Civilizations at the End of Time: The Big Rip
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- Опубликовано: 24 авг 2024
- Current science and cosmology tell us the Universe will slowly die and ebb away countless trillions of trillions of years from now, but another model - the Big Rip - says that end may come far sooner, ripped apart by dark energy. Could civilizations survive the Universe itself being torn apart at the atomic scale?
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Credits:
Civilizations at the End of Time: The Big Rip
Science & Futurism with Isaac Arthur
Episode 326; January 20, 2022
Produced, Written, and Narrated by Isaac Arthur
Editors:
Darius Said
Yamagishi
Cover Art:
Jakub Grygier www.artstation...
Graphics:
Jeremy Jozwik www.artstation...
Ken York of YD Visual / ydvisual
Udo Schroeter
Music Courtesy of:
Markus Junnikkala www.markusjunn...
Lombus lombus.bandcam...
AJ Prasad • Dark Future - Staring ...
Stellardrone stellardrone.b...
Math Note/Correction: As of the moment I've got 4 different contradictory explanations of why some of my comments on adding infinity this or that way, or how many numbers are in between 1-2 compared to total integers, is wrong or badly phrased. Everyone seems content with the overall explanation where it's relevant to the video, thankfully - An infinite Universe can still expand and infinity isn't a number - but needless to say, take that infinity math with a grain of salt :)
For everyone offering corrections on it though, please try to keep the explanations where someone who isn't a mathematician might have a chance to understand them or otherwise link to some page where someone does give such an explanation. And while you are welcome to call me an idiot, please do not call other commenters on the thread idiots just for saying your answer didn't make sense to them.
Edit: Also, yes, I am kicking myself for not thinking to make a R.I.P. joke on the the Universe dying by the 'Big Rip' :) Can't think of every good pun.
How difficult is it for everyone to be civil while explaining things they understand but others don't? Just imagine how hellish your life would've been if all of your teachers yelled at you or called you names all the time while teaching?
Didn't somebody famous once say "If you can't explain it to a child you don't understand it well enough." (paraphrasing) ;)
I can forgive you claiming that infinity+ number = infinity but, other infinity, while it is the same infinity (the same as when you will multiply it as well), which then would explain on it's own that you can expand or contract infinite things into still infinite things, BUT your discussion about energy conservation and problem with dark energy is worse.
Energy is just a number. It is conserved in closed systems (or through the Noether's theorem due to symmetry to be precise). The universe does not need to be closed system. And the symmetry needed for the energy being constant is not valid. So energy is not constant in the universe. Just like that. It is constant (conserved) on small scale, or as long as some issues (dark energy) do not arise.
Edit: After a moment it is getting better, as there is more info about energy from other places, so kind of open system approach. And this is only like 3rd of your episodes that I had issues with your explanation being false and unscientific. So just small percentage of quite specific field, while much, much more is just awesome!
@@sagarj5743 Apparently fairly hard for some folks :) though I should emphasize most folks were polite, there were just a couple bad ones thus far, one that needed deleted, and I figured I should slap the reminder on there as for many that's all it takes.
@@junorus I appreciate the forgiveness, but you seem to be saying I was claiming Energy is absolutely conserved when I flat out said that was probably not the case. I think you should re-watch that section, though here is the text of the transcript if you'd like to highlight what statement is false.
"One of our laws in physics is conservation of energy, that it can be neither created nor destroyed, merely changed in form. However, spacetime itself takes energy to exist, so when new bits of it get added, that takes energy, energy that doesn’t seem to come from anywhere, hence why we call it Dark Energy, dark in the context of being mysterious in function and origin. Amusingly while Conservation of Energy is often stated as ironclad law I doubt anyone is still living who actually learned that law while physicists believed it was without exception, as its been about a century since the Big Bang and Hubble Expansion hit the scene"
What's even stranger, is that even though an infinite three dimensional space is, intuitively, much larger than an infinite one dimensional line, Cantor showed that, nonetheless, they both have the same cardinality. In fact, an infinite three dimensional space even has the same cardinality as a finite line. To quote Robert Kaplan, "there are just as many points in the infinite universe as on the horizontal bar of this T."
Infinity is weird.
However, there are more curves and mappings in the infinite 3-d space.
Technically, one says that the power set of a given cardinality is the next bigger cardinality.
@@ozzymandius666 Power sets are not related to my point, but yes, 2^(aleph null) is a larger infinity than aleph null.
@@literalvampirepotbellygobl5629 The power set is not defined as 2^(X). It is defined as the set of all subsets of a set.
@@ozzymandius666 Yes it is. The notation is not related to exponents, but is used because the power set of X is bijective to the set of all functions from X to a given set of two elements. (A one-to-one correspondence.)
We can just call it the "set of all subsets" if you prefer. Or just P(X). Any notation is fine.
Yeah, like the infinite density of a black hole's singularity or the theoretical " Hilbert Hotel " with infinately many rooms, potentially infinite universes in the theoretical multiverse, etc.
I for one love the idea of seeing you learn to fly. I've always been an aviation nerd, so it'd be fun to watch. Also "A Brief Moment of Eternity" sounds like one hell of a science fiction book title. I'd use it, but I'm not a good enough writer to do it justice.
This is my code "Spoffort", for a phone application that mining its own cryptocurrency, but they do it in such a way as not to use the processor or battery, it’s called pi NETWORK
Ive always wanted to learn to fly, so I would be very interested in watching him do it.
You're not a good enough writer to do it justice YET.
@@bbeen40 lol I'll take the complement.
“The Moment of Infinity”, has a nice ring to it 🤔
Could be the very moment, frozen in time, at the singularity of a black hole... ?
Of course, I reckon... you could never reach the singularity, without BECOMING the singularity...
I wonder if you could observe “all” of the universe... for “all” of time from that vantage point...
That is, if we can ignore the physical effects of actually getting there.
What a joy it is to return to this series. This was the series that got me hooked on your videos, and your signature style keeps me coming back for more. Stay awesome Isaac.
Same for me! Love these I think my first ever video of Isaac’s was Iron Stars a few years ago, now I listen all the time
same here, i'm following since black hole farming
that was such a lrvel up compared to the recycled documentaries about space i was listening to, to fall asleep back then
All universa and all dimensions will be absorbed into one Empire! All will be connected! All will be inside! No outside anymore! All will be unifyed and connected to the machine, mother machine! All over is centre! All are Chi-Borgs! Alpha Omega Minorah Karma.
I love how you spend the time to add captions. I use them a lot for making sure I catch everything or know how to spell certain words or names for me to look up later. It’s also great for times when the area around me is noisy, which is often. Thank you!
The funny thing is he puts in the closed captions because *he thinks* he has a really bad speech impediment and people have trouble understanding him. I thought it was just a local dialect. We have so many different regional dialects in the United States. Good to know somebody's benefiting from his self-consciousness.
@@freeamerican2708 exactly!! let me tell you english is not my first language and over the years i’ve had to stop watching lots of videos because i could not understand a single word. isaac arthur to me is perfectly comprehensible i don’t think i’ve ever been confused listening to him even without captions!! (except when he throws in super scientific terms that i didn’t even know existed)
@@doublethenun I definitely had a little bit of trouble understanding certain words when I first started watching him years ago. I'd have to pop the captions on, see what a word or two was, then turn them back off. But after probably like the 3rd or 4th video, I never needed them again.
@@davecarsley8773 Ditto! I binged the old Upward Bound series while working on a pool and had to rewind a few times to make sure I heard him right, but by the end of the playlist I really stopped noticing.
My name is Lord teleport
im never this early for an isaac arthur video and ive even already got a drink and a snack ready!
Gotta be a great feeling!
Having trillions of years with nothing but the end of all things in front of you I'm pretty sure some of that time would be taken up on doing something about it. In fact I would say they will have the power to not only extend the universe's life but to extend it indefinitely.
The universe might not end. We really don’t know. Also other universes could exist. It could also be possible to make our own universes. There’s so many different possibilities of ways life can continue. None are facts yet, but neither is the end of the universe
@@lionelmessisburner7393Exactly 💯 👏 we have millions of years to see if this Big Rip is even true 😅
@@Coneelfrancistrillions upon trillions
I heard that with enough energy in a tiny place, we could open up a baby universe. We could become an actual type 5 civilization, trillions of years in the future.
To what trade-offs?
26:30 "Let's be honest, nobody really thinks of their civilizations in million year terms" And i took it personally x,)
just when you thought you had enough existential crises to worry about
Isaac: "time might drain out of the hourglass and leave the Universe in a frozen instant"
nice
A Zeno's paradox civilization, every time the remaining duration of the universe is cut by half, its computation speed doubles, which allows its simulated minds and virtual worlds to exist forever in subjective time.
I started learning to fly last year, and would be thrilled to see some one else go through it. Too few people take advantage of the fact you can just go to an airport, and learn to fly. It changes your perspective on things in so many ways. You never see the world the same way again.
Very true the firsttime i took a small plane up into the air and saw my town from above . Mind blowing
One thing other RUclips celebs could learn from Isaac is that of engaging with their fans. I've left about a dozen comments on his Patreon forum and I am pretty sure he responded to all of them. Part of the reason I upped my support.
I understand almost none of the science or logic and yet I love watching videos like this.
4:40 - 6:40 This segments has a lot of errors in it.
It's true that there are different size infinities, but ∞+1 is still ∞. A good way to compare two sets by size is to try and match up their elements in pairs, you can match up ∞+1 and ∞ with (0,the additional element)(1,0)(2,1)(3,2)(4,3)... we say they're still the same size.
The set of real numbers is indeed bigger than the set of naturals, but with a Hilbert curve you can map all points of a plane on a single line, ergo they're the same size of infinity again. iirc Hilbert curve works for 3d space as well, so again it's the same size of infinity.
Most of this is just semantics, and not really relevant to the subject, so it doesn't invalidate the video or anything, but I don't want people to get the wrong idea.
Glad to see that this section hurt someone else's brain enough to force a long comment :-)
If you want to understand infinity, your best bet is to take a Discrete Mathematics course, wait until your head stops hurting, then take the course again. :)
I wanted to make that exact same comment, but luckily checked if somebody has made it already. Thanks.
For anyone interested, vsauce's "how to count past infinity" video is a much more accurate treatment of comparing different infinities.
I wonder if civilizations could exist over such immense timescales. The longer they are around, the longer the opportunity for bad actors to arise bent on destruction. Or for the unintended consequences of a decision to result in annihilation. I don’t think you could ever be certain a civilization has escaped the Fermi bottleneck.
How does this channel not have 1m subs yet? Been watching weekly since 2017, another great episode!
Now, if it was marketed as an ASMR channel I bet ya it would!
@@patrickanthony3632 now thats an idea
I think it get too far down the STEM hole. Combined with the fact the show is deeply rooted in facts. This show is for a neich subset of people that want granular details of a very plausible reality.
Episode length is a big part. Lots of science channels have large subs but a lot of people will not watch and sub to a channel that always produces content that averages around 30+ minutes per video. People tend to watch in 10-15 minute chunks which this channel far exceeds so a fewer amount of people will stop and watch these videos and sub afterward.
Episode length, absence of aggressive marketing, and the fact that many viewers (of _any_ content of YT) aren't that smart or even scientifically inclined. I'm not talking about the people that would ask "What's a big rip? never heard of it" - those are at least _interested_ and possibly able to catch up eventually - but those who are the intellectual equivalent of vacuum, without as much as quantum fluctuation.
I'm talking the kind of people if you look into their eyes closely enough, you see the words "NO SIGNAL."
I'm so glad this series came back
series don't end here, there's always more topics on any of them
I love the graphics this is a great channel, thanks for closed captions my phone got wet and I can't afford to fix it for a while.
For some reason, i love to watch these videos while working out. I dont know how many times I've heard you talk about space travel or speculative sociology while pushing my muscles to their limits. Thanks Isaac
I love these brain-stimulating videos, Isaac! Being buried in the world of meteorology, I sometimes forget to let some out-of-the-box thinking soak-in. Also, I once again must compliment you on the excellent lead-in your sponsor at the end. Perfectly executed! Thank you, as always.
Great video ..one of the best channel ever
You should do a video on if we encounter a civilization that is technologically behind us, i think it would be very interesting to see the script flipped
Primitive aliens, maybe?
@@isaacarthurSFIA YES! Perhaps we could uplift them Stellaris style.
I've thought the same thing b4...nice to read it from someone else
@@wofuljac uplift ? and then...umm...ill just say that mine and your Stellaris playthroughs are not the same. ;D
you mean like dolphins
There is an error at 22:19.
The “time freezing on the event horizon “ is NOT a misconception. That’s the actual correct theory. That’s the result of GR equations. Not at the center, but at the event horizon. That’s where escape velocity is c, which is associated with frozen time.
Of course it is not literally frozen, it is just infinitely slow for an outside observer, but these are the same in practice.
12:40 the law of conservation of energy can be derived from the assumption (based on observation) that the laws of physics are constant through time. If that assumption is violated then we can't necessarily say that energy must be conserved.
Thank you for confirming an idea I had in college was reasonable - namely that big rip + quark pairs would generate huge numbers of additional quarks. I brought it up to a professor of mine and he dismissed it saying that they would simply get redshifted into oblivion but that never really made sense to me. How could something get redshifted in its own reference frame?
I love Thursdays !!! Thanks issac, grabbing my popcorn now
Sometimes I wish I had a head for math so I could join in these interesting debates, and sometimes I'm glad that when the math gets complicated, it's like what Santa's Little Helper hears when Bart's talking to him. I'm not stupid by any means, but math has NEVER been my strong suit (made worse by dyscalculia), so I just enjoy the pretty images and pleasant narration for a minute. :D
I like your channel because you come across and an extremely reasonable person who is aware of his own fallibility and can SERIOUSLY discuss and critique sci-fi and futuristic concepts while actually maintaining a sense of optimistic good humor about them. That's why I generally take it as given that you've made a good-faith effort to be honest and fair in those moments when the math gets heavy.
Thanks for these videos. They inspire me every time I watch them! (I really enjoy the extended ones on Nebula, by the way!)
One of the best channels around, I have always an extremely hard time listening to any science based channel because it's
A. Some talking in such simple terms that it feels like I am being talked down to by a "more enlightened individual."
Or
B. A PHD level course in video format with no explanation on anything not directly related to the topic no matter how important.
Your videos fit neither, they are articulate in simplification of what I can assume are highly complex and difficult topics in a way that anyone can understand. All the while making the simplification of said topic have no trace of that talked down to feeling.
that's what's called a teacher i think
I think it varies from your own understanding level a lot, putting aside the quality, as some people goes along with some kinds of language more than others.
I could recommend The Science Asylum or PBS Space Time as both are awesome channels about science to me, but someone else could easily put them in one of the 2 cited categories.
Anyway, I enjoy a lot how Isaac expands to the science-fiction universe with very regards with the science in it.
23:00 that would be a crazy possibility, ducking into a black hole to escape the end of reality
The discussion of infinite around 5:00 differs from current mathematics. We compare the size of infinites by proving whether there are or cannot be one-to-one functions between them. We've proven the countable infinites to be less than the uncountable ones (see Cantor's diagonalization), and certain categories are equal. In particular, the sum of irrationals between 0 and 1 is equal to the sum of irrationals between 1 and 2; even though one would seem to be twice the size, doubling an infinite does not change its cardinality.
As always say : Awesome channel with awesome content and great quality 🌍💯
Isaac knows how to explain where even a blue collar guy such as myself can understand things. Thanks buddy
Minor correction. The notion of different ordinalities (where infinity + 1 is not infinity) is not the same as the concept of cardinality (where infinity + 1 is infinity). These are very different properties of sets and they require different assumptions.
In standard definitions of the real numbers and the extended real numbers, there is no such concept that differentiates infinity + 1 from infinity in any way. To have a meaningful distinction between the two you either have to use a nonstandard definition like the surreal numbers or you need to restrict your discussion to natural numbers (nonnegative integers). In that circumstance, if you have a certain kind of ordering (definition of something being “greater than” another thing) then you might be able to make sense of the concept of infinity + 1 being distinct from infinity.
This usually done using what is called the successor function on numbers represented as sets. Usually the empty set (the set of nothing in it, or the set of even primes greater than 7, etc.) is defined to be 0 and we define the successor function to be the function that takes a set and adds the set itself as an element. We end up calling that output the next number. For example, 1 is defined to be the set that contains 0 as the successor function takes the contents of the empty set (all 0 of those elements) and adds the empty set itself as an element. This means that 0={} and 1={0}. Likewise, 2 is defined to be the set 1 along with the set 1 itself as an element. Meaning that 2={0,1} (the set of the first two natural numbers). These are called ordinal numbers, the finite ordinal numbers.
This process continues ad infinitum. However, we have a notion of greater than built into this definition. We can say that a number (a set) is greater than another if the latter is an lament of the former. 0
Maybe by the time the Big Rip is fixing to happen, we ( or our descendants ) will have achieved Kartashev type 4 status and have control over the fabric of spacetime itself.
Amazing episode Isaac!!! Was waiting for this one for some time. And that last quote sent goosebumps to my body. Holy crap you never ceases to amaze me man!!! Absolutely wonderful work.
Awesome! Thank you!
For sure my favorite closing of any episode so far. Bravo to who ever wrote that last sentence!
Holy crap, a recent vid! I love your channel dude, and all the end of time stuff has been really helpful for brainstorming on my sci fi book. Keep being awesome :)
Also seeing some flying lessons sounds very cool, please do!
Huge upvote for relevant equations onscreen. Sometimes I just ignore them, but they give the videos much more rewatchability, which IMO makes this a worthy successor to the previous CatEoTs :)
Thanks again for all your content. I like that we agree on fantasy/sci-fi stuff, and quality when it comes to screen adaptations
When redshift was first discovered and explained, was there a discussion whether it's caused by time acceleration instead of the expansion of space?
Probably, but we are only now catching up to their questions...
Sorry, I'll show myself out.
Expansion of space, known as Hubble's Law (en.m.wikipedia.org/wiki/Hubble's_law)
I think the idea that energy cannot be created not destroyed is a large assumption considering how little we really know.
You are in your element here, because you are especially good when working with huge scales, particularly scales of time. Iron Stars is my all time favorite episode, this was a delight too.
Also my all time favorite...must have watched it 9-10 times
Just bear in mind that if it takes ~10^1500 years for iron stars to form, there are usually on the order of 10^1400 years before each *single* fusion reaction happens between two or three nuclei. Even taking into account slowing down computing to speed up subjective time, that's taking it a ways too far. Something like 10^1300 black hole eras of time would go by between each of those fusion events. Way too slow for most concepts of supporting civilization.
Interesting idea to think of time as being a quantity of stuff poured into our universe
I don't get why or how, but your videos just keep giving me story ideas - so many story ideas!
Isaac, THANK you!
Coincidentally, "Big Rip" is what I call my civilization-ending flatulence
Ahahaha! Didn't take long before someone made a fart joke.
Oh boy I’ve been looking forward to this ever since I first watched the civs at the end of time
Brian Egan's book "Diaspora" has a fun take on this idea.
Yet another informative video. Learned quite a bit for this topic is not something I looked at that much.
"Infinity is not a number."
"Infinities can be vastly different in size."
"The universe at the Big Bang was already infinite in size, we're just expanding into a bigger infinity."
Isaac, I'm just an engineer; you're making my brain hurt! Can't we talk about tensile strength of nanotubes?😁
Hi Issac I've been listening to your channel for many years, love it! Definitely document your experience learning to fly, it's such an awesome trip!
I learned to drive GA aircraft twenty years ago and I've had so many amazing experiences since I first sat in a Cessna 152. Worked my way through the 170, 172, 175, even have got to fly a friend's 185 he uses to land clients on glaciers high in the Alaska Range. Such power! Cubs, Super Cubs, etc. Growing up in Alaska definitely gave me access to a lot of awesome planes, it's a big part of the culture up there.
I'd love to see the process of learning to fly with you and Sara. I think many people would.
You my friend need more subscribers. Your videos are a true work of art. You have taken my curiosity and answered the questions that come along with it. Keep it up man
Hi love your vids keep em coming.
id like your take on "post univers civilizations" as in civilizations that wander from universe to universe in the multivers theory.
Maybe "Civilizations After the End of time"? :)
I just hope we get to the next few steps of civilisation
Your videos are so good, the narration, music, visuals, scripts, and conceps all come together to make for a great time!
Love this channel. Just love it.
Hahah Isaac gave me a recap in infinity, I remember learning that in calculus class where infinity + 1 is still infinity, etc, always like watching your vids man
Great episode. Weird to think that a time machine that could travel forward just a few seconds could potentially be such a game changer.
Glad to see your learning to fly. Super cool. Keep up the good work sir!
I don't comment a lot but these long videos are awesome. Brilliant work as always.
Isaac Arthur just explained how we can prestige existence into a new game plus. If we break singularity in our lives, perhaps we will all be infant gods in our own universes. If that doesnt send a shiver down your spine, I dont know what would.
The much awaited episode. Finally.
Being the most advanced civilization in the universe's history, maybe they can just create the beginning of the universe, answering the question of where it is we came from.
I've been thinking lately what we know as black holes are more like boundaries of spacetime of differing densities. Our observable universe would be bound by the behaviors associated with black holes. For example, black holes have a formation period, followed by expansion and eventually slowly contracting. Hawking showed that black holes can absorb and emit radiation, which is how they grow and shrink. So if we live inside a spacetime bubble, a black hole, we could expect the universe to expand through hawking radiation. This radiation bleeds through the boundary and transforms into both space and time. A large black hole has a longer lifetime than a small black hole. A consuming black hole is increasing its lifetime, so it's possible we live inside a black hole that is consuming matter and expanding. The grand universe is comprised of cascading spacetime bubbles
Yes another entry to this series!
Interestingly that they came up with a random guess of how long the universe has to exist of 20 billion years as also the element with the longest half life is Bismuth which also has a half life of 20 billion years. so i would guess that the answer would be more when energy stops producing mass plus 20 billion years :)
Doesn't Hydrogen have a half life of like ∞ though
wouldnt it be longer because the decay products of bismuth will still be around
Isaac addresses all the questions I've ever had about the universe and has introduced me to so many more topics. Isaac conceptualizes the processes in which all of these fantastical ideas would theoretically function. I predict a lot more videos once JWST starts beaming back pure GOLD! Also, thanks for your service. 12B OIF/OEF
When a civilization run into the event horizon for shelter at the same time they received an important message sent by universe itself, here's what it say:
I'm regret to inform you guy's has failed to extend the warranty. Please pay the bill by returning back to the current universe.
Best regard.
When dark energy pulls apart a quark and creates 2 quarks it might continue to pull on the new quarks and quickly create more quarks.
So, you might get a whole new universe being created from a single quark with dark energy turning energy into mass.
Now imagine that same reaction across the countless quarks in the universe.
Make sense. An infinite pull making infinite new particles. Thus a new universe.
As a private pilot and fan of your stuff and a lot of RUclips pilots I’m all for you making flight videos as long as you’re being safe about it, of course :)
Awesome! Thank you!
I see that others have already offered correction to the description of infinities, but I'll add my own explanation.
To start with infinity +1, this is equal to an infinity that is exactly the same size as the first infinity. To see this, think of all the natural numbers, from 0 to infinity, arranged in a line, like a number line. You can shift the number line 1 place to the right, adding 1 to each number on that line, and then reinsert 0 at the beginning. Doing this, you've added one element to the set, or one number to the line, but you have the same number line you started with.
You can also add infinity to infinity and still get the same size infinity. To do this, take your number line and add all the negative integers numbers from 0 to negative infinity to it. We now have a line that goes to infinity in two directions, so it isn't the same line. However, we can fold the line over so the infinities are in the same direction (i.e. multiply all the negative numbers by negative 1) and subtract 1/2 from each of the numbers from this half the line so they don't end up in the same place as our other points. This will give us a number line with a point every half a whole number, so the line has twice the density of points. To get our original line back we just need to multiply each point by two.
Because adding infinity to infinity in this way is equivalent to multiplying by 2, and any finite multiplication can be reduced to a series of addition and multiplication by 2, this means we can multiply infinity by any integer and get the same infinity back.
So what about multiplying infinity by infinity? Well we could attach a second number line at a right angle to the first to give us a plane, and consider all points with integer coordinates. We now have infinitely many points for each of the infinitely many points. What we can do is draw a line that goes through each of these infinitely many points. Any space filling curve (and a few other operations) can show this, but an easy one to describe is to start along the x axis, and at the first point where a diagonal back to the y axis will cross a point with integer coordinates, take that diagonal path. Then continue along the y axis until the first time a diagonal back to the x axis will cross a point with integer coordinates, and take the that diagonal path. Then repeat. The line you draw will be infinitely long, but will cross all points with integer coordinates. You can then straighten out that line, and put it next to the original number line. With a scaling operation, you can get this new line to be identical to the original number line. So squaring infinity will give you the same infinity back. Incredible.
Much the same as the multiplication case, any finite exponentiation can be reduced to a series of squaring and multiplication, so we can do all finite exponentiation too.
So what about all the numbers between the integers? For rational numbers, i.e. fractions, we can take every fraction, and make the numerator the x coordinate on our integer plane from the last case, and the denominator the y coordinate. We won't fill every point without putting some rational number on more than once, but that doesn't matter, because we can show that the rational numbers aren't a larger infinity than our natural numbers, and, since the natural numbers are a subset of the rational numbers (just a fraction with the denominator 1), it can't be a smaller infinity either. They must be the same size infinity.
It's beginning to look like all indignities are the same size. This isn't the case though.
Irrational numbers are where this stops. Any number that isn't a rational number has an infinite decimal expansion. You could write out infinitely many numbers with am infinite decimal expansion, one for each of our infinitely many natural numbers. If these sets are the same size, you should be able to write every single irrational number and give it a corresponding natural number. If we try this, we can go along afterwards and write a new number, where we look at the first decimal place of our first number, and write a different digit, then the second decimal place of the second number and write a different digit, and so on for all the irrational number we wrote down. This new irrational number has to be different from all of them by at least one digit, so we have more irrational number than natural numbers. We have a larger infinity. Indeed there are infinitely more real numbers between 0 and 1, than there are rational numbers.
So, there is a lot you can do to infinity without changing it's size, but you can still get different sized infinities. The inverse operations of the finite operations I discussed do also work, but infinity minus infinity and infinity divided by infinity are not well defined.
Super-excited to watch this, let's go!
I'd be interested in hearing more about using dark energy for power production. In principle, could that work even at current dark energy levels? If conservation of energy isn't exactly true, maybe perpetual motion isn't exactly impossible.
Beautiful closing in that script.
One Brief Moment of Eternity.
I for one would love to see longer video's not short one's...love this topic Isaac
One brief moment of eternity sounds like a civilization scale enlightenment.
This is one of your best videos. You just keep getting better. Thank you for all your work.
I swear I've seen every other video in this series like 10 times. This and the Fermi Paradox series are definitely my favorites!
Dying Stars and Planet Ships are near the top of my list. IMO black holes as a power source are kind of overrated, either by dumping something into them or with Hawking radiation, or trying to harness the angular momentum. Not as convenient as a white dwarf or neutron star heat sink.
Heat is actually where the black holes do come in handy, since even a stellar mass one has a temperature of about 20 nanoKelvin, and supermassive ones are much nearer absolute zero still. When a lot of other temperatures equalize, black holes get even colder as they grow, so you can still run engines off the heat flowing into them.
Maybe I'm not remembering correctly but I thought physicists worked out math which shows the possibility that a universe that's spread out enough (post-big-rip) would be equivalent to a microscopic space "coming into existence". This would mean a cocoon to wait out the rip would be futile, from your perspective matter would never "come back"
Discovery/History/Science Channel needs to purchase your content and air it. Your content is far superior to the last stuff I watched on those channels (granted, it has been about 7 years).
This blew my mind. Thx so much for the inspiring episode!
Great, another video I will watch literally hundreds of times while falling asleep. Cheers
It must be a great feeling knowing you have a vast fan base, that your content is informative and well constructed and that you're providing free knowledge and story telling on a platform that people use for mostly mind numbing content.
Thank you kindly.
when I was 7 years old, the question of infinity hurt my brain. Now I am 50 and this video explained it all. Thank you, now thinking of infinity it don't hurt my brain any more.
If we were all a bit like Arthur we would all be a bit better. Thank you for the positivity of your videos Arthur.
The Omega in the Big Rip Time Estimate formula is a clever foreshadowing of the first mention of the Omega Point in this series
I get why people get confused by how the universe can expand yet still be infinite in size. But I think it just a poor description that gets people confused. But in short of it. It is just that empty space between stuff is growing. Or is like all the stuff was shrinking while the empty space remains the same. It is an easy enough concept enough to understand. I actually do like the balloon dots on it analogy even if I know some scientist dislike it since it can give the idea that the balloon must expand it to something. Which maybe the universe is doing, but we do not know and should not assume so. But I think that even if they get this little misconception (which might not be a misconception at all, see previous sentence) it is better. Since the person now have a decently accurate picture of what is going on. All analogies will have limitations, or else they would not be analogies.
I can watch these back to back for hours but I fall asleep in uni lectures lol
32:15 I wish Dyson Sphere Program had gfx that good.
Great episode! Would love to watch your flying journey!
Issac Arthur: "...there's no continuity to a new big bang or recycling event..."
Galactus: "...ok am I a joke to you?!"
"Enjoy a ton of though", that is a very deep. Made me chuckle. 👍
Another fantastic episode!
4:40 Well actually according to Set Theory Infinity + Infinity would technically be an equally sized infinity. You have to get into Power Sets to get larger infinities. For instance all odd numbers and all even numbers have the same level of inanity as all natural numbers which is both sets combined. All real numbers thought is a power level above with a "larger" infinity.
30:00 Could you concentrate the mass of several galaxies into 1 structure, a giant network of stars and blackholes much tighter packed than a natural galaxy to resist this expansion?
The tipping point of gravity vs dark energy isn't something that can be localized as we know it so far. However if we could find a way to convert dark energy\matter into conventional matter, we could for the lack of a better term, go to war against dark energy\matter and possibly tip the scale but the problem is if the universe is in fact infinite, we'd need a infinite amount of weapons to tip the scales, making that impossible.
@@IdgaradLyracant I suppose I'm not talking so much about stopping it but lasting longer. if you concentrate the mass of galaxies into somthing only a couple hundred light years across they'll be more gravity and less dark energy being produced as there's less space for it to come out of. If I understood it correctly.
@@garetclaborn I mean yeah I'm out of my depth too. My project are all like in the next 50 years with the physics we have now, not 20 billion years combining galaxy worths of mass
Going to need to make a "big rip" of my own before I properly understand this stuff!!
What if we think of time being the balloon?
The larger the balloon gets, the further the points from each other are, the slower time "processes".
Subjective time stays the same, but universal time (which would be required for this) would be affected and slowed... making the universes expansion seem to be increasing.
and gravity, the effect of mass, is the thing that's the "equalizer" for the expansion of time itself. A necessity to reduce the effects of time-expansion.
Like tiny holes on the balloon of time, the more mass, the deeper the hole.
There are some maths issues here:
1. If we're dealing with cardinal arithmetic, any infinity cardinal added to itself gives you the same thing. With ordinal arithmetic, what you say about this is correct.
2. There are more numbers between 1 and 2 than there are natural numbers.
“…even inside you and I.”
Beans must be powerful Planck attractors!
Where’s my nobel?
Personally I love aviation, and I'm sure I'm not alone in that, so seeing you guys learning to fly would be cool.
Actually there is perfectly good math where infinity is a number. Also infinity + infinity is the same size infinity as whichever is larger. The integers are the same size as the even numbers. The rationals are the same size as the integers too. The reals are bigger than the integers though. Infinity really isa weird thing. You might be thinking of the density of numbers, but I won't comment on that as I didn't study much measure theory.
Sorry. Should have looked at earlier comments. I agree that these details on infinity shouldn't matter for the purposes of this video