This image caught my attention for its place in the Transhumanism article, 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 ${\displaystyle dt}$, but this can also be expressed as ${\displaystyle dy}$ since the "difference in time between events" is also the "time between events", so ${\displaystyle dy=dt}$ which can be solved as (ignoring integration constants) ${\displaystyle y=t}$.

Now the trick is that the author plotted this on a log scale with ${\displaystyle t=0}$ representing the present. This effectively turns the new vertical axis ${\displaystyle z=\log(y)=\log(t)}$, which is a singularity at ${\displaystyle t=0}$. 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) 21:58, 14 December 2008 (UTC)

I don't think the graph is tautological: if t₀ is the "present" (presumably at the time the graph was drawn) then the abscissa at t relates to t-t₀ while the ordinate relates to t_n-t_m where m and n refer to the events in question. The graph does not say "time is time" but rather "as time goes on, successive events in the list occur closer together in time." __Just plain Bill (talk) 16:43, 16 December 2008 (UTC)

Let's concentrate the discussion at Talk:Technological singularity#Removing graph PPTCountdowntoSingularityLinear.jpg. -- Petri Krohn (talk) 17:08, 16 December 2008 (UTC)

OK, I agree. __Just plain Bill (talk) 17:17, 16 December 2008 (UTC)

Just to help our dear Samuel with his mathematical problem: try plotting y = t on the graph. Time to next event would be constant in time, thus giving you a horizontal line. If plotting points with the same "time to next event" per time (say 1 event every 10 years) you would have a greater concentration to the left of the graph. Thank you. 23 March 2009

The problem with this formulation is that it is stating that relatively soon, the time to the next event will be less than a second or less. But a second or less is no pratical time to do anything, less to develop and built new AI technology.

Another problem is that it lacks an evolutionary dimension, a Personal Computer, in evolutionary terms is far less advanced than a human brain, and the human brain as ceased to develop.

Computer technology can evolve faster and faster, but the amount of evolution can also be lesser and lesser.

One can foresee a future where the first artificial conscience fuses his brain trying to explain his own complexity and trying to create a AI entity to his own image... and failing. — Preceding unsigned comment added by 194.65.57.37 (talk) 17:22, 25 August 2011 (UTC)

A rebuttal: most of the estimates for the timing of the singularity place it at some time within the next 60 years. this is, in fact as soon as the graph would have us believe. the problem of dimension is not one to be concerned with. this is a linear regression (more or less) which can be constructed by placing a few points, drawing a line and looking for significant advances. the computer, for instance, was the first case of any thought process being conducted faster than a human brain. As technology evolves at an ever-increasing rate methods of update will also increase. we have seen this with rapid prototyping being one concrete example. Ltnemo2000 (talk) 05:18, 1 October 2013 (UTC)

I'd like to suggest that appearances of this file should be replaced with the version where both axes are logarithmic. It's much clearer because the data points aren't piled up on the present.Warrickball (talk) 13:09, 8 May 2012 (UTC)

The age of the picture is beginning to show. the personal computer is nearing 30 years old and the smart-phone could be easily considered the next point on the regression line. Considerations for the next graph:

-Addition of the Smart-Phone -Conversion to log scale for both axes — Preceding unsigned comment added by Ltnemo2000 (talk • contribs) 05:10, 1 October 2013 (UTC)