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Lentil convexity: Difference between revisions
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So it turns out we haven’t been panic hoarding lentils after all. There is a benign explanation for the sudden disappearance of split peas from the nation’s grocery shelves. | So it turns out we haven’t been panic hoarding lentils after all. There is a benign explanation for the sudden disappearance of split peas from the nation’s grocery shelves. | ||
And it is all to do with when seemingly [[normal distribution]]s reveal themselves not to be normal after all. The elegant symmetry of the bell curve goes to hell | And it is all to do with when seemingly [[normal distribution]]s reveal themselves not to be normal after all. The elegant symmetry of the bell curve goes to hell when you are so many [[standard deviation]]s from the [[mean]], that probability theory tells you the risk of independent events happening this far out is ''as good as zero''. We’re talking about [[fat tails]], [[lazengem]]. | ||
===Lentils in peacetime=== | ===Lentils in peacetime=== | ||
In ordinary times, our lentil-buying habits are regular: hippies and vegans buy a lot of lentils, and everyone else buys none. Okay, ''almost'' none. The [[Reasonable man|person on the Clapham Omnibus]] might have ''one'' tin, at the back of the cupboard, that someone got in a weak moment years ago, just in case of unexpected apocalypse or visit from long-lost, vegan, cousin from Australia. | In ordinary times, our lentil-buying habits are regular: hippies and vegans buy a lot of lentils, and everyone else buys none. Okay, ''almost'' none. The [[Reasonable man|person on the Clapham Omnibus]] might have ''one'' tin, at the back of the cupboard, that someone got in a weak moment years ago, just in case of unexpected apocalypse or visit from long-lost, vegan, cousin from Australia. | ||
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The supermarket management will now intervene, alarmed at this sudden run on lentils. Their immediate reaction will be to impose an item limit. It posts a sign on the shelf restricting customers to 3 tins each. Limiting most customers, who would normally be seen dead buying ''one'' tin, to three, has no effect on the problem, since our lentils-for-judgment-day-only types, would have bought one tin anyway: the problem is not that one or two people are bulk buying, but that all people are single-item buying. The three-items per customer (a) irritates the hippies who would ordinarily buy ten tins anyway, and (b) further validates the suspicion among non-hippies that we are indeed in desperate times. After all, one could hardly ask for a clearer sign of of imminent Armageddon than LENTIL RATIONING — I mean, panic buying hippy food: could it get any worse than that? The 95%, one one, up their demand from one tin to the maximum permissible three. | The supermarket management will now intervene, alarmed at this sudden run on lentils. Their immediate reaction will be to impose an item limit. It posts a sign on the shelf restricting customers to 3 tins each. Limiting most customers, who would normally be seen dead buying ''one'' tin, to three, has no effect on the problem, since our lentils-for-judgment-day-only types, would have bought one tin anyway: the problem is not that one or two people are bulk buying, but that all people are single-item buying. The three-items per customer (a) irritates the hippies who would ordinarily buy ten tins anyway, and (b) further validates the suspicion among non-hippies that we are indeed in desperate times. After all, one could hardly ask for a clearer sign of of imminent Armageddon than LENTIL RATIONING — I mean, panic buying hippy food: could it get any worse than that? The 95%, one one, up their demand from one tin to the maximum permissible three. | ||
Still: no panic hoarding, but the shelf is bare. And those latecomers, discovering it is now ''too late'' to stock up on lentils, head to borlotti beans and Mexican bean fiesta | [[File:Lentil convexity.png|300px|right|thumb|The fat tail of the distribution overlaid. In ordinary times, in the middle of the bell, the distributions look the same, but the tails are different. There is a material chance of demand a long way down the tail]]Still: no panic hoarding, but the shelf is bare. And those latecomers, discovering it is now ''too late'' to stock up on lentils, head to borlotti beans and Mexican bean fiesta. To their horror they discover ''these have been cleaned out as well''. | ||
Every distant fear about a forthcoming final reckoning now confirmed, they stampede for the couscous and quinoa. | |||
===Implications=== | ===Implications=== | ||
[[ | The interconnectedness between human decisions like lentil-buying is not stable. You can’t model it. You can’t predict it. The [[correlation]] ''changes'' on account of the very ''existence'' of each buying decision, and each other people’s reaction to that decision. For the most part, one person’s buying decision won’t affect another’s. The decisions ''look'' for all the world as it they are independent. Near to the mean the chart looks a lot like a bell curve. Hence, for most of the time, the bell curve works well enough. But events which are ''really'' independent ''stay'' independent, however weird things get. The odds of flipping heads on a fair coin stays 0.5 however often you flip it, and whatever the previous results.<ref>Practical point though: the longer your sequence of heads, the greater the probability that the ''coin is not fair''.</ref> This makes the job of modelling independent events much, much easier. In fact it makes it ''possible''. Modelling dependent events isn’t just a case of more complex maths. It isn’t possible. | ||
{{sa}} | {{sa}} | ||