# Re: AI: Relative difficulty (Was: SCI:BIO: raw genome length)

Hal Finney (hal@rain.org)
Sun, 19 Jan 1997 17:53:26 -0800

From: Eliezer Yudkowsky <sentience@pobox.com>
> [Elizer is quoting Anders Sandberg without attribution:]
> > where the child seems to lack certain abilities before certain ages, and
> > gradually develop concepts such as object constancy (things exist when I'm
> > not looking at them) or conservation (if I move things around but do not
> > take anything away, then there is the same amount of stuff). Most likely
> > these have to be reinforced by experience, and may be completely due to
> > the environment (at least the later). The way to test it is of course to
> > bring up a child in a virtual reality with different laws...
>
> What a concept. WHAT a concept. Alert Greg Egan. "Bring up a child in
> a virtual reality with different laws!" Do you really think that if one
> plus one always equalled three in the virtual environment, the child
> would begin thinking in new laws of mathematics that were based on this
> basic assumption? Wouldn't he notice that in his own mind, one thought
> and one thought equalled two thoughts?

This raises the question of which concepts are contingent and might be
different in a different reality, and which are fixed. Does it really
make sense to create a VR where 1+1=3? What would that mean? Would it
be enough for the VR, whenever two identical objects came close together,
to create a third identical object? Or what about two different objects?
It creates a third of some kind? Does this really suffice?

> What a concept. I'm reminded of the time that, teaching the Pythagorean
> theorem to someone, they asked: "What if c equalled a times b instead
> the square root of a squared plus b squared?"

Similarly, how would this be done in a VR? I don't see how you could
even display a geometry where this worked. The units aren't right,
hypoteneuses would scale differently than sides. It seems incoherent.
Making one where c = a+b might be more plausible, but even then I'm not
sure you could derive a consistent geometry and display it.

A more interesting idea would be to have a 4D VR. Of course the visual
field would still be 2D, but it could be a projection of 4D objects.
Maybe everything would have some degree of transparency, but that might
not be necessary. Somehow the person in the VR would have to be able to
move his limbs four dimensionally. I recall reading about a 19th century
mathemetician who spent a lot of time building models of four dimensional
objects out of blocks, and who later claimed to be able to visualize them
directly in four dimensions. This could be a short cut way to achive this
skill.

Hal