Thursday, May 14, 2020

Some people favor extremely unlikely, contrived hypotheses

Under the article about Witten's spaceships, we had exchanges with Jakub Scholtz, a postdoc at Durham. Of course, I remember him as a brilliant Harvard undergrad whom I was officially supervising as a coach of a sort – which means about one or two meetings per year. We should have done more than this bare minimum! ;-) But there was something Czech about our staying near the minimum.

At any rate, in Fall 2019, he and James Unwin submitted a paper that Witten has built upon, one proposing that some anomalies in the Solar System are explained by something better than the ninth planet, namely a small black hole. (The word "primordial" is really redundant if not a lipstick on a pig. Because it's supposed to replace a hypothetical planet, the mass of that beast obviously has to be just planetary, not stellar, so it can't be a stellar black hole. The word "primordial" is just a fancy way to describe the disadvantage of the theory that the black hole is much lighter than the range of astrophysical black hole masses that is well supported by observations and theories linked to them.)

OK, it's a very appealing hypothesis that we have some inch-sized black hole at the outskirts of the Solar System. If you followed the conversation, you know that I remained skeptical about the picture. Well, I surely find it somewhat plausible that there are such small black holes around. But I primarily remained skeptical about the suggestion that they have found new evidence in favor of the theory – anything that you only see gravitationally may be suggested to be a black hole but are there specific reasons to think so in this case?

So I simply can't get rid of the feeling that Jakub does some circular reasoning and he is excited by things that aren't surprising at all – by "coincidences" that are (almost or strictly) bound to exist if you allow a sufficiently general form of similar sentences. And you should: it's a part of the look-elsewhere effect.

So such black holes could be formed at the electroweak temperature. Great. But is it evidence in favor of the theory? I don't think so. The "electroweak scale" is just a translation of a number with the units of energy, \(100\GeV\), into English. You can translate many other scales such as \(1\meV\), \(100\MeV\), \(10^{19}\GeV\) into English, too. It's some neutrino (or vacuum energy) scale, QCD scale, Planck scale, and dozens of other names exist and cover the a priori allowed range of exponents. As Feynman said, a good mathematician and physicist covers the real axis with friends. Near every number, there is a number he has befriended! When it's so, and it should be so (yes, he meant that you should be able to do many calculations within a 20% error margin or more precisely), the degree of surprise of being "near a friend-number" is really zero!

There is no good reason to think that the electroweak temperature is better suited for the production of black holes. It's just a scale that is important in the early 21st century because that's what the high energy colliders recently studied in detail. But the year "2000 after Jesus Christ" isn't universally and permanently important at the fundamental level (even if He were real and a Son of God, this phrase isn't because the number 2000 isn't a Son of God) and much higher scales are more likely to be relevant for the birth of the hypothetical primordial black holes. So the need for the electroweak scale black holes is really a disadvantage, not an advantage, of the PBH theory.

The previous text, the Bitcoin puzzle, seems like a great extreme example of the hopelessly unlikely reasoning of some people (much better than Jakub's, I think) where a wishful thinking and a biased support for one's own pet theory seems to get out of control.

OK, 30 minutes ago, the creator of the puzzle posted three hints

-------1. Do you have the Audacity to complete this puzzle?
-------2. 3 track names may help you in your search, but for different reasons!
-------3. Songs 1-9 are all you need. Have you found the right order?
-------4. Chaos and the logistic map are more thematic than they are integral to the puzzle. There is massive misdirection in this puzzle... Was that evil?

Great. Can someone guess the BIP39 private key? It's an ordered sequence of 12 words chosen from a list of 211=2048 BIP39 English words. In total, the information in such a sequence is 12 x 11 = 132 bits but some of them are checksums of a sort. So only 128 bits matter, if I understand well, and the probability to get the checksum right is 1/16. So I consider it hopelessly unlikely that someone will guess the right password given these vague hints but I created my words and they were
rocket west diagram photo flash thunder monitor music magnet tree truck city
OK, it's because a rocket appears in the first song, West appears in the spectrogram of the first song (both in the Morse code and as a part of an octagram of cardinal directions), then there is a bifurcation diagram, a photo of Mitchell Feigenbaum, the vertical coil might be a flash or thunder, a monitor is in another song, then there is music because you should hear and not see (as dictated by a comment "nothing to see hear" in the spectrogram), magnet seems to be the letter in another spectrogram, tree was basically leaked as a hint, the towncar is a personal is a coupe but it could be a truck, and I had one-half of the audacity to complete the password so I added city.

Before I went to write this blog post, I clicked at "check the checksum", expecting "checksum failed" but I got "checksum OK!". Too bad, nothing was inside the wallet. Again, I think that 1/16 of the sequences have "checksum OK" so I didn't win any real jackpot and many others who tried random sequences of words have seen some "checksum OK", too.

(WTUP.YB is a song by Zappa, What Is The Ugliest Part of the Body, and his answer is "mind", another allowed BIP39 word. If you think that you can fix my gaps.)

It's still possible that my sequence will be the closest one to the actual password. I think that it's unlikely that someone will get it right. The passwords are this long exactly because even if someone knows some vague hints about the passwords, he will still face a nearly impossible task of reconstructing one. And the hints seem to extremely vague, especially because the order of the 12 words isn't quite clear (12 words from 9 songs: which song gives you more than one? Or are there non-song words?), some might be missing, and most importantly, different words are obtained by different methodologies. In other words, a basic idea of cryptography is that many operations with sequences of bits are irreversible in practice (at least according to the currently known algorithms): if you hide your words or passwords in some complex ways, you just cannot get them back. They're as lost as if you burn a painting by Rembrandt. You could also say that the fire just cleverly rearranged the atoms... but good luck.

You know, the number of the 12-word sequences is\[

2^{132} \approx 5\times 10^{39}

\] which is a high number. The number of possible Bitcoin wallets is just a bit smaller than that. Now, in each song, only a small minority of the 2048 words may be a good representative of the words. But it may still be some 10 choices for each of the 12 words in the passphrase – e.g. because roughly ten methodologies to "get a word from a song" may be allowed. So the number of possibilities is still roughly 1012 which is called a trillion. No one will really try one trillion options and if he will, the amount of electricity he will consume won't be repaid by the $500 bounty! And he's still not guaranteed to include the right password.

The numbers get hopeless if the order of the 12 words is chaotic because 12! (twelve factorial) is another half a trillion. That should be multiplied by another trillion from the source explained in the previous paragraph. Also, the author (astrophysicist Herman Felker nicknamed Logic_Beach) helpfully added that the bifurcation maps are there just to confuse you (not useful to get the passphrase) and they and/or other hints may are "massive misdirection". Very helpful. A trillion may grow to a nonillion. The number of passphrases compatible with these hints may be smaller than 1040 by a dozen of orders of magnitude or two but it may still exceed the square root of it which is still huge.

I may be wrong and the right password will be found because it's rather straightforward for a clever enough solver. But I would bet that no one will legitimately find the right solution, however, at least not without further hints that must be much more detailed. And this guy – someone who can do electronic music including nice animations and someone who clearly knows something about spectrograms and chaos theory – believes that the solution is "fairly simple".

But is this opinion really correct? I don't think so.

It really looks like the right password is a hodgepodge of 12 words that are indirectly linked to 10 (well, just 9, we were told) WAV files and perhaps the videos accompanying them and the 3 titles (the titles probably tell you what you should do, not what some words are). But it seems that for each word, a somewhat different methodology to extract the word from the appropriate song may be used.

So the number of passwords that are compatible with the hints might be less than those 1040 but it could still be many trillions or much more than that. It is my guess that the author has hidden the words in some way and he believes that the task is reversible – that the words may be extracted – but it is not reversible at all because any promising class of reverse algorithms leads at least to trillions of options simply because the number of "detailed versions of the reverse algorithm" is at least trillions.

Of course, some silly puzzle for $500 served in worthless children's money isn't the real point where I care about the same concepts. It is fundamental physics what I primarily care about.

Lots of people – especially the self-described armchair physicists but even some armchair physicists who are actually considered real physicists by themselves and by many morons in their environment (including a majority of MSM journalists) – are proposing their fundamental theories that are equally contrived and unlikely hodgepodges. The probability that their theory is correct is much less than one trillionth for a simple reason – even the number of qualitatively similar theories as theirs (where some details are slightly tweaked to equally good, commensurable alternatives; where you just switch some switches that the "physicists" have overlooked) is greater than a trillion! And even this larger class may often be "insanely unlikely" to be a promising place where you should look for the truth about Nature. So the probability that the correct theory is included in that class may be one vigintillionth or smaller – and usually strictly zero. Quite generally, such theories with many switches are considered ugly and ugly theories are very unlikely to be relevant for Nature. Their probability is actually much smaller than 1/N where N is the number of similar ugly theories – because Nature has apparently preferred to entirely avoid cesspools as the building blocks for Her theory of Nature.

Some armchairs physicists' proposed theories of everything are similar to the puzzle. You want a theory of everything so you combine a strawberry with a milk and rum (just a suggestion, Leo), turn them into some shape, and then you follow what exact shape the bubbles make, and what poem this resembles, and then what is the 137th word in that poem. The word is translated to a celestial body whose 2nd hardest rock must be added to the rum, and then you can extract another prediction by comparing the cocktail with a brown soda, and stuff like that.

At some level, even a person with common sense must start to laugh because such theories are silly. They just contain lots of arbitrary ingredients that someone obviously made up – they are supported by no "inevitable" arguments of a mathematical or empirical kind. But a physicist may see that the theory becomes hopeless well before there are 10 arbitrarily building blocks that were made up, randomly guessed, and that have no "unavoidability". Even 1 or 2 or 3 such added ingredients may often be too much.

Einstein dreamed about a final theory where everything must be what it is because any other choice is mathematically inconsistent. This uniqueness dream was a wishful thinking that motivated Einstein's search for the final theory. The same philosophy underlied the S-matrix and bootstrap program coined by Werner Heisenberg, Chew, and the early and medieval string theorists.

You know, the assumption that the number of choices is zero – everything is determined by consistency – is indeed a wishful thinking and it often isn't like that. You simply have to try several options, building blocks that look arbitrary, and so on, and one of them sometimes works. The "pool of candidates" is sometimes needed to make progress – and one candidate seems "lucky" at the end. But the idea that you need to "regulate" the proliferation of proposed hypotheses where the number of arbitrary, unproven, building blocks gets out of control surely is true.

String theory as a whole really is totally unique. There is no "equally consistent alternative" theory of quantum gravity and other forces (let alone trillions of them), despite decades of whining, lying, and indoctrination of unchosen crackpots by the chosen and anointed ones. What is not unique is the number of vacuum-like solutions etc. – there are "googolplexes to the 5th or 15th power or more".

But as seen in this combination of traits, string theory really does what is most promising. The part of the problem – the finding of the most general rules that govern physics – seems totally unique and free of any arbitrary let alone anthropocentric choices. The other part of the problem – the finding of the right vacuum-like solution that may be identified with our Universe – is not unique but that's exactly the part where you should have expected the options to be non-unique because thinking that our vacuum has to be a "totally unique" solution of the fundamental rules is just a wishful thinking. There are many conceivable string vacua because we don't know everything about the representation of our Universe in the fundamental theory. The high number of promising vacua is nothing else than a precise representation of our current ignorance about the details of the application of the fundamental theory on our world! To claim that this number of string vacua (or its counterpart in another theory) should be much smaller than it is is nothing else than to claim that we already know everything. But we don't! So string theory is doing it right and those who say that the "right theory only has one vacuum" are saying something wrong about the (in)completeness of our present knowledge.

String theory is exactly as unique and unique at the right place which are needed for a theory that is most likely to be true. A much stronger and more grandiose claim about the uniqueness by a different (incomplete) theory is almost certainly just a very unlikely wishful thinking (someone is bragging that he knows more and he knows it more precisely than he does); and on the other side, one theory chosen from a the "basket of trillions of strawberries" is too arbitrary and anthropocentric to be relevant for the world around us.

People who aren't really good at fundamental physics can evaluate all these things ludicrously incorrectly. A great majority of them ends up rationalizing completely random statements that are really supported by no evidence whatsoever – or, more precisely, the number of commensurable hypotheses that could get the same support from their champions would be at least trillions. All such theories are non-starters, of course, and their proponents who aren't capable of understanding this simple point are hopeless as researchers.

The kind of a deep misunderstanding of "which ideas are vastly less likely than others" is shared by the people who invent puzzles that simply can't be solved (because the amount of ambiguities and vagueness is too high); and by alternative physicists who invent theories that can't be true (because Nature wouldn't have guessed such a weird passphrase).

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