How Fast Could a Computer Be?

In theory, a 1-kilogram computer could process no more than 1.36 × 10⁵⁰ bits per second. This is Bremermann's limit: a limit on the maximum rate at which computers can process information. But where does the limit come from? And are there computations that are still impractical, even for a computer that could reach the limit?
This video is part of the MegaFavNumbers video series.
***
#MegaFavNumbers
***
Spanning Tree is an educational video series about computer science and mathematics. See more at spanningtree.me
To be notified when a new video is released, sign up for the Spanning Tree mailing list at spanningtree.substack.com/
Spanning Tree is created by Brian Yu. brianyu.me/
Email me at [e-mail] to suggest a future topic.
***
Earth texture: www.solarsystemscope.com/text...

[@singingbanana]

This is great.

[@SpanningTree]

Thank you!

[@echometerain]

omg james grime

[@azfarahsan]

the legend himself

[@Rudxain]

*James Prime*

[@sanjarcode]

The second take away is that algorithm design matters, even if you have all the things in the universe.

[@torak456]

It would be interesting to have included the mass of our current best computers (maybe a single silicon die) and then compare it to it’s actual output (a tricky proposition to say the least, since we don’t normally measure in bits per second, but instead in operations per second).

[@asailijhijr]

Operations are usually performed on words, groups of contiguous bytes. 32-bit processors usually have 4-byte words; 64-bit processors usually have 8-byte words. And many modern machines have multiple cores or multiple processors operating simultaneously.

[@oblivion_2852]

Assuming perfect pipelining avx2 (512 bit wide registers) and 92 cores (max server grade socket) at 5Ghz~. A max grade modern cpu can do about 235 trillion bits per second. 2.35*10^14

[@oblivion_2852]

Obviously in practice these rates are never reached... Usually most modern devices are limited by memory/branch prediction and prefetching. But that's the upper bound of modern cpus. Gpus you'd have to ask someone else. Idk what the register sizes are in the thousands of cuda cores across x ghz (plus you gotta consider what the scheduling frequency is).

[@makuru_dd3662]

@@oblivion_2852 well on GPUs, numbers like tera flops are advertised, so you could calculate it with a bit effort and finding the weight of the die.

[@oblivion_2852]

@@makuru_dd3662 The issue is that pcie gen 4 has a max limit of 2 gigabytes per second - 16 gigabits.

[@_abdul]

Not only I'm loving this MegaFevNumber challenge, also this is helping me find great creaters like you. Great Video Sir. I'm going to Bing Watch your other videos.

[@SpanningTree]

Thanks, glad you enjoyed!

[@anushkajaiswal3999]

How are you so good at explaining! I m amazed . I have shared it to my friends. Please keep going , Thanks Brian .

[@electrocubic5116]

6:12 Well, that escalated quickly... 💀

[@jibachhyadav7241]

So beautifully explained! Thank You

[@gt3293]

So could a quantum computer, using the properties of quantum physics to calculate all possible solutions to 512 bit keys and finding the answer by "selecting" the right one when viewed, pass this limit?

[@SpanningTree]

Quantum computing algorithms do have the potential to perform computations more quickly - but trying all possible 512 bit keys still isn't instantaneous. For something like a brute-force attack, the optimal quantum solution is found in Grover's algorithm, which, if there are N possible values to try, can identify the right one in √N (square root of N) time.

[@MrIndomit]

so it is practically only halves th exponent?

[@christianbarnay2499]

This is an absolute upper bound to all physically possible computations based on maximum available energy. This is the computational power you would get if you found a way to instantaneously vaporize the entire observable universe (including your own body) into pure energy and use 100% of that energy to compute data (with no physical support and nobody to read the result since you have vaporized absolutely everything and everyone). The real practical limit of current computers is several orders of magnitude lower than that. Quantum computing may only improve the practical limit of actual computers by exploiting more of the available energy. But they are still limited to using energy that exists in the universe. The Bremermann's limit is absolutely unreachable because we will always need to keep some physical assets in the universe that are not dedicated to pure computing energy, mainly ourselves, everything that we need to stay alive, and something that can channel energy into computing, so that we can input the data and program, do the computation and read the result. The only way to increase that absolute limit would be some huge breakthrough in our understanding of physics laws that would increase the size of the observable universe or reduce the Planck's constant.

[@DallinBackstrom]

​@@christianbarnay2499 That's not correct-- for a quantum computer, their advantage is not that they can "exploit more energy". Rather, they exploit the unique properties of quantum states, which allows information to be processed in a way which is, fundamentally, dissimilar from bits in a traditional computer. To put it another way, the quantum computer does not preform more computations in the same span of time: rather, it solves the same problem with a smaller number of computations.

[@christianbarnay2499]

@@DallinBackstrom The way of processing is different. I agree. But the quantum computer can only process this way because it uses high levels of energy that allow for manipulating quantum states at a subatomic level. Those tiny invisible particles won't work for free. You will compute thousands of similar operations in parallel on thousands of different initial states but at the cost of consuming proportionally more energy to set the initial states, do the operations, read the final states, and also shield everything from external interferences. Because quantum computing is very sensitive to any minor disturbance. A quantum computer as efficient as it can be will never be faster than its own power supply.

[@oelboy]

So the answer is basically "yes, because the universe is finite"

[@anushkajaiswal3999]

Hello Mr. Brian, Happy teachers day, Thanks for your videos, they help a lot.

[@wayneyam1262]

nice one, subbed!

[@costrio]

Another unique take on the universe. I like it.

[@AcunPearce]

This is very well made. I love this video 😍

[@ananttiwari1337]

This was honestly such a cool video!!

[@technorazor976]

6:13 Binary to ASCII -> "Bremermann's Limit defines a limit on the speed of computations." I'm surprised that's exactly 64 characters (512 bits) long.

[@csskevin]

Great video! Would be really interesting to have another video with how fast quantum computers could be.

[@crewrangergaming9582]

this channel is going to blow out soon

[@MatthewOBrien314]

Really nice video! Can you please double check, at 6:10 you said 4.2e71 years was 3 times the age of the universe. I thought the universe was only 13.8 billion years old.

[@rosskrt]

You’re right. If he got right the 4.2e71 years, then it’s more or less 1e60 times the age of the universe

[@KingJellyfishII]

"at least 3 times the age of the universe" well, technically 1e60 is _at least_ 3

[@kovanovsky2233]

@@KingJellyfishII r/technicallythetruth 😂

[@chickennuggetman2593]

aw man, i really wanted to witness every possible game of chess in my lifetime 😢

[@MogaTange]

God finally relieved that he knows where to put the last digit of pi, knowing that there’s no way we’ll ever find it

[@londislagerhound]

How did I not discover this channel ages ago? KZbin, your algorithm really should have sorted this.

[@pingnick]

Nice channel! Thanks!!🤯

[@E-dart]

Imagine cooling that

[@electrocubic5116]

Lol, if *that* sort of computer ever existed, it will release more energy than the total energy released by every star in the universe combined, seeing which we would probably be *toast* by now.

[@VieleDominoes]

Wow very interesting

[@vaakdemandante8772]

Not to mention that the theoretical limit due to maximum energy density would create a black hole ;) Perfect video that gives a sense of scale to our current achievements and better view on how much more we can progress in the future!

[@isableye7164]

Chrome: finally a worthy opponent.

[@adb012]

Quantum computer: Hold my beer.

[@lightning_11]

6:26 "But there is a limit that means certain kinds of computations will never be practical..." Quantum Computing: I'm about to end this man's whole career!

[@tokomnyori6730]

Hello Brian, Your student here from cs50x. You're a great!

[@MrEdrum]

The problem I have with this, is that the mass of the computer is used to calculate the energy of the information that can be processed. Because: If you have a computer that weighs 1kg and you process so much information, that the Energy used is equivalent to the Energy calculated by E = mc^2 Then the weight during the calculation would be 2kg. What E = mc^2 is calculating is not the anount of Energy that can be processed, but the amount of energy you would get, if it was able to convert all the matter (thus the computer itself) into energy. I might be missing something here, and if so, please correct me, but I don't see the connection between the weight of the computer and the amount of energy that can be used.

[@MrEdrum]

What would make more sense (and maybe that's how it's meant?) to use the formula to calculate how much Energy you could use for information processing, if you assume the computers itself had no mass (Basically converting all the mass in the universe into energy and see how many bits that could represent) But first it will probably never be possible to convert all mass into energy (except for if there is as much antimatter as matter in the universe) And second, a computer without mass will not be possible. I'd assume that every atom could at most be used to process a single bit at a time, and the speed, how many bits can be processed in series would be limited by some physical process, like for example the excitation of an atom.

[@wemela]

In my perception, the calculations have a fundamental flow. Because if you turn the mass into energy, apart from having a physically impossible way to get this heat out, also the entire ‘computer’ has been turned into energy to compute. This means that after the hypothetical second, there is no ‘computer’ left. That means that instead of ‘bits per second’, I argue that this limit is more about ‘processed bits’, as an absolute maximum. No matter how long it takes you to compute these.

[@thedelanyo]

Does this also apply to Quantum Computers?

[@hargunbeersingh8918]

you gained a sub :)

[@hifijohn]

One way to make a computer faster is to make software simpler especially the OS.

[@SlimThrull]

That doesn't make the computer any faster, per se. It just means the computer has to do less calculations per second.

[@hifijohn]

@@SlimThrull Yea and having the computer do less calculations per second means the program runs faster, thats why I still use some programs from my win98 days.

[@SlimThrull]

@@hifijohn The program will run faster because the computer is doing less work. But it doesn't make the computer calculate any faster. The computer is calculating at the same speed; It's just calculating less over all.

[@mohamedcherif9878]

Brian you're a great one ! we need more videos if possible about javascript

[@albertosierraalta3223]

But what is your favorite number in all of this?. Also a little correction 10^71years is not 3 times the age of the universe, more like 3*10^61 times the age of the universe

[@drag0vien289]

"That would take *at least* 3 times the age of the universe." He's technically correct.

[@albertosierraalta3223]

@@drag0vien289 Actually I think it's not correct. When you say "at least" you're referring to the minimum that it's possible, so in 3 times the age of the universe the computer wouldn' have done the calculation. At least in 3×10^61 times the age of the universe or more it would be finished

[@SocietyIsCollapsing]

He's not that far off lol. Also, what a nonsense video. I'm into computers and numbers but this is a stretch.

[@Zooiest]

@@albertosierraalta3223 "at least" is a simple assertion that some x ≥ some y. Even if x can't be as low as y, the statement still holds. In fact, asserting that it can't be that low actually _proves_ the statement to be true, assuming that the assertion is also true.

[@michaczerw7510]

Does this apply to a quantum computer?

[@MindJoBizness]

Who would win? A Universe sized computer operating at maximum theoretical efficiency < one Chess-y boi

[@sethapex9670]

So if the universe is a simulation run on a computer within another universe, that universe would need to have different laws of physics, like a faster speed of light?

[@loc4725]

Not necessarily. If the suggested simulation computer wasn't very fast how would you know? Your perception of time would be part of the simulation; all the computer would need to do is ensure everything appeared to happen 'on time'.

[@Eniac42]

The speed of light is everywhere

[@Pheonix1328]

You could get around this limit if you built the computer in a universe where time moves much much faster ;P

[@H3Vtux]

Still not good enough to run Crysis on max settings.

[@londislagerhound]

10 to the power of 53 kilograms doesn't seem very heavy for an entire universe. Great video though.

[@electrocubic5116]

Yeah, same. I thought of *atleast* 10^(100) or more.

[@Guust_Flater]

@1:33 That number is the same as the number of atoms of the earth....

[@sagargaikwad8604]

New direction to think

[@therustynovel7911]

Man, how many digits of pi do you think a computer the mass of our universe could calculate?

[@electrocubic5116]

It's a non terminating, non repeating irrational number, so yeah, it's never going to be able to calculate every single digit of Pi, an amount which is *far* greater than the total possible games of chess.

[@yash1152]

4:30 hmm, interesting to see 10^53 here. i read it somewhere that ancient indian text had a name for 10^53. so, found it interesting to see its use here. (ai'nt saying that it's related to that or anyth)

[@DrGraaff]

Use this galaxy computer to divide by zero!

[@asailijhijr]

And quantum computing doesn't break these physical limits?

[@emperorpalpatine4127]

thats all well and good but can it play crysis?

[@snozking]

what would be the power consumption

[@costrio]

When I'm adding numbers, I'm a half-fast computer, myself, I think. ;)

[@cate01a]

are quantum computers a unique case though since they use fancy weird shit where they can like sorta see every combination at once?

[@devrim-oguz]

Photons also have polarization which could encode more information. Also there could be other properties exploited. This doesn't make sense.

[@angelmarques3124]

Does this apply to quantum computers?

[@oblivion_2852]

Doesn't the possible states of a system rise exponentially with quantum entangled bits?

[@yashmehta9299]

* for a digital classical computer

[@elpsykongr00]

Mining - exists Miners: 4:44

[@kdakan]

Unless quantum computing is advanced enough for practical use, which is estimated to be coming in 2 or 3 decades.

[@ernesto.iglesias]

Does anyone know if the same limit aplies to quantum computer?

[@loc4725]

Yes, quantum computers are just extremely efficient at solving certain problems due to the way they work.

[@mrmr1993]

Bremermann's limit seems ill-thought-out. Why only consider the rest mass as potential energy for computation? There's also energy in electrical charge, heat, etc. that's completely missing from the calculation.

[@jabjab12]

Quantum computer is saying hi

[@marc_frank]

10^75 bits/s for 4.543 billion years to calculate 42

[@AndrewJens]

This is actually a significant downer.

[@de_oScar]

fun fact: that 1.3564… is actually e/2

[@RaphBJ]

But can it run crysis?

[@Rickety3263]

I think thats 24.9 billion KwH per second. I don’t want that electric bill! Thats like $3.5 Billion per second. Thats 25 million megawatts… so 5 full nuclear reactor plants dedicated to a single 1kg computer. Ha.

[@joasb6315]

Isn't using the Einstein equation kind of misleading here? Is it like saying if you have 1kg of fuel, how much data can you process with that amount of energy with it also consuming that 1kg?

[@bob456fk6]

This is going to keep Bill Gates up at night figuring out how Windows can be "enhanced" to eat up this speed advantage. It may take a while, but he will do it.

[@HoD999x]

i don't understand why mc²/h gives you the number of bits.

[@fredthechamp3475]

I predict this will get a lot of views in the next couple of days.

[@zekejanczewski7275]

Hmm ... IDK.. you kind of just assuked that the frequency of light was the fastest. I feel like there could be a much higher upper bound for most computations. The speed of light is basically just the speed of causality. This is more of a bottleneck, not a throughput. Let's assume the computer just needed to flip one bit back and forth. If you had a spotlight on the moon, you could easily make a shadow that moves faster than light across the surface. It's just that the shadow itself would take ~a second to arrive. You could make a fan with arbitrarily number of fine blades, and put a detector on the moon that could switch on or off as fast as you'd like. Yeah, at a certian point the fan would block all but the highest frequency light, but we can use a particle that travels close to the speed of light that doesn't have this problem

[@VigyanJagat]

isn’t there a flaw that you have converted the computer mass to energy ? This does not really make sense. Also if computer is converted to energy, what will Do the calculations?

[@timonix2]

I like the universe computer. Create 2^N separate universes trying one key each. Destroy Every universe the key doesn't work in. Boom a O(1) algoritm for a N bit key.

[@novmoon5724]

Ooops, too tough to me!

[@seriouslee4119]

Unless we can prove p = np

[@mr.cauliflower3536]

The assumption that a computer is a turing machine (each cell can hold only one value at a time) restricts the speed of brute-forcing security keys, since quantum computer can do it faster.

[@Rickety3263]

How much power would the 1kg computer draw?

[@Rickety3263]

What is the electric bill for 8.99 x 10^16 J /s per month?

[@electrocubic5116]

Probably *a lot*

[@samkonstan2333]

okay, but how fast could the computer be if it were moving at 0.95c?

[@ParthPrasharsb]

But will it run cyberpunk at 69fps??

[@charlescox290]

I don't understand why use E=mc2. That would be coverting the whole mass to energy, after which there is no more computer. I don't know if any modern computer that coverts any of it's mass to energy to compute. Who peer reviewed Bremerman's work and thought it was a good idea?

[@PerMortensen]

It's just to put an absolute upper limit. Sure, you couldn't have an actual computer that would work like that, but that's not the point. The point is that we can absolutely guarantee that it's impossible to have a computer that performs better than that.

[@charlescox290]

@@PerMortensen I don't see how that's an upper limit, as modern computers convert non of their mass to energy to compute. Based on the E=mc2 formulation that makes modern computers more that 100% efficient.

[@darken2902]

@@charlescox290 Bremermann limits measure what is the maximum amount of computation that you can have with a given mass, with e=mc^2 then we can replace the mass with energy so if you give 10^17 joules to a computer you would get 10^50 bits in exchange. The mass in the equation doesn't have to be the mass of the computer it could be the mass of an object that you will convert into pure energy and giving to your computer.

[@charlescox290]

@@darken2902 but modern computers don't work like that. They don't convert mass to computational energy. If that were they case we would need to get a new phone every day because it would be gone by the end of the day. I understand what the formula did, but it doesn't model the real world.

[@LURTZcz]

I just found out that my PC is very suboptimal 😢

[@kaddasixseven3581]

This is so abstract that it no longer makes sense.

[@patahgaming]

cool but can it run doom?

[@ixion2001kx76]

Of course, that’s for non-quantum computers.

[@anatolesokol]

It's true only for not using a quantum computer.. if you do use one, then it's probably will be false or true and false at same time, but you got your answer anyway. The mistake here is to assume energy must be used for any calculation, but in reality a mass of 1 kg may is still process all it's internal movements of atoms without any energy costs for any amount of time.

[@maixicek]

Like of course there is limit right :D

[@kales901]

if normal chess takes 2 billion years with ba computer the mass of the universe,imagine how long it would take to anilize all faire chess peices...

[@jolex_nerd8132]

all this possible computing power, and we still cant find who asked.

[@justarandomwoof2247]

Put the computer in a black hole so that it doesn't take any space. Such is the WYS? solution. Also I know it's unpractical. It's just a fictional solution in a fictional universe.

[@handlesrtwitterdontbelivethem]

snots of hicis

[@yepee1]

While the speed at which a computer can manipulate processable units may be limited, I believe that we can still improve the total throughput of information. Bits represent 2^n distinct states, whereas qbits can represent 3^n distinct states, where 'n' is the number of processable units. It's like an engine; without increasing the mass, size, or speed of the engine, you can still obtain more horsepower by using a more explosive fuel. Even though there will be a limit to the speed at which a computer can manipulate each processable unit, this does not limit the amount of distinct states a single processable unit can represent.

[@supergsx]

E =mc² has nothing to do with this.

[@sergiokorochinsky49]

This is an example of "fractal stupidity": it is stupid at every level.

[@Yash42189]

Why are using the mc^2 energy of the computer? Arent we plugging it into a socket or smth? Also how are you using the internal energy of the computer without destroying it?

[@progamer36]

relax bro everything is hypothetical.

[@Yash42189]

@@progamer36 hypothetical didn't include the absurd and physically impossible last time i checked

[@progamer36]

@@Yash42189 by 1 kg of computer he meant the whole 1kg is a 100% efficient computer. And you talking about plugging it into a socket like are you a kid or something?

[@Vrishnaakh]

Yeah this video seems to make no sense.

[@technorazor976]

... until we delve into quantum computing.

[@christianbarnay2499]

Bremermann's limit is the equivalent of the speed of light for computing speed. This is an absolute and unreachable physical limit. Quantum computing is the equivalent of replacing the petrol engine in your car with a nuclear fusion core. It allows you to go faster but you're still way way slower than the absolute limit.

[@technorazor976]

​@@christianbarnay2499 That's fair, I'm not sure why I thought it would be different. Though at the same time, quantum computing algorithms are orders of magnitude faster than regular algorithms, so the way we're thinking about computer speed would probably change. Who knows, maybe one day we _will_ be able to analyze every possible game of chess in one way or another.

[@christianbarnay2499]

@@technorazor976 This analysis already tells us that the only way to analyze every possible game of chess is to find some method to efficiently classify all chess games into a small set of categories. So that we only need to analyze one game in each category and immediately get the result for all games in the same category with no extra computation. That's all the reason for the various strategies of position evaluation and pattern finding.

[@technorazor976]

​@@christianbarnay2499 Makes sense. I'll stay quiet now, I don't know enough about quantum computing or chess to say anything.

[@christianbarnay2499]

@@technorazor976 Please don't feel low. We all improve our knowledge by discussing with others. Sometimes you learn something, sometimes I learn something. Sometimes I think I know something and someone proves me wrong. I have myself been in that position in several occasions. The concept of absolute physical limitations is not so easy to tackle when we live in a world where fiction, bad journalist wording and badly rendered science tend to let us think that some day in the future it could be possible to travel faster than light. And quantum physics is often described as some magical trickery that could break the laws of physics. There are no stupid questions.There are only stupid people who think there are stupid questions.

[@v.f.38]

Add AI to the equation and voilà.

[@gollolocura]

so it's like 1000 googols of computer processing power. How dissapointing.

[@fulla1]

So, what actually IS your MegaFavNumber? (Annoying background music btw....)

[@novmoon5760]

Could not understand it!

[@fdhu9sfsnifs]

This is a bad aproximation, too far from reality