Ok Go - This Too Shall Pass - Rube Goldberg Machine version
Il video gira pure su facebook da qualche giorno. Io l’ho visto da un’amico che aveva letto un buzz di Terry Tao, un tizio che ha vinto la medaglia Fields nel 2006. Il buzz dice così:
Suppose one needs to accomplish n tasks. These tasks can be done in any order, but each require a unit of time to perform. Also, each task i has an independent failure probability p_i, and if any one of the tasks fail, one has to immediately start over and do all the tasks again. What is the optimal strategy to minimise the amount of time required to accomplish all n tasks?
It is intuitively plausible (and a good exercise to rigorously show) that the optimal strategy is to arrange the tasks in decreasing order of failure, i.e. to do the most risky task first. This is a typical example of a rearrangement inequality , of which Chebyshev’s sum inequality is perhaps the most well-known.
This inequality was used when creating the following Rube Goldberg video below (which required 60 takes over 2 days - but most takes failed after just 30 seconds).Se vi andate a leggere l’originale trovate altri commenti interessanti. Questa è la principale differenza tra un matematico (più in generale, uno scienziato) e uno che non lo è. Uno dice “Wow, ma come funziona?”, l’altro solo “Wow!”. Poi ci sono gli estremi, cioè quelli che riescono a darsi delle risposte corrette, e purtroppo anche quelli che neanche il “Wow!”
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