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I don’t really understand what the post is trying to say or whom it is targeted at. But maybe that’s because I only skimmed it. It feels like a big brain dump o

I don’t really understand what the post is trying to say or whom it is targeted at. But maybe that’s because I only skimmed it. It feels like a big brain dump of random notes rather than anything cohesive or particularly complete. I found the frequent self-quotes odd and the self-congratulatory introduction more odd. An example of the lack of target audience would be the section “what are graphs?” It starts with a paragraph which seems to be for someone who has never heard of graphs (yet it doesn’t actually define what a graph is, but maybe that’s because there’s so much variety in what different things may be graphs). It also calls graphs “data structures” which I don’t think I would agree with. It’s then followed by a big list of links and then a paragraph referencing Kotlin∇ and talking about trees and such even though the previous paragraph seems to be for someone who doesn’t know what a graph is. I found other sections weird. E.g. the author seems to think that it is important to treat a matrix as a function between vector spaces but somehow misses the main point (this function must be linear and the numbers in a matrix are in some sense unimportant because they are relative to some basis). Then there’s a section about raising matrices to a power except when you look at it you realise it’s actually a product of different matrices and actually the topic just changed halfway through the paragraph. The “matrix multiplications” in the section on data flow graphs don’t make sense to me, even with the random extra rules given above (the third entry in S' the second row should be 5, but this causes the next row to not have the idempotence property the author wants). It also seems to be confusing matrices with manipulating random numbers in a grid. I don’t want to be overly negative. There’s probably some good stuff in here but at the moment it just appears to be a dump of the author’s notes and thoughts.

brzozowski 6y ago
Hi Dan, thanks for taking the time to read this and leave your feedback. I'll try to address your remarks one-by-one. > I found the frequent self-quotes odd and the self-congratulatory introduction more odd. Thank you for the candid feedback! I have reflected a bit about this and where it comes from. It detracts from the main theme, which I regret, but also gives the reader context. Like many, I have flaws and ego is one of them. I try to be upfront about this, so the reader can bail early. > It starts with a paragraph which seems to be for someone who has never heard of graphs. This is a good point. I did not think very carefully about the audience. It is mostly, as you mention, a brain dump. At the same time, I am trying to explain some ideas which may be familiar to you, but others are encountering for the first time. I agree, this could be clearer what parts are for what audience. > this function must be linear and the numbers in a matrix are in some sense unimportant because they are relative to some basis Not attempting to be mathematically rigorous, but I think you raise an important point here, and I will try to clarify this point more carefully. Linearity can be a constraint in real vector spaces, but is less of a problem in Boolean algebra. The goal here is just to show how matrices can represent a function between vector spaces. > Then there’s a section about raising matrices to a power except when you look at it you realise it’s actually a product of different matrices. Not sure I follow, can you be more specific? I will try to clear this up. > The “matrix multiplications” in the section on data flow graphs don’t make sense to me, even with the random extra rules given above. Completely agree, this algorithm needs to be made more explicit, because it is a poorly written example. The full example can be found in Miller (1987). https://www.cs.cmu.edu/~glmiller/Publications/MRK86b.pdf https://www.cs.cmu.edu/~glmiller/Publications/MRK86b.pdf > I don’t want to be overly negative. Not at all! Again, thanks so much your comments. I would be happy to discuss them further here or by email.

brzozowski 6y ago

Hi Dan, thanks for taking the time to read this and leave your feedback. I'll try to address your remarks one-by-one. > I found the frequent self-quotes odd and the self-congratulatory introduction more odd. Thank you for the candid feedback! I have reflected a bit about this and where it comes from. It detracts from the main theme, which I regret, but also gives the reader context. Like many, I have flaws and ego is one of them. I try to be upfront about this, so the reader can bail early. > It starts with a paragraph which seems to be for someone who has never heard of graphs. This is a good point. I did not think very carefully about the audience. It is mostly, as you mention, a brain dump. At the same time, I am trying to explain some ideas which may be familiar to you, but others are encountering for the first time. I agree, this could be clearer what parts are for what audience. > this function must be linear and the numbers in a matrix are in some sense unimportant because they are relative to some basis Not attempting to be mathematically rigorous, but I think you raise an important point here, and I will try to clarify this point more carefully. Linearity can be a constraint in real vector spaces, but is less of a problem in Boolean algebra. The goal here is just to show how matrices can represent a function between vector spaces. > Then there’s a section about raising matrices to a power except when you look at it you realise it’s actually a product of different matrices. Not sure I follow, can you be more specific? I will try to clear this up. > The “matrix multiplications” in the section on data flow graphs don’t make sense to me, even with the random extra rules given above. Completely agree, this algorithm needs to be made more explicit, because it is a poorly written example. The full example can be found in Miller (1987). https://www.cs.cmu.edu/~glmiller/Publications/MRK86b.pdf https://www.cs.cmu.edu/~glmiller/Publications/MRK86b.pdf > I don’t want to be overly negative. Not at all! Again, thanks so much your comments. I would be happy to discuss them further here or by email.