My wife is an author with an MFA in Creative Writing, and advanced degrees in math, who has published both fiction and math textbooks, so I vicariously know a lot about publishing. The potential problem that exists with your otherwise reasonable plan is that many (all?) publishers will balk at pre published material. You're talking about material that's here, in ebooks, and on lulu, before it ever passes over the publisher's desk -- that could be a big problem, you need to look into it.
There's a common literary technique used in most storytelling in which the author writes alternating "up" and "down" scenes -- it provides pacing and context; it also allows us time to digest the "up" scenes.
It seems to me that the technique is appropriate here -- it might be worth making a goal for yourself to write a mathy post, then to follow up with a post on the same topic but without any math in it at all, except maybe references to the previous post. That would be an interesting exercise for you, I think. It's supposed to accessible work -- how accessible can you make it? Can you write about these mathy topics without numbers?
I don't know, but if you never try to do impossible things...
"You can't judge the usefulness of a definition without specifying what you want it to be useful for."
This was going to be my point:
"Once upon a time it was thought that the word "fish" included dolphins. Now you could play the oh-so-clever arguer, and say, "The list: {Salmon, guppies, sharks, dolphins, trout} is just a list - you can't say that a list is wrong. I can prove in set theory that this list exists. So my definition of fish, which is simply this extensional list, cannot possibly be 'wrong' as you claim."
Or you could stop playing nitwit games and admit that dolphins don't belong on the fish list."
I totally see your point, but I think it's worth exploring why the "nitwit" set is plausible, and why you feel the best defense against a cheeky definition is is an ad hom.
In this instance, I think the answer is that you're drawing the boundary line for one reason, and they are being twitty and drawing the boundary line arbitrarily just because they think the rules of logic allow them to do so with impunity (ad hom away).
However, I can think of a legitimate reason to draw the boundary in the nitwit way: what if I want a label whose members are all creatures that live in water and use fins to propel themselves? That's a legitimate category, but it certainly isn't a boundary appropriate for the word "fish," which has taxonomical implications, as well as physiological implications more complex than "has fins."
It may be worth pointing out to the nitwit that he's drawn a logically valid boundary, but it's not the territory you're talking about. Allow him his Fishoids, but steer the conversation back to creatures who have gills and lay eggs. Ideally you can get away with convincing the nitwit to re label HIS category so you can use the real fish label to avoid confusion, but in the interests of continuing a productive conversation, you might consider relabeling the boundary you mean to something neutral ("Gill Creatures"), that your opponent won't be so comfortable changing arbitrarily.
Cal, the whole point of the post is to introduce the idea of the prototype model versus Aristotelian model of cognition. The stated purpose of the blog is to be at least 50% accessible to the public, and the posts are headed toward amalgamation into a popular book, not a technical book. The point wasn't to rigorously support or defend the prototype model as such -- I would imagine that that has been done in many other places (maybe Eli could post some sources for your research). The point here was to expose it to a larger audience.
In the light of the larger audience, the bird prototype doesn't have to be defined with any particular level of technical accuracy -- robins versus ducks is true a priori; it's accessible to an average reader. It would hurt the overall work to beat that horse, because it's not aimed at a professional, it's not a dissertation, it's an explanation aimed at the lowest common denominator.
My point is that you're missing the point here, Cal. Rip apart falsity here, by all means, but don't think you're the only reader who realizes that it's perfectly plausible that a robin could spread a disease to a duck but not visa versa -- I realize that, and I bet most of the people who read the post also realized that, but it's ridiculous to think that a statistically significant proportion of the population, randomly selected to answer a question like that, would have any knowledge of the specific disease pathways between robins and ducks that would skew the results in any given way. Even if by some magical coincidence, enough people even realized there COULD be different pathways, there is no reason to expect that knowledge to skew the results toward one bird over another, without further explanation. Clearly there is a bias at work. If you don't think the evidence points toward the bias Eli was talking about, then explain why and offer a different hypothesis.
You keep saying we're blind to the errors and biases written here, but I think you don't realize that everyone sees most of what you post, but we choose not to post it, because we don't want to be pedantic. We're trying to digest the meat of the information, and we understand who the intended audience is.
Lee, you're confusing the map with the territory, to borrow Eli's phrasing. Percentages are just a convenient way to label the ratio, or difference, between values, but they are not precisely the difference, just an arbitrary representation.
They can moderate comments, but Cal occasionally makes a (cantankerously phrased) good point, so I doubt that they will.
I wish, but I'm not in the Bay Area until the summer probably. Maybe next time!
This is interesting. When I read the first post in this series about Allais, I thought it was a bit dense compared to other writing on OB. It occurred to me that you had violated your own rule of aiming very, very low in explaining things.
As it turns out, that post has generated two more posts of re-explanation, and a fair bit of controversy.
When you write that book of yours, you might want to treat these posts as a first draft, and go back to your normal policy of simple explanations 8)
Ian, your God argument doesn't follow:
1) Objects behave in certain, predictable ways 2) God can make objects behave arbitrarily 4) No objects behave arbitrarily 5) There is no God
Hidden argumentation:
3) Therefore, God WILL make things behave arbitrarily
You can't assume that an omnipotent God will behave in any particular way.
I'm guessing that merely having written similar material will not stop you from publishing, but it seems like a grey area and I am not an expert. I'd ask an agent or a publisher directly about the whole situation, and I'd do it sooner rather than later, because I'd hate to see any effort wasted.