Comments by "Lawrence D’Oliveiro" (@lawrencedoliveiro9104) on "Numberphile" channel.

  1.  @ythehunter755  There were several varieties of Ancient Greek. Consider Classical Greek versus Cretan Linear B Greek.
    1
  2. Then in India they have “lakh” and “crore”.
    1
  3. This has got to be the most pointless and beautiful thing I’ve seen today. 🏆👏👍
    1
  4. 5:59 That first term is in fact 1 ÷ 0!
    1
  5. 6:06 Convolutions are commonly used in digital signal processing. Interesting to see them pop up in epidemiology as well. What next -- Fourier transforms? (The mathematics of time series is a slippery slope...)
    1
  6. But what if each component of the quaternion was not a real number, but a complex number? In other words, introduce a second level of complexification, if you like, where you could have real/complex/quaternion/etc at each level, independently. What properties would the resulting numbers have? And then, of course, what happens if you have 3 or more levels?
    1
  7. 1:26 No chance you could get that exact answer with logs to only 4 decimal places.
    1
  8.  @JobBouwman  So far 5 people have disagreed with you. Likely more, except YouTube doesn’t show downvotes.
    1
  9.  @JobBouwman  Up to 8 and counting.
    1
  10.  @JobBouwman  Maybe you should just delete your comments and move on.
    1
  11.  @JobBouwman  Comments on what? Try considering that question before hitting that keyboard again.
    1
  12.  @JobBouwman  So you made an irrelevant comment on something you thought was an irrelevant comment? Remember, it’s not too late to delete your comments.
    1
  13. So in higher dimensions, the regular polytopes consist of the simplexes, the hypercubes, and the duals of the hypercubes. Q: Why not the duals of the simplexes as well? A: Brpnhfr gur fvzcyrkrf ner gurve bja qhnyf.
    1
  14. I wonder what bait you could use for a trap. “Here, virus virus ...”
    1
  15. That’s pretty cool. Do you have a stationery storeroom or cupboard? Something like 50 reams pf paper would have 1000 times as many sheets as that, and that would be how much you would need to print a billion digits. Still not too big to exceed the school’s entire paper supply, I would imagine. ;)
    1
  16. 9:12 The Wile E Coyote guide to drying a Klein Bottle.
    1
  17. 1:39 So the number of crossings in the not knot is ... nought.
    1
  18. 11:44 There is only approximate equality between this formula and the construction. Remember the construction consists of a sequence of quarter-circles, so the radius only decreases in discrete steps when going to the next quarter-circle, whereas this formula produces a continuously-decreasing radius of curvature.
    1
  19. 4:17 That’s Clifford Stoll. You know, The Cuckoo’s Egg ? Yeah, that Clifford Stoll.
    1
  20. 2:17 8:17 Actually, no, the Wankel rotor doesn’t need to be a Reuleaux triangle. The curvature of the sides can be shaped to give a particular compression ratio. Remember, the rotor slides around the casing while spinning, it doesn’t roll, so the Reuleaux property is irrelevant. In fact, you can see the discrepancy between the curvatures of the Reuleaux and the actual rotor in that diagram at 2:17.
    1
  21. 0:22 Pigments or dyes. The difference is, pigments are inorganic compounds, dyes are organic. I think.
    1
  22. 4:39 You could just say it’s a differential equation, and density is the differential of mass.
    1
  23. What’s different about the pentagon is that it cannot make a periodic tiling of the plane.
    1
  24. Seems on a par with ancient Cretan writing, don’t you think? That is, primarily for accounting, not for anything literary.
    1
  25. Common programming languages nowadays let you express numbers in binary, octal, decimal and hex bases, and that’s it. Ada, on the other hand, let you use any base from 2₁₀ to 36₁₀, inclusive. E.g. 9 * 6 = 13#42#
    1
  26. 8:18 I’m thinking that the common cinematic screen aspect ratio of 2.35:1 isn’t too far off the silver ratio.
    1
  27. Has anybody mentioned that the Brits kept the flaw secret, so they could sell Enigma machines to unsuspecting victims other countries after the war?
    1
  28. 0:15 >>> import math >>> print(math.isnan(math.inf)) False Python seems to disagree with the notion that infinity is not a number.
    1
  29. 0:23 Positive integer ℤ⁺. Aka a natural number ℕ.
    1
  30. 3:02 If all the possible moves are recursively enumerable, then it is still possible to conduct an exhaustive search to any given finite depth. That won’t be enough to prove impossibility, but it could still find a solution if one exists, at least not too far along.
    1
  31.  @Om_1337  To show that the holy book was wrong!?
    1
  32. 17:06 It makes sense for finite-sized particles, not infinitesimally-small ones. Do I sense a repeat of the whole Planck-oscillator business? That if you take the classical formula down to the zero limit the numbers blow up, but if you stop at a nonzero size, you can get answers that make sense? That are quantized, even? Just suggesting that you stop thinking like a mathematician, and start thinking like a physicist ... ;)
    1
  33. He’s really Wallace, isn’t he? But where’s Gromit?
    1
  34. 7:03 A patch of nonzero area, in other words.
    1
  35. >>> 1j * 1j
    1
  36. (-1+0j)
    1
  37. 1:30 It’s the infinity of the counting numbers, which is probably why it’s called “countable”.
    1
  38. 1:07 Low-poly fingernails? Could a new fashion.
    1
  39. Fun fact: Don Knuth’s first published article was in MAD Magazine, a spoof item on the “Potrzebie system of weights and measures”.
    1
  40. 10:18 There seems to be an asymmetry in the diagram, in that 1 and 2 occur three times each, the others only twice.
    1
  41. 6:46 Not ASCII, but Unicode! ASCII has no code for “ö”, while Unicode has a code for everything.
    1
  42. I think it’s called a “perfect information” game in game theory.
    1
  43. The way I learned it, you had this hierarchy of mathematical structures, e.g. groups, rings, fields, number systems. A “group” starts out with one operation defined on its elements (you might call it “addition” or “multiplication” or whatever), while a “number system” has two separate operations (so you call one “addition” and the other “multiplication”), and they have to interact in certain ways: the operations must be closed on the set of elements, every addition and (nearly) every multiplication must have an inverse, and so on.
    1
  44. 2:26 But air, being compressible, means that more mass might be entering a point than leaving it, if the pressure (and hence density) at that point is rising, and conversely if it is falling.
    1
  45. Nice animations.
    1
  46. 5:28 Should really use “×” instead of “x”.
    1
  47. 18:58 It seems to me you are confusing the physics with the mathematics. The mathematics predicts physically-impossible situations, and you feel that means something is missing in the maths. But it’s not missing there, it’s missing in the physics. Understanding the discrepancy isn’t going to come from any deep insight into Navier-Stokes as it stands, but in altering the model in some way (like introducing the quantization limit I mentioned earlier) to be more physically accurate. Will this lead to new maths? Maybe ... maybe not.
    1
  48. 6:18 There is a problem with that construction: it never terminates. Remember what an “algorithm” is: it’s supposed to produce an answer after a finite number of steps. Therefore, the Cantor diagonal construction is not an algorithm. So your proof that the infinity of the reals is greater than the infinity of the integers can never actually be completed.
    1
  49.  @MuffinsAPlenty  The specification of each decimal place allows you to define convergence. That still doesn’t allow for Cantor’s diagonal proof.
    1
  50.  @MuffinsAPlenty  But the Cauchy construction only gives you one real. At each step, you get closer to the number you are approximating. Cantor’s construction is infinite and does not converge: after any number of steps, you are no closer to the final answer than when you started.
    1