[ExI] Scales of comparision

Anders Sandberg anders at aleph.se
Sun Oct 27 20:59:35 UTC 2013

On 2013-10-27 19:50, Kelly Anderson wrote:
> On Fri, Oct 25, 2013 at 1:51 PM, Eugen Leitl <eugen at leitl.org 
> <mailto:eugen at leitl.org>> wrote:
>     > that point puts computers at many billions of times smarter than us in a
>     Many billions times smarter than us, using which metric?
> Any you wish to put forward.

This has on and off been the matter of discussion at the office. "A 
hundred times smarter than X" - what kind of scale is implied? Looking 
at https://en.wikipedia.org/wiki/Level_of_measurement one can see that 
statements like this requires the measured thing to behave according to 
a ratio scale - you can meaningfully multiply and divide.

But this is not true for IQ scales: while indicating a real number that 
can certainly be multiplied, there is no inherent meaning of double 
IQ-intelligence beyond "can get a higher score on the same test that 
places the person in a twice as high IQ bracket". It is not twice as 
many correct answers, and it is not being part of a half as large 
population fraction.

Elo scales does something similar: if you score X and I score 2X, the 
probability of you winning against me is 1/(1+10^(X/400)) - a bit more 
well defined, but still not obvious in any way. One can imagine chains 
of ever greater players reaching up from our human level to some mind 
playing at score 5744, but this might only make sense in a space where 
ranking is nicely one-dimensional - there is also an assumption that we 
are dealing with a scalar scale.

In the game of real world statesmanship it is not clear that Hitler, 
Gandhi or Shi( Huángdì played for maximizing the same kind of score. 
Maybe one was "twice as good" at military conquest as another one, but 
that does not imply much about the score on empire building or moral 
rectitude. While one can sum together ratio and interval scales, the 
result is not necessarily meaningful (consider human development indices 
- an ordinal "higher is better" is likely the only possible conclusion 
one can draw from them, but it is not clear that the equal country is 
better off than the country with great education).

For superintelligence I am willing to assume one could construct 
something like an Elo scale by comparing different minds gaming against 
each other and/or nature across a wide set of problems. I also think for 
many kinds of minds general problem solving is able to generalize to new 
kinds of challenges, creating enough correlation between the ability to 
solve them that it makes sense of speaking of one score. (But see 
http://www.aleph.se/andart/archives/2013/10/silicon_dreams.html - it 
might be that talking about "twice as smart as humans" would require 
using humanity as a whole as a test subject, not just a representative 

In short, while it might be possible to rank intelligences roughly along 
some kind of scale linked to their intelligence, it looks like saying 
"twice as smart" doesn't convey much useful information. One would at 
the very least need to get into the tedious explanation of what kind of 
test it is. It might be better to say *what* the superminds are supposed 
to be able to do, and then discuss how one reaches that conclusion.

(Example: I can imagine and argue for minds that solve standard IQ tests 
at the same accuracy as humans a million times faster, for example fast 
brain emulations. Incidentally, given 
their performance would likely not be super-good score-wise thanks to 
extra time. However, given past group problem solving papers it is 
likely that running a million emulations in parallel and then using 
agreed to be best answers could improve scores a lot, up to 55 IQ points.)

So, *please*: no more "a billion times smarter than us"!

(Could a beauty a million times more beautiful than Helen of Troy launch 
a billion ships? Is the admiral's wife who launches one ship a 
thousandth of Helen?)

Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University

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