Right. If 50 generations grew up digging cherries like potatoes we’d think that’s natural too.

Latkes growing on trees might look like a feature and not a bug.

]]>Latkes growing on trees?

]]>** On the other hand, given that the universe has run bug-free for nearly 14 billion years means that the Bayesian probability that the universe is a computer is extremely close to 0. **

How do we know the universe has run bug-free? What would a bug in the universe-program look like to us?

]]>* The appendices to Sean Carroll’s “The Particle at the End of the Universe”

* The article

“Physics and Feynman’s Diagrams”

Kaiser, D.

American Scientist, Vol 93, 2003

gives a quite well-written and accessible historical overview of FD’s impact and how its usage by the Physics community has evolved over the years.

* I found a book with a quite promising title

“Quantum Field Theory in a Nutshell”

A. Zee

http://press.princeton.edu/titles/9227.html

Again, thank you for your answers, they’ve helped me a lot.

]]>On the other hand, given that the universe has run bug-free for nearly 14 billion years means that the Bayesian probability that the universe is a computer is extremely close to 0.

]]>Thank you for the pointer, Scott. I’ll need to get into Jordan et al. paper, in order to be able to comment about your observation about “often the better thing to do is to switch to a better-defined nonperturbative formulation”.

Regarding the assumption on the number of interaction vertices being bounded

[…]

In my previous answer, I simply assumed that the number of interaction vertices (in the Feynman diagrams we wanted to sum over) was specified in advance.

[…]

That’s very interesting. The natural question that comes to my mind is “who and how such set of vertices is determined?”. How hard is to “pre-process” the input theory so as to circumscribe the set of potential particle interactions to those where the path integral converges? That makes me think somebody (or something) is playing the part of an extremely powerful – computationally speaking – oracle here.

[…]

If we can’t impose any cutoff on the number of vertices, then there’s an excellent chance that our Feynman integral is divergent, and poorly-defined even at a physics level!

[…]

Indeed, there needs to be some sort of “terminating condition” for the whole thing to make sense. As I understand the physics – and here I might be dead wrong – particles – which are low entropy forms of energy – in a infinite vacuum – and I think that a region of ever expanding space-time can be indeed taken as being infinite for all practical purposes – will be resulting in an overall state with higher entropy, as the result of the interactions tend to end up in stuff which doesn’t interact at all with other particles. So I’d say that there isn’t an explicit cutoff per se: we get to a certain state where further interactions are so improbable that just take amounts of time so big so as not being “interesting” or “useful” any more.

In an experimental setting, it’s quite reasonable to expect that those particles will be interacting eventually with some detector, which for all practical purposes I think is a well-defined “terminal condition”.

That the unbounded “generation” of possible system histories by evolving through possible, valid interactions which conserves energy , can end up in an “inconsistent” state is even more interesting. From a purely logical stand point, consistent theories do indeed allow for “evaluations” which aren’t “true” according to the theory.

This sort of reinforces my intuition that it makes sense to understand the Standard Model (encoded as Feynman Diagram + parameters over a finite state space) as a proof theory of sorts. That by following “valid” steps we end up with a “bad” state, doesn’t seem to me to be a problem in the formulation of the problem, but rather in the computational approach to the problem.

If one takes the space of possible system evolutions to be a directed-acyclic graph, with the edges corresponding to possible sets of particle interactions, the fact that you are able to follow a path ending up in a inconsistent state isn’t “bad news”. Actually, I’d say it’s “good news” as it would imply that the theory (from which you describe states and transitions) isn’t tautological.

I hope this doesn’t sound like pure crackpottery 🙂

]]>‘Time Reborn,’ by Lee Smolin

Comments? Has anyone read it? I’m not sure whether this is serious work or somewhat crackpotish?

]]>——————–

**A Hog under an Oak**

A Hog under a mighty Oak

Had glutted tons of tasty acorns, then, supine,

Napped in its shade; but when awoke,

He, with persistence and the snoot of real swine,

The giant’s roots began to undermine.

“The tree is hurt when they’re exposed.”

A Raven on a branch arose.

“It may dry up and perish — don’t you care?”

”Not in the least!” The Hog raised up its head.

“Why would the prospect make me scared?

The tree is useless; be it dead

Two hundred fifty years, I won’t regret a second.

Nutritious acorns — only that’s what’s reckoned!” —

“Ungrateful pig!” the tree exclaimed with scorn.

“Had you been fit to turn your mug around

You’d have a chance to figure out

Where your beloved fruit is born.”

An ignoramus, likewise, in defiance

Is scolding scientists and science,

And all preprints at lanl_dot_gov,

Oblivious of his partaking fruit thereof.

*I. A. Krylov (1825)*

Translated by **Alexander Givental and Elysee Wilson-Egolf**

——————–

Kudos especially to (UC Berkeley student) Elysee Wilson-Egolf for this apt translation!

]]>