Archive for March, 2007


Recall that Motives are about projective geometry. Naturally then, Motivic Cohomology should be about diagrams with lots of points and lines. We want to build very complicated geometries, perhaps to probe the region close to a Black Hole, from such diagrams. Now we see that dualities abound in motivic pictures. The most basic of these is the one between Space and Time. So there are also singularities in Time, as we observe.

Maybe this is all an April Fool’s Joke? Who knows?

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Some people are having difficulty understanding Louise, even when she draws very simple Space Time diagrams. Let’s use a slightly different diagram. We see that an observer at Now looks back to the past, and the infinite future looks back to Now. How much simpler can it be?

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Upcoming Seminar

Next Thursday, on the 5th of April, I will give a seminar for the in-house gravity meeting at UC. Everybody is welcome. If I am mysteriously detained by authorities before the talk, which is at 4pm in room 701, I will endeavour to put my slides on this blog.

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M Theory Lesson 35

One day, many years ago, I wanted to catch a bus from Sikkim down to the plains. It was my first lesson in the theory of order-under-chaos. A major landslide had blocked the only road out of the mountains, and yet in no time at all a relay of buses was setup. Travel between buses simply required a short walk along the goat track over the landslide debris.

It looks like M Theory needs to discuss the concepts of operadification and cooperadification. Don’t worry, I am not suggesting that we adopt this cumbersome terminology. Instead, let’s name the 2 functors that describe these processes entropy and information respectively. Entropy describes the process of leaping up to the next quantum level, which is far more complex and intricate. Information is the dual process of dropping down whilst investigating a question. It might not be humans asking questions. The galaxy might want to ask Computer Earth a question now and again.

Baez et al have been describing a program of groupoidification. This lives in the realm of n-category theory, and we expect that such categorical structures will arise as algebras of master operads.

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M Theory Lesson 34

What is a Machian principle for inertia in a quantum world? Inertia is a property of moving bodies in a classical reality, but this reality must emerge from quantumness at all scales. Once we understand such a reality, inertia is more fundamental than mass or distance or time, because it is a statement that the dynamics of any given body should be related to those of all others.

In M Theory, the classical reality is built with levels of quantumness. That the levels themselves are quantized is clear by looking at the world: the atoms and molecules, the planets and solar systems, the galaxies and clusters. The lowest interesting level describes the observed particle spectrum of light particles. This level is a universal manifestation of the prime number 3. Matti Pitkanen has described such a reality in detail. There is no vacuum concept but nothingness itself, as Schwinger described it, and this primitive generator of the Number Theory Universe is also everything.

Louise Riofrio, who is speaking at Imperial College today, has amounted a large body of evidence in support of a Machian cosmology.

As Schrodinger said in the 1944 book What is Life?
“From the early great Upanishads the recognition ahtman=brahman … was in Indian thought considered, far from being blasphemous, to represent the quintessence of deepest insight into the happenings of the world.”

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The bloodhound commenter nosy snoopy has found this paper by Schlesinger. It is a remarkably clear exposition of the notion of a tower of quantisations, in terms of deformed Turing machines. All of String theory fits onto the lowest rungs of this tower. On a related note, Never Ending Books informs us of a new paper on the Manin-Marcolli cave, inspired by Plato.

The physical principles of M theory also include the n-alities that arise from the Machian nature of inertia. Carl Brannen has made great progress undertanding inertia for the first rung. See this PF post about the particle masses. They are organised according to the primes 2 and 3. This number 3 is the 3 that we have been discussing in recent posts. In the world of 3, one would work with trialgebras, rather than bialgebras; trioperads rather than bioperads. Naturally that is a master idempotent-swapping trioperad.

Physically, we observe that the classical reality that emerges from considering all scales is nothing short of a Mathematical God. The unreasonable effectiveness of mathematics is no longer unreasonable.

Behold, I come quickly: hold that fast which thou hast, that no man take thy crown.

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Countdown III

This new kneemo (Michael Rios) paper should make interesting reading. And don’t forget Louise’s talk!

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M Theory Lesson 33

Let’s have some more fun with pictures. A ribbon can be drawn on a boundary tube, even if the tube has to twist to keep up with the edges of the ribbon. Using the edges of the ribbon as boundaries for square pieces of tube, we could draw swiss cheese pictures on the cylinder. But instead of disc operad circles we could add in points and make a swiss cheese cubes operad picture. I apologise if I’m making up inappropriate names for these diagrams. According to Aaronson, M Theory will probably not be able to show that P = NP. This hypothesis is about packing cubes inside bigger cubes in polynomial time.

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Countdown II

Oh, all right, I can’t resist. For the conference countdown, let us ponder the fact that the correspondence between the prime three and the simple particles may give us an M theory derivation of the baryonic mass fraction, which would agree with Louise Riofrio’s result of $\frac{\pi – 3}{\pi}$.

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M Theory Lesson 32

Well, I can’t compete with Louise’s, Tommaso’s and Mottle’s blogs for conference blogging this week, so let’s continue with a few remarks on p-adic logic. Mahndisa made an interesting comment on kneemo’s blog. She said:

Any three vertex shape could represent three adicity in context and the lines that connect each vertex could be seen as a swapping morphism of sorts. I played around with this geometry a while ago and you can extend it up to n rational dimensions. A four adic system is represented by a trapezoid, rectangle, rhombus or square, each of the vertices are connected via lines and each of these lines represent swapping.

Mahndisa has been studying Matti Pitkanen’s p-adic physics for quite some time now, and has a unique perspective on where all this is heading. From a categorical point of view, it is interesting to note that we are discussing new structures. I recall Batanin discussing a mysterious kind of operad which swaps sources and targets. Recall that sources and targets are idempotents for us.

Thus the usual 2-adic situation is the tip of the iceberg. And since categories can arise as algebras for operads, the p-adic logic would give rise to new kinds of category.

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