User blog comment:TheValeyardOfGallifrey/Food for Thought./@comment-4674838-20120329090325

Some food for thought: The furthest day away from today is most certainly not today. If today does not exist, then there is nothing to prove. If today exists, then today can be defined as a day which satisfies exactly 1 of 3 possible conditions: (A)Assumption: An empty timespan is not a "day." Each day consists of a timespan which is at least 1 Planck time, but no more than 24 hours.
 * 1) (A non-empty subset of) the very first 24-hour period of time to occur proceeding the beginning of time (if there is a beginning of time).
 * 2) (A non-empty subset of) The definitively last 24-hour period of time to occur preceding the end of time (if there is an end of time).
 * 3) An exactly 24-hour-long period of time which is preceded by another day ("yesterday") and succeeded by another day ("tomorrow").

(B)Assumption: There are at least 2 days in quantity which exist in the span of all time. If this were not the case, every human being alive would necessarily be 1 day old.

(C)Assumption: There are no gaps in the span of time. Time is a quantity which demonstrates linearity and continuity. If this were not the case, the definition of "day" would not be solid enough to give any meaning to the statement "The farthest day away from today is today."

(D)Definition: The difference in time between 2 days is measured by measuring the difference in time between the beginning of the two days. The unit of measurement is Planck time, tP.

(E)Lemma: According to (A) and (D), the difference in time between two distinct days is at least 1 tP. According to (D), the difference in time between two non-distinct days is exactly 0 tP.

If today is defined under (1), then, per (B) and (C), today is succeeded by tomorrow. Using lemma (E), the difference in time between today and today is 0 tP. The difference in time between today and tomorrow is at least 1 tP. Thus, there exists a day different from today which is further away from today than today.

If today is defined under (2), then, per (B) and (C), today is preceded by yesterday. Using lemma (E), the difference in time between today and today is 0 tP. The difference in time between today and yesterday is at least 1 tP. Thus, there exists a day different from today which is further away from today than today.

If today is defined under (3), then, per (B) and (C), today is preceded by yesterday. Using lemma (E), the difference in time between today and today is 0 tP. The difference in time between today and yesterday is at least 1 tP. Thus, there exists a day different from today which is further away from today than today.

In all cases, there exists a day different from today which is further away from today than today. Therefore, today cannot be the furthest day away from today.