In trying to design our own universe, we are faced with what may be a major limitation: our own system of logic, the logic we use in everyday life. The way our minds operate within the confines of this universe is firmly rooted upon the logic of Aristotle, a logic that itself is based upon the law of the excluded middle: any given statement can either be true or false, but it cannot be true and false at the same time. There is no “in-between”. A middle between truth and falsity is completely excluded, hence the name of the law.
But recently, we have come to the realization that there are other types of logic besides the logic of Aristotle, each with its own set of rules and axioms, each capable of providing results that can be stated mathematically. Among these logics we must cite fuzzy logic, a logic that derived with a now classic paper on fuzzy sets published in 1965 by Professor Lofti A. Zadeh. Fuzzy mathematics provides the framework to deal with phenomena that are vague, imprecise, too complex, or that cannot be subjected to analysis with the conventional means. And nowadays fuzzy logic is no longer a concept confined to the classroom as a mathematical curiosity in the hands of students pursuing an advanced degree in Mathematics. Quite the contrary, fuzzy logic has found its way recently into many industrial applications. Another example of a logic that departs from the logic of Aristotle is quantum logic, one of whose foremost exponents is David Finkelstein, head of the School of Physics at Georgia Tech. Let us quote again from the book Quantum Reality by Nick Herbert the following passage attributed to science philosopher Ariadna Chernavaska:
“Suppose we pass cattle through a gate which only lets through horses and rejects all cows. Next we pass these horses through a second gate which lets through only black animals and rejects all white ones. Only animals which are both horses AND black can pass through both gates. To our surprise, approximately half of such animals turn out to be cows! Of course, cattle don’t behave this way, but if we believe the quantum logicians that’s exactly what happens to polarized photons when they go through little sheets of plastic. A photon’s attributes obey a non-human logic which we must learn to understand if we want to make sense of what’s really going on in the quantum world.
It is possible that Aristotelian logic is valid all the way up to the very moment when the Big Bang took place. It is possible that it still remains valid even before the Big Bang took place. But if this is not the case, then all of our efforts in trying to go back in time to a time when time itself did not even exist (does this logic make any sense to you?) are doomed to certain failure, as if we were blindfolded by our own mode or reasoning, and only by breaking away from the mold would we be able to aspire to make some progress. We believe that our logic must be the same in every possible world, that there is no possible world were a statement can be true and false at the same time, where 5 plus 9 always equals 14 all the time and where the order of multiplication does not alter the end product; until we are confronted with fuzzy logic statements where a given statement can be 60% true and 40% false, and where this type of statements can actually be combined under the rules of fuzzy logic. Likewise, many students of higher Mathematics must come to terms with other types of arithmetic such as modular arithmetic where 5 plus 9 may not equal 14 but instead may equal something like 2 (if it’s 5:00 o’clock in the morning then nine hours later it will be 2:00 o’clock in the afternoon, unless the dial clock hanging in the office has a 24-hour span, and even then beyond the 24 hours it will start again from zero instead of continuing upwards). Or fields of study where the product of two non-zero elements will yield a zero element (this happens all the time in matrix arithmetic), and where the order in which the “multiplication” is carried out does matter (the operation “a•b” will not necessarily give the same result as “b•a” in operations involving matrices or non-commutative elements from certain groups studied in group theory). So we must accept the fact that we are rather limited in our design capabilities to what we are mostly familiar with, and if there are other possibilities those possibilities are beyond our reach and beyond our way of thinking and beyond our system of logic.
We have already seen that in the process of assigning values to the physical constants of the universe we are designing, we may have some freedom of choice. There is the possibility that we can assign independently a numerical value to each physical constant, or as an alternative we can try to manipulate the rules from which each physical constant would be derived from another more fundamental entity so as to force each physical constant to take the value we so desire. Having agreed upon this, the next important question would be: How many physical constants are we going to preordain? Five? Ten? Twenty? One hundred? This is another issue that even at this very moment we are unable to address completely with our current knowledge. Among the things we would like to set “straight” from the very beginning perhaps we should include the following:
The universal constant of gravitation G.
The speed of light c.
Planck’s constant h.
The physical constants that describe quarks.
The physical constants that describe leptons (small particles like the electron).
besides other bric-a-brac. Notice that we have not included in the above list things such as the mass of the neutron and the charge of the proton. This is because, according to current models, neutrons and protons are “derived” entities that are made up of the more “fundamental” entities we call “quarks”, and that the force that binds them together can be described in terms of other particles called “gluons”. Thus, if the more “fundamental” entities have their values assigned from the very start, when they get together to form other particles such as the neutron, the proton, the mesons and many other different subatomic particles all those “derived” particles will come up just with the values we expect them to have. Let us assume that we have the most advanced theoretical model in our hands and that this model tells us very clearly that we need to specify independently a total of sixty different “fundamental” physical constants. Among those constants it is very likely that the speed of light will have to be included. For the universe we live in, we have already stated that the known experimental value is close to:
c = 299,793,000 meters per second
This is more or less the value that we have been able to measure. But the value we have been able to measure for the speed of light is most certainly not known to an accuracy of, say, twenty or thirty significant figures. If we had much more sensitive measuring instruments, perhaps our known value for the speed of light would be something like:
c = 299,793,000.005,457,235,293,487,238,498,347,934,798,347,974 meters per second
The digits shown above are unknown to us not because they are not there, but because we are unable to measure with such a precision. The existence of those additional digits and the many digits that follow (infinite?) has to be accepted as a fact of life, just as we accept the fact that the square root of two can only be written out in the decimal number system (or any other numerical system we can think of) with a never-ending string of numbers.
In order to come up with a universe just like the one we live in, we need to specify for the speed of light as an initial condition the exact same value it now has (we are assuming that the value for the speed of light is an absolute constant that has never changed since the moment of creation). The astute reader will immediately grasp the implications of this. We are not talking about an approximation correct to something like fifty or a thousand significant figures. We are talking about the exact same value, all the way down to infinity itself. Let us take a more mundane approach and assume that the best we could ever do here would be to set for the speed of light the following value:
c = 299,793,000.005,457,235,293,487,238,498,347,934,798,347,973 meters per second
Compare this value with the value given above. It is off with respect to the one above by only
0.000,000,000,000,000,000,000,000,000,000,000,001 meters per second
With such a small difference in the “known” value for the speed of light, and assuming all other physical constants retain exactly the same values as the values they already have in this universe, could we expect the alternate universe to be almost identical to our own universe? Most probably not. Indeed, we could end up with a completely different universe. We have already stated that the equations for general relativity are nonlinear. To make matters worse, the value for the speed of light appears very explicitly in those equations (it is not usually “seen” by newcomers written out because of the use of so-called “normalized” units that assign to the speed of light a symbolic value of c = 1, although in actual calculations the full “real” numerical value has to be used in order to make experimental predictions). And remember, we are assuming they begin to act almost immediately after the birth of the universe, when everything is just starting to expand from a state of almost infinite density. In such a state, with all matter and energy and space and time (and everything else) tightly tied together at close range, any nonlinearity in the equations that govern the behavior of this almost infinitely dense state will most likely amplify enormously any difference, however small, there might be in the initial conditions that precede the primeval explosion of the alternate universe from the initial conditions that preceded the primeval explosion of this universe, and as time goes on the amplification effect keeps on growing. When Edward Lorenz came to the conclusion that long-range forecasting was impossible when he used a set of nonlinear equations to model the atmosphere, his simulations showed the differences becoming more and more obvious after just a matter of “simulated” days. In our case, we are talking about a total lapse time that runs in the billions of years, more than enough time to amplify the smallest numerical differences we could possibly ever imagine in our wildest dreams. This means that, unless we can set the accuracy of our initial conditions such as the speed of light exactly (all the way down to an infinity of decimal digits!) to the same values this universe had at the moment of its creation, with an infinite level of precision, we will never be able to create a universe even remotely similar to the one we are living in right now. It is possible that an alternate universe with a very small difference in its initial conditions from the values we had in our own initial conditions might still manage to develop stars, galaxies, solar systems, neutron stars, pulsars, black holes, comets, etc., in an entirely different arrangement from the arrangement we observe in our universe. But knowing that nonlinearity has the potential to introduce a lot of unexpected surprises (such as allowing the appearance of dissipative structures that seem to defy the second law of thermodynamics), the only way to know for sure what would come out with a different set of initial conditions would be to actually build such a universe as if it were a giant computer program and run the program to see what happens; unless we are all-knowing, capable to exist simultaneously in the past, the present and the future at the same time in which case we could be true creators to the fullest extent of the word by fixing the initial conditions rigidly so that certain things will (instead of may) take place. An inventor who cannot anticipate the behavior of his contraption becomes really just an observer, whereas an inventor who knows beforehand every possible outcome and adjusts the initial conditions of his experiments accordingly to force a certain outcome becomes a bona-fide designer. For a grand scale complex project, it would appear that being able to exist in the past, the present and the future at the same time would be the only alternative to steer a project in a certain direction from the very beginning.
And why not? Yes, it is inconceivable for most of us to accept the possibility that we could exist at the same time in the past, the present, and the future, because we are three-dimensional beings confined to living in linear time. [In linear time, the "past" always comes before the "present", and the "present" always comes before the "future"; and past, present and future are unable to coexist simultaneously.] But for a multidimensional being existing above the rather limited number of dimensions we seem to have at our disposal that would be no problem whatsoever. We ourselves know that it is possible for our minds to digest simultaneously different sources of information and still make sense out of it. Someone who is driving his car can pay close attention to the road where he is driving and at the same time listen to the radio and enjoy his favorite music and at the same time smell the warm pizza he has just bought. Performing these three different activities at once is second nature to him because the mind has a wonderful capability, which is called multiprocessing. This is one major difference between the electronic digital computers that work their way through a sequence of millions of preprogrammed instructions one-by-one and us. Our eyes each moment take simultaneously millions of bits of visual information (instead of one-by-one), and that information is processed simultaneously by our minds, enabling us to act accordingly. For a person deprived of all of his senses except his vision, driving a car and listening to the radio and smelling the warm pizza all at the same time would seem to be an almost inconceivable feat. That person would assume that such activities would necessarily have to be done individually one-by-one in order not to be confused. To that person it would be as unimaginable to be able to do all such things at once as it would be unimaginable for us not to be able to do them. Of course, trying to explain the sense of hearing to a person who has been totally deaf since birth would be like trying to explain the meaning of colors to a person who has always been blind. It is the lack of senses what limits our intellect from conceiving other possibilities, even though those possibilities may be a reality, a reality currently beyond our reach.
The possibility of being able to look into the past, the present and the future simultaneously should not be confused with what has come to be known to many as the “gift of prophesy”. Some people among whom we can cite the Irish-born Saint Malachy who lived in the 12th century, the French physician Nostradamus who lived in the 16th century, and the more-recent American Edgar Cayce, have claimed to have been able to look into the far-away future by predicting the outcome of certain world-wide events. Whether these men could actually predict future events with an accuracy that cannot be accounted for by assuming lucky guesses is something that will be left for the reader to decide. The crux of the matter here is that all these prophets and clairvoyants, during their moments of “rapture” when they were receiving their visions, were still trapped within the limitations of linear time. Even if they could become mentally detached from their bodies while their minds were receiving images of future events, mentally they were also detached from the present during their visions. The human brain is just not built with the capability to process images from different time frames simultaneously, and the same can be assumed to hold true for all other seers, prophets, and whatever.
It sometimes comes as a surprise to many that there actually is one way of looking at the past, the present and the future all at the same time. Take for instance the motion of an object that is moving on a plane. The position of every single object in our universe can be determined uniquely by using a set of Cartesian coordinates and locating the distance of the object with respect to an agreed-upon reference point. Thus, with respect to that reference point, the object could be located by moving ten meters to the right from that reference point (a motion in the x-axis corresponding to the dimension of length), and then moving five meters in a direction above that reference point (a motion in the y-axis corresponding to the dimension of width), and finally moving three meters at a right angle from the plane that contains the x and y coordinates (a motion in the z-axis corresponding to the dimension of depth). If we agree to restrict the motion of the object to a plane (two dimensions) then the trajectory of the object could be plotted on a flat sheet of paper, just as we were able to describe the jump trajectory of the rider on Chapter One with a curve, the parabola. However, if we draw another axis perpendicular to the plane, a time axis, then we are able to draw the location of the object for every instant of time and visually see not just its position along the plane but also the actual passage of time as if it were a “still” picture. In effect, the three-dimensional curve would allow us to look simultaneously at the past, the present, and the future, all at the same time. This curve is commonly referred to as the world line for the object. Unfortunately, if the motion of the object is not confined to a plane but is instead a motion in three-dimensional space, then in order to include the time parameter we would require a four-dimensional plot. But our brains are physically limited to perceptions restricted only to three dimensions, not four. A being capable of perceiving at least four dimensions simultaneously would have no problem in looking at the past, the present and the future simultaneously, and then the problem of making the past “fit” to make certain future events possible would be reduced to a geometrical problem. A very crude point of comparison would be the rider trying to jump the ditch on Chapter One. We saw there that the passage of time was not the decisive factor in determining the minimum jump speed required to clear the ditch, that the problem was really a problem of geometry, of trying to make the parabola that describes the jump trajectory fit the end points. Once the parabola has been made to fit, the jump speed is automatically set. This becomes possible because the parabola that describes the motion of the rider is in a sense a projection of the “world line” of the rider, enabling us to look simultaneously at his past, his present and his future. It goes without saying that the capability to “see” in four dimensions or more would automatically make it possible for a higher intelligence to design a universe and perceive the long-range outcome simultaneously in such a way that the images of the future could be used to modify the initial conditions of the images of the past allowing an immediate evaluation of the long-range outcome in the future that could be used in turn to “fine-tune” the initial conditions of the past, and so forth, all simultaneously. The consequences of such capabilities would be well beyond our comprehension, for they could make it possible in principle to modify at this very moment some of the early initial conditions in the past that has already gone by in order to produce certain results in a future that has not yet arrived. To us this may sound impossible and incomprehensible. But then, we must ponder on the fact that to a blind man the possibility of something like the colors of the rainbow will also sound not only impossible but also incomprehensible, and without any vision capabilities of his own to experience the sensation of color no amount of explanation we might try to give to the blind man will suffice to convey him the exact idea of what a color really is.
In closing this chapter we must keep in mind that all of our current knowledge is based on experimental data and theoretical models which in spite of their current success may very well break down entirely at the moment the Big Bang took place, cast aside by some other physical laws yet-to-be discovered valid perhaps only at the very moment of creation were our concepts of space-time appear to vanish into thin air. Extrapolating without justification our current knowledge into limits that defy our limited comprehension may put us in the same spot as an artificial intelligence scientist who upon climbing a tree on his backyard has become firmly convinced he has taken the first step to go to the Moon.
