October 12, 2017 at 03:33AM

Today I Learned: 1) It turns out that the whole medieval system of economics, and particularly the thing where YOU DO WHAT YOUR FATHER DID, NO MATTER WHAT, was laregely the result of one Roman emperor. That emperor was Diocletian, and he may have been the worst thing that ever happened to the free market in Europe. Diocletian ruled at the end of the 3rd century, a time when the Roman economy was in a rough spot. Centuries of coin debasement (replacement of valuable metals in coins with mundane metals) and inflation had completely devalued currency, and with it the ability of the Roman government to collect taxes and pay its servants (by which I mean its soldiers). Diocletian sought to fix this problem, and accordingly made a huge set of sweeping changes to the Roman economy. One thing that apparently worried Diocletian pretty badly was the idea that people might (*gasp*) leave an industry(!). After all, pig farming isn't very pleasant. What if all the pig farmers decided to up and move? Or, worse, *change jobs*? Where would the army get its bacon? That wouldn't be acceptable -- the army calculated its consumption of goods and services very carefully, and (partly because of the way Diocletian restructured the Roman tax system) any major supply changes might seriously damage Rome's ability to defend itself. Diocletian's solution was to simply fix everyone's jobs. Diocletian's government quietly, slowly took over all of the guilds of Rome, which had previously been voluntary unions of professionals. Then he removed the voluntary bit of the guilds. Then he mandated, by law, that you couldn't leave a guild, and that membership would be hereditary. Bam. Medieval serfdom achieved. Thanks, Diocletian. Thanks. 2) Zebrafish stripes aren't fixed patterns -- they're dynamic, moving (if slow) waves. If you laser ablate a section of stripes, the nearby stripes will move to fill the gap. 3) One of Alan Turing's many delightful insights was that of the reaction-diffusion network. A reaction-diffusion network is a simple mathematical model of chemicals that can a) react with each other and 2) diffuse around in space. Thus, reaction-diffusion. Anyway, it's a kind of neat simple descriptor of chemistry-in-space, but the *really* cool thing is that many Turing-style reaction-diffusion networks look an awful lot like the patterns of stripes, spots, and shapes found on animals. Just about every animal's skin/coat/shell pattern, from jaguars to giraffes to snails and fish, can be described by a Turing pattern. This is awesome and all, and it suggests a mechanism by which animals get their patterns... but I do have a bit of a fear that we're overfitting. After all, maybe reaction-diffusion networks can just make *any* pattern, including those of an animal. If that's true, then it's not tremendously likely that we've discovered the mechanism of animal pattern formation, any more than discovering how to render pictures with a computer tells us how the stars are arranged the way they are. Today I learned that there *are* some restrictions on what Turing patterns can do! Example: A Turing pattern on a tapering cylinder (say, a tail) can form spots near the base of the tail and stripes at the tip, but it *cannot* do the opposite. That is to say, if cat coat patterns are formed by reaction-diffusion newtorks, then there can be spotted cats with striped tail-tips, but not striped cats with spotted tail-tips. Indeed, there are plenty of examples of spotted cats with striped tails (see cheetahs, ocelots, and to a lesser extent jaguars), but to my knowledge there aren't striped cats with spotted tails (extra kudos to anyone who proves me wrong!). So, that's nice. For details on the cat tail thing and others, see "How the Leopard Gets its Spots" by James Murray. (http://ift.tt/2xAbM94)