The decolonisation of mathematics

John Armstrong and India Jackman write:

We describe a mainstream "universalist" approach to the understanding of mathematics. We then conduct a systematic (but not exhaustive) review of the academic literature on the decolonisation of mathematics and identify how this challenges the universalist view. We examine evidence of whether the experience of mathematics in the UK is systemically racist, examining both the decolonial arguments and the empirical evidence.

The paper makes good arguments that mathematics is universal, that attempts to decolonize math have been big failures, and that math culture is not racially discriminatory.

There are some examples of Western books being more likely to credit Western sources, but that is to be expected.

All this may seem obvious, but it is good to see a paper defend Mathematics against the increasing attacks from leftist decolonizers.

Poor Reasons for Rejecting Many-Worlds

Sabine Hossenfelder has posted her video, The Many Worlds Interpretation of Quantum Mechanics -- And why I don't believe it. I don't believe it either, so I was hoping to agree with her. Nope. Let me explain some basic points.

All scientific theories are probabilistic. Just read any scientific paper that reports experiments. There are always probabilities, error bars, p-values, or something to indicate probability. Even classical celestial mechanics, which is commonly thought to be deterministic, is always applied with probabilities. Astronomers estimate the position and other parameters for a planet, and then predict its future position, with probabilities.

Collapse is not really nonlocality. Anytime you make a probabilistic prediction, and then observe a definite value, you are ruling out the other possibilities. In quantum mechanics (QM), this is called collapse of the wave function. It happens in every other scientific theory. It does not mean that nature has any nonlocal properties. It only means that our knowledge of what is possible changes when we obtain new information. The Bayesians say this is essential to all of science.

QM is not inherently probabilistic, any more than any other theory. The wave function is not a probability. What it gives, most directly, is expectation values for observables. If A is an observable (self-adjoint operator), then <ψ|Aψ> is the expectation value of that observable. Usually a range of values is possible, and you can similarly get expectation values for the variance. If you want the probability that a particle is in a certain region, then you calculate the expectation for it being in the region.

QM is probabilistic in the sense that it predicts expectation values and variances, but the same can be said of any other scientific theory. They all predict expectation values and variances.

Any theory can be converted to a many-worlds theory, by rejecting the probabilities. Any time a theory predicts an event with probability p, you could disregard the probability, and say that observing the event splits the universe into many worlds, some with and some without the event.

Many-worlds theory (MWI) is just applying this to QM. It is not useful because the parallel worlds are imaginary, and because we lose the ability to interpret the probability. There is no real notion of being in a high or low probability world.

At this point, the MWI advocates start talking about the measurement problem, or the Bell problem. But MWI does nothing to solve the measurement problem. Measurements do not become less mysterious by postulating that world-splittings go along with them.

Bell's Theorem only says that QM is not a local hidden variable theory. Hossenfelder is wrong to say that Bell proved QM is nonlocal.

The obvious problem with MWI is that it hypothesizes parallel worlds that cannot be observed. There is no scientific value in discussing such things. The main problem is worse. Accepting MWI is the same as denying probability.

Suppose theory predicts a 90% chance of rain tomorrow. That means that if conditions are repeated 10 times, you can expect 9 rain days. But in MWI, it means that it will rain in some of the parallel worlds, and not others. You might think it will rain in 90% of the parallel worlds, but MWI has no way to count the worlds or make a statement like that. You don't know anything about the likelihood of rain in your world, because the MWI view is that there is no such thing. So arguing for many-worlds is the same as saying that the 90% probability is meaningless.

All of the above is mathematical fact, not opinion. Some physicists, like Sean M. Carroll choose to believe in MWI, but only because they choose to believe in unobservable parallel worlds with no scientific value, and because they reject probability theory.

What would Carroll say to defend MWI against these arguments? First, he would say that belief in wave function collapse is unnecessary because it is conjectured that solutions to the Schroedinger equation will exhibit a decoherence that is effectively the same as collapse. I say that may be true, but it does not have anything to do with the fact that the parallel worlds have no scientific value.

Second, he would say that you can still believe in the probabilities, even if they have no direct meaning. I say he has become detached from reality.

MWI takes a perfectly good theory about the world, destroys the part that gives it predictive power, and adds zillions of ghosts that can never be seen. What is the point? There is no practical or computational value to any of it. It is contrary to science. No good has ever come out of it.

MWI is one of those ideas that is so crazy that if anyone advocates it, then his views are on all other subjects are suspect. Other such ideas are determinism, free will denial, and the simulation hypothesis.

New Video on Non-Euclidean Geometry and Relativity

The latest Veritasium video is on:

How One Line in the Oldest Math Text Hinted at Hidden Universes

It is excellent as usual, and concerns the development of non-Euclidean geometry, from Euclid to relativity. It separates special and general relativity, and non-euclidean geometry being essential to general relativity.

In particular it tells how a supernova was seen 4 times in 2014, and predicted to be seen again in 2015, all being an illusion from gravitational lensing.

This is all correct, but special relativity has had a much bigger impact on XX century Physics than general relativity, and special relativity is also founded on non-euclidean geometry.

In the Veritasium model the "one line" is Euclid's Fifth Postulate about the existence of parallel lines. The "hidden universes" are model geometries where the postulate fails. Relativity is non-euclidean because it curves space. But it does not mention the bigger non-euclidean aspect -- light rays have null length. In euclidean geometry, every line segment has a positive length.

Euclidean geometry is based on Euclidean distances. The distance between two points is given by the Pythagorean Theorem. Time is the fourth dimension. The Minkowski metric applies, not a Euclidean one.

The non-euclidean geometry was appreciated early on, at least by Poincare in 1905, Minkowski in 1907, and Varicak in 1910. Einstein disagreed with it.

Whiteness in Physics Classrooms is Epistemicide

I try to avoid political topics, but woke papers are now infecting Physics journals.

Last year, the American Chemical Society published a paper on deconolonizing chemistry education, in a special woke issue.

Now the American Physical Society has published Observing whiteness in introductory physics: A case study. It is criticized here, here, here, and here.

The paper tries really hard to relate white supremacy to learning thermodynamics in a physics class. I don't see it, but that is supposed to be the original contribution. My whiteness prevents me from seeing it, the authors would say. More striking to me is the conventional woke wisdom they regurgitate.

Our goal in this paper has been to “make whiteness visible,” in the tradition of Critical Whiteness Studies. In particular, we have sought to make visible how everyday physics classroom interactions reproduce whiteness as social organization, and how physics representations, values, and pedagogical tools play a role in this reproduction. That whiteness is “ordinary” in physics classrooms is not surprising, given critical race theory’s assertion that whiteness is endemic to every aspect of U.S. society [7]. The ordinariness of whiteness’ reproduction is not surprising either, given critical scholarship’s emphasis on the invisibility and hegemony of whiteness.

Since the paper is about whiteness, you have to understand what it means by "white". It is not the skin color or the biological race. The paper is emphatic that there is no such thing. It does occasionally identify particular people as being white, but it is not clear what makes them white, if not race or skin color. It also makes a point of not capitalizing white, as it capitalizes Black, Color, and Hispanic. This is because whites have no culture, and no common identity. Even "Activists of Color" get two capital letters, but whites get none.

These papers are just lying when they say that race is a social construct with no biological reality. Popular racial classifications are nearly identical to results of objective DNA tests.

The impact of whiteness in physics classrooms cannot be understated. One outcome of enforcing a social organization with a (consistent) center and margins is epistemicide [45], or “the extermination of knowledge and ways of knowing” [37] (cited in Ref. [45]). We see glimmers of this in the data we have shared in this paper.

It goes on to explain that some white student solved a thermodynamics problem using an energy interaction diagram at a whiteboard. This was "an example where one form of knowledge building was discontinued (or extinguished) in service of another." Apparently he is called white because he solved a physics using white patriachal thinking, not because of his skin color.

This is analogous to white supremacy and patriarchy driving genocide. We are not killing Students of Color in the classroom, but we are marginalizing their bad science ideas.

The work is funded by the National Science Foundation. You tax dollars are funding this garbage, and our leading science journals are publishing it. You would probably be ostracized as a racist, if you disagreed with it.

The current Scientific American says:

The Theory That Men Evolved to Hunt and Women Evolved to Gather Is Wrong

The influential idea that in the past men were hunters and women were not isn’t supported by the available evidence ...

The inequity between male and female athletes is a result not of inherent biological differences between the sexes but of biases in how they are treated in sports.

They must think we are really stupid. Or that we will blindly accept scientific authorities. Or that we will be afraid to dispute woke pronouncement. I don't know. Scientific American was a great magazine for about 150 years.

Modern experts like to make fun of medieval scholars for trying to turn lead into gold, and the Sun going around the Earth. But what will our descendants think of 21st century science?

Update: Here is another example of bad science cited to support woke ideas. Coleman Hughes is a Black podcaster who gave a talk in favor of color-blindness, as pushed by M.L. King. He just posted a response to criticism. In brief, the TED folks tried to blackball his talk, claiming that it was disproved by social science saying that we must have racial preferences for Blacks. The social science is bogus, of course.

Update: Biologist Jerry Coyne debunks the rest of that SciAm article. Referring to the above quote:

Here the authors are wading into quicksand. In fact, the entire quote is offensive to reason, for it implies that, if women were treated the same as men in sports, they would do as well. Given the differences between the sexes in morphology and physiology, such a claim flies in the race of everything we know.  ...

In the end, we have still more evidence that Scientific American is no longer circling the drain, but is now in the drain, headed for, well, the sewers. It used to have scientists writing about their field, with no ideological bias, but now has ideologues (these authors are scientist-ideologues) writing about science in a biased way and misleading. 

Sapolsky Podcast against Free Will

I mention the New Sapolsky Book on Determinism, and he explains his views on the Skeptic podcast, and also on the Lawrence Krauss Origins podcast.

He is against all forms of free will, including compatibilism. He particularly argues against theories of criminal responsibility, where criminals are convicted if they knew what they were doing, understood the consequences, and did the crime anyway. He denies that anyone could make a criminal decision, or deserves punishment for it.

He does not even talk about true (libertarian) free will, as he says that is too silly to consider.

I am trying to understand this view. He seems to make two arguments.

(1) Free will is a form of magical thinking, akin to witchcraft. Centuries ago, people believed that witches might cause thunderstorms. Now that we have a more scientific understanding of the world, we see this as absurd. Likewise, we will someday see free will as absurdly contrary to a rational worldview.

(2) While he cannot prove determinism on a individual human level, he can on a statistical level. For example, given a sample of children who are abused, neglected, low IQ, criminal parents, poor, etc, he can predict that a certain percentage of them will turn out to be criminal.

While some say a lack of free will would be depressing, he says it is liberating to know that we are not responsible for his actions.

It is legitimate to argue that people have more causes than they realize, and the causes might be external, genetic, or biochemical. But even if your choices are 90% determined, I don't see how this is an argument against free will.

He says that instead of punishing criminals, we should be figuring out ways to prevent crime. But what is the point of figuring out anything, if we do not have the ability to make the choices to make a better society? It all makes no sense to me.

There is an amusing thought experiment, where he has to explain an infidelity to his wife. Is he really going to tell her that he had no choice, and that his actions were a product of his upbringing? He said that he would try to show empathy for his wife's feelings.

Krause is also a free will denier:

I have long felt the issue of free will is overplayed. The laws of physics are deterministic, and since biology and chemistry are based on physics, I have never doubted that free will is an illusion, but have also felt that for all intents and purposes the world we live in is indistinguishable from a world with free will, so we should take responsibility for our actions.

As is often the case when reading Robert’s works, my view has now become more nuanced. His book masterfully discusses the neurobiology behind the illusion of free will, what actually interests me the most, and he effectively demolished claims of numerous philosophers, including Dan Dennett and others, that some magic occurs between the level of neurons and the level of the full brain that allows for some uncaused behavior.

Krauss knows a lot more physics than I do, but I do not get how he can say that the laws of physics are deterministic. I thought that the consensus for the last century was that quantum mechanics is not deterministic.

Since Sapolsky and Krauss believe that they are completely determined by their genes and upbringing, they spend a lot of time talking about their Jewish backgrounds and other early influences.

Update: Listening to more of the podcast, Krauss emphatically says that quantum mechanics is deterministic, contrary to common understandings.

Krauss compares belief in free will to belief in God. He says Daniel Dennett gives arguments for free will that sound like arguments for Gad that he would never accept.

Sapolsky promotes determinism, which I thought meant that the past determines the future. No, his definition is that things happen with no magic.

This is a huge dodge. Anything we do not understand can be called magic. That might include consciousness, free will, intanglement, multiverse, and maybe even neutrinos.

They implicitly accept this argument for atheism. Centuries ago, most of the natural world was unexplained, and it was reasonable to attribute various things to God. When science got much better, then at some point it became more reasonable to assume scientific explanations for everything, and deny God.

Likewise, now that we know much more about genes and neuroscience, we don't need the free will hypothesis anymore.

Sapolsky gives the example of prairie voles which were thought to be more virtuous than mountain voles, because prairie voles were monogamous. But then someone discovered a single gene that controls the difference, and mountain voles can be made monogamous by changing the gene.

Okay, I can believe that some apparently-virtuous humans are just behaving as they have been programmed. And some people believe in God because they are overly impressed by natural mysteries that have good scientific explanations.

But my belief in free will is mostly hased on my ability to make my own decisions. Not on any scientific ignorance.

Update: I listened on to where Krauss says quentum mechanics is deterministic. He says that solving the Schroedinger equation is deterministic from a previous wave function. Only the measurement is random. And while radioactive decay is random, macroscopic statistics from millions of decays are accurately predictable. Wow, I thought that he would have a better argument.

The wave function is no observable. You can never know what it was in the past, and you cannot use it to make a deterministic prediction.

Krauss says, at 2:25:20:

It is undeniable that we don't have free will, based on science. There's no loopholes, no places for the magic to occur.

No, I do not see how a smart physicist can say that. Sapolsky accepts his physics expertise, and says:

Clinical depression is the pathological failure of the ability to rationalize away reality.

These guys have a bizarre world view. He does say that people with an injured prefrontal cortex have no free will. So maybe that is were consciousness resides? But consciousness is just a tool for rationalizing what is forced on us.

Was Copernicus a Genius or Lucky?

Wikipedia says:

The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in mathematics, physics, astronomy, biology (including human anatomy) and chemistry transformed the views of society about nature.[1][2][3][4][5][6] The Scientific Revolution took place in Europe in the second half of the Renaissance period, with the 1543 Nicolaus Copernicus publication De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) often cited as its beginning.[7]

My view is that Copernicus was not really more scientific than his predecessors. He stumbled on some good ideas, but did not really have good scientific arguments that his model was superior.

The ancient Greek Aristarchus had a heliocentric model. Details have been lost. So the idea of heliocentrism was not new to Copernicus. There were a lot of good arguments for and against, and not enough data to reach a scientific conclusion.

Vincenzo Crupi writes in a new paper:

From Copernicus himself up to Kepler and Galilei, Copernicans have been "right for the wrong reasons" (Finocchiaro 2010), because there were no epistemically compelling reasons objectively favoring the Copernican position at that stage – a good deal of research in the history and philosophy of science has converged on this claim. The situation of early Copernicans would then be regarded as one of "epistemic luck".

It is not so simple, and this paper has a good overview.

The issue is central to the philosophy of science, as it shows big differences in what people think science is all about.

You could say motion is relative, and the heliocentrism geocentrism debate was a trivial argument about a preferred frame of reference. The biggest scientific concern was to predict what we see in the night sky, and either model could be used for that.

Others say we didn't really start to make sense out of cosmology until we rejected the stationary Earth. There is some merit to that, but it is exaggerated.

Dr Bee's Quantum Update

@SabineHossenfelder posts her latest video:

What's New in Quantum Computing? 2023 Update

She makes it sound as if a lot has happened in the last two years, but not really.

There is still no true qubit. A researcher may claim to have a functional equivalent of 50 qubits, but he does not even have one logical qubit.

There is still no convincing demonstration of quantum supremacy. Some say quantum advantage, but no convincing example of that either.

There is still no quantum computer to solve a problem. The claims are based on generating random numbers in a way that is hard to simulate.

Compare all this to the hype reported here, such as Google's Neven's Law, which said in June 2019 that quantum computers were advancing doubly exponentially. If that were true, then we would have a convincing example of quantum supremacy by now.

Unless it is impossible, of course.

Happy Columbus Day. The 1492 Columbus discovery of the Americas was one of the greatest events in the history of the world. Without that, where would science be?