Given any simply consistent formal theory F of the state complexity L(S) of finite binary sequences S as computed by 3-tape-symbol Turing machines, there exists a natural number L(F ) such that L(S) > n is provable in F only if n L(F ). The proof resembles Berry’s..

Taxation policy is driven by many factors, including public opinion, but little research has examined the strength and stability of the public’s taxation preferences. This paper demonstrates one way in which preferences for progressiveness depend on the framing of the question asked. Participants indicated how they would share a fixed tax burden between two individuals who earned different amounts of money, either by adjusting the amount of tax paid by the two individuals, or by adjusting the amount of post-tax income (...) retained. The units in which tax was described — amount of money or percentage tax rate — were manipulated orthogonally. There was a strong metric effect: Participants favored progressiveness more when tax was described as a percentage rather than amount. However, there was also a clear interaction: for amounts, participants favored progressiveness significantly more when considering post-tax money retained rather than tax paid; for percentages, no such effect was found. (shrink)