Saturday, February 15, 2014

Galileo Galilei: 450th birthday

Off-topic. Finally some Czech gold in Sochi: a women's snowboard cross event. It is a violation of the rules to inject testosterone into the veins but a few years ago, a rookie and saxophone player named Ms Eva Samková found out it is perfectly legal to paint a nationally colored mustache above her lips and it has worked; she has won every stage of the competition. The only other duty she had was one during the ceremony – she had to dress the jacket inside out and use the golden liner the designers hid on the other side from the white cloth. So far, Facebook has failed to include "mustache woman" among the 10 officially recognized sexes. :-) Czechia is now 15th with the 1-2-1 medal tally; our Slovak brothers have 1-0-0 thanks to "their" biathlete Nastya Kuzmina who said she was grateful for the Slovak passport (after she was thrown away in her homeland) but Slovaks shouldn't get carried away because despite the passport, she's obviously still Russian! ;-) Due to the excess shame, I chose not to discuss the results of the Czech and Slovak ice-hockey teams.

Incidentally, another cute Czech snowboarder Ms Šárka Sharky Pančochová deserved a medal as well – according to virtually all observers – but the referees screwed it. A journalist and ugly, stuttering, favored spoiled brat Mr Pavel Novotný suggested that Sharky shouldn't whine. So Sharky offered you a prize: if you slap the spoiled journalistic brat into his face and if you record the well-deserved punishment and send it to Sharky, you will get a new snowboard from her including her signature and "thanks". Good luck; similar journalists should be beaten approximately 24 hours a day. ;-) You will need to be fast because lots of Sharky's fans have already found the address of the son of the famous host and comedian.

Galileo Galilei, the father of science, the scientific method, physics, modern physics, and astronomy, among other things (including 2 daughters and 1 son, all of them out of wedlock), was born on February 15th (unadjusted Julian calender i.e. Old Style), 1564 in Pisa, a town in the Duchy of Florence.

That's exactly 450 years ago today. Congratulations, Galileo!

See National Geographic for some fresh out-of-TRF article on Galileo.

His father Vincenzo Galilei was an achieved lutenist (like an obsolete guitar player) and music theorist and the family was doing fine. Nevertheless, this father needed lots of money for some dowries and extra expenses required by Galileo's younger brother Michelagnolo Galilei (another lutenist, one who never earn any real bucks with his music). Despite the relative wealth and fame, one could say that Galileo (who became a lutenist himself) needed extra income and many of his early inventions were actually motivated by the thirst for extra money.

Despite his prestigious background, I would count him as a self-made man who shared many of the typical character features with great folks who come from poor families.

When he was in his late 20s and early 30s, he would study why the pendulum had a constant period and how it depended on the length/geometry. He created a thermoscope (a father of the thermometer), studied hydrostatic balance, and was hired as the boss of the maths department in Pisa, before he moved to Padua to teach mechanics, geometry, and astronomy. He would study the acceleration by freely falling objects from the tower of Pisa. Does the velocity increase by the same amount per unit time or unit length? He was able to settle this question in the scientific way. Yes, it's per unit time.

He wrote not only Dialogue Concerning the Two Chief World Systems but also other masterpieces of the polemical literature. At some moment, he would become a staunch heliocentrist who wasn't afraid to point out that the Pope was an idiot. Some people tried to resist this insight; see Galileo as the tragic hero for comments about the trial as well as Galileo vs Benedict XVI.

Dozens of other blog entries about Galileo have been written, too.

Some of his testing questions that helped him to understand early physics better were concerned with the tides (it was in the pre-Newtonian era so there were still some major technical mistakes in his answers: for example, he couldn't understand why the tides have two periods per day and not just one); the 1604 Kepler's supernova (he could show that it was a distant star – no parallax – which contradicted some bizarre Aristotelian dogmas about the immutability of the heaven – the heaven is defined as the things that are "infinitely far" and those should never explode); the Milky Way (he appreciated it's there and what it is probably made of); and observations of other planets and their moons, some of which he observed for the first time with his telescope that was one of the first good ones. He was not necessarily the guy who invented telescopes with all of their know-how but much like great IT industrialists today, he knew how to put these ideas floating around to work.

Aside from the telescope, he invented a geometrical and military compass and lots of various gadgets for sea navigation etc.

Galileo's battle for the heavens, 1:49:00. I hope that some readers will find the time to watch it! I have watched it. Galileo's daugher Maria Celeste and her relationship to her father is given a lot of time. A tragic story. Even though it could have been realistic, I found the actor starring as a senile, old, ill, unintelligible Galileo annoying and excessive; he actually wrote the most accurate works as a very old man. For the last 4 minutes, see the Italian version.

There's way too much to say about Galileo Galilei so I gave up any plans to be comprehensive at the very beginning. But I want to say the following thing. Galileo Galilei wasn't infallible and his comments about particular questions in physics and astronomy weren't always 100% right. However, he was right about the key things and more importantly, he pioneered the very scientific method that allows us to be increasingly right and accurate. In a sense, the scientific method mimics Galileo's own life. It isn't producing flawless results from the very beginning; it is a process to gradually eliminate the flawed hypotheses and – with the help of observations and experiments – converge closer to the correct ones. This methodology to learn about the truth was revolutionary and, to a large extent, new – even though it looks obvious to us today. By finding this method, he established a new religion of a sort, one that actually works in its goal to make progress.

The reason why he couldn't get as far as Isaac Newton almost a century later was that unlike Newton, Galileo was no ingenious mathematician. His knowledge of maths was "standard" at most and he didn't make any major breakthroughs in maths. And this does slow down everyone who would like to become a revolutionary in physics. In maths, Galileo became famous for childish insights of recreational mathematics such as the observation that the set of perfect squares has the same number of elements as the set of integers, despite their being subsets of one another ("Galileo's paradox"). That's too little relatively to, say, Calculus.

Although Galileo's contributions had to look formidable even during his lifetime, he was often harassed for having contradicted some dogmas, stereotypes, and the authority of the lesser minds. He was tried as a possible heretic and the verdict was a life in (home) prison. He was arguably lucky not to be executed. Centuries later, the Catholic Church and others were gradually rehabilitating him.

Indigo Girls: Galileo. Warning: the song isn't necessarily historically and scientifically accurate.

While Galileo played a key role in the birth of science (or modern science) or physics as we know it and even though he was clearly versatile and extremely skillful and smart in many different ways, I would say that the bulk of these achievements depended on his unusual courage, self-confidence, political influence, and his ability to provoke rather than his being one of the smartest men of all time. In particular, the very fact that he could get away with this self-evident heresy (according to the traditions at that time) was very important for the Western civilization that could suddenly notice that some important ideas may arise from corners that aren't fully endorsed by the church's group think. This "relative victory of a heretic" brought lots of meritocracy – desire to find independent-of-religion, new methods to judge the validity of claims – into the smart folks' thinking. Don't get me wrong: he was extremely intelligent. But the intelligence was nowhere near Newton's. But that doesn't matter for us; he has still done amazing, unprecedented things and it was up to him how to achieve those things.

Deja vu doesn't necessarily prove that you live in the Matrix.


  1. I like the argument that Galileo's life mimics (or perhaps embodies) the scientific method, a very nice analogy.

    At the risk of starting a "Galileo's greatest hits" commenting trend, I have always been most impressed by his understanding of relative motion, and his clear and poetic thought experiment describing its irrelevance:'s_ship

    This is why we refer to "Galilean invariance", and it's a damn good reason.

  2. Nice overview.

    Galileo died the year Newton was born, 1642. They were a relay team.

    Gold medalists! :)

  3. OT, but still on great men.

    G.H. Hardy had a classification for mathematicians. If I recall correctly his Bradman class was comprised of Newton, Gauss and Archimedes.

    Why Donald Bradman? Two reasons: the lesser being that Hardy was very keen on cricket; the greater just being Bradman who was a cricketer (

    Yes, but why Bradman? Here's why: take a look at his Test batting average — see the histogram here:

    Now there's a human outlier if there ever was one.

    Fcuking Aussies. :)

  4. "Galileo was no ingenious mathematician. His knowledge of maths was "standard" at most and he didn't make any major breakthroughs in maths. Mathematicians need pencil and paper. Scientists need pencil, paper, and a garbage can. Physics arises from Equivalence Principle vacuum symmetries. EP violation requires physics be rewritten.

    Physics excludes geometric chirality. Green's function on Newton explicitly removes it. Parity violations, symmetry breakings, chiral anomalies, Chern-Simons repair of Einstein-Hilbert action witlessly patch it. Opposite shoes violate the EP. Visually and chemically identical, single crystal test masses in enantiomorphic space groups violate the EP. Contrasted P3(1)21 vs. P3(2)21 single crystal alpha-quartz test masses violate the EP.

    Physics says " BRST invariance postulates are as valid as Euclid's Fifth Postulate." Agreed. Then, cartography.

  5. Eelco HoogendoornFeb 16, 2014, 1:17:00 AM

    Rather than a childish insight, it is actually a rather profound observation I would say; though he certainly wasn't the first to notice such properties of infinity, this particular instance of the many 'funny things about infinity' really brings into the spotlight the question as to how to deal with infinity in mathematics in the most direct way.

    Modern myth has that Cantor 'solved' such problems, by 'discovering' one to one mappings. But he didn't discover anything; he merely decided (without giving any motivation whatsoever) that he preferred one to one mappings as a notion of 'size' over things being constructible from eachother by adding or removing elements.
    That something gets smaller when you take something away from that something seems like an excellent axiom to me; its the kind of near-tautology that integrates directly with almost everything we know, and of which one would be happy to accept any more abstract downstream implications, much like 1+1=2.

    As for the important questions as to 'what makes a good axiom', there is no substitute for our own critical thinking. But if I had to rely on any authority to decide such matters, it would be a renaissance man like Galileo, who had a view of the total body of human knowledge rivaled by few, and as such a solid perspective on how any given axiom integrates with that body of knowledge. A manic depressive basement dweller like Cantor had better come up with some good arguments before I follow his lead on something fundamental like this. But he never had any such arguments; only a burning metaphysical desire to get rid of contradictions in mathematics, physics or sound philosophy of science be damned.

  6. It's great that you grace the comments section of TRF with your presence, Dr. Zajc. It raises the level of discourse.

    True, the comments section looks like a madhouse on some days, but most of us are actually quite friendly and reasonable people. (Except for John Archer. That guy is a real terror! and I suspect also a cannibal.)

  7. Well, as I wrote 5 days ago, I consider these games with infinity to be childish when done by Cantor, too.

    They're childish in the sense of being available to the average laymen, too. That's how laymen's recreational games with infinities look like.

    One may design and present lots of pseudoarguments about infinity, but one needs to have some mature sense of taste and inner functioning to invent integrals and derivatives. Or analytic continuation to calculate 1+2+3+4+....

    The things that are mature end up being important in physics and lead to tons of accurate ramifications; the childish things will remain recreational games.

  8. Eelco HoogendoornFeb 16, 2014, 10:04:00 AM

    I agree; it is the physical implications of either adopting an axiom or not adopting an axiom that decides its 'truth'.

    But even when the implications are not directly evident, its not just recreational. Ones choice of axioms usually have a large stylistic implication, which influences your direction of thinking. Having a very constructivist style of thinking myself, I am none too happy about having to communicate with a field which has rejected a lot of its constructive foundations for no good reason.

    As far as I am concerned, pre 20th century physicists had it figured out best. Newton and Gauss were capable of doing calculus just fine; even though they didn't have a set of axioms optimized to skirt around logical issues with infinity. The best solution to this 'problem' is simply not giving a fuck when people like Berkeley are trolling you with 'ghosts of departed quantities'.

    From my perspective, the whole issue boils down to a choice between three controversial positions:

    1: Reality does not share our obsession with self-consistency; even if only wrt non-observable matters involving infinity.

    2: Infinity should play no role in a fundamental description of reality. If 'physics is about what we can measure', what is infinity doing there in the first place?

    3: Cantor somehow had it all figured out from inside his ivory tower, and the fact that many theorems and branches of mathematics which are the result of this foundational direction seem meaningless or even unphysical, is just our lack of imagination.

    I respect that that most people prefer 3; but I myself am not so sure.

  9. laboussoleestmonpaysFeb 16, 2014, 10:32:00 AM

    Talking about the fathers of modern physics in our post Higgs era, don't you think we could have been a little bit brainwashed* by the classical inertia concept inherited from the old telescopes of these giants? I mean, with our contemporary attoscopes, would it not be more natural to think about some kind quantum inertia with zero mass term particles "living" at the speed of light, and should we not build new mathematics to describe a genuine quantum dynamics, in a proper arena (a new geometry dressed by quantum fluctuations) with proper rulers and clocks (a new calculus to play with dimensional regularisation)? Hopefully Newton has probably shown us the way with his spectroscope and the Higgs boson could be the post Galileo pendulum clock ...

    (*I paraphrase the title of a famous P.W. Anderson's article and I have found inspiration in,, and )?

  10. Your off by 13 days. 15 February 1564 (Julian) plus 450 years is 28 February 2014.

  11. Eelco,
    … (without giving any motivation whatsoever)? How about having an inverse function?

  12. Eelco HoogendoornFeb 16, 2014, 5:55:00 PM

    I don't have a problem with one-to-one mappings proving equal size; that seems perfectly sound to both me and Galileo; and I doubt anyone disagrees. What I have a problem with is adding or taking things away not disproving equal size. 'Sets which are a proper subset of themselves'? Rephrasing the problem at hand as a definition is not clever philosophy.

  13. Eelco,

    Well, uncountable infinities are weird indeed. If you worry too much about it you can find yourself even doubting the reals, and that probably isn’t a good place to be.

    According to the constructivists, the source of the weirdness is the law of the excluded middle. Seems to me that Godel’s theorem has some relevance there, so I kind of like their camp. At the very least, they pretty much ridicule those who always start a proof with “Suppose not”.

  14. Thank you for the kind words Eugene; they are much appreciated.

    All I will say regarding Mr. Archer is that his occasional useful observations are enormously diminished by his overt racism, which is also a disservice to TRF.

  15. Well, everyone has their own political taxonomy. In my version, racists are people who obsess about race (or "race", as the dividing lines are mostly arbitrary) every waking hour. I prefer to see our friend as a hardline nativist, a romantic reactionary whose image of the past is seen through rose-tinted glasses while his vision of the future is colored red. Like the Roman, he sees "the River Tiber foaming with blood". I cannot really fault him for that. European demographics, immigration and culture clashes make such a future, if not inevitable, a likely one.

    I don't take his occasional juvenile provocations ("Breivik!") seriously, but I quite understand why someone would find them offensive and unacceptable.

  16. As often happens Eugene wrote first most of what I wanted to write (he has saved me a lot of time by doing this, for which I am grateful ;-)) .

    It’s interesting that he managed to obliquely refer to Enoch Powell, about whom I sort of intended to write as a fulfilment of a promise to John (it was to do with his suggestion that there is an “isomorphism” between Israel and the UK, although I have to state clearly that I do not believe that an “isomorphism” exists, since the principal threat to Israel has been and remains external.) Our thoughts (I mean Eugene’s and mine) often seem to run in the same direction…

    Of course, I remember Enoch very vividly. The meaning of the “like the Roman” speech was explained to me by a friend in my English school who was studying classics (Greek and Latin). I could barely speak English then and in communist Poland they did not teach us such things. The British press was, of course, writing about “rivers of blood”…

    I admit that I also don’t much like John’s occasional bringing up “colour” (and not just because my wife is Japanese) although I take it more like the words of the Duke of Wellington that “the Irish make good soldiers provided they are lead by white officers”. A mitigating circumstance, in my eyes, is the fact that some of John’s comments are the kind of thing that can now land you with serious legal problems in present day Britain. What could be a greater incentive to defiance?

    Although in many ways I would agree that “Enoch was right” on some important things (and also quite wrong on others) and I am also often appalled by the way Britain has changed since I emigrated there in 1968 (although it has also greatly improved in some respects - thanks above all to Mrs Thatcher, who unfortunately was only human) I find John’s apparent animosity to all immigrants, and especially the Indians expelled by Idi Amin, somewhat irritating. I have a strong and old fashioned belief in the need for any state preserve its “honour”, which essentially means keeping the promises made in the name of the state - something that was the number one principle in the foreign policy of Lord Salisbury. In particular, if you at all doubt that you are not going to be able to keep a promise, you should never have made it and awarding your citizenship is making a promise. As prime minister, Salisbury avoided making promises as much as he could, which was the main reason why his policies were described by the term “splendid isolation”, a misnomer actually.

    However, again I find it a mitigating factor that John’s dislike of Indian immigrants seems to be quite matched by that of the Poles ;-)

    On the whole then, I would rather withhold the term “racist”, which should be used very sparingly and only for the real thing, otherwise it will simply become a term of abuse (which has actually already happened).

  17. Dear Eugene, nowadays, in civilised countries, racism is ethno-differentialism without hate. Humans still naturally recognises differences which doesn't mean they disrespect them.

    Denying a country's identity, which Europe wants, is like denying the pre-existence of the country's identity. There is no more a host/receiver and a received/immigrant. No more opportunities to pass on the country's heritage, as it is seen as some form of colonialism.

  18. Steven Earl SalmonyFeb 17, 2014, 2:17:00 PM

    What is Galileo is doing tonight? My hope would be that the great man is resting in peace and that his head is not spinning in his grave. How, now, can Galileo possibly have peace? So few scientists speak out clearly and loudly regarding whatsoever they believe to be true about at least one root cause of the distinctly human-driven global predicament looming so ominously before humanity: human population dynamics/ overpopulation of Earth. The human community could soon be confronted by multiple global ecological threats to human wellbeing and environmental health that appear to result directly from the unbridled overproduction, overconsumption and overpopulation activities of the human species now overspreading the Earth and threatening to ravage the planetary home we are blessed us to inhabit? Many too many leaders and a predominant coterie of the 'brightest and best’ experts are choosing to remain silent rather than acknowledge science. Please consider how the elective mutism of so many of the most fortunate and knowledgeable elders among us could be contributing mightily to the ruination of Earth and its environs as a fit place for human habitation.
    Where are the intelligent leaders and established professionals with appropriate expertise who will stop colluding in silence, who are willing to examine and report on science that exists in the form of sound research? Look at the dismaying disarray in which we find ourselves now and how far we have to travel in a short time to move the human family away from precipitating some unimaginable sort of global ecological wreckage. What would the world we inhabit look like if scientists like Galileo had chosen not to disclose science and instead adopt a code of silence? In such circumstances Galileo as well as scientists today would speak only about scientific evidence that the super-rich and most powerful people of the day believe to be politically convenient, religiously tolerable, economically expedient, socially correct and culturally prescribed. By so doing, Galileo and modern-day scientists would effectively breach their responsibilities to science and duties to humanity to tell the truth as they see it, as best they can report it.
    Heretofore hesitant and inert scientists are called upon now to follow the good example of Galileo. The politically correct silence of so many knowledgeable but apparently dumbstruck experts on one hand as well as the incessant mass media jabber of sycophants and other minions of wealthy power brokers on the other hand could be killing the world we inhabit as well as life as we know it. Most scientists have not actively engaged in inimical ‘sins of commission’, as have many too many deceitful, chattering experts; and yet too many scientists on our watch have chosen to maintain their silence by not speaking out ‘as if each one was a million voices’. It appears scientists have been and continue willfully to deny the best available scientific evidence that specifically regards human population dynamics. Is their collusion to remain electively mute correctly described as a sin of omission? If science does not overcome silence, then much of the world the human community believes we are preserving and protecting will be irreversibly degraded and unknowingly dissipated, if not destroyed outright. Surely, truthful empirical reports from intellectually honest and moral courageous scientists regarding the population dynamics of the human species and the human overpopulation of Earth will give Galileo Galilei peace.


  20. Shannon, I hear you. I have sympathy for nativists and nationalists. I would have more sympathy for them if they did not so frequently turn out to be antisemites raving about Jewish power and Jewish evil (the people who buy tickets to Dieudonné) and hypocrites (buying imported instead of domestic; hiring undocumented aliens and paying them under the table to work as cleaning ladies etc.)

    Both nativism and nationalism are legitimate political ideologies and should not be excluded from the political arena by sticking the worst-sounding adjective (currently, "racist") on them.

  21. "Hypocrites", "antisemites", "nativists" (lol, what's that? Jesus nativity crib defenders?), "nationalists" : mmh nah, not me, none of that. You?

    Patriot yes, definitely, always ;-)... I like patriotism.

  22. English wiki:

    French wiki:

    Well, your country has the best anthem by far, that's for sure... it can turn a person into a French patriot in the blink of an eye.

  23. Well, it's a good thing Napoleon banned the other one ;-)

  24. Ha ha, yes, string the aristocats from the lamp posts etc.

    Well, if you've been in France on Bastille Day (in Paris or out in the countryside, it doesn't matter), you know that the French go absolutely nuts on that day. They dress up in period costume, sing all the old songs, get totally hammered, and have a royally good time (whoops, did I say royal?)

    Now as for nativism, it's funny how the French wiki article on the term is not even one-hundredth the length of the English-language one. I think they can't, or won't, recognize the concept. Apparently, the French consider Front National either "patriotic" or "fascist". But of course, FN is neither, they are the epitome of a nativist party. (All parties claim patriotism for themselves, so that hardly counts as a distinguishing feature.)