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Lentil convexity: Difference between revisions
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{{A| | {{A|devil|{{image|Lentils|jpg|Out of my cold dead hands.}}}}''Author’s note. I mean no slight on people who buy tinned lentils. Personally, I quite like them.'' | ||
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. | ||
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National weekly lentil purchases therefore usually cleave to a [[normal distribution]]. A small part of the population (say 0.5% — the hippies) may buy 8, 9 or 10 tins. A slightly bigger section (say 4.5% — vegans, health-food fanatics etc.) may buy one or two, and the remaining 95% will buy very few (let’s say on average 0.1 tin each: one tin between ten, which is probably generous). Since these lentil buyers’ decisions are ''independent'' events<ref>BUT ARE THEY? I don’t want to spoil the punchline but HOLD THAT THOUGHT.</ref> weekly overall tin purchases will fluctuate but overall the random variations within individuals will tend to even out the total. In the same week that your hippie stocks up for his bom shankar summer solstice druid’s convention cauldron ''partay'', a vegan might skip a tin, and your 95% who hardly ever buy lentils make little difference to the acquisition rate in any weather. | National weekly lentil purchases therefore usually cleave to a [[normal distribution]]. A small part of the population (say 0.5% — the hippies) may buy 8, 9 or 10 tins. A slightly bigger section (say 4.5% — vegans, health-food fanatics etc.) may buy one or two, and the remaining 95% will buy very few (let’s say on average 0.1 tin each: one tin between ten, which is probably generous). Since these lentil buyers’ decisions are ''independent'' events<ref>BUT ARE THEY? I don’t want to spoil the punchline but HOLD THAT THOUGHT.</ref> weekly overall tin purchases will fluctuate but overall the random variations within individuals will tend to even out the total. In the same week that your hippie stocks up for his bom shankar summer solstice druid’s convention cauldron ''partay'', a vegan might skip a tin, and your 95% who hardly ever buy lentils make little difference to the acquisition rate in any weather. | ||
[[File:Lentil distribution.png|300px|left|Lentil buying projections in peacetime yesterday. The average per 100 people is 15, and any more than 28 is genuinely unthinkable.|thumb]]The odds of ''everyone'', including the normals, ''all'' going large on lentils ''in the same week'' is extremely low.<ref>With genuinely unconnected events the probabilities quickly fade into cosmic radiation: the odds of tossing heads just 100 times in a row with a fair coin is one in ''half a googol''. You wouldn’t expect that to happen in ''several lives of the universe''.</ref> The consequence, across the community, is a [[normal distribution]] of weekly lentil acquisition. The random variation in purchases by people in the different demographic groups will cause a small fluctuation in in demand for lentils from week to week, but from a | [[File:Lentil distribution.png|300px|left|Lentil buying projections in peacetime yesterday. The average per 100 people is 15, and any more than 28 is genuinely unthinkable.|thumb]]The odds of ''everyone'', including the normals, ''all'' going large on lentils ''in the same week'' is extremely low.<ref>With genuinely unconnected events the probabilities quickly fade into cosmic radiation: the odds of tossing heads just 100 times in a row with a fair coin is one in ''half a googol''. You wouldn’t expect that to happen in ''several lives of the universe''.</ref> The consequence, across the community, is a [[normal distribution]] of weekly lentil acquisition. The random variation in purchases by people in the different demographic groups will cause a small fluctuation in in demand for lentils from week to week, but from a grocers’<ref>DID YOU SEE WHAT I DID THERE?</ref> perspective, the demand curve is predictable and manageable. | ||
===Lentil buying decisions are ''not'' independent=== | ===Lentil buying decisions are ''not'' independent=== | ||
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The point? Modelling normal distributions of independent events is easy, and safe. Modelling distributions of interconnected events isn’t. It isn’t just a case of more complex maths. It isn’t ''possible''. Now, mis-modelling overall lentil demand is a relatively low-stakes game: liable to annoy peaceniks — who are by nature unlikely to foment insurrection, and annoying them is kind of amusing anyway — plus, realistically (unless it ''is'' Armageddon, in which case lentil shortage is not the problem) actual consumption of lentils won’t change, so the supply-shortage will quickly sort itself out. | The point? Modelling normal distributions of independent events is easy, and safe. Modelling distributions of interconnected events isn’t. It isn’t just a case of more complex maths. It isn’t ''possible''. Now, mis-modelling overall lentil demand is a relatively low-stakes game: liable to annoy peaceniks — who are by nature unlikely to foment insurrection, and annoying them is kind of amusing anyway — plus, realistically (unless it ''is'' Armageddon, in which case lentil shortage is not the problem) actual consumption of lentils won’t change, so the supply-shortage will quickly sort itself out. | ||
So a spot of [[convexity]] might not matter for the | So a spot of [[convexity]] might not matter for the world’s lentil purveyors — but how about those in the multi-billion dollar global transport and hospitality industries? What would ''they'' do if everyone, all around the world, without warning — you know, ''billions'' of people — as one, ''indefinitely'', stayed indoors? | ||
Like ''that'' would ever happen. | Like ''that'' would ever happen. | ||
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{{ref}} | {{ref}} | ||
{{Technical Tuesday|26/1/21}} | |||