The Biggest Ideas in the Universe | 4. Space

[@hero227]

Thanks Sean, for putting out these videos. We often take for granted how the internet grants us a wealth of knowledge at our fingertips, but it's like you're literally giving us a 1-on-1 lesson on these topics from the comfort of our homes. I find them incredibly interesting & informative.

[@avrenna]

This comment made me pause and reflect for a moment on how incredible it is that we have this ability. "Any sufficiently advanced technology is indistinguishable from magic."

[@CMDRunematti]

1-on-1 lol... i was asking "yeah but why..." and he actually started explaining what i asked from the video XD

[@CMDRunematti]

@@avrenna or otherwise: anything that looks magical is probably some fancy tech. knowing this saves you from a lot of woo

[@ritemolawbks8012]

I know it's an understatement, but has anyone else noticed how smart this guy is?

[@vansdan.]

These videos are exactly what I need. I could listen to you talking about science for hours, and you're granting me that ability; thank you!

[@shikulli]

FACTS

[@JasonWalsh-b4n]

I AGREE. AS FAR AS SPACE GOES, CLASSICAL PHYSICS IS PERFECT.❤

[@sandrasandra7593]

Thank you dr Carroll, great lessons! High school made me hate physics, now I love it! Thank you for using your intelligence, your knowledge and skills to make the world a better place

[@soulremoval]

so grateful the internet exists, letting people like Dr. Carroll and Dr. Greene give these amazing lessons.

[@321rafwaf123]

Jessy Nemati dr greene can u share his channel? thxx

[@frede1905]

@@321rafwaf123 He has a series called "Your daily equation" on the World Science Festival channel.

[@avrenna]

I love how relaxed and friendly these are. Check out the phenomenal sound effects at 16:43. :)

[@beenaplumber8379]

Totally! If my uncle were a physics professor and I asked him to explain all that crazy technical crap to me, he might smile and say sure! Easy! Then we'd sit down over a coffee and this is what would happen. This format helps me learn so much better than lectures. We're just chatting. He knows how much I don't know, but he also knows I have a brain. He just helps me to discover it and explore it. It's bigger than physics. There's a lot of "how to think" in these videos.

[@veroosh]

I showed this to my dad and it turns out he's a fan too. His words, "he's a really great teacher." I agree.

[@harshvardhan4766]

yeah and look at you doing shit like horoscope

[@pierfrancescopeperoni]

@@harshvardhan4766 Well said.

[@ScattMatt3000]

Tell your dad you love him for me 😞💪… greatest teacher you’ll never truly appreciate.

[@hifibrony]

Both Sean and Brian Greene have a remarkable ability to clearly explain highly abstract and complex physics to intelligent and interested non-physicists. Two of my favorite science communicators, along with Jim al-Khalili and Brian Cox.

[@christopher6971]

Sean, the production quality paired with your concise communication style makes this series an invaluable asset to the physics/cosmology community. We sincerely appreciate the time, effort, and thought you invest in these learning tools. All the best to you, Mr. Carroll.

[@edmeko3262]

Sean, what you are trying to do here for all of us trying to learn about this Universe is really fantastic. Each episode gives me another small window into what is happening around me every day. Knowledge of the immense space in which I am swimming. Thank You so much. I also enjoy many of the episodes in Mindscape.

[@supersleeper8545]

The quality of content here and your podcasts are a massive contribution to science education. Thank you. May God bless you with a long and healthy life. It is a privilege to be alive in a time when access to this knowledge from such a deep knowing perspective is accessible.

[@PavaniGanga]

Thank you! Only one physics course decades ago. It took me twelve hours, reduced playback speed, pausing the subtitles, multiple repetitions, and so much scratching my head, mulling my notes, and wrinkling my math-challenged brow. But I finally pulled through. I a 73 yo retired nurse was motivated, because you make the subject so interesting! (The other videos were much easier for me, but for some reason the Hamiltonian was tough.)

[@jcliggett53]

Great series! I love that you bring up questions to which you don't have an answer, and even say "maybe one of you knows the answer". Great way to entice budding physicists to explore the ideas that interest them!

[@BishopNE1]

Sean, thank you SO MUCH for the free education. You are my favorite professor. We loved you on Joe Rogan as well. I wish you and your family the best!

[@tonib5899]

Thankyou Professor Carroll, not just for the maths but for also being a decent person exactly when we need it. T.B from the U.K.

[@danstrtelagergren6389]

You are making the lockdown bearable, and through this video series reaching people all over the world. Sean, keep spreading knowledge to the world! It’s your gift! Thanks from Norway!

[@TontoBongRonto]

If it's unbearable why do you accept it ? If you really beleive it is warranted it wouldnt be unbearable

[@TheJonlamb12]

I’m trying to “wrap” my head around thinking in four dimensions, but the idea seems to pass right by. Oh wait... Great video! Thanks for making this quarantine interesting.

[@archaicentity38]

This is genuinely one of the biggest ideas in the universe: "Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space." - Douglas Adams

[@archaicentity38]

@Vendicar Kahn I'll answer that on the next conformal cycle.

[@PazLeBon]

its not very far from here so his logic was wrong. Also peanuts ? I dispute that too, it's more pistachio, def from a tree; he also prob thought a tomato was a vegetable ;)

[@agimasoschandir]

@@PazLeBon Adams logic is a mixture of sarcasm and wit, and sort of an anti-logic. Most of the books after all are during the use of the improbability drive, which you program by bistromatics. In a sense, it is the use of the drive that probably cause the improbable reconstruction of the Earth after it was destroyed. Not sure why the nut has to be from a tree, people are familiar with sayings such as "I worked all day and all the boss paid me was peanuts"

[@PazLeBon]

@@agimasoschandir I think peanuts grow in the ground ;)

[@agimasoschandir]

@@PazLeBon Correct. If you are implying it isn't a true nut, you would be correct as well if using the botanical definition, but not the culinary definition. Bit like the fruit tomato is classified as a vegetable

[@dizy3513]

Sean what you dont get is this is extremely important... you do these to educate and expand minds .... even if only 500 ppl watch these ... idk man I've spent years reading physics books ...what you are doing breaking it down and keeping it real ... is massive ... if I had these 20 years ago ... my life would be different... thank you is all I can say

[@veroosh]

This is brain candy - just in the first five minutes you've explained several concepts in a totally unique way I have never heard them explained before.

[@veroosh]

Listen, I think you SHOULD teach us. Yes the delivery is super approachable, as is all your content I've encountered, but I don't think you should downplay the benefit these "sessions" ;) offer to anyone who wants to expand their understanding of physics. In some ways this is a topper to a course, and I hope you really get into this and make 1000 of these.

[@Cemselvi1988]

I am doing an astrophysics PhD and I enjoy this very much

[@johnphil2006]

Can we expect your next book: "The Biggest Ideas in the Universe". Much deserved one.

[@beenaplumber8379]

It would have to be a coffee table book or something informal like that. Nothing resembling a textbook. What about a big, thick comic book starring Alice & Bob?

[@dazecm]

Can I just say thanks for a great book (Something Deeply Hidden), a great podcast (Mindscape) and these great videos. You are single-handedly keeping me sane and entertained throughout this infuriating virus lockdown.

[@raf69777]

This is so incredibly fun, thank you Sean.

[@brendonhammer6108]

I loved the cool way you made "dimensions" (literally the word) disappear, in a time reversed kinda way, from 19.25 to 19.45 min ;) Meanwhile, just such a great series. Thank you so much.

[@0endofsilence]

Sean, you are one of the best educators on physics out there. I always hated physics and math but after seeing you on JRE I am now fascinated by it and want to know more. I'm in the middle of Susskind's Cosmic Landscape and im binging your podcast and the PBS Space-Time. Thanks for making me realize how awesome the universe is.

[@iuliandoroftei5088]

I am a huge fan of Physics and you are my new hero! I have never watched something more engaging. What can I do to contribute to you continuing these lectures? Life has taken me to other endeavors but science will always be my number one reason to excitement and inspiration. One day soon, I will finance one of your projects, Sean!

[@michaeljehlik5393]

Thanks a million Sean it's really great that you are teaching and sharing your ideas about physics on KZbin! You are such a great teacher! Your videos and presentation style are top notch. You teach advanced concepts in comfortable inspiring way that helps me postulate and want to dig in.

[@minaghavimi4843]

Thank you so much for taking the time to prepare these fantastic sessions to explain physics to the public.

[@KieranGarland]

I'd been meaning to bug you with a question about Lagrangians and Hamiltonians, and here you've beaten me to the asking of it. This is all really great, like a Theoretical Minimum for the layman. Thanks again.

[@DCardinell1207]

Thanks for your time and energy sir. These videos are great.

[@robertgoss4842]

Dr. Carroll: Thank you for this superb series. I have seen about 8 or 9 parts of your series and I am just a bohunk boy from Georgia. But I must say that you speak intelligibly on even the most complex topics. I have reaped huge benefit from this series of programs. Thank you again.

[@crisdellani]

Sean makes an apparently dull and mundane topic such as space look incredibly interesting, mysterious and mathematically complex. You're a terrific communicator. Thanks for doing this

[@peterpackiam]

Thanks, Sean for sharing your Precious Time & Services, most appreciated Cheers.

7:36 like the "2000 miles long man" (as he stated) in Leonard Susskind's lectures on GR :) OK, different context (there it was about explaining the tidal forces) but still it made me smile :)

[@_Messiii]

Thank you Sean, these videos are gems!

[@edmundodelagarza4418]

Thanks doc Carroll. Your matter-of-fact disposition is most inviting and whets my imagination for more; all the while smoothing the rough edges of uncertainty remaining from school.

[@chromabotia]

That was great, a little more freewheeling, but fun and intriguing! Thank you Dr. Carroll.

[@Rich-rp9xy]

Hello Sean Carroll, thank you for these videos! you and other physicists that post videos on youtube made me love to learn about physics. I used to hate physics in my school because we had a teacher who made it impossible to understand it for most of us, and back then with no internet, there was no one other to explain it.

[@galleoboutique1852]

Love your talks & have much respect for what you guys do. Im a true physicist at heart. Thanks Sean, very interesting.

[@ankiesiii]

Absolutely amazing, and so well communicated.

[@FergusScotchman]

Sean, these are great and welcome during the covid experience. At 8:44 you essentially talk about the energies of different wavelengths. This obviously has relevance to red and blue shifting of stars... moving away shifts the spectrum toward red. - Can you tell me if energy is conserved in the spectrum shifts cast off by celestial objects, since red-shifting must mean a loss of energy. - How much does relativistic space-time have to do with the conservation of such electromagnetic radiation. (I know Einstein wanted to find an eclipse to try to look at these curvatures) Thank you for your service!

[@AbyssLMachiine]

Nothing wrong with a little extra hair! Keep up the great work Sean

[@pinball1970]

This is such a good series. I am writing up these notes into a book

[@Schneeger-zk3uq]

Very nice series Herr Carroll, keep it up and dont avoid too much mathematics, which is nice to really understand the idea behind the phenomena. Vielen Dank! Liebe Grüße, Leon

[@Okla_Soft]

Read “the big picture” and it’s one of the most comprehensive theoretical physics books. I’ve read all of Brian green’s work as well as Susskind and Krauss. Sean is among the best physicists /public figures there is when it comes to understanding the laws of nature. So much fun to learn about this stuff.

[@etprecisionmachine2379]

Greetings Professor Carroll, I am so happy that you are so driven to teach, Though Science and The Scientific Method (should that be capitalized?) have been important in my life since I was a child I ended up being a Machinist. I am very good at what I do in large part because I use science to achieve the best results. Even though I like machining and all that's involved with complex metalworking, I still seek out a physics education that I missed. Folks like you really help. The math is fine, I struggle through some of it though because I'm an auto didact, and the concepts sometimes elude me. Your videos really help. Not just these latest however, but many previous videos of your lectures have also helped me to understand our universe. Thank you so much for spreading knowledge, you are making an important contribution to general human knowledge. Cheers, Eric

[@Wandering_Chemist]

Just wanted to say thank you for these sir.

[@ChaineYTXF]

This is a very, very good series. I certainly will spread the word.

[@akumar7366]

Thank you Sir for sharing great post.

[@drwaynebuck]

To sum up - space is the thing that enables stuff to bump into other stuff. So without space we wouldn't have to social distance!

[@rayguthrie7489]

I'm enjoying your conversations on the biggest ideas in the universe. thank you for sharing your knowledge and invite to the common man such as me.

[@emilylowrance7930]

the key to growth is the introduction of higher dimensions of consciousness into awareness - Lao Tzu

[@Bill_Garthright]

What does that mean? Seriously. I know what each of those words mean, but when put together into a sentence like that, I don't have the slightest idea what the sentence is supposed to mean.

[@emilylowrance7930]

@@Bill_Garthright like you can't solve a new problem with the same thinking that created it...that's what it means to me anyway

[@Bill_Garthright]

@@emilylowrance7930 _like you can't solve a new problem with the same thinking that created it_ Um,... OK. I can't for the life of me see how you got that meaning out of it, but... OK. :) Thanks for the reply.

[@hayden9127]

Q&A. For the spooky action at a distance. Does the entangled particle branch instantly or does the change spread out at the speed of light?

[@tommasoforni]

Instantly, but Bob wouldn't know the result unless he himself performs an experiment or Alice tells Bob with good old-fashioned slower than light communication. In other words when Alice performs an experiment nothing changes for Bob

[@-AndAllThatJazz..]

extremely grateful for making complexity into simplicity.

[@brendandarmetko7646]

the way Sean articulates these complex ideas is parrelled only by people like Neil Tyson and Brian Greene. We live in an amazing time for information.

[@gr500music6]

I am watching a version of you in two dimensions and it seems to be doing just fine !

[@kenwolf887]

At 28:20, in space of 2 dimensions, the Pauli exclusion principle does not necessarily hold, hence the food could 'overlap' with the animal for some finite amount of time before totally digested :-)

[@peterb9481]

Good video. Interesting topic and facts put over. Whilst I watch these videos for the physics, it was also interesting to hear about the psychology of time. And very funny at around 38 minutes, when David Eagleman measures time perception by throwing his subjects off buildings. (I know he is a good guy, and he has a good BBC series - and book - on the brain.) I am really loving The Biggest Ideas In The Universe episodes and am learning from them (I have been studying physics for some years).

[@mokopa]

15:09 Here's how I visualised it: It's easy to imagine that two strings in 3D space CANNOT pass through each other, but if you add the dimension of time, it's easy to imagine how one string passes first, and then the second string passes. Obviously they do not need to pass through each other because they are separated by time, that is, they are separated in the 4th dimension

[@David_Last_Name]

Nice, I like that analogy.

[@itellyouforfree7238]

That's more or less the proof, you can make it rigorous. What you get also, is that every knot in 4D is trivial, you can always untie it. In particular, you cannot tie your shoes in 4D.

[@tetraedri_1834]

The analogy doesn't quite work, as strings in 3+1 -dimensional space-time are 2-dimensional. Unless I'm misunderstanding something

[@mgenthbjpafa6413]

Thank you, better late than never. Eric Weistein is talking about 4+6+4 equals fourteen, Brian Greene is still on it. We thought String theories are zombie like, as in refusing to give up... We, common people, knowing how epistemology and proof theory are really evolving into other emergent paradigms, appreciate your step by step approach .We should be very grateful for your pedagogical capabilities. I am not trying to patronize anyone, since you are above and justifiable so. Congrats, Professor

[@AltonMoore]

These are really excellent videos. I still won't be converting to the many-worlds view, but the level of presentation is about right. The hair is looking good, hah!

[@MikhailBarabanovA]

Thanks for the video! Finally some understanding of how dimensions could be 'curled'. Could you(or somebody else) recommend some sort of introductory textbook with description of math behind such processes?

[@MikhailBarabanovA]

@@michaelsommers2356 Thanks!

[@fatmaoylu5374]

You are an excellent tutor, thank you.

[@alvarorodriguez1592]

00:00 Sean Carrol looking like a lovecraftian god. Because why not

[@antoninbesse795]

This series is brilliant. Full strop.

[@Cooldrums777]

Well I finally have an understanding of the Hamiltonian. I have read Wikipedia and a few other tutorials on this subject, but I never really understood them. Thank you for the excellent tutorial.

[@Peterskovtvermoes]

This is truely a gift. I tried to push it to my daughter and her Tik Tok infected friends. Asking for defeat, I know but I was too excited to realize. Thanks Sean for donating your time and invite us to your realm of physics👏

[@BoazRosenan]

Thanks for this series. Although I know (some) physics, it's always good to reiterate on the basics. Regarding the claim that 2D space is not sufficient to do anything "interesting", Conways Game of Life is an example of something "interesting" (a Turing-complete computational model) that lives in 2D space + time. Furthermore, Rule 110 is an example for a cellular automaton that does something "interesting" (Turing complete) with 1D space + time. The extra 3rd dimension makes the computational models we can have in our universe much more efficient (e.g., the human brain), but overall, I don't think there is a fundamental difference.

[@zefSF]

Dear Sean Carroll, I really enjoy the knowledge you are sharing and I would like to thank you for making it so clear and accessible. I always have 2 recurrent interrogations about the scope of physics though: 1) does the physics describe our representation of the reality or does it describe the reality itself? If we are living in some kind of simulation, does the physics describe the rules of this simulation or is it grasping something more fundamental and absolute? Do we have a way to make the difference? 2) If we are inside a kind of shoe box (call it the observable universe), can we guess the shape and the color of this shoe box, or all its properties, from inside or are we fundamentally missing more dimensions to observe this shoe box entirely (from outside). I really wish you could address these questions someday. Thanks and good luck with the lockdown.

[@chrisn.3096]

Sean, have you taken a cursory look at Stephen Wolfram's new work and claims about finding a "path to a fundamental theory of physics"? It's making the rounds right now!

[@beeble2003]

Self-published books are a huge red flag. Science being published in books rather than papers is a huge red flag.

[@papsaebus8606]

In the third part of your recent Book you mention that Space could be something that emerges from the quantum entanglement between degrees of freedom, maybe you could elaborate on what is actually meant by that a little more. Are individual degrees of freedom things that could be thought of as “Quantum of Space”? And also, is it even possible for them to decohere?

[@paulotheman8734]

man, I almost fall from my chair as the video was displayed in my 50" tv. Thanks for the great video.

[@marwanelmobader7851]

this is the best presenter I've seen so far

[@w6wdh]

Lovely video! Two of the weirder aspects of 3D space and bounding surfaces that I’ve heard about: 1. The maximum information content of a volume of space is proportional to the area of its bounding surface, and 2. Logically our 3D space is equivalent to a holographic projection onto a 2D bounding surface. Maybe these things will come out in a future video? In any event, I’m hooked on these videos.

[@TheNORRA100]

This is just Great Mister Carrol.Greeting from Northern Europa...

[@jochemvanderspek9287]

Sean says (at 41:41) that in dp/dt = F and dx/dt = p/m there is no mention of velocity. I don't understand that. Since p = mv, p/m = mv/m, which seems equal to v? What am I missing, can anyone explain?

[@crusherolies8195]

mr carroll, i saw a lecture or group lecture where spooky action was said a little differently. the two particles are created together, and they have opposite spins. so when you detect one and its spin up, the other is spin down, their pairing is similar to electron/positron pairs released from energy state changes. they still have the no distance issue, as you know one you know the other. personally i believe the opposite spins explanation is better because its isnt as usable for WOO peddlers like deepak chopra, since their spins were determined at their paired creation, its not them communicating in any way. by the way im loving this series. thank you.

[@shmackydoo]

thank you for these videos. I am learning so much.

[@Pycrih]

You are a great teacher! Thank you!

[@withanametocome]

Riddle me this: At 58:40 is stated that "space is the thing in which interactions are local" implying -I think- that locality and space are the same concept*, yet we know that quantum entanglement exists: wouldn't it be more precise to say that space is 'the sum of all coordinates' and locality the 'capacity to interact with adjacent coordinates'? With those definitions we can then say that some interactions break locality, but "locality" and "space" would still function as different, yet useful in their own terms- concepts. *The other option being that when separate coordinates interact via quantum entanglement they are still "local", thus rendering mute the definition

[@BlackHermit]

Thanks for the free content Sean. You’re the man!

[@lowellkalman2424]

AT 32:50 you say that you can't tie a knot with a 1 dimensional string in 4 dimensions. Could you tie a knot with a 2D surface in 4D though?

[@chrihipp]

This was fun. Thank you.

[@benfurstenwerth]

Thank you so much Sean, this series is amazing! Side note, your preferred interpretation of quantum physics solved the devs machine lol... One more episode to see if they screw it up :)

[@yannisvaroufakis9395]

I love watching your videos! In fact, I just ordered your book "Spacetime and Geometry: An Introduction to General Relativity". I anticipate it will be way over my head, since I am a layperson who even found this presentation challenging. But I will have it to inspire me to learn. Anyway, I still can't get past my lack of comprehension of the concept of space as having physical geometric properties. You mention Kant as believing in the a priori existence of space. How about Descartes, whom Einstein mentioned, and who expressed the view that space is nothing but the function of extension between bodies and thus there can be no space without bodies? How can "space" exist as an entity in and of itself apart from matter, since it is nothing but the distance of separation between bodies? If there is no matter in the universe, I cannot conceptually wrap my brain around the idea that space would still exists. Indeed, I can't imagine the existence of space even if there was only one object in the universe. As a thought experiment, I imagined that there was only one physical object in the universe, a billiard ball. Nothing else. No energy, no quantum fields, nothing at all. Just the eight ball. I can't imagine any way that it would be at all meaningful to ask what its position "in space" is. I would find it meaningless to ask whether it could move one foot to the left or right, since there would be no other object anywhere to define its position and therefore the existence of space outside of itself. It appears to me that the concept of curved space is a mathematical one to describe the motion of an object under gravitational influence, and not a physical one, just as a graph drawn on a blackboard with x, y and z coordinates is not a real place but merely a mathematical expression of some physical phenomenon. Moreover, while the idea is that an object in motion merely follows a curved path in space in the region of gravity, if the object were at rest, what would impart the motion to the object so it is drawn into that path?

[@raedshaiia3976]

Thank you very much for this fantastic series. I wish if you talk about theories that posit the existence of more than one time dimension :)

[@pizzacrusher4632]

Fantastic, thank you so much!

[@DIVINITYSAID]

question about Alice & Bob. Bob doesn't know Alice knows their spin, yet his spin is know nonetheless... does that give Bob's field potential? If (while entangled) a force is applied to Alice, it would reflect in Bob. correct? way off? It seems like 'Bob knowing nothing' would be irrelevant to accessing his location (position?/field?) and influencing his momentum. Could Bob ever become aware of their entanglement? Curiouser and curiouser. Thank you for another rad video ✨🤍

[@logicomix7976]

In 32:00 Mr. Carroll states that orbitals in 4-dimensions aren´t stable by pertubation, but is this true for every force law F(r), or was this statement connected to the asumption of an 1/r^2-law?

[@logicomix7976]

Or in general for force laws F(r)~1/r^(d-1) with d as the dimensionality of space

[@markdeslauriers6549]

Dr. Carroll, huge fan here. When you were describing string gas cosmology and how the strings unwinding in higher dimensions can allow our 3 macroscopic dimensions to grow, I couldn't help but think that if this process (unwinding) is still ongoing, can this not be an explanation for expansion?

[@michaelginever732]

So, a wonderful takeaway from this is that we live in 3 spacial dimensions, because how else would we tie our shoe laces. This really made me laugh while I was trying to get my head around the whole idea of a more than 3 dimensional space. I have always loved your voice. It's the way you inflect. Where does that come from? Is it a Californian thing? Perhaps a very regional thing?

[@carldehez3117]

When Kant says space, time and causality are "a priori" concepts, these have little to do with physics but all the more with our cognitive abilities. We order and interpret reality automatically as we experience it. Visually, we order it in a 3-dimensional space. Even before we see something, we have this ability. Hence, space is an "a priori" concept. It is a condition of our understanding.

[@bartk07]

Dr. Carroll, great series! Can I ask about information vs entanglement? It is said that entanglement pass no information since it seems otherwise it would break locality. But isn't it a piece of information that spin of one particle is immidiately known as the other is measured? If Bob opened his box after the measurement by Alice but before information reaches him, could he deduct that Alice just made her measurement? And the second question: I know there is no universal "now" for everyone. But since entanglement seems to be somehow outside of the locality, what if we could theoretically conduct independent simultaneous measurement of both particles so we cannot say one of measurements determines the state of the other particle. Can it be possible in QM?

[@julianngan9135]

Sean made physics more accessible, appreciate that

[@ZemiEmperor]

Thanks for the great content, Sean. I've listened to all your The Great Courses lectures and I'm glad to continue here :) I'd have 2 questions about this talk: (1) You mentioned "a two-dimensional little sphere" (23:34). In what sense can a sphere be 2-dimensional? And then, just briefly after that, you don't talk about a sphere but a "tiny little circle" (24:12), seemingly referring to the same thing. (2) Why did you say that "phase space" is 6-dimensional (45:41)? Cannot it have some other number of dimensions as well? Thanks!

[@burtgoldstein7864]

First - I love your videos, Sean! Second - What is missing from my understanding such that I am bothered by your saying at 47:17 "they don't interact until they are at the same point in space". I thought: a. points were infinitesimally small, a math idea not a physical finding b. two things cannot occupy the same point in space". You use these words to be more specific, it seems, after using the more layman phrase - "until they touch". So (stop me if I am spinning off into space!) what does it mean exactly, in physics-talk - for two objects to 'touch', or to "smack into each other"? I understand objects are not solid at the microscopic level, so even if two things could occupy the 'same point in space', what would the thing be called that's doing the 'occupying"? The electron shell? A quark?" [Part of me feels I am simply revealing an obsessional psychological disorder better addressed with meditation or counselling! So feel free to disregard this question! ;-)

[@ManWhoUsesComputer]

Thank you Dr. Carroll. *Question:* {preface} Put mass in spacetime and it is said the mass "warps" or "bends" or "curves" spacetime. For example, placing a bowling ball on a trampoline - the 2D plane of the trampoline warps into the 3rd (up&down) dimension. My question is where can a 3-D spacetime "bend/warp/curve" to? Does this necessitate a 4th spatial dimension? Or is this a consequence only of the analogy. Maybe spacetime doesn't deflect but becomes denser or stronger or something. Does you think about spacetime as actually warping/deflecting in the presence of mass? Thank you.

[@royalbloodedledgend]

16:02 Let’s see if I can do some magic here. Move it over, copy it, paste it. Look at that, oh my goodness I’m getting good at this.

[@Adrian-me4qz]

Thatstring wrapping thing is mind blowing