Why no one is exponentially smarter than others

One common counterargument to why universality trumps IQ (which was often misunderstood and misinterpreted) is that “some people are exponentially smarter than others.” Right off the bat, it is not even clear what this statement is supposed to mean. We suspect that it is deliberately vague. In any case, it has one of two meanings, the former of which is more popular, but the latter of which is much more likely.

The first meaning is that some people can somehow do exponentially more work than others. Is it possible? Yes. Is it plausible? Let’s look at this through the lens of computation. One of our working hypotheses is that everything in Nature — including human thinking — can be viewed as computations . Figure 1 illustrates the difference between two people who do significantly different amounts of work in the same amount of time.

Figure 1 : The difference between deterministic versus nondeterministic computers. Deterministic computers can take one action at a time given some input, with no access to randomness, whereas nondeterministic computers can take different actions all at once.

To restate the first meaning, the claim is that “muggles” do m^k or polynomial amount of work in m time steps, whereas “geniuses” do c^m or exponential amount of work in the same amount of time (where k is any positive integer, and c is a constant greater than or equal to 2). Some readers would have noticed that there is a connection to the million-dollar P vs NP problem, which is as follows.