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No. 2840: Supertaskfield

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Supertaskfield

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Strip by: Levellass

Garfield: I'm going to supertask around the block.
{Garfield walks halfway around the block}
{Garfield walks half the remaining distance in half the time, now being three quarters of the way around the block}
{Garfield walks half the remaining distance in half the time, now being seven eighths of the way around the block}
{Garfield walks half the remaining distance in half the time, now being fifteen sixteenths of the way around the block}
...
..
.
{In the final panel Garfield completes his walk around the block}
Garfield: In a finite amount of time!

The author writes:

A supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. The classic example of this is Achilles and the tortoise. Suppose that Achilles is a fast runner, and moves at a speed of 1 m/s. Achilles chases a tortoise that moves at 0.1 m/s. However, the tortoise starts 0.9 metres ahead. Common sense seems to decree that Achilles will catch up with the tortoise after exactly 1 second, but it can be argued that this is not the case. Achilles must inevitably come up to the point where the tortoise has started from, but by the time he has accomplished this, the tortoise will already have moved on to another point. This continues, and every time Achilles reaches the mark where the tortoise was, the tortoise will have reached a new point that Achilles will have to catch up with; while it begins with 0.9 metres, it becomes an additional 0.09 metres, then 0.009 metres, and so on, infinitely. While these distances will grow very small, they will remain finite, while Achilles' chasing of the tortoise will become an supertask.

Given however that each 'catch up' requires a tenth of the time of the previous step, the total amount of time taken to complete this task, even if infinitely many steps are taken, cannot exceed 0.9 + 0.09 + 0.009.... or 0.9999.... seconds. In this submission we see Garfield undertaking a similar task, though possibly at a far lower rate of speed. To fit infinite panels into a finite space each panel has been geometrically reduced in size from that previous. By utilizing an ingenious MS Paint feature known as 'Because I said so', I was able to place each panel in a shorter time than the previous, making this strip contain infinite detail. Sadly due to the limits of most monitors most viewers of this strip will be unable to see past the first half dozen iterations.

It should finally be noted that should Garfield, in true Garfieldian tradition, stop to nap or dine after each step, then the task will take an infinite amount of time and also require an infinite amount of catnaps/pans of lasagna to complete.

Original strip: 2016-07-25.

Original Square Root of Minus Garfield: 2016-10-14.