File talk:PPTCanonicalMilestones.jpg

This image is mathematically trivial, therefore cannot illustrate a "technological singularity" or anything of significance

This image caught my attention as part of a series of graphs shown in various Transhumanism articles, namely for its axes titles. On the vertical axis is "time to next event" and the horizontal is "time to present". As a physicist, plotting two of the same variables against each other is a clear indication that something has gone wrong, and without suitable analysis can indicate that the graph could literally express any relationship one wants. This seems to be the case here.

It doesn't matter how we define an "event", or how far apart we space them in history. Given this assumption, the time between events can be expressed as $dt$, but this can also be expressed as $dy$ since the "difference in time between events" is also the "time between events", so $dy=dt$ which can be solved as (ignoring integration constants) $y=t$.

Now the trick is that the author plotted this on a log scale with $t=0$ representing the present. This effectively turns the new vertical axis $z=\log(y)=\log(t)$, which is a singularity at $t=0$. Therefore, if we plotted the graph simply linearly, it would be a trivially-obvious linear graph where the time between events becomes 0 at present. This graph therefore proves nothing except that the "time between events" is equal to the time between events.

I ask, given this information, that this graph be removed from all articles unless used as an example of triviality. SamuelRiv (talk) 20:18, 15 December 2008 (UTC)