Sunday, December 29, 2013

Kittens investigate Newton's cradle

We often think that the humans are the culmination of the Creation. However, kittens are ahead of us.

Dr Panda, Dr Pikachu, and Dr Pavel (the principal investigators above) decided to do some research of Newton's cradle. Their research strategy was wise and the tactics were clever.

And the performance was so cute and their creativity was so mesmerizing that it is no wonder they received a $300 million grant from NSF.

For those readers who are not that far, Newton's cradle demonstrates the conservation of energy and the conservation of momentum.

Both quantities are conserved during a collision – if we neglect some losses that are small if the balls are hard enough. Such constraints are so strong that they effectively imply something very simply about the final velocities of the balls.

For example, if \(L\) balls with the same velocity \(V\) hit a collection of \(N\) balls at rest, the total momentum is \(LMV\) and the total kinetic energy is \(LMV^2/2\). The only way to guarantee the same final value of these quantities is to separate \(L\) balls from the total group of \(L+N\) balls on the right side and make them move to the right with the same velocity \(V\).

We get the same result even if we separate the collision of "groups of balls" to a sequence of several collisions of pairs of balls (1 on 1), assuming that they are separated by a tiny but nonzero distance. The animation above shows one of the neat but counterintuitive processes in the case \(L=2\), \(N=3\).

At the beginning, two balls on the left side are moving and the right three balls are at rest. At the end, two balls on the right side are moving and the left three balls are at rest. The process looks counterintuitive because in the approximation of vanishing distances between the balls, the middle (third) ball stays at rest all the time. Nevertheless, it is able to transmit the energy and momentum from the left two balls to the right two balls! You may make this conclusion look less counterintuitive if you admit that there are tiny gaps between the balls most of the time. In that case, the middle ball is moving by the velocity \(V\) to the right side for a short moment of time, too.

In the NSF research project, the three kittens also studied the condensed matter physics of the balls and the ropes, knot theory, and the invisibility cloak.


  1. Actually elastic compression and expansion is all that is needed, no gaps.

  2. Darn, how I curse the slow and limited internet connection we have at my parents place that prevents me from watching any videos ... :-(

    The kitty physicists are soooo sweet and cute :-)!

    And of course, all kitties are immensely interested in and excited about string theory, as everybody knows ... :-D

  3. I prefer not to engage in any "prophesy" particularly concerning individuals. But in terms of "ideology" I believe that putinism most likely will be replaced by "national democracy" along the lines represented by Alexei Navalny ( ) because it is by far the most popular "outlook" among the educated Russians under 40, who are now the most important political class. It would be a big mistake, however, to consider "national democrats" as being fundamentally more aligned with the values that dominate in the West, see

    What one can say only that compared with Putin and his entourage, which derives mostly from the KGB, Navalny has no "inherited' hostility to the West, except when it clashes with what the Russian view as their "national interest".

  4. Particle PhysicistDec 29, 2013, 4:42:00 PM

    Motl, you have absolutely no clue what you're writing about. Please, write only about things you're actually good at - e.g. physics, or climatology.

  5. The illustrated maximum gap when the two bounce is the same as the gap when the three bounce. Given m(1,2)gh(1,2) = m(1,2,3)gh(1,2,3), how can the gap be identical in the two cases? The centers of mass cannot rise to the same height from the initial identical height. Consider the case of 1 and four. The one must zoom upward and the four will be laggards.

  6. Ah, General Lebed. I miss him and his granite jaw. If the benighted Riot Pussies are straight out of Dostoevsky, Gen. Lebed seemed to have sprung from the pages of War and Peace -- a straight shooter who would have rode an open-hatched tank at the head of his troops en route to flatten Grozhny but kept his men there not one day longer than necessary: because he loved each and every one of them and wanted no harm to come to them, just as he was loved by his men.

    It's probably just as well that he did not become Russia's president: the man was like a fish out of water negotiating the treacherous diplomatic shoals, nor could one imagine him chatting up a powerful female editor of a news magazine: too honest, too prone to say what he was thinking. (I hope you'll indulge me my brief moment of reminiscing.)

    As for the rest of your reply, I thank you for taking the time to set out your view of history in such detail. I find it valuable to read and ponder.

  7. Homosexuals have had a very mixed history within all societies. Ancient Rome, for in stance, was similar in this regard to the US today. Some Romans looked on it as an unspeakable horror while others openly accepted it. The first absolute ruler of Rome after the fall of the Roman Republic, Lucius Cornelius Sulla, was gay and everyone knew it but few talked about it.
    The operative principle is, of course, that acts done in private by consenting adults are nobody else’s business, period.

  8. Hi, thanks. A problem is that it is easy to find your name out from DISQUS and check that you are not a particle physicist.

  9. I was touched by their playing but hesitated to embed such internet banalities to my blog - self-strike one - but thinking about you, I decided for Yes at the end. ;-)

  10. Luboš, your argument that "consensual sex between two 28-year-old men is the moral equivalent to a 28-year-old man raping a little girl" is rather weak logically. As much as I enjoy the majority of the material on your blog, you embarrass yourself when you make posts and comments such as these.

  11. The kind of demagogy and unfair double treatment you are committing in this comment is so self-evident that I don't believe that you don't see it. You are doing it deliberately.

    You are using the word "raping" because you want to suggest - without any glimpse of evidence or a justifiable reason whatsoever - that pedophiles' interactions have to be a "rape" while homosexuals never "rape".

    But this is bullshit. Things that pedophiles are doing may be allowed to and pleasant for their younger partners as well - and in the same sense, homosexuals may rape others. There is absolutely no qualitative difference here.

    The only difference is that you decided to be an asshole and spread the worst things about one of these groups while pretending that the other group is nearly saint.

    The truth is that both of these activities are non-procreative, both of them were considered sodomy, and both of them may be tolerated and made "mostly harmless in a big majority of cases" under some liberal, relaxed policies. All the asymmetry here only reflects the level of your dishonesty, not a difference from the real world.

  12. I made the remarkable observation that many very serious and knowledgeable physicists often appreciate some good physics related fun and humor, and many even seem to like kitties a lot. For example Patrick Labelle thanked his adopted kitties by name for proof reading his SUSY Demystified book :-D

    So I guess your cute video in this post and my image in the comments do not much harm to the good image of TRF ... ;-)


  13. This is really beside the point but your comments about the Romans attitude to homosexuality omit a significant point. The Romans, in common with many pre-Christian societies made a very big distinction between “active” and “passive” homosexuality. “Active” homosexual relation, especially with a younger partner (most of the time what we would call pedophilia today was considered socially completely respectable). Of the Roman emperors of the Julian dynasty only one, Claudius, was known to be 100% heterosexual, the rest were all what today would be called bisexuals. Emperor Trajan had sexual relationships with young boys and so did Hadrian. In fact Hadrian’s love for the Greek boy Antinous was very public and resulted in Antinous being deified after his earl death.

    On the other hand, passive sexuality was despised except in very young boys.

    Julius Caesar, who was very actively heterosexual, was alleged to have had a single homosexual episode with the King of Bithynia Nicomedes IV ( when he was 20 years old. There is no evidence that it actually took place (and if it did it was certainly motivated by gaining a political advantage since Nicomedes became Caesar’s supporter and when he did bequeathed his entire kingdom to Rome) but this single allegation pursued Caesar throughout his life. He was called “the Queen of Bithynia” and various crude songs were composed about this alleged relationship. In fact, during Caesar’s Triumph, Caesar’s own soldier’s sung one of such songs, that greatly annoyed the Dictator (who always denied the allegation), but it was an ancient Roman custom that during a general’s triumph his soldiers were allowed to do such things and Caesar , who was remarkably unconcerned about verbal insults, accepted it.

    The first “passive homosexual” to become emperor (and in fact the first important public figure) was the third century emperor Elagabalus ( ) This fact (or allegation) enormously contributed to Elagabalus unpopularity and he when he was assassinated his memory was “damned” and all references to him were erased from public records.

  14. Yeah, but what happens if the cats are in a box?

  15. Kittens still know more physics than Smoit.

  16. They would still be playing OR not:

  17. Cute string phenomenalism practiced by kittens with little paws for thought. ;)


  19. Granted that you know more about sexual behavior in ancient Rome than I do, lucretius, you are using the word “homosexual” to describe a physical activity while I am using it to describe sexual desire/gender orientation, which is independent of any sex act. This is the common usage, I believe, and it is far more useful in discussing the ongoing evolution of sexual mores.

    In ancient Roman politics, just as in current-day prisons, actual sexual behavior deviated/deviates greatly from the natural urges, which we all have.

  20. I don’t disagree with anything you are saying here, Lubos, but I still think that it is unhelpful to describe homosexuals as abnormal because the word is often used either to demonize gays or to suggest that homosexual orientation is a problem that can be fixed through re-education.
    You are right in pointing out that their are other ways in which peoples inborn gender drives conflict with societies expectations thus leading to huge frustrations. That’s why San Francisco’s Gay Pride movement has evolved into LBGT Pride.

  21. It does seem that there is hope that the turbulence in Russian politics is leading to a more open and, hopefully, more meritocratic society.
    Thanks, lucretius.

  22. Wow! I think you’ve taught all of us TRFers a lot about Russia. Thanks, lucretius.

  23. Schroedinger's cat did this type of thing when he was a kitten. See how far that got him...

  24. Which reminds me:

  25. Having seen and read the first interview with Kodorkovsky I conclude that:
    1) Kodorkovsky is a man of integrity and he has a lot more going for him than does Putin. He looks like the perfect guy to run a large organization. I am impressed!
    2) Your view of Russian politics is perfectly consistent with Kodorkovsky’s view of things.

  26. Reading your response, I think now that our disagreement stems merely from a differing selection of axioms for judging the morality of a given sexual act, rather than any type of conflicting logic.

    The single criterion I utilize to make a judgement as to the morality of a given sexual act (and this criterion is not strictly limited to sexual acts, really) is classically libertarian: "Is the given act we are talking about in the given situation consensual in an unambiguous fashion?" Legally speaking, this would translate into "Is XYZ sexual act in ABC situation able or not to be proven as consensual beyond a reasonable doubt?"

    The main criterion you seem to be applying appears to be a traditional conservative criterion: "Has the given act we are talking about been judged in the past as moral within my particular ethno-religious culture?", alongside another seemingly haphazard criterion of: "Is the act strictly procreative in nature?" (Presumably old people having heterosexual sex, or infertile young people, or fertile people using birth control, would be rendered immoral and socially permissible to repress under this moral rubric, although as I mentioned, the first criterion seems to have some sort of unpredictable precedence over the second).

  27. Sorry but the morality concerning sexual acts always depends on the cultural background. Your denial of this fact is nothing else than an attempt to promote your own culture to the absolute truth.

    No sexual act may be guaranteed to be agreed as consensual forever. Every sexual act may later be held against one of the participants. This is true for heterosexual, homosexual, age-comparable, and age-asymmetric acts, too.

    Some people may believe that a man can't possibly agree - be consensual - when his anus is being penetrated. Gays may feel differently but they may always exploit the prevailing opinion in the society when they find it convenient.

    The situation with children or teenager is absolutely analogous. An act may be pleasant for both sides butt one side may always later use the societal feeling that the intercourse wasn't right.

  28. "No sexual act may be guaranteed to be agreed as consensual forever.
    Every sexual act may later be held against one of the participants."

    I'm going to have to strenuously disagree with this statement on basis of common sense. The fact that "borderline" cases of consensuality / nonconsensuality exist, or the fact that some societies have institutionalized nonconsensual sexual acts, doesn't imply that consensuality "doesn't exist" as you imply. Shades of grey don't imply that black, or white, or dark grey, or light grey, don't exist at all.

    Furthermore, I find it somewhat troubling that you claim consensuality as a concept is "illusory" or "nonexistent" because it implies, that there is no fundamental distinction between rape and consensual sex, even from a strictly heterosexual point of view.

  29. It's not just about "shades of grey". Certain acts may be perfectly OK - white - in some societies and totally unacceptable - black - in other societies.

    One may say that the classification of acts into consensual and non-consensual exists. But what I am saying, and I am insisting that it is true and vital for the understanding of any related issues even though you clearly misunderstand it completely, is that the classification is never unique. It is different in different societies at different times and none of the classifications is "permanently" or "objectively" truer than others.

  30. "One may say that the classification of acts into consensual and non-consensual exists ... [but that] classification is never unique. It is different in different
    societies at different times and none of the classifications is 'permanently' or 'objectively' truer than others."

    I think I understand your assertion reasonably well - it's just the traditional postmodern assertion that "anything other than a strictly factual statement is simply a cultural construct." I simply happen to disagree with that assertion - or, more precisely, I believe that the concept of "consensual versus nonconsensual," or more generally "voluntary versus nonvoluntary" is in fact a type of factual statement, and has nothing to do with "cultural construction" or "societal dependence" or anything like that.

    Put in other words, you seem to be arguing that the 8 or 9 year old girl who is auctioned off and raped within the context of traditional "Islamic marriage" in, say, Yemen, in fact is completely and utterly consenting to such an arrangement, because consent is by definition a nebulous term 100% dependent on a particular cultural context, whereas I am arguing that the concept of consent or voluntary agreement is in fact quite nearly culture-independent.

  31. But if one removes society's assumptions and preconceptions and only looks at the factual part of the consensuality, it's by definition possible for the acts participated by children to be consensual, too.

    The *only* power that "prevents" children from having consensual sex are the society's traditions or laws. There is nothing "factual" about the assumption that children can't participate in consensual sex.

  32. Dear Lubos,
    first of all happy new year and many thanks for your excellent blog.

    Regarding pedophilia and homosexuality they may be very comparable in all aspects except for one. This is that homosexuality when executed is a thing between adults and for adults we usually say that they are free in their decisions so we don't see an issue. For children we can never be quite sure what is there free will and we even assume that their free will may even be harmful for them so that it needs to be suppressed and it is accepted that we take decisions for them. As everything in real life this distinction is fuzzy and it is somwhat conventional whether we draw the line at the age of 16, 18 or 20. But at its core I think this difference will not go away as culture changes..

  33. I'm pretty sure we are having some sort of miscommunication right now, so I'm going to try and communicate as simply as I can:

    1) I am *not* saying nor have I said that it is impossible in principle for a child to have consensual sexual relations.

    2) I am *not* saying that law (in the West) or tradition (most other places) isn't the only thing preventing pedophilic relations (or any other proscribed activity) from taking place.

    3) I am *not* saying I "want society to decide" what is moral or immoral, or what should or should not be a proscribed act.

    *All* I am saying (and all I have ever been saying in this argument) is that I disagree with your moral axioms. My primary moral axiom with regards to how I believe society and law should be structured revolves around the principle of maximization of the consensuality of any given action between two or more sentient actors.

    Your primary moral axiom on the other hand seems to be (and correct me if I am mistaken) "I will defend automatically whatever [God/tradition/religion/my own culture's historical circumstance] says about any given ethical question," along with an apparently unconnected ancillary axiom of "Any sexual act that is not strictly procreative should be forbidden," whose precedence with regards to the first I am not entirely sure.

  34. Well, I am obviously much further from an uncritical belief in any god or God than you suggest (or think) LOL.

    But yes, I also cherish moral principles that cannot be reduced to mere consensuality. But even if consensuality were the issue, it's just not the case that homosexuality is white and pedophilia is black.

  35. "What I am saying is only that it is wrong to attack whole nations just because they follow different principles [on what is consensual]."

    Yeah, I am in nearly diametric opposition to this opinion. I think, for example, that native and external pressures upon, say, Yemen and Saudi Arabia to end child marriage, or pressures upon northern Africa to end female genital mutilation, or other pressures upon certain societies to alter their ethical norms, are quite positive things, which I'm assuming you would rate as wrong and immoral according to this framework you have set up.

    "I also cherish moral principles that cannot be reduced to mere consensuality."

    Of course so do I; I really misspoke when I wrote that consensuality is the "only" moral principle I hold. I would imagine that most of our respective moral principles are in fact quite similar.

    "Lying may be mutual and consensual but it's still wrong"

    I'm having trouble thinking of a case of consensual, mutual lying. What example did you have in mind?

    "even if consensuality were the only issue, it's just not the case that homosexuality is white and pedophilia is black."

    I'm sorry, but I must disagree here again. Pedophilia versus consensual homosexuality really is a black and white issue: prepubescent brains are generally not fully developed, and ergo, as Mikael above states, "we can never be quite sure what is their free will and we even assume that their free will may even be harmful for them so that it needs to be
    suppressed and it is accepted that we take decisions for them." Although the particular age-cutoff (14, 16, 18, 20, whatever) may differ from culture to culture, this principle, as Mikael states, is entirely culture-independent and simply an objective statement of fact.

  36. Holy tl;dr, Batman! Just kidding, it was well worth the read. I have found Wikipedia's article on homosexuality frustrating. It does not answer the question how many are genetically determined, how many caused by environmental influence and in particular, due to being molested as children.

    I suspect that the gays who are relaxed about it are disproportionately genetically determined, those who are deeply troubled were disproportionately homosexually molested as children. But where to find the data to confirm or disconfirm?

  37. Thank you for this post. Pity this level of honest discussion appears almost impossible today in the West, within the public sphere, as opposed to the more limited audience of a blog or conversation amongst friends.

  38. Homosexuality? Well, someone mentioned it here. Not my favourite subject — I'd much rather think about pussy.

    But anyway, to stay on topic, I have to say I don't know much about it. Not that
    I'm that interested in it though. To me it's a queer thing.

    I've tried to understand it but just can't see the attraction, especially not of that chocolate ring obsession they have, the puckering notwithstanding. Nice on those big raspberry nipples though. And goose pimples on tits are very attractive too. Mmmmmm ... very nice. But I digress.

    Don't get me wrong — I like chocolate. But only the milk variety, not that crappy darkie continental stuff that the wogs south of Calais eat. Yuk! AWFUL. Bitter! No, no, no. Philistines!

    Hey, have any of you tried eating chocolate and drinking milk at the same time? It's lovely. It's not the same with dark chocolate but if you're desperate it's ... well ... it's not the same — sort of like a wank when you're caught short for a woman instead of a proper fuck, if you know what I mean. Beer is good too.

    Where were we? Oh yeah, queers.

    I wouldn't fuck 'em myself but each to his own.

    If I sound a little incoherent right now it's because my mind has turned to thoughts of quim. It happens.

    You'll have to excuse me. I've gotta give Fuquette a call, or something. I can discuss morality with anyone but right now I have more urgent needs to attend to.

    See y'all next Tuesday as our Murcan cousins might say, at least the real (Anglo) ones. And in five minutes I hope, if Fuquette is in. I just love looking at it.

    Toodle pip!

    P.S. A girl who lived across over the road from me when I was about nine years old used to take her knickers off and show me her private parts. I don't know why I kept asking her to do it but I loved it when she did. I was very grateful to her. She was a nice girl. There was nothing sordid about this. Completely innocent. Of course, if I'd have been a little older and clued-in, sordid wouldn't come into it. I would have instead.

    P.P.S. I LOVE looking at beautiful naked women. Lovely! Lovely! Lovely! More importantly though, I've looked for an axiomatic basis for that impulse, but every time I think about I get distracted by the quim thing. Do you think I'm queer? Should I seek advice?