Controlled by randomness cartoon

I am not sure what this New Yorker cartoonist is trying to say, or whether I agree with it. Yes, we live in a complex system, and unpredictable events affect us all the time. Is he paranoid for thinking that? Is that more or less disturbing than some evil conspiracy controlling us?

Free will observations

I am seeing intelligent scientists and philosophers saying really silly things about free will.

Existence of free will is not a scientific question. There is no way to directly test free will by experiments such as putting two people in the same state of mind and seeing whether they make the same decision.

There are experiments by Libet and others showing that the timing of a decision, as measured by brain scans, can be slightly different from conscious expectations. There are optical illusions that show that your brain perceives images in a way that is also slightly different from conscious expectations. But none of these experiments deny the apparent ability of your brain to make decisions.

Possibilities of solipsism are fruitless. We cannot rule out the possibility that some sort of super-determinism controls everything we see and do, or that we are all part of some vast computer computer simulation. But so what?

Here is a much less radical, but similarly worthless, statement: A hammer is mostly empty space. You can believe that if you want, but you can still hammer nails, and it still hurts if the hammer hits you.

Daily life is impossible without a belief in free will. Everyday we make decisions, or at least we think we do, and we often put a lot of effort into those decisions. What would I do otherwise?

Suppose someone came to me and said: The forward march of time is just an illusion, and time is really going backwards. What would I do with that info? I still have to live my life as if time is marching forwards, as nobody knows how to do anything else.

Denying free will serves leftist political goals, and encourages irresponsible behavior.

Scientific reasoning does not require determinism. There is an argument that unless you believe in religion or dualism or the supernatural, then everything must be determined by initial conditions, except maybe for some quantum randomness. That is, everything is determined except for what is not determined. People give this argument as if determinism is some obvious consequence of scientific rationalist materialism.

It is not. Scientists do try to make predictions, based on whatever data they have, but there is never a claim that everything is predictable.

If we had free will, how would that show up in our physical theories? They would be mostly deterministic, except for some unpredictable aspects. In other words, just like the physical theories that we have.

Here are examples of the argument from two prominent Skeptics in published articles. Physicist Victor J. Stenger writes:

So where does this leave us on the question of free will? Libertarians are correct when they say that determinism does not exist, at least at the fundamental physics level. Nevertheless, it is hard to see how physical indeterminism at any level validates the libertarian view. As Harris points out, “How could the indeterminacy of the initiating event [of an action] count as the exercise of my free will?”22 For an action to be mine, originated by me, it can’t be the result of something random, which by definition would be independent of my character, desires and intentions. To originate and be responsible for an action, I have to cause it, not something indeterministic. So the libertarian quest for indeterminacy (randomness) as the basis for free will turns out to be a wild goose chase. Neither determinism norindeterminism gets us free will.

Philosopher Massimo Pigliucci writes The incoherence of free will:

The next popular argument for a truly free will invokes quantum mechanics (the last refuge of those who prefer to keep things as mysterious as possible). Quantum events, it is argued, may have some effects that “bubble up” to the semi-macroscopic level of chemical interactions and electrical pulses in the brain. Since quantum mechanics is the only realm within which it does appear to make sense to talk about truly uncaused events, voilà!, we have (quantistic) free will. But even assuming that quantum events do “bubble up” in that way (it is far from a certain thing), what we gain under that scenario is random will, which seems to be an oxymoron (after all, “willing” something means to wish or direct events in a particular — most certainly not random — way). So that’s out as well.

Essentially the argument is: It does not matter if the laws of physics seem to allow for free will. Those laws must be deterministic or indeterministic. If deterministic, then everything is pre-determined, so we have no free will. If indeterministic, then there is some randomness we do not understand, so also we have no free will.

My FQXi essay also has a discussion of this aspect of randomness.

This is illogical. It is like arguing:

Studying cannot help you get good grades in college. Social science models show that college grades are 50% correlated with parental income, with the other 50% being random. Studying will not increase your parents income. Randomness will not get you good grades. Therefore studying will not help.

There error here is that the models do not consider studying, so studying shows up as random. The random component is just the sum of unexplained factors. The argument excludes studying from the models, and then tries to draw a conclusion from studying being excluded.

Likewise, brain models do not consider free will. They cannot do that as no one even knows what consciousness is. Quantum randomness is unexplained. You cannot just say, "the brain is explained by factors that are currently unexplained, so therefore there is no free will."

You might say:

Of course the models do not factor in free will. The whole concept of free will is that of "mind over matter", and it is intrinsically unscientific and cannot be modeled. We can understand how studying for college exams might get you a better grade, but there is no way an immaterial dualistic mind can influence a material body.

We certainly have an appearance of having conscious minds that made freely-chosen decisions. No, I cannot explain how it works, but I cannot explain how it could all be an illusion either. Believe what you want, but it is not true to say that science has given us an answer.

Here is an argument from a prominent leftist-atheist:

The events that Sam Harris talks about in the you-tube clip “Sam Harris on Free Will” include descriptions of weak free will events. For example, he asks the audience to think of a city then points out that the audience did not call up an exhaustive list of cities from which a particular city is carefully selected. Instead, a city name (or two, or three) pops into your head. Even if only one pops into your head, you can make a weak free will decision to accept it or to go back to city name retrieval process.

Harris argues that because you cannot explain a fully causal mechanism for how you chose the city, then it does not feel like free will, and it feels more like some demon in your head is forcing the choice on you.

I think the opposite. If I followed a deterministic algorithm for the city, then that would not feel like free will. Spontaneously making some inexplicable choice feels like free will. His argument continues:

Now here is the part that gets a bit tricky. Harris suggests that you often aren’t even aware of why you picked Tokyo, even if you have a story to tell, such as you had Japanese food last night. Even if that story did somehow influence your decision (though he goes on to say how bad we are at assessing such), “you still can’t explain why you remembered having Japanese food last night or why the memory had the effect that it did. Why didn’t it have the opposite effect?”

This point is extremely important here. Even if you remembered the Japanese food, why didn’t you think “Oh, I had Japanese food last night so I’ll choose something different from Tokyo” instead of perhaps “Oh, I had Japanese food so I’ll choose Tokyo”? The fact of the matter is, one of these were forced to the forefront of your consciousness, resulting in your decision. But the chances are you really don’t know why one did and not the other.

Harris goes on to say “The thing to notice is that, you as the conscious witness of your inner life, are not making these decisions. You can only witness these decisions.”

I wonder what he thinks that free will would feel like. To me, it seems quite consistent with free will to assume that part of your brain stores memories of food, and another part makes decisions, and that I am often unable to give a causally-deterministic explanation for my decisions.

The quantum artificial intelligence

Here is some silly quantum hype:

Steve Wozniak maintained for a long time that true AI is relegated to the realm of science fiction. But recent advances in quantum computing have him reconsidering his stance.

Here is Here's How You Can Help Build a Quantum Computer:

Quantum computers—theoretical machines which can process certain large and difficult problems exponentially faster than classical computers—have been a mainstay of science fiction for decades. But actually building one has proven incredibly challenging.

A group of researchers at Aarhus University believes the secret to creating a quantum computer lies in understanding human cognition. So, they've built computer games to study us, first. ...

To build a quantum computer, researchers are first mapping human thoughts.

These would be some big advances in a field that has spent $100M just to discover that 15 = 3x5.

Peter Woit is back online, reporting more physics hype. He quotes Weinberg:

I am not a proponent of the idea that our Big Bang universe is just part of a larger multiverse.

Once other planets, stars, and galaxies were named, we had to have names for our planet, sun, and galaxy. I don't know the history, but I am guessing that it took a while for a term like "our Milky Way galaxy" to catch on.

So now we have the term "our Big Bang universe" to distinguish our universe from all the other universes. None of those other universes have names, as they cannot be observed. But we can name our universe, and cosmologists seem to be moving away from the idea that "universe" means everything.

The term "our Big Bang universe" suggests that it includes Earth and everything we see going back to the Big Bang, and everything emanating forward in time, but nothing before the Big Bang, and nothing that is so separated from us that relativity precludes any interaction with us.

Testing relativistic mass

Yesterday's Astronomy Cast Ep. 370: The Kaufmann–Bucherer–Neumann Experiments covered:

One of the most amazing implications of Einstein’s relativity is the fact that the inertial mass of an object depends on its velocity. That sounds like a difficult thing to test, but that’s exactly what happened through a series of experiments performed by Kaufmann, Bucherer, Neumann and others.

This was pretty good relativity history, except that if you listen, you might wonder about a couple of things.

Why were they testing relativistic mass in 1901 if Einstein did not invent it until 1905?

Where did they get those formulas involving velocity and the speed of light without relativity?

Relativistic mass for electrons was predicted by Lorentz in 1899 and confirmed by experiment in 1901-1902. Lorentz got the Nobel prize for his electron theory in 1902.

Others found rival theories that were also consistent with experiment, and it took another 5 or 10 years to distinguish Lorentz's relativity from the rival theories. That research eventually concluded that the "Lorentz-Einstein theory" matches the data. It was the first real test of special relativity.

Number line invented in twentieth century

A Russian mathematician has a new paper On the History of Number Line

The notion of number line was formed in XX c. We consider the generation of this conception in works by M. Stiefel (1544), Galilei (1633), Euler (1748), Lambert (1766), Bolzano (1830-1834), Meray (1869-1872), Cantor (1872), Dedekind (1872), Heine (1872) and Weierstrass (1861-1885).

My first thought -- is "XX c" some Russian name for an ancient Greek or Egyptian city? Didn't Euclid have the number line?

No, "XX c" means the twentieth century, from 1900 to 2000. (Or 1901 to 2001, maybe if you quibble about the invention of the zero.) It will always be the greatest century in the history of intellectual thought, and a term like "XX c" gives it a dignified respect. Just like WWII was the greatest war.

I have been using "XX century" to denote that century for a while. I will consider XX c.

The paper is quite serious about arguing that pre XX c concepts of the number line are all defective. It does not explain who finally got it right in the XX c. I would have said that Cauchy, Weierstrauss, and Cantor all had the concept in the 19th century. Surely Bourbaki had the modern concept in the XX c.

I would have said that early XX c great mathematical concepts (related to the number line) were the manifold and axiomatic set theory. But maybe the number line itself is from the XX c.

The paper argues that Cantor's formulation of the reals was deficient, but the references are in Russian, and I do not know whether it is correct.

I posted below about a famous modern mathematician who did not understand axiomatic set theory. The concept of Lorentz covariance was crucial to the development of special relativity by Poincare and Minkowski, but Einstein did not understand it until many years later.

Physicists will be especially perplexed by this. My FQXi essay discusses how mathematicians and physicists view random and infinite numbers differently. Non-mathemathematicians are endless confused about properties of the real numbers. See for example the Wikipedia article on 0.9999 or Zeno's paradoxes.

If it is really true that 19th century mathematicians did not have the modern concept of the number line, then I should assume that nearly all physicists do not either today. I just listened to physicists Sean M. Carroll's dopey comments on Science Friday. He said that we should retire the concept of falsifiability, because it gets used against untestable theories like string theory. He also argued that space may not be fundamental. I wonder if he even accepts the number line the way mathematicians do.

Another new paper says:

The novice, through the standard elementary mathematics indoctrination, may fail to appreciate that, compared to the natural, integer, and rational numbers, there is nothing simple about defining the real numbers. The gap, both conceptual and technical, that one must cross when passing from the former to the latter is substantial and perhaps best witnessed by history. The existence of line segments whose length can not be measured by any rational number is well-known to have been discovered many centuries ago (though the precise details are unknown). The simple problem of rigorously introducing mathematical entities that do suffice to measure the length of any line segment proved very challenging. Even relatively modern attempts due to such prominent figures as Bolzano, Hamilton, and Weierstrass were only partially rigorous and it was only with the work of Cantor and Dedekind in the early part of the 1870’s that the reals finally came into existence.

The paper goes on to give a construction of the reals, based on a more elementary version of Bourbaki's. It also outlines other constructions of historical significance.

As you can see, the construction is probably more complicated than you expect. And it skips construction of the natural numbers (usually done with Peano axioms) and the rational numbers (usually done as equivalence classes of ordered pairs of integers).

This puts the number line before the XX c, but there is still the problem that set theory was not axiomatized until the early XX c.

Trying to kill the mathematical proof

SciAm writer John Horgan still defends his 1993 article on the Death of Proof:

“For millennia, mathematicians have measured progress in terms of what they could demonstrate through proofs — that is, a series of logical steps leading from a set of axioms to an irrefutable conclusion. Now the doubts riddling modern human thought have finally infected mathematics. Mathematicians may at last be forced to accept what many scientists and philosophers already have admitted: their assertions are, at best, only provisionally true, true until proved false.”

I cited Thurston as a major force driving this trend, noting that when talking about proofs Thurston “sounds less like a disciple of Plato than of Thomas S. Kuhn, the philosopher who argued in his 1962 book, The Structure of Scientific Revolutions, that scientific theories are accepted for social reasons rather than because they are in any objective sense ‘true.’” I continued:

“‘That mathematics reduces in principle to formal proofs is a shaky idea’ peculiar to this century, Thurston asserts. ‘In practice, mathematicians prove theorems in a social context,’ he says. ‘It is a socially conditioned body of knowledge and techniques.’ The logician Kurt Godel demonstrated more than 60 years ago through his incompleteness theorem that ‘it is impossible to codify mathematics,’ Thurston notes. Any set of axioms yields statements that are self-evidently true but cannot be demonstrated with those axioms. Bertrand Russell pointed out even earlier that set theory, which is the basis of much of mathematics, is rife with logical contradictions related to the problem of self-reference… ‘Set theory is based on polite lies, things we agree on even though we know they’re not true,’ Thurston says. ‘In some ways, the foundation of mathematics has an air of unreality.’”

After the article came out, the backlash—in the form of letters charging me with sensationalism – was as intense as anything I’ve encountered in my career.

For your typical naive reader, this just confirms a modern nihilism, as expressed by this comment:

If it is impossible to codify mathematics, and it is possible to state mathematical ideas that are true, but cannot be proven true, then the same applies to every field. Thus, the mere fact that you cannot prove some idea axiomatically proves nothing. People often demand proofs of that sort for moral or philosophical notions, like, say, the existence of God, but the whole exercise is empty. Thanks, Kurt.

Horgan deserved the criticism, and so did Thurston. It is not true that Godel proved that it is impossible to codify mathematics. It would be more accurate to say the opposite.

Russell did find an amusing set theory paradox in 1901, but it was resolved over a century ago. Set theory is not based on anything false.

Thurston was a great genius, and was famous for explaining his ideas informally without necessarily writing rigorous proofs. He was not an expert in the foundations of mathematics.

The quotes are apparently accurate, as he published as essay defending his views, and his record of claiming theorems and failed to publish the details of the proofs.

His essay complains about the theorem that the real numbers can be well-ordered, but there is no constructive definition of such an ordering.

From this and Godel's incompleteness theorem, he concludes that the foundations of mathematics are "shakier" than higher level math. This is ridiculous. I conclude that his understanding of the real number line is deficient. There is nothing shaky about math foundations.

It sounds crazy to question Thurston's understanding of real numbers, because he was a brilliant mathematician who probably understood 3-dimensional manifolds better than anything.

Doing mathematics is like building a skyscraper. Everything must be engineered properly. But the guy welding rivets on the 22nd floor may not understand how the foundations are built. That is someone else's department. So yes, someone can prove theorems about manifolds without understand how the real numbers are constructed.

It is still the case that mathematicians measure progress in terms of what they could demonstrate through a series of logical steps leading from a set of axioms to an irrefutable conclusion. The most famous works of the past 25 years were Fermat's Last Theorem and the Poincare Conjecture. Both took years to be accepted, because of the work needed to follow all those steps.

The idea that "theories are accepted for social reasons" is the modernist disease of paradigm shift theory.

A NY Times Pi Day article says:

Early mathematicians realized pi’s usefulness in calculating areas, which is why they spent so much effort trying to dig its digits out. ...

So what use have all those digits been put to? Statistical tests have suggested that not only are they random, but that any string of them occurs just as often as any other of the same length. This implies that, if you coded this article, or any other, as a numerical string, you could find it somewhere in the decimal expansion of pi.

That is a plausible hypothesis, and you might even find people willing to bet their lives on it. But you will not find it asserted as true in any mainstream math publication, because it has not been proved. Yes, math relies on proof, just as it has for millennia.

Bouncing oil droplets reveal slippery truth

Ross Anderson writes:

I am a heretic. There, I've said it. My heresy? I don't believe that quantum computers can ever work.

I've been a cryptographer for over 20 years and for all that time we've been told that sooner or later someone would build a quantum computer that would factor large numbers easily, making our current systems useless.

However, despite enormous amounts of money spent by research councils and government agencies, the things are stuck at three qubits. Factoring 15 is easy; 35 seems too hard. A Canadian company has started selling computers they claim are quantum; scientists from Google and NASA said they couldn't observe any quantum speed-up.

Recently, the UK government decided to take £200m from the science budget and devote it to found a string of new "quantum hubs". That might be a bad sign; ministerial blessing is often the last rites for a failing idea.

So will one more heave get us there, or is it all a waste of time?

Not only that, he has co-authored Maxwell's fluid model of magnetism. He claims that physics went bad about 150 years ago, and some ideas that were abandoned then are really right.

Scott Aaronson says that it is extremely safe to say that he is wrong, but is not able to pinpoint the error. Aaronson trashed some related work in 2013.

I sometimes get comments saying that mainstream physics has been wrong for a century or more. I don't know how to evaluation such claims. Science is never that completely wrong.

Anderson's theory seems to be some sort of hidden variable theory. I am persuaded that XX century quantum theory and experiments have ruled these out. So I do not see how he can be right.

Anderson is one of the world's experts on cryptographic security for banking and related industries. My guess is that he is frequently asked whether banks should use quantum cryptography, or worry about attacks from quantum computing. He surely comes to the conclusion, as do I, that both subjects are almost completely irrelevant to banking. Then he must be frustrated by bankers who doubt him because so many big-shots are over-hyping the quantum stuff.

I think that he is right that quantum computers will never work, and that failures so far give good reason for skepticism. I differ from him in that I doubt that there is anything fundamentally wrong with quantum mechanics.