Comments by "zenith parsec" (@zenithparsec) on "What IS a Number? As Explained by a Mathematician" video.

  1. 19:42 As a programmer who learned to code in C, "it's a pointer. A reference is not the object." As a mystic "do not confuse the map for the world". [29:39 for anyone who cares, this is not the same as pointer -- this is copying "by value". A pointer is copying "by reference". That means there can be "no set of unique elements in the world". If you were to treat the pointers as referring to but (probably) not actually being the same thing, (you could point to yourself, and it's useful sometimes, says this person typing this comment), then you could. ] A reference to a thing is not the thing. When you say someone's name, you do not create the person themself. When you add a thing to a set, you add a reference to the set, not the "actual" thing. When you add a list of lists to a list, it is "in the set", but it hasn't moved. It's just that someone has talked about it. Lists are not like rooms which contain objects, or like boxes. They are like lists written on paper, or stored in computer or human memory. It's conflating the word "contain". Does July contain a Wednesday? It's not like any Wednesdays in July are unable to go somewhere else, they are just entities that are referenced. By following pointers you might find yourself in a loop, or down some other path which never ends. And that's where infinities come from. 20:19 if you are a paradox, you do not contain yourself. So you go in the list. Or if (Goedel) G is actually ~G, then you don't. Up to you. Well, it's up to you which rules you use, and then it depends on the rules, so that doesn't mean you can choose arbitrarily. Just to be clear.
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  2. Those "three red balls" are just 3-dimensional projections of a single hyper dimensional "superball". [24:10 you came so close to showing a visualization of this here, with the strings! if you had put the string over two red balls....] First, imagine their trails in the time dimension. The "ball" object has a length in time spanning from when the raw materials they they were manufactured from combined, past now, and off into the future when they will eventually stop being "balls". (Or "It starts at the beginning (a little gooey) and goes all the way to the end where it just gets more diffuse as it fades away, futureward", if you are viewing time like a spatial dimension.) You might then consider each ball from that same batch of chemicals used to make the ball itself to be the object. All "three" of those projections you "have on your desk" are really one 4-d object. We can't even have an objective definition of thing which doesn't depend on subjective experience. Someone who saw that way though would still have a definition of three-ness... it's one more than the number that is one more than the number that is one more than the number which is nothing. No subjective objectivity required.: a number is just a thing that you start having when there is more than nothing. Nothing more, nothing less. (Assumption: all nothing is the same.) This video was not an objective definition of three-ness. We can't even objectively define of objectness. (I'll go back to my bench between the philosophy and mathematics departments now.)
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  3. The cake/pencil method assumes the cakes still represent three after they come out of the box. We're assuming they don't suddenly represent a new number which we don't have a standard for. Now, when you put the cakes back in the box they don't refer to three, but this new number (throur ... the integer between three and four). As you no longer have a three you can trust, all you know is that this new number is between two and four. So it could be three, but also be another integer, throur or twee. ) We can't get rid of assumptions. (Perhaps these rules only apply until this video gets 2 billion views, after which every number moves down by 1. We will never know. ;] ) 15:13 "existing in mind alone" <= what?! you don't think numbers are real things? Next you'll be saying that there is no such thing as "abstract concept space". Heretic! And it's another assumption you are needlessly making. You don't know that they aren't defined by something in the universe. (Imagine that the universe itself only exists in this configuration because the definition of numbers "here" allowed the formation of a universe. For every potential universe in "metamathematics-space", all of the one which were inconsistent don't exist (because they can't), and most of the ones which do exist are just tautological (probably. It's much easier to prove something is true if it is true, because if it is true, it is true. but if it is false, it is not true, so it is not true. Compared to proving 3, it's exactly trivial. But must there be a 3, in every possible universe? I might write a simulation with some genetic algorithm search stuff, with the genes encoding rules, and fitness being "rules which work that are still producing stuff after N validation steps." While it's not "realistic" as an initial bootstrap, it does allow starting in a more interesting place than "assume nothing, and evolve everything" would. )
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  4. 27:38 And this is why mathematicians don't pull the lever to save 5 people in the Trolley Problem. "There's no difference. Why bother?" 30:43 "at least something exists" implies thoughts cannot exist without a thinker, and that sensations cannot exist without a something which can perceive them. Descartes was wrong. "There is thought" is all we know for sure. Do thoughts "exist" now depends on your opinion, like asking if numbers exist. 31:14 So um... how do you know when you should apply extensionality? If it's "when it's convenient for the target we want, which we can know somehow" then you're really only defining a space of potential mathematics. Interesting, but not particularly useful in the real world (except maybe to accountants?).
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  5. 5:55 Do you want ants? Because that's how you get ants. (Sorry, had to say it.)
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  6. 31:53 Highly irregular (ironic that there is an exception, and I wish it much successor. Infinitely much.) [38:35 this section explains that exception. I think if you just said "There is is another rule I 'll explain later," in stead of saying "It means you can't have a set inside a set, and except for some stuff I'll explain later)"it would have been less confusing. Especially as you didn't even mention it. You could have at least been more reassuring with a "no, you're not crazy, this is part of that thing I'll tell you about later." or something] [41:30 - Assuming infinity? That's like.. oh. that thing under this. Piece of cake indeed.] [41:40 - so some more assumptions off the cuff, are that you can 1) identify a set, 2) identify that it is empty, or identify it contains a set which contains a set. 3) You can somehow store the depth of recursion without using any paper or marking anything, and 4) that sequences of operations can be performed (the unique members rule implies duplicates can be deterministically removed, but that would require checking that you don't have duplicates again after removal of duplicates in sets; there somehow would need to be a fixed ordering to use between inconsistent sets at some "instant" in time.... what if you were a duplicate, but then you weren't and then you were depending on which of two literally indistinguishable things you were checking you happened to check first? This kind of ruins the ability to perform atomic operations, or to have consistent sets. Weird.. who'd've guessed?) Things become true by their definition (all of mathematics is either tautological or false once you've followed the algorithm. Otherwise it would be inconsistent, which is the problem you're trying to avoid. so yeah, )) [Ironically at 38:27 you act out this next paragraph. The possibility of mathematics" "getting eaten" is what invalidates the "assumption of induction". Not specifically being eaten.] 37:03 Everything also needs the assumption of induction. Or assuming addition and multiplication. (what if the rules say it will change in 4 days so 0 is now actually what you get after removing an empty set from the set you were using? We won't know (at least until then, but if that changes, I don't think the universe can last long. We don't know that it can't happen, so we have to assume constancy too. and in a sufficiently powerful system, you can emulate any other system, so how do you know we're not really using numbers in a "virtual machine" implemented in a totally different way of calculating? And that Regularity is not a requirement, if you have other rules : perhaps "encode any situations which take more (as defined) than 100,000,000 (as defined) iterations to determine the truth value of in (an already described) canonical form, and whichever result maps (using an already described mapping function) to the smallest result (as defined) always wins." as an axiom. This would get rid of paradoxes. You could make it work for long algorithms too by allowing it to recursively increase the size of each iteration step, but only a finite number of times. Choosing the right value would any every possible calculation that could be performed in the lifespan of the universe (which operates under those same rules.)
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