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Jeff Huffman
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Youtube comments of Jeff Huffman (@tejing2001).

I thought I had a decent general background in this, but your presentation, despite being aimed at a layman, really helped solidify my understanding. It's not easy to make explanations that can be followed by anyone, but also actually hit the mark from the perspective of those with more knowledge. Well done guys :-)
481
As a culture, we seem to have lost sight of the distinction between "people shouldn't do X" and "we should prevent people from doing X". Even in most cases of the former, the latter still does NOT apply, and trying to do it would send our society into an authoritarian downward spiral. Hopefully we'll rally and find some balance.
196
I'm really glad you took the time to talk about this, since your channel spends most of its time presenting visually intuitive proofs of mathematical things. It's important to acknowledge that while visual intuition is really useful for aiding understanding, it is NOT a substitute for carefully checking every aspect. The devil is in the details often enough, even in the beautifully idealized world of mathematics. I got the triangle one, but probably only because I've seen a similar fake proof before, which purported to prove a 90 degree angle was equal to a 100 degree angle. It really is very sneaky. Actually the most confounding one for me was the sphere one. I couldn't quite put my finger on what the issue was. Thanks for the clear explanation there. I was very glad to see how you explained the pi=4 one. I've seen a lot of bad explanations out there, which make the error seem complicated, when in fact, it's exactly what you said: the limit of the property is not the same thing as the property of the limit. It's probably the most broadly applicable cautionary tale among these, though "make sure your diagrams are at least topologically correct" is pretty broadly applicable too.
171
@wodddj Hitchhiker's Guide to the Galaxy. The answer to life, the universe, and everything is 42.
135
I really love the graphical intuition added onto that one sentence proof. It makes it a lot clearer WHY that function is an involution and has exactly 1 fixed point. Also, you misspoke. At 28:54 you said "b squared" instead of "c squared." >.< Gotta be tough to get through that stuff without any mistakes. At least it's clear what you meant cause of the written equations.
72
I'd love to see a comparison between how much it would cost to deal with the eventual effects of climate change vs how much it would cost to reduce CO2 emissions quickly. Essentially view the reduction of CO2 emissions now as an investment, and (probabilistically) determine what its interest rate looks like. Is it a good investment? or will it actually disrupt our society less to let things go for a while? I'm all in favor of pushing nuclear past the NIMBY problem and switching to it over coal. CO2 aside, it's far safer, and with higher marketshare it would become yet safer and likely a lot cheaper as things get streamlined and more R&D goes into improving designs. With better designs, the amount of nuclear waste produced can be made extremely small, and you can even avoid ever needing to handle it at all. I'm also all in favor of manufacturing hydrocarbon fuels using atmospheric CO2 and nuclear energy. It needs more R&D, but it has a huge potential to deal with CO2 emissions without drastically changing our society and the way we do things. Renewables like solar and wind? ... not a fan. They need large amounts of grid energy storage of some sort, which isn't really feasible with current technology or anything on the horizon. They take tons of land area away from nature, and they take lots of manufacturing to make all those solar panels/wind turbines, and energy storage devices too (and all that manufacturing often releases CO2), and all that equipment needs to ultimately be disposed of when it breaks down, which is yet another source of environmental issues. Not to mention repairing and maintaining such a large amount of equipment takes a lot of human effort and isn't actually all that safe.
52
Git-annex is absolutely amazing. You really have only scratched the surface. My personal favorite thing you can do with it is distribute large files intelligently through repos on external drives, aka sneakernet. Each repo keeps track of what other repos have and need during syncs, so you can set the external drive to "need" anything that the other side of the transfer needs but doesn't yet have, and then the sync --content will load exactly what needs to be carried to the other side, automatically. Once it gets the other side, the content will of course be loaded by the target, but it will also be cleared from the external drive, since the target repo now has it, and it no longer meets the criteria.
33
This perspective makes the 'update' concept so much cleaner. I've long believed that until something is utterly obvious to you, you still don't truly understand it. I just got much closer to understanding bayesian updating. I could already do it, and even explain it, but it wasn't the same. True understanding is precious. Thank you for what you do, and as always, I look forward to the next video.
26
@ameynarkhede8264 The issue isn't really with anything that already happened. It's with the plan to increase censorship capability. I'm not exactly convinced by the "just trust us, we'll only use our power for good" argument, no matter who it's coming from.
26
The spider comment had me laughing out loud. It's so true! Although rather than fears exactly, you could say dragons are a combination of every awesomely powerful thing in nature instead. Related to fear, but not the same... and definitely doesn't include spiders >.<. Also, that lines up pretty well with your argument about their central theme.
24
Karsten Hoff: Actually the storm at the start didn't bother me. True, martian atmosphere is very thin, but wind speeds are higher, so as I understand it the actual dynamic pressure isn't that much lower than what you get from winds on earth. Combine that with the low gravity and it sounds pretty plausible that a once-in-a-decade storm, say, would have enough wind force to tip the ascent rocket. What bothered me about the martian was how people didn't think about obvious issues until so late in the game, and how they ignored fairly obvious alternatives to their choices. How can they not start thinking about whether the mav can intercept the hermes until AFTER they've committed to the plan and the hermes is already on its way to do the hyperbolic flyby? Also, blowing the front hatch near the end seems like a stupid risk given that they still had more fuel. They can sacrifice some of the fuel allotted for the capture burn into earth orbit, so long as they still have enough that they stay bound to earth (and that's way more than enough delta-v). They would end up in some higher elliptical orbit around earth instead of a nice circular one, but it's not much harder for nasa to get a resupply vessel to them (than it would have been anyway) so long as they're actually gravitationally bound to earth. Also, given that they had the maneuvering backpack thing, why was disconnecting from the tether not even an option? Yes, it's risky, but it's way better than mark poking a hole in his suit.
20
The best definition I've seen of the word "reality" is this: "reality is what you run into when you're wrong." What I love about it is that it points out something that I think is important to this discussion: if you can't be wrong about something, then it's not real. Throughout this video, you keep talking as though there is an answer to what the "one way speed of light" is, but we just don't know it. But why do you even think there is an answer? If there is no experiment that could measure it, then it's not a property of physical reality, just our model of it. To make the issue clearer, consider the same argument that was used in regard to simultaneity here applied to what it means for 2 points to be at the same height in different places (ignoring for now the curvature of the earth's surface and gravitational field). What if "horizontal" is actually different than we think? What if objects to the north are actually higher than we think they are, and the ones to the south are lower? What is the real "slope of horizontalness", and how could you possibly measure it?
19
If you look into a far future interstellar context, though, kinetic weapons become truly scary. Relativistic kinetic missiles are just terrifying in damage potential. Planet-wide extinction-level events can be created by just a single one.
19
I think you've missed a lot of the issue with systemd (not that I blame you... most people who hate systemd express themselves very poorly). To preface this, I use systemd. I'm just not entirely happy about it, and still on the lookout for something that sets off fewer warning flags in my head. Systemd (the project, not just the init system) takes an approach to low level system management that assumes monoliths are good. Using systemd tends to be an all-or-nothing affair for the most part (not systemd-boot, but that's the exception, more than the rule). If you use one part of systemd, you kind of end up having to use the rest of it, too. The pieces all interlock without understandable, stable interfaces between the components to allow interchanging them. Functionality sprawls across the interconnected pieces, and the sheer quantity of obscure features is downright disturbing to anyone who understands the value of the unix philosophy, and bothers to really look at what's going on. Systemd-init also has a couple of really excellent ideas at its core. The event/transaction system it uses to manage services has changed how people think about ongoing state in their systems in general, and given them a much more powerful language to express how they want their system to behave. The idea of treating many different sorts of system state with the same concept of "units" has a lot of power. The dependency relationships that are possible among units, though not very consistently structured, are very expressive, allowing you to ensure things you had no hope of ensuring before. Having an "init" for each user allows user-level configuration to gain these same benefits as well. It's no wonder it took over, despite the issues. So I use systemd. It has some really nice features, and the cost of using anything else is just really high right now. But I continue to keep my eye out for a solution that gives similar benefits, but is more modular, keeps the agility to replace components fairly painlessly, and avoids lock-in and feature creep.
17
I moved into a new place (northern US, we get plenty of snow here) most of a year ago, and was surprised, given the climate, to find the central heating was an air-source heat pump. I haven't had the slightest issue with it, though. Things have clearly improved since my knowledge on heat pumps was gained.
13
@mannohneschuh Actually no. Heisenburg was a practicing lutheran and was explicitly against dismissal of religious thought as somehow 'replaced' by scientific thought. He saw the two as separate and equally valid. Many of the most profoundly successful scientists in history felt similarly. (Sorry to rant; I realize you were just making a joke. It just bugs me when people assume science, and therefore the scientists that pursue it, are somehow anti-god. Certainly some are, but it's not at all an inherent aspect of science)
12
On the subject of infinity: Strictly speaking, none of rigorous mathematics deals with actually infinite constructs. You fundamentally can't. You can, at most, allow infinitely many possibilities with a finite description of which possibilities are allowed. It's just a matter of how honest you are about what you're really saying. Coming at things from a more constructive perspective often illuminates a little better what supposedly infinite constructs are really about. And playing at the edge of them leads to interesting conclusions which are often misunderstood to say more than they really do, like how observations about the logical contradictions inherent in supposing you can "pair up" possibilities from 2 finitely-describable spaces leads to the declaration that there are "multiple levels of infinity"... which is a much bigger statement, and doesn't really make any sense. The error was in identifying the philosophical notion of infinity with those equivalence classes of "pairable" spaces in the first place. The same goes for non-standard analysis with its "actual infinitesimals". They're no more "actually infinitesimal" than any other "infinite" construct in mathematics. What makes them different from limits is that they're *actually numbers*, not that they're "actually infinitesimal". "What if we could make limits fully behave like numbers, instead of only mostly? And maybe some other stuff like dirac deltas while we're at it?" I'm all in favor of that, and I think it can definitely lead to more intuitive ways of teaching and understanding calculus.
11
Convention, mostly. The equivalence classes mod n are normally named by the smallest element in them >= 0. Though honestly it's often more intuitive to think of the classes just under n as negative numbers instead.
7
It's too bad you didn't mention NixOS here. It has immutable system files, generated declaratively, and atomic updates and rollbacks, but it's not image based and doesn't involve containerization. It's also quite configurable, especially if you're willing to learn the nix language a bit. I'd say it's perfect for exactly the sort of people for whom the image-based distros are too much work to customize to their liking. Got some special patches you want to compile a certain package with? That's fine, just add a few lines in your configuration and it's done. Oh, you want to run a custom shell snippet in the initrd? Sure. Easy enough. You can even throw home-manager in the mix and have large portions of your user dotfiles managed declaratively and immutably, too.
7
It's too bad we don't actually teach the fundamental theorem of arithmetic in a fully qualified way... the most accurate way to say it is that each number, up to an invertible factor (1 and -1 for integers) has a decomposition into a unique product of primes, and some invertible factor. Said that way, it extends straightforwardly to more complex sets, such as the gaussian integers.
7
Regarding that last question, a set being totally ordered no longer means points have to have predecessors/successors in the case of infinite sets. There is no "point just before 1". As for Zeno's paradox, the most compelling response to it that I know is this: Why exactly are you assuming that space can be infinitely divided, but time can't? I could imagine both being infinitely divisible, or neither, but having them be different just seems silly.
7
@DerKiesch I thought it was pretty clear that mark was on a hyperbolic trajectory during the rendezvous: as you said, the whole point of lightening the mav was to make up the difference in delta-v between orbital insertion and escape. But it actually doesn't matter, since no matter what their overall trajectories looked like, the fact that the intercept was very low velocity means they can achieve another intercept a short time later with a quite small amount of thrust. So basically the "only get one shot" idea and the "low intercept velocity" idea are mutually incompatible unless both craft have almost no maneuvering capability at all. Admittedly, however, if the hermes has to change orientation to achieve thrust in the desired direction, they might not have enough time for another intercept before mark runs out of air. With that big rotating habitat section the hermes is probably tough to turn.
6
@johnschmidt1262 The space and time thing was a response to Zeno's paradox itself, not a response to you. As for the "next point" thing, I already said it pretty clearly. Just because the points come in order doesn't mean there's a "next" one. That logic only applies to finite sets. What's the "next" real number after 0? For any positive real number x you suggest as "next", x/2 would come before it, contradicting the assumption that it is, in fact, "next". That's a proof by contradiction that no number is "next".
6
wow, that is a beautiful little problem. My first thought was to transform it into a discrete state machine (with a state including the point that is the pivot, and which of the point-separated regions of projective space around that point that the line falls in, so that each pivot switch is a state transition). I'm not sure where I would have gone after that... I went ahead and watched the video without trying to solve it myself.
4
Had me totally cracking up. Well done 🙂. I can't believe you managed to say all this without cracking up yourself.
4
@maxv9464 Nope, you have to vaporize them, and with enough lead time for the mass to spread out to the point that the kinetic energy density is not dangerous.
4
@jpisello That's a common misconception. See https://www.quora.com/Is-there-anything-smaller-than-a-Planck-length-1 for more detail, but this statement is only very very tangentially related to truth. There is some length scale at which determining position that accurately requires amounts of energy that distort space, possibly even creating a black hole, and defeating the original purpose of determining position, however without a proper theory of quantum gravity, no one knows how exactly this would work, and even then, it doesn't mean that space isn't continuous in at least some senses (there should still be a truly continuous concept of translation, for example). And even if position certainty is limited, that doesn't mean that smaller lengths don't conceptually exist. The planck scale is ROUGHLY the scale at which this is expected to occur, but it could be an order of magnitude off easily enough.
4
@SSkinner901 The chance of a random permutation of n things having a loop of k length is 1/k if and only if n < 2k. It works because the length of the loops precludes having more than one in a given permutation. As soon as you can fit 2 loops of that length in a single permutation, things get a lot harder to count properly. Fortunately in this case you can find the answer you're looking for without solving that problem. EDIT: To elaborate, the number of permutations of n things is obviously n!. The number of permutations of n things with a k-cycle (n < 2k) is the number of ways to make a k-cycle with a "marked" start point in n things (n!/(n-k)!) divided by the number of possible start points (k) times the number of ways to permute the remaining n-k items ((n-k)!). Putting that together is n!/(n-k)!/k*(n-k)! which reduces to n!/k. That's 1/k of the total number of permutations, n!. Also, none of these counts for distinct k overlap, since k+k' is always bigger than n and thus the 2 cycles can't coexist in the same permutation, so adding up those counts is fine.
3
@_modiX Kerbal Space Program. It's a game where you build and fly rockets.
3
@DerKiesch When it comes to whether the mav can intercept the hermes, I wasn't so much talking about the crew's decision as the discussion of possibilities back at nasa. The whole working out of how to lighten the mav enough to make it happened after nasa had considered and rejected the plan and the crew had gone against orders to force their hand. How did the question of whether the mav could be lightened enough to make the intercept not come up far sooner, when the plan was still under initial consideration? Also, the thrust doesn't really matter much. Assuming they have almost any maneuvering capability at all, then the only real time constraint is the time till mark runs out of air. Given that it is (and must be) a very low velocity intercept, they don't have to make the first intercept, they can set up a second one with very little thrust. Also I didn't get the impression they were even considering using the ion thruster at that point. They were using some kind of maneuvering thrusters with a different fuel source. And all their discussion at the time was about having enough fuel, not about having enough thrust. Also, if the final stage of the mav really has zero delta-v, and the hermes really has so little maneuvering capability, how was a rendezvous supposed to work under normal conditions?
3
@Jake P Technically there are multiple different hyperreal number sets, of which the surreals are the largest (though the surreals are a proper class, not a set, but I'm getting off topic now). However, any of them should allow this. The differences between them don't really come up so long as you're using them for calculus.
3
You can specify absolutely anything by surrounding it in single quotes (apostrophes, same thing), then replacing each single quote in the filename with '\'' (singlequote, backslash, singlequote, singlequote). Most people don't realize you can start or end quoting mid-word, but it does work, and allows you to escape the single quotes with backslashes, and everything else with the single quotes. This is the method used by many programmatic "escape for shell" routines.
3
You really made field theory hang together for me a lot better. Prime power galois fields, in particular, make so much more sense to me now. I could work with them before and not get things wrong, but it was all not quite as well founded. Now it's so obvious what's going on there. And in my book, if it's not obvious to you, you haven't truly understood it yet. Thanks so much for connecting all this together on a subject I never got the chance to work my way through alone.
3
Tiling window managers don't fit your target audience here of course, but maybe they deserved a sentence, just so people know those alternatives exist?
3
Great build up. I'm more partial to type-theoretic foundations, myself, but set theory is the standard, and you put it all together really well, glossing over the right things, and focusing on the right things. A minor issue: At 1:05:08 you didn't make clear that it needs to be a strict subset. Technically you defined "less than or equal", not "less than", since you used a non-strict subset symbol in what you wrote down. A bigger issue: Your hand-wavy proof of the completeness of the reals is really only a proof of the density of the real numbers. One way to prove completeness would be to take dedekind cuts of the reals and prove that they always define an existing real number.
2
The 2-ness comes from the squaring in the pythagorean theorem, basically.
2
@volbla "Although one might ask how different a philosophical construct of infinity is from a mathematical one" Heh, I suppose that's fair. And I don't mean to suggest math can't inform philosophy. It definitely informs mine quite a bit. It's really easy and really dangerous to believe you know more than you do, though.
2
The mach effect thruster (as he described it in this video) doesn't seem theoretically problematic to me. Isn't the reaction mass just in the form of gravity waves?
2
@jakehildebrand1824 I believe both types of concentrated solar do exist, though I don't know which is more prevalent.
2
@defalt2384 Qutebrowser does use the blink engine at its core, though unlike, say, brave, which is basically degoogled chromium with a few new features, qutebrowser completely rewrote all the high-level code, making it a truly distinct browser even if it still inherits a lot of its website compatibility from chromium. Browsers actually not based at all on chromium or firefox are pretty rare and not very good afaik.
2
Hmm... The method proposed here doesn't actually have perfect anonymity. If there are more than 2 people, I always know that the person I'm buying for isn't buying for me, since the method here always gives a permutation with a single massive cycle. To give perfect anonymity, you would need a method that gave other possible cycle structures (just no 1-cycles allowed so no one buys for himself).
2
As someone who, until a year ago, lived in a remote area with frequent-ish power outages, an LED lantern that runs on D cell batteries makes way more sense than any of these combustion lanterns. Coleman makes them too :-).
2
@raffaeledivora9517 When it comes to quantum physics, I also subscribe to the "give up realism, not locality" concept, especially since on reflection, giving up realism isn't as bad as it seems. What you're really giving up is definiteness (the idea that there is always, in principle, an answer), but you're not actually giving up coherence (the idea that if we have incompatible knowledge, one of us is wrong), which is all you truly needed for the intuitive notion that "reality is real".
2
I resemble this more than I'd like to admit. Got a good laugh out of me.
2
The problem is, who gets to decide what's factual and what's disinformation? Any sort of centralized mechanism for doing so is inherently incredibly dangerous, as history has proven time and time again. Censorship is censorship, and even with good intentions, it's a very scary thing. Mozilla is showing no recognition of these issues either, which is a pretty bad sign.
2
@DerKiesch Yeah that seems like the most sensible option really. I don't know how much delta-v those packs have, but I have a hard time believing it's less than like 200m/s, which would do the job just fine.
2
Decent summary of the issues. Since I use a chromium-based browser, rather than use an electron app, I just run my browser with `--app=<webapp_url>`. It integrates into the desktop basically the same as an electron app, but it shared the browser's resources, and gets sandboxed away from my system. I also don't have to deal with updating it. (Discord is somewhat infamous in distro maintainer circles for releasing a new version and instantly requiring everyone to switch to it, with no grace period for it to make it into package repos...)
2
You actually didn't mention the worst aspect of this for me. If a driver uses a turn signal and engages or disengages the the brakes at approximately the same time, it can be easy to mistake which signal flip is the change in braking status and which is the turn signal, I have more than once interpreted this set of events as a turn signal in the opposite direction and a slightly differently-timed application of the brakes than what it actually was. I don't mind the red turn signals too much if they are actually separate indicators, though you're right that the different color speeds up the brain's processing of the information and reduces ambiguity, definitely increasing safety.
2
You missed "poweroff". It's more likely to be what you want than "halt" in most circumstances (It is the same as "reboot -p" though). Also, the sysrq method is actually a slightly more graceful shutdown than just hitting the power button. It at least tries to flush writes to disk and unmount filesystems before shutdown, so if you can remember it, it's worth doing even if you have access to the power button.
2
That final section took me a second view to fully comprehend (which is rare for me, even on your channel). I got there, but it would have helped a lot to know in advance how the "super-pairing" would be related to what we were trying to prove. Just a statement at the beginning of the section that we're going to make a pairing to give us an equation among counts of things which we can massage into a formula for p(13) would have made following the specifics a lot easier for me. I love how deep you go into serious math topics as well as how accessible you make the ideas. Keep it up! Also, I made it to the end :-)
2
Basic principle: government is terrible at being efficient. Really, really, terrible.
2
I once heard this as "if mirrors reverse things left to right, when I lie down in front of one, why don't I see my feet?" I prefer the 3D answer (mirrors reverse front and back) combined with the following insight: our brains know that objects can't be "pulled through themselves" in the way that would be necessary to invert just 1 dimension, so we instinctively seek out the 3d rotation of the object that is the "closest match" to what we're seeing. Since many objects in our environment have left/right symmetry, that generally leaves a discrepancy in the left/right direction after the rotation. (but when I lie down in front of the mirror, now I have up/down symmetry, and I find a rotation to match that).
1
You think it's bad now, wait till you're several regions into apocalypse mode :-) (watch http://youtu.be/v-4C6Cx2LVg for some idea)
1
@Tinybabyfishy Yup.
1
3:30 "the flase statement" ... oops :-P
1
@IIIRobIII True, though it may still be an interesting fact that ANY rules can make the concept work.
1
@volbla We seem to be mostly on the same page here, I'm just applying the same caution you mentioned about the boundary between math and physics to also put a boundary between math and philosophy. As long as we're clear that we're only talking about a mathematical construct, it's perfectly fine to call those infinite numbers and to say one is bigger than the other (Though in constructive mathematics, for example, you may find that cardinalities can't be proven to be totally ordered, and other wierdness. It's worth some caution even then). It's also worth remembering that there are a lot of different ideas about how to extend the concept of a number or a quantity into the transfinite, and they don't agree about a lot of things. What people often do with the cardinality thing is claim that mathematics has discovered something about the nature of infinity (the philosophical concept), but to understand what really has and hasn't been proven, you need to unpack the stack of definitions you used and be conservative about how you map them to anything real.
1
You said here that antimatter gets you 100% matter to energy conversion, and while this is sort of true in theory, the problem is that, as I understand it, a nontrivial percentage of the energy goes into creating fast-moving neutrinos, and there's just no feasible way to harness that energy to any purpose. I think the highest achievable energy/mass ratio would actually be from feeding matter into a micro black hole and letting it come back out as hawking radiation.
1
Your rant on breaking up relationships at 11:28... Seriously! What is up with that? This has ruined my investment in more stories than I could possibly count.
1
Honestly, given the amount of time we'd have to prepare for something like this, I'd think we could save everyone. We'd need to build power infrastructure that doesn't depend on solar (in other words, nuclear), and artificially lit, warmed and oxygenated farms and dwelling spaces. It would be a huge task, but we're talking about having many centuries to prepare. No doubt it would be pretty not-fun in a number of ways, but the idea that most people would die on the surface seems to be underestimating the adaptation capability of humanity to me.
1
@thepuksu But the main reason we care about climate change is its impact on humans. The cost of mitigating that impact deserves consideration relative to the cost of lowering CO2 emission. It's still not the whole picture, since not all the impact on humans can be mitigated or is economical in nature (if people are generally less happy because the weather is worse, for example, that's not really translatable into dollars in a fully satisfactory way), but I think it'd still be enlightening.
1
@jakehildebrand1824 I wouldn't exactly say the "near" future. Fusion is famous for always being just around the corner. There are promising indicators recently, but I'd say it's still ~20 years to production scale at the absolute minimum. More likely double or triple that. On the timescale on which people want to deal with the CO2 issue, it's not really too relevant.
1
@davidpape5548 Yeah, solar induced thermal power doesn't have as much of the manufacturing and waste issues as photovoltaic. Note though that that kind of solar plant cannot work without the mirrors moving, unlike a photovoltaic array, so there's maintenance to be done on the mechanical parts that move all those mirrors. It has somewhat less of the power storage issue, since there is some storage in the thermal capacity of the working fluid, but it's still problematic that you can't get power whenever you need it, so it can't really be the workhorse of the power grid without major advancements in energy storage.
1
"but then this breaks the idea of relativity and light being the same speed no matter where you measure it." I'm not entirely certain what you mean by this, but if I'm understanding the intuitive problem you're having correctly, the issue is that you can't see how the speed of light can be the same for both the stationary observer and the moving observer, but have the moving observer see more "video frames" of the oncoming light in the same amount of time. If that's your issue, the answer is fairly simple: you're not taking account of length contraction. Distances in the direction of motion are contracted, so the oncoming "video frames" get closer together in space, and now the video plays faster despite the "frames" moving through space at the same speed.
1
I've been looking at the same thing, and wondering how the scattering works. Thanks for a little illumination on that. At least where I am though, I'd describe the sky color more as sickly yellow most of the time than angry orange, though I did get some of that too. It made me double-take every time I looked outside. So alien.
1
Just want to mention again the issue with this explanation of Fourier transforms: the "center of mass" idea works, but with the caveat that there's a constant amount of mass per angular distance, NOT a constant amount of mass per arc length.
1
AI's tendency to hallucinate, as it's often called, just completely invalidates its usefulness in a code generation, code explanation, or reference replacement role, for me. I operate as a programmer by understanding exactly what's going on, so low-quality data sources are worse than useless. Where I do think it might have some value is in catching mistakes. For that purpose, it can have a notably higher error rate and still provide value overall. At least to a sufficiently capable human. Who knows if its error rate is even low enough for that yet, but I could see it getting there, at least.
1
Thanks for actually saying this... it's bothered me a lot that the environmental movement doesn't consider the full picture in these kinds of ways, but nobody talks about it. You summed up most of the problems I have with renewables, though you did fail to mention that even if you did use batteries on a massive scale to store energy from renewables, the batteries would have serious disposal issues just like you were saying solar panels do.
1
Anyone know of a keyboard-oriented browser (or a browser configurable enough to create a good keyboard-based experience), that's still compatible with extensions for chrome or firefox? I'm using brave with the surfingkeys extension right now, but there are some fundamental limitations to what an extension can do as far as keyboard customization. (for example, surfingkeys key shortcuts don't work while the current tab is still loading, some keys (like ctrl-n) are not capturable by the extension, and I believe some websites override the js code injected by surfingkeys.)
1
The unix philosophy needs a bit of translation for modern times. The core principles are making your software components composable, using well-defined, interoperable interfaces between components, and defining the boundaries of components in such a way that each component has a single, easily abstractable purpose. Those core principles are still very relevant, even in the spaces where they aren't applied much right now. The linux kernel is one example, things like blender and web browsers are too. You could build something like blender in such a way the it was essentially just a UI, which made manipulation of underlying software components, which had interoperable interfaces, easier. The linux kernel could also be a LOT more modular than it is, if the infrastructure was designed differently.
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I think the fact that GPLed software can't feasibly be sold actually constitutes a "bug" in the GPL. The explicit allowance of sharing the software should perhaps be limited to only those who have bought a license (this would have to be worded in such a way that redistribution through distro package managers was clearly allowed). The other freedoms the FSF defines could all still be protected in a copyleft manner, and the license could automatically "convert" to full GPL after a set amount of time (initial suggestion: 10 years, though it would probably vary depending on the software). I think it's a reasonable compromise between the freedom of the end user and the need to pay for the development. We could call it something like "user serviceable software." It might catch on among more open-minded commercial software creators. You could also implement license-reminder systems, which, unlike DRM, wouldn't be designed to control what you can do, but just to help prevent accidental violation of the license, by requiring the user to make an actual action signifying that they believe the system is in error and they actually have a license in order to override it. (This would also be important if it was distributed through distro package managers, since users could easily mistake it for free software if they weren't paying attention) Somewhere in this set of ideas I think we can get a solution that actually works for the whole society. Right now, open source software developers are giving their talents away as a kind of charity, and I don't think that's a viable way for software in general to work for the whole society, but we should have a path that is, and is also ethical in regards to how it treats the end user.
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@Deborah Hearne Technically, yes. Realistically, no. The GPL license requires you to allow whoever has a license to make copies and give them to whomever they wish, granting them a license in the process. So basically, pirating is explicitly allowed in the license. Who would pay for what they can legally get for free? Some people actually would, yes, but It's really more like a voluntary donation than a price at that point, so I can't really call it "selling".
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@Deborah Hearne Correct. That's why I said "Technically, yes."
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@Deborah Hearne I'm really not sure how to respond at this point. Repeatedly asserting the same thing doesn't address the points I made about why it's not realistic, but at this point, I doubt continuing the discussion will be fruitful for anyone.
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The graph at 1:03 has a typo... in the labels on the bottom, 1085 should be 1985.
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How did I not know about this? It actually seems like a surprisingly reasonable approach to off-earth high thrust propulsion.
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I knew a guy who once accidentally overwrote the first few hundred megs of the partition currently mounted on /. He specified the wrong partition, and by the time he canceled the command, the damage was done. The system still kinda-sorta worked, some stuff was on the unaffected portion, other stuff was cached in RAM, but he was scrambling to try to find executables that still functioned that he could use to extract important files >.<
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This is a great way to build an intuition for fourier transforms, and better than I've seen before, but if I can nitpick a bit, the center of mass concept is not perfect, even ignoring the multiplier issue, since the "mass" needs to be considered distributed uniformly by angular motion if you consider it as a polar plot, or by the independent variable if you consider it a parametric plot. Either way, that is not the same as being distributed by arc length, which is probably what people will imagine when you talk about the plot being made of wire and taking the center of mass. Still, great explanation. It definitely helped the whole subject feel just a bit more intuitive to me.
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What I wish you covered here was the other sense in which chaotic systems are actually independent of initial conditions. In the lorenz attractor example, the long-term proportion of time that the system spends in any given subset (open set anyway) of states turns out to be totally independent of initial conditions. In the case of the weather, this would correspond to the fact that all those butterflies flapping their wings cannot change the overall frequency of storms.
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The idea of instantaneous rate of change does actually make sense for a slightly modified definition of "instantaneous." Although the rate of change is not a property of a single snapshot of time, it IS a property of a small window of time around the instant no matter how small the window is . This is the sense in which the rate of change is "instantaneous;" if you take any (open) interval of time that includes that instant, no matter how small, the derivative at that instant is fully determined by only that interval. This means that the value of the function at all other times is demonstrably unnecessary to knowing the derivative, just zoom in on an interval of time that cuts off before, or starts up after, the time in question, and you still have enough info to determine the derivative.
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I took a moment to come up with my own guess from my general physics knowledge, and was pleased to find I was mostly spot on. I did underestimate the likely power of the... moonquake? (is that a word?), but otherwise I'm glad to validate my general notions of scale in physics. P.S. Seriously, lets have a boring 2021. That would be WONDERFUL.
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What is often overlooked in talking about the grey goo scenario is thermodynamics. The growth would not actually be exponential, at least, not for very long, since heat dissipation limitations would limit the growth to something proportional to the surface area of the transformed matter, not to mention that these tiny machines can only transform nearby material into new machines, and so in the long run most of them would be sitting around with nothing to do, again limiting the rate of conversion to something proportional to the surface area of the transformed matter. It's hard to really imagine this transformation actually traveling at any appreciable velocity, after all, bacteria and fungi basically are grey goo, and they can't spread all that frighteningly fast.
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@Br3ttM Or just make a pair of rings spinning in opposite directions, and tie them together so their gyroscopic forces cancel.
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I know I'm raising a raising a dead thread here, but I've found a good solution to this problem on nixOS (it should also work when using nix + home-manager on a non-nixOS distro): References (most recent first, but the reasoning of why to do this is explained best in the original one) https://elis.nu/blog/2020/06/nixos-tmpfs-as-home/ https://elis.nu/blog/2020/05/nixos-tmpfs-as-root/ https://grahamc.com/blog/erase-your-darlings I think I prefer having grahamc's approach with snapshots rather than the tmpfs route, since I don't really want to take up system memory, but the idea is this: Delete everything every boot (maybe even more often)... EXCEPT what you have personally decided you want to keep. Using home-manager allows you to declaratively create your static dotfiles from a single central configuration file which you can comment all you like, and follow DRY principles with (it is, in fact, written in a full-fledged programming language), but for the data actually saved and/or manipulated by programs, you can instead add that a file or directory should be redirected to your permanent store. This means that a necessary part of installing and using any piece of software is determining where it saves information, deciding whether you want to save that information, and if so, changing your home-manager configuration to redirect that to your persistant directory, of course with comments to remind you, in your own terms, what program/purpose you're saving it for. Any program that silently adds files to your homedir will just get them obliterated, and so anything that IS there is either something you ran quite recently, or you have a comment about what it's for in your home manager configuration. A nice side effect of this is also that you know your backups work. As long as you back up your persistent area, you're essentially loading from a backup every time you boot. If some state you care about isn't getting backed up, you're going to know it pretty quick.
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It's a bit unsatisfying to end the video there, yes. But since I was already aware of the convolution theorem, the connection was somewhat satisfying in itself. I'm looking forward to the convolutions video, though.
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Have you looked into geometric algebra? It includes the valuable aspects of several other systems, like quaternions, and unifies them in a wonderful way that feels almost as general as tensor algebra, but a lot more intuitive, since the metric is essentially baked into the algebra.
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The centripetal force only goes as the speed of the object squared under galilean relativity. Under special relativity, it approaches infinity as the velocity approaches the speed of light.
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I don't think I've ever been able to clearly see the macroblock grid before outside of just ludicrously abysmal bitrate. Nicely done :-)
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I'm definitely looking forward to a proper proof that all primes equal to 1 mod 4 can be written as a sum of 2 squares. 3blue1brown did this same topic (it's probably my favorite video he ever did) and skipped that part as well, and it's been floating in the back of my mind as an unsolved problem ever since.
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@Jop_pop Actually I did get the basic gist of it, and I'm going to take the time to analyze it better later, but still :-)
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I think it's easiest to understand from a rotating perspective, where the water stream is curved by both centrifugal and coriolis forces. Centrifugal force is intuitive enough... it just pushes the stream away from the center of rotation. The coriolis force, however, is what makes the stream lead or trail the spout in the rotating reference frame. Because the coriolis force is proportional to velocity, if the velocity is reversed between the outward and inward facing cases, then the leading/trailing phenomenon must be reversed as well.
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After mulling this over for a bit, I realized there's an issue with this explanation: as stated, it seems to apply just as well to the principal axis with the smallest moment of inertia. For a complete intuition, you would need to understand why it DOESN'T happen there. I believe the answer to that question will probably center around the coriolis force on the 'flipping' mass, and how the torque from that affects the primary rotation. That torque should be small in comparison to the primary rotation's angular momentum in the intermediate axis case, but large in the smallest axis case.
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You might want to consider using nixos to mitigate this issue. If you want to, you can install a particular package from a specific version of nixpkgs, rather than your normal channel. It will use dependencies from that version of nixpkgs as well, without holding back those same dependencies for the rest of your programs, so you can pick and choose what updates you want for that specific program, try a new version, and if it doesn't work, just go back. It should, at least, always allow you to use a known-working version if you want to.
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It doesn't have to be nixos, for that matter, you could use home-manager on arch, and get the same benefit.
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You said in the video that non-rocket launch systems all need to deal with crazy amounts of air resistance... this isn't necessarily the case if they hit the atmosphere at a high altitude, which pretty much requires an active support structure ( maybe you can do it with buoyancy, but given the scale involved, probably not), but it is possible. Of course active support structures are a lot farther out of the realm of tested technology than the systems you were probably thinking of, but a caveat on that would probably be appropriate. On the main topic though, this does sound like it's not very useful given the high g forces the payload endures and the low velocity advantage gained, plus exiting low in the atmosphere. However it might be worth considering for launching materials off of the moon for use in in-orbit construction, given the lack of atmosphere and lower orbital velocity.
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@JohnDoe-ki6yd Fundamentally, it doesn't have much to do with probability. It's another way to do calculus in general. If you look into using hyperreal numbers to do calculus, you should be able to find some interesting stuff to get you started, but the way it applies to probability problems isn't really any different from how normal calculus applies.
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Sorry for the wall of text, I've had this on the mind for a while and just had to say it. Why postulate many worlds at all, when you can think in terms of knowledge, probability, and correlation? The density operator (wave functions only represent pure states, and thus aren't a sufficiently complete description in my view) represents your knowledge about a system, much like a classical probability distribution (and in fact diagonal density operators are classical probability distributions over the basis states. Also, by choosing an appropriate state basis, any density operator can be made diagonal). The difference from classical probability distributions is that there is no assumption that there are any density operators that make every property of the system definite simultaneously (this is the key idea, take some time to think it over), which also means it's no longer possible to do away with the probability stuff and deal with a single fully definite state instead, since those don't exist. You still get determinism though, in the sense that no information is created (or destroyed, for that matter) through time evolution. Entanglement is just correlation (so no action at a distance), superposition is a result of your knowledge about the system not being applicable to the question at hand (rather than your lack of knowledge, like classical uncertainty), wave function collapse is the change to your knowledge that results from interaction (much like the classical probability distribution for what hand of cards you were just dealt "collapses" when you look at the hand). It's also worth noting that both decoherence and wave function collapse are a result of interaction of the system with things that aren't being modeled, namely the environment and yourself, respectively, so the apparent creation/destruction of information in how we think about those processes isn't real (no "dice" involved, even in measurement). The No Cloning theorem just says that when you run an object through a perfect copier, the outputs will be perfectly correlated (nawww, really? copiers do that?) (and you'll need raw materials about which you have maximal information in order to make the copy too). The No Communication theorem is no surprise since nothing about this whole perspective involves action at a distance. And so on. Once you accept that there are no probability distributions that make every property of a system definite, everything else falls into place quite intuitively. You lose the expectation of definiteness of reality, sometimes called "realism" (that your questions have definite answers, even though you don't know them), but this is a much smaller sacrifice than it might at first seem, since you still have the expectation of coherence of reality (that if you and I have incompatible knowledge about reality, one of us is wrong).
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Another thing that I think deserves to be mentioned here is that different distros have different "rules" that you should follow if you want a smooth experience. The primary one on almost any distro is to install things through the package manager when possible, but depending on the distro, there may be many more aspects to doing it the <distro name> way, and instructions "for linux" that you find out there often won't be correct in those senses for the distro you're on. This is more common in the advanced user distros, since a lot of new-user-friendly distros are ultimately based on ubuntu, and work very similarly in underlying architecture because of that. So the basic advice nugget is this: learn what practices and methods are particular to your distro, and be aware that instructions and guides may need some translation before they work smoothly for your distro.
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As more of an 'Alice' myself, this really was a good reminder not to be afraid to just dive into calculation if it seems like it might get me somewhere.
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What I want to know, is if you pay for youtube premium, and use an adblocker, do you still get the 5 second pause? It would not surprise me in the slightest if the answer is yes...
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If you like the configurability of gentoo, but don't want to compile literally every package on your system, there's also NixOS. It provides the same level of customizability as gentoo, being a source-based distro, but because of the reproducibility demands it makes on build processes, it can transparently use cached build results from the main nixos organization. So you only run compiles for things you actually change. With NixOS, you also actually create configuration files as part of your system build process, from a single declarative config (which is actually written in a full-fledged programming language). So your entire system, as you've customized it, aside from your genuinely stateful data (what programs need to actually change at runtime), can all be built as part of a single process, and atomically updated and rolled back. The stateless nature of this process, combined with the organization of having all your tweaks documented in a single place, can be very freeing. That said, NixOS is quite different from normal distros in order to accomplish this. You need to do a lot more things differently due to the extra layer involved in creating all your config files, and in fact general linux binaries will not even run on nixos without some special tweaks, due to it not having an ld-linux.so in the normal place.
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Regarding installing things by piping curl into sh (which you brought up briefly), it's not necessarily that bad. Nix uses this method for its standard install script, and that rubbed me the wrong way, but try as I might, I couldn't come up with a concrete reason this was any less secure than other potential ways of installing that software. The shell script is entirely contained in one big code block, so the shell will actually not execute any of it if you get an incomplete download, because of the bracket mismatch causing a parse failure. If curl has an error of some kind, that goes to stderr, and stdout gets an empty string, causing sh to do nothing. The url is https, so you're not vulnerable to a man in the middle attack. Assuming you trust the website creators enough to run their code on your system (which you do*, *obviously*, if you're trying to *install their software), there's no reason not to pipe something downloaded from their site into sh, if appropriate care has been taken regarding these details. All of this only applies to a one-time event of software installation from a trusted source, however. Doing this on an ongoing basis is... bad. I agree this example was horrible advice. The source was sketchy, it was totally unnecessary, and very open to lots of things going wrong.
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I never use ls -a, since ls -A is the same, but skips . and .., which are ALWAYS there and thus not useful information.
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@japanada11 Yeah, I forgot to add that unique factorization only applies to multiplicatively cancellable numbers, which discounts zero. Thanks for pointing that out. I would take the view that -3 is a prime number, but it's "the same" prime as 3. Viewed that way, 6 = 2*3, 6 = (-2)*(-3), -6 = (-2)*3, and -6 = 2*(-3) are all "the same" factorization of "the same" number. (This is slightly different from what I said before, I know.) Explained by example like that, I don't think it's too hard to follow, though the precise abstract statement is indeed too complex to use as an introduction to the subject. I just think it's a shame that when we teach it, we don't even address the issue of negative numbers at all.
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After digesting this for a bit, I've settled on the idea that the electrons are a thin interface between the fields and the energy source/sink. The chemically-forced movement of electrons against the E field in the battery moves energy into the fields, and the tendency of electrons to vibrate nuclei in the resistive load provides a means for them to transmit the energy from the fields into heat. In both cases, though, the electrons themselves carry almost none of the energy at any time. They are dragged around by the fields and whatever the source or sink of energy is, like a piece of paper in between a heavy pushing object and another being pushed by it. One illuminating thought experiment along these lines is to consider the value of the poynting vector inside the conductor. It's near zero because the electric fields are small compared to outside, but what power flow there is actually points into the wire, not along it. Energy from the fields is entering the wire to be converted into heat due to the wire's resistance, but the power flow along the wire is all outside. Really the only power flow that's actually inside the wire is the (non-thermal) kinetic energy of the electrons, which is minuscule, both because the drift velocity is quite low, and because electrons weigh almost nothing. That minuscule amount of energy is the transfer medium all the power goes through when interfacing with some other physical system, but carries basically no energy itself.
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I use btrfs, but not because I think it's fast. I just want a filesystem that's in the mainline linux kernel and has snapshots. Only one meets those criteria last I checked. I run it over a separate raid layer, of course, due to the write hole.
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The interesting question for me is why only the orange hue gets a new name for its darker variant. I suspect it might be because we actually have 4 kinds of photoreceptors, not 3, and although the sum of the red, green, and blue response curves is pretty similar to the rod response curve, it dips a good bit between the red and green peaks in comparison, so spectral orange light can get the rods responding more than would be predicted from the response of the red, green, and blue cones. This extra dimension of perceivable color, though we have low fidelity in it, might be the reason brown gets its own name. It might also be a notable difference between what our eyes can see in reality and what can be shown on a screen. Does anyone know how big an issue this is?
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I'd love to see you guys bring attention to orbital rings too. They're a massive initial investment in comparison to skyhooks, but for sufficient volume, they'd be quite a bit cheaper. Simply put, orbital rings are actually much more deserving of the widespread awareness that the space elevator concept enjoys, since they need no new technologies or materials, and are much more versatile in their usage (including potentially taking over a lot of the long-distance intra-planetary transport on earth).
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@MattsAwesomeStuff The faster an RKM is going, the more time and distance is needed to accelerate it up to that speed, which gives you a decent amount of lead time as long as you're looking far enough away. Faster projectiles are also easier to detect at longer distances due to increased heating on the front surface from interstellar dust impacts. So practically, you do have quite a bit of advance warning if you are actively looking for them with enough imaging equipment and compute power. Isaac Arthur has some great videos exploring the practical limits of such things.
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Even without an atmosphere, unless the exhaust actually goes fast enough to escape the gravity of the body (which rockets aren't even close to in earth's gravity well), the angular momentum of the whole system can't actually change, so your rotation ability is limited to the same type of mechanisms that let reaction wheels and falling cats turn themselves, however that would still allow you in principle to move the target city of an ICBM by essentially temporarily storing a large amount of angular momentum in the suborbital trajectory of the rocket exhaust, much as reaction wheels store angular momentum in a spinning wheel.
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Rotational dynamics are perhaps the most persistently unintuitive thing in physics, but this penetrated that at least a bit. Well done.
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I came up with the coloring proof on my own with the video paused. I do like it better than the swivel proof, but mostly just because it feels more rigorous. EDIT: To answer your final question, the diameter of the circle is clearly larger, since one of the diameters of the other shape forms a non-diameter chord of the circle.
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Brave has a sync feature, though I don't actually sync much beyond bookmarks, so I don't know how how usable it is for more complicated stuff.
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You skipped a pretty important point: I'm fairly certain the energy required to get nuclear waste out of the sun's gravity well is more than the energy you get from the nuclear fuel it came from in the first place. No matter how efficient your space launch system (and rockets are quite inefficient), you actually get net negative power out of the whole process. You're better off just burning all that hypothetical rocket fuel for power than using it to get rid of the nuclear waste from nuclear power plants.
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