# Justin Li

## Distance Perception

2009-03-16

Last week's question: How often does square root day, and other higher order root days, occur?

Because of the way square root day is done (and written in general culture), there are only nine square root days in each century. This boils down to a square root day on average every 11 years.

I read a blog post with more interesting interpretations of dates.

If dates were written 3-3-09, then one person commented that 3 and -3 are both roots of 9. It is unfortunate that the is a dash before the year - because it should more properly be 3i-3i-09.

A more momentuous day, a commenter suggested, is 2/2/2008, which could be called "cube root day", because 2*2*2 = 2\^3 = 8. But no one ever takes apart the year like that.

My personal favorite is rather than celebrate square root day, we should celebrate exponent day. This occurs whenever the month taken to the power of the date gives the year. While this is a more general holiday, it doesn't occur very frequently either, because the exponential quickly goes above 100. Dates raised to the month power works slightly better.

The list of month\^date=year is below:

• 01/01/01
• 02/01/02
• 03/01/03
• 02/02/04
• 04/01/04
• 05/01/05
• 06/01/06
• 07/01/07
• 02/03/08
• 08/01/08
• 03/02/09
• 03/03/09 [EDIT: clearly I do not know how to do math]
• 09/01/09
• 10/01/10
• 11/01/11
• 12/01/12
• 02/04/16
• 04/02/16
• 05/02/25
• 03/03/27
• 02/05/32
• 06/02/36
• 07/02/49
• 02/06/64
• 04/03/64
• 08/02/64
• 03/04/81
• 09/02/81

This week's question: Why do things appear smaller when they are further away? In what world is this not true?