From the discussion over at slashdot:

Troi: Captain, I can 'feel' the amplituhedron.

Data: It's become sentient

Q: Foolish humans ... you could never hope to understand this.

Wesley: Oh sure, I made one in science class last week.

ALL: Wesley, STFU.

And more serious stuff:

IANAPOM (I am not a physicist or mathematician), but from what I could gather from the article, it sounds like this isn't a new model that approximates the old, more complicated one, but rather a massive simplification of the existing one that produces provably identical results in all cases. To drastically oversimplify using my extremely limited understanding while putting it in terms I can wrap my brain around, it sounds like when you first learn about the arithmetic series in calculus (e.g. the summation of i from 0 to n). At first, the only way you can approach it is by actually adding 0 + 1 + ... + (n-1) + n, but eventually you learn that you can skip that whole process if i starts at 0 and use n*(n+1)/2 to reach the result with far less work, and then you're shown how to derive that formula yourself.

It sounds like something similar here. They previously had to calculate the results of every single Feynman diagram and then sum them together to reach a final result, which would involve billions upon billions of calculations for even a very simple particle interaction. Now, however, rather than having to calculate all of the component parts and summing them, they've derived a formula that produces the same answers with far less work.

Again, I may be way off, but that's the takeaway I had from the article.

Guys, we've been down this road about a million times in physics. Just because a mathematical model simplifies certain calculations, does not mean that the actual underlying physical geometry matches the theoretical model. Mathematicians have been adding extra dimensions to equations and finding they simplify things for years. It doesn't mean we live in a 27 dimension manifold. All direct observations to date point to a 3D universe.

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It doesn't mean we live in a 27 dimension manifold.

Doesn't mean we don't. ;-)

All direct observations to date point to a 3D universe.

Ummm ... hang on a second. Won't any direct observation we make as 3D critters point to a 3D universe? Isn't that sort of inherent to us being only able to perceive 3D?

I'm not sure how we'd do any direct observations in any other dimensions. (Honestly, not a flame, I'm genuinely puzzled by how we could see anything else and every now and then something like this hurts my head)

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Check out Richard Feynman's lecture regarding space-time and his analogy of bugs on a sphere. If you tell them that the rule for making a square is to go N units in one direction, then turn 90 degrees and repeat until you complete the square, they would find that they cannot actually make a square. This leads them to conclude that there is "something wrong" with their space.

The point is that while the underlying nature of their universe as a sphere is unavailable to them because they cannot escape it to see the bigger picture, they can still infer that because Euclid's rules of geometry don't work there must be something going on that they can't see. Moreover, they should be able to guess that there is curvature - without knowing for sure - because of exactly how the rules break down.

This is essentially what people talk about when they refer to the difference between larger objects like clumps of atoms and smaller ones like electrons and quarks. For some reason our 3D (technically it's 4D according to Einstein) universe only behaves "normally" until we start measuring it at a small scale. Then we start seeing where our rules about the behavior of "observable" objects - i.e., the stuff we can perceive with our senses - break down and are replaced by the true nature of the subatomic universe. In other words, when we look at quarks do stuff, we can no longer make the square.

Constructs like the one described above are the result of us trying to get our little bug heads around the way in which our every day rules break down when really tiny things are involved. It's a way for the bugs to correct Euclid to account for the spherical nature of things.

Physicists Discover Geometry Underlying Particle Physics - Slashdot

*Edited by rbp, : No reason given.*