I think something like a logarithmic measure on actual time might give the hyperbolic discounting model.
That's true. Let's say we live at time 0; the correct (exponential discounting) value of a payoff of 1 at time t is e-rt. The value of a payoff of 1 at time T under hyperbolic discounting is 1/(1+rT). Setting these equal, we get
Solving for each variable in terms of the other,
So roughly speaking, from looking at the first equation, the discounting that people actually use instinctively is obtained by taking the logarithm of the time T they're discounting over (up to some scaling, which really just sets the units of time), and then applying the correct (exponential) model. This reminds me of a logarithmic timeline, but in reverse. People see the period from, say, 16 to 32 years ago as being as long as the period from 32 to 64 years ago. This is also why I don't believe in a technological singularity even though I'd like to; the arguments often seem to be based on "look! lots has changed in the past hundred years, more than changed in the hundred years before that!" but our memories of "change" are somewhat selective.