The Monster Group - John Conway
ฝัง
- เผยแพร่เมื่อ 28 พ.ย. 2018
- Part of an interview, found under:
www.simonsfoundation.org/2014...
Links:
en.wikipedia.org/wiki/Monster...
i.redd.it/gn5cimd92mh11.jpg
References:
deepblue.lib.umich.edu/bitstre...
eudml.org/doc/143210 - เพลง
![บุกร้านไอศกรีม VJ วุ้นเส้น !!!! [ดูคลิปเต็มหน้าช่อง] #Short | PANG ORNHIRA](http://i.ytimg.com/vi/g549nEhKZdc/mqdefault.jpg)
RIP John.
it's always a pleasure to listen to John Conway
I'm sorry, brother. Wish you could have stayed for the day when we finally find the insight you dreamt of all your life. I'll keep seeking it, if not quite as successfully as so many others: holding those pieces of you which shaped us deep within ours psyches/souls so that such a sliver of you can in some faint way partake anew in this grand and tragic adventure.
RIP John Conway: an excellent mathematician, indeed - a genius, sure - but more than that, just an absolutely genuine, admirable, generally incredible human being.
The whole interview is worth watching. Very good interviewer too.
I feel smart just listening to him
An F for conway
F
Duly recorded.
RIP Dr. Conway
John Conway.......is fantastic.
Such a small amount of people are interested in this kind of topics. That's kinda sad.
Yeah, most people only care about bringing food to the table and having a roof over their head.
Having time to study niche things like this is ultra privliged and I wish it wasn't.
Amount of people or number of people?
Means more quality conversations amongst like-minded individuals.
Or the self drawing hand
Looks young for 81
RIP Mr. Conway
I hope there's an afterlife where John can continue his studies. Maybe you need to be dead in order understand why the monster group is there. RIP
Maybe the monster is like the end of the famous short story by Andy Weir: ‘The Egg’. Can highly recommend it.
He was not religious, which makes alot of sense given his area of study.
@@zhang_han me neither, but it's a nice thought
Me too, it's my only hope to understand all this as well.
The monster has nearly 10^54 symmetries 🤯
It resides (if real) in a place of 196,883 (or 4) dimensions 🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯🤯
What did you mean by (or 4)?
@@CR-og5ho it is how JC said it
Simple question. Is there any point someone with zero mathematical knowledge trying to get a feeling - just a feeling - for why this is so fascinating / spooky? The mere fact that it was enough to remain the Holy Grail for such a guy piques my interest, having heard an obituary of him, but this video gives no actual insight into the matter and I just wonder if there's any way of getting some kind of idea of it, without the first line of the explanation being an equation.
VERY roughly: In mathematics as in every field of science and art, symmetry is an absolutely central concept, and the theory that approaches maths from the angle of symmetry is called group theory. A group is essentially all the ways that an object can be symmetrical: for example, a square is symmetrical along the diagonals, the central lines, etc... and the collection of those is the symmetry group of the square.
In the 20th century, a huge collaboration of mathematicians worked to a classification of all possible finite groups. There is a long list of infinite families of groups attached to specific objects. For example a "family" could be the groups of the traingle, the square, the pentagon... which will all be kind of similar.
In this classification, however there are 26 exceptions: 26 groups of symmetry attached to 26 geometrical objects that are not part of any family and are completely unlike any other form of symmetry we can describe. The smallest of these "sporadic" groups is attached to a 10 dimensional object. As it turns out, most of the sporadic groups are pretty much shadows or projections of the biggest sporadic group of them all: the Monster group. It seems somehow to be at the origin of all the exceptional groups of symmetry, and no one understands why it is there, what it means, why there are only 26 and not more, basically what any of it is all about. All we know is that there is this 196 883 dimensional *thing* out there that has Lovecraftian symmetries unlike any we have ever seen or could possibly understand, and for the life of them nobody can tell why it is there.
Even more intriguing (or disturbing!) is how the Monster is intricately linked to very important problems. For example, someone chanced on a strange coincidence between the dimensions of the monster group and a problem involving prime numbers, and only recently did a mathematician invent 'Monstrous Moonshine' to help explain the link. The bridge between the Monster and this problem is so strange and unexpected that many consider itb miraculous.
For some reason that we don't understand, the Monster seems to be at the very core of Mathematics itself, pulling the strings on its infinite web. That is why John Conway wanted to know, before he died, what the whole thing was about.
@@johnduale430 Thank you so much for taking the trouble to do that, and I hope your reply will be as helpful to me as I'm sure it will to others. As to to whether it will, well I'm in mid-proofread right now, but I've pasted it into a Word document and first chance I get will meditate on it. It looks accessible enough to guarantee that if I can made no sense of it the fault will be mine entirely. It was listening to a piece of John Conway audio on the 'Last Word' Radio 4 obit stream, the week he died, that got me intrigued, in case anyone wants to seek that out. Thanks again ... what TH-cam would be for had the lunatics not taken it over.
@@Yoyimbo01 Thank you. I'll be checking it out as soon as i can see my way clear.
It's been a year since you commented so I don't know if this comment will be of any help. You could see th-cam.com/video/mH0oCDa74tE/w-d-xo.html by 3blue1brown. This video explains it in a very easy manner.
@@johnduale430 best explanation I've seen online. Thank you
RIP John
Sadly, rip
is there no way to represent the elements of this group? it doesn’t have symmetries? i can’t find much information in terms of animations, about it.
oh apparently it has connection to something called vertex operator algebras. michael penn has been making videos on that if you’re curious. i’m afraid it’s a bit too complicated for me
RIP cuz 🙏
being completely naive, how does Gödel's incompleteness theorems impinge on the statement that there are _only_ 26 (or 27) sporadic exceptional groups? what part(s) of the classification of the finite simple groups deals with showing the space is fully described?
they are unrelated statements
You look very confused. Well, actually most people who talk about Godel's incompleteness theorems happen to be completely baffled by their actual meaning, so I guess you're not entirely to blame. The incompleteness theorems state that there are sentences (including sentences about groups) that are true but not provable (within the theory of groups). However, if you find a proof for a statement, then _obviously_ that statement is provable. And since there is a proof that there are only 26 (or 27) sporadic simple groups, then you don't need to do anything special to avoid the dark magical influence of Godel's spooky incompleteness theorems... The statement is true and it has been proved. End of the story.
@@aaaab384 I may be confused as well, but aren't there two implications of Gödel's incompleteness theorem. One about incompleteness and the other about inconsistency. That if you can't prove if a system is complete then you can't prove that the system is consistent. That you need a stronger axiomatic system to prove the consistency of a weaker one. But then we wouldn't be able to prove the consistency of the stronger one either and we are kind of back at square one. And if an axiomatic system isn't consistent than you can prove any statement to be true due to the law of explosion. If the axioms of group theory are inconsistent than wouldn't that mean that our statements about there only being 26 (or 27) sporadic groups as Joe mentioned be reasonable to question.
@@JhonCJR Incompleteness means you can't prove everything, not that everything can't be proved. Inconsistency means it is impossible to create a set of axioms that can never create a paradox, but if there is no paradox in what you're proving then it is possible to attain truth, even by means of contradiction.
These groups might end up being future axiomatic bases for logic systems. Godel proved that there isn't a finite logic system which is both complete and consistent. We have a great one, Calculus of Inductive Constructions, but perhaps this is one of the final symmetry groups a future race could use in their advanced logic systems.
I thought Godel's Completeness Theorem established the completeness of logic, and his Incompleteness Theorem established the incompleteness of arithmetic. I'm not sure in what sense logic needs to be finite.
gg
I still dont know what the monster is
An inhabitant of Loch Ness.
The self drawing hand. Or the hand that draws itself. That’s the explanation. Perfect symmetry that’s constructing itself in an ongoing everlasting timeline. It’s simple to understand when you realize the beauty of it. While it seems mysterious, it really boils down to having the humility to accept that a super intellectual being has absolute and perfect manipulation of time, space and symmetry. These three concepts are easily tangible to someone who exists beyond the dimensions that we live in. Including the 4th dimension and even the theorized 12 dimensions.
I want whatever this guy's smoking
gay that he died. he was a chad mathematician. his works was always so entertaining
gay - archaic meaning happiness or cheerful attitude, or same sex orientation. Do you mean it's sad that he died ?
@@iridiandotnah he meant that is lame or it sucks that he died
Cryptography