I wonder why that table looks like a periodic table, It would be really interesting to know it it looks like that because it was desinged to look like that as a joke, or it it looks like that because that is acctually the most straight forward way to represent it.
In the video he said it was, "a bit of a tongue-in-cheek approach" so, there is perhaps a bit of both. I have no ability to say, but I'm sure there's a group of mathematicians giggling somewhere about their "parody" of the chemistry community.
If you look closely at it you'll see that it was made to be like the periodic table intentionally: irandrus.files.wordpress.com/2012/06/periodic-table-of-groups.pdf
Thanks for sharing the pdf kikones though I have to admit that I don't know enough about groups to figure out if the design makes sense or if it was artificially altered to fit the form of the periodic table by simply looking at the pdf^^
Although looking at it again I just realized that in the lowest row there is always the general formula, and above it there are examples, and it seems like there is now direct reason why they stopped after the given number of examples (except of course to make it look like the periodic table =D! )
Sam Fed You're welcome ^^ And I know absolutely nothing about groups, but you can see that in every column there are first some concrete cases, and then the general rule. They could have showed any other number of concrete cases, or none at all, but they made it look like the periodic table for the lulz :D
What I don't understand is how can the monster be a simple group and yet have another simple group as a sub group? In the first video, the simple groups were defined as the building blocs of groups like elements in chemistry so they shouldn't have smaller groups they are made of?
He never said the monster had another simple group as a subgroup. He said, very vaguely "other simple groups can be found within the Monster". I think he meant that aspects of them, or certain of their properties, could be found in the Monster.
The Monster group is such that it cannot be defined as the composition of two or more smaller groups. The Baby Monster group is a subgroup of the Monster group, but you cannot compose the Monster group in terms of the Baby Monster group and some other group. In the videos where he was talking about equilateral triangles (with points 1, 2 and 3), the triangle symmetries G = { R0, R120, R240, a, b, c } (where a, b and c are the reflections that touch points 1, 2 and 3 respectively) can be defined in terms of two groups -- rotational symmetries R = { R0, R120, R240 } and reflection symmetry S = { R0, a } -- such that G = RS (with R0 = R0.R0, R120 = R120.R0, R240 = R240.R0, a = R0.a, b = R120.a and c = R240.a). Therefore, for triangle symmetries G is not a simple group, but R and S are. In terms of the classification of groups, R and S are both cyclic groups (they are generated from a single invertible associative operation -- for R this is rotation, for S this is reflection) with prime order (i.e. |R| = 3 and |S| = 2).
Because the Monster is not the product of subgroups. It has subgroups which are simple, but they don't 'construct' together to form the Monster, likely due to leftover bits that don't fit in any of the other subgroups.
A simple group can have subgroups, but none of them can be 'normal subgroups'. A normal subgroup is a smaller group which you can 'divide' the larger group by to obtain another group. So even though the baby monster lives inside the monster, the monster group cannot be divided so easily!
If I'm understanding this right, the monster group is then the equivalent of that group from the other grid that linked with the equilateral triangle in that both sets not only relate to specific shapes/structures but to significant structures. Or, to rephrase; the same way that a circle, square, equilateral triangle, etc are significant in 2D space and the cube, sphere, etc are significant in 3D space, the monster's structure is significant in that many dimensions and the monster would be significant in that it is directing us toward that object?
Astonishing thing... i believe Ramanujan was able to operate at that level, as if he was shown the symmetry groups, like a roadmap. we're only just figuring out how to use it. His last paper on Mock Theta functions... was only a beginning.
Even the best graphics cards without company (i.e. just one graphics card, even hardcore gamers use like 2-3 GPUs) have trouble with rendering some more advanced 3D. I really doubt such a thing will be possible anytime soon, would be really cool though!
@@laurel5432 Well, clearly what games are rendering is rarely symmetrical or simple. So in a sense, that shoudn't really be the challenge. Not to mention, even if you can calculate it, how will you render something in so many dimensions in a way we will be able to visually understand it? Even 4D being visualised for our 3D brains is messy.
+JOSE LUIS GOMEZ RAMIREZ Actually you can find 20 of all 26 sporadic groups in the monster! The simpleness is little bit complicated. Being simple means being able to be a building block for all groups in some specific sense. Simple group CAN have subgroups, but it can't have such a subgroup, that can be 'killed' (factored out). Simple means, that you cant 'factor it', whatever that means. Analogy: prime numbers does not have a factor, let's think of that as 'simple'. And your answer would read in this context something like: "how can primes be simple when there are numbers smaller than them?". Being smaller (subgroup) doesn't mean, you can factor by it. I hope I gave you the gist of it. For what it actually mean, you would have to study some algebra book.
+Czeckie oh ok, thanks. so basically as addition and factorization are different, being a subgroup and being the factor of a group are different. thats what i got from it. anyways, as you said, I shouldacquire a book on group theory 😊thnxs anyway
I have a bizarre inquiry from an engineering perspective. I am a CS major and we evolved in a 3d environment and we have evolved 3d imagination. Now if I create an 4d environment in a computer and allow creatures to evolve there will they actually be able to have 4d imagination? I would assume so. Which just blows my mind. This really means that they will be things in the future that are so much better than me in thinking that my thought will be 2 dimensional to it. That is a somewhat terrifying thought for me.
Also, the speed of AI is terrifying : for them to converse with us would be like us talking to a snail that took 100yrs to answer each question. (I'm guessing. The time span may be 1000yrs per answer. The point is, AI will be orders of magnitude faster than us).
Well, if they evolve _general intelligence_ like we have, then yes, there's a sense in which they'll think in 4D. But, aside from curiosity, there's really no reason to even sketch such a model, much less throw the necessary compute at it.
@@vinm300 Wayyy speculative here. In hardware terms, the human brain makes the Fugaku look like an abacus. While it's true that a computer can execute a _hand-written, pre-optimised, definite procedure_ before a human could finish reading it, even a simple neural net is orders of magnitude more complicated, and a _general intelligence_ would be orders of magnitude on top of that. Frankly, it'll likely be close to the reverse of what you describe.
The elements are symmetries of some object. So the numbers associated with these groups are how many symmetries, or "finite simple groups", the object has.
This is already in your second channel, so why is it still unlisted? I had hoped you would stop with the unlisting thing; it's just annoying. I don't watch the videos on RUclips, I download them straight from my subscription list, and watch them with a proper media player. Bunched up, when I got time. When you put links to videos in the annotations, I have to manually open each video, seek to the end and click on them.
stay calm - I just list this one a bit later so that when people open their subscriptions they are less likely to click on this one BEFORE the main video, etc, which could also be annoying! I'm just trying to annoy the fewest people - but people will always be annoyed!
So the Baby Monster fits within the Monster, but they're both simple groups. Meaning you can't "subtract out" the Baby from the Monster and leave a complete group. Otherwise, the Monster would not be a simple group. Is that correct? Do all the sporadic groups nest inside each other like matryoshka dolls? Or some of them?
I imagine they share some amount of subgroups, but not completely. Or perhaps there's at least 1 segment of the Monster group that can't live on it's own as a simple group, nor lives in any of the other simple groups.
it occurs to me that as they discuss this seemingly endless set of symmetries they cant explain, they have a sort of symmetry between two theoretically distinct groups of data with respect to a human's conscious interpretation of the universe they inhabit. The sporadic groups are not the periodic elements and yet through human imagination, we have a symmetry.
What's the significance behind the ordering of this periodic table??? Is it just arbitrarily illustrated to look like Chemistry's periodic table or is there deeper meaning there??? How can you not address that question in this video???????? Ahhhhhhhh!!!!!!!!!!!!!!!!!!!!!!!!!!!! just curious, =)
Wait, along the 26 sporadic groups, is there a finite number of infinitely large families of groups or is there infinitely many groups of infinitely large families of groups? Great, I confused myself even more
+zoranhacker there are 16 families of finite simple groups. Each of those family is infinite. Basically the families are described by some very general structural idea depending on a given number N - then the family consists of all these groups for every possible N. One such family are groups that have prime number of elements. It can be shown, that there's exactly one group (cyclic) with given prime elements.
I'm very disappointed in Tim Burness for not honouring Monstrous Moonshine by using its true name. Monstrous Moonshine is a thing to be celebrated and rejoiced upon, not to be hidden.
Is there a chance that the monster grp is the set of symmetries in a hyper sphere? I know it sounds crazy but Conway was describing Christmas baubles and I believe the a hypersphere is rather like a spiky bauble.....
I certainly have no expertise in advanced mathmatics or group theory, but it would seem to me unless there's a proof that says the number of possible fundamental groups is finite, then find a 58 digit long number of a groups doesn't seem odd at all. Even if there is a finite number though, so what? This is just how it happens to be. Symmetry is an abstract concept we define, and self-consistency dictates there just happens to be this many possible symmetries there are for a particular possible 196,000 dimensional object
+bob smith The number of simple groups is infinite, however, there are infinite families to which they belong to. There's a finite number of these infinite families. What is surprising is that there are exactly 26 groups which do not belong to any of the infinite families. But what's more surprising is that it is actually proved that this classifies *all* simple groups. There are a finite number of families of groups and then there are 26 others. This is not at all expected, and I believe it was thought for awhile that these 26 would be at some point shown to belong to some weird infinite family, but they don't. Indeed it *is* odd that there is some largest (sporadic) group and it is known that there isn't any others. I will have to heavily disagree with you about symmetry being simply an abstract concept we define, but I doubt my ideas would sway your thoughts there.
Must admit, this is better than a mystery novel lol
It should be Fg for Fischer-Greiss or Friendly Giant. A double acronym!
FG²
Greiss, who first constructed the Monster, was my professor for advanced linear algebra in college
Jacob Goodman UMich represent! I actually have him now, he’s a great guy.
That's awesome!
More groups please! You could make videos on Lie Theory for example.
I really do not fully grasp the whole concept in the video but somehow this was one of the most enjoyable video that I was watched in my entire life.
Wow, that was both a wonderful and intriguing story throughout those 3 videos.
Thank you again!
well... this was a long and interesting journey... :D
Brady, you always ask the most darned interesting questions! Thank you!
Skirting around Conway''s Montrous Moonshine conjecture....
Not even a conjecture any more as it was proven in 1992.
Please do more on groups and things like that!
I wonder why that table looks like a periodic table,
It would be really interesting to know it it looks like that because it was desinged to look like that as a joke,
or it it looks like that because that is acctually the most straight forward way to represent it.
In the video he said it was, "a bit of a tongue-in-cheek approach" so, there is perhaps a bit of both. I have no ability to say, but I'm sure there's a group of mathematicians giggling somewhere about their "parody" of the chemistry community.
If you look closely at it you'll see that it was made to be like the periodic table intentionally: irandrus.files.wordpress.com/2012/06/periodic-table-of-groups.pdf
Thanks for sharing the pdf kikones though I have to admit that I don't know enough about groups to figure out if the design makes sense or if it was artificially altered to fit the form of the periodic table by simply looking at the pdf^^
Although looking at it again I just realized that in the lowest row there is always the general formula, and above it there are examples, and it seems like there is now direct reason why they stopped after the given number of examples (except of course to make it look like the periodic table =D! )
Sam Fed You're welcome ^^
And I know absolutely nothing about groups, but you can see that in every column there are first some concrete cases, and then the general rule. They could have showed any other number of concrete cases, or none at all, but they made it look like the periodic table for the lulz :D
Sorry, was that the Fisher-Price monster? Because I had a bunch of those as a kid.
What I don't understand is how can the monster be a simple group and yet have another simple group as a sub group?
In the first video, the simple groups were defined as the building blocs of groups like elements in chemistry so they shouldn't have smaller groups they are made of?
He never said the monster had another simple group as a subgroup. He said, very vaguely "other simple groups can be found within the Monster". I think he meant that aspects of them, or certain of their properties, could be found in the Monster.
The Monster group is such that it cannot be defined as the composition of two or more smaller groups. The Baby Monster group is a subgroup of the Monster group, but you cannot compose the Monster group in terms of the Baby Monster group and some other group.
In the videos where he was talking about equilateral triangles (with points 1, 2 and 3), the triangle symmetries G = { R0, R120, R240, a, b, c } (where a, b and c are the reflections that touch points 1, 2 and 3 respectively) can be defined in terms of two groups -- rotational symmetries R = { R0, R120, R240 } and reflection symmetry S = { R0, a } -- such that G = RS (with R0 = R0.R0, R120 = R120.R0, R240 = R240.R0, a = R0.a, b = R120.a and c = R240.a). Therefore, for triangle symmetries G is not a simple group, but R and S are.
In terms of the classification of groups, R and S are both cyclic groups (they are generated from a single invertible associative operation -- for R this is rotation, for S this is reflection) with prime order (i.e. |R| = 3 and |S| = 2).
Because the Monster is not the product of subgroups. It has subgroups which are simple, but they don't 'construct' together to form the Monster, likely due to leftover bits that don't fit in any of the other subgroups.
but then could you not group the "leftovers" to form another simple group?
A simple group can have subgroups, but none of them can be 'normal subgroups'. A normal subgroup is a smaller group which you can 'divide' the larger group by to obtain another group. So even though the baby monster lives inside the monster, the monster group cannot be divided so easily!
If I'm understanding this right, the monster group is then the equivalent of that group from the other grid that linked with the equilateral triangle in that both sets not only relate to specific shapes/structures but to significant structures. Or, to rephrase; the same way that a circle, square, equilateral triangle, etc are significant in 2D space and the cube, sphere, etc are significant in 3D space, the monster's structure is significant in that many dimensions and the monster would be significant in that it is directing us toward that object?
some more of the Monster, and maybe John Conway please? It's incredibly interesting
Astonishing thing... i believe Ramanujan was able to operate at that level, as if he was shown the symmetry groups, like a roadmap. we're only just figuring out how to use it.
His last paper on Mock Theta functions... was only a beginning.
How about a PDF of the table!!!
Would love to see an explanation of Borcherds proof of monstrous moonshine?
no extra bit here? xD
More groups plz
rest in peace, conway
I'm calling it now. The Monster is the shape of the multiverse!
oh damn he called it
is it possible to create a graphics card, which is able to contain all the vectors, and do math with the monster?
Even the best graphics cards without company (i.e. just one graphics card, even hardcore gamers use like 2-3 GPUs) have trouble with rendering some more advanced 3D. I really doubt such a thing will be possible anytime soon, would be really cool though!
@@laurel5432 Well, clearly what games are rendering is rarely symmetrical or simple. So in a sense, that shoudn't really be the challenge. Not to mention, even if you can calculate it, how will you render something in so many dimensions in a way we will be able to visually understand it? Even 4D being visualised for our 3D brains is messy.
I just want to see the formula that spits out that huge number, tho I wouldn't get it.
I have a question. Of the monster and the baby monster are both simple, how come you can find the baby in inside the monster?
+JOSE LUIS GOMEZ RAMIREZ Actually you can find 20 of all 26 sporadic groups in the monster! The simpleness is little bit complicated. Being simple means being able to be a building block for all groups in some specific sense. Simple group CAN have subgroups, but it can't have such a subgroup, that can be 'killed' (factored out). Simple means, that you cant 'factor it', whatever that means. Analogy: prime numbers does not have a factor, let's think of that as 'simple'. And your answer would read in this context something like: "how can primes be simple when there are numbers smaller than them?". Being smaller (subgroup) doesn't mean, you can factor by it. I hope I gave you the gist of it. For what it actually mean, you would have to study some algebra book.
+Czeckie oh ok, thanks. so basically as addition and factorization are different, being a subgroup and being the factor of a group are different. thats what i got from it. anyways, as you said, I shouldacquire a book on group theory 😊thnxs anyway
At some point, AI will understand the structure and interrelations of the Monster... and won't tell us.
I have a bizarre inquiry from an engineering perspective.
I am a CS major and we evolved in a 3d environment and we have evolved 3d imagination.
Now if I create an 4d environment in a computer and allow creatures to evolve there will they actually be able to have 4d imagination?
I would assume so. Which just blows my mind.
This really means that they will be things in the future that are so much better than me in thinking that my thought will be 2 dimensional to it.
That is a somewhat terrifying thought for me.
After reading this I am also terrified of the future for entirely different reasons.
Also, the speed of AI is terrifying : for them to converse with us would be like us talking to a snail that took 100yrs to answer each question.
(I'm guessing. The time span may be 1000yrs per answer. The point is, AI will be orders of magnitude faster than us).
Well, if they evolve _general intelligence_ like we have, then yes, there's a sense in which they'll think in 4D. But, aside from curiosity, there's really no reason to even sketch such a model, much less throw the necessary compute at it.
@@vinm300 Wayyy speculative here. In hardware terms, the human brain makes the Fugaku look like an abacus. While it's true that a computer can execute a _hand-written, pre-optimised, definite procedure_ before a human could finish reading it, even a simple neural net is orders of magnitude more complicated, and a _general intelligence_ would be orders of magnitude on top of that. Frankly, it'll likely be close to the reverse of what you describe.
why it is similar to the periodic table structure
I discovered what the ground of monster group, and then they will make since
Do we know that these 26 are all of the sporadic groups, or could there be another one even bigger than the monster?
+jfb-1337 I'm wondering this too
+jfb-1337 we know the list is complete, no other finite simple group exists
What's the elements of such groups? Numbers? It's not clear to me.
The elements are symmetries of some object. So the numbers associated with these groups are how many symmetries, or "finite simple groups", the object has.
Your table is missing 3 large elephants, the spherical elephant's foot and the spherical elephant.
Fortunately the pink elephant is already there.
What does it have to do with chemistry???
Which are the names of books near the stapler?
Monster groups and string theory pls.
when the Brady man throw in a lil extra
is it just a coincidence that it's the same shape as the actual periodic table? that just seems crazy unlikely.
"Tongue in cheek," he said, so it's a forced fit.
This is already in your second channel, so why is it still unlisted? I had hoped you would stop with the unlisting thing; it's just annoying.
I don't watch the videos on RUclips, I download them straight from my subscription list, and watch them with a proper media player. Bunched up, when I got time. When you put links to videos in the annotations, I have to manually open each video, seek to the end and click on them.
stay calm - I just list this one a bit later so that when people open their subscriptions they are less likely to click on this one BEFORE the main video, etc, which could also be annoying!
I'm just trying to annoy the fewest people - but people will always be annoyed!
Okay :)
Plus, some of us get annoyed with channels that clog up our subscription page with too many videos at once.
Numberphile2 I had the same thought as Sven Hesse, but I changed my mind upon reading your reply.
Numberphile2
Always thinking, Brady. I usually follow the annotations anyway.
So the Baby Monster fits within the Monster, but they're both simple groups. Meaning you can't "subtract out" the Baby from the Monster and leave a complete group. Otherwise, the Monster would not be a simple group. Is that correct?
Do all the sporadic groups nest inside each other like matryoshka dolls? Or some of them?
I imagine they share some amount of subgroups, but not completely. Or perhaps there's at least 1 segment of the Monster group that can't live on it's own as a simple group, nor lives in any of the other simple groups.
Very entertaining, never heard of the monster before.
it occurs to me that as they discuss this seemingly endless set of symmetries they cant explain, they have a sort of symmetry between two theoretically distinct groups of data with respect to a human's conscious interpretation of the universe they inhabit. The sporadic groups are not the periodic elements and yet through human imagination, we have a symmetry.
What's the significance behind the ordering of this periodic table??? Is it just arbitrarily illustrated to look like Chemistry's periodic table or is there deeper meaning there??? How can you not address that question in this video???????? Ahhhhhhhh!!!!!!!!!!!!!!!!!!!!!!!!!!!! just curious, =)
What is the shirt of Tim about? Does it have any meaning? Is Tim single?
Wait, along the 26 sporadic groups, is there a finite number of infinitely large families of groups or is there infinitely many groups of infinitely large families of groups? Great, I confused myself even more
+zoranhacker there are 16 families of finite simple groups. Each of those family is infinite. Basically the families are described by some very general structural idea depending on a given number N - then the family consists of all these groups for every possible N. One such family are groups that have prime number of elements. It can be shown, that there's exactly one group (cyclic) with given prime elements.
I'm very disappointed in Tim Burness for not honouring Monstrous Moonshine by using its true name. Monstrous Moonshine is a thing to be celebrated and rejoiced upon, not to be hidden.
Use Tau instead of 2.
You guys should change your channel logo to Tau, since Tau is 2 Pie
Is there a chance that the monster grp is the set of symmetries in a hyper sphere? I know it sounds crazy but Conway was describing Christmas baubles and I believe the a hypersphere is rather like a spiky bauble.....
I certainly have no expertise in advanced mathmatics or group theory, but it would seem to me unless there's a proof that says the number of possible fundamental groups is finite, then find a 58 digit long number of a groups doesn't seem odd at all. Even if there is a finite number though, so what? This is just how it happens to be. Symmetry is an abstract concept we define, and self-consistency dictates there just happens to be this many possible symmetries there are for a particular possible 196,000 dimensional object
+bob smith The number of simple groups is infinite, however, there are infinite families to which they belong to. There's a finite number of these infinite families. What is surprising is that there are exactly 26 groups which do not belong to any of the infinite families. But what's more surprising is that it is actually proved that this classifies *all* simple groups. There are a finite number of families of groups and then there are 26 others. This is not at all expected, and I believe it was thought for awhile that these 26 would be at some point shown to belong to some weird infinite family, but they don't. Indeed it *is* odd that there is some largest (sporadic) group and it is known that there isn't any others.
I will have to heavily disagree with you about symmetry being simply an abstract concept we define, but I doubt my ideas would sway your thoughts there.
I do not care much for these hidden videos.
They are not easy to find on you mobile.
And some times your not close to a pc.