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420

It's a small world (after all) - May 25, 2011
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Spiked Math Comic - It's a small world (after all)


Thanks to MT for posting a link that motivated the above comic.


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125 Comments

Regarding question 4. The number of times you can watch yourself recursively cannot be determined, so.. it wouldn't be a finite number after all

There will be a moment when the deepest you will occupy less than a pixel, so at some point this would fall into one scene already seen.

This xkcd might be relevant to this idea: http://xkcd.com/878/

But this is something different that could have happened in real life, while being represented in the box the same was as a different event. So the number of ways you could live your life is not confined to the finite videos in the box.

How many atoms are there in the universe. I suspect your box of of videos has more entries than there are atoms in the universe.

I'm also fascinated by how hard it would be to find *anything* in this box that was distinguishable from noise, yet the box contains everything.

from http://en.wikipedia.org/wiki/Observable_universe:

4.1 × 10^34 cubic light years in the observable universe. It has about 3 to 100 × 10^22 stars. Two approximate calculations give the number of atoms in the observable universe to be close to 10^80. Which is infinitesimal compared to the number of possible videos.

@Sednus - eventually one of the "you"'s you are watching degrades to less than a pixel and disappears, at which point the next you watching a series of you watchings becomes just like the last, unless you shift something else in the images, in which case you just delay the inevitable.

Just a note, the box only contains videos with an integer number of seconds. To get all possible videos, you would have to change it a bit. For example, no 3700005 frame videos are in the box.

But all of those length videos would be in the box, with the remainder of the final second going black. or white, or any other color, or to static (lots of those!). In fact, there would be videos with only 1.365 seconds of "real" material, followed by nearly 1000 years of black, or... (you get the idea, I hope)

touche

CD-quality audio, and movies, usually have stereo sound.
You're gonna need a bigger box.

I wouldn't worry too much about this crazy man with a box. . .

Besides. . .

I hear it's bigger on the inside.

I love the dr.who refrence

This is a great mathematical concept and a fun idea, but I disagree with the statement that the number of ways you can live your life is finite. Although a discrete system such as digital video and audio can simulate a visual and auditory experience beyond apparent noticeability (usually defined by the ability to distinguish between two samples), one's consciousness is a result of continuously defined positions and states of subatomic particles.

A photoreceptor cell is located at any continuous position on the surface of the retina, so any infinitesimal change of position of a viewed object may cause an infinitesimal change of a chemical amount released, delay of an electric pulse produced, or the state of a neuron in the brain. Because of this, an infinite number of external possibilities is required to account for every possibility of internal states.

To reproduce a perfect representation of an experience which precisely aligns each molecule in the brain to trigger the exact thoughts during that unique experience, a video recording with an infinite image resolution, infinite frame rate, and an infinite audio bit rate would be required to achieve this. Thus, the number of ways you can live your life is infinite.

As a matter of fact, a lot of physicists (I am not one, just a math student living with a physicist) could tell you that distance as well as time is actually discrete... and thus making only a finite amount of locations for the photoreceptor cell possible, as well as a finite amount of choices (only once per "time unit"). Though these smallest units are of course extremely small, they are still finite.

As a physicist, I can tell you that there is no evidence whatsoever that time and length are discrete. Even though that is the case in some theories, these have not been verified by experiment and remain speculative.

Even if space and time are continuous, you must admit that the number of distinguishable combinations is finite.

A change of 1/100^100^100^100^100^100^100^100^100^100 will be absolutely indistinguishable.

This argument is derived from the section Finite Possibilities in the chapter Endless Doppelgängers from Brian Greene's The Hidden Reality.

Forgot the unit to the very small number, but just put seconds or inches...

Zeno of Elea.

So, you mean Keanu Reaves and Tom Hanks actually have potential for good acting? Sorry, but 44100 samples per second and 10 million colors per pixel STILL can't capture THAT!

Oh, and with the audio data, what about stereo? Surround? 5.1?

No. It just produces every possible video. Keanu and Tom Hanks acting well is not possible, so it wouldn't be on the box.

'Fraid that's not so. The box contains videos of, say, _African_Queen_ (or any other movie) where Keanu Reeves acts exactly as himself--but also one where he acts exactly as Humphrey Bogart did! (Also, exactly as Katharine Hepburn did--Eeeewww!)

Just curious and did a calculation.
The actual sum is of the order 10^(4.19*10^18)

Thanks, been too lazy to figure out how one might calculate it.

your right in that this would produce every possible image for a video of s seconds. but to make it a seemless movie, the subset of images actually a part of that movie would have to be teased out the mess of every possible image and placed in the proper order. It can be done, but it makes the huge number above an even bigger (yet still finite) number. its still interesting, but the magnitude of that large number is too big for my mind to think about, its easier to say that its close to infinity.

In fact, the process of teasing out sensible 'movies' from the overwhelming volume of pure noise inside the box of which you speak is not one of increasing the number of possibilities in the box, but one of removing most of them, leaving only the ones which seem to make some sort of sense. Remember, according to the 'theorem' every possible set of image/sound of any size 0s to 1000 yrs that can be displayed by the TV is already in there.

And no, there's no such thing as a finite number that's 'closer' to infinity. Sorry. It's one of those brain busting things about math: A ridiculously gargantuan number like the above is in fact still infinitely smaller than infinity, by the definition of infinity. /troll.

This is something I've often thought about myself, though I never extended it to video, just photos. Your collection would contain not only video of everything that has ever existed and will ever exist, but everything that could ever possibly exist - as well as things that can't possibly exist - from every possible angle, in every possible configuration, in every possible lighting, etc...

Somewhere in there is footage of your entire life as seen through your eyes, including the stuff that hasn't happened yet. Somewhere in there is a video showing exactly how the dinosaurs died. Somewhere in there is a video which is just a lot of still text frames revealing every piece of information ever. Every top secret file that will ever exist, every mathematical constant and formula that will ever be discovered, every password to everything ever.

HOWEVER.

All of this will be pretty useless to you. Why? Because along with all that real footage and information will be a practically endless stream of fakes.
Somewhere in there is a very realistic video of the dinosaurs being killed by UFOs. Somewhere in there is footage of your entire life as seen through your eyes, except after 48 years it diverges from reality and shows a completely different scenario than what really happens. Somewhere in there is every piece of information, every mathematical constant, every password - but they're all completely wrong. And there are an unimaginable number of these incorrect versions.

And you'd be lucky to even find one of those, because nearly every single video in that box is going to be nothing but static; an hours/days/years-long jumble of random pixels and noise.

Still, it's pretty fun to think about.

That thought gave me some chill moment, but I think I got an idea for some sci-fi short story. Thanks!

Check out Borges' Library of Babylon

Regards the possibility of discerning meaningful content from meaningless static noise. There might exist a finite fractal-like formula or index that could easily allow one to arrive at arbitrary yet meaningful videos. We know that static noise is at least mathematically distinct from a regular image, there might be ways to use that to select videos.

Oh, and if anyone wanted to actually try to calculate some of these insane numbers, some things you might want to take into account:
-DVDs often use 48khz audio.
-A pixel can generally display 224 different colours - each has a red, green and blue component which can each display 256 different shades.
-"Even fewer pixels". :p

This is wonderful! After hours of studying, this cheered me up by the end of the second panel. Thank you! [=

What about deaf and blind people (i.e. people who are both)? Are all their lives the same? Or just blind people: does anything they do that is not audible count?

More practically, what happens if at some point something happens in your life that makes no difference to you visually or audibly? Pressing buttons without looking at them?

Essentially: lives can't be defined purely by what you see and hear, there are multiple lives with the same audio and visuals, and legitimately different content.

I'd think there are limits on what we can discern with all senses (putting your hand in 100 degree celcius water is going to feel pretty much the same as in 100.0000001 degree water), so if that research has been done into those limits (I don't know if it has), that information could be applied, and there would still be a finite number of discernibly different lives one could live.

I would say the real result is that all the video recordings of all the ways of living your lives, assuming you live less than 1000 years or so, can be partitioned into a finite number of sets (equivalence classes), such that any two recordings in the same set are indistinguishable by an average human.

I don't think this implies that the number of ways of living your life (even assuming the time constraint, breaking which does not require immortality, since a variable can take only finite values but still be unbounded) is finite.

Any thoughts?

"a variable can take only finite values but still be unbounded"

to say this is spurious would be generous.

No, you're right. I think all the comic is saying is that to a human, living their life while looking at it with human eyes, there are only finitely many ways.

And why wouldn't the diagonal argument work in this case, thus rendering the argument for finiteness invalid effectively?

Well the diagonal argument forms a set with everything you want in it (like pairs of natural numbers and real numbers), then consider some element that must be in the set but can't. In this I don't know how you would construct such an element. In the real/natural number case you add one to the ith decimal place (9 to 0) for the i th number. We cannot do something similar, as there are only finitely many conditions for elements, and more elements that conditions, so you form your new element, but find it's already there.

Realized the issue with what I was claiming. My argument would require infinite length of the movies so that one could always have a place where it can differ. By the way, I don't see how this isn't really just a restatement of the idea concerning a library with every single book. The difference seems like a superficial means to imply some thoughts concerning free will and the infiniteness of possibilities.

Did someone else think of David Deutsch's Fabric of Reality while reading this?

I loved the book. I've just finished his new one as well "Begging of Infinity", which was in some ways more difficult, but still a fascinating read by the person who has thought very deeply about things.

It's like the Youtube of Babel :D
or D:

I always thought about making an audio file with all the possible rythms and sue every music company in the universe for using my music!

Rule 34?

Yeah, but Rule 34 is actually for the internet..

We would have to make all of those videos available (via youtube or something) so that the rule becomes completely true. (Or maybe a live stream of a camera filming the tv, which would actually appear inside the box as well!)

That's like using backtracking to solve a problem. You generate every single, freaking possible video to find just so few that are actually corect.

The images, wont it be the other way around? Each pixel can show 28 different colors, and we got three of them. So 16 million colours. With 2.1 million pixels, that is
(2.1M)16M

Or?

No, (16M choices for pixel 1)(16M choices for pixel 2).....(16M choices for pixel 2.1M) = (16M)^(2.1M).

Corollary: There is no God.
Proof: Trivial.

Refuted by the existence of binary arithmetic - at least according to Leibniz.

There would be a video in there of them living there life from a birds eye view ;)

I... don't get it, yet I am already a Math Year 1 University Undergrad.

The conclusion of finite ways to lead your life is incorrect. The differences are tiny fluctuations smaller than the videos can show (assuming continuity of things, a philosophical hot potato).

The sentence "Other televisions have less pixels." is incorrect grammar. Since "pixels" are a countable item, the proper grammar is "Other televisions have FEWER pixels." This mistake is understandable, however, given that we've been brainwashed by all the incorrect signs at the 'quick lane' at the store which say "10 items or LESS", when the correct grammar is "10 items or FEWER", since, again, items are clearly countable. Just a friendly note from the 'grammar police'! :-)

Thank you, I was going to post the same. It has got to the point that I'm impressed when someone gets that correct.


I doubt one thing,
The maximum time is assumed to be 1000years..But different persons starts living from different position of time (Ofourse there will be a base time from which we can take time measure, can be assumed to 0?).If you take the time from 0 to 1000years you will get only the same set of videos in the same sequence in video box always with this equation. But there will be difference between somebody living from 0 to 1000yr and 10 to 1010yr(both are 1000yr long!). So we have to add some criteria to specify the start and end time consideration to the equation(or atleast the start time). So if i want to get every video that related to me and my friends i have to specify my exact birth time and calculate the probobilic arrangement of sound and video pixel according to that start time, rite?.So these equations must be re-calculated to include the permutation and combination for different point of second!!! ??? May be this lead to an infinite number of arrangements possible for different start position of time???? I think if we can find a system which can arrange the pixels and sound and find an accurate sequence based on a start time it will be revolution!!!! (ofcourse everybody can see their own death in video!!!).The video box will contain all the data for the all the possible video but the arrangement is what really matters, i think.

No, I don't think so. The equation as it stands, since it does not involve any reduction of the total choices based on repetition, includes all of the possible arrangements of individual images as well. The argument, after all is not based on the technology or experience of living in a particular year, but only in the arrangement of coloring and sound produced by your theoretical television. That is finite.

On the other hand, given that no known human has an infinite lifetime, and the number of different things we can choose to do at any given moment is also finite, I think that the final conclusion can probably be reached without the specific example. Not that we'll ever notice the difference.

Breaks down to (2^441710000 * 5^441000000) per second. I'm not capable of taking the math any further.

This is just like Jorge Luis Borges's "The Library of Babel", except in that work it's about a library with every permutation of books possible to write.
It's a wonderful short story, everyone should read it.

exactly what i was going to say. i'm surprised that yours is the only comment on borges. i thought he was somewhat canonical for math people. maybe not in the us...

Of course this whole comic reminds me of the Universal Library, containing all possible books. And the short scene where a librarian is going around the library, removing all books that are gibberish. He comes to the last existing copy of Principia Mathematica, opens it, and then holds it over the reject bin, pondering...

bahahahaha

Now the MPAA will want to sue you.

Given that the theoretical video library contains every biography possible, you managed to put a bound on the number of individual human lives using information unrelated to human developmental factors. Presumably, using this fact, the average number of distinct events in a human life, and the pigeonhole principle, you can put a bound on the impact that any given event can have on the development of your life/personality.

Cool, no?

You should rather say, "There's only a finite number of ways you can _experience_ your life".

I'd think there are limits on what we can discern with all senses (putting your hand in 100 degree celcius water is going to feel pretty much the same as in 100.0000001 degree water), so if that research has been done into those limits (I don't know if it has), that information could be applied, and there would still be a finite number of discernibly different lives one could live.

But if you did have access to The Box, you'd have to live ridiculously long to ever stand a chance of finding some video that makes any sense to you (i.e. something that defies the random way in which it was created to accidentally make sense to you). It would be fun to try to calculate the expected length of time one must sample from the box in order to find something worth watching.

First we would have to find a quantitative way to define "making sense". Perhaps something to do with low entropy, high cross-correlation between nearby frames (where "nearby" is frames a few seconds apart), and so on. Of course, if we found a nice way to "measure" the "sensibility" of a video after having created it, we could already limit the box to contain only reasonably sensible videos. Then we could just randomly pick something and it would be ok.

What's most interesting to me is that there would be in that box a video of, say, Elvis Presley presenting a proof for the Riemann hypothesis (or a refutation, if it's false) in the Klingon language.

Actually both of those videos would be present.

Mike sure has hit a nerve here!

For this to be accurate, you assume that the human experience can be defined only by what can be seen and heard from a television. There are other senses, too, as well as things that are less understood, such as emotions.

Stupid comment is stupid but how can we say that reality is limited by the number of pixels we can get on a screen or the capabilites of our senses? If we made a T.V. with even greater resolution then there will be more possible images and hence more ways for life to unfold, similarly even though we can only see 10 M colours what if we made a device that can differentiate among more colours, then we could tweak the colours of the pixels and use it to study the difference in the lives.

What I am asking is, how can the possible amount of information be said to be finite on the basis of resolution and number of diffenerntiable colours both of which can be, in principle, infinite?

‎*Other televisions have even :fewer: pixels.

OK, firstly we take a concept from philosophy of art, courtesy of Renee Magritte's painting "The Treachery of Images" (La trahison des images): "C'eci n'est pas une pipe". This is not a pipe: the image of a thing is not the thing in itself.

What the comic is saying is that there is a set number of possible permutations of a sequence of images, such that there is a set number of possible representations of life.

This seems to be contradicted by Magritte: the representation of a thing is not the thing in itself. To completely replicate all sensation, behaviour, environment, would require a vastly higher number of representations - films.

Functionally similar behaviour that could be captured visually wouldn't at all represent all of the different possible sensations and thoughts whose variation makes for a startlingly different life, even if from a functionally visual perspective were identical.

N.B. when I talk about functionality, I refer to functionalism, the philosophy that if two things behave in exactly the same way, they are functionally equivalent.

Two identical characters in two identical films would be considered the same character. Yet if there were a different film for every possible thought and sensation of those characters, despite that they are visually functionally equivalent (i.e. the same), the number of films necessary to even functionally recreate the world would be unimaginably vastly increased.

But we don't need that to assuage ourselves of our 'free will', whatever that means (a whole other area of much debate). The fact is, even if the number of representations is finite - which, shock horror, it is. The maths is good as far as I can tell, and I have reasonable respect for the source, despite poor grammar in the cartoon - even if the number of representations is finite, the collected boxset of 1000-year DVDs of your life outnumbers the visible particles in the universe.

The scale and range of possible lives is unimaginable to a human being. When we talk about these box sets, we do not realise the scale: not only every possible combination of shape and colour, but every possible ordering of those images to depict every event in the universe. They would have to, to be a complete set of moving images. The unimaginable things that would exist in that box set: a whole lot of meaningless static, a billion billion messages, meaningful or garbled, every single work of art, pornography, every image of human existence, images of impossible beauty and horror and every piece of horrible art on the internet. Every possible image, every possible life, over a thousand years.

Extrapolating backwards, let's move from the referent (the films) to the object it represents (the universe). Analogously, we can imagine bodies of matter as imagery in 3D, particles as pixels, and imagine the films not just as records, but as the actual arrangement of particles over time within the universe.

The numbers involved shoot up, but the fact remains the same: there is a non-infinite number of possible permutations of lives that we might live. Scrap every arrangement of particles that isn't a human life. Scrap every one that isn't possible for someone born at your birthplace, at your time - everyone who doesn't share your spatio-temporal coordinates, and therefore isn't you. The unimaginable numbers are still unimaginable, but there are a whole lot fewer possible permutations of your life than there are permutations of any and all possible things happening (which, by the way, contains all possible representations of the impossible, humanly comprehensible or otherwise).

It doesn't matter. The number is still unimaginable. There are still so many possible variations of your existence that even if you lived every single one in a second you wouldn't even have scratched the surface in a thousand years.

A far more pressing issue if you want to question human free will is the determinism/chaos paradox: if the universe is a closed, ordered system, there is only one possible sequence of cause and effect given the initial starting conditions of the system, and we cannot be in control of our actions. If chaotic and unpredictable events on a subatomic level mean that the universe is not ordered, then cause and effect cannot be considered almighty, and we cannot be in control of our actions. Either way, the workings of our mind are subject to the laws of physics, and our consciousness is reduced to the process of rationalising our actions after we've made them, an illusion of self-control retro-spliced into our memory so that we feel like we were in control the moment after the decision is made for us by unalterable, uncontrollable nature.

Come at it from a different angle, say that our environment, our upbringing and our biochemistry are completely beyond our control, and totally shape the formation of our character - our beliefs, decisions and behaviour. This again leaves us out of the picture, acting according to the drives that are bred into us and the world which shapes those drives into desires and beliefs and actions.

Solve that one and you've got a Nobel Prize in Philosophy, if they make those. Do they make those?

http://en.wikipedia.org/wiki/Nobel_prize

They do not. How disappointing. Although Bertrand Russell did get one in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought." What a don.

I'd think there are limits on what we can discern with all senses (putting your hand in 100 degree celcius water is going to feel pretty much the same as in 100.0000001 degree water), so if that research has been done into those limits (I don't know if it has), that information could be applied, and there would still be a finite number of discernibly different lives one could live.

I love how this is comic 420... it's totally "stoner philosophy". :)

You made a systematic error. My head does not only contain one 1080p eye and one ear but many additional senses, like smell, taste, accelerometers (I know when I rotate or when a force influences me).

You have to show, that my perception of ALL this data is discrete. You may even have to show, that the thoughts that are produced by my brain are deterministic and discrete as well (depending on my input and my (discrete) genes alone).

Nice try, though :)

Ah, but Physics really has/is already doing that, of course!

Even if Physics does as much as showing that even thoughts are deterministic it would only imply the ways of life WE can *percieve* is limited and that doen't imply that the numer of ways themselves are limited, as I asked before(and no one answered me D:), what reason do we have to think that information is limited by human preception? Isn't it like saying that Pluto didn't exist before it was discovered?

I never said anything whatsoever about thoughts being deterministic. I was noting the fact that everything is, when you look "close" enough, quantum in nature. Thus you only need a high enough resolution to get to this level to apply a similar argument as the comic to everything. None of it relies on human beings at all.

Well, in known physics (Quantum Field Theory) the position/time and momenta/energy of particles are still described by continuous variables (energy is only discrete in a bound state), so no, there is no indication that the number of particle configurations is finite. Granted, like "A Person" said, the possible number of equivalent perceptions by our senses probably is finite anyway.

Regards eyes and senses. Let's be realistic here. For all practical purposes if you've videos from all 360 degrees around you for each and every single moment and possible action in your life, you basically have all possible states in there. Even thoughts will be present as subtitles in some videos. The only thing left is raw sensations of taste, smell, etc. But apart from that even a low resolution black and white video suffices to show all distinct events in your life.

Even if there were a way to include other senses (including proprioception) in this (and I'm not sure if it's necessary to include taste, for example, because you don't choose how things taste, and your reaction to whatever taste it is is already recorded) and the video resolution were as good as our eyes', the tiny differences we can't perceive could still be considered different ways to lead our lives in that they might affect others. Let's say we look at one of the videos that shows the life of a butterfly from the butterfly's perspective. It's possible that if the butterfly flaps its wing in an imperceptibly (either to the butterfly, to a human, or to the video system) different way, it will cause a hurricane in Oklahoma instead of Toledo (first two place names I thought of. I have no idea whether hurricanes are likely there.) So in order to capture all possible ways of living one's life, we'd really have to extend everything to Planck resolution.

I'm not entirely sure what the point of it all is though. Such a box has about as much use as a answering all questions in a test on integer arithmetic question with 'An integer between -G and G, where G is Graham's Number'. Or, if you want to get philosophical, it's like Deep Thought saying that the answer to the ultimate question of life, the universe and everything is an integer between -G and G, where G is Graham's Number.

Angela: of course you are right, he is not atall representing all choises that can be made during a lifetime, he's only putting an upper bound upon the possible ways your life could be concived through a film.
But your counterexample is also incorrect, while the butterfly might have this impercetible change in the wingflap, the movie about him flapping the wing causing an hurricane in Oklahoma, as well as the one where it causes the hurricane in Toledo (which was the original movie), is allready in the set of movies!
As the set of movies does not care about why the hurricane is happening, it merely cares about wheter the hurricane is representable or not on a tv.

Sure, there will be movies about a tornado in Oklahoma or one in Toledo. My point was the movie from the perspective of the butterfly is identical whether the hurricane is in Toledo or Oklahoma (I'm assuming the butterfly is in Sweden), even though the butterfly's action of moving its wing imperceptibly differently is a cause of the hurricane (although I guess you could argue that it didn't decide on this slightly different movement that it can't even feel itself doing, so the movement could be ignored in the same way I proposed ignoring taste, assuming a 'different way to lead your life' implies 'making a different decision about what to do' rather than 'doing/sensing something differently without having any say in the matter') For these two movies to be different, we have to increase the resolution past what can be perceived by the butterfly. (Note that it could equally be a human causing the hurricane to be in a different place, and a movie from the perspective of that human, and therefore the human's limits of perception that matter; I'm just saying it's a butterfly because I'm referring to the butterfly effect. Also because a butterfly is less likely to watch the hurricane on TV.)

Consequences of an individual's actions only have meaning for that individual if there is some form feedback. As you suggest, since the butterfly does not regularly, or meaningfully, peruse television newscasts, it is not effected by a hurricane (or tornado to make Oklahoma and Toledo more likely) it's actions may or may not cause.

It doesn't matter that the causes are being modeled or are not being modeled at a planck scale. The possibility of causing a hurricane or not causing as well as doing so in arbitrary location exists in the video files. So all the events exists even if the reason for them existing and differing might not be present.

The simple fact is that a human body viewed from all possible angles in all distinguishable states via a video will exist in the video box, it doesn't matter if there are subatomic imperceptible differences whatever these differences cause will also be in discernible video form if they're meaningful. There is no need to rely on the subatomic physics, that said there are also images of the binary states of different sections of the memory of a planck scale simulation in the video box.

My only problem with this is the assumption that we live our lives at 30fps. If something happened in our lives that lasted less than 1/30th of a second, it's possible that it wouldn't show up in the video. But it would still be a difference to our lives, would it not?

Would there be an extra edition of this box with the deleted scenes, directors comment and a making of?? :P

So, What is the data storage required to build such a box? how physically large would it have to be using today's technology?

There may be a finite amount of videos but each of these videos represents an infinite amount of events.
Thus, life is infinite and order has once again been restored to the cosmos. Phew!

um... no.

Please take care to explain why. thanks.

The title of this comic should really be, 'It's a mind-bogglingly big, but still finite, world (after all)' unless you mean that the actual world is very small compared with all the implausible or impossible things represented in the box.

I just tried the summation on my 89 titanium, and it had an overflow just calculating s=1.

Nice idea with the video box, but you will face several "real world" problems if you want to build and use such a thing:
* Given the number of atoms in our universe and you only need one atom per movie to build and you use all existing atoms (maybe excluding yourself), it would, by far, not suffice to build all movies having only a SINGLE FRAME
* Maybe you make out some extra material somewhere to build all SINGLE FRAME movies, you face another problem, which is even harder i think: If each video (atom) needs a little 3D space to store, your video box would be so large, that you could only reach a very little proportion of all single frame movies in your methusalem-live when you travel with the speed of light in your video store. This will actually limit the number of available videos to watch for a single person pretty hard (hopefully not to the boring single frame movies). Probably a black hole where atoms do not need space can make your video store more compact?, however, video players using light and photons probably do not work there.

Here's a thought: taking the example from the comic where you have the video of you watching yourself watching the Lion King. This video would last the same amount of time as the video of the Lion King. What about the video of you watching yourself watching yourself watching the Lion King? Also lasts the same amount of time.

Surely all the videos of your watching yourself watching yourself...etc... waching the Lion King, could be considred an infinite set as you can always add another level to the watching?

Is the sum really necessary? Since every video of every length less than the max will be embedded in another longer video, it seems as if the total should be the number of videos with the maximum length, minus a very large number of repetitions, spliced videos, etc.

More disturbingly, there would be a video of the Lion King watching my life :-/

IMO there still are infinite possibilities but in this case, there are finite number of possibilities because of the 10M colors the human eye can distinguish.
In reality there are an infinite number of colors and thus there would be infinite number of possible videos.

I find it amazing that even though this comic is unusually long, the comments are at least 10x as long

We're just trying to approximate the universal video box.

Not sure if this has been mentioned but this is limited to the ways in which the TV can express the pictures and sounds of your life. Thus, it's there's a finite number of ways that a recording of your life can be made given the restrictions of using a monitor of 1920x1080 and sound sampling done at 44.1KHz, rather than a limit to how you actually live a life, which would take into account other senses, your specific interpretation, understanding, and new knowledge acquired from specific situations, and that's without taking into account the context of the situation, the knowledge and concepts that will be gained in time and changes in perception and understanding that would take place accordingly, as well as the specific place you happen to be at different points in time.

So, while it's true that given enough time, you can watch a video of everyone's lives with the given parameters (remember the specific ordering of frames also matter in this case, which would still make the number of videos finite, though the length of time is not specifically defined, though given that every human's lifespan is limited, there's also a finite limit, but that's only if we assume that humans will some day die out (which is also a realistic assumption), it does not mean that the possibilities (that is, ways) that lives will be lived is finite.

Comment's a bit messy, but it's late.

This is going to please a finitist but not a ultrafinitist.

Still that does not involve the possibility of 'enhancing' the reality/human, cerating a 'new' colour, new sense, non-spacial arrangement of objects or anything like 'deus ex machina'

THIS IS HYPER-GEEKDOM!

Maybe if our world was made of pixels.
And it doesn't contain emotions and thoughts

HOLY. CRAP. I had a conversation almost identical to this one with my dad about a month ago.

I just realized that if space is infinite then there are infinitely many parts of space that look exactly identical.

From the math forum where you git your inspiration from http://mathforum.org/library/drmath/view/55871.html

Dr Benway seemed to not fully read the question which as such seems to be a trick question; "Many years ago I read somewhere that if you had an infinite number of
monkeys sitting at an infinite number of typewriters for an infinite
number of years typing at random then it could be accepted as a
probability that one would eventually type the entire works of
Shakespeare" and the very fact that is would be impossible for ONE of these monkeys to churn out all of Shakespeare's work, the question doesn't indicate that the monkeys are immortal just infinite!

Someone's been reading Borges recently.

Even if it took only the mass of (say) 1 electron to store each datum, the box would have to far exceed the size of the observable universe, or it would collapse into a black hole. So most videos would be unreachable.

Just imagine a video of me sitting on the couch and pondering for an hour. How would you know what I was thinking about? Even if you included all senses, as seeing and hearing are just not everything, thoughts would escape your video box.

There are also videos with subtitles of thoughts as occurs in today's movies.

no problem doing it for infinite values (i.e. on resolution, colors or even time), its still countable infinite, so there is a finite time for you searching in the infinite box (think of it as generator) for the right video i.e. from time s to time s+t instead of from time 0 to time s.

the only real problem is, that time is assumed to be sampled to discrete values, while time is mostly a real value to most persons.

I suppose someone else has probably already pointed this out, but the problem with the statement that the number of possibilities for your life is finite has two problems.

1. The limitations of 2D video (example, a video of my life filmed from exactly in front of me throughout my life would have an enormous number of variations due to invisible (to a 2D camera) differences, such as a scar on my back.

1a. The limitations of any sort of recording. Each video represents not one variation of my life, but one perception of a tremendous number of (albeit similar) variations of my life.

2. Non-audiovisual phenomena. If I live my life twice in the exact same way except that at one point I think in my head the word "was" in one life and "were" in the other, there are two variations that would be identical in the hypothetical video box.

3. Again, the limitations of the video. No matter how high the resolution, there will be variances that it can't pick up (such as if I'm half a nanometer to the left of where I was in another variation). Although this point is arguably moot in the event that the resolution exceeds that of the human eye. Same for framerate.

"1. The limitations of 2D video (example, a video of my life filmed from exactly in front of me throughout my life would have an enormous number of variations due to invisible (to a 2D camera) differences, such as a scar on my back."

The box contains even two slightly different images yielding stereoscopic 3d if you use them. There are also images from all around you, 360 degrees, and in x-rays, infrared, etc.

"2. Non-audiovisual phenomena. If I live my life twice in the exact same way except that at one point I think in my head the word "was" in one life and "were" in the other, there are two variations that would be identical in the hypothetical video box."
No there are videos with subtitled thoughts, so all possible thoughts are subtitled on all videos.
"3. Again, the limitations of the video. No matter how high the resolution, there will be variances that it can't pick up (such as if I'm half a nanometer to the left of where I was in another variation). Although this point is arguably moot in the event that the resolution exceeds that of the human eye. Same for framerate."
Let's be honest here, nanometer and femtometer variations that do not yield any discernible difference to the description of your life, shouldn't really be counted as distinct ways to live your life.

I should add when I say all videos are subtitled, I meant that there are copies of all videos with subtitles of course copies without subtitles also exist in the box.

The thing that bugs me the most about this comic is that it doesn't say why it matters that there are only a finite number of ways you can lead your life. Why even try to prove/disprove that? I don't particularly care whether there's a finite number of ways I can lead my life. Should I? I only get to lead it one way anyway, and which way that is might be entirely predetermined (this would be a more consequential thing to debate, but it's been done to death.) Whether the number of other imaginable ways is infinite or just mind-bogglingly large really doesn't concern me.

Excellent post! The empty set and the complement of the empty set contain the same amount of information. This giant box, therefore, has zero information. Not unless you marked some of the movies.

I think you all are missing that some videos won't have synced audio. And also you can have 2 similar videos, with the exact same images but entirely different audio.

It's a small world for large values of "small."

I know this has already been pointed out (sort of) and I'm (really) late to the party, but :

Consider image data alone in an extreme case. Consider that we are watching a man walking toward a wall on the far right of the screen. Because this is an extreme case let's say the resolution of the screen is such that each pixel is the width of the man. In real life the man could choose to repetitively walk less than the width of his body toward and away from the wall, however the low resolution of the screen would only show a column of pixels standing still and would not represent his choice.
Now consider these facts:
(1) Each time you walk a certain distance the exact distance you walk has infinite resolution.
(2) All TVs are made up of pixels and so they have finite resolution and can not represent every distance walked.
(3) While not every distance walked is not a conscious decision they are different outcomes of the same decision (to walk to a general area) and therefore are different ways to live that portion of your life
(4) Considering the above, everyone who has walked an arbitrary distance has made a couscous decision with infinite outcomes. Therefore, there are an infinite number of ways to live your life.

The question "if distance walked has infinite resolution?" is an open one, if space is discrete then it is false. We know that the action potentials traveling down the spine are discrete events involving discrete numbers of ions moving across the membranes. The only possible differences are subtle temporal differences, and given the way muscles work it is likely that minute subnanosecond temporal differences are averaged out in general and thus make no real difference to outcome.

While the displays have finite resolution something like the video box can have extreme close-ups which can likely exceed human eye resolution. IF you've sub-millimeter resolution of the walking of a human for all practical purposes you've captured that event.

There even are likely Atomic force microscopy-like images of the atoms on your feet making contact with the atoms on the floor at different areas within the video box.

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