Richard,
I know it's peripheral to your main argument, but in this example ...
Suppose that the computational effort that evolution needs to build
"different sized" language understanding mechanisms scales as:
2.5 * (N/7 + 1)^^6 planet-years
... where "different sized" is captured by the value N, which is the
number of conceptual primitives used in the language understanding
mechanism, and a "planet-year" is one planet worth of human DNA randomly
working on the problem for one year. (I am plucking this out of the
air, of course, but that doesn't matter.)
Here are the resource requirements for this polynomial resource function:
N R
1 2.23E+000
7 6.40E+001
10 2.05E+002
50 2.92E+005
100 1.28E+007
300 7.12E+009
(N = Number of conceptual primitives)
(R = resource requirement in planet-years)
I am assuming that the appropriate measure of size of problem is number
of conceptual primitives that are involved in the language understanding
mechanism (a measure picked at random, and as far as I can see, as
likely a measure as any, but if you think something else should be the
N, be my guest).
If there were 300 conceptual primitives in the human LUM, resource
requirement would be 7 billion planet-years. That would be bad.
But if there are only 7 conceptual primitives, it would take 64 years.
Pathetically small and of no consequence.
The function is polynomial, so in a sense you could say this is an
NP-hard problem.
I don't think you're using the term "NP-hard" correctly.
http://en.wikipedia.org/wiki/Complexity_classes_P_and_NP
"
The class P consists of all those decision problems that can be solved
on a deterministic sequential machine in an amount of time that is
polynomial in the size of the input; the class NP consists of all
those decision problems whose positive solutions can be **verified**
in polynomial time given the right information.
"
[This page also reviews, and agrees with, many of your complaints
regarding the intuitive interpretation of P as easy and NP as hard]
http://en.wikipedia.org/wiki/NP-hard
"
In computational complexity theory, NP-hard (Non-deterministic
Polynomial-time hard) refers to the class of decision problems H such
that for every decision problem L in NP there exists a polynomial-time
many-one reduction to H, written . If H itself is in NP, then H is
called NP-complete.
"
-- Ben G
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