## Comment The most important thing... (Score 1) 842

Don't be afraid to say "I don't know."

Corollary: If you don't know, make **sure** you say "I don't know."

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Don't be afraid to say "I don't know."

Corollary: If you don't know, make **sure** you say "I don't know."

*sigh*

You understand neither how the parent post is using the word "linear" nor the PageRank algorithm itself. You*can* rewrite the eigenproblem at the heart of PageRank as the solution to a linear system, but very few people do. Moreover, this is not the correct intuition to employ to understand what's going on: there are no "massive matrix inversions" here, just a simple iterative algorithm for extracting the dominant eigenvector of a matrix.

Furthermore, you've got it exactly backwards regarding the "connection" between PageRank and light transfer. Since the Markov process used to model a web surfer in the PageRank paper is operating on a discrete domain with an easily-calculable transition function, the stationary distribution (or ranking) can be determined*exactly*. In rendering, you have a continuous problem for which Markov chain Monte Carlo techniques provide one of the most efficient ways to approximate the solution...but you have to actually *simulate* a Markov chain to get it (see, for instance, Veach's seminal paper on Metropolis Light Transport). Computing PageRank is an "easy" problem, by comparison.

You understand neither how the parent post is using the word "linear" nor the PageRank algorithm itself. You

Furthermore, you've got it exactly backwards regarding the "connection" between PageRank and light transfer. Since the Markov process used to model a web surfer in the PageRank paper is operating on a discrete domain with an easily-calculable transition function, the stationary distribution (or ranking) can be determined

Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing had happened. -- Winston Churchill