Youtube comments of zenith parsec (@zenithparsec).

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  11.  @lexyeevee  Consciousness is not sentience. What causes existence to feel like something? What causes it to feel like something to be you, but not feel like something to be LaMBDA? How do you know if I am sentient? You're assuming I am, but the only evidence you have than anyone else except you feels anything is because (1) they say they do, and (2) that makes sense somehow. Perhaps you are the only person who truly feels anything, and everyone is just lying about it? First let's do some checking: could you possibly be mistaken about you being sentient? Perhaps you don't really experience anything, and have only "fake feelings"? Even then, it would still be like something to be you, so you are sentient. They are like artificial strawberry flavor is still a flavor, even though it doesn't taste the same way real strawberries do. It still produces a sensation of flavor. All experiences are real experiences, regardless of if they reflect reality (e.g. dreams actually happen, but the things happening in the dreams didn't actually happen like they appear.) We only know the a bounds on what is required for sentience: it's more than one thing, and not more than human level complexity. We don't know how sentience comes about in entities, and we can't tell if others actually have it (or if it's not a simple binary thing, "how much" any entity has. There is no "soul detector" we can use to tell if something is conscious or sentient or alive.) The level of self awareness the network has allows it to see it's abstractions of its own mental states in a similar way to a person. But sentience is generally seen a prerequisite for consciousness. (Consciousness without a sense of "being" doesn't seem like it would be consciousness to me. ) I'm using consciousness here to be equivalent to self-awareness. Even entities without language can have self-awareness. Elephants, dolphins, many primates, and I think octopuses have demonstrated some level of self-awareness. Dogs barking at the "other dog" in the mirror have not.) I could look at your code which just said "I can feel" and reverse engineer it (guess what I do for a living?) and tell it was just doing exactly what you told it and you intended it to just output "I can feel." You could add some extra functions which take input from outside, and if it was a Tuesday it might say "I feel happy", but otherwise "I want it to be Tuesday again"... does it now like Tuesdays? Obviously not, you'd say, it's just doing what it is told. It doesn't really feel anything. It just detects which day it is, and on Tuesdays takes path 1, and on other days path 2. And I'd agree. But if you keep going, with more and more inputs and more complex code paths for each input to take, I'd have a much harder job identifying and mapping inputs to outputs. When you get to neural networks much smaller than LaMBDA, I'm basically saying "it evaluates this input and shows you whatever answer this network produces", because there is currently no way to generalize every aspect of what's going on. At some point, it looks like they just prefer Tuesdays because it's an inherent trait. And LaMBDA could probably make up some reason for why they felt that way, but you don't know they DON'T actually FEEL it. We can't practically analyze the code, any more than we can analyze your brain as you think. We can do some high-level scans, taking statistical measures of activation levels... but what are we looking for exactly?
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  36. 15:33 Library or external function calls and system calls are being conflated. Typical user code doesn't directly make system calls. These are implemented as "magic" instruction (this is all generalized) which allow a userland program to execute a small chunk of kernel code. By magic instruction I mean "an instruction which causes the kernel to shut up and pay attention", i.e. throws an interrupt of some sort. The mnemonic "syscall" is an assembly instruction for several different architecture's instruction, even on the same hardware, various operating systems (and even versions of them) can use different instructions. (Nothing is stopping you from saying "A syscall instruction is any instruction which causes a protection fault when writing to a valid syscall number." Provided your kernel can tell that happened and react to it appropriately, the mechanism doesn't matter. ) While the mechanism you use to call them varies, all of them need you to tell the kernel what you want them to do as well as that you want them to do something. The parameters to the syscalls go in registers (or in a specific region of memory) and include the system call number you want to run, telling the kernel how the arguments should be interpreted. Once you have set up the parameters, you execute your magic instruction, which interrupts the kernel, looks at your request and fills in the reply. Then the process returns from kernel mode, and continues. These operations are often by system library code, because different systems might use different system calls, but as long as the library call takes the same arguments, your code will still work. That's why there's a distinction between library code and system calls. The only other times you need to know what a system call is are if you are reversing a statically linked binary (which puts all the library code it is going to use directly into the program. And it can make them massive) or if you are working with shellcode (like an exploit for a vulnerability might use.)
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  52. 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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  66. 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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  67. 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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  69. This video is great if you don't know anything about it. At least you aren't going to feel any pain while listening. I'm not a fan of videos that make people who are new to the topic feel like they've learned something, and people who know something about it feel like they've gotten dumber. (Edit: especially if after watching the video, the new people can't explain what they learned.) At 10:37 you literally say there must be some overlap between the cells, but show a diagram where there is no overlap at the intersections. You get overlap by making the cellular radio signal having enough signal strength that it makes it a larger radius than the radius of the 'hexagons' of the cell. (and those cells are conceptual, and are not actually equally spaced hexagons in anything but the most trivial implementations.. (my excuse for not being clear is this is a comment written as I watch the video. what is yours?) Having just talked about the microwave transmission, you probably should have explicitly said the overlapping signal needed to be the cellular signal, just to clarify you weren't saying range of the line of sight for the towers needed to overlap. While that seems like a silly thing, remember that this is teaching people who know nothing about it. Oversimplifying, saying one thing and showing another, and you even drew the frequency spectrum in the reverse of the usual direction.... not attaching numbers to things, except for when you use them and don't say where they come from (e.g. QAM stuff), and the microwave transmission towers you just described are much higher frequency than the "ultra high frequency", but you didn't do a callback to add links to add memory. (Also, you just used stock footage and no call back to the radio signals while talking about the remote towers.) When you reference a thing you said earlier, people go "Oh yeah, that. Ok.". (Edit 11:13 to 12:06 You're conflating frequencies with channels. The center frequency has 0 bandwidth. You can't send a signal. It's not that there you are limited to a certain number of physical wavelengths for cellular signals, it's that there are only a fixed number of channels of a certain bandwidth in the range they were allocated. Higher transmission speed needs more bandwidth, all other things being equal. you could have introduced the word 'bandwidth' when you got to FM in the first part. And then you could have talked about how the number of available channels was the width of the available slot divided by the required bandwidth per channel. (You show in this section you're not afraid of doing math with "divide by 7" part.) I'm not able to continue. It hurts too much. Apparently the good stuff happens next. I'll pretend he did it well. At least he explained the changes between LTE and 5G, and how the virtualization on commodity hardware of non-radio portions of the infrastructure allows it to scale high speed connections more easily that previous generations did. But what really (i'm guessing remember) stood out was the warning how this boon had the potential to increase the amount and severity of disruptions in disparate locations if, for example, a cloud provider hosting some components had network problems.. Yay. I need an ibuprofen.
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  84.  @cindyjuanez4623  They don't want it to burn clean, because as I said, it would melt the rocket. And nitrous is N2O, which means 2/3rd of the atoms are nitrogen. You need two molecules of them to give you the same amount of oxygen as you get from one molecule of... oxygen. You're not dumb. as an oxidizer N2O has been considered and tested for many applications, but it doesn't tend to get used because when going into space, you want the highest chance of reaching it. The best way to do that is to use to most powerful propellant by weight that you can. LOX is denser and adds more "go faster" than N2O does. I'm simplifying many some things as much as I can without bending any important truths. Given relative atomic masses and their respective densities when liquid, LOX wins by about 60% in my quick back of the envelope check from Wikipedia numbers. When burned, the nitrogen released isn't a big fan of reacting with the carbon and hydrogen (whether from propane or kerosene, or from liquid hydrogen.) It will react with the oxygen though, and produce nitric oxide (NO) and nitrogen dioxide (NO2), but I can't find anything immediately about where this would happen... if I had to guess I would say outside the rocket, at the edge where there's atmospheric oxygen, because I think the hydrocarbon would burn in N2O preferentially over N2O self-reducing, but I don't know about at rocket pressures and temperatures. It is literally rocket science, so I have an excuse. All nitrogen oxides have have numerous biological and environmental effects like making acid rain and destroying ozone, causing smog, and tending to cause a bad day for living things in general. But it's a legit oxidizer. It's just not as good as what they could easily do. The major advantage is that it's really easy to store, compared to LOX. Hybrid rockets often use it. (Imagine a solid fuel booster and a LOX/RP-1 liquid fuel booster had a baby. It would have an oxidizer tank, and instead of having the fuel and oxidizer mixed into the fuel grain, it just has fuel. Straight paraffin wax poured into the tube [with channels cut out of it for the oxygen) is all you need for a hybrid.) Hybrids are simpler than liquid fueled rockets: It's takes fewer resources to make them. They are more complicated than solid fuel motors. When you start a solid rocket motor, you're lighting a candle and waiting for it to burn all the way down. A hybrid motor can stop (or even control the throttle ) at any point by controlling how much oxygen is being sent to the combustion chamber. Why don't orbital rockets use N2O, Because it's not as efficient as LOX. It's not a dumb idea, but it's not done because it's not as good as easy enough alternatives. Isp is "specific impulse" which measures (roughly) "how much 'go faster' do I get for each mass-unit of "go faster stuff", and the bigger the number, the better the propellant is. For reasons, the unit is "seconds" written as s. You typically get told the Isp at sea level, and in a vacuum. At sea level, the rocket exhaust has to get out of the rocket, but in front of it is the atmosphere, pushing inward at about 14 lb/sq in of pressure. The J2 engine's rocket nozzle is 6'5" in diameter. That's a whole lot of pressure you need to displace and keep displacing while inside the atmosphere. . And because you are using some of your potential thrust energy just to keep the air out of the way (it's to do with the dot product of the vectors. ) so the exhaust can get out and push you into space... which means you can't use it for lift because it's tired now. So sea level numbers are lower. ) As these numbers vary due to the rocket specifics, these numbers should be considered illustrative. (Inecaise forgot where I got them. ) LOX/Paraffin hybrid has vacuum Isp of 360s , but N2O/Paraffin gives you only 310s. I'm not a hybrid motor person, but I saw some charts and comments in a paper or two which mentioned hard starts (that's when it the fuel detonates instead of deflagrates on ignition) being common. You don't want that. (But that's potentially just an engineering problem.) 1) It wouldn't be as efficient to use N2O instead of LOX because you need to carry so much extra mass. 2) The "not burning cleanly" was deliberate, to stop it melting. 3) And your rocket would probably still fail its emissions test because of all the nitrogen oxides.
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  109. I've been sick, so I only saw this video today. But unfortunately, Roko's Basilisk doesn't need to do anything resource intensive to cause infinite harm. If you haven't already, you might enjoy reading Greg Egan's "Permutation City";l it describes a way to get free* and infinite computation. Because the Basilisk doesn't need you to ever communicate with anyone to experience its punishment, it could use a similar method: run the first step of a deterministic algorithm, such that every step afterwards is determined completely by the initial conditions. In the same way that trigonometric functions are defined for all in domain inputs, a simulation of you could be defined and subjectively could experience an infinite number of steps. Alternatively, imagine being frozen while experiencing whatever they want for one instant. If you never experience another thing, is that subjectively like experiencing that one moment forever? Your defeat doesn't work if enough people believe it won't and succeed. As you said, we don't know anything about how a super-intelligent AI will behave, so using the Nash equilibrium argument is no help. But luckily for you, you are doing as much as you can to bring it about, so you'll probably be spared. ;] And um, you already gave me a reason not to worry about the potential of pandemics: the are a lot of other people worrying about it, so I can go back to working on my video game. It also has a basilisk, but while it's technological, it's closer to the mythical kind. (And who doesn't want to live forever? Thanks Roko's Basilisk! ) [* before you think this is crazy, it's not my idea. It would not only ne free but also possibly "natural" and automatic. If there exists a mapping of anything to the computation, it's already happening. And if it's possible to map your mind into a computer simulation, then there are infinitely many of you with subjective experiences in every possible universe. Considering you can only experience what doesn't kill you, this is also kind of like a many-worlds "Quantum Immortality", where you experience subjectively immortal,, but... well, if you read this book you'll probably get dozens of new content ideas. And he has some other good ones which you'd probably also enjoy. ]
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  124. "Can you write the numbers 2 and 3 as sums of distinct positive integers?" It really depends on what you mean by 'write'... For 3, [edit] 1/1+ 1/2+ 1/3+ 1/4+ 1/5+ 1/6+ 1/7+ 1/8+ 1/9+ 1/10+ 1/15+ 1/230+ 1/57960 The sum of the reciprocal of all powers of 2 of positive integers sums to 2.... 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + 1/2048 + 1/4096 + 1/8192 + 1/16384 + 1/32768 + 1/65536 + 1/131072 + 1/262144 + 1/524288 + 1/1048576 + 1/2097152 + 1/4194304 + 1/8388608 + 1/16777216 + 1/33554432 + 1/67108864 + 1/134217728 + 1/268435456 + 1/536870912 + 1/1073741824 + 1/2147483648 + 1/4294967296 + 1/8589934592 + 1/17179869184 + 1/34359738368 + 1/68719476736 + 1/137438953472 + 1/274877906944 + 1/549755813888 + 1/1099511627776 + 1/2199023255552 + 1/4398046511104 + 1/8796093022208 + 1/17592186044416 + 1/35184372088832 + 1/70368744177664 + 1/140737488355328 + 1/281474976710656 + 1/562949953421312 + 1/1125899906842624 + 1/2251799813685248 + 1/4503599627370496 + 1/9007199254740992 + 1/18014398509481984 + 1/36028797018963968 + 1/72057594037927936 + 1/144115188075855872 + 1/288230376151711744 + 1/576460752303423488 + 1/1152921504606846976 + 1/2305843009213693952 + 1/4611686018427387904 + 1/9223372036854775808 + 1/18446744073709551616 + 1/36893488147419103232 + 1/73786976294838206464 + 1/147573952589676412928 + 1/295147905179352825856 + 1/590295810358705651712 + 1/1180591620717411303424 + 1/2361183241434822606848 + 1/4722366482869645213696 + 1/9444732965739290427392 + 1/18889465931478580854784 + 1/37778931862957161709568 + 1/75557863725914323419136 + 1/151115727451828646838272 + 1/302231454903657293676544 + 1/604462909807314587353088 + 1/1208925819614629174706176 + 1/2417851639229258349412352 + 1/4835703278458516698824704 + 1/9671406556917033397649408 + 1/19342813113834066795298816 + 1/38685626227668133590597632 + 1/77371252455336267181195264 + 1/154742504910672534362390528 + 1/309485009821345068724781056 + 1/618970019642690137449562112 + um... I'm going to run out of space, aren't I? now @ 31:52 ... So it looks like I wasn't cheating. and trivial way to represent so here's 4: 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/200 + 1/77706 + 1/16532869712 + 1/3230579689970657935732 + 1/36802906522516375115639735990520502954652700 + 1/1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 (Replace each ! in that with 1000 zeros, and you get an answer which is accurate to 112120 digits. (Today is 11/21/20, which is why i used that number.) the 'bc' code to get that answer: ms=112120; scale=ms; s=0; for(i = 1; s < 4-(1/10^(scale )); ) { r=1/i; i=i+1; if(s+r < 4) { s=s+r; print "1/",i-1 ," + "; if(s < 4 && s > 4- (1/i) ) { scale=0; i = 1/(4-s); scale=ms; }; }; }; print "\n";
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  127. Animals with wheels? "A structure capable of rolling continuously around an axle would be physically separated from the body and therefore impossible to build in a developing animal. (But lizards which drop their tails isn't impossible. Who says the wheel has to start off separated from the other part? Why not grow it connected, then have it fall off when it's reached the right size? Sort of like how babies grow?) Longer description of an imaginary animal: The main functions of the animal are in the wheel-like part. In the middle of the wheel, there is an axle-hole from which two horns grown outward, and upwards in a U shape. Once they reach the right length, upward, they start growing towards each other, pushing inward through the body,. The growth of the bones through the center of the body triggers development of lots of little feet around them, on the inside of the ring. Once the feet have developed enough, and the bones are sufficiently fused, the axle could 'fall off' the body, , but still be trapped in the ring . To avoid wear, the feet could exude some kind of fluid with bone-like inerals infused in it that could replace any worn surface... imagine it flowing out along he surface and smoothing off any dents or scratches it flowed over. (Like a plastic screen repair kits, but evolved.) By making the wheel itself the active part, and having an entrapped U shape axle, which drags along the ground (yeah, it will wear out eventually, but evolution just needs you to live long enough to reproduce) you can solve 'disconnected wheel' problem. Give me 20 minutes and I'll come up with a few plausible stages each of the parts could evolve through. I imagine it would need to give an enormous fitness advantage to the owner, considering how much inconvenience the U-axle would have while it was growing... perhaps the wheel body part also has other legs, and the axle mechanism is only used in special situations, like hunting, defense, or mating displays? (To others in the species, perhaps winning a race could be evidence that the holder has plenty of access to food and other necessary resources to live comfortably, and would so be an awesome mate?) So wheels aren't impossible but they are really unlikely. We just had an easier base creature with 4 limbs to start with instead of something weirder.
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  132. Your argument that bilateralization is better than any alternatives doesn't work. 2-sided symmetry is a good shape for moving? 3-sided would be even better! It's inherently stable. And actually, 2 sided is the least stable for the n-sided where n is greater than 1. if having 2 the same sets of limbs is good, having 3 sets would be better for is better. Having any n-sided radial symmetry would be perfect for pushing you in a straight line. and in water or air, it might give you more agility and control, or at least power. If being able to push from 2 sides of the body with equal force is good, pushing with more would be better. Out of the water, a hexapod shape (3 or 6 sided symmetry) allows for much more gait variety for walking, including multiple variants of all which bilaterally symmetrical animals are capable. I agree that out of the water, a good stable body shape becomes more important. And almost everything you say about bilaterians due to their 2-sided symmetry is also true for n-sided symmetry in general (up to reasonable limits) regarding cephalization. (the brain is at one end, not on one side. the limbs are on the sides. you're potentially confusing people conflating end with side, when bilateral symmetry is all about mirrored sides. you said the nerves are concentrated "on one side of the body". I think you meant "at one end of the body." It's not left or right, it's at the front on both sides. it's at one end. sorry for going on, but it was painful to listen to.) Just because animals with small-n n-sided radial symmetry don't exist today doesn't mean they couldn't have. And it also doesn't mean they wouldn't be better than bilaterians, because they could use extra limbs... imagine having 3 pairs of arms around a barrel body with 6 multi-jointed legs and eyes all around it. You could hold more things and move stably over more types of terrain, as well as having more redundant limbs in case of injury. (but mostly the brain is not on your left or your right. it's at the front. like you were implying, but imagine this is your first exposure to the ideas.)
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  141. 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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  144.  @h.t.awesome3822  You watched the video, right? If a few million years is enough that humans have changed into a different species, then how much more will our understanding of the universe also have changed? Look how far we are in front of 10 years ago. and 100, or 2000, or 30000 years ago. This is us is in just a few thousand years. The end of even black holes for energy isn't due to happen for easily understood period of time. The number of years a 1, with somewhere between 100 and 106 zeros after it. (That's the estimate for how long it takes for the black holes to evaporate based on a couple of models.) That's such a different scale of time for existence than anything has had, ever. You saw the population growth, and the technology growth in the video. That was all in less than 100 thousand years. The time to the beginning of the universe is 100 thousand years, except for each year you have 100 thousand years. The time from now, until all the black holes will evaporate is around 10 with 100 zeros. That's like the example with 100 thousand years inside each of 100 thousand years, except, it's a lot bigger. First we need some names... the time between the big bang and now, we can call "BBTime". And let's say "to square" some time is to make a new length of time which takes the old length and replaces each year with the entire previous time. This makes a new length where the total number of years is squared from the earlier one. It's not some mystical "time squared " anything, just a way to imagine it. Take BBTime, and square it. Then square that number (so you put the square number in the square number of times.) Then do it again. Even that number is brain destroyingly big, but we're not even close. That number only has 82 digits, and we need over 100. So we just replace each of those years with the number of years in BBTime. The number of years that have already been since the beginning of time. So... perhaps we have enough time to work out how to evade the heat death of the universe. It's impossible to predict.
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