You are quite right Geoff. I failed to cover two split seconds of every day.
Let me endeavour to rectify that.
12 am and 12 pm are meaningless points that divide the day. At one second past Noon or 12.00.01 it becomes pm, same as one second past midnight is AM.
Still not very satisfactory...
From google:
Each and every day begins exactly at midnight, and each A.M. begins precisely thereafter. Similarly, each P.M. begins immediately after noon. No meaning can be assigned to 12:00 A.M. (00:00 A.M.), or to 12:00 P.M. (00:00 P.M.). They are merely reference points meant to simplify timetables for us.
From Wikipedia:
The 12-hour clock is a timekeeping convention in which the 24 hours of the day are divided into two periods called ante meridiem (am, Latin for "before noon") and post meridiem (pm, Latin for "after noon"). Each period consists of 12 hours numbered 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. The am period runs from midnight to noon, while the pm period runs from noon to midnight.
The 12-hour clock is especially common in Australia and the United States of America. It is also commonly used, alongside the 24-hour clock, in Canada (except for Quebec, which uses the 24-hour clock), the United Kingdom, some other English-speaking regions, some of the Spanish-speaking regions of South America, Albania and Greece. The Latin abbreviations "A.M." and "P.M." are used in English and Spanish.
According to the actual meaning of the terms ante meridiem (am) and post meridiem (pm), as well as standards bodies such as the National Institute of Standards and Technology in the United States, 12:00 or noon (another word for meridiem) is neither am nor pm, because noon is neither before nor after itself.
Despite this strict logic, it is common practice in the United States to designate noon as 12:00 pm. This has been justified as a convention because the hour from 12:01 pm through 12:59 pm comes immediately afterwards (or post) the meridiem. Following this logic further, midnight is designated as 12:00 am. These conventions nevertheless can be confusing, because the hour immediately following 11:00 am is noon, not midnight.
As a result of the confusion (and technical inaccuracy) of these conventions, it is clearest if one refers to "noon" or "12:00 noon" (rather than to 12:00 pm) if one wishes to express a reference to midday. References to midnight remain problematic because its usage could refer either to the midnight at the start of the day referenced or the midnight at its end. (This problem occurs even if one employs the inaccurate and confusing term 12:00 am). It is therefore best to employ additional context clues to indicate timing in such circumstances.
Some style policies suggest "12:00 n" for noon and "12:00 m" for midnight, but this conflicts with the older tradition of using "12:00 m" for noon (Latin meridies), and "12:00 mn" for midnight (media nox). It also does nothing to correct the ambiguity inherent in references to midnight without additional context clues.
Because of the confusion possible with midnight, some legal contracts start or end at 12:01 am, which removes the uncertainty. Similarly, airplane and train schedules avoid midnight, using 11:59 pm for arrivals and 12:01 am for departures.
The 24-hour clock avoids such ambiguities.
Does this help somewhat? Regardless of my inability to put this across in any meaningful way the convention is that 12am is midnight and 12pm is midday.
Sleep well,