IV: The Point of Origin

In the preceding chapter, it was pointed out that according to the singularity theorem, the Universe must have evolved from or into a very dense state.

And just exactly what is a singularity? It is of the utmost importance to clarify this concept before we proceed any further, for herein lie the very roots of our beginnings, herein is where we come face to face with infinity itself, herein is where mathematics and logic as we know them lose all meaning.

Mathematically speaking, the concept of a singularity can be easily understood with a simple example. Take, for instance, the following formula:

Let us assume in the above formula that we can give Q₁ and Q₂ any numerical value we so desire, and for our discussion we will assume that k is a numerical constant that will be given the value of one. If we assume that r takes also the value of one, then it is not difficult to verify that if Q₁ has a value of 2 and Q₂ has a value of 3, then F will be computed to have a value of 6. Let us now assume that both Q₁ and Q₂ have a value of one and that r takes on a value of 0.5, in which case F can be computed to take on a value of 4. If we give r a smaller value such as 0.1, then F will take on a value of 100. If we give r an even smaller value such as 0.01, then F will have an even larger value of 10,000. If we give r an even smaller value such as 0.00001, then F will have an even greater value, which is:

F = 1,000,00,00,000

It is not hard to see that as we keep on giving r even smaller values, F becomes larger and larger and begins to grow without bounds. Since the smallest value we could possibly give to r, besides very tiny values which are close to zero, would be zero itself, it becomes obvious that the value

r = 0

cannot be used for an actual numerical computation, since the result for F could only be denoted by a number so large that the number would be none other than infinity itself. This is what we mean by a singularity.

Imagine now for a moment that you had the strength of a mythical Titan, and that you could be able to go to you car, grasp it with your hand, and applying enormous pressure you were able to compress that car into a tiny sphere the size of a marble. Now imagine you could grasp your entire city and applying enormous pressure you could compress everything to fit in the palm of your hand. As a next step, imagine yourself with enough strength to grasp and compress the entire planet Earth, with all its mountains, all its rivers, all its seas, all its continents, into a tiny sphere the size of marble. This marble, even if small in size, would be an enormously massive object, capable of exerting a tremendous gravitational pull on any other objects nearby. Having compressed planet Earth into a small marble, you would then reach for the Moon, compress it to the size of a marble, and compress both marbles into one, at which point you could go to grab another planet and repeat the process, crunching everything into the size of a small marble. But at some point, as you kept on adding more mass to the marble, you would be amazed at what would happen next. First, there would be a tremendous explosion, because you would have just created a nova by the sheer act of compressing so much matter into such a small volume, with an outer shell of debris being thrown out into space and a very massive inner shell remaining. After this, because of the enormous gravitational pull concentrated in such a small volume of space, the remaining accumulated mass would collapse into something known as a neutron star. But if you are unlucky, the gravitational pull of the concentrated mass might just be enough to enable it to compress itself into something even smaller than the marble you had in your hand, even smaller than the head of a pin. The accumulated mass would still be there, somewhere, but its gravitational pull would be so strong that even you, the mighty Titan, would be sucked into such strange object. Not even light itself can escape from such object. It goes without saying that this object would have to be something way beyond belief. This object, in fact, was predicted nearly a century ago by Einstein’s theory of general relativity, and is commonly known as a black hole. A black hole, brought about by this process of gravitational collapse, is not just a theoretical curiosity to explain a possible solution to the equations of general relativity. As a matter of fact, its existence in several parts of the Universe has been confirmed by recent astronomical data, and there is strong reason to believe that at the very center of our own galaxy, the Milky Way, there is a massive black hole powering a galactic engine almost beyond our capabilities of comprehension [since 1971, Cygnus X-1 in the Milky Way galaxy has now been accepted as a black hole. Other black holes in our galaxy are V404 Cygni, GS 2000+25, H1705-250, GRO J1655-40 and A 06020-00. At the nucleus of nearby spiral galaxy NGC 4258 there is another black hole. By June 1999, according to an article published in Scientific American entitled Revisiting the Black Hole, the authors Roger Blanford and Neil Gehrels mention that we had about 15 mass estimates for black holes in the nuclei of nearby galaxies that are quite secure, adding "No longer is there any serious debate as to whether black holes exist. We know that they must be quite common, and we can now study them in increasing detail"].

It was the German astronomer Karl Schwarzschild who in the winter of 1915, in an accomplishment that impressed Einstein, found a simple yet exact solution to the equations of general relativity. Among the conclusions drawn from the solution was that for a sufficiently compact mass there was a finite radius at which emitted light waves would have an infinitely long wavelength, which in simple terms implies that light cannot escape from such object.

In the book Gravitation by Charles Misner, Kip Thorne and John Archibald Wheeler, we find a more accurate description of what would happen to an unlucky traveler who might happen to pass near a black hole and get trapped by its gravitational pull:

“Consider the plight of an experimental astrophysicist who stands on the surface of a free falling star as it collapses to R = 0. As the collapse proceeds toward R = 0, the various parts of the astrophysicist’s body experience different gravitational forces. His feet, which are on the surface of the star, are attracted toward the star’s center by an infinitely mounting gravitational force; while his head, which is farther away, is accelerated downward by a somewhat smaller, though ever rising force. The difference between the two accelerations (tidal force) mounts higher and higher as the collapse proceeds, finally becoming infinite as R reaches zero. The astrophysicist’s body, which cannot withstand such extreme forces, suffers unlimited stretching between head and foot as R drops to zero …But this is not all. Simultaneous with this head-to-foot stretching, the astrophysicist is pulled by the gravitational field into regions of spacetime with ever decreasing circumferential area, 4πr². In order to accomplish this, tidal gravitational forces must compress the astrophysicist on all sides as they stretch him from head to foot. The circumferential compression is actually more extreme than the longitudinal stretching; so the astrophysicist, in the limit as R approaches zero, is crushed to zero volume and infinitely extended length.”

As William Poundstone more aptly puts it in his book Labyrinths of Reason, “A human body that enters a black hole is transformed into Euclid’s ideal line”.

The description given above can be found under the heading “THE FATE OF A MAN WHO FALLS INTO THE SINGULARITY AT R = 0”. This is because at the center of the black hole there is a singularity, a point of infinite compression and infinite curvature of space-time.

Let us now go back to our original line of thought, and imagine that once we have created a black hole with all of the combined masses of the solar system, from the Sun all the way out to Pluto, we bring into such black hole millions upon millions of other stars and planets from the galaxy, to form an incredibly massive black hole. For an outside observer, it would appear as if first the entire solar system had disappeared out of existence (well, not quite so, for in the process of falling into a black hole the accelerating matter emits a lot of very intense radiation, including X-rays, which can be used by the outside observer to infer that were there once was a system of stars there is now a massive singularity in the space-time continuum), and after that the entire galaxy had also seemingly disappeared into nowhere. After this, we go to other galaxies, with their millions upon millions of stars and planets and any black holes they might contain, and toss those entire galaxies into our super-massive black hole [from the equations of general relativity it can be formally proven that two black holes can be merged into one; the proof is contained in the work by Stephen Hawking entitled "Black Holes in General Relativity" published in 1972 on "Communications in Mathematical Physics"]. Continuing this process, we go even further and toss not just galaxies but entire clusters of galaxies with their millions upon millions of galaxies, stars, planets and black holes into our colossal black hole. We go even further, and toss super clusters of galaxies, with their millions upon millions of clusters of galaxies into the black hole. As a final push, we reach out towards the entire Universe, and bring all of its contents into our super-colossal black hole. It is possible at this point that such an incredibly massive object would have enough gravitational pull to suck into it not just the entire matter contained in the Universe but even the fabric itself upon which the Universe is built, the space-time continuum. In effect, everything in the entire Universe, and by this we mean absolutely everything, including space-time itself, would fold unto itself and vanish into a singularity that we cannot even possibly try to comprehend, much less analyze with our current knowledge.

Yet, it is precisely from a singularity such as this one where the Universe is supposed to have begun some ten to fifteen billion years ago. The singularity from which the Universe was born would indeed be the ultimate black hole, the mother of all black holes.

But if nothing can escape from a black hole, how then could the Universe have begun, with everything bursting out of the singularity in the midst of a tremendous explosion? This is one of the major puzzles being confronted by cosmologists nowadays, and several explanations have been advanced, among them the observation that if we go back in time the Universe will contract into a point for which quantum effects such as Wolfgang Pauli’s exclusion principle will become important. Also, recent astronomical evidence points to a growing possibility that the rate of expansion of the Universe is not slowing down nor is it keeping a steady rate but rather it is accelerating, and such effect can only be due to another unexplained force that is counteracting the pull of gravity on a cosmic scale.

One thing appears to be certain. If such a massive concentration of mass and energy and space and time and everything else there may be into a small point like object could be duplicated “somewhere else”, the concoction would be highly unstable. Our own Universe is “living proof” of that. It has been estimated that when our Universe was only a tenth of a nanosecond old (one-tenth of one-billionth of a second) the temperature was in the neighborhood of about 10¹⁵ degrees Kelvin (to get the equivalent in degrees Centigrade we add 273 to whatever reading we may have in the scale of our Kelvin degrees thermometer). Written out in full, this is a temperature of about

1,000,000,000,000,000 degrees

(Just for comparison purposes, if the outside temperature on a hot summer day was about 100 degrees Fahrenheit, then its equivalent would be a “cool” 310 degrees Kelvin.)

This enormous temperature has been decreasing ever since the explosion took place; down to the 2.7 degrees Kelvin it is today (the heat left over from the Big Bang) permeating all of outer space as the cosmic microwave background radiation (in the Centigrade scale, this temperature is close to 270 degrees Centigrade below freezing).

Besides, we now know that a black hole such as the ones we would expect to find in our own Universe at this very moment will not last forever, thanks to a discovery that took the scientific community by storm. Stephen Hawking proved it by resorting to quantum mechanical arguments that black holes are “evaporating” continuously by sending out a radiation that is now known as the Hawking radiation. In relation to his discovery, Hawking tells us in his article “The Quantum Mechanics of Black Holes” published in the January 1977 issue of Scientific American:

“To my great surprise I found (in 1974) that the black hole seemed to emit particles at a steady rate. Like everyone else at that time, I accepted the dictum that a black hole could not emit anything … What finally convinced me it was a real physical process was that outgoing particles have a spectrum that is precisely thermal: the black hole creates and emits particles and radiation just as if it were an ordinary hot body with a temperature that is proportional to the surface gravity and inversely proportional to the mass …Since that time the mathematical evidence that black holes can emit thermally has been confirmed by a number of other people with various different approaches … As a black hole emits particles its mass and size steadily decrease … In the long run every black hole in the universe will evaporate in this way. For large black holes, however, the time it will take is very long indeed: a black hole with the mass of the sun will last about 10⁶⁶ years … The final stage of the evaporation of a black hole would proceed so rapidly that it would end in a tremendous explosion.”

There is, however, one important difference between an ordinary black hole and the singularity from which our Universe was born. The black holes that inhabit our universe and which are constantly evaporating by sending out their radiation do so into a vast preexisting space, whereas the primeval singularity created its own space, since before the singularity exploded there was no space in which to explode! And since all of the space that fills our cosmos came from within the confines of that singularity, the singularity vanished into every point of our expanding Universe. In effect, any region of all the known space of the Universe can now be considered to be the “center” of the primeval explosion, and no observer in any part of the Universe can take himself to be a “privileged observer” in the sense that while he standing still is at the very center of the Universe all of the other stars and galaxies are receding from him at a very fast pace. This agrees completely with the precepts of both the special and the general theories of relativity, in the sense that there are no privileged observers capable of detecting “absolute” motion with respect to some hypothetical point of reference, since no absolute point of reference exists in the Universe. While it is true that the more massive the black hole is the longer it will take to evaporate into outer space, we cannot infer from this dictum that the primeval singularity –being the most massive object in existence with an infinite density of matter- should have been the most stable object of them all, since whereas a black hole radiates particles into the space-time continuum which the singularity threw out, the singularity itself became the space-time continuum before any black holes could be born. The enormously high temperature at the moment of creation and the enormous speed at which the galaxies are now receding from each other confirms that a singularity like the one that gave birth to our Universe is inherently unstable.

Reviewing the singularity theorem which states that the Universe must have evolved from or into a very dense state, we can see that if the Universe will keep on expanding forever, without any possibility of evolving in the future into a singularity because of its never ending expansion, then it must have evolved from a singularity in the past. There can be no other conclusion at present.

It is ironical that in order to explore the Universe itself which in all likelihood began as a point like particle, scientists are now resorting to the tools provided by relatively new subjects such as “quantum field theory” and their offspring “unified field theories”, which deal with almost point like subatomic particles, in order to explain the first stages of the newly born Universe. But these models only allow us to go back so far, and at present the farthest back we can go with our current knowledge is about 10^-35 second after the Big Bang took place, which written in full reads out as follows:

0.000,000,000,000,000,000,000,000,000,000,000,01 second

This is a very small time lapse indeed. But as remarkable as this achievement sounds, it stills leaves many doubts as to what events could have taken place between the actual moment of creation (time = 0) and the 10^-35 second after that.

On final analysis, whatever characteristics the singularity from which the Universe came from could have had at the precise moment of creation (time = 0), it is those characteristics the ones which ultimately set the stage for the creation of stars, galaxies, comets, and planets capable of sustaining intelligent life. At the very moment of creation the singularity had all of the right initial conditions required for these things to happen. Once the explosion has taken place, the singularity cannot go back and reconstitute itself in order to alter those initial conditions, at least not within the framework of any of the workable theoretical models we have nowadays. The primeval explosion appears to have been such a fiery and overwhelming event that it just doesn’t seem possible for it to be undone on its own once it has started, no matter how small the time span after the actual moment of creation, be it 10^-35 second, 10^-100 second, or even 10^{-1,000,000,000} second (try to write this number down; it is a one preceded by one million zeroes!)

We have assumed throughout that general relativity is still valid at the start of the early Universe. Of course, we could all be wrong, and there is a possibility that all known physical laws including relativity itself may break down completely once we have reached the singularity, and our known physical laws would have to be replaced by other yet-unknown physical laws to describe the point of origin. Nevertheless, we need to carry on with what we already have and which we know is true and has been confirmed by experimental data here on Earth, for the alternative is to just sit back and do nothing while something else comes to mind. It has been said that “good things come to those who wait”, but in this case this old adage would be out of place, and a more proper one would be “good things come to those who work.”

All around us, we are surrounded with what appear to be infinities, from the infinitely small (unless we take the subatomic particles from which everything is built to put an absolute limit to the extension of how small the very small can be) to the infinitely big (unless we consider the possibility that our Universe is a “closed” Universe with a finite though very large volume, a possibility allowed by the equations of general relativity, which would put an absolute limit to how big the very big can be). But we know ourselves all too well to be finite creatures, confined to live in a finite planet which can be measured with our finite yardsticks, inside a finite solar system which can also be measured with finite yardsticks, inside a finite galaxy which can also be measured with finite yardsticks, and within us are the finite discrete parts we call our internal organs, made up of a finite amount of differentiated cells, with each finite cell and everything else such as the water molecules which flow through them made up of a finite amount of atoms. The dilemma many might have asked themselves at one time or another is this: How can things that are the purest embodiment of infinity itself give rise to things that are very definitely finite?

It turns out that, at least from the perspective of mathematics, this is not only possible but indeed it should be expected. To see how this could take place, imagine you have a cube in your hand containing a known finite volume V. Assume each side of the cube measures one centimeter, in which case the cube will have a volume of one cubic centimeter. If we double the height h of the original cube, then in order to contain the same volume V of one cubic centimeter as in the original cube we must reduce each side l of its square base to:

By the same token, if we increase the height h of the original cube tenfold, in order to still contain the same volume V of one cubic centimeter the cross sectional area of its base must now be a square with an even smaller length l of about 0.306 centimeter. That the volume remains the same can readily be verified the reader as follows:

V = (0.316 centimeter)(0.316 centimeter)(10 centimeters) = 1 cubic centimeter

This procedure can be repeated indefinitely with no end in sight, and we can have an ever-thinner rod with an ever-growing length still containing the same finite volume V provided that as we increase the height we adjust the sides of the base accordingly:

Side of square base	Height	Volume = 1 cubic centimeter
1	1	(1)(1)(1)
0.707	2	(0.707)(0.707)(2)
0.316	10	(0.316)(0.316)(10)
: : :	: : :	: : :
0.1	100	(0.1)(0.1)(100)
0.001	1,000,000	(0.001)(0.001)(1,000,000)
: : :	: : :	: : :
0	∞	1 cm3

In the last row, we have used on the first column the symbol zero to represent a quantity so vanishingly small (though not exactly zero which stands for “nothing”) that to us it would appear to be the smallest quantity we can think of (by this we mean a quantity so small that whatever small number we may write down we may assume that this quantity is even smaller), and we have used the symbol “∞” to represent a quantity so large that it cannot even be written down. Yet, the product of these disparate quantities is known to yield a very finite result. Taking this procedure to the very extreme, we can see how the product of a quantity that is infinitely small times a quantity that is infinitely big will produce a result which is neither infinitely small nor infinitely big but, to the contrary, will be quite finite. Indeed, this is what happens to our astrophysicist who fell into a black hole becoming Euclid’s “ideal” line with infinite length and zero thickness but still managing to retain a finite volume as he falls deeper and deeper into the singularity. This remarkable fact can be expressed symbolically in the following manner:

In other words, the product of something that can be taken to be infinitely small times something that can be taken to be infinitely big can yield any finite number we can think of, whether it is ten, one million, one thousandth, or whatever. This is one way in which infinities can meet together to yield finite results. This agrees somehow with our common everyday experience, as we ourselves having finite bodies are fully aware that towards the outside of our bodies we peek at the infinitely big and towards the inside we can go deeper and deeper into the infinitely small, and thus the surface of our skins acts like an “interface” between these two extremes, a place where the two meet together.

In the physical world, it is quite possible that infinity may just be an illusion. The modern science of Quantum Mechanics owes its very existence to the fact that matter cannot be split down forever with a knife without encountering sooner or later those discrete finite units we call “atoms” and “molecules”. [It was precisely an abhorrence of the concept of infinity which lead Democritus nearly 2,500 years ago to postulate that matter could not be split down forever without encountering that it was made up of those small discrete finite units for which he himself coined the Greek word atomos which means that it cannot be "cut down" any further]. Likewise, the intensity of a beam of light cannot be dimmed indefinitely without finding out that at some point the beam of light is made up of small yet finite discrete lumps we call “photons” which cannot be split any further (whether these tiny lumps are themselves made up of something else even smaller is at present just a matter of speculation). Even Albert Einstein believed in the possibility of a very big but finite “closed” Universe, a possibility that is allowed by the equations of general relativity and mathematics itself within the framework of what we call “non-Euclidean” geometries. Nevertheless, many infinite quantities can be rigorously defined and manipulated. The taming of infinities becomes crucial in order to have workable theories that can predict many physical phenomena we observe in our laboratories, especially if those theories are to be extended for the exploration of the Universe and its origin. In the book Perfect Symmetry: The Search for the Beginning of Time, we read the following from Professor Heinz Pagels:

“Although the ideas of relativistic quantum-field theory successfully predicted the existence of antimatter, theoretical physicists in the 1930s and 1940s found lots of mathematical difficulties and problems with these new ideas. If they calculated quantum interaction processes using these new ideas they obtained infinite numbers, so clearly something was going wrong. Nature does not have physical quantities that are infinite … Yet others continued to struggle with this problem and eventually managed to tame these infinities by a mathematical trick called the ‘renormalization procedure’. They showed that the infinite numbers appeared only in calculations of a few quantities like the mass or electric charge of the quantum particles involved, and that if these quantities were redefined, or ‘renormalized,’ by subtracting an infinitely large number, they would then yield finite predictions for all experimentally measurable quantities. Subtracting these infinities seemed like a mathematical trick, but it worked … When the renormalization procedure was carefully carried out, the calculational results of quantum electrodynamics could be compared with precision experiments. To many people’s amazement, the theory, in spite of its abstract mathematical tricks, agreed decimal place for decimal place with experiments. Not since the time of Newton’s predictions of planetary motions had theory and observation accorded with each other so completely. Even physicists were astonished by the experimental success of quantum electrodynamics … Not every relativistic quantum-field theory is renormalizable –the mathematics of renormalization works for only a few kinds of quantum-particle interactions out of a possible infinite number. Remarkably, the renormalizable interactions are precisely the ones we observe. Is Nature trying to tell us something by using only renormalizable interactions? Some physicists, struck by this fact, think that renormalizability is a fundamental imposition by nature, just like the principle of special relativity.”

V: For Us, Prediction Becomes Impossible

In the golden age of classical physics following the discovery of the laws of motion by Sir Isaac Newton, the old postulate that “behind every effect there is a cause responsible for producing such effect” was finally placed in firm mathematical grounds, and the Universe all of the sudden became quite a predictable place. The motions of the planets around the Sun could be predicted, their masses could be estimated, and even the possibility of artificial satellites put into orbit by Man came into the picture. And the laws were proved to hold valid even as they applied to small objects such as cannonballs being fired or to a person jumping across a ravine from one ledge to the other. Once the current state of affairs of a physical system is known or fixed, its unfolding as time goes on is already determined by its obedience to the laws of Nature. Not surprisingly, this point of view came to be known as determinism. Indeed, the Universe became fully mechanistic, and it was thought at the time that if we knew all of the initial conditions of a situation down to their most minute details, then a long-range prediction into the future was possible in principle, the only limitation being the accuracy with which we can carry out our calculations. And since a mathematical procedure when carried out correctly cannot give two different answers to the same problem (otherwise, mathematics itself would be inconsistent), for a given set of initial conditions occurring in Nature there can be only one possible outcome, regardless of the amount of time which has elapsed. This is the mechanistic, deterministic, view of Nature that necessarily follows from Newton’s laws of motion.

Such was the belief until the start of the twentieth century. The arrival of a new science, quantum mechanics, essentially threw the old concepts into disarray, by showing us that the state of affairs of the basic constituents of matter itself cannot be known with an unlimited degree of precision (this idea came into being with Heisenberg’s Uncertainty Principle), and there is natural limit to the amount of information we can extract from the building blocks of nature such as atoms and molecules. The stunning success of quantum mechanics in the prediction of many new phenomena and its daily verification in the most advanced research centers of the world leaves very little doubts as to its validity. If there is a level of uncertainty already built into the basic building blocks of nature that prevents us from determining what is going on at the microscopic realm with an unlimited degree of precision, it follows also that we cannot predict the precise outcome of something which is going on at the atomic and subatomic levels, be it here on Earth, the Moon, or even the entire Universe for that matter. In effect, it is as if Nature was playing dice all over the place. The inherent uncertainty that lies at the very core of matter itself is a concept so repulsive to many philosophers that even Albert Einstein himself once replied, “God does not play dice with the Universe”.

Still, since quantum mechanics applies to the realm of microscopic phenomena, which is the realm in which the postulates of quantum mechanics hold valid, many supporters of the mechanistic view of Nature held steadfastly to the belief that, at least on a macroscopic scale, Newton’s laws of motion could still be applied with some disregard to things such as quantum mechanics.

It was back in 1960 when an MIT meteorologist, Edward Lorenz, carried out a computer simulation of the earth’s atmosphere. The computer itself was required to solve a number of “nonlinear equations” used to model the atmosphere, and the initial conditions he used for his data included such things as the wind speed, the wind direction, the air pressure and the temperature. After the simulation was run once, Lorenz repeated his simulation a second time rounding off the decimal figures in the equations to three decimal places instead of the six employed in the first run. Much to his surprise, the result he got was not even an approximation of the first forecast. It was a completely different forecast. Upon closer examination, it was confirmed by him that the three decimal place differences between both computer simulations was eventually magnified by the repetitive procedures used to solve numerically his starting set of nonlinear equations. To quote his words published on Discover magazine:

“I knew right then that if the real atmosphere behaved like this (in reference to the mathematical model he used), long-range forecasting was impossible.”

If we assume that the set of equations used by Lorenz to model weather phenomena is the right one (the “correct” model perhaps is much more complicated than we can even imagine), then it stands to reason that our forecast will be more precise if we increase the accuracy of our computer by using ten decimal places instead of six. But if we had used one hundred decimal places instead of ten, we must accept the fact that the difference between using ten decimal places instead of one hundred (something which many would consider a “small insignificant error”) will eventually be amplified through the repetitive numerical procedures used by the computer in the solution of the problem, and again we will have two different outcomes. We can only guess that the long-range outcome using one hundred decimal places will be closer to the truth than the one using ten decimal places. But as time goes on, even our solution using one hundred decimal places will quickly become obsolete. The only way to compensate for this is to use an even more powerful computer capable of handling figures with something like one hundred million decimal places. But even then, as time goes on, the difference between using one hundred million decimal places and two hundred million decimal places will eventually be magnified by the computer, and this difference will creep up and throw our long-range forecast astray. The only way in which we can come up every time with a unique and exact solution is to use a computer with an unlimited degree of accuracy, capable of handling an infinite amount of decimal figures and capable of giving us a final result within our lifetimes. But such a computer does not exist, nor can we build such a machine either today or in the foreseeable future. Even the “quantum computer”, the most powerful computer conceived by Man, a computer which is yet to be built some time in the future provided some major technological obstacles can be overcome, would not even come close to the performance we could expect from an “infinite computer”. In principle, we cannot even conceive of such a machine, with an unlimited degree of accuracy, capable of handling numbers all the way up or down to infinity. To complicate matters even further, if we take for granted that, under a completely mechanistic framework, for a given set of exact initial conditions there can be only one possible outcome for those conditions, regardless of the amount of time that has elapsed, even if we had a computer capable of doing math with infinite accuracy, in order to be capable of carrying out long-range forecasting we would need to know the initial conditions with unlimited accuracy. Few instruments around the world can measure anything precisely with more than ten significant figures [see, for example, the August 1980 article of Scientific American entitled "The isolated electron", which describes how a property of the electron called the g factor was measured to be 2.0023193044, correct to eleven significant figures]. Any instrument capable of doing measurements with one hundred or more significant figures is well beyond our current technological capabilities and perhaps even beyond our understanding. And even if the accuracy of our computer and the accuracy of our measurements were allowed to extend with unlimited precision, it would not be long before quantum mechanics itself enters into the picture and spoils the party.

The results obtained by Edward Lorenz had actually been anticipated for quite some time by mathematician Henri Jules Poincaré, who wrote in 1903:

“A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But this is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.”

It is possible that if a mathematician as talented as Poincaré could have had access in his time to a modern computer, he could have verified for himself his suspicions using one of the many mathematical models he used to play with. The implications of the observations made by Poincaré and their confirmation by Edward Lorenz are more profound than even both of them could have realized at the time. Many natural phenomena besides the weather can be modeled by sets of nonlinear equations, similar to the ones used by Lorenz, from economic growth models all the way to models describing the evolution of ecosystems and life itself. And just like the weather, long-range prediction for all these phenomena becomes impossible, at least for us. This puts an absolute limit upon the knowledge that Man can expect to posses, even if he could somehow manage to live for an eternity.

There is another important conclusion we can draw from all of this. If something like the Universe itself is about to be created, and if such a creation is to fulfill a certain promise, a long-range plan, with its evolution path inscribed from the very outset upon the initial conditions with which it will be created, then in order to ensure that the plan will be carried out as expected the initial conditions of the act of creation itself must be set with an infinite degree of precision, and even the uncertainties introduced by the quantum mechanical nature of matter itself must be carefully taken into consideration. Anything less is very likely to produce in the long run an outcome completely different from the one expected, as Edward Lorenz himself found out early in 1960.

The availability of an “infinite computer”, capable of doing math with an infinite level of accuracy by handling an infinite amount of significant figures and coming up with exact (and not just approximate) answers in a finite length of time, would enable us at this very moment to obtain real definitive answers to some of the most vexing problems being faced by mathematicians nowadays, such as proving or disproving the validity of Goldbach’s conjecture (which states that every even number is the sum of two primes) or the twin primes conjecture (which states that there are infinitely many twin primes, with twin primes being defined as consecutive odd primes such as 11 and 13.) And in cases such as these, an infinite computer might be the only way to prove or disprove the conjectures, since it has already been shown by noted logician Kurt Gödel in what we know today as Gödel’s incompleteness theorem that there are mathematical assertions and statements whose validity cannot be proven nor disproven within the framework of mathematics itself [A more technical way of enunciating Gödel's incompleteness theorem is the following: "No algorithm (procedure or cookbook recipe for solving a problem) exists that can determine the truth or falsity of any logical proposition in a system of logic that is powerful enough to represent the natural numbers." For many mathematical theorems and propositions, there will be an algorithm to prove their truth or falsity, provided that the mathematicians attempting to prove them are clever enough to find them. But this cannot be generalized to all mathematical theorems and propositions, for there will always be some theorems and propositions for which no algorithm to prove their truth or falsity will ever be found since that algorithm does not exist, not even in principle]. We already know beforehand that any mathematical statement must be either true or false; it cannot be both at the same time. But there is a very uneasy feeling with the knowledge that rigorous mathematical logic alone will never be able to provide answers to problems that fall into this category. And even if we had an infinite computer at our disposal, we would have no other choice than to accept its conclusions at face value, since we ourselves have no means of verifying those conclusions. There can be no doubt whatsoever in our minds that any being who could have access to an infinite computer or who could be able to grasp and comprehend infinity would have a lot of knowledge (besides the solution to Goldbach’s conjecture and the twin primes conjecture) that we ourselves will never be able to derive with logic alone or perhaps even to comprehend. And this includes not just peeking into the distant future within a purely deterministic framework, but even more, arranging things from the very outset in such a manner that some major events will inevitably take place as scheduled even after the passage of billions of years.

We close this chapter with a discussion of an interesting irrational number (an irrational number is one that cannot be represented as the ratio of two whole numbers) which we will call Ω (this symbol is the Greek letter omega), which we know beforehand will have a value somewhere between zero and one (since it represents a probability). This number, discovered by Gregory J. Chaitin at the IBM Thomas J. Watson research center, thus known as Chaitin's constant, is supposed to be so random that in the long run no gambler would do better than break even if he were to place bets based on the successive digits of this number. In other words, no matter how many decimal figures we may have written down of such number, there is no way of predicting what the next missing digit will be, and the digits follow no discernible pattern we can uncover through any of the known statistical analysis tests. One of the most interesting properties of Ω is that it can be defined precisely but it cannot be computed. In his article “Mathematical Games” published in the November 1979 issue of Scientific American, Martin Gardner quotes the following:

“Throughout history mystics and philosophers have sought a compact key to universal wisdom, a finite formula or text that would provide the answer to every question. The use of the Bible, the Koran and the I Ching for divination and the tradition of the secret books of Hermes Trismegistus and the medieval Jewish Cabala exemplify this belief or hope. Such sources of universal wisdom are traditionally protected from casual use by being difficult to find as well as difficult to understand and dangerous to use, tending to answer more questions and deeper ones than the searcher wishes to ask. The esoteric book is, like God, simple but undescribable. It is omniscient, and it transforms all who know it. The use of classical texts to foretell mundane events is considered superstition nowadays, yet in another sense science is in quest of its own Cabala, a concise set of natural laws that would explain all phenomena. In mathematics, where no set of axioms can hope to prove all true statements, the goal might be a concise axiomatization of all ‘interesting’ true statements … W is in many senses a Cabalistic number. It can be known of through human reason, but not known. To know it in detail one must accept its uncomputable sequence of digits on faith, like words of a sacred text. The number embodies an enormous amount of wisdom in a very small space inasmuch as its first thousand digits, which could be written on a small piece of paper, contain the answers to more mathematical questions than could be written down in the entire universe –among them all interesting finitely refutable conjectures. The wisdom of Ω is useless precisely because it is universal: the only known way of extracting the solution to one halting problem, say the Fermat conjecture, from Ω is by embarking on a vast computation that would at the same time yield solutions to all other simply stated halting problems, a computation far too large to be actually carried out. Ironically, however, although Ω cannot be computed, it might be generated accidentally by a random process, such as a series of coin tosses or an avalanche that left its digits spelled out in a pattern of boulders on a mountainside. The first few digits of Ω are probably already recorded somewhere in the universe. No mortal discoverer of this treasure, however, could verify its authenticity or make practical use of it.”

VI: Is the Watchmaker Truly Blind?

In the jacket of the book The Blind Watchmaker by Richard Dawkins, we can read the following:

“Natural selection, the unconscious, automatic, blind yet essentially nonrandom processes that Darwin discovered, and that we now understand to be the explanation for the existence and form of all life, has no purpose in mind. It has no mind and no mind’s eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of watchmaker in nature, it is the blind watchmaker.”

Darwinism, or natural selection, is the theory whereby if we accept the possibility that small changes are constantly taking place in the genetic makeup of all living organisms (we need not concern ourselves at this point on how those changes would take place), then as those changes begin to accumulate in each individual organism the competition for survival will favor those individuals whose variations have given them an advantage over other members of their same species. Thus, by fierce competition or “survival of the fittest”, Nature selects those individuals and species better equipped to survive in the long run. This in turn favors the predominance of more complex organisms and the extinction of the less fit. So goes the argument of “traditional” evolution.

There is such an overwhelming amount of evidence in favor of natural selection that even among the Catholic Church, a long-time bastion of creationism, eminent theologians are now open to discuss and accept the possibility that if a supreme being created all of the living organisms we know today, it did so through evolution and natural selection but with premeditated planning to allow such things to occur. [As John F. Haught points out in his book "God after Darwin: A Theology of Evolution", the sterile debate between Darwinian evolutionists and Christian apologists is fundamentally misdirected with both sides focusing on an explanation of underlying design and order in the Universe, suggesting that what is lacking in both sides is the notion of novelty. As we will see later, the conditions required for the creation of a Universe that will allow evolution to take place are so staggeringly specific that the odds of this event coming from out of nowhere are mathematically very close to zero (strictly speaking, the odds are not exactly zero, but they come so close to nil that they are practically nonexistent). And these conclusions do not come from any sacred texts; they come from hard facts that modern science is not able to explain away. If, as some critics maintain, religions do not provide satisfactory answers to some of the many unanswered riddles, science is in no better shape either to explain these riddles away.] Since natural selection operates entirely under its own rules, seemingly without any divine intervention whatsoever while it is taking place, the only way in which an act of creation could have paved the way for complex organisms to appear some time after the creation of the universe would have been by preparing the whole scenario from the very beginning in such a way that indeed natural selection would happen sooner or later. And this would send us back to the initial conditions that preceded natural selection itself.

Before going any further, we will take a departure to talk about a game called “Life”, devised back in 1970 by John Horton Conway, a mathematician at Gonville and Caius College of the University of Cambridge. In his book The Recursive Universe that deals extensively with some of the results obtained by carrying out the game of Life, William Poundstone states the following:

“Life is described as a game or, sometimes, a video art form. Neither label quite captures the appeal of Life. Certainly Life is nothing like familiar video games. No one ever wins or loses. Life is more like a video kaleidoscope –a way of producing abstract moving pictures on a television screen … But it’s more than that. The Life screen, or plane, is a world unto itself. It has its own objects, phenomena, and physical laws. It is a window onto an alternate universe … Shimmering forms pulsate, grow, or flicker out of existence. ‘Gliders’ slide across the screen. Life tends to fragment into a ‘constellation’ of scattered geometric forms suggestive of a Miró painting … Much of the intrigue of Life is the suspicion that there are ‘living’ objects in the Life universe. Conway adopted (John) Von Neumann’s reasoning to prove that there are immense Life objects that can reproduce themselves. There is reason to believe that some self-reproducing Life objects could react to their environment, evolve into more complex ‘organisms’, and even become intelligent … Conway wanted to create a game that would be as unpredictable as possible, yet with the simplest possible rules. Conway experimented with many sets of rules. He is said to have devised a game he called Actresses and Bishops. After further thought, he concluded that the rules could be more simplified yet. The simplified game became Life.”

The game of Life is a particular case of a much wider variety of mathematical entities known in technical terms as cellular automata. A cellular automaton is a one-, two- or three-dimensional grid of cells, with each cell representing an independent automaton which in the case of the game of Life can be in one of two states: “dead” or “alive”; and whose next state will depend on the current state of its neighbors. It is dynamic, and starting from an initial condition it will evolve according to a strict set of rules.

The rules for the game of Life are as follows:

Birth: If exactly three “live” cells are neighbors to an empty (“dead”) cell, the empty cell comes to life, and if the cell was already “alive” it will remain so.

Survival: When a cell has two “live” neighbors, it retains its current state (if it was “dead”, it remains dead; if it was “alive” it remains alive).

Overpopulation: When a cell has four or more “live” neighbors, the cell dies from overcrowding.

Underpopulation: Any cell with one or no neighboring “live” cells dies.

These rules were picked out by Conway among many other possible sets of rules in order to satisfy the following design requirements:

1. The effect of the neighboring cells in any of the cells upon which the rules are being applied is position independent, and by this we mean that it does not matter where a specific neighboring cell may be touching, whether it is touching just on a corner, above, below, to the left or to the right. Only the quantity of “live” cells actually touching a given cell matters.
2. Only the immediate neighboring cells produce an effect when going from one generation to the next. There are no rules incorporating effects from cells that are not immediate neighbors.
3. No simple patterns should grow without limit.
4. Some simple patterns should be able to grow, provided they eventually reach an upper limit.
5. A simple pattern should be able to evolve for a long time before it becomes stable.

A neighboring cell is any cell that touches another cell either along an edge or at a corner.

As an example of how the game evolves, let us start out with a square grid consisting of only 64 cells arranged as eight rows and eight columns. A “live” cell will be represented by a darkening of the cell, whereas a “dead” cell will be represented by a blank cell. Let us begin with the following initial configuration:

Figure 6.1

The reader should take some time to convince himself that if we start with the above initial condition, the pattern corresponding to the second generation will look like this:

Figure 6.2

Take, for example, the “live” cell located in the third row and sixth column of the initial configuration. Since it is being touched (in the lower left-hand corner) by another “live” cell (the one located in the fourth row and fifth column), by the rule of “underpopulation” this cell dies, and when it dies the darkened cell will be replaced by a blank cell in the second generation. Likewise, the “live” cells located in the fourth and fifth rows of the third column of the initial configuration will also die out as a result of the rule of “underpopulation”, since each one only has the other one as its sole neighbor. However, the “dead” cell located in the fourth row and fourth column of the initial configuration will come “alive” by the rule of “birth” because in the initial configuration it had three “live” neighboring cells: the two cells in the fourth and fifth rows of the third column, and the cell in the fourth row of the fifth column, and thus in going from the first generation to the second generation this blank “dead” cell will be replaced by a darkened “live” cell.

The reader should also take some time to verify that the game will evolve into the next three generations as follows:

Figure 6.3

Figure 6.4

Figure 6.5

If we keep applying the same set of rules, the line of three cells now goes into a perpetual cycle, oscillating from the horizontal pattern of the fifth generation to the vertical pattern of the fourth generation and back again. Not surprisingly, this pattern is called a blinker.

There are many other patterns, such as the glider. This pattern moves through the grid by copying itself, and in one of its possible configurations it has the following shape:

Figure 6.6

Among other interesting simple patterns we can mention, capable of evolving into more complex structures, we can cite the T-tetromino (it is made up of four live cells and is shaped like the letter “T”, resembling a similarly arranged stack of dominoes), which will develop into what has been dubbed as the “traffic light pattern” that consists of four symmetrically arranged blinkers:

Figure 6.7

An even more interesting simple pattern is the R-pentomino, made up of five live cells arranged as follows:

Figure 6.8

This amazing simple pattern will evolve into several patterns. At the 48^th generation, it will have turned itself into a pattern known as the “Herschel”. As it continues to evolve, it will take other shapes, such as the pattern known as the “Honey Farm”, besides creating and ejecting gliders. It has been found that the R-pentomino will eventually settle down into a final steady state when it has reached the 1103^rd generation, filling a low-resolution screen with 25 different Life objects.

There are still many other Life patterns exhibiting “organisms” that may be stationary, periodic, surviving, and disappearing; such as the “barge”, the “snake”, the “mango”, the “hat”, the “fishhook”, the “lake”, the “shillelagh”, the “sinking ship”, the “aircraft carrier”, and so on. There are even patterns such as the “eater” that will do precisely that: eat other patterns they may encounter.

The game of Life is usually implemented and carried out on personal computers; and the grid normally contains some 20,000 or more cells (containing at least some 100 horizontal rows by 200 vertical columns) [many interesting executable programs for John Conway's game of Life are available throughout the Internet (for free!), so if the reader wishes to expand experimentally his knowledge and experience of cellular automata, or is just interested in playing around with this type of technical gadgets, the World Wide Web is a good place where to start hunting for them. Just be sure to search under the topics "game of Life" or "cellular automata"], so there’s plenty of room to create many interesting initial patterns. At this point, the reader may be wondering if there could be other rules we can devise to try to come up with other variants of the game of Life. However, the reader can verify for himself that some of the possible alternatives will lead to nothing of interest, regardless of how the initial patterns are defined to be. To cite just one example, perhaps the simplest, assume that the rules for a new game which we will call the “game of Nothing” are defined as follows:

Birth: If a “dead” cell has one or more neighbors, the cell comes to life.

Survival: If a “live” cell has one or more neighbors, the cell remains alive.

Death: If a “live” cell has no neighbors, the cell dies.

If we start out with a completely blank grid, filled with “dead” cells, it will remain forever blank. Nothing will ever come out of it. If, on the contrary, we start out with a grid completely filled up with “live” cells, the grid will remain forever stagnant. The only way we can extract some action is to start out with at least two “live” cells touching one another. But, alas, this pattern will quickly grow from a small blot in the screen to fill up the grid completely in just a few cycles, with nothing interesting happening “in-between”. No oscillators, no gliders, no nothing. And if we start out with other complex patterns, their fate is sealed even before the game starts, since we know they will eventually and very quickly disappear into a big blot or vanish into a blank grid. We can predict the two possible outcomes with absolute certainty, and we do not even have to set things into motion to foretell the two possible outcomes.

It should now be crystal clear that in order to make it possible for certain complex patterns to evolve into many interesting shapes and situations, the starting patterns are not enough; an adequate set of rules are also needed. Taken in conjunction, the initial patterns and the rules of the game are both the necessary and sufficient initial conditions for an interesting game to evolve. Once the initial pattern (or patterns) on the entire grid has been chosen, everything else will take place entirely on its own, and all we have to do is just sit back and watch as the drama of our creation unfolds.

A much more interesting game of Life would be one in which each cell can take not just one of two possible states but perhaps ten or even a hundred different possible states, with each state being represented by a different color out of the many different possible colors available from a rainbow. Thanks to the widespread availability of fast modern personal computers, this is actually being done throughout the world, and is the subject of intense and active research. Even with all that has been discovered to date regarding these cellular automata, there is the firm conviction among researchers that we have barely scratched the surface. More about this will be said in the next chapter.

An even more interesting variation would be one that, besides allowing for a cell to take many different possible values instead of just two, would also allow us to use a three-dimensional grid instead of the flat two-dimensional grid we have used so far. But then, if we call each cell an “atom”, wouldn’t this start to resemble a game much more familiar to us, the honest-to-goodness true game of everyday LIFE itself?

Again, as in the case of the much more simple game of Life devised by John Conway, we suspect and indeed can quickly verify that the evolution of an interesting three-dimensional multivalued game of Life will depend solely not just upon the initial patterns we choose to put into our three-dimensional grid, but also upon the way in which the rules of the game are written. In such a game, if we use the following rules (to cite an example):

Birth: If a non-colored cell (completely blank) has one or more neighbors with any color, the cell will come “alive” taking at random any of the many possible colors available, regardless of the colors of its neighbors.

Survival: If a colored cell has one or more neighbors that are also colored, then the cell will remain “alive” retaining its original color.

Death: If a colored cell has no colored neighbors, the cell will “die” going blank.

We can verify for ourselves that this apparently more complex game will quickly lead nowhere. The three-dimensional multivalued grid will go completely blank in just one single step, or it will quickly fill up with a stagnant assortment of variegated cells, in spite of the fact that we have introduced an element of chance into the game by allowing a cell coming to life to take at random any of the possible colors available in the game.

The conclusion is inescapable, and we cannot avoid it. The only way in which a cellular automaton such as the game of Life can allow interesting patterns to evolve and interact is by using an adequate set of rules. The rules and the initial patterns are both the necessary and sufficient initial conditions for this to happen, whether we throw in or not an element of chance into the game. For a much more complex game such as this one, it stands to reason that the initial conditions need to be chosen with the utmost care among a myriad of possible choices; otherwise we may quickly end up with stagnant scenarios or dead universes with nothing worthwhile happening “in-between”.

When specifying a cellular automaton, we can take one of two different approaches: either the naturalist approach, or the engineering approach. If we take the naturalist approach, then we are really just experimenting, trying out a specific combination of rules and initial patterns just to see what may come out of it as the patterns begin to evolve, perhaps waiting to see if order will arise out of chaos. A naturalist is primarily looking for patterns that may occur naturally as the cellular automaton evolves. But when we take the engineering approach, we are then trying to build our rules and initial patterns with some specific purpose in mind, we expect that our creation will be equipped to carry out some anticipated actions, most likely complex actions. The naturalist approach requires no more than an observer, whereas the engineering approach requires a designer. When John Conway came up with the game of Life, he took an engineering approach; he very definitely had some specific objectives in mind that he wanted to accomplish. The naturalist approach requires a tinker, whereas the engineering approach requires a clever designer (perhaps extremely clever!).

In his book The Age of Intelligent Machines, Raymond Kurzweil cites a quotation attributed to Robert Wright in a comment to Edward Fredkin’s (former head of MIT’s Laboratory for Computer Science) theory of digital physics (according to the theory of digital physics, the ultimate reality of the world is information processing–or software- and thus this reality should not be described as particles and forces like the atoms and the force of gravity but as bits of data that are being modified constantly in accordance with prescribed computational rules):

“Fredkin…is talking about an interesting characteristic of some computer programs, including many cellular automata: there is no shortcut to finding out what they will do. This indeed, is a basic difference between the ‘analytical’ approach associated with traditional mathematics, including differential equations, and the ‘computational’ approach associated with algorithms. You can predict a future state of a system susceptible to the analytic approach without figuring out what states it will occupy between now and then, but in the case of many cellular automata, you must go through all the intermediate states to find out what the end will be like: there is no way to know the future except to watch it unfold…There is no way to know the answer to some question any faster than what’s going on…Fredkin believes that the universe is very literally a computer that is being used by someone, or something, to solve a problem.”

Grudgingly voicing a similar opinion, Frank Wilczek and Betsy Devine in their book Longing for the Harmonies write:

“We therefore suspect, from its design, that our world just might be an intricate program working itself out on a gigantic computing machine. This form of paranoia may seem extravagant and, of course, doesn’t get to the bottom of explaining the world. We would still need to understand the principles on which the computer was built. For instance, if it is made of silicon, why do the electrons in that silicon obey the laws of physics –are they perhaps fantasies in yet another computer? … Nevertheless, it may not be completely useless to follow up on this suspicion. First of all, it does begin to address the great ‘why’ questions in a rational, if possibly mistaken, way. Second, it suggests a fascinating new sort of question: How would errors in the workings of the computer show up? Could we look for them systematically, by experiments, and thus put the idea of an underlying machine to a scientific test? … Finally, and perhaps most important, thinking along these lines will help prepare us for the day when we –or, more likely, our distant descendants- will develop the machinery and cleverness to begin to program worlds ourselves (and watch –with what feelings? –as the inhabitants of those worlds come to start suspecting …).”

Let us now go back to our discussion of natural selection. Richard Dawkins writes the following near the end of his book The Blind Watchmaker:

“The whole book has been dominated by the idea of chance, by the astronomically long odds against the spontaneous arising of order, complexity and apparent design. We have sought a way of taming chance, of drawing its fangs. ‘Untamed chance’, pure, naked chance, means ordered design springing into existence from nothing, in a single leap. It would be untamed chance if once there was an eye, and then, suddenly, in the twinkling of a generation, an eye appeared, fully fashioned, perfect and whole. This is possible, but the odds against it will keep us busy writing noughts till the end of time. The same applies to the odds against the spontaneous existence of any fully fashioned, perfect and whole beings, including –I see no way of avoiding the conclusion- deities … To ‘tame’ chance means to break down the very improbable into less improbable small components arranged in series. No matter how improbable it is that an X could have arisen from a Y in a single step, it is always possible to conceive of a series of infinitesimally graded intermediates between them. However improbable a large scale change may be, smaller changes are less improbable. And provided we postulate a sufficiently large series of sufficiently finely graded intermediates, we shall be able to derive anything from anything else, without invoking astronomical improbabilities. We are allowed to do this only if there has been sufficient time to fit all the intermediates in. And also if there is a mechanism for guiding each step in some particular direction, otherwise the sequence of steps will career off in an endless random walk … It is the contention of the Darwinian world-view that both these provisos are met, and that slow, gradual, cumulative natural selection is the ultimate explanation of our existence. If there are versions of the evolution theory that deny slow gradualism, and deny the central role of natural selection, they may be true in particular cases. But they cannot be the whole truth, for they deny the very heart of the evolution theory, which gives it the power to dissolve astronomical improbabilities and explain prodigies of apparent miracle.”

Let us assume that, in order to watch our rudimentary “life” forms evolve, we have a digital computer at our disposal and a monitor (preferably a color monitor, though this is not mandatory). We must now ask ourselves again the very important question: Can primitive, rudimentary patterns resembling some of the happenings which take place in ordinary life (such as moving around while preserving shape, competing, coming together, eating neighbors, etc.) be expected to appear spontaneously after the simulation has started? The answer is a definitive YES. If we have already started out with a given set of initial conditions, and if the rules of the game are followed rigorously with no deviation whatsoever, then what seem to be primitive “life forms” may indeed show up in the screen of our monitor or whatever other scenario in which the simulation is taking place.

Simulations that can produce these primitive patterns resembling life forms have sparked the imagination of many computer programmers allowing them to consider the possibility of creating within the bits of software flowing inside a digital computer what has now been dubbed A-Life or “Artificial Life”.

But, wait a minute!

The assumption that out of sheer randomness we can expect to see primitive “life form” patterns evolve in the monitors of our computers is whimsical at best. Earlier we have noted that in order to carry out the computer simulations with some degree of success it is important that the rules which we will now call “natural laws” be followed rigorously throughout the simulation. Any alteration of the rules in the middle of the simulation will most likely ruin our simulated evolution. And if the rules are being followed precisely down to the letter, there is nothing random about the way in which the game is proceeding.

On the other hand, in order to happily watch our rudimentary life forms evolve, the margin of error for each calculation inside our computers must be zero. If just a single bit out of the many thousands or perhaps hundreds of thousands of bits is interpreted as a zero instead of a one or a one instead of a zero (this could happen if a very small portion inside one of the memory chips of the computer is starting to experience electrical failure), then this may be enough to bring our simulation into ruins. The margin of error allowable inside the computer for the correct simulation (or evolution) to take place is zero. This requires a computer that works correctly not just 90% or 99% or perhaps 99.999999% of the time, but 100% of the time. The reliability of the computer must be 100% throughout the simulation. Anything less will just not do. And there is nothing random about this. Reliable machines are designed on purpose to be reliable, and the warranty each machine carries with it is a tribute to this fact. Furthermore, if we take a look at the entrails of our computer, from the major components all the way down to the microscopic integrated circuits, we can bear witness to the fact that there is absolutely nothing random, nothing left to chance about the way in which a computer is built, and everywhere we look inside we find evidence of the knowledge and intelligence possessed by those who designed the building blocks of our computer. Something as sophisticated as a modern personal computer cannot be produced by random chance alone either here or anywhere else in the universe, regardless of how long we may wait for such a thing to happen. And this is the very substrate that we are using to let our “game of Life” evolve! The designers of personal computers, far from being “blind watchmakers”, are for the most part people with college degrees, many of them with advanced degrees in fields such as solid-state physics and electronics engineering.

Likewise, the mathematician or computer programmer who creates on purpose the rules for the game of Life or any other similar cellular automaton game turning those rules into precise steps that will have to be obeyed rigorously by the computer since the simulation begins is no “blind watchmaker” either (as we will see in the next chapter, the selection of the rules out of a vast universe of possibilities will almost certainly demand a good degree of cleverness from the creator). True, he may not be fully certain as to how a particular game will evolve with certain patterns once those initial conditions have been chosen. But at all time he has full control over the experiment, and if he so chooses he can stop the simulation and modify the initial conditions in order to carry out a different simulation, using his free will and his intelligence to carry out his plans. There is absolutely nothing we can find to be random here either.

So much for the supposed “randomness” which the game of Life is assumed by some to have!

So, the answer to the question “Is the watchmaker truly blind?” depends on the extent to which we define the watchmaker. If we exclude all of the initial conditions from the big picture and assume that all of the necessary conditions for evolution to take place (the right temperatures, an adequate atmosphere, enough diversity of chemical elements and compounds to allow in time for complex systems to assemble and evolve out of simpler ones, enough usable energy sources to overcome the second law of thermodynamics and beat large overwhelming odds, etc.) have been handed down gratuitously from out of nowhere, then indeed the watchmaker is as blind and as dumb as it can be; just as in the game of Life where once the existence of a computer or any other equivalent medium in which to carry out the simulation is assumed and the rules have already been given, then the evolution of the game itself will be an automatic process which will inevitably take place even without the presence of any intelligent being to witness it. But if we draw into the big picture the initial conditions themselves, then the only way in which the watchmaker can still be considered to be blind is to assume that the initial conditions themselves are also blind, coming out of nowhere and perhaps rearranging themselves without any help very much as we would expect from any evolutionary process. We have already seen that the very substrate in which an interesting game of Life is played out obeys strict rules which leave nothing to chance; and the machinery itself in which the game runs, far from being a random contraption, bears the mark of an intelligence more advanced and complex than any pattern which might appear and evolve on the game of Life grid. Even a blind watchmaker such as evolution will not be able to assemble a mediocre watch if it doesn’t have any usable parts to begin its work. The real “brains” must be found in the initial conditions that are being prepared for the drama, not in the actual unfolding of the drama itself. If the minimal initial conditions necessary for evolution to take place at some point in time are not there, there will be no evolution, regardless of how many billions or trillions of years have elapsed. Evolution is as dependent upon the initial conditions for its own survival as we are dependant upon the very air we breathe to carry on.

We praise the hardware allowing Windows, Linux and the Internet to run on personal computers as the end result of intelligent engineering, yet many despise the substrate allowing ourselves to run as as the end result of something that according to them cannot even be classed as dumb, a Janus-faced attitude with which many of these skeptics somehow manage to feel comfortable and sure of themselves. Or at least that’s the image they seem to project.