Upper and lower bounds

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<p>Upper bounds for theoretical impossibilities, lower bounds for theoretical impossibilities as well, given the model that one uses.</p>

<p>For example, one can use George Miller’s theory of “cognitive bottleneck” of 6 +/- 2 items in working memory at any time + maximum lifespan to derive maximum possible productivity in a lifetime. This upper bound is unusually high, of course. It can be realistically reduced by giving a lower bound estimate of 2 hours of sleep per day (it could be more, but let’s assume that there are drugs in the future that allow one to sleep less).</p>

<p>We can also give upper bound estimates based on the entropy of the universe (since there is only so much usable energy). This assumes that we know enough about the total mass and energy of the universe, which is subject to massive uncertainties of which I have not taken the care to look up yet. </p>

<p>I am thinking of upper bound of time, of course. </p>

<p>Lower bounds are also quite important. </p>

<p>As is probability. Since one has to think of probability of one’s assumptions. Bayesian probability is ideal, since it adjusts itself to new evidence and because we haven’t seen all possible outcomes in the world. </p>

<p>The Internet went down as I typed this and submitted it. Thank you Firefox for preserving the entire message when I hit the back button. I must be mindful that this will not always be the case.</p>

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<p>A corollary to upper bound theory:</p>

<p>John Stuart Mill once mentioned that he was worried that the number of possible music tunes was going to run out soon. He was wrong, of course, as combinatorial rates of increase quickly increase beyond figures like the total number of atoms in the universe. Those figures help set an upper bound on maximum realized creativity. While combinatorial arrangements of a number of numbers also set an upper bound on the amount of potential arrangements of words and tunes, such upper bounds are negligible compared to the upper bound set by (a) the limited energy/resources of the earth and of the universe, which in turn sets a lower bound (b) of the number of humans that the earth can support.</p>

<p>Hence, for all practical purposes, the number of creative arrangements of words is set by an upper bound that is limited by the number of humans on the planet. Hence for all practical purposes, the number of possible arrangements of words/tunes is practically infinite.</p>