Wednesday, March 13, 2019

Horgan admits math proofs are not dying

SciAm writer John Horgan finally concedes
Okay, Maybe Proofs Aren't Dying After All

Two experts argue that proofs are doing fine, contrary to a controversial 1993 prediction of their impending demise
It appears that a famous mathematician led him astray:
But influential figures were behind the changes. One was William Thurston, who in 1982 won a Fields Medal — the mathematical equivalent of a Nobel Prize — for delineating links between topology and geometry.

Thurston, who served as a major source for my article, advocated a more free-form, “intuitive” style of mathematical research, communication and education, with less emphasis on conventional proofs. He sought to convey mathematical concepts with computer-generated models, including a video that he called “Not Knot.”

“That mathematics reduces in principle to formal proofs is a shaky idea” peculiar to the 20th century, Thurston told me. Ironically, he pointed out, Bertrand Russell and Kurt Godel demonstrated early in the century that mathematics is riddled with logical contradictions. “Set theory is based on polite lies, things we agree on even though we know they're not true,” Thurston said. “In some ways, the foundation of mathematics has an air of unreality.”
The Fields Medal is not really the mathematical equivalent of a Nobel Prize. The Abel Prize is much closer.

No one showed that mathematics is riddled with logical contradictions. Thurston was not knowledgeable about the foundations of math. He was a brilliant mathematician, and he was good at explaining his work to others, but he was lousy at writing up his proofs. Some of his best work was written up by others.

Thurston's ideas were not accepted until proofs were written and published. Probably his biggest idea was that all three-dimensional manifolds could be decomposed into one carrying one of about eight geometric structures. This was always called a conjecture, until Perelman published what appeared to be a proof, and others filled in the gaps so that everyone was convinced that it really was a proof.

Russell showed that certain set theory operations led to contradictions, and then showed how an axiomatic approach could resolve them. Goedel gave much better axiomatizations of set theory, can examples of undecidable statements. An undecidable is the opposite of a contradiction.

Horgan's concession is based on quoting two bloggers. It would have been better if he had asked someone who was trained in mathematical foundations, instead of computer science and particle physics.

BTW, Scott Aaronson comments:
More importantly, I’ve been completely open here about my unfortunate psychological tic of being obsessed with the people who hate me, and why they hate me, and what I could do to make them hate me less. And I’ve been working to overcome that obsession.
I seem to be one of his enemies, but I do not hate him. I don't disagree with his comments about proof, but he is not a mathematician and he does not speak for mathematicians.

Monday, March 11, 2019

Why Cosmologists hate Copenhagen

James B. Hartle explains:
Textbook (Copenhagen) formulations of quantum mechanics are inadequate for cosmology for at least four reasons: 1) They predict the outcomes of measurements made by observers. But in the very early universe no measurements were being made and no observers were around to make them. 2) Observers were outside of the system being measured. But we are interested in a theory of the whole universe where everything, including observers, are inside. 3) Copenhagen quantum mechanics could not retrodict the past. But retrodicting the past to understand how the universe began is the main task of cosmology. 4) Copenhagen quantum mechanics required a fixed classical spacetime geometry not least to give meaning to the time in the Schrödinger equation. But in the very early universe spacetime is fluctuating quantum mechanically (quantum gravity) and without definite value.
There is some merit to this reasoning, but jumping to Everett many-worlds is still bizarre, and does not help.

The decoherence and consistent histories interpretations of quantum mechanics are really just minor variations of Copenhagen.

While Copenhagen says that observers notice quantum states settling into eigenstates, these newer interpretations say it can happen before the observer notices.

Many-worlds just says that anything can happen, and it is completely useless for cosmology.

Sean M. Carroll has announced that he is writing a new book on many-worlds theory. He will presumably take the position that it is a logical necessity for cosmology. Or that it is simpler for cosmology. However, I very much doubt that any benefit for cosmology can be found.

Friday, March 8, 2019

Physicist fired for expressing valid opinion

Lubos Motl writes:
After five months of "investigations" that weren't investigating anything, the vicious, dishonest, and ideologically contaminated individuals who took over CERN have said "good-bye" to Alessandro Strumia, a top particle phenomenologist with 38k citations according to Google Scholar and 32k according to Inspire.
This firing was political, obviously. You can compare male and female employment, but your conclusion must favor females, or else you will be censored, fired, and ostracized.

I don't think that the Physics community has thought this thru. Everyone now knows that women are promoted over more competent men, and the system is maintained by firing anyone who points out the facts.

Monday, March 4, 2019

Nature mag denies existence of gendered brains

You would think that our leading scientific journal would not be consumed by leftist ideology.

Nature mag reports:
The history of sex-difference research is rife with innumeracy, misinterpretation, publication bias, weak statistical power, inadequate controls and worse. ...

Yet, as The Gendered Brain reveals, conclusive findings about sex-linked brain differences have failed to materialize. Beyond the “missing five ounces” of female brain — gloated about since the nineteenth century — modern neuroscientists have identified no decisive, category-defining differences between the brains of men and women. ...

Whatever the subtitle, the book accomplishes its goal of debunking the concept of a gendered brain. The brain is no more gendered than the liver or kidneys or heart. Towards the end, Rippon flirts with the implications of this finding for the growing number of people transitioning or living between current binary gender categories.
If the concept is bunk, then why is anyone transitioning?

The world is crackpots saying silly things, but I get worried when I see those things in our most elite intellectual journals. I would be similarly dismayed if Nature started publishing an Astrology column.

When some otherwise intelligent man denies human consciousness, or denies free will, I wonder how they get thru the day and manage their lives. Likewise, when they believe in infinite doppelgangers, or that we live in a simulation, or when they have certain religious or anti-religious opinions.

Men and women obviously think differently. Otherwise, why would feminism be a thing?

The differences are obvious to anyone who has gone out on a date. This article is silly.

Friday, March 1, 2019

But what’s contracting in relativity?

The "Ask a Physicist" blog explains:
Q: In relativity, length contracts at high speeds. But what’s contracting? Is it distance or space or is there even a difference? ...

This situation is sometimes explained as a consequence of length contraction. But what is it that’s contracting? Some authors put it down to space itself contracting, or just distance contracting (which it seems to me amounts to the same thing) and others say that’s nonsense because you could posit two spaceships heading in the same direction momentarily side by side and traveling at different speeds, so how can there be two different distances?

So what is the correct way to understand the situation from the astronaut’s perspective?

Physicist: Space and time don’t react to how you move around. They don’t contract or slow down just because you move fast relative to someone somewhere. What changes is how you perceive space and time. ...

Einstein’s big contribution (or one of them at least) was “combining” time and space under the umbrella of “spacetime”, so named because Germans love sticking words together
I agree with his explanation, except that the view he described was not Einstein's view.

Minkowski was the German who combined space and time into spacetime, and he based it on Poincare, not Einstein.

Einstein's contribution was not putting time and space together, and he very much disagreed with the view that what changes is our perception of space and time. I explain the point here and in my book, and in other posts. Einstein insisted that his view of the contraction was essentially the same as Lorentz's, and contrary to the non-Euclidean geometry view that is nicely explained in the above blog.