タイムテーブル - 3Blue1Brown - 切り抜きDB 3Blue1Brownのタイムテーブルです。 https://favtu.be/timelines-rss/c/UCYO_jab_esuFRV4b17AJtAw Tue, 06 May 25 00:00:08 +0900 The visuals are crazy. How did you make them?（00:01:23 - 00:05:41） https://favtu.be/timelines/v/3foYyPDp0Ho/s/83/e/341 Tue, 06 May 25 00:00:08 +0900 Summer of Math Exposition #4 | Teachers, I'd love to hear from you - The confusion（00:00:00 - 00:01:25） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/0/e/85 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Introduction and Confusion About Grover's Algorithm（00:00:00 - 00:00:57） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/0/e/57 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Classical Verifier Functions and Examples（00:00:57 - 00:02:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/57/e/143 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - Example: Sudokus（00:01:25 - 00:07:58） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/85/e/478 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed The sudoku grid at has 11,447 solutions so this is already a good example of a function with multiple correct inputs.（00:01:30 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/90/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed Trivia: I wanted to try my hand at the example sudoku at , so I entered it into a grid on a website and asked it to check. It turns out that puzzle has 11447 solutions, so it cannot be solved logically. Oh well.（00:01:30 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/90/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed Don't try to reverse-engineer SHA-256, kids - you'll just make a hash of it.（00:02:07 - 00:05:42） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/127/e/342 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Utility and Speedup of Grover's Algorithm（00:02:23 - 00:02:58） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/143/e/178 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed "Its not like the key value is hiding inside the function behind some curtain, its more of a difficult to find EMERGENT PHENONMENON of the function of itself". THIS, i believe is the primary source of the confusion. Its not necessarily the inputs or the outputs of the function: its the behavior of the function itself that is of interest. I believe this is the fundamental point that you need to elaborate on, and when you develop your exemples you need to tie it back to the behavior of the function itself.（00:02:29 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/149/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Compiling Classical Functions into Quantum Logic（00:02:58 - 00:04:27） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/178/e/267 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed . This is a minor correction on terminology. When you take a function and turn it into logic gates in classical computing that's called synthesis, not compilation. I understand that using the correct term in the video won't help the average viewer understand the core point of the video any better, but maybe It could be adjacently useful for someone early into studying CompE.（00:03:25 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/205/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Quantum State Vector Manipulation（00:04:27 - 00:05:37） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/267/e/337 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Grover's algorithm leverages the translation of classical verifier functions into quantum operations that manipulate vector states, enabling the search for solutions without knowing them beforehand, thus bridging classical verification and quantum computation.（00:04:52 - 00:11:58） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/292/e/718 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I think I had my confusion resolved within ~ min. I failed to grasp, that the quantum algorithm manipulates the probability distribution of the current 'state' and is programmed for a specific case (like a sudoku solver). Now I can just accept the mentioned operations (multiplication by -1, or flipping around some vector) exist and be happy with the explanation. I also wonder if I could have just reviewed the first video, but the opportunty to that experiment is now lost to me 😆Thanks!（00:05:30 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/330/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Clarifying the Quantum Operation and Addressing Confusion（00:05:37 - 00:08:05） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/337/e/485 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed A quantum leap?（00:05:42 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/342/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed At about @-ish you're talking about whether it was too much of a leap - it wasn't, I'd come to that conclusion from what you said, but it still felt pretty magical I think mainly because you skimmed over it quite quickly. It was almost like sleight-of-hand in that I got the idea but it did leave me with a slight dissatisfaction/unsureness about whether I'd extrapolated correctly what you were driving at. This clarification was exactly what was needed, and honestly I can't say it doesn't work better as an addendum rather than being a diversion in the main video!（00:05:50 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/350/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed @@kindlin Well, he did sort of explain how it would be translations of the logic gates into operations on the state vector (which would be rotating it, flipping it in certain ways etc.), but that () going into more detail wouldn't actually give better clarity, which was the point of this video. So basically he said that's too into the weeds for this video 😉（00:05:56 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/356/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed Hey, I really respect you as an educator, I think you generally do great work, but I think you do yourself and your audience a disservice at when you imply a large language model like Claude can help explain a topic like this. You've done videos on how LLMs work- surely you know their output has no real relationship to the truth. They're great at producing probable sequences, but they're much more likely to produce plausible or almost-correct misinformation than any actual answers. Offering it for a complicated topic your audience may already be confused about is disappointing to say the least!（00:06:02 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/362/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed in Video（00:06:04 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/364/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed Also as a side-note, the Brooklyn Nine-Nine reference at was totally unexpected but I absolutely love it!! Instantly recognised it - name one law :) pretty cool to see that you (probably) like it too.（00:06:55 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/415/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed For me, the biggest revelation of this video was . In order to translate it to a quantum computer, you DO need to know the contents; it isn't just a "quantum wrapper" around a normal function. This is what I would have thought was the case, but, as you identified, the combination of the "black box" phrasing and showing that the function clearly knows the search value made it seem like this couldn't be the case. Then you would find the answer in the process of translating the function to quantum. Perhaps an example such as "can make platonic solid n-gon with pentagons" is a good example since it clearly doesn't "know" it's own answer, would theoretically be difficult to check, but it's also pretty clearly just 12.（00:07:08 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/428/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed that to return true we flip the ENTIRE input vector (every "bitstring's" vector), but then it feels like suddenly to return true we only flip the vector at a certain bitstring. This is almost certainly my misunderstanding of the difference between the k dimensional representation or whatever and the vector of a specific qubit, but it really is confusing me. Like in a classical sense it feels like I would need some huge number of "bitstring" positions to represent every sudoku position to even begin to use the verification function, how could a quantum computer even set up that environment to work under? Does it require a huge number of qubits to work? If each qubit could only represent（00:07:18 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/438/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed "Which specific key input does this is a difficult to find and emergent property of those logic gates"（00:07:50 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/470/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - Linearity（00:07:58 - 00:14:19） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/478/e/859 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed i like that the "half of the reason for making this video" comes at the halfway timestamp（00:08:03 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/483/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Quantum Superposition and Linearity（00:08:05 - 00:10:30） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/485/e/630 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed hate to break it to you but that is a misunderstanding of quantum superposition grant! It doesn't correspond to north and east. Mahesh Shenoy posted a video targeting this misconception.（00:08:50 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/530/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed that velocity analogy was helpful to understand superposition（00:08:57 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/537/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed When you can't even say my nameHas the memory gone? Are you feeling numb?Go and call my nameI can't play this game, so I ask again...（00:08:59 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/539/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed The state vector component magnitudes can be a complex number as well?? Yikes.. Just as I thought I was maybe starting to understand it just a little bit.. 😅（00:09:16 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/556/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I think the confusion must come from the fact that we don't know the actual vector, only the measured result which comes from the probabilities. And the trouble is |1011⟩ gives the same probability as -|1011⟩ (it's squared right?) but even then, we only get one sample result when we measure it. So the function itself doesn't get us much.（00:09:21 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/561/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed this is the kind of explanation I was hoping for in the main video when i was confused about the same thing. "i know quantum computing is an entirely different beast than classical, so what logic gates do we have to work with and what do they do?" just as a baseline understanding to show that translating an arbitrary classical function into a quantum one is possible. The sudoku case is a great example as its easy to understand what the check function does, and the key value that gets its axis flipped by the quantum check function is not because it is "the sudoku solution we are looking for" but instead because its is "a valid sudoku solution"（00:09:46 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/586/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Linearity in Complex Quantum Functions（00:10:30 - 00:12:22） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/630/e/742 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed At the term "solution" is a little overloaded. The mention of "every possible solution" means incorrect solutions also. A few seconds later "solution" is used to mean just the correct solution.（00:10:50 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/650/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I think the part that confuses me the most is at . In classical computing it feels like this would be like generating every possible configuration (the shear size of the possible configurations here is what really breaks this for me), asking the function if it's valid (idc whether or not it's parallel, it just happens), and then returning some array of booleans where one of them is true, but due to some arbitrary physical limitation (quantum computing) it takes us a little bit to "retrieve" that solution from the result array. It feels as if the algorithm requires that the blackbox return some sort of state other than true false (I know I'm beating a dead horse sorry). Like I thought I understood from 2 bitstrings max (it has the 0 and 1 axis) then wouldn't we need tons of them to represent all possible states of a sudoku board in the input (very high dimensional) vector of the verification function? I really would love to understand this, and I think it comes from just a misunderstanding of the physical implementation of that input vector for the verification function.（00:11:20 - 00:07:18） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/680/e/438 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed As you see in , the quantum gate somehow flips a value (which is a fair function), but (a) why is it statistically very likely in every run the same vector index, (b) how does Z behave when the number of dimensions is low / in the RSA prime size and keeps its statistic significance on the vector index, and (c) why does the flipping happens in exactly the qubit that is statistically very likely to be of (cryptography) relevance here?（00:11:24 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/684/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed phase (I think this is where the "in parallel" analogies stem from ( in Video 2)). It's not so much a question or confusion around Grover's Algorithm. But that first step that causes us to need Grover's Algorithm is the confusing magic that is just too much. I know you said you didn't want to show how the gates works because showing classical gates wouldn't help you understand a calculator (2), but I think THAT is the crux of it for most people... even though your video clearly clarifies that it's about Grover's Algorithm with the parenthetical title. For me I think I do want to study up on quantum compilation, so thank you for calling that out.（00:11:28 - 00:06:04） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/688/e/364 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed Does the part at tell us that at the end it's just : "quantum computing does all thing in parralel but we need O(sqrt(N)) to decode the result" or is there something big I missed ?（00:11:30 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/690/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed That is an excellent point about whether quantum computing can be considered parallel or not. I think the most important part about it is what usefulness we can get from it that we can't get from other forms of computation. However, since we never actually get more than one input out despite the amount of "parallelization" we can get depending on the design of the machine, it depends on how we want to say we got the result.For instance, performing an operation on a superposition of North and East may not matter whether we do it on both directions at the same time or on the superposition itself, what matters is whether we need to pay attention to something happening to a specific direction, as in the case of quantum computing. If you need to know which cardinal direction you are closest to facing at the end of a bunch of turns, it may be more useful to think of each cardinal direction being operated on separately rather than as a single angle, for instance.Of course, it all depends on the problems, the framing, the operation, and the interpretation of results. I still like to think of Grover's algorithm as being a parallel operation on many elements of a vector with the same operation, even though one can only get a "scalar" result. At least that is how it makes sense to me.（00:11:30 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/690/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed This analogy really cleared things up for me. Choosing this basis for the state space certainly makes it look like the function "knows" which direction is the answer, but the function exists independent of what basis we chose.（00:11:35 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/695/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I found the hiker explanation at very helpful! (Also it is comforting to know that even 3b1b, best at explaining there is, sometimes is unsure whether he's over- or under-explaining :)（00:11:36 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/696/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I still don't get it, but I feel that the vector composition part at maybe helps a bit. What if instead of talking about a bunch of 3D vectors combining, it was illustrated as a bunch of 2D vectors, all added head to tail. Maybe each little vector is like a each state, and then the vector as a whole is what you get added up, and then the algorithm will change those and we can see how the vector as a whole changes. I'm just not sure what the analogy would be. Maybe it would be like rotating all but one vector? But then we can still subtract the two vectors to get the true answer. Maybe it's more like all of the vectors are random, except the one true one? So you can find the most likely average vector? But then I don't understand how that would pertain the iterating it.（00:11:42 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/702/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Understanding the linearity of quantum operations helps clarify that Grover's algorithm, while theoretically powerful, offers limited practical speedup for extremely large problems, tempering expectations about quantum computing's impact.（00:11:58 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/718/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed so - if i understand it correctly, the key is simply the only one to respond properly or respond at all to you trying to flip it（00:12:17 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/737/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I'd say Yes, because as someone else said, each section holds a unique piece of information that do not affect each other , but also because in every practical term of the process, specially in the context of this algorithm, it is applying the check algorith to all parts of the vector in the same function and command. I think for me personally the confusion came from the statement "not just running parallel" with an emphasis on "not", when the algorith relied on a check that was effectively just "running parallel" what needed emphasis was the "just", nevertheless, the rest of the explanations made sense in the context of assuming the shorter leaps in logic to be true, it was the major leap of assuming there was a function that was both impossible outside quantum and was not effectively just running parallel checks on all parts of the vector. Which just to clarify, to me and many others, that is what is happening because it is applying the function to each part of the vector at the same time as even with the linearity, it's not the same effect for all like in the cardinal directions example (even if it technically is because of rotating around an axis in this case, as with many others it will not be simply one rotation), I do understand the danger of the generalization of parallel computing, but I believe it would be more understandable for most if it is stated that there are more required steps BESIDES the parallel computing rather than saying there is no parallel computing.（00:12:20 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/740/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Grover's Algorithm Basics（00:12:22 - 00:13:31） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/742/e/811 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed At about was the place where it all cleared up for meWe dont make, but already have the initial function that flips one value out of many (the quantum equivalent of sha256 for example)and then we apply to the result out new functionthats pretty much where i got confused in previous video（00:12:44 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/764/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed Great job on adding clarity! does a great job of explaining the conditions under which Grover's Algorithm applies, but your summary at（00:12:45 - 00:14:00） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/765/e/840 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I think the root issue is that the point at was not emphasized enough, and the way it's visualized implies we know what the vector looks like. If it was a vector with all values "blurred" until we get the final output, that might have made it more clear that we can't see the vector the way the video portrays it（00:12:48 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/768/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed aah, so the operator that we're applying onto the state is the quantum translation of the original verifier. This is what was missing for me! This is fundamental to understand the whole idea. Thank you for explaining better.（00:12:48 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/768/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed that clicked for me（00:12:51 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/771/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed so how is the well chosen set of inputs chosen, and what is that other operation? Does it entirely depend on the original problem and the verifier? If so, how are they used to find the input set and the 2nd operation?（00:12:53 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/773/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I think the animation in is clear（00:12:55 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/775/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed Instead, we need to do the full M steps of Grover's algorithm to slowly increase the likelihood of reading outcome |k> when we take a measurement of the latest vector output by the "circuit" after each of the M steps (the vector shown as "wires" between boxes at in the first quantum video, let's call those M vectors the "result" vectors, since the video doesn't give them a name). We keep doing more and more steps until we maximize the probability of measuring a "result" vector as outcome |k> (and M steps is the right number of steps for this). The fact that we have to do this M times is why it's not an O(1) algorithm. The fact that we have to do this M times is why it's partially misleading to say we're "testing all the outcomes in parallel" (since WE can't just connect a multitester lead to check the probability of an individual outcome of any given "result" vector) though I still think it's CRITICAL FOR TEACHING to say that the quantum computer is trying all the outcomes "in parallel" so people can have a sense of what's going on and why there would ever be any speedup.（00:13:06 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/786/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed sir you're under-explaining things and over-explaining things at the same time, it's quantum computing DUHH（00:13:25 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/805/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Geometric Interpretation of Grover's Algorithm（00:13:31 - 00:14:16） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/811/e/856 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed this was the only part that was a little confusing from the last video for me, thank you（00:13:37 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/817/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed undermines the explanation, because one of the operations necessarily confines the state vector to the 'critical planes' which contain valid solutions.（00:14:00 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/840/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed at In fact, the fact that the vector is confined to a plane is a consequence of the fact that there is only 1 "right" solution we are looking for, which effectively create a single "cutting plane" for the algorithm. But if there were 2 solutions, it would not be a plane anymore, but a volume for instance.... (if my understanding is right).（00:14:08 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/848/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - | Practical Limitations and Realistic Expectations（00:14:16 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/856/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - Is this useful?（00:14:19 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/859/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed There are applications where you can narrow the search space such that the square-root speedup becomes practically relevant. E.g., if you are trying to crack an 8-character password based on its hash value, the difference is between O(2^64) and O(2^32), which under a few reasonable assumptions is years vs. minutes. Hence the trend toward using long passphrases instead of short passwords.（00:15:12 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/912/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed [] Even if other algorithms don't break cryptography, at least the Shor's Algorithm will.（00:15:35 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/935/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed -- the brown Pi shitting on the quantum computing hot shuff is a nice touch :)（00:15:36 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/936/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed I love the small easter egg at with π and φ 👌（00:15:43 - 00:16:23） https://favtu.be/timelines/v/Dlsa9EBKDGI/s/943/e/983 Sun, 04 May 25 20:45:24 +0900 Where my explanation of Grover’s algorithm failed - Misconceptions（00:00:00 - 00:06:03） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/0/e/363 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) The video starts with a "mystery function f(n)", and it really looks like a black box algorithm setting. ()（00:00:42 - 00:20:30） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/42/e/1230 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) 12 is my favorite number. i am somehow flattered that it's the one that is highlighted.（00:01:00 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/60/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) @ , 42 is always the answer to the universe. THanks for this great video otherwise.（00:01:19 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/79/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I'm glad to know the answer at was 42. It verifies that Hitchhiker's Guide to the Galaxy was a quantum computing primer!（00:01:20 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/80/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) For a list of N elements, it takes (N+1)/2 attempts on average, not N/2.（00:01:22 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/82/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) as stated at ? If we have N numbers from 0 to N-1 and one of them is the key, the expected value of the number of required guesses is then essentially the same as the average position of the key in the sequence of N numbers, which is (1+2+3+....+N)/N = N(N+1)/(2N) = (N+1)/2. Did I miss something? Thanks again.（00:01:26 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/86/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Because of this very setup, one can ”improve” almost any algorithm that can be checked in linear time by simply checking all the possible inputs. Bruteforcing a password for example is an O(n) operation.（00:01:37 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/97/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) going with the video, as far as I know this depends wildly on the setup you can getwith lowest being around O(1) when you have N qbit device and you can chug entire superspoition through that function and if it can bring one probability to a 100 and rest to 0 it would only need one cycle to preform whole operation but if that probability is just high like 50% of being right and 50% of beign wrong, maybe dependable on N etc. this will elongateand at the other side if the functon isn't very "quantable" or you have very small qbit register or whatever it can go as high as O(n)（00:02:20 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/140/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) omg this is soooooo satisfying to watch and understand-ish（00:02:50 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/170/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) About the misconceptions on the speed of quantum computers () :（00:02:55 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/175/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) It’s so weird to me that not only people guess this answer, but that it’s the most common guess.（00:03:06 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/186/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) well its probably also that when one answer is O(1) it sounds like a trick question so „it has to be that“ in the minds of people（00:03:06 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/186/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) quantum computers can't have exponential speedup, because they are turing complete and can be represented by a turing machine (albeit a ridiculously fast and large one). And if a turing machine can achieve exponential speedup, that would basically mean NP=P which is unproven and highly unlikely to be true.（00:03:20 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/200/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) On the topic of why people might guess O(log(n)) (at ): I think you're thinking too much with your math brain, not your CS brain. O(log(n)) is divide-and-conquer style solutions, where you can divide your "problem-space" into smaller and smaller chunks. For this problem, if the quantum chip could say yes or no on if the True value was contained in a set, you could take half of the remaining numbers for each step resulting in O(log(n)). Nearly all sublineair solutions are basically some version of this.（00:03:24 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/204/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) This actually is no longer correct! As of November 2024 a new variation on Grover’s Algorithm has been created known as the partial oracle Grover’s algorithm that *does* give an exponential speed up, with the caveat of only working sometimes (and other times slowing back down to a polynomial speed up) But for the question of “best possible time complexity” O(log(n)) is actually correct（00:03:24 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/204/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I was able to guess the right answer because I knew square root can be found in probabiloties from your video with min of 2 dice rolls)（00:03:50 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/230/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) The factors of the big number are just first few digits of pi and e（00:03:50 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/230/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) i loved when you said that Shor‘s is the most famous example, while it’s actually the *only* relevant problem we know that is exponentially sped up（00:03:51 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/231/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I got it right!（00:03:55 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/235/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) , well ceil(pi/4) is just a fancy name for 1 😛😛😛, didn't you mean something like ceil(pi*sqrt(n)/4)?（00:04:30 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/270/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - The state vector（00:06:03 - 00:12:00） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/363/e/720 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) At , it’s interesting that this kind of broke my internal ordering/deviated from what I would have been inclined to do.（00:06:26 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/386/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Love how "01000011" is actually 67 and 'C'. Such attention to detail!（00:06:28 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/388/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) "[...] teaching computer science without discussing hardware."Fun fact: In German, the term for computer science is "Informatik", which is like mathematics but for information. This word tells you that you can do CS without a machine, it is just about information processing. We just so happen to have machines that are scaringly good at processing information.（00:07:07 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/427/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I planned to watch missed Asianometry episodes, but then, bam! This came in! I'm now at and already i love this video :D（00:08:43 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/523/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) "if you kept reading out from memory over and over, you would just keep seeing that same value" I'm afraid that might be incorrect, or at least somewhat misleading. In a quantum system, if you repeatedly measure a register that's in superposition (re-initialized each time to the same state), you'll observe outcomes according to the probability distribution defined by the amplitudes — not always the same value. Perhaps what you meant is: if the system has already been measured and thus collapsed into a definite state, then repeated readings would indeed return the same value — but that's a different scenario :)（00:09:45 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/585/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) “think of it as some super high dimensional space” yeah man i got what you are trying to say, continue（00:10:15 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/615/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) ^k notion of dimensions at ) if that's ever a future idea of a video (especially in ER = EPR for describing how the Einstein Rosen bridge gets "longer" as the entangled black holes evaporate).（00:10:16 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/616/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I love how you throw out in the vector demonstration around “instead k^2 dimensions instead of 3 dimensions” yeah super easy to comprehend, thanks（00:10:30 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/630/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) if you square any real number (positive or negative) you'll always get a positive number（00:10:45 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/645/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Take ''Alot of people don't know what the state vector represents'' re why we square the magnitude of each component of the vector.- The sum of all possible state vectors equals zero, and a plot of this results in a unit n-sphere. The sum of square equals the square of the radius of the sphere (in this case 1²=1). But how do I know it's a unit nsphere? Cause the state vector consists of probability components. And the cumulative probability of any Universal set must equal 1.（00:11:00 - 00:32:20） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/660/e/1940 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) just guessing but is state vector, wave function, because we square that to get the probability, right?（00:11:12 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/672/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Qubits（00:12:00 - 00:15:52） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/720/e/952 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - "After all, something is going to happen"（00:12:56 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/776/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Instead, we need to do the full M steps of Grover's algorithm to slowly increase the likelihood of reading outcome |k> when we take a measurement of the latest vector output by the "circuit" after each of the M steps (the vector shown as "wires" between boxes at in the first quantum video, let's call those M vectors the "result" vectors, since the video doesn't give them a name). We keep doing more and more steps until we maximize the probability of measuring a "result" vector as outcome |k> (and M steps is the right number of steps for this). The fact that we have to do this M times is why it's not an O(1) algorithm. The fact that we have to do this M times is why it's partially misleading to say we're "testing all the outcomes in parallel" (since WE can't just connect a multitester lead to check the probability of an individual outcome of any given "result" vector) though I still think it's CRITICAL FOR TEACHING to say that the quantum computer is trying all the outcomes "in parallel" so people can have a sense of what's going on and why there would ever be any speedup.（00:13:06 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/786/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) , it would have been extremely helpful for my quantum computing course. Howeevr, I need to correct you in . It's not just a unit circle, its something called a Bloch Sphere, which in itself is what we call a CP^1 or a complex projective space of dimension 1. Its because of this that we take |x|^2 instead of simply x^2, and that's because the coefficient of |0> and |1> can also be complex, with the restriction that |x|^2+|y|^2=1（00:13:38 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/818/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) “Added *bit* of *complex*ity” 😂（00:13:45 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/825/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) As someone who took introductory quantum mechanics course the first aha moment is at showing what a qubit REALLY is（00:14:38 - 00:15:00） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/878/e/900 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) TODO continue from（00:15:00 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/900/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Nice Schrödinger's Cat reference at（00:15:14 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/914/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - The vibe of quantum algorithms（00:15:52 - 00:18:38） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/952/e/1118 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I found this bit where the circuit is drawn just gorgeous（00:16:01 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/961/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) -bit CLA, seeing one pop up at gave me a sensible chuckle（00:16:05 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/965/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I bet that circuit does something interesting. Waiting to hear from people that know.（00:16:08 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/968/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Example: a coin (deterministic) + Quantum vector = would be to have a 50/50 probability it would land either "heads" or "tails?"（00:16:49 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1009/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) @ Minor pedagogical point - applying a Hadamard gate twice would actually take a |0> state to a (negative) |1> and not back to |0>. I find it useful to think of the Hadamard transformation as half of a bit flip. Leading directly to the intuition that two Hadamards simply flips the bit.（00:16:50 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1010/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I have a suggestion for ur visuals as ur visuals are the best of the best but to touch the elite line u can put the anime style in this, particularly on（00:17:08 - 00:17:08） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1028/e/1028 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) in this（00:17:08 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1028/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Grover’s Algorithm（00:18:38 - 00:29:30） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1118/e/1770 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Question here: At , why do you flip the sign of only the secret key? if it is supposed to be unknown???（00:19:00 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1140/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) but how do i know beforehand what is the secret key value im looking for? How would this work in practice if say i try to force a password?（00:19:30 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1170/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) perhaps it’s on my brain a whole lot lately, but every time you talk about using this algorithm as a search, my brain adds to the list of applications “finding the most probable next word in a sequence of words”（00:20:09 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1209/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Nice video as always, but the logic gates circuit for the function at is just bad. You only need 3 2-input and gates & 2 not gates to verify a 0101 (5). Boolean algebra.（00:20:24 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1224/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Why is that: "Grover knew that given any ensemble of logic gates like this, you can translate it into a system of quantum gates, so that if in the classical case the function takes in some binary input and returns a one, for true, then in the quantum case, the effect of all of these gates is to flip the sign of that state; the state associated with the same bitstring."（00:20:30 - 00:25:52） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1230/e/1552 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) But at , we have to translate the function to a quantum equivalent, that instead of verifying if the answer is correct, flips the sign of the correct coordinate. The "you can translate it" is not about a theoretical possibility here, you really have to (very carefully) translate the classical verification algorithm into the quantum "secret axis flipping" algorithm.（00:20:30 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1230/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Great video as always! The only part that’s still unclear to me is how the system of quantum gates at is able to invert the amplitude of the key item. More specifically, how is it possible for this to happen in so few steps that the overall complexity remains proportional to √N? This is something many textbook explanations don’t really clarify, and I was really hoping for a more precise understanding of this part of Grover’s Algorithm from the video.（00:20:36 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1236/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) it reminds me of Cook-Levin theorem（00:20:44 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1244/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I feel like the real magic is happening with the quantum gates (), and I really don't understand it. So to take all the input values then run them through the quantum gate, with the goal of reversing the logical value of the key, would take N time, right? And why couldn't the process just end once a value has been flipped? Everything else just seems like a cool algorithm to find a needle in a haystack, but what I want to know is how they take a haystack and turn the key straw into a needle in seemingly constant time.（00:20:59 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1259/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I think tries to answer my question, but the operation does not feel "useless" it feels like: if we can flip the sign of the key component, then we are already done because we already know the key direction.（00:21:00 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1260/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) mentions that the quantum gate "simply" flips the key value. Wouldn't it have to process a N dimensional vector every time ? Isn't the difference between the quantum gates doing something very different here(parallelism?) that enables much of the speed gain?（00:21:12 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1272/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I think you may misunderstand me (or I'm just not understanding). We only know the key direction because a value was flipped (turned negative). In order for the state vector to be originally flipped, the value corresponding to the solution for the given problem, the states needed to be passed through the quantum gate (). Once the specified state vector was given a negative value, then the probability shifting occurs. I don't understand how first process occurs, in what seems to be constant time.（00:21:25 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1285/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) why does he use the term "state vector" at then? Does me mean to say that a specific component of that state vector is flipped?（00:21:27 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1287/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Something I don't really understand, if you need flipping the sign of the value at the position corresponding to the solution of the problem, then shouldn't that require that you know the solution already? I've probably missed something that tells about that, but just quickly asking it here.（00:21:34 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1294/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Always love your videos. One thing a layperson like me might hold onto is, how does the Algorithm "know" which one is the secret key? And therefore even start to run that process show in（00:22:31 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1351/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Another great video, I just didn't get one thing - you say quantum computer can put the key value on one axis and "average" all the other values into the other axis - but isn't the whole thing about not knowing what is the key value in the first place? If we don't know where to go, does it mean we just try every direction? And how do we know we went into the correct answer direction and not some random one?（00:23:02 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1382/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) How do we find equibalance of the non-key states ?（00:23:06 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1386/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) This reminded me of your lecture about AI embedding spaces, how with the growth of number of dimensions, you are guaranteed to find more and more perpendicular vectors.（00:23:40 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1420/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Please explain this, i am ultra confused - : if we don't know key value how can we perform flipping it's sign or any other reflection operation regarding it's position.（00:25:33 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1533/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) *focuses in learning（00:25:45 - 00:30:16） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1545/e/1816 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Great explanation! Admittedly, I’m still a bit confused by how you “flip about the x-axis” (or flip the sign of the key value) when the x-axis seems to be defined by “not the key.” It seems the key needs to be known to flip the sign associated with the key value (flip the sign for the component associated with the key value?（00:25:45 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1545/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) when flipping the state vector around the "equal balance direction", how do you avoid also transforming the key vector?（00:25:45 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1545/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - yes, indeed... "In general, if you can clearly describe and access one of these state vectors, it's also perfectly possible to reflect around it."（00:25:52 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1552/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) b does seem to imply this at , but I'm not sure this is what he meant.（00:25:57 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1557/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) if we can access the vector then it's possible to reflect around it but how we have the access to vector aligning the x axis（00:26:00 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1560/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I doubt that's it, but just in case you're talking about applying a fast-exponentiation-like approach for the part by rotating the vector by 2theta, 4theta, 8theta and so on and so forth (choosing a recently obtained vector as an axis instead of |b> each time). That approach doesn't work because you cannot duplicate quantum states (no cloning theorem). Basically, if you want to use a quantum state twice you have to build two copies from scratch and that defeats the point.（00:26:15 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1575/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) This was extremely helpful to me, confirming the vague notion I had about what quantum computing is about while also providing intuition about what a quantum algorithm is.However, I am still confused at , where you "first flip around the x direction and then flip around this off-diagonal direction" these seem to be unlike each other. The x direction stands for the orthogonal to the (unique solution) y direction, so it is in fact the hyperplane of all directions that are not y. But the other direction is given by just your single initial-state vector. so flipping around it is not well defined, in any case not as a geometric reflection. So it looks like you are trying to compose a reflection with something that is not a reflection in order to obtain a rotation, and that does not seem to work (except in dimension 2).（00:26:20 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1580/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) After the first reflections, why can’t you then reflect around the new higher vector you created, to get to the top faster?（00:26:50 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1610/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) so its just a computer（00:27:42 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1662/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) This video is great. you could use classical computers to calculate the root of N but it is a bit expensive.（00:28:13 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1693/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) I started to understand at around（00:28:50 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1730/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Until you finally mentioned at ish that... you can just check it, since the premise was that the answer is quickly verifiable.（00:29:05 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1745/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Support pitch（00:29:30 - 00:30:11） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1770/e/1811 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Complex values（00:30:11 - 00:31:27） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1811/e/1887 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) complex numbers elegant application（00:30:16 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1816/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Why square root?（00:31:27 - 00:34:01） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1887/e/2041 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) The fascinating thing about the section is that I took the square visualisation of the beginning and basically immediately understood why it is squared thanks to Pythagoras. Because even if we consider parallelism, picturing it with a square or cube or whatever, leads us to consider "going along" all the edges at the same time. Which, in the simplest case of the square, means that we, well, have to put all of the possible outcomes into a square. Which we, of course, can't do without taking the square root.（00:31:27 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1887/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) ofc its pythagoras its always pythagoras（00:32:20 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1940/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Hey I recognize this!!That's the Cover Art for Richard Hamming's The Art of doing Science and Engineering!（00:33:10 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1990/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Wow, that created an optical illusion that glitched my mind HARD（00:33:19 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/1999/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) "Panoply of additional directions" Beautifully put（00:33:27 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2007/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) why is the shortcut squareroot sized when the vector doesnt move the whole way (just an approximation of pi over 4)? Wouldnt that mean that the shortcut the vector takes is ALMOST squareroot sized? (Kinda like the almost pi endzone in your last video)（00:34:00 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2040/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Connection to block collisions（00:34:01 - 00:35:08） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2041/e/2108 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) finally, *the* one Brown（00:34:26 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2066/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) - Additional resources（00:35:08 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2108/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) flashbang alert（00:35:08 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2108/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) Q 1 – Early stop at sixty degrees• Chance of measuring the correct item: 75%.• Grover iterations used: roughly 0.52 times the square root of the database size N, which is about 2/3 of the work in Grover's original algorithm.• Why: each Grover step rotates the state by a tiny fixed angle; stopping when the total turn reaches 60 degrees means you have not yet maximised the success amplitude, but you have saved time.（00:36:42 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2202/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) interesting so the function we're optimizing here is essentially（00:36:43 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2203/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) "More fun homework": When the state vector rotates to a 60 degree angle, the probability amplitude for the secret key vector is root 3 over 2; the probability that we will get the right answer on the first try is 3/4, or 75%. The probability that we will get the wrong answer on the first try is 25%, or 0.25（00:36:45 - 00:36:54） https://favtu.be/timelines/v/RQWpF2Gb-gU/s/2205/e/2214 Wed, 30 Apr 25 21:32:19 +0900 But what is quantum computing? (Grover's Algorithm) @@GustavRex They do, but Grant very clearly says "Watching it through a telescope, night after night, ..."（00:00:14 - 00:01:45） https://favtu.be/timelines/v/M6LUPYsjods/s/14/e/105 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons @@Localnimation Hmmm... Terrence is talking about when the earth is on the opposite side of Jupiter. He even draws a diagram () to make the point.Okay, maybe he didn't mean it strictly, but, even if it was in that 5 o'clock configuration you described; as long as the sun's visible (i.e. it's not night time), I reckon the sun would be too bright for anyone to see Jupiter's much smaller moon, IO, with 17th century telescopes.（00:00:51 - 00:01:45） https://favtu.be/timelines/v/M6LUPYsjods/s/51/e/105 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons @@GustavRex If you watch the full video you will see that it is rather unclear about the role of Huyghens vs. Rømer (see e.g. ,（00:00:58 - 00:01:20） https://favtu.be/timelines/v/M6LUPYsjods/s/58/e/80 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons hour, on the hour. So at it turns light, at 2 it turns dark, so on. If you move a light-minute away, it now goes light at（00:01:00 - 00:01:01） https://favtu.be/timelines/v/M6LUPYsjods/s/60/e/61 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons and dark at（00:01:01 - 00:02:01） https://favtu.be/timelines/v/M6LUPYsjods/s/61/e/121 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons ). That's what I reacted to. As far as I know the measurements as well as the conclusions were made by Rømer alone. Huyghens may have been involved in the aftermaths of this result.（00:01:20 - 00:01:45） https://favtu.be/timelines/v/M6LUPYsjods/s/80/e/105 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons @@GustavRex no it isn't. Holy jupiter, watch the video. At the text is on the screen saying "Huygens estimat"（00:01:20 - 00:01:45） https://favtu.be/timelines/v/M6LUPYsjods/s/80/e/105 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons .（00:02:01 - 00:01:45） https://favtu.be/timelines/v/M6LUPYsjods/s/121/e/105 Tue, 08 Apr 25 00:57:13 +0900 Measuring the speed of light using Jupiter's moons We're all in his heart?? ❤️ it seems?! Wow! 😮🥲 Ephesians -23 will blow you're mind!!We're ALL in this together you know, doesn't matter how much you messed everything up or what you did.. He loves YOU.. Remember that whenever you're in the dark, alone.. He's with you.. Only repaying ppl back with love ❤ will TRULY make someone actually think about their deeds..（00:01:22 - 00:01:38） https://favtu.be/timelines/v/C8baNzpnZ7o/s/82/e/98 Thu, 27 Mar 25 03:37:29 +0900 Zooming out by powers of 10 - Intro（00:00:00 - 00:00:48） https://favtu.be/timelines/v/6dTyOl1fmDo/s/0/e/48 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi oh the coolest math video I've ever seen?（00:00:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/0/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi anyone else felt nostalgic from the reference（00:00:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi "to link to link to"?（00:00:11 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/11/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi 3 blue Pis and 1 brown Pi（00:00:13 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/13/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi advance Happy pi day!! Every one 🎉🎉（00:00:13 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/13/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi six seconds in utter fear of cutoff released by instant gratification at（00:00:42 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/42/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi - Recap, the surprise pi（00:00:48 - 00:03:58） https://favtu.be/timelines/v/6dTyOl1fmDo/s/48/e/238 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi 0 = 215（00:01:10 - 00:01:10） https://favtu.be/timelines/v/6dTyOl1fmDo/s/70/e/70 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi 00 = 74（00:01:10 - 00:01:10） https://favtu.be/timelines/v/6dTyOl1fmDo/s/70/e/70 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi 0000 = 455（00:01:10 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/70/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi = 21（00:01:10 - 00:01:10） https://favtu.be/timelines/v/6dTyOl1fmDo/s/70/e/70 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi What you hear in the hood（00:01:41 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/101/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi STANDING HERE, I REALIZEYOU WERE JUST LIKE ME,TRYING TO MAKE HISTORY（00:01:45 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/105/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Imagine the cow as a sphere ahh problem😆（00:02:06 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/126/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Spherical Cow!🐮 ^.^（00:02:07 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/127/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I just want to point out that there's a meme in Russian internet about the ideal of something - a spherical male horse in a vacuum. Disclaimer: I also forgot the English word for a male horse (not sure if stallion is correct).Disclaimer two: it used to be the ideal of a horse but now it's a phrase that's used as a meme to talk about anything. The word for a horse just gets swapped with whatever thing you want to talk about the ideal of（00:02:09 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/129/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I’m a physicist. I feel seen. Thank you for this point cow.（00:02:11 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/131/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi wait.. im dumb. is sound is a sign of energy transfer? because why no sound?（00:02:34 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/154/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi wow you reed all the comments（00:02:37 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/157/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi love that you knew someone would complain about the sound even though it's an obvious simulation where you add "light" flashes and sound to demonstrate collisions（00:02:44 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/164/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi But isn’t it literally 3000 collisions and not almost?（00:02:56 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/176/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Do you know what else is massive?（00:03:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/180/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi U know what else is MASSIVE?（00:03:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/180/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi yk what else is massive??（00:03:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/180/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi you know whats also massive?（00:03:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/180/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi M-m-massive?（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Massive you say?…（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi This is the first time I notice that the word "massive" is actually derived from the word "mass".（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi and do you know what else is massive?（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi and you know what else is massive?（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi do you know what else is MASSIVE?（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi massive（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi massive?（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi you know what else is MASSIVE?（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi you know what else is massive?（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi you know what else is massive? LOOOOW TAPER FA-（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi 😏Do yo- *GET OUT*（00:03:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/181/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Do You Know What Else Is Massive?（00:03:02 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/182/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi ultrakill door sound（00:03:07 - 00:06:27） https://favtu.be/timelines/v/6dTyOl1fmDo/s/187/e/387 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi really caught my attention i would like to see what relativistic effect exactly would happen（00:03:08 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/188/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi It's so funny how 1 kg block is starting to break a time-space continuum because of how fast it's being squished（00:03:10 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/190/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Finished watching at exactly here. Toucheé, world（00:03:14 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/194/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi If you puttes the time at but thanks! Happy pi day（00:03:14 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/194/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi now（00:03:14 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/194/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I feel like the small cube is screaming in pain when I hear that sound（00:03:27 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/207/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi bruh you think that i have 10 billion kilograms of mass hanging around with me?（00:03:27 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/207/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi @ just noting, (as explained in Matt's video) that the result shown here wasn't exactly a 100:1 mass ratio, and that they started at 100:1 but it didn't give 31 collisions, so they kept changing the mass of the larger object to "tune" it until they actually got a result of 31 collisions - this had to do with the fact that the problem wasn't perfectly translatable into the real world (still non-zero friction, not 100% elastic collisions, and I believe the actual biggest issue was the imperfect coefficient of restitution). In the end they used a mass ratio of 93:1 in order to get that 31 bounce footage.（00:03:41 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/221/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Was that a parker square（00:03:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/237/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi it never gets old :D（00:03:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/237/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi that parker square damn😂（00:03:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/237/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi the brief parker square was perfectly timedI really like these collaborative videos you guys make, keep it up :3!（00:03:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/237/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi - The game plan（00:03:58 - 00:05:31） https://favtu.be/timelines/v/6dTyOl1fmDo/s/238/e/331 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi @ just make an attempt. I love it!（00:03:58 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/238/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi its the parker square!!!!（00:03:58 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/238/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi UK AND US（00:04:38 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/278/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi 3Blue2Brown（00:05:12 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/312/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi - How to analyze the blocks（00:05:31 - 00:14:59） https://favtu.be/timelines/v/6dTyOl1fmDo/s/331/e/899 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi "use the defining features of the problem" do you also put in this category the fact of generaizating or restrenght the problem (opposite to "simpler version" but strangelly efficient sometime)（00:05:51 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/351/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi edit: Machine Mentioned（00:06:27 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/387/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi the ultrakill brainrot is getting to me（00:06:27 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/387/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi mildly accidental Ultrakill reference（00:06:28 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/388/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi my ultrakill brainrot is so bad i had this playing in the background and i actually had to pause and rewind when i heard him say this（00:06:28 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/388/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi （00:06:29 - 00:06:34） https://favtu.be/timelines/v/6dTyOl1fmDo/s/389/e/394 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi V1 and V2…. Is that… IS THAT AN ULTRAKILL REFERENCE?!?（00:06:29 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/389/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi ultrkill reference（00:06:29 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/389/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi ultrakill reference（00:06:34 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/394/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi at instead of 5.00. The 1 kg block velocity is also wrong. Correct values start at（00:06:42 - 00:08:13） https://favtu.be/timelines/v/6dTyOl1fmDo/s/402/e/493 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I'd also list the comparison of m1 >= m2 for the sake of simplicity - if m2 > m1 it may be too difficult to compute at this time as it's a small block pushing a big one into the wall.（00:07:09 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/429/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi ULTRAKILL reference???????（00:07:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/477/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi .（00:08:13 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/493/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi "OH MY GOD IT'S A CIRCLE!!"（00:08:37 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/517/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Not letting the square hit the wall at made me so upset. Great video though, really interesting.（00:08:45 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/525/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Why didn’t you let the square touch the wall 😭😭😭 that felt so unsatisfying（00:08:48 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/528/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Wow, wow, wow...@ min plotting the velocities! 20 year physics teacher and never seen that display. Brilliant!（00:09:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/540/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Amazing! Gosh, this is so good ❤（00:10:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/600/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi *[****]:*That would explain why the omni-directional symmetry of a circle is so powerful, as well as the fact that any triangle is one linear transformation away from being equilateral.（00:10:10 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/610/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Nobody:Math: RESPECT MAH SYMMETRY!（00:10:10 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/610/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi "and pi has everything to do with circles, relating distances around the circumference of that circle to the radius"Oops, seems you meant to say TAU here ;)Pi would be the diameter.（00:10:20 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/620/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I think my brain exploded at around when I realized the equations for x and y were used in the project currently open on the computer in front of me as I'm writing this.（00:11:10 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/670/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Hang on... if we look at the 1:1 mass case, that gives a slope of -1, meaning we go from (-1,0) to (0,-1). The mass on the right stops while the one on the left moves... so far so good.Then we jump up from (0,-1) to (0,+1) when the left mass hits the wall. But there is a 90 degree angle around the circle between each of these. So there should be a 4th point at (+1,0), following the -1 slope from (0,+1). This implies that the first digit in the 1:1 approximation should be equal to 4.Indeed, the only way the first digit can't be 4 is if the angles are a miniscule fraction above 90 degrees, such that only 3 segments can fit in the circle. But then we're saying the intercepts are (-1,0) -> (>0, -1) -> (>0, +1). But think what this implies - the right mass never goes stationary at any point, and in fact starts to move a miniscule amount to the RIGHT upon first contact with the left mass.EDIT: Best guess why I'm wrong is that, if we sum to precisely 360 degrees, that implies we can exactly equal pi with this approximation. But that implies pi is a rational number (finite length), when it is not.（00:11:26 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/686/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi That was clean（00:12:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/777/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Me, having watched þe oþer video, at_”þe sine what now?”_（00:13:50 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/830/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi half way point（00:13:51 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/831/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I'm confused. You said some momentum was lost to the wall, but the small block approached it with -1.82 and rebounded with +1.82. Where's the loss?（00:13:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/837/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi This is amazing. But I have a question for . I thought we made an assumption that no momentum went into the wall (was negligible or that our system was completely ideal) and was conserved between the two blocks. This seems to be confirmed by the graph, since the magnitude of velocity is the same for the small block after a collision with the wall. Why then does total momentum change?（00:14:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/840/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi at this moment I realized that Einstein (yeah, that guy again) shows us we put the momentum back into the wall, which is the whole universe. If we ‘zoom out a bit’, we would see our whole reference frame starts to move to the left. This makes me wonder what we would uncover if we take note the wall as our steady state of reference, but the large block?（00:14:14 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/854/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I would like to mention here that also geometrically this end zone is forced, because whenever a point lands there you cannot hit the circle again with the slope going downwards or the vertical line going upwards. So the end conditions were already baked into our geometry the way we created it. I suppose you also show this at（00:14:20 - 00:18:20） https://favtu.be/timelines/v/6dTyOl1fmDo/s/860/e/1100 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi There's a programming technique for making collisions(I forgot the name of),similar to the figure generated in , Is there any connections to this study and that programming technique（00:14:43 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/883/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi - The geometry puzzle（00:14:59 - 00:20:05） https://favtu.be/timelines/v/6dTyOl1fmDo/s/899/e/1205 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi @ Strange that the longer the slope line, the faster the small block is hitting.（00:15:20 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/920/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi That just sounds to me like you're missing a dimension. Like you went off the Eastern end of the map and you popped up on the Western side, only because you were moving on a 3D sphere and not on a 2D map. So this circle is probably the projection of a sphere, maybe.（00:15:20 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/920/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Wow, thath's trippy!（00:15:40 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/940/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Having seen this I now realise there's easier ways to draw circles in graphics 😅（00:15:45 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/945/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Around , it became apparent to me where the Pi comes from. It's basically like the infinitesimal slices used in building an integral, except instead of working with areas, it's lengths.（00:16:25 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/985/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi in the video. Cool to consider and makes me imagine what similar math is computed in modeling / rendering software programs when adjusting your cameras viewpoint to your（00:16:32 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/992/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi It can be proved easier. The vertical lines are parallel, therefore the vertically-opposite arcs have the same length. Also, the sloped lines are parallel, therefore the sloppy-opposite arcs have the same length. That is, each arc is equal to 2 opposite arcs: the vertically opposite and the sloppy-opposite. Because it applies to all the arcs and they are contiguous, all of them are equal to each other.（00:16:35 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/995/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi cue Circle of Thales as a special case of this.（00:17:07 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1027/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I do not know if it’s true but maybe drawing parallel lines crossing the circle can also explain why the length of the arcs is always the same ?（00:17:38 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1058/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi , but to me it feels a bit more obfuscated there.（00:18:20 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1100/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi collisions? edit: I can see the answer at（00:18:22 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1102/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi OMG this update help me to understand truelly/deeply why it's related to pi ! thanks you !（00:18:50 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1130/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I know pi has infinite digits, so setting something to <= pi wouldn't matter in actuality, but couldn't this expression *technically* be equal to pi?（00:18:58 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1138/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi -（00:19:51 - 00:20:00） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1191/e/1200 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi this is the exact moment when he knws we dont understand shi1 about what he's saying（00:19:51 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1191/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I love that the navy π creature goes from delighted to angry when it is revealed that he was wrong at（00:19:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1197/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi i like how the pi creature got mad when he was told he was wrong（00:19:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1197/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi lil blue pi bro be mad 😂（00:20:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1200/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi - Small angle approximations（00:20:05 - 00:25:00） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1205/e/1500 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi What is slope? Baby don't curve me, don't curve me, no more（00:20:17 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1217/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi lol, this has been mentioned under your previous video, no, just because arctan(10^-k) ≈ 10^-k does not at all imply floor(π / (10^-k)) = floor(π / artcan(10^-k)), effectively it's saying "the interval [π / 10^(-k), π / arctan(10^-k)] doesn't contain any integers just because its length is tiny" it might as well be that for any k it doesn't and I'd assume it's probably the case, but it is a non-trivial fact about the number π, but it'd be honest to a) mention this caveat once you know about it b) give some context on whethere this has actually been proven or that it's an open problem or whatever is this the status of this statement（00:21:21 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1281/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi sir you could simply say as n increases (0.1)^n gets smaller and approximation of arctanx=x becomes better and thus error reduces and for equal masses ie n=0 , we verified ourselves thus for next values of n we obviously wouldn't get any error（00:21:39 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1299/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi @@babyeatingpsychopath *（00:21:53 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1313/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi okay this law is actually so good though 😭😭😭（00:21:54 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1314/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I laughed out loud; the delivery is PERFECT.（00:21:55 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1315/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi the small angle law - so true 😂（00:21:56 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1316/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Knowing all of this, let's look back at . Using the meaning of the tangent function that I've given here, we can come up with an alternative geometric view to the one shown in the video. When we look at that small angle measure θ on the unit circle, we can draw the line segment representing the value of tan(θ). To sum up, this line segment:（00:22:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1320/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Ooh, I never ever miss an opportunity to bring up what I'm about to say.（00:22:00 - 00:22:00） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1320/e/1320 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi im not a math person, and maybe this is a dumb thing to say, but if you have the arctan and the tan, wouldn't you not need to approximate? since it looks like the original line is directly in between the two all the way through, so couldn't you just average the two of them to get the original line?（00:22:02 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1322/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I feel like there is even a more visual geometric reason: since the tangent is also the lenght of a line tangent to the circle between the horizontal line and the prolongation of the radius you can see how for small angles it's very close to the arc length（00:22:03 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1323/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi I think it is related to one of Taylor sequence formulas for Pi. Edit: Wrote this before watching to（00:23:40 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1420/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Isn't that exactly the caveat he talks about starting at ? If π / 10^(-k) is smaller than and sufficiently close to an integer (the decimal expansion contains enough 9s in a row behind the decimal point), then the interval you're talking about does contain an integer and the number of collisions does not match the digits of π. That's what he's talking about, right? He explicitly states that this is an open problem. Did you not watch the full video before commenting this?（00:23:49 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1429/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Interestingly, when I was young and learned about the existence of statements that are true but not provable, I thought up an example of something that would very likely fall into this category (though of course not provably so): the statement that the decimal expansion of pi, some finite initial (and non empty) sequence of digits would repeat itself identically immediately after its first occurrence (after which it must at some point start non-repeating, since pi is not rational). I never imagined such a statement would be of any use, yet it comes eerily close to the condition mentioned at in this video! (But the way, it would seem you need about twice the number of digits 9 in order to risk breaking the pattern of digits, and even then it would not seem a necessary and sufficient condition.)（00:23:58 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1438/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Can someone explain the argument in with the nines?（00:24:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1440/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi sorry a naïve question: if, starting from any given digit, all the digits of pi were 9, wouldn't be pi rational (which is not)?（00:24:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1440/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi At whenever I see pi written out I pause and check.In high school (over 40 years ago) I had a contest with a friend to see who could memorize the most digits of pi over a weekend.I memorized 100 digits and went back to school confident in a victory. He had memorized 250. (Hello Ed!). It was a good experience, I like to stay humble.But I still have my 100 digits memorized and checked Grant's approximation. Everything is square: Grant's digits were correct!（00:24:01 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1441/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi but pi is infinite right? So there has to be a point where there is a sequence of 9ns is as large as the numbers that come before?（00:24:05 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1445/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Dear Grant, thanks for the great work! When trying to derive for myself the condition for the accumulated error to really make a difference in our counting process, I think it shall be more strict here: Consider the first (2n+1) consecutive digits of pi, if the last n of them are all 9s, we’ll get the off-by-one error. The condition shown in the video is more loose thus would not necessarily guarantee an error.（00:24:09 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1449/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Just imagine the expression on the first people to discover the run of nines in pi that eventually takes up half the known digits of pi. After the start of seemingly endless nines, an algorith for determining if the next specific length of digits is all nines. And so the known number of digits soon doubles as larger and larger runs are checked one after another, all returning with a sequence of nines. Mathematicians around the world are deeply disturbed by this discovery, some form new doomsday religions. However there are no consequences for wider science and technology, let alone society overall.（00:24:14 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1454/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi the worst part of this is that because of the nature of Infinity, this scenario does exist. 😭（00:24:17 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1457/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Just for context, a string of nine 9s (999999999) occurs at position 590,331,982 and the next one at 640,787,382.（00:24:18 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1458/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi when the newly introduced vertical line of the cubes shows in this animation, it is almost as if you are observing the cubes from a camera panning around them - rotating in a circle around the cubes at a distance that appears to be equal to the segment of the circumference of the circle that was calculated earlier at 3D model or that of a video game character in a game.（00:24:34 - 00:16:32） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1474/e/992 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi 🔍 “The fact that a simple physical system like colliding blocks can reveal something as profound as π is just mind-blowing. It's a beautiful reminder that math isn't just numbers — it's hidden in the motion, rhythm, and laws of our universe.” 🧠💥（00:24:40 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1480/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi . We can fiddle around with it in order to determine the number of collisions in the experiment; indeed, the video contains a formula to do so at . So what if we make the number of collisions 10, and then 100, and then 1,000? Nothing's stopping us from doing that. As we continue, we get the decimal expansion of the number 1. This still follows the reasoning present in your comment: at each iteration, the number of collisions increases by a finite amount, the angle of the end zone decreases by a finite amount, and we get more and more digits as we go further and further. But the special thing about an irrational number's decimal expansion isn't just that it goes on forever, which we've already established doesn't mean anything; it's that it goes on forever without ever entering an infinitely repeating loop.（00:24:41 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1481/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi He does briefly talk about other bases at . Whenever the larger block is (b²)^n times the mass of the smaller block, you get the first n digits of π in base b. There is nothing special about base ten（00:24:46 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1486/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi technically because one hundred is just your base number squared this is something special about 100（00:24:50 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1490/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi EDIT:（00:24:52 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1492/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi NO WAY i actually got my question from SIX YEARS AGO answered（00:24:57 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1497/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi i was wondering if it worked in other bases.（00:24:58 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1498/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi - The value of pure puzzles（00:25:00 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1500/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi "I just wanna leave you with one point".（00:26:45 - 00:26:47） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1605/e/1607 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Yes, I got a point!（00:26:46 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1606/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi , the point in question:（00:26:47 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1607/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi Langlands Program（00:27:07 - 00:27:43） https://favtu.be/timelines/v/6dTyOl1fmDo/s/1627/e/1663 Fri, 14 Mar 25 00:36:52 +0900 There's more to those colliding blocks that compute pi