Saturday, 13 May 2023

The March of Time

I've written about what I term AD and BC numbers in a post titled, quite sensibly, AD and BC Numbers. I was reminded of them because my diurnal age today, 27068, converts to 69BC in hexadecimal. For some time now, these BC numbers have been occurring every 256 days.

24764 --> 60bc

25020 --> 61bc

25276 --> 62bc

25532 --> 63bc

25788 --> 64bc

26044 --> 65bc

26300 --> 66bc

26556 --> 67bc

26812 --> 68bc

27068 --> 69bc

However, this regular march of time is now at an end because if 256 is added to 27068, the resultant number (27324) is 6ABC. The decimal equivalent of 70AD is 28845, representing a jump of 1792 or 7 x 256 days.


Similarly, I recently turned 27053 days old which is 69AD in hexadecimal. Notice the difference of 14 days between 69AD and 69BC. This number was also the end of a run of numbers differing by 256 days.
 

24749 --> 60ad


25005 --> 61ad


25261 --> 62ad


25517 --> 63ad


25773 --> 64ad


26029 --> 65ad


26285 --> 66ad


26541 --> 67ad


26797 --> 68ad


27053 --> 69ad


The decimal equivalent of 70AD is 28845, again a jump of 1792 or 7 x 256 days. Taken over a long enough time period, this represents an average advance of a little over 395.6 days, about a month longer than the solar year. Both AD and BC dates are advancing at this average rate.


However, it will almost five years before I encounter another hexadecimal AD and BC number so I thought it important to mark the fact in this post. While exercises like this may seem frivolous, they nonetheless provide an opportunity to work with hexadecimal numbers and convert from decimal to hexadecimal and vice versa. I'm always thinking in terms of the former mathematics teacher who I once was.


How can hexadecimal numbers be made interesting for students? These AD and BC numbers are a way of doing this. The question could be asked of students:

Find out your diurnal age and determine when you will next have a connection to AD or BC year (via decimal to hexadecimal conversion). What was significant about that year.

See my post titled 69BC for details on what was significant about this year in history. Students could be shown how to determine their diurnal age using Wolfram Alpha and they could also use it to convert between decimal and hexadecimal. Overall, a useful and interesting exercise.

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