The Three Worlds

I’d be shocked if you’ve ever come to this site and not once wondered what’s going on with that picture across the top of each page.  Who is this old scholarly dude and why is he looking at me?  What are the balls all about?   Well, this post is meant to give you my own reasoning for it, and interpretation of it.  You’re certainly free to have your own interpretation, and if yours differs from mine I’d love to hear about it!  Accordingly, this post will be purely philosophical, but that’s why it’s a post and not a lesson—I reserve the blog posts for shamelessly waxing philosophical.

The picture is a cut-off version (because can’t fit the whole thing) of M.C. Escher’s “Three Spheres II”.  I won’t explain the picture, because there’s nothing I could say about it that you couldn’t deduce by looking at it (“there are three spheres, one is white,…”).  First and foremost, if you’re not familiar with Escher’s work, Google image him right now because the guy was a total genius.  Many of his prints are highly motivated by mathematical ideas, and some of these ideas are rather sophisticated (hyperbolic geometry, periodic tilings, impossible shapes, etc.).

This print in particular is, or at least I view it to be, a representation of Roger Penrose’s extremely gorgeous philosophy of mind, math, and physics.  In his view of things, the world is divided up into three “smaller” worlds: the mathematical world, the physical world, and the conscious world.

The mathematical world can be viewed in a similar way as one views Plato’s world of forms—i.e., of supreme and eternal perfection, containing the truest essence of things.  The only difference now is that this world of “forms” is a purely mathematical one; our forms are now nothing but mathematical structures.

The physical world is precisely what it sounds like: the world consisting of physical objects like your computer, this cup of coffee I’m drinking, stars, galaxies, black holes, atoms, and your body.  This is the world that knows about the laws of physics, and has all of its constituents abide by them.

Lastly, the conscious world is that which consists of those things which are pure manifestations of consciousness.  Seeing as consciousness is still not very well understood and extremely difficult to define, I’ll simply leave the definition to whatever the reader feels is that “obvious” sense of “being conscious” that we all (presumably) experience.

The key idea behind this philosophy is that these three worlds are not independent of each other.  Instead, they influence and interact with each other in ways that are hard to deem as anything other than miraculous.  In particular, the conscious world is able to interact with the mathematical world, since (assuming that humans are conscious) we use our consciousness to discover various mathematical structures and to understand their various relationships with each other.  I.e., when we “do math”, we’re really using our consciousness to access this “other world” of eternal mathematical structures.  Additionally, the mathematical world influences the physical world due to the fact that, as far as we can see, there is mathematical consistency to the laws that govern the physical world.  I.e., the physical world is somehow nothing but a “manifestation” of certain structures that exist in the mathematical world.  Lastly, the physical world affects the conscious world because (again, only as far we currently know), conscious things require a physical background to be implemented.  I.e., whatever it is that makes us (or anything) conscious lies somewhere in our brains, and/or our bodies, and/or somewhere in the physical universe.  In this way, these three worlds are completely interconnected in precisely the way that figure 1 depicts.

Figure 1  (Drawn by Roger Penrose himself)

Figure 1 (Drawn by Roger Penrose himself)

The reason I find this philosophy so pleasing is that each link interconnecting one world to the next is in no way obvious, or necessary.  I cannot think of, nor have I encountered, any convincing argument for why any of these links had to be there.  There is no reason that the laws of physics have to be mathematically consistent (assuming they are), or even that mathematics would be the proper language for describing them.  One could plausibly imagine a world of genuine chaos (and indeed, some people do believe this to be our own physical world at the deepest levels, for which there is no evidence to either support or deny at this point).  Moreover, it is in no way obvious that consciousness, whatever it is, has to use some physical object (like a brain) as a medium.  We could perfectly well imagine some consciousness “floating around” out there which is not “tied down” to a physical embodiment.  And lastly, there’s no a priori reason why anything that is conscious has to be able to know how to do math.  I.e., it is perfectly reasonable to assume that something could be conscious without ever being able to develop some sophisticated logical machinery through which to access the world of math (and therefore the world of physics, by the transitive property of figure 1).  The fact that all of these links appear to exist, at least to an extent, is incredible (in my view).

Note, however, that there are more to these worlds than their ability to influence “the next” world, in that there is more that our consciousness can do than just math, and there is more that math can do than just describe the laws of physics, and there is more that the physical world can do than just give rise to consciousness.  This is embodied in figure 1 by the fact that only a part of each sphere is used to “hit” the next sphere.

Now let’s get back to the picture on each page of the site.  What I see (and feel free to disagree) are these three worlds, sitting on M.C. Escher’s desk.  The middle sphere, containing a reflection of Escher, is the conscious sphere (this is obvious, since it’s the one with a human “in” it!).  The sphere on the left (as viewed from the artist) is the physical world, as it appears to be made of glass, a very “physical” object.  And the sphere on the right is the mathematical world—completely clean and perfect.  Moreover, we can see the reflection of both of these worlds in the middle sphere, which is the conscious world.  In my mind, this signifies the fact that while the arrow goes from consciousness to mathematics, we can still posit the existence of the physical world via our conscious world.  In other words, each world “knows about” the other two, but we can only “see” out of the conscious world, as that is in some clear way the world that we interact with the most.

I could write forever on this, but I think I’ll stop here.  Now you at least have some explanation as to why this picture was chosen—whether you agree with this interpretation or not is entirely up to you.  I have no pretentions of believing that this is anything but an untestable and unprovable philosophy.  Regardless, this set of ideas has given me a very meaningful relationship with my craft (mathematical physics), and maybe others will find some beauty in this way of viewing things as well!

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About TrueBeautyOfMath

Lover of math, and lover of teaching it.
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3 Responses to The Three Worlds

  1. Anonymous says:

    love when you wax philosophic, and the artwork of escher is cool! keep it coming it’s BEAUTY-ful!

  2. Bowen says:

    Does the physical world affect our conscious world as well as our mathematical world? Most obviously, our consciousness is due to the fact that we have brains, hearts, and other organs to keep us alive. As for the mathematical reality, isn’t something like number and quantity due to the fact that we can visualize things as distinct things? If our perception of the world were just one big blur its hard to imagine that we would conceive anything like numbers.

    • Well it’s all about the direction that the arrows point in (in Penrose’s drawing). Namely, it is indeed the physical world that allows the mental world to be accessed, as you mentioned. Similarly, it’s the mental world that allows the mathematical world to be accessed. Note that this doesn’t mean that the mental world CREATES the mathematical world. I.e., the mathematical world would (in this philosophy) still exist regardless of whether or not there were a mental world, and regardless of what form the mental world took (i.e., if our view of the world still existed). The philosophy suggests that all three worlds are already “out there” in an objective sense, and that remarkably they are connected (at least partially) in the way described. No world “creates” any part of the other, they all just let us “see” (in the appropriate sense) the others.

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