the blogger's paradox

Recovering nicely from the flu, still have time read more from the Notebooks, this entry on the Hungarian mathematician, Kurt Gödel.

I could not help but be taken back to my school-days where I spent many a pleasant hour reading, Gödel, Escher, Bach.  One of the fruits of that dalliance lead me to Tristram Shanty, and his awful paradox as espoused by Bertrand Russell, which seems more topical the older it gets:

"The retention of this axiom leads to absolute contradictions, while its rejection leads only to oddities. Some of these oddities, it must be confessed, are very odd. One of them, which I call the paradox of Tristram Shandy, is the converse of the Achilles, and shows that the tortoise, if you give him time, will go just as far as Achilles. Tristram Shandy, as we know, employed two years in chronicling the first two days of his life, and lamented that, at this rate, material would accumulate faster than he could deal with it, so that, as years went by, he would be farther and farther from the end of his history.

Now I maintain that, if he had lived for ever, and had not wearied of his task, then, even if his life had continued as eventfully as it began, no part of his biography would have remained unwritten. For consider: the hundredth day will be described in the hundredth year, the thousandth in the thousandth year, and so on. Whatever day we may choose as so far on that he cannot hope to reach it, that day will be described in the corresponding year. Thus any day that may be mentioned will be written up sooner or later, and therefore no part of the biography will remain permanently unwritten. This paradoxical but perfectly true proposition depends upon the fact that the number of days in all time is no greater than the number of years."

 

Tristram Shanty project