Searching for an acausal computer speedup

You think that quantum computing is the ultimate computer speedup? No, as long as theorists are living in an untested fantasy world, it is just the beginning.

An FQXi article says:

Quantum experiments mix past and future on the microscopic scale — opening the door to faster computers and revising our notion of causality. ...

"All events are causally ordered such that for every pair of events you can say that one event is cause or effect of the other," says quantum physicist Caslav Brukner. Causality is so ingrained in the texture of our lives, and our brains, that it is hard to imagine letting go of it. Yet this is exactly what Brukner addressed with the help of an FQXi grant of over $63,000. The implications of this idea could be enormous: we might find that space, time and causality are not the basic building blocks of nature. It would have practical consequences too—potentially helping us to build quantum computers to outperform today’s devices. ...

Removing causality is more than just an interesting conceptual shift; it may also have benefits for those attempting to build super fast computers that exploit quantum laws to outperform today’s machines. While our personal computers store information as bits that can either be 1 or 0, quantum computers — which were first proposed in the 1980s — use quantum bits, or qubits, that can represent a 1, 0, or any superposition of these states. The ability of qubits to hold multiple states at once would allow quantum computers, in theory, to solve problems more quickly than classical ones.

Here’s where causality (or a lack of it) comes in: Calculations in a quantum computer follow a fixed sequence of quantum logic gates, at the end of which one number drops out. But quantum information without causal order could, in theory, allow for an even bigger speed-up because it would no longer be necessary for the calculations to follow a sequential route. The effect would be amplified, explains Brukner, when the question is scaled up from just two ports of call — Alice and Bob in Brukner’s research — to numerous others.

Without causality, how do you ever know when the computation has started, and when it finished?

If you drop causality, then you can do time travel, and get another speedup. Instead of doing a computation iteratively a million times, you could just go back in time a million times, and get a huge speedup.

Then there are paranormal and psychic influences. If mental energy can direct the computer towards a solution, you could get another speedup.

Of course there is not a shred of evidence for causality violations, or for time travel.

And there is no proof that a quantum computer can get a speedup from qubits holding multiple states at once.

There is plenty of evidence for quantum mechanics, and there are interpretations of it that suggest all sorts of weird things. I say to reject those interpretations.

Speaking of interpretations, Lumo seems to accept collapse of the wave function, but denies that it is unitarity violation. This seem peculiar, because collapses are given by a Hilbert space projection, and projections are not unitary.

He wants to hang onto unitarity, because that is associated to probabilities adding up to one. Probabilities adding to one seems like a mathematical necessity, and hence a physical law, in the view of some.

I am not sure of his argument, but I do agree that abstract considerations of mathematical probability do not forbid collapse of the wave function.

If I toss a coin, and keep the result covered, then there is probability of 0.5 that it is heads, and 0.5 that it is tails. If I then show the coin to be heads, then the possibility of tails disappears. But no one would argue that discarding that probability of tails violates the law that probabilities add up to one.

Likewise, collapse of the wave function discards some possibilities.

The people who promote the many-worlds interpretation (such as Sean M. Carroll) would say that unitarity requires that all those possibilities stay alive in some parallel universe. So if I toss a coin and see heads, I will have split into two men with the other seeing tails.

There isn't really any physics behind many-worlds. There is just a mathematical belief that probabilities cannot be eliminated, so they must be shoved into a parallel universe. Unitarity is just a fancy way of saying that.

Statisticians complain about p-values

Nature reports:

Misuse of the P value — a common test for judging the strength of scientific evidence — is contributing to the number of research findings that cannot be reproduced, the American Statistical Association (ASA) warns in a statement released today¹. The group has taken the unusual step of issuing principles to guide use of the P value, which it says cannot determine whether a hypothesis is true or whether results are important.

This is the first time that the 177-year-old ASA has made explicit recommendations on such a foundational matter in statistics, says executive director Ron Wasserstein. The society’s members had become increasingly concerned that the P value was being misapplied in ways that cast doubt on statistics generally, he adds.

In its statement, the ASA advises researchers to avoid drawing scientific conclusions or making policy decisions based on P values alone. ...

The statement’s six principles, many of which address misconceptions and misuse of the p-value, are the following:

1. P-values can indicate how incompatible the data are with a specified statistical model.

2. P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

3. Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.

4. Proper inference requires full reporting and transparency.

5. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

6. By itself, a p-value does not provide a good measure of evidence regarding a model or hypothesis.

In the medical and social sciences, p-values rule. Every paper cites them. The p-value determines whether the paper is publishable or not.

Paper do not get retracted for bogus use of p-values, but people raise a storm when the word "Creator" sneaks into a paper. It appears to be just a mistranslation, as the author intended "nature" or something similar.

Popularity of string theory, explained

From today's Carpe Diem comic.

Quantum computing is as possible as 3x5=7

Scott Aaronson writes about the latest big advance in quantum computing:

Briefly, the new work uses Kitaev’s version of Shor’s factoring algorithm, running on an ion-trap quantum computer with five calcium ions, to prove that, with at least 90% confidence, 15 equals 3×5. Now, one might object that the “15=3×5 theorem” has by now been demonstrated many times using quantum computing ...

Nevertheless, as far as I can tell, the new work is a genuine milestone in experimental QC, because it dispenses with most of the precompilation tricks that previous demonstrations of Shor’s algorithm used. “Precompilation tricks” are a fancier term for “cheating”: i.e., optimizing a quantum circuit in ways that would only make sense if you already assumed that 15 was, indeed, 3×5. So, what’s new is that a QC has now factored 15 “scalably”: that is, with much less cheating than before.

Of course, as I’m sure the authors would acknowledge, the word “scalable” in their title admits multiple interpretations, rather like the word “possible.” ...

In conclusion, let me suggest the following principle:

I will not assign a nonzero probability to something like 3×5=7, for which there’s no explanatory theory telling me how it possibly could be true. That doesn’t mean that I’ll assign a zero probability — i.e., that I’ll accept a bet with infinite odds on anything that strikes me (perhaps mistakenly) as a logical or metaphysical impossibility. It just means that I’ll refuse to bet at all.

It is still cheating to say they factored 15 "scalably", because the method does not scale up to larger numbers.

In the make-believe quantum world, anything is possible. Everything is just probabilities. If it doesn't happen here, then it happens in some parallel universe.

Scott admits that no one has demonstrated quantum computing, but he like to study, so he likes to believe it is possible. And even if it is not possible, it is a rewarding thing to study. And he cannot positively rule it out, just as he cannot rule out 3×5=7.

Speaking of possibilities, it is possible that the elusive dark matter is black holes. Until the LIGO discovery, we only knew about star-sized black holes and giant million-star black holes. The star-sized ones show up as part of a binary star where the other star is visible. The big ones are at the nucleus of galaxies, and could be essential for galaxy formation.

Common sense would indicate that there must be some intermediate sizes. The LIGO team claims they say 2 30-Sun black holes collide. This could be a freak event, or there could be billions of them scattered all over the place, and we would never notice. If the latter, they could be the dark matter whose gravity is essential to holding galaxies together.

I posted some skepticism about LIGO, but we could soon have a lot more data to settle the question. Maybe another country with build a LIGO, and not build in the capability to fake results.

Update: Sean M. Carroll responds to the possibility that LIGO discovered the missing dark matter.

Poincare spread quantum mechanics

Poincare's last work was a ground-breaking paper on quantum mechanics that spread the idea outside Germany and even to America.

A Univ. of Illinois professor wrote this 1913 essay in Popular Science Monthly:

IT has not seemed to me appropriate, nor would there be time, nor should I be able, to enter into an exhaustive study of the life-work of a master-mind like Jules Henri Poincaré. Indeed, to analyze his contributions to astronomy needs a Darwin; to report on his investigations in mathematical physics needs a Planck; to expound his philosophy of science needs a Royce; to exhibit his mathematical creations in all their fullness needs Poincaré. Let it suffice that he was the pride of France, not only of the aristocracy of scholars, but of the nation. He was inspired by the genius of France, with its keen discernment, its eternal search for exact truth, its haunting love of beauty. The mathematical world has lost its incomparable leader, and its admiration for the magnitude of his achievements will be tempered only by the vain desire to know what visions he had not yet given expression to. Investigators of brilliant power for years to come will fill out the outlines of what he had time only to sketch. His vision penetrated the universe from the electron to the galaxy, from instants of time to the sweep of space, from the fundamentals of thought to its most delicate propositions. ...

Poincaré's conception of science can be summed up in these terms: Science consists of the invariants of human thought. ...

We are witnesses too of an evolution in science and mathematics from the continuous to the discontinuous. In mathematics it has produced the function defined over a range rather than a line — a chaos, as it were, of elements — and the calculable numbers of Borel. In physics it has produced the electron, the magneton, and the theory of quanta, 5 about which Poincaré said shortly before his death:

A physical system is capable of only a finite number of distinct states; it abruptly jumps from one state to another without passing through the inter- mediate states.

See also Wikisource.

The Literary Digest, April 15, 1912 p.751, had an article titled, Does Everything Go By Jerks?

Do all the processes of the universe, which appear to go on smoothly and continuously, gliding from one state to another, really take place with a series of infinitesimal jerks? Does a ball, when thrown into the air, move with a series of tiny leaps so close together than they blend to the eye? This is precisely what takes place in a moving picture. Is nature, in this respect, one vast cinematograph? This would appear to be the result of a striking and almost revolutionary theory propounded first in Germany, but elucidated and extended in the Revue Scientifique (Paris, February 24) by Henri Poincaré, an eminent French physicist. According to this theory, energy consists of discontinuous portions just as matter does. There are "atoms" of energy as well as of matter, and possibly also "atoms" of time, causing all duration to be jerky instead of smooth, as it appears to be.

Poincare's last essay in 1912 was on The New Conceptions of Matter. He tells how he was finally persuaded by atomism. Presiously he had been a proponent of continuity, and referred to the "atomic hypothesis" as it were just a convention.

Logic is not a failure

Gregory Chaitin writes:

How has the mathematics community reacted? With Gödel, at first there was a lot of shock. As a student in the late 1950s and early 1960s, I would read essays by Weyl, by John von Neumann, and by other mathematicians. Gödel really disturbed them. He took away their belief in the Platonic world of ideas, the principle that mathematical truth is black or white and provides absolute certainty.

But now, strangely enough, the mathematics community ignores Gödel incompleteness and goes on exactly as before, in what I would call a Hilbertian spirit, or following the Bourbaki tradition, the French school inspired by Hilbert. Formal axiomatic theories are still the official religion in the mathematics community. ...

Gödel incompleteness is even unpopular among logicians. They are ambivalent. On the one hand, Gödel is the most famous logician ever. But, on the other hand, the incompleteness theorem says that logic is a failure.

Yes, of course mathematicians use axiomatic theories. They have for over two millennia. That is what mathematics is.

Godel certainly did not prove that logic is a failure. He would have vehemently resisted interpreting his work that way.

Top post-WWII philosophers

An over-opinionated law professor posts this poll:

Best Anglophone philosophers of science since 1945: ...

1. Rudolf Carnap (Condorcet winner: wins contests with all other choices)
2. Thomas S. Kuhn loses to Rudolf Carnap by 92–89
3. Carl G. Hempel loses to Rudolf Carnap by 106–64, loses to Thomas S. Kuhn by 99–74
4. Karl Popper loses to Rudolf Carnap by 99–64, loses to Carl G. Hempel by 94–73

I am surprised at this, because Rudolf Carnap and Hempel were a logical postivist, and today's philosophers say that was wrong. Popper was an anti-positivist, but people like him because they think he was a positivist. Kuhn was even more anti-positivist, and popularized denying objective truth.

Update: Here is a philosopher whining about philosophers not getting respect from a science popularist Bill Nye. For example, Pigliucci complains that Nye falls fort he fallacy that dropping a hammer on his foot convinces him that the hammer is real. I don't know, this seems as good an argument as anything else that the hammer is real. But I guess philosophers like to live in a pretend-world where nothing is real.