There are so many discussions happening here in the comments. Philosophy, statistics, infinity, quantum mechanics. I'm loving all of it! 🤓 It's the _perfect_ response to this video.
If speed of light is not constant and it was much much faster in the beginning and its slowing down, it’ll explain the inflation as well as why it appears further galaxies are getting away faster and appear speeding up in current slot of light speed. Maybe time stops when the universe reaches absolute zero and our only frame of reference for it is infinite time.
Already the ancient Atomists understood the concept in the video. Given that space and time are infinite, the eternal atoms in the universe will always by chance arrange themselves into a new world after sufficient amount of time, and therefore it is not in need of any Creator.
@@januszdelondres Inflation had to occur _after_ matter and light was created. The entire purpose of inflation is to give matter and light time to mix in the early universe.
Maybe the instance of THIS (our) universe is one of all REAL implementations of an endless circuit of quantumphysically realized bounced universes and everybody lives HIS life exact again and again ;)
I think the problem with this argument is that the "rules" for the monkey and air molecules did not change over time. The monkey types forever and the molecules move forever. But in the universe, if everything has moved so far apart that they can't interact with each other, there's no force that can bring them back together. The "rules" changed over time.
Funny thing, I was thinking exactly this but having trouble finding the form of words to express this point. Wouldn't everything have to reverse the expansion of the universe by reversing their trajectories for billions of years ? ..... In other words, the big crunch !
I think The Science Asylum tries to get around the problem you mentioned by using "Infinite Space" in his argument. It works only if he is using Actual infinity (instead of Potential infinity) to describe this "Infinite Space". If he is using an Actual infinity, then it implies at least two things : there is an actual infinite amount of matter in the Infinite Space and there are sections somewhere in the Infinite Space where it's possible for massive amounts of matter to come back together. It looks like our section of Infinite Space would not be one of those sections. The part I'm having trouble with is 10:14 where The Science Asylum says, "Luckily, our universe is expanding forever into an infinite future." Here is where The Science Asylum should have told us if he means an actual infinite future or a potential infinite future. Of course whenever Actual and Potential infinities are brought up some questions have to be asked : How can someone detect if they are on a timeline with an actual infinite future (a timeline made of an infinite number of moments) or if they are on a timeline with a potential infinite future (a finite number of moments that is growing with each new moment being added to it)? What evidence is necessary to determine the universe is an Actual infinity of space? What evidence is necessary to determine the universe is a Potential infinity of space?
What is Missing here is Rodger Penrose. His cyclic cosmology gets around that by using scale invariance: The high entropy future universe forgets its state when only photons whizz around. With No massive particles left, the universe had No size and time doesn't pass, which for All practical purposes is the same as the initial low entrophy state resulting in the Big Bang. However we don't need an infinite future for that to happen by chance, just a Very Long time.
I’m a science teacher in the UK, I recognise that the amount of thought and and care put into your videos is staggering - it must be like playing Kasparov at chess and mapping out action and response a 100 moves ahead in make this so fluent and effortless. Thank you.
Well in chess you need to keep it [the moves ahead] in your human memory, in creative work you can actually add step by step, correct and adjust. It's like Kasparov having the option to take back moves at any time to create the perfect game. Not as hard as having to keep it in memory.
the Library of Babel is one of my all time favorite things to think about. I thought of the concept as a kid & was a little heartbroken to know it was a very old concept. non the less I love & appreciate it
I'm a big fan of Jorge Luis Borges. He allways made tales based on cool concepts. Obviously "The Library of Babel" is great. But I would recommend also "The Aleph".
The late Quentin Crisp said that he never cleaned, because after a while, things didn't get any dirtier. I guess in physics, it would be stated as reaching a saturation point.
That's basically the Boltzman brain, isn't it? But cleaning instead. I propose we call it Boltzman cleaning, requires zero work but most definitely an unreasonably long time.
I love that you clarified that the second law does NOT say that the entropy of the universe MUST increase, just that it TENDS to do. I find it rather annoying that the second law is often incorrectly stated as "The entropy of an isolated system MUST increase or stay the same. It can never decrease." It's much more accurate to say "The entropy of an isolated system TENDS to a maximum". That's partly because, as you said, entropy actually CAN decrease, it's just _really_ unlikely for a system composed of more than a few particles, but also because, even ignoring that possibility, entropy of a finite system CANNOT increase forever, because eventually everything will be as spread out as it possibly can be. At that point, the entropy must either stay the same or decrease because there's simply no way for it increase. That's why we ought to talk about it tending to a maximum, not always increasing no matter what.
"everything will be as spread out as it could possibly be" Not in an expanding universe. As the universe expands, the potential to "spread out" increases.
It's like the inertia in a swinging pendulum. It wants to be in the straight position, but to get there it needs to accelerate towards it. Once it reaches there, it already has intertia and must swing the other way.
@@kidzbop38isstraightfire92 What does that even mean, when a vibration in a particle field is so far away from another that they can never causally interact? Or quantum fluctuations create particles from nothing? I don't see entropy increasing as Mikayla poised....
I have found it incredibly beneficial to your educational work that you dissect every detail of a topic, even routinely digging into the etymology of words to illustrate meaning. As you said in one video, "If you want to descend into pedantry, be advised you're talking to the Master!" It really matters in science. Often with other teachers or after reading about something I can be left with, "Yes... but what about?" That rarely happens with your material.
That's three vsauce references in one video. When will the great minds of Nick Lucid and Michael Stevens collaborate for a project? I want to see The Vscauce Asylum!
@@andrews1795 he would need to start doing more hands on demonstrations. Not that he hasn’t, but once he grows he’ll be able to afford thingy that Vsauce was able to afford around the same subscriber count.
As much as I like the idea of a cyclic universe myself, there's a HUGE problem. In both the room metaphor and the monkey metaphor, infinite repetition is enabled by the existence of spatial boundaries. The walls place a limit on the number of particle configurations in the room, and the number of keys places a limit on the number of character combinations. As far as we can tell, there is no analog for the walls of the room when it comes to the universe. The more interesting question, I think, is whether this concept can answer the question of "fine tuning" without requiring a multiverse. After all, there is a certain sense in which the universe seems to have only so many keys to press (a finite number of particle types and forces), which puts a finite limit on how many types of interactions are physically possible. Moreover, we have discovered that several of the forces we see now are unified at higher energies (meaning a smaller keyboard), and the physical space of the universe was much, much smaller near the Big Bang (meaning faster typing). Assuming the speed of light is constant, the "space of all possible interactions" was explored to the greatest degree close to the Big Bang. If we were to discover that the universal constants are not arbitrary but somehow interdependent (as String Theory seems to suggest), and their relationships could have been mediated by the kinds of high energy interactions that happened near the Big Bang, then Darwinian logic could explain why the constants are the values they are. It's like countless monkeys all jamming out on tiny keyboards in those first few microseconds, their results getting passed through a coherence filter (their interdependence), and getting set as constants as the universe cools.
Don’t you think it’s possible that the universe does actually have a boundary? I’ve been getting strong insights lately telling me that the universe is a bounded infinity, one of many universes within a parent universe, ad infinitum (steady state creation model). Think of a mobias strip or a Klein bottle, or driving on the circumference of a sphere. We can travel infinitely, sure, but the universe itself isn’t infinite. It’s simply a heartbeat, a breath. Expansion, contraction, expansion, contraction. To me it seems so obvious that it can’t be any other way. We just can’t see the whole cycle in our lifetime.
I just got the most simple and elegant explaination for two very difficult concept: Infinity and entropy that I have ever heard. This is coming from a math and chemistry teacher and I have pHd in theoretical physics so I have heard a ton of attempts at explaining entropy and infinity.
I used to watch Vsauce all the time a decade ago and that was a huge inspiration for my interest in physics. Now I'm getting my PhD and get to see you talk about the same concepts in those earlier videos with a little more scientific rigor applied, it's amazing!
Infinity is a concept, not a number. Very rightly said Nick. All weird things are supposed to happen at infinity. For an e.g. parallel lines (or parallel beam of light rays) meet at infinity. I have always liked to imagine in my head that big bang is not the beginning of universe because an ever flowing journey such as universe' can't begin with a finite event. It doesn't feel right. So 'probably' an infinite number of big bangs had already happened in the past, and an infinite number of big bangs will happen in the future as well. Thanks a lot Nick for this wonderful video. Somehow I feel relieved now. 😊
I didn’t know a law of truly large number existed, but I always intuitively (sort of…) thought and understood that, given an infinite amount of time, any possible event would happen at some point. Thanks for making it clearer in my mind, pal!
I'm not convinced of this. If I have an infinite string of random numbers 0-9, one possible string is 010101010101 all the way down, never using any of the other possible numbers.
@@HeyHeyHarmonicaLuke Right, so: infinity is weird. An infinite list is itself made up of infinitely many infinite lists. This allows there to be an infinite list of 1010101010101etc and also 2020202020202etc. All of these types of lists can be contained within it.
@@HeyHeyHarmonicaLuke that isnt really how it works. given an infinite set, any finite set can be found with in it. that is not to say that any infinite set can be found with in it.
@@boycefenn Hmmm there you seem to be flat out denying that there could be an infinite list of only 0's and 1's. Maybe you can expand? I think that given a random list of numbers, the longer that list is, the less likely it will exclude some numbers (or sets of numbers) within it. The less likely it will happen to be all 0's and 1's. So for an infinitely long list, you might say it's infinitely unlikely to end up with all 1's and 0's. That's the strongest rebuttal to what I said I can think of. But I don't think it works, because every unique end result should have the same probability, and finding patterns special is a subjective thing. Like how a royal flush has the same chance of being dealt as any other random hand of cards. Random looking hands just aren't on the winning hands list in the rules, but we could add them and they would be just as rare as a royal flush. If a perfectly random shuffler shuffled a deck of cards, call that arrangement 1. Then it shuffles them again, the chances of getting arrangement 1 again are the same as the chances of putting the deck back into proper order, arranged by suit and size. If an infinite set of purely 0's and 1's isn't allowed because it's too improbable, surely the same can be said of any infinite set? It's like there's an infinitely sided dice, and then of course one of the faces does have 0's and 1's all the way, surely. That is a number, and so our infinity dice can land with that face up just as well as it can any other... surely. :)
Great video as always Nick! I have a thought from your video: since universe is expanding, there're more and more space/room created every second. And as space expands there're more configurations for particles to be in. So the likelihood of them being in a single spot decreases as space expands. As the universe is expanding at an accelerating rate, the probability of a "big bang" repeating itself decreases exponentially. While time is only increasing linearly. Granted that possiblity never goes to zero and with infinite time it always "can" happen, but it's getting less and less likely.
Actually, the remnants running away from their causal patches. It is forbidden to go back to the low entropy state again since the universe is expanding.
Afaik anything outside of the Local Group containing the Milky Way, Andromeda, and their satellite galaxies will eventually be flying away faster than the speed of light.
@@ScienceAsylum On top of that, in an accelerated expanding universe, at some point, each particle will move away from every other particle faster than light (since their distance is greater than the observable universe now). From that point on, it IS impossible for them to ever clump together again. And after the big rip (which i think is also a inevitable consequence of an accelerated expanding universe?) it is even impossible for atoms to ever form again, no? Infinite time cannot fix that in my opinion.
The real mind Funk with infinity isn't that everything that is possible happens...it's that everything that is possible happens an infinite number of times...
I once tried explaining this concept to someone who claimed that human existence would be meaningless unless humans can create an eternal consciousness. I said that if the universe is eternal, then the chances are an eternal consciousness already exists, because eternity extends both to the past and future, and given eternity, anything that can exist must exist now. He didn't get what I was saying and called me a religious idiot.
@@vejymonsta3006 it doesn't have to be multiple universes, in an infinite universe, if there are a finite number of configuration of atoms, than all configurations exist.
The biggest problem I see with this is that the probability of all particles coming back together into a singularity is not constant over time, it is ever decreasing as the universe expands. For instance, if the current period of exponential expansion of the universe, where the Hubble constant indeed stays constant, persists, the particles per volume would evolve something like this: d_t = d_0*e^t where d_0 is the particles per volume at the current time, t is the time in seconds and e the fraction of particles per volume remianing after one second of expansion at the current rate (and is thus < 1). If we integrate that from 0 to infinity we get -d_0/log(e), log(e) is a negative number, so we get a finite, positive number. If we assume that the probability of the universe randomly rearranging itself into a (near) singularity is linearly dependent on the density of the universe, we get that this is not actually inevitable, even with infinite time. What's more, the expansion of space is faster than the speed of light across large enough distances. Partcles which are too far apart can actually never reach eachother again, even if they spend the rest of eternity speeding towards eachother at light speed.
Yeah this is a very satisfying theory philosophically, but the fact that the probability is decreasing at an exponential rate makes it unlikely even given infinite time. And that's not even considering that even things like quantum tunneling can't "move" matter faster than light to overcome faster than light expanding space.
Was about to make identical point, less then math, as I never studied physics academically. 2nd law of thermodynamics explicitly talks about a CLOSED system. Issue is the universe, because of its inflation, looks more like an open system, hence it is illogical to apply this law to the whole universe.
I mean, as time approaches infinity, isn't it becoming exceedingly likely that quantum fluctuations alone cause local high energy spots? That is the nice thing about this idea I'd say. My problem with it, is that it is exponentially more likely (as far as I know) to form a universe with just 1 galaxy, which then forms a planet that supports human life over time. But our universe is waaay bigger. Unless it is necessary for it to be so big, to be able to form something like earth, what gives?
In infinite time, I have typed this sentence and you have read it an infinite number of times. You have give it an infinite number of 👍. Thank you, again. 😁
Sorry to be that guy... but that site is just smoke and mirrors. The phrase you're searching for gets hashed, and used as a random seed to generate the background gibberish, and the position the text is found, as well as what book/shelf/page, etc. IT'S A LIE!
@@graybot8064 It's not a lie, it still does what it says. I still think a reversible hash is cool. Theoretically everything is written in there, it just needs to be looked up.
@@ScienceAsylum It might feel odd for you as creator but for me as viewer it was just part of your style and I always watched (end enjoyed) it to the end.
Most of the currently-observable universe will not be causally connected anymore in, say, 100 billion years because of (accelerating) universe expansion. How can those elementary particles so far apart get close together without violating special relativity?
Heisenberg uncertainty principle. The probability field of every particle extends to infinity in all directions, and is never perfectly zero. In a sense, at every moment all particles have a non zero chance to be in the same location. No movement needed.
@@Tom-u8q That's a tricky question, but it doesn't matter in this case. (i think?) You only need propagation if there is a change. Fields are always and everywhere. A particle can potentially be observed / interacted with, as long as the probability is not zero, regardless of distance and relative speed of other particles. Just like the Tunnel-effect, the particle suddenly "jumps" to a region it couldn't possibly get to via continuous motion. I don't know how this "jump" affects the probability field though, if at all.... ლ(ಠ_ಠ ლ) this might interest you: www.scientificamerican.com/article/quantum-tunneling-is-not-instantaneous-physicists-show/
It depends on whether it's physically possible that something might make the whole space-time change in a shrinking way at a certain point instead of expanding.
"Ford, there's an infinite amount of monkeys outside, and they want to discuss a screenplay by Shakespeare, they have worked out.." - Hitch Hikers Guide To The Galaxy by Douglas Adams
But... while the probability of those air molecules being concentrated in one corner of the room is incredibly small ... isn‘t the probability of a universe expanding faster than the speed of light to clump together again exactly 0? It‘s called cosmic event horizon for a reason, right?
I was thinking the same. Then it hit me: Quantum tunnelling. The probability that a particle would quantum tunnel somewhere decreases rapidly with distance, but it never reaches zero. So the probability that a particle from your body would quantum tunnel to somewhere outside the observable universe is extremely (and I mean EXTREMELY) low, but it is not zero. This breaks the speed limit that us mortals are cursed with, that is, the speed of light. Of course, this was considering a single particle. The probability that all the particles in the universe quantum tunneling to the exact same location to start a big bang is, once again, mind bogglingly small. Although mind boggingly small != 0, so the premise of the video still stands. I am not a physicist, just curious about these topics and learned it all from RU-vid, so take all that I say with a grain of salt. But who knows, it just might be that this is the answer.
@@11regnartseht The universe is already expanding faster than the speed of light. But space itself is moving apart not an object in space, so no relativistic effects.
Best video so far. I knew all of these methaphors, monkey, library, hotel well, but you made it all so easy and digestable then to explain something so insanely complex as the big bang! Brilliant and a lot of fun!!
Ok. Now this is one of the best theories I have ever seen. It takes one of my favourite fun facts , the infinite monkey theorem, and kinda predicts the existence of a multiverse... Or a future that is not so cold and uneventful
Once we move away from thinking about time as a purely durational dimension, we will quickly unite quantum and relativity. You are on the right track here. :)
I thought about this at some point after learning about the second law of thermodynamics because I was trying to make myself feel better. Then I read an essay by Isaac Asimov that matched my thinking, and now I've seen this video. Well Nick's and Isaac's smarts are enough to make me feel validated.
I always thought that was a sly way of stating the corollary - some things have always been, and will always continue to be - like her way of telling Neo that something of his spirit/life force/etc existed before his mortal life and would continue afterward, and that his sacrifice would be towards something bigger than him, even if his body's death is inevitable.
Well, the point of the video was that the universe has no end, and therefor it has no beginning. This is compatible with the statement of the (fictional😉) oracle.
"If the future is infinite, anything that can happen, will... eventually." the problem I see is, if every particle in the universe is moving away from every other at the speed of light, then all of those particles coming back to one spot becomes impossible because the furthest particles would be beyond the cosmic horizon. Right?
@@Fade2GrayOG it doesn't have to be all of the particles happening to all meet up at a single point. Random fluctuations of energy happen all the time in empty space, due to the uncertainty principle. Usually these are very small fluctuations, but what's to stop a sudden, incredibly dense high energy fluctuation from occurring in an empty light-bubble of spacetime 10^^^^^^^^^^^^^10 years from now?
It requires the big bang to spontaneously come into being. Not just from entropy collecting back into a point. Thing is we know it's possible because of the fact we exist, so there must eventually have been the first 'fluctuation' of entropy that given enough time created a universe. That is the only thing that makes sense to me. We have already existed infinitely many times and will be existing again at some point simply because time is infinite. If all of time and space just stopped and became 'nothing', it would be reborn again because some tiny particle needs to go from a higher to a lower state of energy even though moments before it wasn't in a state of entropy at all.
@Remember The FutureAn interesting what if. It is not that the universe is expanding faster than the speed of light, per say. Instead the distance between objects gets larger and at a certain point the distance becomes so large that in order, get from one galaxy to the next a person would have to go faster than the speed of light in order to reach the next galaxy. Use the balloon analogy. If you draw any number of points on the surface then blow it up. Every single point would appear to move away from each other. As the balloon gets larger the points move away from each other faster. At a certain distance if you were on one point, the others would appear as if they are receding away faster than the speed of light but it is not. Because the points are not moving (if you deflate the balloon, the points would be right where you drew them), the space between them is expanding. I will admit, if we stick with the balloon analogy there are 3 outcomes. It keeps expanding forever, it pops, or it deflates. While all three are theoretically possible, there is no reason to believe either of the latter since the former is what is happening right now, and has been happening since the begining of what time we could measure. Both of the latter options "could" happen but I'm going with Occam's razor and sticking with the simple solution until we find even thale smallest bit of evidence that contradicts the current state of the universe. Thank you for listing to my TED talk.
I CANNOT believe I found a video perfectly explaining my own hypothesis on the nature of the universe. I've wondered about the possibility that time is actually infinite backwards as well as forwards. I've wondered if our neighborhood of infinite spacetime which we call "the universe" is a tiny and insignificant speck among infinite neighborhoods, separated in space and time by distances unfathomable magnitudes larger than the neighborhoods themselves, but still occupying the same fabric of spacetime that we do. Infinity could be infinitely larger than not only the observable universe, but the unobservable universe, and change how the universe looks beyond the unobservable universe. Who are we to say that the pattern of galaxies that we can see stretches on forever? It could go on for 100,000 septillion lightyears, but then nothing blackness for even more distance than that until there is another neighborhood. When I've asked very educated science-minded people about the singularity and the Big Bang, I often get very definitive answers. "There was no before the Big Bang, that doesn't make sense and here's why. There was no space outside of the singularity, the universe was once the size of the singularity and it continued to expand forever after the Big Bang." Given how theses things are taught, I didn't think I'd find a serious physicist (serious enough lol) actually entertain the idea as if it may be true. Given the size of infinity, I find it very possible the sudden expansion of spacetime that we call the Big Bang was a local event, able to occur due to the sheer quantum possibilities opened up by infinite time, and not an event that lead the expansion of all spacetime everywhere. This doesn't conflict with relativity because while the central location of the Big Bang might be discernable in such a universe, it would be far from the only one, and not the center of the universe. Is there harsh resistance to this idea among scientists? I think we may be uncomfortable acknowledging an idea that indicates the universe is actually so large and non-uniform that cosmology, the science of studying the universe as a single object, is essentially a hopeless endeavor, and in addition to no hope of ever being able to verify whether or not this is the case at all. I guess part of my surprise about hearing this hypothesis coming from a scientist is how untestable it is, which scientists tend to call not science. I get why, but that approach seems take ideas that may exist in actual reality, but aren't testable, and throw them in with mermaids.
An actual infinite is impossible. That's the whole point of Hilbert's Hotel. Just like it would be absurd to add guests to an infinite hotel where a all the rooms are full by moving each guest to the next room, it would be absurd to add another cycle to an infinite number of cycles. Think about it. If there is an infinite number of cycles before we get to this cycle, then we can't get to this cycle.
You've convinced me, we live in a simulation.... or every possible future exists. I'm thinking I dismissed Sean Carroll awhile back (with his many universes) too hastily....
Subscribed because of the VPN ad spot. Zero disinformation, 100% scientifically rigorous marketing. I lose a lot of faith when I see people advertising something they don't understand to begin with. Very pleasantly surprised!
BTW if true, this also means that every conscious person, being a finite pattern, occurs an infinite number of times. "You" are a somewhat fuzzy pattern, changing as you grow older and gain experience from this instance. "You" are closest, statistically to most other humans, particularly relatives and those sharing your life, but there is a spectrum all the way down to insects (and below?). If there is one 'field' of consciousness, then free will is expressing a choice to change your pattern, to move it along the field in a desirable/optimal direction. You would expect that those who use the universe around them to forge their ideas would converge on similar patterns, become more alike...and they do. One might even speculate on a "merging" (becoming overlapped, or similar to a large degree) of such like minds, as they are all following the same giant script. (Buddha, God, etc.) Those who prefer constructs that are not based on the universe around them (dogma) tend to make up any old shit, of which there is an infinite supply, and so will always diverge from others rather than converge. So although there are infinite ways to descend into irrational "hell", there are also infinite paths to the common good, and infinite time to get there. Metaphysics can be scary, but as a guru once said: If you must fall down a well, a bottomless one is the best kind.
I believed this when I was a child, really I thought thats what reality was when I was 2-3 years old, I think it was similar to Murphy's law, stating that everything that can happen will happen, and never stop, apply infinite possibilities to infante time, every possibly will be exercised, but not by a sequence, so life is going to be experienced like this again because we know it's possible as we are here now, but upon further thinking if it was like a quantum lottery, say each atom was a lottery ball numbered, the odds of each atom being the way it is say like predicting the lottery everyday for a thousand years, then although it's possible, the odds are astronomical and I dont think every possibility would be, but saying that, time never ending, I really dont know, I think we sre part of a greater conscious one that will return, I hope not but I fear this is our reality.
@@Δενβρισκωνικ That's the lottery winner paradox. The person who wins the ticket feels special since the odds were low but for the lottery organization it was ~100% chanse of having *SOMEONE* win since that's the rules they arranged.
What about the expansion, though? Everything is flying away from everything else (on the cluster level at least). How could random walks result in everything coming together again? Also, isn't the expansion faster than the speed of light on large enough scales?
@Remember The Future the speed of expansion is the same everywhere but it isn't necessarily the speed of light. The more space, the more expansion between two bodies. The smaller the universe gets, the slower the compression.
One of my thoughts is that if Dark Energy is everywhere in the universe, working like a reverse Gravity, then maybe once all of the particles in the Universe have expanded to the point where the pull from Dark Energy is magnified at a certain point that it causes another Big Bang. Imagine an infinite pull from all sides, ripping a hole in spacetime itself.
7:11 That depends on what type of infinity you're talking about. If we're working with infinite ordinal numbers, addition isn't commutative. The first infinite ordinal is usually denoted ω. 3+ω=ω≠ω+3. Vsauce did a video on this a while ago called "How to count past infinity." If we're working with the infinite cardinal numbers (yes, mathematicians *do* call them numbers), then addition is commutative and adding finite numbers to them doesn't change anything. To be fair though, in the context Nick is talking about, it makes the most sense to consider infinity as a limit, in which case it's just shorthand for a function or process which grows arbitrarily large.
I think it would help us a lot to think about infinity as a number of a different type. Similar to imaginary or complex numbers. Infinity is the result of 1/0. Lets call it I. So x=3/0 is 3*I. And this I is not a number on the number line but all numbers at the same time. Like a function with multiple solutions. Same with imaginary numbers this might have consequences in physics. Especially relativity, singularities and quantum mechanics. Just my 2 Cent
Sure, I do. There's one about to happen in about 38 seconds - just 'bout a 104 millimetres from your left ear. Hmmm... Y'all, might wanna move just a little bit to your right. 'K. Maybe, juuuust a bit more than that - y'know, like 5.713 tera light years...
Great video. Unfortunately there is the following problem with this argument: Polya's theorem shows that the probability of a random walk returning to its origin is 1 in one or two dimensions, but unfortunately only 34% in three dimensions. Meaning, even with infinite amount of time, the chance that only one particle is returning to the same position it once was is NOT =1. Meaning, the chance that "anything" will happen at some point in time if we wait infinitely long is not =1. Moreover, the chance that all particles in the universe randomly end up at the same location in three dimensions is virtually zero (34% for each individual particle, so really really low for all particles at the same time), even with an infinite amount of time. If we were able to say that the chance for "anything" happening in the future is =1, there would be a 100% guarantee that, after death, the molecules which once formed your body will again come together and you'll live again the same life, if you just wait infinitely long. But, as far as I understand the math in three or more dimensions, it doesn't work like that. Please comment, if you feel I am misinterpreting Polya's theorem, I am very much open to read your opinions.
Nothing has changed. There’s been two options: either its infinite, or its finite. If finite, then it probably has no boundary (space will not be flat, but curved.) If its infinite, then there’s probably no boundary (space will be flat.) There are other scenarios, but these are the two most likely.
No boundaries to a finite curved space time is analogous to the surface of our moon. There is a finite amount of surface area, but you can walk in any given direction just as far as you wish, and never come to an end.
We are inside the big bang, science told me that it originated from everywhere when I asked "where was the big bang", they told me that because all the matter in the universe came from the big bang. My question should have been, "Which point is most matter moving away from." The singularity may have been bigger than the observable universe, but we can still pinpoint its center by following the direction of most mass backward. It has boundaries, just like any other explosion/expansion but outside the big bang has no boundaries that we could ever be aware of.
@@crazyfakar1 There is no central point to everything. The big bang just means that things started to move away from everything else, equally. If it exploded, then yes, there’d be a central point, but there isn’t. But its not even that stuff is moving, but rather the space between stuff is increasing. An expanding balloon helps to visualize.
@@tbardoni5065 Even a balloon has a centre, science can't tell because the singularity was bigger than the observable universe, if it is expanding then it is expanding away from somewhere, from here it looks like it is expanding from everywhere, because of relative motion and the doppler effect, but if the big bang was smaller, we could easily see. From outside the big bang, it would be a different story. The big bang might not be the entire universe. "Everything moved away from everything equally" Not the matter that makes me, it all moved together, came together to make me. That would be entropy at its finest, everything equally being equal to everything else.
Infinity cannot be comprehended. It exists conceptually outside of our understanding and does allow anything to happen eventually. The fact that anything exists ever is mind blowing
Fun fact about the library of babel : Some of the books contains a lot of information, but the entire library contains a very small quantity of information.
First of all, this is a great video on a really thought provoking topic. But I do have a nagging question. If the universe carries on expanding to such an extent that most particles in it are causally disconnected from one another, how can they all condense into a single point to produce a singularity?
There are definitely problems that would need to be addressed. Ludwig Boltzmann came up with this before we knew the universe was expanding. Then again, it was also before quantum mechanics, so there might be a solution there.
Btw, if understood the idea correctly, there is a possibility that big bangs happen infinitely in different places, and our big bang is not a unique one. So elementary particles constantly fly in the infinite space in all directions, and from time to time some amount of particles happen to be in one place giving birth to a new big bang. But in this case there must be some amount of particles flying into our "big bang bubble" from the "outside". Is there any evidence of that?
Isn't there a point of no return with entropy? Like, 2 particles moving in opposite directions in an infinite vacuum would technically have a 0% chance of interacting. Isn't this more or less what heat death describes?
One hypotesis that you brought during the whole video about the room and molecules is that it was in a FINITE room with INFINTE amount of time to colapse into the corner, but as you said later, the universe if INFINITE in space (all directions) and INIFNITE in time (one direction). So to think about convergence in and INFINITE amount of time of the particles you need to consider which INFINITE is "bigger" and if there can exist a limit of which one is growing faster ...
Hilbert's Hotel - Veritasium uploaded a (faulty) video about it just a couple of days ago, titled _"How to Exceed Infinity."_ Causally related, or just coincidence? Because, as you said, given enough time, it was guaranteed that two guys would independently mention it in their videos just days apart. (And yes, I noticed your Vsauce t-shirt. Nice!)
@@ebenolivier2762 Because Derek assumes that there are an *uncountably* infinite number of passengers in the last bus. That's wrong because the passengers are discrete individuals, not continuous like points in a plane. So they are *countably* infinite.
@@ebenolivier2762 A more detailed explanation: Derek uses infinitely long strings of A and B as passenger names. These are, of course, equivalent to real numbers, which are uncountably infinite. He assigns these real numbers to passengers. Then he says, without proof, that all the real numbers have been assigned to all the passengers. That's the mistake. Next, he tries to assign the same real numbers to the countably infinite hotel rooms. Using Cantor's diagonal, he shows that many real numbers are left out. So the real numbers outnumber the hotel rooms-that's not in doubt. But because earlier he incorrectly assumed that there are as many passengers as real numbers, he concludes-incorrectly-that there are more passengers than rooms. To see why he's wrong about the passenger size, you can apply the same Cantor's diagonal to the real numbers and the passengers, and show that there are fewer passengers than real numbers. For sure, he removed the seats in the bus to make this correspondence difficult, but that didn't change the passengers from countably infinite to uncountably infinite. So the correct conclusion is that you can always accommodate any number of passengers in the hotel. Note that if say there's nothing wrong in assuming that the passengers are uncountably infinite, then there's nothing preventing the number of rooms from being uncountably infinite either. So again you can accommodate all of them.
@@nHans Okay so you're not nitpicking his actual argument, but how the the video is presented. He never had to prove that the number of passengers in the last bus was equivalent to the size of the real numbers, because that's how he DEFINED the bus in a THOUGHT EXPERIMENT. Saying that the passengers can't be uncountable because a passenger is something discrete rather than continuous is like saying that there can't be an infinite number of passengers because there's no such thing as an infinitely long bus. True if we're applying real world logic, but missing the point of the video.
@@nHans I can't see anything wrong with the way he presented it. No proof is required that all the real numbers are assigned to passengers, this is the definition of the bus. He even says: "On this bus there is a person with every possible sequence of these 2 letters". This doesn't need to be proved, it is a statement of what the bus (a set) contains (all the real numbers). Following on from this statement is the fact that you cannot assign all real numbers (passengers) to integers (hotel rooms). As with all analogies this hotel analogy does not have the rigor of a mathematical proof, but I think his presentation of David Hilbert's analogy is as good as it can get.
The second law of thermodynamics where everyone's in your house partying and making a mess and you're the only one able to clean it up and maybe your friend.
Hilbert’s hotel is even crazier when the infinite bus rolls up with an infinite number of new guests. Everyone moves to double their room number, making enough room for everyone on the bus. That lobby must be frightful with that many guests checking in.
I just had a crazy but fascinating thought: since the universe was uniform when it began ( even if enclosed in a very, very, very small amount of space); could it be that after the universe we live in results in a "uniform" emptiness in the far future, that itself is the new point from which the next big bang will occur? Essentially making that unimaginably large amount of space, the next "point" for the next big bang- the universe that comes from that, would be orders of magnitude bigger than what we have today, but the civilizations of that bigger universe wouldn't even know the difference. I hope that made sense!
Boltzmann, his arms wide, measuring discretely. Tanagra, where stochastic apples fell. Leibniz, the Patent trolled deep with partial respect to notation. Thanks for giving me fewer decisions, I definitely know which Vsauce shirt to wear when I get up.
Excellent video as always Nick, but I have two issues: 1) If the Universe is expanding at an ever-increasing rate, wouldn't all particles end up too far apart to interact at all, let alone come together to form a Big Bang? I can imagine particles cycle through all possible configurations if space remains the same size, but if it's ever expanding... 2) I don't really see the problem with an infinite future but not an infinite past too? It's like the positive x-axis, which starts at the origin and heads right forever with no end. At x = 10, you have ten units behind you but an infinite number ahead of you.
1) This is definitely a problem that would need to be addressed. I wonder if quantum wave function collapse could fix it 🤔 2) My personal view here is that lists like the natural numbers don't feel like complete lists. The list of _integers_ feels more complete to me.
If anything that can happen will happen eventually in the infinite time horizon, world as we know will be remade infinite times. In many of these your exact genetic copy and personality will return, infinite times, and in ONE of these you can end actually getting a girlfriend.
Wow okay that's a very very honest and factually accurate vpn ad. I was expecting the usual "overselling" marketing phrases but you surprised me and showed you value your integrity of your labour. Props to you!
"Can big bang happen randomly in infinite time?" No. The mistake you are makeing here is that molecules are moving randomly. But they do not - they move in a straight line until they hit another molecule (or an atom). So no room filled with air (under or near standar preasure) will have all the air molecules in one, small part of it.
@Jay Eifler Yes, humanity will probably merge with machines at some point. I doubt we will ever leave our solar system though and our doom is inevitable. Good luck with your TCAD simulations.
I actually have a potential mathematical issue with this: you would be correct in a static zero entropy universe. But the universe isn't static, it continues to expand; which means the chance of everything ending up in the same spot goes down with time... which means that as you tend toward infinite time, you tend towards infinitesimal probability, so it likely won't happen, even given infinite time. As an analogy, if you have two objects flying away from each other in an empty universe, they will NEVER come together, no matter how long you wait. Even if you apply gravity between them, if the universe expands faster than they can move towards each other, they will NEVER meet.
