# Scott Garrabrant comments on Asymptotic Logical Uncertainty: The Benford Test

• Char­lie, note that I am talk­ing about the first digit of A(n), not the last digit. The par­ity of A(n) does not mat­ter much. The rea­son pow­ers of 10 are spe­cial is that the A(n) is a power of 10, and must start with a 1.

I per­son­ally be­lieve the as­sump­tion I am mak­ing about S, but if you do not, you can re­place it with some other se­quence that you be­lieve is pseu­do­ran­dom.

• This af­terthought con­fused me. I spent fif­teen min­utes try­ing to figure out why you claim that Ack­er­mann num­bers are all pow­ers of 10 and start with 1. I guess you wanted to write some­thing like: »The rea­son […] is that if n is a power of 10, A(n) must be a power of 10, and start with a 1« Right?

• Oh, whoops! Man­aged to con­fuse my­self. I’m not to­tally sure about Ben­ford’s law, but am happy to as­sume for the sake of ar­gu­ment now that I’m not ac­tu­ally de­luded.

Dou­ble Edit: Hm, the con­verse of the equidis­tri­bu­tion the­o­rem doesn’t hold even close to as strictly as I thought it did. Nev­er­mind me.