# [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
human)

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
http://www.pearsonassessments.com/NR/rdonlyres/E9B43B7C-E94C-44CF-89D0-B59BABB0147C/0/TimedUntimed.pdf
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

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.extropy.org/pipermail/extropy-chat/attachments/20131027/367e7c1f/attachment.html>
```