Space, Time, and Twinearthability




kant kan

Originally uploaded by Pete Mandik

This is one of those requests for references and reflections post. I’d be grateful for thoughts and recommendations concerning the following questions: Which spatial properties are Twinearthable and which are not? Which temporal properties are Twinearthable and which are not?

Regarding “Twinearthability,� I’m following the usage of John Hawthorne’s “Direct Reference and Dancing Qualia.� The way Hawthorne puts it, a concept like “water� is twinearthable because we can easily imagine an epistemic counterpart that is epistemically just like us but locks onto a different property by “water� than we do (XYZ instead of H2O). A concept is not Twinearthable when beings epistemically just like us would lock onto the same properties that we do. Non-twinearthable properties are so fully present to the mind that epistemic possibility is a guide to metaphysical possibility.

Properties broadly describable as spatial may differ with respect to their Twinearthability. I consider as relevant the following reflections by Roy Sorensen

The volume of a two inch cube is eight times
the volume of a one inch cube. But the surface of the two inch cube
is only four times as large as the surface of the one inch cube. The
ratio of surface to volume further decreases when the cube achieves
a size of three inches. Now all six sides must be dedicated to
maintaining the organism. Thus the geometry of the cubical
organism imposes a limit on its growth. Since the volume of the
organism is cubed while surface area is squared, the animal must
eventually exhaust its ability to feed. The ratio of an organism’s
surface area to its volume is an internal relation. Hence, the size of
an organism is an intrinsic property.
Size is also an intrinsic property of environments. Doubling
everything would not create a duplicate environment. Although the
increase would not be detectable by linear measurements (for our
rulers would have expanded), the increase would make a difference
to planetary orbits and other phenomena governed by geometrical
laws.
Any purely spatial property of an organism is an extrinsic
property. Identical twins can be duplicates even though they stand a
meter apart. Nor is their duplicate status threatened by rotation. If
one spins clockwise while the other spins counter-clockwise, they
remain duplicates. If one twin sleeps with his head to the east while
the other sleeps with his head to the west, they still wake up as
twins. Given this indifference to space, we see that the twins are
duplicates even if they are mirror images of each other.
(From Mirror Imagery and Biological Selection, Biology and Philosophy 17/3 (June 2002) 409-422)

I wonder if temporal properties are similarly split with regards to Twinearthability. I wrestled with this a bit in the puzzle raised in “The Slow Switching Slowdown Showdown� wherein I wondered out loud about how long slow switching would take on a demonically slowed Twinearth. I wonder now about which properties broadly describable as temporal would be Twinearthable and which would not.

Further pointers on space as well as time are welcome.

8 Responses to “Space, Time, and Twinearthability”

  1. A.G. says:

    Since I think it’s still an open debate whether space is euclidean or hyperbolic, that means to me that it isn’t obvious that one geometry or the other would affect how we perceive things on earth. So let’s say it’s euclidean and twin-earth is hyperbolic. In that case, When I see two triangles with sides of different lengths, I see two triangles with different areas. When twin-AG sees two triangles with different side lengths, then twin-AG is seeing two triangles with the same area.

  2. Pete Mandik says:

    A.G., I’m not up on anything recent about this. Who are some contemporary defenders of the view that space is Euclidian?

  3. djc says:

    This is one of my favorite issues. The best treatment of it I know is Brad Thompson’s
    “The Spatial Content of Experience”, which gives a number of Twin Earth cases for spatial properties. I also discuss the issues a bit toward the end of “The Matrix as Metaphysics” and “Perception and the Fall From Eden”.

  4. AG says:

    Penrose, Road to reality p. 48

    What, then, is the observational status of the larg-scale spatial geometry of the universe? It is only fair to say that we do not yet know, although there have been recent widely publicized claims that Euclid was right all along…..On the other hand, there is also evidence that seems to point fairly firmly to a hyperbolic overall geometry..

  5. Anibal says:

    But if we continue reading at the same page (48 p, The Road to reality: A complete guide to the laws of universe) seven lines below, we notice that Penrose himself is and advocate of hyperbolic geometry.

    Quoting literally:(and I do not attempt tp hide my own opinion in favor of the hyperbolic case, while trying to be as fair to the others as i can)

    In this heated debate about the true nature of physical space we have to know that in our ordinary life Euclid geometry is almost right, but when we focus on the mirocospic scale or cosmological scale dealing with strange things like properties called spins or black holes… some theretical entities are needed, so we can assure that geometry is fundamentally a formal, abstract discipline, and n-dimensional space are also valid to give an account of physical space depending on the assumptions.

  6. Probably I’m missing something in that quote, but what is supposed to be Twinearthable there? Size?
    But doesn’t the person and his twin-earth counterpart need to be atom by atom identical? If one is bigger than the other, then he can’t be atom by atom identical it seems to me.

  7. OK, I’m a bit slow, i guess it says that it is position and rotation that are twinearthable, and not size.

  8. Pete Mandik says:

    Thanks for the recommendations, Dave.

    Brad’s paper was already on my reading list for this project. In fact, his related talk at the last Tuscon meeting was one of the main triggering events for my interest in this stuff. I think we can agree: good stuff.

    (Which reminds me, NC/DC needs to start working on some Zombie Blues pretty soon…)

    It’s been a long time since I read either your Matrix or your Eden paper, and certainly not since I’ve had these questions in mind, so I’ll definitely give them another read. Cheers!