# Chuck Missler and the Existence of Infinity

Along with my (slow) endeavor of exploring and critiquing the ideas undergirding intelligent design, I want to resume a project I started a while back that involved addressing the claims of Chuck Missler.  As I have previously mentioned, Chuck Missler is a well educated man.  That being said, I also get the strong impression that Missler pretends to know a lot more than he really does.  What annoys me the most is that he seems to present himself as an expert in, well, just about everything.

In his Bible studies, Missler lectures his flock on everything from cosmology to quantum mechanics to information theory and beyond.  Missler has everything figured out it seems, and, while he might deny it, presents himself as having just about everything figured out.  It’s shocking that he hasn’t been awarded a Nobel prize.  Listening to his talks, one cannot help but be impressed by the depth and breadth of his knowledge.  However, once one gets over the dazzle of Missler’s apparent expertise in everything, one begins to pick up on very questionable claims and ideas.  Most of the time Missler alludes to very deep ideas, but glosses over them to spare his audience the details.  OR, maybe Missler really doesn’t know or understand the details.  This is my suspicion, which is motivated by several cracks in his intellectual veneer amounting to questionable claims on his part.

The first issue I’d like to address regards the size of the universe.

Missler is fond of proclaiming there are two central mathematical concepts that we don’t find in nature: Infinity and randomness.  I’ll save randomness for another post.

Does Infinity Exist?

Certainly infinity exists conceptually, but the question is whether it describes anything real.  In particular, Missler focuses on size.  This can go in two directions: (1) small scale infinity, and (2) large scale infinity.

Small Scale ∞

Most people are familiar with number lines.

For our purposes we can focus on the interval $[0,1]$.  We can cut this interval in half and get $[0,\frac{1}{2}]$.  This can be cut in half again to get $[0,\frac{1}{4}]$.  In fact, we could carry out this cutting procedure indefinitely, always obtaining a new interval $[0, \frac{1}{2^{n}}]$.  This means that we can make the interval as small as we like.  Put differently, we can cut the interval infinitely many times in the sense that there will never be a limit to the number of times we can cut the interval in half.

Now suppose that our interval $[0,1]$ models a length in space-time, say an inch.  If the correspondence were true, then it would follow that space could be indefinitely halved.  According to Missler, this is actually not true.  It turns out that there is a limit to smallness in space-time.  In other words, there is a smallest distance.  This distance is known as the Planck length, which is defined by

$\ell_{p} = \sqrt{\frac{\hbar G}{c^{3}}}$

where $\hbar$ is Planck’s constant, $G$ is the gravitational constant, and $c$ is the speed of light.  This length is exceedingly small, a mere $1.6\times 10^{-35}$ meters (approximately).  Missler is fond of saying that if at any point you divide a distance into lengths smaller than $\ell_{p}$, then you lose locality, the thing you are cutting is suddenly everywhere all at once.  What he concludes is that our reality is actually a “digital simulation”, terminology he uses purposely to insinuate that our world is created by God.  Such loaded language seems to be characteristic of Missler.

So, what is the nature of this mysterious length?  Where does it come from and how do we know it is the smallest length?

The Planck length has profound relevance in quantum gravity.  Put differently, it is at this absurdly tiny scale that quantum effects become relevant and the question regards how gravity behaves or should be understood at this scale.  Both general relativity and quantum field theory must be taken into account.  The definition of the Planck length now makes sense since the speed of light $c$ is the natural unit that relates time and space, $G$ is the constant of gravity, and $\hbar$ is the constant of quantum mechanics. So the Planck scale defines the meeting point of gravity, quantum mechanics, time and space.

Theoretically, it is considered problematic to think of time and space as continuous because we don’t appear to be able to meaningfully discuss distances smaller than the Planck length.  Unfortunately, there is no proven physical significance to the Planck length because current technology is incapable of probing this scale.  Nevertheless, current attempts to unify gravity and QM, such as String Theory and Loop Quantum Gravity, yield a minimal length, which is on the order of the Planck distance.  This arises when quantum fluctuations of the gravitational field are taken into account.  In the theory, distances smaller than $\ell_{p}$ are physically meaningless.  Two “points” at distances smaller than $\ell_{p}$ cannot be differentiated.  This seems to suggest that space-time may have a discrete or “foamy” nature rather than a continuous one.  Unfortunately for Missler, however, we just don’t know at this point.  Thus, the declarative nature of his claims are hasty.

Nevertheless, even if this turns out to be the case, the question becomes: what follows from that?  As mentioned above, Missler is fond of saying that the universe is a “digital simulation”.  Certainly the term “digital” would be apropos, but his use of “simulation” seems loaded and dubious.  “Simulation” suggests that this world isn’t the “real” world.  It suggests that our world merely imitates some meta-world.  Of course, Missler purposely uses the term as a way to smuggle in a simulator.  That simulator is God, and the meta-world is the spiritual world.

Large Scale ∞

The more questionable of Missler’s claims regards the size of the universe.  He brazenly declares that we have discovered the universe to be finite.  This is just flat out false, and such carelessness makes me question his credibility.  It is likely that he is simply confusing the observable universe with the universe proper.  There is no doubt that the observable universe is finite.  It is estimated to have a radius of 46 billion light years and due to expansion grows ever larger.  However, this does not necessarily imply that the universe proper is finite in size.  Sir Roger Penrose, one of the most respected mathematical physicists in the world, says, “it may well be that the universe is spatially infinite, like the FLRW models with $K = 0$ or $K<0$.” (see The Road To Reality, p. 731)

Note: FLRW models refers to  Friedmann–Lemaître–Robertson–Walker models and $K$ is a density parameter governing the curvature of the universe.

Even a quick search on Wikipedia reveals that, “The size of the Universe is unknown; it may be infinite. The region visible from Earth (the observable universe) is a sphere with a radius of about 46 billion light years, based on where the expansion of space has taken the most distant objects observed.”

In fact, the possibility of an infinite universe is the stuff of some multiverse models.  Max Tegmark, a mathematical physicist at MIT puts it this way:

If space is infinite and the distribution of matter is sufficiently uniform on large scales, then even the most unlikely events must take place somewhere. In particular, there are infinitely many other inhabited planets, including not just one but infinitely many with people with the same appearance, name and memories as you. Indeed, there are infinitely many other regions the size of our observable universe, where every possible cosmic history is played out. This is the Level I multiverse.

Tegmark goes on

Although the implications may seem crazy and counter-intuitive, this spatially infinite cosmological model is in fact the simplest and most popular one on the market today. It is part of the cosmological concordance model, which agrees with all current observational evidence and is used as the basis for most calculations and simulations presented at cosmology conferences. In contrast, alternatives such as a fractal universe, a closed universe and a multiply connected universe have been seriously challenged by observations. Yet the Level I multiverse idea has been controversial (indeed, an assertion along these lines was one of the heresies for which the Vatican had Giordano Bruno burned at the stake in 1600†), so let us review the status of the two assumptions (infinite space and “sufficiently uniform” distribution). How large is space? Observationally, the lower bound has grown dramatically (Figure 2) with no indication of an upper bound. We all accept the existence of things that we cannot see but could see if we moved or waited, like ships beyond the horizon. Objects beyond cosmic horizon have similar status, since the observable universe grows by a light-year every year as light from further away has time to reach us‡. Since we are all taught about simple Euclidean space in school, it can therefore be difficult to imagine how space could not be infinite — for what would lie beyond the sign saying“SPACE ENDS HERE — MIND THE GAP”? Yet Einstein’s theory of gravity allows space to be finite by being differently connected than Euclidean space, say with the topology of  a four-dimensional sphere or a doughnut so that traveling far in one direction could bring you back from the opposite direction. The cosmic microwave background allows sensitive tests of such finite models, but has so far produced no support for them — flat infinite models fit the data fine and strong limits have been placed on both spatial curvature and multiply connected topologies. In addition, a spatially infinite universe is a generic prediction of the cosmological theory of inflation (Garriga & Vilenkin 2001b). The striking successes of inflation listed below therefore lend further support to the idea that space is after all simple and infinite just as we learned in school.

So, it seems that unless Missler knows something all other physicists don’t, he is being much too hasty and cherry picking possibilities to support what he wants to be true.

# Mathematics as Reality (Introduction)

One of the most interesting and provocative ideas to emerge from the intersection of mathematics, philosophy, and physics is the proposal, by MIT cosmologist Max Tegmark, that our universe is a mathematical structure.  Everyone knows that mathematics is indispensable for understanding our universe, but the Mathematical Universe Hypothesis (MUH) says something rather more remarkable.  Two of the most salient questions in all of philosophy are:

(1) Why is there something rather than nothing?

(2) Why is mathematics so effective in describing reality as we know it?

The profundity of these questions is quickly made manifest upon the slightest reflection.  MUH is an ambitious, albeit ingenious, solution to the inherent problems raised in these two questions.  It postulates that reality is mathematics in a very real and well-defined sense; more specifically, physical existence equals mathematical existence. One might describe such a view as a form of radical Platonism or, equally, a mathematical version of modal realism.  In fact, these are the very descriptions employed by Tegmark himself.  As such, MUH answers (1) because it entails that there really is no such thing as an ontological nullity or universal negation.  Something necessarily exists, namely all possible mathematical structures, which Tegmark refers to as the Mathematical Ensemble or Level IV Multiverse.  It also answers (2) by making it trivial.  Certainly, if reality is mathematics, then science is merely the endeavor of uncovering how our particular mathematical system operates or behaves.

Now, as a mathematician, this suggestion resonates with me and isn’t so hard to imagine being the case.  For most people, however, MUH probably sounds outlandish at best, if not incoherent!  After all, what could it possibly mean for reality to be mathematics?  You mean, the chair I’m sitting on is no different than the equations I write down when doing my math homework?

I grant that, at first sight, the idea seems a bit absurd; but  the fog begins to lift, I think, upon a reflection of what mathematics really is.  It is my hope to explore, and clarify, this most fascinating idea in a series of posts.  Included in this investigation will be an incorporation of Douglas Hofstadter’s ideas espoused in his landmark work, Gödel, Escher, Bach: an Eternal Golden Braid, which, I believe, specifically fleshes out Tegmark’s notion of a Self-Aware Sub-Structure (SAS).  On Tegmark’s (and presumably Hofstadter’s) view, a human would be an example of a SAS.  Hofstadter, however, uses the terminology “strange loops” or “tangled hierarchies”.

These posts are primarily for my own benefit, to engage these ideas and to deepen my understanding.  But for anyone who might be reading this blog, I hope that what I write is both interesting and enlightening.  Of course, if I totally botch something or if clarification is needed or if there are other ideas that would be interesting to fit in, please feel free to contribute and participate in the comments.  Happy reading.