Do you like this website?
Please support Integral World!
INTEGRAL WORLD: EXPLORING THEORIES OF EVERYTHING
An independent forum for a critical discussion of the integral philosophy of Ken Wilber
Publication dates of essays (month/year) can be found under "Essays".
David Christopher Lane
Professor of Philosophy, Mt. San Antonio College Lecturer in Religious Studies, California State University, Long Beach Author of Exposing Cults: When the Skeptical Mind Confronts the Mystical
(New York and London: Garland Publishers, 1994) and The Radhasoami Tradition: A Critical History of Guru Succession
(New York and London: Garland Publishers, 1992).
SEE MORE ESSAYS WRITTEN BY DAVID LANE
SEE MORE ESSAYS WRITTEN BY ANDREA DIEM-LANE
Exploring the Universe
as a Mathematical Superstructure
David Lane and Andrea Diem-Lane
“Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.”
As I glance around the room, I notice that after lecturing for an hour and a forty-five minutes straight on quantum theory, desultory decussation, and Wolframís new kind of science, I see a Krispy CrŤme glaze descend over a few of my studentís eyes. The fantastic implications of chance and necessity (to echo the title of biologist Jacques Monodís famous 1970ís book) appears either to have gone over their heads or, more likely, seems of little practical consequence in their day to day lives.
I then try to draw out more clearly how understanding probability can radically alter how one views life. Imagine in this moment that you have a California Lottery “scratcher” ticket and as you systematically scratch off your numbers and their adjoining prizes you realize in the middle of class that you have won a mega jackpot of 5 million dollars. What would you do? I suspect that most of my students would stand up and leave the room there and then. One thing is for sure, however: it would wake them up and give them a huge and intoxicating adrenalin rush.
The winning student might later ruminate about his or her good fortune and reflect upon how lucky they were (given the astronomical odds against them1 in 2, 400,000) in securing that particular ticket.
I give this illustration to my students because a winning lottery number exponentially pales in comparison to the odds against them being alive and breathing (even if they nod off a bit here and there) at this very juncture in history. But in order to appreciate the anomaly of oneís existence it is necessary to get a deeper understanding of the theory of large numbers.
The very fact that you are alive reading this essay is beyond any moneyed lottery you will ever enter.
Just think of your fatherís sperm as a starting off point. A usual male produces about 100 million sperm per ejaculation. Only one of those sperm will survive the arduous journey to its terminal apex. How many sperm does a male produce in, say, an 80-year life span? No precise count is possible, since it varies with each individual, but one can roughly estimate the number to be around 500 billion or perhaps more impressive sounding as a Ĺ trillion. If your own father had five children, this would mean that just in terms of sperm, you are a 1 in a 100 billion winner! Couple this with the rarity of your motherís egg (of the nearly half million follicles where only about 400 or so will become viable) and the very fact that you are alive reading this essay is beyond any moneyed lottery you will ever enter.
But this is only an infinitesimally small fraction of the monumental odds against you being here since one has to factor in all the preceding ancestors who came before. Roughly speaking, and depending on how many children were sired, the odds of 1 in a 100 billion doubles every generation, so that if you trace your lineage back to Africa 85,000 years ago, the odds become ever more daunting. This too, of course, is but a smidgen when one realizes that each of us trace our evolutionary past from humans to single cell organismsa journey stretching back to the origins of life on this planet some 4.5 billion years ago. And even this is only 1/3 of the story since the atoms that comprise us have their basis in a history that is nearly 14 billions years old.
A visual infographic entitled “What are the Odds?” (which has gone viral on the Internet) puts the number against you being alive right now as innumerably greater than all the particles in the universe. This has led erstwhile sober scientists to theorize that the universe appears to be consciously designed with humans ultimately in mind. Naturally, such statistical comparisons can from the very start be misleading given that we are already alive and one can, if he or she so desires, do relatively the same odds for anything on terra firma, including the astronomical odds against that bottle of Coca Cola your uncle drank last night.
Yet, there is no getting around the fact that evolution is a universal version of the Hunger Games writ large. The survival of our distinctive genetic code over eons of time is a remarkable testimony to its fitness and adaptability. But what is even more remarkable is how much luck was involved in our temporarily resisting the 2nd law of thermodynamics. In other words, regardless of whether we calculate the odds for a wild grain of rice, a bottlenose dolphin, or a Tibetan monk, to liveeven momentarilyon this third planet from the sun is a rarity enjoyed by a diminishing few.
In sum, you are a probability avatar. It is as if (metaphorically speaking) we are the result of some cosmic poker game where all the players are blind and where the winning hand is both selected and randomly determined. Perhaps the universe is built upon a mathematical superstructure such that all that we see around is the result of numbers and their relations fleshed out over time. Max Tegmark, currently a Professor at M.I.T. and a well-regarded cosmologist, argues that “Our reality isnít just described by mathematicsit is mathematics in a very specific sense.”
Tegmark defines his idea as “The Mathematical Universe Hypothesis” which “implies that we live in a relational reality, in the sense that the properties of the world around us stem not from properties of its ultimate building blocks, but from relations among these building blocks.”
Tegmarkís idea is not new (even though how he formulates it certainly is), but has a long pedigree dating back through Plato and Pythagoras. One way to understand his view is to look at any smart phone today. Take, for instance, the iPhone 5S or its larger brother the iPad Air. There are several levels to how they operate, but we usually only access the surface level, more commonly known as the user interface. However, such ease of use is predicated upon large chunks of code derived from long and painstaking computer programs which most of us remain dutifully unaware unless we look a bit deeper and access directly the underlying operating system. Occasionally, as happened to me when I was doing rudimentary programming at UCSD back in my graduate school days, one can mess up a certain algorithm and some ungainly computer code will rear its head and be displayed on the screen itself. Thus the illusion of seamlessness is broken and one realizes (sometimes more often than one might wish) that under all the pretty pictures, movies, and fancy text, there are long and usually undecipherable strings of computational instructions. But there is an even more powerful subterranean level that most programmers never glimpse. This is where binary bits of electrical energy carry out their masterís wishes in relational packets of off and on modes of behavior. How these electronic episodes behave, however, is geometrically prefigured by integrated circuits within ever shrinking silicon chips.
The iPhone 5s or iPad Air is magic to those of us playing on its “oleophobic coating, multi-touch, gorilla” glass. Most of us donít have a clue about what really makes these intelligent devices work. Analogously, Tegmark believes that physics reveals a projective world that is not what it seems.
We experience the world around us through the nine orifices of our anatomy. Yet, this is merely topical and akin to the screen on an Apple or Android device, which we can only touch, but where its constituent core remains hidden from view. If the virtual reality of a computer projection is ultimately based upon unseen digital electronic nodes, is it really a stretch to imagine, as Tegmark suggests, a universe which is in truth mathematical in structure and which coordinates quite literally the emerging patterns we see around usfrom a tree, to an ocean wave, to a babyís smile?
As Tegmark remarks,
“When you look around you, do you see any geometric patterns or shapes? . . . Try throwing a pebble, and watch the beautiful shape that nature makes for its trajectory! The trajectories of anything you throw have the same shape, called an upside-down parabola. When we observer how things move around in orbits in space, we discover another recurring shape: the ellipse. Moreover, these two shapes are related: The tip of an elongated ellipse is shaped almost exactly like a parabola. So, in fact, all of these trajectories are simply parts of ellipses . . . . [There] are many additional recurring shapes and patterns in nature, involving not only motion and gravity, but also electricity, magnetism, light, heat, chemistry, radioactivity and subatomic particles.”
Is the universe the product of a mathematical skeletal schema, such that what we see around us is akin to a holographic projection that betrays its underlying geometric and numbered origin? While the scientific jury is still out on answering this particular query, it is interesting to note that we now have a sufficient series of telling analogies from our virtual lives (as expressed in our varying computational smart devices) to better understand the implications of Tegmarkís M.U.H. hypothesis.
The theory that the universe is “math made flesh” is an instructive one, even if it only turns out to be part of a larger mosaic. We already know that Einsteinís theory of relativity can only be properly understood within a geometric framework where gravity is geometry. Likewise, our deeper appreciation of quantum mechanics necessitates coming to grips with indeterminism and how probability plays an elemental part in how we not only measure the very small but also how we alter it by our array of instrumentations.
Bringing some of these ideas up to my students seems to have sparked them into a deeper appreciation of how precious life is and how studying the theory of large numbers can awaken a keener perspective on why numeracy is just as important as literacy, particularly when calculating the nearly impossible odds against oneís very existence.
Tellingly, science seems to be confirming the ancient gnostic and Indian view that the world we see around is an illusory one in the sense that it betrays its real origination. As Tegmark personally concludes,
“If my life as a physicist has taught me anything at all, itís that Plato was right: Modern physics has made abundantly clear that the ultimate nature of reality isnít what it seems.”