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Birthday Bit Boundaries

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My family and I recently celebrated my 63rd birthday. As we were eating dinner that night, one of my sons asked me if I had anything special planned for this upcoming year? I hadn’t given next year much thought, but since 6310 is 1111112, it occurred to me that this was my last birthday for which my age can be represented in six bits, as it will take seven bits (10000002) to represent my age when I turn 64. When I mentioned this, it triggered a surprisingly long and whimsical discussion. (My sons have both graduated with CS degrees and my wife teaches statistics, so…) Some of the points raised during that discussion included:

• We might define a birthday bit boundary as a birthday that requires an additional bit to represent one’s new age. On my next birthday, I will cross a birthday bit boundary when my age changes from 1111112 (63) to 10000002 (64).
• After birthday #64, my next possible birthday bit boundary would be #128. According to the Guinness Book of World Records, the most long-lived person on record was Jean Calment of France, who was 122 when she died in 1997. With no intention of being morbid, barring a medical longevity breakthrough, #64 will almost certainly be the last time I cross a birthday bit boundary.
• Our culture places special emphasis on some birthdays. Often these are multiples of ten (e.g., 30, 40, 50, 60, …), presumably because our culture primarily uses decimal numbers. What birthdays would be deemed special if we used a different number system, such as base 12?
• A few other birthdays also receive special attention, such as #12 in some cultures, or "Sweet Sixteen" in popular U.S. culture.

• My previous birthday bit boundary—#32—is quite close to 30, which is commonly regarded as the threshold-age separating youth from non-youth. (E.g., "Never trust anyone over 30.") Why not use 32 instead of 30 as that threshold?

• Each birthday bit boundary—#2, #4, #8, #16, #32, #64—is reasonably close to a key threshold in one’s life stages. If our culture were based on binary numbers instead of decimal numbers, might we celebrate these birthdays as having special significance?

If we were to celebrate birthday bit boundaries as the entry points to new life stages, the following table shows the result:

 Decimal Age Binary Age Life Stage 0 0 Infant 1 1 2 10 Toddler 3 11 4 100 Child 7 111 8 1000 Adolescent 15 1111 16 10000 Adult 31 11111 32 100000 Middle Age 63 111111 64 1000000 Senior Citizen 127 1111111

In this table, the bit-boundary ages map surprisingly well to the start of significant life-stage transitions. For example, the start of adolescence is often associated with the onset of puberty, which can occur anytime in the age-range 8-14. In many U.S. states, teenagers can get their drivers licenses at 16, marking their transition to adulthood.

Likewise, in the U.S., 60-65 is commonly thought of as the age at which one becomes a senior citizen, and 65 has long been thought of as the typical "retirement" age. However, 65 seems fairly arbitrary; 64 is obviously close by and might be used instead.

As a result of our family discussion, I’ve decided to: (i) declare my next birthday (#64) to be one of extra-special significance, and (ii) hold a special party to celebrate my crossing of this final birthday bit boundary. Assuming, of course, that I am still around.

If you’ve read this far, you may well be thinking that this seems like an especially geeky idea. You may even think this seems like evidence of encroaching elderly eccentricity. This would be difficult to dispute.

However before you render a final judgement, it’s worth noting that there is a well-known Beatles song about reaching old age, and the title of that song is not "When I’m Sixty Five" but rather "When I’m Sixty Four"!

Joel C. Adams is a professor of computer science at Calvin University.

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