Marcus du Sautoy: Symmetry, reality's riddle
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- Опубліковано 28 жов 2009
- www.ted.com The world turns on symmetry -- from the spin of subatomic particles to the dizzying beauty of an arabesque. But there's more to it than meets the eye. Here, Oxford mathematician Marcus du Sautoy offers a glimpse of the invisible numbers that marry all symmetrical objects.
TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world's leading thinkers and doers give the talk of their lives in 18 minutes. Featured speakers have included Al Gore on climate change, Philippe Starck on design, Jill Bolte Taylor on observing her own stroke, Nicholas Negroponte on One Laptop per Child, Jane Goodall on chimpanzees, Bill Gates on malaria and mosquitoes, Pattie Maes on the "Sixth Sense" wearable tech, and "Lost" producer JJ Abrams on the allure of mystery. TED stands for Technology, Entertainment, Design, and TEDTalks cover these topics as well as science, business, development and the arts. Closed captions and translated subtitles in a variety of languages are now available on TED.com, at www.ted.com/translate. Watch a highlight reel of the Top 10 TEDTalks at www.ted.com/index.php/talks/top10 - Наука та технологія
And in 2020, Andrea Mia Ghez became the fourth woman to be awarded the Nobel Prize in Physics! How amazing is that!
Here is how you calculate the number of symmetric positions in the rubix cube:
(Edge permutation) x (Edge orientation) x (Corner permutation) x (Corner orientation) x (Centre rotation) = 12! x 2^12 x 8! x 3^8 x 4^6 = 2.12592265x10^24
It's important to remember that the universe exists as we know it because of an asymmetry. But I really like his quote regarding that breaking symmetry leaves room to grow :)
You don't have to necessarily need to have a practical use for something. It's the joy in studying Mathematics that's the reason for even concerning yourself with it. Like Art, in my opinion there is no practical use for it but people take joy in viewing and expressing themselves within it.
The sixth symmetry of the star fish reminds me how mapping a figure to itself is a fundamental mathematical structure of reality, made use by Turing trying to solve the 'halting problem' in his computing machine, by 'self-reference' in which the input and output terminals were plugged in his original. computing machine.
Thank you!
ahhh thanks for shedding light on this man. =]
Indeed it is very dumbed down. Although, if it wasn't for him and me reading his books when I was 17, I may not have been revising for my fields and galois exam right now. Sorry for replying to such an old comment!
So the winner sat down initially on the
I'll be honest here, this whole talk went straight over my head. This is maths far beyond what I understand.
cool lecture :)
I gave the lecturer a standing ovation. :)
The triangle example reminded me of how in cmoputer graphics you often rotate an object first, and then translate it out into the distance. It matters which operation you do first.
But those symmetry examples didn't really provide enough info to define the ways in which the rubiks cube could be understood. I guess it's the normal amount of configurations, times the number of ways you can place the object on a table.
That rolex ad at the end was kinda neat, lol.
Thanks!
Yogilix, thanks for replying! i do think you have a point worth looking at! I am very sure most religons have some sort of similar view on this.. the reason i used Christianty as the example is because Gk Chesterton used it to distinguish the Christians from other religions.. and he did it in a way that made allot of sense to me.. I am a Christian and we tend to believe that we ALWAYS know better although this is often not the case! I will look deeper into your point.. Thanks again!
I love this channel
WOW, there's a whole lot of ignorance in this comment section. I thought it was a great talk.
@Gadgets7777777
Well... I'm no mathematician, and I'm just fascinated by this lecture. Guess I need more reading on the subject. Dumbing down is what popular science is all about and as I mentioned I can't tell if he overdoes it. Thanks for comment anyway.
You couldn't begin to imagine just how far mathmatics take things like this.
There are some very obvious applications, such as theories about universal order, architectural development, and even the biology of life. Everything that exists has symmetry, and understanding it will help you understand everything.
But again, it can go even deeper than that. The best way to say it, I guess, is "if you take the red pill, you stay in wonderland, and I will show you just how deep the rabbit hole goes."
kevintype, asymmetry can also be the marker of an exceptional individual. Lack of symmetry is just as important in identifying unique or outstanding individuals. Asymmetry in an adult can be just as indicative of 'special' circumstances in the individuals life and upbringing.
Thanks for sharing that. :)
Genial !!
That puzzle was so mean. :)
Thanks! Couldn't get myself to finish the video before lol
the fact that it's sponsored by rolex is a good thing,
Well said Philkapune. i question the tenuous nature of our perceptions too and from day one of our lives reality is a construct we presume others see as we do. Agreed, proof of anything is hard to find I grant you, but doesen't the thought of a real one sided object tickle you at all ?
Ok I gave this a fair try, but now I go back to listening Kyuss.
MARCUS: "In everything... uniformity is undesirable"
ROLEX: "A Passion for Perfection"
how ironic...
I don't know why there are all these angry comments. I thought this lecture was great and really made me passionate about math!! Which is a miracle for someone like me, by the way.
I like this channel.
i got a very "ok, that's great. So what" feeling from watching this
She is the astronomer Andrea Ghez. wow
Thank you Captain! I was sure I recognized her from somewhere.
Symmetry is key.
@psychobollox Thanks for your support David. I don't think IB4 knows what he is talking about, but he's certainly no troll. He linked me to a forum where he's been posting rants that go in circles like this for some time. Either way, I'd try not to get involved.
He does have a little bit of a point (I don't think he made it though) that asymmetrical objects can have symmetry, since it depends where you define the symmetric axes. But that doesn't mean he is saying anything here either :P
Fair call. Art is different though... that's a creative thing, to express your inner feelings/thoughts/ideas etc and comes in many different forms. I guess symmetry is also a sense of art then isn't it? we do find symmetrical things more likable.
This is interesting I've heard before that symmetry is more beautiful.
I glance in the comments and see that there is a religious discussion. I then scan through the lot of posts looking for the first comment with grade school level spelling and grammar to find the Christian. It works every time. The co-relation between religion and intelligence is very significant.
Symmetry means perfect harmony; an equilibrium of forces. What is one is the other - that is the language of the universe...
The winner of the Rubik's cube game was Andrea Ghez, an astrophysicist at UCLA.
This symmetric object seems quite famous now that is has been mentioned and even named at TED, so maybe I could write a Wikipedia entry on it, no?
@islandbuoy4 Again, asymmetry is something that LACKS symmetry. Rotational symmetry is a type of symmetry. Therefore a swastika is not an asymmetrical object, because it is not lacking symmetry, since it has rotational symmetry.
Loss of teeth and development of jowls and irregular creases reduce the symmetrical features of the face. Asymmetry can also be a result of aging.
when will teachers understand that the important thing is not what they say but what the people in the audience understand. This would make them speak slower and more clearly. Talking too fast is a waste of time if nobody can follow the explanations.
I can't help thinking he maybe could have showed us the 2D or 3D representation of the Ghez shape.
The great artist gave as two eyes in symmetry. two ears, a mouth, two arms, legs, so when you dig into the body and you find the hart, you mite expect to find the same on the other side.. but the Great Artist changed just there! this is one of the things that make Christianity unique.... it goes "rite" were nature goes "rite" and "Wrong" were nature goes "wrong" ... Modified from GK Chesterton" is it possible that i got so many thumbs down that the comment was removed??
@jimmayl1
Welcome!
Well, I'm not sure about asymmetrics having symmerties - reasons obvious - but I can see how projections can give rise to some mappings that look symmetrical when you look at them as larger neighbourhoods and points within those neighbourhoods, but - well, his example was crap.
All the best with the comp-geom... I just hope you can find a good therapist to help you reconstruct your mind when you get back out of that stuff ;) Have fun :)
Numb3rs cameo!
Objectivity (and consequently scientific reliability) implies logical antisymmetry. This antisymmetry is always the theoretical frame of reference within which any symmetry has to be displayed or conceived or described. Intersubjectivity implies antisymmetry because of the Leibniz identity principle of the indiscernibles. There is no other universally valid criterion of identity. But without such an concept if identity (a definition of "=") a theory is a bare calculus, not a theory of something.
What does he mean by "working" with 4,5, and sixth dimentional objects? I didn't know we had evidence of any other dimensions beyond the 4th!
no, because if he flipped the 6 corner shape, the points would be pointing the other way.
@islandbuoy4 I don't think there is anything more to discuss, is there? Obviously how when you define symmetry, you refer to at least one axis. I would hazard a guess that a rotationally symmetric object can be defined by a cartesianally symmetric contour in the complex plane. I've taken up to the third year maths at a university level (and done quite well with them), so I think that my opinion does hold at least some merit. This argument has nothing to do with 2012 as it stands.
wasn't winning the riddle a rather easy thing. Yo just had to be closest and he was saying those with less than something sit down and the like. You just had to keep standing till the last and you will automatically win.
Just because you don't know about it does not mean it can't be done.
from what I gathered, it was a higher dimensional symmetry. So no point in reducing it to a lower dimension.
Reality itself is necessarily asymmetric. The slight excess of negative energy at the Beginning, anti-gravity, to leave our expanding universe. There had to have been the slight asymmetry of matter over anti-matter. Asymmetry is what makes things interesting. Tiny asymmetries: as natural as natural can get.
The essence of Reality is minuscule asymmetry.
@anoopmknair I think this is the kind of man that we need for the 21th century
I want a simmetrical multidimensional object too.
I agree you have missed the point completely :)
He mentions some examples of symmetries of nature, i.e. snowflakes and virus particles. But in a sence, symmetry in purely abstract mathematical form is also symmetry in nature, since mathematics are a part of the code of absolute laws that nature and the universe are built on
Galois was a genius, if he had a longer life, he would have found something very very special IMO
feeling about as enthusiastic as his kid looks.8-I
@islandbuoy4 No need to get upset and/or hostile. I guess where you define an asymmetrical object depends on your axis of reference. A swastika might be asymmetric with respect to the Cartesian axes, but not the polar ones.
wow
Hahaha. Honestly I was just not born with a very mathematical sided brain, yet the way he explains and the entire subject after a while started to make a different kind of sense.
I'm not sure how.
@islandbuoy4 And your the expert?
there is so much symmetry in a Rolex
@jimmayl1
jimmy is wrong wrong wrong
the LEFT ROTATING ASYMMETRICAL SWASTIKA has a 'symmetrical twin', the RIGHT ROTATING ASYMMETRICAL SWASTIKA....
this symbol, the OLDEST most traveled symbol over HISTORY, is a KEY to understanding ASYMMETRY
@jimmayl1
goggle >> FOUR FOLD rotational symmetry and the swastika
the swastika is ASYMMETRICAL but rotationally symmetrical.
It depends on how many legs it has.
3 fold rotational (rotate 120 degrees) swastika is the triskele
4 fold rotational (rotate 90 degrees) swastika is the common swastika we are used to seeing
5 fold rotational (rotate 72 degrees) swastika is our 5 arm milky way
etc...
72 elders
precession moves 1 degree in 72 years....
seeing a pattern?
namaste
i wouldnt say that people would choose the lower two faces as more beautiful. it always looks awkward and unpleasant when faces ae perfectly symmetrical. so as the japanese essay confirms: "uniformity is undesirable." symmetry too, id say..
What's your question? You mean, "Figments of imagination without any real counterpart"?
No, I don't think working in multi-dimensional space is "just" a rationalization, but a working hypothesis that has many real-world implications that you're probably taking for granted.
Why did you limit yourself to four dimensions? Isn't that a bit arbitrary?
He kinda doesn't, in relation to 'nature' anyway. I think the importance of the speech is in identifying that symmetry is its own unique branch of math, that it is applicable to science, and that it is found in nature. That's what I got.
The great artist gave as two eyes in symmetry. two ears, a mouth, two arms, legs, so when you dig into the body and you find the hart, you mite expect to find the same on the other side.. but the Great Artist changed just there! this is one of the things that make Christianity unique.... it goes "rite" were nature goes "rite" and "Wrong" were nature goes "wrong" ... Modified from GK Chesterton
I have to take a nap now
I think I missed the point of this completely. What's he going on about..and why is all that significant? Where does he start on the symmetries of nature?
Wow. people study symmetry?! i didn't realise it could be read this deeply. O_o ... so knowing all this.. what do we do with it? =/
For every boson, there is an anti-boson. For comments, for every bozo, there is an antibozo. Nature is full of symmetry whether subatomic or morphological. Fractals occur in nature, and to me, a mathematical pharmacist, appear to be an infinitely symmetrical design.
lmao
@psychobollox
I love it when the low brow humans bond and form a MOB...hahaha
birds of a feather 'fuck together'?
I googled Dunning-Kruger, I must I was ignorant of their THEORY
DUH here is what I found...
I must post it in 2 parts...BTW the word ASYMMETRY is mentioned.....
hehehe
PART 1
Abstract
People who score low on a performance test overestimate their own performance relative to others, whereas high scorers slightly underestimate their own performance...
cont'd...
sorry can "any one" tell me how she did the math for it,,or how any way?,,coz I'm not really that good to understand this talk "lingual".
just need a simple hint or a special time in this talk to focus on.
thanx.
The artist of symmetry, M.C.Escher cd answer most of this chaps questions, and then pose one of his own that ties science in a knot, like, how can the infamous Moebius strip exist? It is an impossible, but genuinely one sided object! No one can deny it exists, yet how do you explain it? You can make this one sided strip with a piece of paper - then get the kids to explain to you how a one dimensional object can exist in the real world. Of course - it must be some sort of trick! Only it's not...
@jimmayl1
duh your question is soooooooo easy to answer.
the right rotating SWASTIKA is asymmetrical
its symmetrical twin is the left rotating asymmetrical SWASTIKA
duh why else do you think this symbol is so powerful
yes, he is. your typical garden variety east ender.
@islandbuoy4 Can you name an asymmetrical object that is rotationally symmetric? By definition, an asymmetrical object is something that is LACKING symmetry of any kind. By that definition, an asymmetrical object cannot be rotationally symmetric.
@islandbuoy4
"the swastika is ASYMMETRICAL but rotationally symmetrical."
Oh boy. What bit of ASYMMETRICAL did you not get? It means 'has NO symmetry'. In other words, if it has ROTATIONAL symmetry, then it has SYMMETRY, ergo cannot be ASYMMETRICAL.
I don't know about seeing a pattern, but I think I can spot a Dunning-Kruger type trying to argue that black is both black AND white! Jimmyl1 is right. You messed up by trying to show that you're and expert in something you don't understand.
1 year and then a response...
Im a speedcuber. My name would have been on the object lol! I was yelling 42 Quintilion throughout the whole vid :(
Anthony Nguyen still wrong though. A quintillion is 10^18 but the correct answer was 10^24 and the lady in the audience said 10^20 (21 digits), so she beat you by a factor of 100.
...
Anthony Nguyen
O...K...
The Pantheistic Atheistic Mystic Universalist Materialist has said of Origins: I don't know. Life is what you make of it. It began and it will end. Make something of that.
All of your reality is Memory (which occurs in consciousness only), Now, and Plans for the future (which planning is stored as memory now).
Now. The Center of a symmetry. It is beautiful in its own right.
fine line exists between symmetry and asymmetry
an object that is asymmetrical can be rotationally symmetrical...
AND hey if symmetry is such a WOW
two things....
WHY do those temples have an asymmetrical error AND WHY is matter and anti-matter asymmetrical?
This guy has his math, art, and the big picture kinda screwed up.
namaste
But to end this now.. I just posted my original comment from GK chesterton because the video reminded me of it. If you dont agree with me its ok!! I did not expect you to! but i still have a rite to air my views just like you have the rite to air your views?
Thanks to those who have responded! We can pm if you like!
❤️
@jimmayl1
"your BS degree cannot explain why Stonehenge, many of the henges, wood and stone, were geometrically mapped out ASYMMETRICALLY."
That bit of the Dunning-Kruger's comment should tell loads! He has no understanding of mathematics, nor of physics, nor of archaeology it seems! I've studied all three, although my undergrad major is in psychology; so I'm nowhere near as far up as you are with your comp-geom! We should ignore IB4 as a troll, methinks.
All the best, mate!
David
anomalies are OFTEN asymmetrical
WHY?
No really, I thought he would make some interesting points about symmetry but there was little more than symmetry basics and some arbitrary multidimensional object
awesome. geeks rule.
Yep, I lol'd.
damn..
. J. Kruger and D. Dunning attributed these ASYMMETRIC errors to differences in metacognitive skill. A replication study showed no evidence for mediation effects for any of several candidate variables ASYMMETRIC errors were expected because of statistical regression and the general better-than-average (BTA) heuristic. Consistent with this parsimonious model, errors were no longer ASYMMETRIC when either regression or the BTA effect was statistically removed.
ASYMMETRY is reality
SYMMETRY = god
@Hottides I think in this instance he is talking about conceptual entities that cannot physically exist in our universe, and so literally cannot be seen with our eyes. Nothing to do with religion. Although I do happen to agree with your ideas on religion. I view religion more like a kind of virus.
Fascinating talk about transcendently beautiful mathematics. However, I wish Du Sotauy would stop using religious metaphors like "things unseen" to communicate his wonder. Mathematics is the quintessential rational pursuit, whose epistemology and method form the model and ideal for all inquiry and reasoning. Religion by contrast is the deadly antithesis of reason. Using inchoate, empty metaphors to describe higher dimensional symmetry desecrates the splendor of reason incarnate.
watching this makes me feel really stupid!
Practicing loving kindness and mindfulness with the knowledge that everything is in fact One is a mental illness? I'm sorry, but I happen to know for a fact that you are wrong in this instance. Don't worry, I used to be wrong, too.