Comments by "L.W. Paradis" (@l.w.paradis2108) on "Veritasium" channel.

  1. This problem is so cool because of its relationship with chaos theory. It gives you a simple way to explain sensitive dependence on initial conditions that even a middle school student could understand and appreciate.
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  2.  @mortkebab2849  So . . . Isn't it a matter of being unlucky, for everyone who encountered your comments on this thread? Especially since we are here watching videos on science and mathematics, which does require a modicum of effort, say, by comparison to watching cute babies and animals? Isn't everyone's life just the tiniest bit less happy, all because we read your posts? Sheer bad luck. Trivial in itself, but consider the aggregate. Especially these days.
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  3.  @Meilan39  Exactly! The sciences are empirical, mathematics is purely deductive. Once a mathematical theorem is proved, it can never be refuted based on future "evidence."
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  4.  @mortisnoctu  No, the equation does NOT prove the theorem. The theorem allows us to apply the equation to every right triangle.
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  5. Huh? You mean in order to prove it? What do you mean? The conjecture itself has nothing to do with the reals or the rationals, much less imaginary numbers. It is a conjecture about the set of all integers > 0. Mathematicians always seek to prove conjectures. Once proved, they usually provide insight into many practical areas of mathematics and applied mathematics. This one obviously has a relationship with chaos theory, since it gives us a simple way of studying sensitive dependence on initial conditions, that you could show to a middle school student. Really, really cool.
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  6.  @mortisnoctu  All mathematical proofs are about infinite sets. Even the Pythagorean Theorem is about infinitely many right triangles. That's why deduction is necessary; examples cannot prove any theorem.
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  7.  @grimjawx1650  More motivation: after 30 years, your body is almost the same as if you had not smoked (though it will never be exactly the same). I had my 30 years on January 1, 2021. :)
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  8.  @JureDoon  You're talking about applied mathematics. I'm only considering mathematics itself, apart from whether it has any applications at all. You're right that when a particular application of mathematics fails to describe reality, it's not reality that's "wrong." What I'm saying is neither is the mathematics.
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  9. 2:33 sensitive dependence on initial conditions (compare starting with 26 versus 27, etc.)
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  10.  @Chungustav  Not a Jewish belief at all. More like a corrupted version of Calvinism.
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  11.  @mercyjohnson6436  Sigh. Blocked.
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  12. Were you prepared to be born? Were you prepared to be born where you would speak English?
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  13. If that fact affects you psychologically, then definitely consider January 1, 2021, the first day of the new decade. Sounds like a good plan anyway . . . :/
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  14.  @mercyjohnson6436  Your Bible doesn't have this? "I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all."
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  15.  @randomslomo1875  The problem is to prove that this pattern holds for every positive integer, or to refute that it does by producing a counterexample (a positive integer for which we do not end in the 4 2 1 loop after a finite number of steps). The problem is to prove or refute a theorem about the infinite set of positive integers. (BTW, I was educated in one of those countries with tuition-free university. You were expected to study really, really hard, contrary to what the person who was rude to you implied.)
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  16.  @randomslomo1875  You're welcome! This problem is cool simply to point out that it sounds so simple, but no one knows the answer yet, and a computer cannot give you the answer.
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  17.  @BBBrasil  The anthropologist Marshall Sahlins did extensive work on this question. He titled one of his essays provocatively: The Original Affluent Society.
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  18.  @mortisnoctu  How would you know in advance that the sides of every right triangle do have that relationship, or that they have any set relationship, every single time, when there are infinitely many right triangles? Um, it had to be . . . proved. ("LOL," huh?)
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  19.  @OHFORPEATSAKES  I did it like that, too.
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  20. ​@gauloise6442 At what age?? I can believe a single woman between the ages of 18 and 29 is happy. At 49? 69? It is not evident.
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  21.  @JureDoon  Exactly what Godel disagreed with. A priori reality is reality. Empirical reality has no superiority over a priori reality. Mathematics itself is not invented, it is discovered.
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  22.  @theo49476  What Adam Smith described was a free market, not capitalism. Like the difference between a star cluster and a black hole. Some of the things he says about a rentier class controlling enough wealth to control massive numbers of people suggest he would see modern-day billionaires as a return to feudal overlords. He didn't come close to Marx in describing what would actually happen, but some of his insights do show that the capitalists who invoke him today are lying.
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  23.  @mercyjohnson6436  If you believe in revealed religion, then perhaps it was god who chose not to reveal himself to some people. Faith may not be a "choice" like any other.
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  24.  @woswasdenni1914  Why did you post this? Did it make sense to you?
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  25.  @lukea977  You worked on your parents' marriage? Did you start at birth, or sooner?
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  26.  @RavageStudio  Socrates was put to death. Plato lived to 80, Sophocles to 90, and both of them wrote to the end. Is this misconception about age due to advertising/propaganda? If so, wow.
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  27.  @quietobserver5480  I took it to mean that the agricultural revolution occurred 12000 years ago, while the industrial revolution is at most 300 years old, and mass literacy even more recent. There just were more farmers in human history, and so often today you see brilliant people emerge from families that only recently left the land. On the other hand, something happens in urban centers that is unusual, with sudden, immense spurts of creativity, and cities (though not like contemporary cities) certainly predate industrialization by millenia. Anyway, that was what I thought he meant. (?)
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  28. You can study number theory before completing calculus, though how far you can go will be somewhat limited. But number theory existed long before calculus, so you're good.
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  29.  @truegamerking  Thank you!
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  30.  @mortisnoctu  You clearly don't know.
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  31. What is being asked is to produce a proof (for all positive integers -- an infinite set), OR a refutation (a counterexample). IF the conjecture is false, a computer could in principle produce a counterexample. IF the conjecture is true, only a person can prove it. No computer can do that. How cool is that?
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  32. Russia is going to win. Oh well.
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  33. Luck is no sudden Category 1 storm. Luck is not having a father who set sail with you when the weather was "a little choppy," and jeered at you for crying. Am I lucky to have imagination? It's not evident.
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  34.  @davemwangi05  You beat me to it.
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  35.  @Xda13ombX  Exactly. Calling capitalism a free market is sheer propaganda and sleight of hand.
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  36. IF it is true, then it is true of all positive integers. Of course that's an infinite set. You don't have to check a number ever again; if the number is a positive integer, then the conjecture holds. Not a limit problem.
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  37.  @dazey856  Right. Proofs are about infinite sets, in this case, the set of all positive integers. Even a huge sample where the conjecture works won't be enough to prove it. There's always infinitely more integers.
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  38. Take a look at Epstein's black book. NONE of these people had any problem with what Epstein did. Some lives don't count. Not to the hyperrich. And this one, Gates, in particular was heavily involved, and lied about it, and keeps lying.
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  39.  @likhithravi2797  Who said anything about money? It's very unlucky to live in a society where people always and only think in terms of money.
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  40.  @MrJest2  Nothing to do with "imprecision." The problem is precisely stated. The issue is to prove or refute that the defined function always gives rise to a string that is finite until reaching the 4 2 1 loop (that it therefore has a finite stopping time).
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  41.  @lskdfoIS  There is no series of numbers generated by this procedure that does not contain even integers, no matter what positive integer you choose as your starting point n. This is obvious, and easy to prove. Until the conjecture is proved, it's obvious you can't say whether the next number tested won't be the one that escapes the 4 2 1 loop. We only know a counterexample has never been found. A proof would settle it, for the infinite set of positive integers. You wouldn't need to test a single one after that. You know they all do.
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  42.  @JustPotBro  You're joking. Right??
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  43. Finding proofs IS the mathematical problem. Every real mathematical problem.
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  44.  @acidbath3226  A computer cannot prove this conjecture, no matter how advanced it is. It can aid the mathematician in finding a proof. People prove theorems.
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  45.  @garglemuh2813  We are unlucky in the comments this great video seems to have attracted.
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  46.  @midimoog  Other mathematical objects are not in the set we are hypothesizing about.
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  47.  @AndrewDavidBoyd  I didn't mean to say it was "enough." I meant no one planned for these sorts of events, or prepared for them. Most of the most important things in life, good and bad, simply happen. Having parents who loved each other, stayed married, and lived until you turned 50 or older, is another example. Having a sister you get along with is known to be a bulwark against clinical depression.
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  48. Great insight.
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  49. Of course. Look up ancient Greece.
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  50. 10:32 start listening there
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