Michio Kaku - Are There Extra Dimensions?
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- čas přidán 14. 05. 2024
- Extra dimensions-beyond length, width, height-seem like the stuff of science fiction. What would extra #dimensions be like?
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Michio Kaku is an American theoretical physicist, the Henry Semat Professor of Theoretical Physics in the City College of New York of City University of New York, a futurist, and a communicator and popularizer of science. He has written several books about physics and related topics; he has made frequent appearances on radio, television, and film; and he writes extensive online blogs and articles. He has written two New York Times Best Sellers, Physics of the Impossible (2008) and Physics of the Future (2011).
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Closer To Truth presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.
If there is other dimensions, i hope there is one where the volume to this video is higher
hahaahahhah :D the most catchy comment here.
Lol, well said.
Wonderfully said my friend!
- I was just now messing with the volume controls wondering if it was me!
Thank you for letting me know right through the door that the problem here wasn't just me. Now THAT'S a Helpful Comment, if Ever I've seen one! : )
Lool
In another dimension your hearing is better.
MK: "Let me tell you a story."
Me: *listening intensifies*
Quite eerily similar to Robert Kuowosaky (rich dad poor dad)
*Wow !!!*
So thats why YOGIS and MYSTICS
Says that u can travel in other dimensions through "Sookshm Shreer" (Ultra small Body which is not physical in nature)
@@WhiteMetal_ i do travel to other dimensions everytime i go to sleep, i could've written countless novels by now, but once i wake up i don't bother thinking about my dream(s) unless they are very special, which happens once în while
@@rodicapopescu2038 true! I thought i was the only one that felt that way.
@@ShamefulSheep oh sometimes i really feel i have other lives i'm living in the same time, last night dream was a abt a man who was rich and interested în me so he invited me and my gf out for lunch and gave us both expensive perfumes as gifts. He liked me but thought if he îs nice to my gf as well, he'll gain my heart.. Strangely enough he was somehow familiar, almost like i've seen him somewhere, you know when you have a strong feeling you know someone from before..to tell you the truth i don't like it when that happens, can't find that person although they are close somewhere
I love how Michio Kaku explain a complex topic in a simple way with analogies. He is a very intelligent physicist. He would be the best teacher in university.
This is the way of philosophers.
Isn’t it amazing how humans have evolved to be able to theorize these concepts?
In a way that almost feels like we ourselves can move into another dimension.
Imagine I’ll probable loose my 🧠
Except we didn't evolve to understand these concepts. we were created by a hyperdimensional being we call God
Love how he’s able to explain something so complex in simple relatable ways
Albert Einstein - "If you can't explain it simply, you don't understand it well enough."
His explanation really reminds me of Carl Sagan. He even uses a lot of the same terminology. czcams.com/video/N0WjV6MmCyM/video.html Also, now I know where Agent Smith got his voice!
Wtf are you talking about?
@@loraleiffxi agent Smith from the matrix? Where did he get his voice then? Are you saying he sounds like one of these dudes or Carl sagan? Because I must disagree with you. I don't think any of them sound like agent Smith. Hello Mr Anderson
@@TheMan-WithNoName The video of Carl Sagan explaining the 4th dimension sounds exactly like Agent Smith to me.
If Michio Kaku were my teacher I would've become a physicist.
U would have beome zibberzabber.
I would prefer some one whoworks in his lab day and night to be my teacher rather than someone who spends time in discovery film making and giving same old nonsense interview
More likely a fortune teller, or a science fiction writer, unfortunately.
If he were my teacher, I would have referred him to a therapist.
He is very likable but like other physicists they don't tell you the whole truth. In fact many like Tyson I believe mislead you. Although in a very entertaining and admirable way.
Me too
I feel like I just heard a super-genius interview a mega-genius, and the super-genius' questions helped me understand the mega-genius' answers.
They're both quacks.
Incredible scientist. Incredible personality. The way he describes incredibly complicated concepts is astounding. I'm addicted. Respect 🙏
The interviewer did a really great job.
ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟ ᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟᅟ yes I agree.
awesome know
Prashant Sharma
See right side
he's name for another Dimension
just use earphones
Man their outlook on life most be way different than the average human being due the their knowledge. Wish I could see the world through that knowledge. ugh, we waste so much time with trivial stuff when we could be getting closer to real power which is understating existence through knowledg. Just my thought.
i can barely hear it too
Just take an existential point of view. Be simply... the observer of the world, be neutral, and not of the world. Man is naturally a scientist at heart. We see things in our environment and immediately imagine what it applies to... where it came from... and where it's going... if we can use it to our advantage or is it harmful. A simple way too grasp it all is ... remember everything is in constant motion, the universe is forever expanding and as these atoms and microscopic material we, and everything around us, processes its way through life we will experience something new everyday even if it's your very own body.
Strawman for hire I dont know if i should like or dislike your phrase "when we could be getting closer to real power"
History shows up till now and i bet in a bit far into the future what human beings do with power.
We are not worthy of great power just yet. Our still primate minds use power for. Well power over others or something bad. Luckily we dont all think that way and we also got nuclear power beside nuclear weapons for instance.
Tarragon Mugwort I am not a physicist but am one for a hobby :P and i think that would probably be the hardest achievement we can accomplish.
Perhaps real power was discovered long ago. like MP suggests due to the finite possibility of dimensions, power and knowledge are too finite and therefore limited and therefore boring and therefore tortuous (imagine knowing everything that is and that will ever be - the epitome of being trapoed). One method of escaping such a loop would be the method of perpetual creation and destruction. In between the pertuation creation and destruction is 'probability' or 'the expiriencing of unforseen events' or the essence of 'adventure' or you could just call it life and that is what we are experiencing right now.
I believe there is every chance there is an all knowing source and to alleviate its sense of trapped in finicy. The foundations of randomness to dispel finicy and freeing creation were started long ago.
I just found this show and love it. The interviewer and host is underrated. It's very impressive to be able to have an intelligent conversation with experts across all of these different domains.
I've read several of MK's books and I not only think his theories are right but I also think he's one of the super smart people who has issues. Nobody as sharp as Miko can keep it together. I totally admire him at the same time I pray for him. Genius and society don't mix and this dude is a genius.
Everyone knows brilliance teeters with insanity.
@@michaelfarar4232 In all cases?
@@1111tull No!
@@1111tull Yes...
This guy explains stuff so good I wish he was my teacher mate.
It will to expensive for you to teach you more then Stanford and Oxford professors combine :) :) :) :)
Yes. He explains very well. And he make physics sound very interesting.
He was mine at City College NYC. Great guy!
Just look at his hairs! All his life, he only Think Think Think...
He is
There are things that cannot be seen but truly exist
Such as malevolence & dominance hierarchy
So a higher entity possibly exist?
@@naturalLin u mean aliens?
@@user-is3yn7xr4c anything, aliens sure if by aliens you mean anything that's 'alien' to us.
Like oxygen
Love his story about the carp in the pond as he explained a 2D vs. 3D perspective 🐟
The word stability here refers to the stability of the simulated model with the math done on paper (or on a computer), not the actual stability of the universe itself. That one is very stable and does not rely on our comprehension, or acceptance of it.
This guy knows a lot about this topic. He should become a physicist.
Wtf do u think he is fuck people are dumb
@@gdgdhdbdb913 r/woosh
Actually he is
@@gdgdhdbdb913 "fuck people are dumb". As Emperor Palpatine would say "Ironic".
@@gdgdhdbdb913 You did not get the joke.
I love all his analogies, their brilliant, it hurts my head trying to comprehend something that we don’t know for a fact. But.. I then think that, the universe has no obligation to make sense to you!
You don’t know what ‘Theoretical’ means do you? Must be strange to believe anything someone says as fact as long as they sound smart.
jocaguz18 welp, you changed my mind!
@@Dan_Fahl ok , explain what a theory is in physics please ?
Exactly so:)
@@Dan_Fahl but theories have been proven mathematically and you can’t deny mathematics
Dr. Kaku has an amazingly simple way to explain very hard concepts. Absolutely fascinating stuff.
Very, very impressive intelligence. This man is a genius. He can really simplify complex theories without diminishing their aspects and without losing focus.
How fun to be able to play with these concepts as someone fluent in mathematics and physics. To speak the mathematical language well enough to move beyond equations into abstractions and philosophy.
Indeed 🌚✨✨🌛🦉
Veronica very nice photo.
Yes, It's very revealing, almost like one pus one equals three.
Yes
Be honest: is that your best pic of you out of the hundreds you took?
Wow! He explained the topic very well that even I-with my very limited undertstanding of science-understood it. Thank you so much. 🙂
He gud teacher u knooo
I love the guy so much , he makes everything interesting and leave me wanted to know more and more . Micchio Kaku !!!👏🏼👏🏼
Kaku, Master explaining complicated things so simply!
I'm almost as much impressed by the interviewer as I am with Kaku himself.
Good job guys!
The idea that dark matter could be matter in other universes existing in other dimensions blows my noodle. That is insane.
Or is it a force like magnetism or gravity but doesn’t rely on matter to exist in our universe and is purely a force exerted from other dimensions. Who knows
Do other dimensions have matter? In simulation scenarios they might.
Now first tell me the meaning of *blows my noodle* , I have applied all the partitions and quantum physics, but I still didn't decoded it.
Makes me rethink my perception of life.
So that would mean that the universe we see and live in would be another universe’s dark matter.
I wonder if you were a higher dimensional being how math would fit together in your higher dimension.
i really love how simple he explains things
The way he explains like pond of fish , cigs, crystals and here's my teacher giving me a 3 light year derivation.
!!!!!!!!!!!!!!!!!!!!! :0 :) ;)
I love MK, such a blessing to human kind. Imagine spending your life and dedicating it to understanding this crazy, miraculous and extremely unlikely existence we call life and everything in it. I wish I could wrap my head around all the knowledge this guy holds
Honestly, just keep watching these videos. And type things like "black hole lecture" into CZcams. Its hard to understand this stuff the first time through but the more I watch the more my brain can handle these wild concepts. Sometimes understanding is scary(ignorance is bliss?) But it's very interesting and mysterious nontheless.
Man... The interviewer...so much informed, the conversation goes so smooth
His books are excellent. He writes in depth about the stuff he talks about here, but he still explains everything he talks about in a way that helps people who don't have the same advanced knowledge that he has understood it. The guy built a particle accelerator as a kid for fun, he knows his stuff.
Imagine him giving you lectures everyday and you can't wait to go school everyday 😉
Every once in a while, I sort of understand what the hell he’s saying.
Haha me too
Then you need to see a shrink.
kaerbear 😂😂😂😂 I don’t understand any of it, so well done you!
@@williamrthompsonjr556 dang bro. Your so smart. Teach me your ways!!!! I'm so omg jealous of your smartness!
I pretend to understand.
Fascinating topic and he explained it well.
*2 years later*
Yeah he's really good at explaining these complicated things. I don't know why people hate on me, and that makes me hate on them.
I think it would be magical to be able to sit down with Michio and have a cup of tea or coffee and brainstorm these topics further ... into possibly infinite possibilities.
What a refreshing meta vision on something explained by so many others. Thank you so much.
I could listen to him talk about this stuff all day long.
This man is a legend. I grew up watching him. I wish I could talk to him one day
In order to talk with him, you must be in his dimensions.
This fish analogy is told almost exactly the same in his book Hyperspace.
This is exactly what I’ve been unable to explain to myself. Absolutely the right line of thought 💭 (I don’t understand maths that’s probably why)
I don’t understand what I heard but feel more intelligent. That must be coming from another dimension.
LMAO... Thats just your brain firing up its nervous system trying to comprehend Michio Kakus story on dimensions
GOD=7_4 whereas G is the 7th letter, a circle O is either 15 or zero or ---, D=4. String theory's 7D hyperspace + 4 common dimensions (3D regular space + 1D time). See GOD=7_4 Theory at GOD704.fandom.com .
GOD=GOOD
Haaaahaaaa 😂 that's a good One. Not there's, but there are other dimensions.
@@BradWatsonMiami Exactly right, GOD is Good and the Devil is very Bad and Crazy Boy...!!!
🙄🙄🙄🙄
It may sounds cliche, but I smoked DMT and saw higher dimensional movement and geometry in the room, impossible to grasp and describe. The experience was very profound and awe inspiring, and it feels real, because the mind can not really make it up it seems, indeed it has a very hard time to understand and integrate it.
It's a hallucination.
What a great scientist... How he explains just love it❤
Michio kaku is a wonderful scientist. Always love listening to his theories.
We're gonna need another spatial dimension just to fit all of Michio Kaku's analogies. Jesus Christ man.
Good one
I love his analogous explanations, makes it really easy to understand the complex things he's talking about.
It’s like eating a banana, peeling off layers of skin before taking a bite.
Underrated comment.
@Victor Gibson: The greatest book on Earth is the Bible and #2 is 'The Aquarian Gospel of Jesus the Christ'.
My simple mind is glitching. Cannot wrap my head around any of this.
Thank you for this video and all your inspiring work!
Just wow!! The explanation as well as the possibilities of parallel universes
I love how the interviewer listens and is very interested on what mr.kaku is saying. This is why i subscribe.
He Is longing for truth, he is now closer to the truth than before
I have a big mouth, but when michio kakku is speaking iam all ears,and my mouth agape. He talks universal truth.omg
I need to get all of Michio's books right now!
Yes! Yes! Yes! It's no wonder why SO MANY PEOPLE are turned off by the subject of astrophysics. You need a brilliant mind and someone gifted and most importantly of all: someone who truly cares about his students and people in general. Not some hollow, egotistical, arrogant, holier than thou, maybe even racist, "professor", whose more concerned about his/her reputation or research! This man is one of the greatest teachers of our time! Thank you Dr. Michio Kaku!
First of all we can never lose you 🤣 Secondly I wish I had the vocabulary to describe how much I've learned in the last 11 minutes, thank you 💜
you learned nothing sweetie...he is a fraud.
@@cnitevedi4832 Not everybody has a single digit IQ like you. If you hate him so much, wtf are you even doing watching this?? Go get a life.
@@princeofficial6998 i am watching him make a fool out of people. nice hustle...if you ask me. i don't hate him. i am fascinated by people like him, Bernie madoff..etc.
if vocab effect useless..now you learn
Love the channel, but please include the date the interview was recorded in description.
Since I was a little kid, I liked to imagine that our whole universe is just a mere cell of some enormous being and we'd be like the viruses or bacteria or something that had no idea of any of that, no ability to comprehend scale so huge such as a cell, let alone the whole body of the being with our very limited understanding and perception. This of course, still doesn't answer the ancient question "what's in the end of the world" (in this instance, for that enormous being).
The knowledge shared here is very special,I admire and love the conversations
Have any of you ever had the experience of looking into the future while sleeping?
This has happened to me a lot in the past. It's a little difficult to explain, but I try:
When I am half asleep, I dream (or feel that something will happen in the next few seconds) and it actually happens. I heard my mother say something once, half asleep, and a few seconds later, she really said it.
I'd like to hear more on this
I’ve had it happen numerous times!
sychronocity
Yeah I've experienced this. Could be funky stuff happening with your memory while you're in a drifting state between being awake and being asleep.
my experience is different. if i get woken up while in the middle of a dream, the next time i sleep i can continue that exact same dream.
There is so much science to be discovered. Imaging where we would be in 500 hundred years from now and more.
This story reinforces my thoughts that I was here in another dimension. I Like the way Michio Kaku explains Things. Very essay to grasp. I wish when I was in school there were more teachers on his order. Being dyslexic I would have understood this.Thank you for sharing.c];-)
Many important, logical things by micho sir and a way to connect ourselves to the higher dimensions
Michio Kaku is excellent in providing anwers through analogy. I really undestand it well.
Such a pleasure listening to Mr. M Kaku. Very well explained.
They explain A LOT and make it well make sense yet will not the end that just leads to more questions.
Though I am ignorant of such high level physics. His lucid interpretation of very high concept modern physics to an ordinary scince graduate is absolutely fascinating.
:)
I am amazed about how metaphors and simple comparisons can bring highly complex topics to the understanding of regular people like me. That was just amazing!
I hear ya' :)
I can’t wait for all of us to really begin studying the work of Allan Kardec from 1857 on, including “his” 5 main books and the Journals of Psychological Studies.
Him and Tyson are my favorites. Thanks for the clip.
This may explain deja vu... I am so intrigued by this conversation
Maybe not smaller.. but bigger?
much bigger, like what if the dark space is actually a single "atom" so large and vast.
Or what if each Galaxy is actually a single atom in the next dimension?
I actually agree with this speculation more =)))
Sean Carroll does not agree with this cosmology. I believe it's called fractal cosmology. He talked about this on Joe Rogan, and he said, essentially, that the proportions are just not the same.
Our whole galaxy, and universe is on a flower like Horton hears a who
I want to see Roger Penrose and Michio Kaku debate it out on the existence of extra dimension.
Include Neil de Grasse Tyson
A great teacher is a treasure
Fascinating talk, I really enjoyed it. It also explains why gravity is ridiculously weak compared to the weak force.
Kaku: Logical possibility is a thing.
every philosopher ever: ... we know.
I love the videos on this channel. I do wish though that you could post the date the videos were *recorded*, in addition to the date they are posted. At time philosophers and scientist here have subtly and not so subtly changed their views since these discussions were recorded...So it would be great if we could take the date of the discussion into account while we watch. But again, excellent channel!
+2b Sirius how exactly do u view the recording date
It was recorded April 20, 2021
I love how Michio uses words/ phrases like "we think" or "It seems.."
I absolutely love michio kaku! What a brilliant mind !
I wish Joe Rogan would get him on his podcast.
9 months ago I’d say it was possible. Today? Idk if Joe even believes the earth is round any more.
@@thaevilgenius3 lmao I know. Joe gets geniuses on, but is more often surrounded by morons and conspiracy theorists
Why?
Doubt it will happen. Kaku was pretty rude to Joe Rogan years ago on the O&A show, long before he was the biggest podcaster. Rogan was spouting off about psycodelics and interspecies communication, and KaKu basically laughed at him like he was an idiot not in touch with reality. You could tell that Joe got pissed
Dude, DMT can like really show you the 11th dimension - wanna try?
Arguably the best explanation of higher dimensions ever.
When i was a child i couldnt conceive the idea of infine, truth be known i still stuggle with that.
i knew the universe could not simply go on forever,thank you for the knowledge to seek answers within and yet the many more questions to ponder haha
Merveilleux les possibilités infinies du mystère de la création. Michio Kaku nous l'évoque si bien.
Michio "Let me tell you a story" Kaku 😂
And that's all it is. Just a fairytale story.
Petteri Heino many things were supposed to be a fairy tale but they did come true .....
@@martialarts4095 science is not fairy tale. We need experimental proof to even talk about extra spatial dimensions
@@aishwariyasweety2433 Yes, you're right. But making hypothesis is also important to understand things. Like observing chess moves. If a right person makes right moves, you'll know chess and vice versa. We have to see what is right in a way😄
:)
Michio Kaku is my hero. I thought I was crazy thinking about this things that popped into my head and now look at him explaining what I thought it was just me being crazy
So happy such wonderful scientist lives in our times!!!
This man is super genius. They way he explains, even a 6 years old child can understand. I never see Einstein but this man is nothing short of him..
a genius with no proof, yes thats us humans, he has as much proof as you do, in fact your ideas might even be better
Amazing interview.
I'm reading his book Hyperspace rn and it's very thorough
Thanks for posting this. This is the second time I watch it. I want to know what dimension the souls stay. I wish someone can ask him that question. The way he explains is very easy to understand. 🙏🏽
You mean ghosts?
Grazie per tradurlo, davvero bellissimo.
EXCELLENT Physicist! Thanks for your wonderful explanation~
When physics sound much like spirituality.
Daniel Ospina
That's because really is not phisics, is speculations.
Daniel Ospina I agree. In fact, the soul might very well be our 4th dimensional entity. Lighter than mass with the ability to touch our surface.
Spirituality exist between dimensions.
Get your head out of the sand.
Daniel Ospina exactly...
Thanks Dr Michio Kaku. Great thoughts. Keep going everyone who are interesting in physics, mathematics and the nature of universes.
They destroy mylife I need to command the (300)
Very very good explaining of Michio in common language.
...Oh Michio and your damn fish story. Heard him say it a million times but the analogy is still cool as hell!
Well, Carl Sagan already borrowed from _Flatlanders_ ; both make sense.
Unfortunately it's a very bad analogy, as the fish and everything in the analogy already and only exists in 3 dimensional space. A better analogy would be pulling Mario out of Super Mario World into our universe.
@@aloisraich9326 Indeed, it's all just theories. Everything he said in this video is all just based on theory, not on physical or even empirical evidence. So it makes no sense to say it's factual OR not factual. So quit saying he is wrong. It's not bad either. It is, inter-subjectively, the strongest theory to this day. Unless you can provide a better theory, of course.
@@aloisraich9326 You know he's not the only one who's on that theory, right? By far not the only one.
Only because no one succeeded yet it doesn't mean they're wrong and they're not going to stop just cause you're being a pessimist, lol.
@@aloisraich9326 Why do you keep saying they are wrong? Unless you have proven it so, it's still not, in any way, wrong. Just unconfirmed. Hyperspace and dimensions are still just an idea, true but they are the best science can offer and scientists have to work with the best they got. If those things actually exist, I can't imagine that they will be discovered in the matter of a decade, only. They are still only at the beginning of its research. It's far too early to draw final conclusions.
I think it's amusing that so many in the comments think they know better than this guy 😂
Tell me about it! He's been into theoretical physics for 50 years yet people think they are better than him without even knowing what inertia is.
It's just as silly to act as if he is infallible.
+Robert Galdr +aTouchOfEvil
Well its not every day the world stops to listen to someone versed in _both_ metaphysics _and_ physics or some other scientific discipline. On the whole, our species is too steeped in cognitive biases to try to reconcile the two bodies of knowledge.
William Fotiou
He would probably be a better source on his field than someone who has been preaching for only 50 minutes. After 50 years most people have discovered and either challenged or justified their own cognitive biases.
Welcome to CZcams!
wonderfully explained
3:00 wow he is Extremely Well explaining Very complicated things intuitively to all .
I'm depressed knowing that I will likely never be able to see the 4th dimension with my own eyes. OR...perhaps death could be the TICKET to this higher dimension? Who knows? That would be simply incredible
Could be,
Meditation
@cosmicVox13 wait, you've been there?
I agree. Our souls/consciousness is locked into these bodies. Death is like a ripple or disturbance because of which we, as souls or whatever, are unlocked into higher dimensions.
4th dimension is like a being that can live outside our dimension which is earth. And they have power on us. He said we are the fish in the pond, and then "being" pulled the fish outside the pond, then the fish saw the 4th dimension. Then fish was put back into the pond which is the 3rd dimension. You must have understand it now.
From this I must conclude.. don't fear death 🙂😉
Fear life
I am really glad that the video was able to provide a better understanding of how the universe works. We often think everything in this world is random, but it is really not.
Every day we are faced with an infinite number of random events so it is impossible for us to see all of them. The general principles that govern all science are the laws of nature and mathematics..
We talk about those principles in our videos;)
07:22 - słuchając tego przypomniała mi się bardzo zabawna rzecz sprzed wielu wielu lat. Podczas studiów na wydziale przyrodniczym mieliśmy wykład z "ogólnie przyjętej matematyki". Przesympatyczny acz bardzo sędziwy profesor podczas wykładu o macierzach wielowymiarowych opowiedział nam, że jego największą przyjemnostką jest zgłębianie wiedzy n.t. wymiarów. Opowiadał dość długo a my słuchaliśmy z zaciekawieniem (podobnie jak robi to tutaj Michio Kaku), ale najbardziej rozwaliła mnie końcówka. Stary profesor powiedział "niestety, gdy przeskoczymy z 10 wymiaru do 11 obliczenia znacznie się komplikują..." po czym posmutniał i sobie usiadł na krzesełku 😆Niesamowite, że po tylu latach znowu usłyszałem o tym temacie, haha!