Foolish and absurd in Philosophy

When Galileo appeared before the Inquisition in 1616, consultants were hired to appraise his heliocentrism, reporting:

The sun is the center of the world, and entirely immobile by local motion.

Appraisal: All have said the stated proposition to be foolish and absurd in Philosophy; and formally heretical, since it expressly contradicts the sense of holy scripture in many places, according to the quality of the words, and according to the common exposition, and understanding, of the Holy Fathers and the learned Theologians.

The earth is not the center of the world, and not immobile, but is moved along Whole itself, and also by diurnal motion.

Appraisal: All have said, this proposition to receive the same appraisal in Philosophy; and regarding Theological truth, at least to be erroneous in faith.

This translation is from a new paper, The Inquisition's Semicolon: Punctuation, Translation, and Science in the 1616 Condemnation of the Copernican System, by Christopher M. Graney:

This paper presents high-resolution images of the original document of the 24 February 1616 condemnation of the Copernican system as being "foolish and absurd in philosophy", by a team of consultants for the Roman Inquisition. Secondary sources have disagreed as to the punctuation of the document. The paper includes a brief analysis of the punctuation and the possible effects of that punctuation on meaning. The original document and its punctuation may also have relevance to public perception of science and to science education.

Nearly everyone omits the first semicolon above, thereby giving the impression that a scientific idea was "foolish and absurd" just because it was contrary to the Bible. The consultants only used the Bible as a reason for saying that the Earth's motion is "formally heretical".

There were legitimate scientific arguments against Galileo's Copernicanism, such as those listed here, here, here, and here. There were also theological arguments on both sides.

Wikipedia recently deleted this statement about Galileo's telescopic discoveries:

None of these findings, which were difficult at first for other astronomers to verify, proved that the Earth moved, or directly contradicted either Aristotle's model or Christian doctrine.

The statement is correct. The sources all agree that Galileo did not have the proof that Cardinal Bellarmine wanted, but the editors deleted the statement anyway because of an argument about "how science works". They say it was unreasonable to expect proof.

Owen Gingerich points out that decades later the great scientist Robert Hooke was also asking for proof, just like Bellarmine. Gingerich argues that stellar parallax by itself may not have convinced Bellarmine or Hooke. Scientists were convinced by the combination of the Newtonian framework with certain crucial experiments like stellar parallax. He does not mention that the relativistic framework of the 20th century showed that motion was relative and both arguments are valid.

It is impossible for an experiment to prove the Earth's motion because the laws of physics are valid in any frame of reference. Poincare made this argument, and later Einstein did also. Galileo gave a version of the argument, saying that we might not notice motion in the lower deck of a ship, but he also claimed that his goofy theory of tides proved the motion of the Earth. Bellarmine's position was closer to the modern view than Galileo's.

Rigorous math v physical heuristics

Israeli Rutgers University math professor Doron Zeilberger writes in the AMS Notices:

What Frenkel and Ross did not tell us is that the “math” that led to the discovery of the Higgs boson is not their kind of (pure-and-rigorous) math, but the much more effective, and efficient, nonrigorous mathematics practiced by theoretical physicists called quantum field theory. This highly successful (and precise!) mathematical theory would not be considered mathematics by most members of the American Mathematical Society, since it is completely nonrigorous.

I would not phrase it that way. I agree that the nonrigorous math is not really math, and that this is a dividing issue between mathematicians and physicists. Most physicists are sloppy in their math and do not really appreciate mathematical rigor.

But there is a lot of legitimate math behind quantum field theory, even if most physicists ignore it.

He appears to have a legitimate gripe about how the math community devalues computational math.

Proof is the only way to determine mathematical truth, and experiment (or observation) is the only way to determine scientific truth. When you have neither, then you have abominations like string theory.

He doubles down:

Traditional “rigorous proof” is yet another religious dogma, which did some good for a long time (as did the belief in God). Of course, it is not surprising that people can get deeply offended when someone denies the existence of their “God”.

But the God of (alleged!) rigorous proof is dead (well, not yet, but it should be!), and we should allow diversity. Rigorous proofs should still be tolerated, but they should lose their dominance, and the Annals of Mathematics should mostly accept articles with mathematics that has only semi-rigorous or non-rigorous proofs (of course, aided by our much more powerful and superior silicon brethren), because this way the horizon of mathematical knowledge (and mathematical insight!), broadly defined, would grow exponentially wider.

The Annals of Mathematics does not prohibit computer-assisted proofs. It published this paper of mine. It was a rigorous proof, not a heuristic or experiment.

Yes, rigorous has been the standard for a long time. Ever since Euclid's Elements in 300 BC.

His web site has many opinions, starting with this:

First Published (in Hebrew): ... The history of science supplied us with many examples of true "geniuses" that were kicked out of high school because of poor achievements, and one of the most prominent examples is the greatest scientist of our time, the physicist Albert Einstein. But Einstein was the greatest scientist of all times, and hence he managed somehow to find his way in life (but it wasn't easy, even for him).

No, Einstein was not kicked out of school or anything like that. He had very good grades and progressed thru a fairly rigid system to get a doctoral degree in physics.

Einstein did not succeed in doing any rigorous math. I am not sure he ever proved anything. Relativity is very mathematical, and he needed mathematicians Poincare and Minkowski to figure out the special theory, and Grossmann and Hilbert for the general theory.

For an example of math that seems sloppy but can actually be made rigorous, see
this NY Times account of how the natural numbers sum to -1/12. Or read Terry Tao's rigorous explanation or others.

Kepler used epicycles

A new paper says:

I discuss the problem of secular inequalities in Kepler by giving account of a manuscript note that has not been published until 1860. In his note Kepler points out the need for a model, clearly inspired by the method of epicycles, that describes the secular inequalities as periodic ones. I bring attention to this point, that seems to have been underestimated, since the references to Kepler's work usually report only that he observed a decreasing mean motion for Saturn and an increasing one for Jupiter.

Kepler is widely credited with abolishing the evils of epicycles in favor of elliptical orbits, but I did not know that he used epicycles himself. The paper starts:

The discovery by Kepler of the elliptic shape of the planetary orbits is often considered
as a discontinuity with the traditional models of Classical Astronomy, based on geometrical tools such as circles, epicycles and equants. The enthusiastic announcement of the discovery in chapter LVI of Astronomia Nova [6], where Kepler says that he was “quasi e somno expergefactus, et novam lucem intuitus” (like suddenly awakened from sleep, and seeing a new light) seems to confirm that this was his feeling, too. But, as often happens, reality turned out to be complex enough to escape our theories: the orbits of the planets are not exactly elliptic. This is well known today, but it seems that the circumstancy that long term deviations from the elliptic motion have been investigated in great detail by Kepler himself, with an explicit conjecture that these deviations should be periodic, is not so known, even among astronomers.

Epicycles are widely mocked as being contrary to science and rational thought, but they are legitimate tools for representing orbits.

You might say that the planetary orbits, as seen from the Earth, are circles. The first order correction is the Ptolemy epicycles, related to the Earth's orbit around the Sun. The second order correction is the Copernican epicycles, related to the elliptical orbits, The third order correction is the Kepler epicycles, related to the gravity of other planets. Modern representations might use a Fourier series with hundreds of terms.

Counterfactuals: Law

Many court actions are contingent on counterfactual reasoning. Tort law is based on the idea that if someone commits a wrong act against you, then you can sue for damages. For example, if someone crashes into the rear end of your car, you can sue for the cost of restoring your car to its condition before the accident.

The court has to somehow figure out what would have happened if the tort had never happened. The counterfactual is the plaintiff's life without the tort. If someone slanders you and you sue for damage to your reputation, then the court has to estimate the dollar value of the difference between your actual reputation and your counterfactual reputation if you had not been slandered.

More common are lawsuits over contract law, and these also depend on counterfactual reasoning. This is one of the most misunderstood points in all of law. If you sign a contract to rent a house from someone for $1000, and you break the contract, then he can sue you for the $1000. But the court will only award the counterfactual damages. If he could have easily found another tenant to pay the $1000, then you may not owe anything. Or you might even owe more than $1000, if he has lost business because of your vacancy.

The debate about Trayvon Martin asked questions like: What if Martin had been white? What if Zimmerman stayed in his car?

At the Zimmerman trial, the prosecutor misunderstood the role of the expert:

Prosecutor Bernie de la Rionda: In order to give an opinion, when someone gives you a hypothetical, it has to based on facts that are accurate and truthful, correct?
Di Maio: A hypothetical doesn't have to be true. A hypothetical is just "suppose this and this happened ...".
Prosecutor Bernie de la Rionda: So we would be speculating, I guess, or potentially speculating?
Di Maio: It is not even speculating. You are giving a presentation and asking what it is.

Di Maio is correct. An excellent expert witness could testify entirely by answering hypothetical questions, and never even look at the facts of the case. For example, a witness might be useful just answering these hypothetical questions: "What does a gunshot would look like if the gun is pressed against the skin? If the gun is 3 inches away? 12 inches? 24 inches? How is that known?" The jury could then apply his knowledge to the facts of the case.

Most witnesses in court are not allowed to speculate, or offer counterfactual reasoning. That is restricted to lawyers making arguments (not under oarh), and expert testimony. A expert must follow the Daubert standard, as codified in US federal court as FRE 702:

A witness who is qualified as an expert by knowledge, skill, experience, training, or education may testify in the form of an opinion or otherwise if:

(a) the expert’s scientific, technical, or other specialized knowledge will help the trier of fact to understand the evidence or to determine a fact in issue;
(b) the testimony is based on sufficient facts or data;
(c) the testimony is the product of reliable principles and methods; and
(d) the expert has reliably applied the principles and methods to the facts of the case.

When the expert describes those reliable principles and methods, he often tells how they apply to hypothetical situations. As the jury (or maybe the judge) determines the facts, testimony about counterfactuals in the most useful. Often there is no need for the expert to offer any opinion about the facts of the case, if the jury is taught how to apply the generally accepted knowledge.

Thus counterfactuals are essential to the law.

Update: A 2010 US Supreme Court decision said that a lawsuit "does not require precise proof of what the Board's policies might have been in that counterfactual world." I mention this because it is understood that lawsuits are all about proving scenarios in counterfactual worlds, even tho that terminology is uncommon.

Nearby star is oldest in the universe

A new research announcement says:

The Oldest Star in the Known Universe

A team led by astronomers at The Australian National University has discovered the oldest known star in the Universe, which formed shortly after the Big Bang 13.7 billion years ago.

The discovery has allowed astronomers for the first time to study the chemistry of the first stars, giving scientists a clearer idea of what the Universe was like in its infancy.

"This is the first time that we've been able to unambiguously say that we've found the chemical fingerprint of a first star," said lead researcher, Dr Stefan Keller of the ANU Research School of Astronomy and Astrophysics. ...

The ancient star is around 6,000 light years from Earth, which Dr Keller says is relatively close in astronomical terms. It is one of the 60 million stars photographed by SkyMapper in its first year.

I am surprised that the oldest star is so close. I would have guessed that the oldest known stars would be outside the Milky Way. After all:

In physical cosmology, the Copernican principle, named after Nicolaus Copernicus, states that the Earth is not in a central, specially favored position in the universe. ...

Michael Rowan-Robinson emphasizes the Copernican principle as the threshold test for modern thought, asserting that: "It is evident that in the post-Copernican era of human history, no well-informed and rational person can imagine that the Earth occupies a unique position in the universe."

So if we are in the oldest galaxy, then maybe we are in the center of the universe!

Perhaps the researchers only looked at stars in our galaxy. If so, they should have explained that.

Arguing that photons are massless

Physics professor Brian Greene was on Comedy Channel Colbert Nation plugging worldscienceu.com, and spent most of the time arguing that light has energy, but not mass. Even Colbert knew that E=mc², so he was confused. So were most viewers, I am sure. Greene was there to explain science, and he did a lousy job.

Textbook terminology has changed over the decades on this point. Here is how Wikipedia explains mass in special relativity:

A so-called massless particle (such as a photon, or a theoretical graviton) moves at the speed of light in every frame of reference. In this case there is no transformation that will bring the particle to rest. The total energy of such particles becomes smaller and smaller in frames which move faster and faster in the same direction. As such, they have no rest mass, because they can never be measured in a frame where they are at rest. This property of having no rest mass is what causes these particles to be termed "massless." However, even massless particles have a relativistic mass, which varies with their observed energy in various frames of reference,

John Baez explains:

Photons are traditionally said to be massless. This is a figure of speech that physicists use to describe something about how a photon's particle-like properties are described by the language of special relativity.

A figure of speech? Yes, you can say that photons have mass, or do not have mass, as long as you define your terms carefully.

Here is a modern opinion:

For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass, that is the mass–velocity relation, and this is probably still the dominant mode in textbooks. More recently, however, it has been increasingly recognized that relativistic mass is a troublesome and dubious concept.

Obviously Greene was concerned that he might be embarrassed before his colleagues using some antiquated terminology.

It would have been better to say:

Yes, photons have mass and momentum. Some physicists like to say that the rest mass is zero, but the photon is never at rest anyway.

Greene is teaching two new courses on "Einstein's special theory of relativity". It is funny that he always has to say that it is Einstein's theory. Everything he mentions was discovered by someone else, not Einstein.

Counterfactuals: Grammar

Consider the sentence, "if pigs had wings, they could fly." This is a very strange thing to say, as pigs do not have wings. And yet the sentence is readily understandable to children.

The English language has a construction called the "subjunctive conditional" for counterfactuals like this. Statements that describe reality are in the indicative mood, such as "pigs do not have wings" or "pigs do not fly". So are straightforward conditional statements, like "if pigs have food, they eat." If you want to suggest some sort of imaginary world in which pigs fly, you need the verb to be in the subjunctive mood.

Consider this illustration of the English subjunctive:

If he was in class yesterday, he learned it.
If he were in class today, he would be learning it.

The first is a simple statement about a boy learning in class. The second suggests that he was not in class, but it says something about some false scenario anyway.

Here is another example:

If Oswald did not shoot Kennedy, someone else did.
If Oswald hadn’t shot Kennedy, someone else would have.

The first is a true statement because it is indicative conditional with a false antecedent. Oswald did shoot Kennedy. Even if you are not sure that Oswald shot Kennedy but know that Kennedy was shot, then you will still accept the statement as true. It is only an assertion about actual historical events.

The second statement is much more complex. It uses the subjunctive mood to alert you that it is hypothesizing some counterfactual world and trying to reason about that world as if it were real. It is hard to say whether the sentence is true or false because you have to make assumptions about what else might be funny about that unreal world, and speculate how events might play out.

The counterfactual conditional is a false history scenario. In other cases, the counterfactual is a future hypothetical. For example, you could say that "if the Antarctic ice melts, New York would go under water."

The subjunctive is commonly misunderstood. In the famous 1968 zombie movie, Night of the Living Dead, Barbara says, "Johnny asked me if I were afraid." No, Johnny wanted to know whether she was actually afraid. He was not trying to create some counterfactual scenario. The correct grammar is "Johnny asked me if I was afraid."

The subjunctive "were" would be appropriate if Johnny said "I would run if I were you" or "I would be angry if I were you." Obviously Johnny cannot be someone else, and the subjunctive mood alerts the listener that she is getting a superficially nonsensical scenario.

Here is another example:

If he was in line, give him a ticket.
If he were in line, he would be eating by now.

The first is indicative and factual. The second is subjunctive and counterfactual.

The subjunctive is not used often in English, unless there is some counterfactual being expressed. The verb "be" is subjunctive in "I suggest that they be removed." Then sentence does not say that anything has been or will be removed. It creates a hypothetical scenario where something is removed.

The counterfactual concept is essential, and so is the English subjunctive mood for expressing it.

Classics scholar Phuc Tran argues in a TED talk that his Vietnamese relatives are unable to ponder counterfactuals because their language lacks a subjunctive mood.

I am not sure how other languages deal with these concepts. Chinese does not even have past and future tenses, so it has trouble with expressing time as needed for counterfactuals. (I am not sure about all Chinese, as there are at least 300 different varieties of Mandarin that were more or less mutually unintelligible.)