This is a 2-dimensional projection of E8, a 248-dimensional object seen here simplified into only 8-dimensions to help preserve sanity. Essentially, if I understand it correctly, it’s like a 2-D shadow of a 248-D sphere, an object so symmetrical you could theoretically rotate it in any direction in up to 248 dimensions and it still appear the same. Talk about a stick in the mud. It took 18 mathematicians four years to produce the calculation for this object, its formula weighing in at 60 gigabytes. The computation was announced at MIT by David Vogan this Monday, the 19th of March, 2007.
LINK/IMAGES ["Representations of E8"]
DOWNLOAD [E8 projection, 200kb EPS]
ARTICLE [E8]
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27 comments
It is amazing. It looks amazing. Whatever it is.
i dont get it
You’ve seen Imagining the Tenth Dimension right? A point is extended by a line, is extended by a plane, is extended by space, by time, by possibility and so on. Take that kind of logic and extend it to the 248th dimension. Go ahead I’ll wait here.
It’s seemingly incomprehensible, but my analogy of the above image being a shadow is the best way I can rationalize it. Like a circle would be the 2D shadow of a sphere, or a sphere the 3D shadow of a hypersphere, the above is a 2D shadow of a kind of sphere far more complex — probably the kind of ball gods use for bowling.
Come to think of it, I’ve begun reading Sagan’s Contact (I know, saw the film, but was interested in the real stuff) and I’m now imagining the mothership slash planet slash ‘entity’ to look like this.
Nils, just added that to my to-read list. I was in 8th grade or something when I saw the movie, but I remember it more clearly than most other films I saw back then.
Note to self: do not drink 5 vodka tonics and then attempt to look at 8-dimensional figures. Bad, bad, bad idea.
Some clarifications:
The picture is a 2-dimensional projection of an 8-dimensional collection of points (there are 240 of them) known as the E8 root system.
This root system is related in a certain way to the exceptional Lie group of type E8, which is a much more complicated object of dimension 248. The calculations done by Vogan et al. tell us something about the representations of this group.
On a less technical note, I should add that although the picture is kinda pretty, it doesn’t really have the ability to highlight any of the amazing properties of the E8 root system.
For instance, one neat thing is that it gives the unique tightest packing of 8-dimensional spheres in 8-dimensional space. This is analogous to how you can fit exactly 6 pennies around the edge of a single penny on a flat surface with no room left over (that would be the 2-dimensional case).
The only other dimension besides 1 in which this type of extremely symmetrical unique tight packing is known to occur is 24. Look up the Leech lattice if you’re interested. (another amazing object!)
greetings !!!!
the 2 d ‘projection’ is a better expression than ’shadow’ leading to a slight increase in communication of the understanding achieved. look up ‘M ‘ theory for further basics. when scaling down the truth from pure maths to cheap english a similar projection method is used & i have repeatedly found prose to be wanting in many areas – poetry works best – specially if it emotionally reflects the mathematical wave in any of its harmonics. ever tried to feel the intellect ? if required & curious enough to still go beyond the dimensions look up the Vedas & Upanishads. where the inexpressible has been explained by analogy. modern maths is coming close to it soon. it will reach that level in our lifetime. i believe it will. thanks.
About Imagining the Tenth Dimension: this is the equivalent of a 2-D figure, with 82 dimensions making up every point, according to the video. don’t ask how, or why. just go with it.
In mathematics time doesn’t play a factor in higher-than-three dimensions. Don’t confuse physics (specifically relativity) with mathematics. A physicist would say that a three dimensional universe with one dimension of time is “3 plus 1 dimensional”, not “4 dimensional” so as to not make the confusion of a 3+1 dimensional spaceTIME with 4 dimensional space (not spacetime).
As E8 is a mathematical structure and exists in the mathematical world with its own language one throws away with the whole spacetime concept and talks strictly of 248 dimensions of space. Thus, if one were to live in a universe the “shape” of E8 with one dimension of time we’d say that the universe is 248+1 dimensional…see the difference?
Also, that Imagining the 10th Dimension site is full of garbage anyway. I don’t know why the author chose 10 dimensions but by the time you hit the 8th you’ve not already amassed 2 temporal dimensions. That would be a 6+2 dimensional spacetime….but the 8th dimension of space is something different.
Just tired of false information being spread and being taken as truth. Believe me or not.
steve: If the physical and mathematical concepts of a multi-dimensional universe disagree then it throws both models into suspect. You’re probably right in stating that this is a representation of 248 dimensions with respect to the latter.
I agree, but E8 isn’t a physical model of the universe, it’s just a possible underlying structure of the mathematics that govern certain principals. Just like the Standard Model has gauge group SU(3)xSU(2)xU(1), one of the heterotic string theories (HE) has a gauge group of E8xE8…which necessarily takes time out of the equation. But I agree, time is necessary in the context of physics, just not in the case where E8 comes in to play.
OK… it looks like the art project my son did in the 5th grade with nails on a board and colored string.
I don’t find it all that enlightening…
what an utter waste of time for 18 idiots. whatever this means – and meaning can be derived from a stone if you wish – has no bearing on anything of any value. shoot these oxygen thieves!
^I fail to see makes these people “oxygen thieves” moreso than those who do absolutely nothing useful or innovative with their lives… care to explain? Perhaps my spending four years at an institute for a simple engineering degree makes me a thief of O2 as well, hmmm.
In other news, great picture; I really love the symmetry and think this was well worth the computational time!
Looks like someone owns a really fancy Spriograph set!
WTF?
Spirograph!
What I find most interesting about both this image and popular science ‘imaginings’ like those of the Tenth Dimension is the attempt to render abstract mathematics in non-mathematic terms. This must be impossibly difficult–something like describing the smell of your lover in numbers. Yet images with accompanying text such as is given here allows the non-initiated some insight into the vast complexities of contemporary mathematics.
And before we criticize non-mathematical models of, well, mathematical models, we should remember that what they are offering is not the truth of the formulas (for that is only contained in the formulas), but an aspect of the complexity. In that way, the image on this page represents, or presents, two things to me: the description given, no doubt, but also popular representations of science are but shadows of the machinations and productions of scientific research.
Isaac: well said
wow, that’s really unbelievable. Hope its not photoshop work ?
When I was a kid I used to stuff like that in 5 minutes using my “Spirograph”. Who knew I was plotting multidimensional objects. Huh.
And mom said I’d never amount to anything.
This is representation of the underlying physical structure of the universe…
It is also a piece of common string art, an expensive one… It also is resonate with representation of the apttern in other cultures and in Nature herself, some would call it The Mandala. I’m no math wiz, but I am told this it, “the simple explanation of everything”, hmmm…
Google “Garrett Lise”…
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Dallas112263
i would like to know more about E8 and its use in finding the ultimate unified equation
I just don’t understand how is there a thing in the whole universe that can exist in more than 3 dimensions??
and if we consider the world in four dimensions, we then used another new dimention called “time”
but how can more than those 4 dimensions appear in our world??
in the 3 dimensions, the three coordinates of the x,y and z are perpendicular to each other, but if we consider a 248 dimensional space, what will be the angle between them?
i’m keen on understanding the e8 so please if anyone knows the answer to any of the previously answered questions pls send me a mail.
thanks
this post is amazing. cool share. thx .
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