When were Negative Numbers Invented?

I thought that negative numbers were ancient, but have recently learned that mathematicians of a few centuries ago distrusted them.

Wikipedia says they go back to China and India a couple of millennia ago. I doubt it.

I am looking for an example of an algorithm:

1. Compute a number X that can be positive or negative.

2. Use X to compute something else, without dividing into two cases.

In doing my income taxes, I cannot find any example of IRS using such an algorithm.

I am guessing such algorithms started to appear around 1800 or so.

Wikipedia explains:

For a long time, understanding of negative numbers was delayed by the impossibility of having a negative-number amount of a physical object, for example "minus-three apples", and negative solutions to problems were considered "false".

But that is not impossible at all, as having "minus-three apples" means owing 3 apples.

Furthermore, lots of other natural measurements can be negative. I could ask "how far are you east of the landmark?" and get a negative answer. Likewise, feet below sea leval, freezing temperature, or a countdown to an anticipated event. If I ask the cost of something, and it turns out to be a benefit, then it has negative cost.

Newtonian Physics was invented around 1680. Today, textbooks explain it with force diagrams, where force vectors are added. These seems to require negative numbers, as forces can cancel out. It also seems to require vectors, but vectors were not invented until about 200 years later. It is hard to imagine that Newton did not understand negative numbers, but maybe not, if he did not understand vectors either.

The Witten Family Eugenics Project

Ed Witten is supposed to be the world's smartest theoretical physicist, if not the world's smartest human. To have kids, he married an Italian string theorist, and had three daughters, at least two of which are also geniuses. Curiously, they are both in brain science specialties that might help explain why their family is smarter than everyone else.

Politically, they all seem to be typical academic leftists. Ed recently tweeted in favor of Australia ban tennis star Novak Djokovic for not taking the covid vaccine. An appellate court has since ruled that he has complied with all requirements, but he was deported anyway out of fear that he might influence public opinion.

This is just typical academic foolish leftism to side with experts outside his field in order to give an opinion on who should play tennis on the other side of the world.

One of his daughters has been active in canceling statistician and geneticist Ronald Fisher, based on some politically out-of-favor opinions associated to him on his Wikipedia page. In particular he wanted to use genetics research to improve the human condition. Plus, she wanted to join all the academics making a statement about the death of George Floyd.

It is not clear what Fisher said that was so offensive, but I don't see why it should matter. If he were wrong, then demonstrate his error. His critics are not doing that. He smoked cigarettes and denied that they cause cancer. Okay, he was wrong about that. But he still made a great many other positive contributions, and I do not agree with applying an ideological litmus test on scientists.

There is a great reckoning going on where famous men of the past, like Charles Darwin, are being scrutinized for their opinions on slavery. Why would anyone care? I don't. Whether Darwin had political opinions for or against slavery, or on various other political issues, is of no relevance today. He is not judged for his politics.

If we are really going to apply weird George Floyd racial theories to scientists of the past, what will future academics make of Ed Witten's refusal to breed with a low-IQ woman?

There is something creepy about our elites being so leftist. It is just their way of saying that they are better than the rest of us.

Eugenics has a strange history. Here is a review of a new book on the subject.

Strong Determinism

New paper on Strong Determinism, a concept different from superdeterminism:

In this paper, I focus on strong determinism. According to Penrose (1989), it is “not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time” ...

On an intuitive level, we can say that the multiverse of the Everettian Wentaculus has “more branches” than that of the Everettian Mentaculus. The Everettian Wentaculus multiverse has all the branches that the Everettian Mentaculus one has and more. Speaking loosely, all the nomological possibilities of the Everettian Mentaculus multiverse will be embedded somewhere in the actual Everettian Wentaculus multiverse. However, on the Everettian Wentaculus, there is no fundamental nomic contingency or possibility beyond the actual fundamental world. If notions of contingency, chance, probability, and counterfactual make sense in this world, they have to be emergent at the level of branches and subsystems in the multiverse. It is important to appreciate that the theory does not contain any notions of probability or typicality at the fundamental level of physics. Hence, this is a proposal that completely eliminates the Statistical Postulate in fundamental physics.39

I could not make any sense out of this.

Horgan Prefers Free Will over Superdeterminism

SciAm columnist John Horgan has a column on superdeterminism and free will:

Physics, which tracks changes in matter and energy, has nothing to say about love, desire, fear, hatred, justice, beauty, morality, meaning. All these things, viewed in the light of physics, could be described as “logically incoherent nonsense,” as Hossenfelder puts it. But they have consequences; they alter the world.

Physics as a whole, not just quantum mechanics, is obviously incomplete. As philosopher Christian List told me recently, humans are “not just heaps of interacting particles.” We are “intentional agents, with psychological features and mental states” and the capacity to make choices. Physicists have acknowledged the limits of their discipline. Philip Anderson, a Nobel laureate, contends in his 1972 essay “More Is Different” that as phenomena become more complicated, they require new modes of explanation; not even chemistry is reducible to physics, let alone psychology.

Bell, the inventor of superdeterminism, apparently didn’t like it. He seems to have viewed superdeterminism as a reductio ad absurdum proposition, which highlights the strangeness of quantum mechanics. He wasn’t crazy about any interpretations of quantum mechanics, once describing them as “like literary fiction.”

Why does the debate over free will and superdeterminism matter? Because ideas matter. At this time in human history, many of us already feel helpless, at the mercy of forces beyond our control. The last thing we need is a theory that reinforces our fatalism.

He gets some pushback on his Facebook page. In particular, Scott Aaronson says that he understates how bad superdeterminism is, and Sabine, Hossenfelder claims that her superdeterminism views have been distorted.

To me, free will is real simple. If you are a normal conscious human being, then you directly experience free will. You make free choices. It should take a pretty strong argument to convince you that your personal experience is false.

Science could prove our intuitions wrong, but the arguments against free will are not scientific at all. They are based on a belief that the past determines the future, or a belief that science would never explain consciousness so we must be unconscious automatons.

Superdeterminism goes further, and says that not only are we pregrammed robots, but even when we do controlled experiments, the setup parameters are forced on us in a way to make the results fool us.

There is no proposed superdeterminism theory that makes any sense, and it has few backers. Dr. Bee pushes it as the logical consequence of rejecting quantum mechanics, nonlocality, and free will.

While Aaronson rightly rejects superdeterminism as madness, he accepts many-worlds theory that has most of the same problems. It does not let us do any controlled experiments either. It also cannot say that setup X predicts outcome Y with probability P. It says that everything happens, and what you see is just a reflection of what world you ended up in.

Horgan is the journalist who says the emperor has no clothes. He is saying the obvious, while prominent scientist profess crazy ideas.

Science Backs Transgender Voodoo

The Science Friday podcast is mostly straight science, but often ventures into leftist politics.

Yesterday, it claimed science supports gender-affirming care for kids:

Attorney General Ken Paxton issued an opinion that defined providing access to certain gender-affirming treatment as child abuse, leaving some parents worried about the safety of their families and some advocates concerned about the well-being of trans kids in Texas. ...

Student Hayden Cohen is a non-binary 17-year-old and co-president of their schools’ Gay Straight Alliance at Houston ISD. Last Wednesday, they received a rush of panicked messages from members of the club.

These treatments are very controversial, at best. I would not mind if the show gave scientific arguments and data for and against them. But of course it did not do that.

This was about like a program in the 1950s praising lobotomies as a miracle of modern science, without ever mentioning how they can be bad.

Free Will is Called a Dice Throw

I have posted on free will many times. Here are some hard-core empiricists who deny free will.

From Coel's blog:

I get the compatibilist argument. You are essentially saying that if a cause is unknown, then it cannot be free will. In particular, if quantum mechanics is unable to determine something, then there is no free will involved. I am just noting that this opinion is not found in any quantum mechanics textbook or scientific paper. It is not based on any empirical data.

So your suggestion is that a “will” is responsible for the outcome of a “quantum indeterminacy” event and hence a brain’s decision? In that case we have one of:

1) The “will” is non-material, non-physical. This is dualism, a “soul” that is telling matter what to do and producing the brain’s decisions.

2) The “will” is physical, and is a manifestation of the state of the physical stuff. If so, this is straight back to determinism, such that the brain’s decisions are a product of the “will” and thus of the prior physical state. Essentially, this is just a “hidden variables” version of QM, where the indeterminacy is replaced by deterministic causation by the (physical) “will”. This then gives a compatibilist account of “will”.

3) The outcome is still indeterministic, that is, it is still a chance, dice-throwing process. Thus, the outcome is not caused by the “will” (regardless of whether that will is material or non-material), it is still a dice throw. But if so, I really don’t see how the brain’s decisions can be regarded as “willed”.

So I don’t see how this helps at all. Either the brain’s choices are determined by the prior state (call that a “will” if you wish), or they are chance dice throws. The latter doesn’t give a free “will”. The former gives compatibilism.

Here is a similar view:

“But plain old determinism is bad enough because it says that we human beings are all a pack of fools who think WE are doing things, like trying to defend a country from Putin’s aggression, when actually everything, including our own selves and what we do, is nothing but the outcome of deterministic laws of nature.”

As opposed to what? Like, what could your “thoughts”, “decisions” and “actions” be based on besides prior state of the world? Which is the definition of determinism… there’s only either causality or randomness, there’s nothing else out there to make you feel better about your own decisions/actions. One could maybe imagine a world where future outcomes influence retro-actively past decisions, with closed timelike loops (basically counterfactuals become a possibility), but even in that model a state is determined from a prior state (just that time is not strictly linear, and things evolve until some equilibrium is reached).

And if you posit you have a magical soul that’s somehow living outside a reality that’s covered by the law of physics, or your decisions are maybe influenced by an omnipotent god or some universal sense of good and evil, there’s still only two ways for dynamical systems to evolve: direct causality or randomness.

I don't know whether free will is material or physical. I do not know how to answer that question for an election, a wave function, or a Higgs field.

It is bizarre to me that he can imagine a world with closed timelike curves, but not one with free will.  

I do know that I experience free will. It is probably the one thing that conscious beings are most sure about. The compatibilists and other determinists say that I am being fooled. Okay, maybe, but I would like to see some explanation as to how I could be fooled so badly.

The above explanations are commonly given. I would rephrase them as:

Events are either predictable or not. Free will is very strange in that a human making a choice might be able to predict his own choice, while others cannot.

My reaction is: Okay, you think it is strange. But if you are taking a scientific stance, then you should either accept it as possible, or show me some empirical evidence against it.

There is no empirical evidence against it. Some claim that the Libet experiments disprove free will, but that has been debunked.

The above argument is that free will can be disproved by pure philosophizing about causality and randomness. The whole approach is foolish. People claim to be empiricists, but refuse to look at any empirical evidence.

Update: The March 7 NY Times Mini Crossword puzzle has this clue:

1. With 5-Across, philosophical concept opposed by determinism

The answer, of course, is Free will.

Russian Science is Boycotted

You know it is bad when the West politicizes science more than the Communists did. That is where we are today.

Jerry Coyne reports:

Anna told me she got an email from one of her collaborators, who was reviewing for a journal a paper written by Russian scientists. (“Reviewing,” as you probably know, is when anonymous scientists determines whether a submitted manuscript in their field merits publication in the journal. Here’s the email that Anna’s collaborator got from the journal named below.

Thank you for reviewing this manuscript. I have to inform you that the editors of the Journal of Molecular Structure made a decision to ban the manuscripts submitted from Russian institutions. You must know that it is a ban on Russian institutions and not a judgment on scientists. Therefore I cannot accept the manuscript.

Therefore, the reviewer had to send the Russian authors this rejection letter:

I regret to inform you that your manuscript cannot be considered for publication in the Journal of Molecular Structure. The editors of this journal, in the full assumption of their responsibilities as scientists and academics, decided not to consider any manuscript authored by scientists working at Russian Federation institutions as a result of the invasion of Ukraine by the Russian Federation. Such invasion violates international law, jeopardizes world peace as well as the human rights of innocent citizens, and does not conform to the civilizational ideals of the 21st century. This decision will be in force until international legality is restored, and is extended to the institutions of the Ukrainian territories occupied by Russia.

The Russia chemist has nothing to do with the Ukraine war. Banning a chemistry paper will not help the Ukrainians.

The International Congress of Mathematicians meets every four years, and was going to meet in St. Petersburg this summer, with the generous sponsorship of Russia. Now the meeting has been boycotted and canceled, leaving the local sponsors in debt for years to come.

A more sensible journal announced:

As of the time of writing, no government sanctions are in place which impact the handling of papers that include Russian authors, and we ask editors to follow usual practice on “Fair Play”: “The editor should evaluate manuscripts for their intellectual content without regard to race, gender, sexual orientation, religious belief, ethnic origin, citizenship, or political philosophy of the authors.”

This is an evolving crisis and we will keep you updated on any developments that may impact your work. We stand by our belief that restrictions on publishing are inappropriate, and any exceptions should be narrowly crafted.