6264

Identifying patterns in numbers that I come across in daily life, as well as performing mental arithmetic on them — these are continual threads of activity that run in my mind.

For example …

1. 1. I might recognize that a 3-digit or 4-digit number I notice is a 4th power, or
   2. I might split an observed 4-digit number as the sum of 4 squares.

Now the first one involves a simple one-step action— I know the first dozen or so 4th powers, so it’s just a memory lookup.

The second one is a bit more involved.   It involves an assortment of simple steps — lookups, additions, subtractions, etc.  In any case, most of the steps are not automatic, but are executed in a deliberate and consciously-performed manner.

The other day, however, something intriguing happened …

I was returning home from work when I spotted, in a vehicle’s license plate , the number 6264.

The very next instant the number 3968 flashed in my mind.  It was surreal.

I set out to analyze the relationship between the two numbers that led to the second one’s appearance upon noticing the first.

Here’s what I think happened in my mind from the time I spotted 6264 until the next instant when 3968 flashed.

1. 1. 6264 spotted
   2. Split midway into 62 and 64
   3. 62 x 64
   4. (63 – 1) x (63 + 1)
   5. 63² – 1²
   6. 3969 – 1
   7. 3968 flashed

Steps 2 to 6 happened subconsciously.

Perhaps such subconscious computing has occurred in my past, but this was an instance that made me sit up and left me yet again in amazement at how the human brain works.

–nmbrguy!