[Retric]

This is filled with a lot of hand waving bad math, which distracts from some reasonable points.

rule of 70tells us that the time it will take a system or collection to double in size is 70 divided by thepercentage growth rate. The time units depend on how the time over which percentage growthis expressed—like 2%per dayor 2%per year, for instance. The rule works most accurately forsmaller growth rates, under 10%.

Actually showing 1.10^7 = 1.949 vs 1.01^70 = 2.007, so you can approximate by dividing percentage by 70 between 1% and 10% is fine. Stating it as true in the text then adding a note well no not actually latter on is problematic.

[zaphod4prez]

Sorry if I’m missing something, but… what’s the problem with that quote? That’s a widely-used heuristic that helps to estimate doubling times without using a calculator (see [the Wikipedia entry](https://en.m.wikipedia.org/wiki/Rule_of_72).

He does walk the reader through a lot of “back of the napkin” math, in order to help the reader get an intuitive sense of the models he’s using. But my impression overall is that he backs those hand-wavey calculations up with more serious calculations throughout the book.

[Retric]

The issue is he then uses the approximations to do with math without calling them approximations. 1.10^7 is reasonably close to 2, but 1.1^21 is 7.4 which is a fair distance from 8.

He goes so far as asks someone to do the approximation across several hundred years of compounding. And sure it get’s a big number but one no even close to accurate.

[Loanor]

You do realize the rule of 70 is used to approximate continuous compounding not periodic compounding right?

[Retric]

There are a bunch of them though compounding normally uses the rule of 69 / 69.3, or rule 72. https://en.wikipedia.org/wiki/Rule_of_72

[Loanor]

The rule of 70 isn't "hand waving bad math".. perhaps you just don't understand its derivation?