logic. This is where the quantum computing advantages come from rather than just speed and miniaturization.

No.

Yes, it appears so. He quickly moves on to deeper advantages of flexible learning compared to pre-wiring.

I need a clarification. I can logically show that for any prime number there exists a greater prime number. Is it a negative or a positive?

Like this, I guess. PC, Windows 11, Edge.

DNA is neither a blueprint, nor an instruction set, and I am not a fan of metaphors /analogies. The point is that it, as you say, is not a "map" of the final product. The paradox he describes does not exist, this is my point. He says that it is a paradox, that the final product contains more details than a source used to build it. But this happens all the time, e.g. with algorithms. For example, a number that represents square root of 2 contains infinite number of details (infinite non-periodic sequence of digits), but it is produced by a short simple algorithm, which knows nothing about them.

Oh, the headline writers ... Scientists Find A Hole In Earth’s Centre, Through A Secret Duct Under Panama (indiatimes.com)

@joigus Yes, of course. Regarding the experimental tests or microscopic studies, I wish, but (a) they don't grow in aquarium, as you suspected, and (b) I can't and wouldn't cut a piece off a living coral, as all terrain here from the water surface down to the depth of 200 m is a protected Marine Park. Regarding prevalent direction of light - no such thing at that depth (30+ m). The water is very clear but the light is scattered and comes "from everywhere." Thank you.

Unfortunately, he does just the opposite. He takes this starting point as a correct description and goes to conclude that actual brain structure is a result of learning rather than genes. Of course, the mistake is to see genes as a "blueprint", while they rather are an "instruction set". I was surprised to read this in a very recent book, written by a well-known author.

Regarding this last unanswered issue, I don't know the specific answer, but it is not a puzzle anymore, because we already got asymmetry where it is needed. E.g. since new polyps are added not linearly, but helically, they secrete a new piece of the tube in an asymmetrical way, which can easily lead to a helical tube. And sorry @joigus, I should've clarified it already: regarding a front-back direction for the polyp I kept it in a spirit of the earlier "assumption 2", i.e. back is where the closest neighbor is while front is open. As we know by the "assumption 1", they sense each other.

Stanislas Dehaene is an important psychologist and cognitive neuroscientist, but I think that he is grossly mistaken in genetics, in the following passage from his book, How We Learn: Why Brains Learn Better Than Any Machine . . . for Now: He goes on suggesting his idea for the paradox resolution, but I think that there is no really a paradox, just a mistake in the assumption on how genome works.

Yes. Yes. (They did calculate the amount of uniformly distributed dark energy using GR, as you know.)

Sorry, but this is one of the specific cases where Newton gravity just can't answer the question, but GR can: gravitational effects of an infinite mass distribution. What it means is, that applying Newton in such cases can give a variety of contradictory answers, depending on how you want to calculate a diverging integral.

His book, Naturalist by Edward O. Wilson, was a required reading when I studied Biology. I liked it.

Thank you. Just wanted to clarify this.

Yes, I completely agree. There is one thing left unanswered still, on the next level up rather then down the scale. This scheme explains a helix that polyps make around the tube that they grow on, but it does not explain yet the helix that the tube itself presents to us.

That's correct. There is a theorem that any BH is entirely defined by these three parameters: its mass, charge, and angular momentum. Dark matter falling into a BH would increase the BH mass, but would not be detected otherwise as it doesn't radiate. BTW, we can talk about "flowing into" BH, but not about "passing the event horizon", because nothing ever can be observed passing the event horizon, by an external observer.

Are they thought not necessarily to interact via the weak interaction, or certainly not to interact via the weak interaction?

Ah, I see what you mean. But the baby coral doesn't grow radially but tangentially to the cylinder surface. Here is a scheme (borrowed from the circular polarization of light.) As you move along X, each arrow, representing next baby polyp, is tilted to the right. The result is right-handed helix. (My previous image was only to illustrate a budding process in general, nothing to do with my suggestion.)

For some reason I can't see the attached image. I think what you said is not correct. When you look outside from the cylinder's central axis, you have right and left well defined regardless of your orientation. (And the baby polyp is attached to the outside of the cylinder.)

Here is how I reformulate the puzzle to make it clearer without, hopefully, pushing a specific way of solution: Let's say, the apples are marked and their weights are x1, x2, ... . He takes out the apple #1 and finds that, e.g., x2+x5+x9... = x3+x4+x6... Then he puts the #1 back, takes out #2, and finds that x1+x7...=x3+x4... Etc. 17 times. Each side of each equation has 8 apple weights in it. We are asked to show that x1=x2=x3...

@TheVat I was thinking in the same direction and got an idea of where the chirality leading to that byproduct could start. Although the body of polyp is radially symmetrical, the budding process is not. See illustration below. This provides an opportunity to make a "one-sided liver", like in the @joigusexample above. If the genetic instructions of this coral cause a baby polyp to be a bit tilted say to the right, the next clone will be tilted again to the right, and so on, and voila, we get a helix with the specific chirality. Thanks a lot for the contributions!