A small mistake in Numberphile’s videos about Graham’s number

[ not about math with my kids, but about some cool Numberphile videos that came out yesterday, and sorry this one was a little rushed]

Yesterday (July 20, 2014) I saw two absolutely incredible Numberphile videos about Graham’s number.  Part of what makes them so amazing is that the explanation of the number comes from Graham himself!   I love Numberphile’s work in bringing math to the masses.

There is, unfortunately, a little mistake in the text overlay in one of the videos that I wanted to point out.  The somewhat humorous result of this mistake is that Graham’s number is actually larger – vastly larger, in fact – than what the video indicates.

Since the formatting a blog post with the arrow notation and power towers was going to take more time than I had this morning, I decided to just go to the whiteboard. The mistake, which I explain in the first video below, is easy to make since all of the numbers are so large.  It involves confusing the number 3 ↑↑↑ 3 with 3^3^3^3.

After my video are the links to new Numberphile videos (that you might want to watch first if you aren’t familiar with Graham’s number) and two a few other fun Graham number articles, including a Family Math project about Graham’s number I did with my kids last year (which is the only reason I noticed the mistake in the new Numberphile videos).

Here are the new Numberphile videos (the text overlay error is in the 2nd video):

and here’s Evelyn Lamb’s piece on Graham’s number for Scientific American:


Finally, here’s our old Family Math project on Graham’s number, which is a really fun project to work through with kids: