I am currently attending a conference that is housing everybody in a rather large hotel. When I checked in last night I was given room 3025.
My first thought when I looked at the number was “Ah, this is a perfect square”. So as I carried my bags to the room, I mentally set about working out the square root of my room number.
Being lazy, I did this the easiest way I could think of: I multiplied by four to find a number with zeros at the end. This gave me 12100. Which is clearly 121 × 100, or 112 × 102, or 1102.
Having multiplied by four to get the square of 110, I now needed to divide 110 by two. So by the time I arrived at my room, I knew that the square root of 3025 is 55.
But how did I know, in that first moment at the registration desk, that 3025 is a perfect square?
I remember that I had immediately been struck by seeing “30” followed by “25”. This suggests that I may have subconsciously recognized the visual pattern 2500 + 500 + 25 as an instance of (a2)100 + (2a)10 + a2, or (10a + a)2.
If this is true, it would mean that my conscious and subconscious minds had gone in completely different directions. And it would also mean that my subconscious mind had been a whole lot quicker than my conscious mind.
Alas, if only my conscious mind could be as quick as my subconscious mind.