[QUOTEWell, SUFFICE to say, in relative format, a 57 dimensional coordinate against the ratio of geometry, it WOULD NEED an 8-dimensional configuration. [/QUOTE] No, this is simply not true.
In fact, if you study this guys mathematical analysis strongly enough, you will see he displaying a configuration that can be extended to 114 dimensions, and continued further, squaring the results. All this man has done, is made a beautiful mathematical design. And why is this simply not true?
I would guess it is the image of a 248-dimensional object. That would be a logical induction from the article..... Ben, I have a question about the SO(3,1) thingy. Is that only a part of the E8? I mean... the E8 has 248 dimensions, but we live in 4 dimensions. Are those 4 dimensions only 4 out of 248 (and there are 244 left out there), or are the 4 dimensions some sort of compressed form of all the 248 dimensions (that is, that we can unfold our 4 dimensions into 248 ones)? Please Register or Log in to view the hidden image!
Lisi's inspiration lies in the most elegant and intricate shape known to mathematics, called E8 - a complex, eight-dimensional mathematical pattern with 248 points first found in 1887, Who found it in 1887??
So what you saying Ben, the time dimension exists, but doesn't, because it's inside some kind of confinement... I simply don't understand you...
This may be kind of hard to understand without understanding representations. Think about it this way: if you've ever taken calculus, then you probably have some experience with basis vectors. That is, given a vector space, you can find a minimal set of vectors (a ``basis'') such that any other vector IN that space can be generated by some linear combination of those vectors. The easiest example is the plane---how many independant directions can you move in the plane? Well, two---left and right or up and down. So, call one unit of moving up \(\hat{y}\) and one unit of moving right \(\hat{x}\). Then (after specifying an origin), you can specify any position in the plane as \(\vec{r} = a\hat{x} + b\hat{y}\). You may be more familiar with the notation (a,b)---i.e. you are at a point (a,b) in the xy-plane. So, \(\hat{x}\) and \(\hat{y}\) form a basis for the xy-plane. There are two vectors, and the xy-plane is two dimensional---this is, of course, no coincidence Please Register or Log in to view the hidden image! The basis of E8 is 8 dimensional. THIS is the important number, not the 248 thing. Of these eight directions, one is time. Lisi's work is interesting (though I'm not altogether convinced that it's right) because no one (as far as I know) has ever found a way to get the symmetry of space-time SO(3,1) out of E8. E8 was discovered in 1887 by Cartan, I think. He discovered it in a really elegant piece of maths called the classification theorem---basically, he set down to classify all of the known symmetries, and discovered five ``exceptional'' symmetries that people had missed before. They are E6, E7, E8, F4 and G2. Anyway, I hope this wasn't too confusing.
Because time is special in the sense that it is unlike other dimensions. Simply dividing 57 by four doesn't give the number of time dimensions. Time has a very special character, and one must prove a dimension is time-like, as opposed to just waving one's hands and writing down an answer.
Hi BEN Are you talking about (0_3,1) OF LORENZTIAN rotations, or have i got this wrng again>? Also, : you said; ''Because time is special in the sense that it is unlike other dimensions'' But space and time are inseprable....???
I suspect one of the ways that a time dimension would be special is that we don't have freedom of movement along its axis. I'd be interested to learn just how time dimensions are special.
The thing Nexus, is that Einstein and Minkowski PROOVED that a coordinate in space was relative in time, and if this is so, the old proverb... ''They are inseprable,'' Holds strong. If this be the case, then String Theory is intentionally going against this configurate. time is a dimension called ''an INVARIANT OF'' space, which means, neither can be removed or can simply dissappear. In other words, String Theory is wrong. Or this E8 mathematical beautification.
Yes. But, you can only travel one direction along the axis of time. You can't travel backwards in time without violating the speed of light limitation. Edit: Oh. And by the way, careful with that word 'proved.'
