Author’s note — Coming to work this Tuesday, I found the following in my mailbox from Monday. The work is mine; the content, I fear, is the result of a Monday rashly started, with no heed given to proper plus-minus stretching before trying to engage serious mathematical issues.
NOVEL APPLICATION OF A TIME-COUNTING THE KARTOFFEL-CAUCHY-BUNYAKOVSKY MEASURE
(submitted to Utt. Bull.)
I have heard that this kind of a device is used to measure seconds:
“One potato, two potato, three potato” (etc. etc.),
the logic being that the addition of the word “potato” pads the number-repetition to approximately one second in duration, like this:
(t=0 s) “One potato” (t=1 s) “two potato” (t=2 s) “three potato” (t=3 s; etc. etc.).
I have heard this is an easy way to count time, and that any fool (i.e. a “standard person”) can do it.
The word “one” is clearly shorter when said (i.e. its common saying-out-loud measure is less) than the word (and measure of) “two thousand seven hundred and ninety-eight”. For the Potato Method (PM) to work as described above, the enunciation of the word “potato” needs to be commensurably briefer.
However, it is well know that for any length of time, we can find a number whose enunciation takes, for a standard person, approximately that length of time. (To an error of less than epsilon for the average over a set of sufficient size, obviously; also see note one.)
Thus we can assume a number such that it cannot (by any standard person) be said in an amount of time less than one second. When that number is reached using PM, the standard person needs to pronounce the word “potato” in the remaining time, which is, zero point zero, zero repeating, seconds or less.
Worse still, we can take a number such that its pronunciation takes two seconds (to an epsilon); and our standard person is then required to pronounce “potato” in minus one second, i.e. to cause the reversal of time’s arrow solely by the enunciation of three common syllables.
Since I am assured by good practical sources, who never expected to be involved in the creation of a mathematical paper, that the PM is usable by all standard people, I thencefore have proven the existence of time travel.
Applications to follow in a later article. Referees, get cracking like you got this yesterday! Potato potato potato!
yrs obdnt srvnt,
LORD OF TIME
potato potato potato
Note one: The existence of numbers of arbitrarily long enunciation
Due to the fact that the enunciation of numbers uses the decimal system, this follows from the well-known nine-filling principle, i.e. that numbers of the form require instances of the number 9, and thence the word “nine”, to be expressed.
Ex. Let . Then , and , pronounced “nine hundred ninety-nine“, emphasis mine. Note the three repetitions of the word “nine”.
If the enunciation of the word “nine” takes seconds, then we achieve a number of enunciation-length seconds if , that is, no later than at the number