Kurt Gödel, in a paper published in 1931, proved that any mathematical system that includes the natural numbers (1, 2, 3, and so on) contains questions whose answers can neither be proved nor disproved using the axioms to be found within that system. This is now known as Gödel’s Incompleteness Theorem. It implies that there are many mathematical truths that can never be proved, and, by extension, that any system will contain questions that cannot be answered from within that system. Since any meaningful questions that we might ask about the nature of any possible supersystem will inevitably involve use of the natural numbers, there are questions we will never be able to answer. Asking if our universe was “designed to meet some kind of purpose,” is just one such question.
Another way of using Gödel’s theorem to address why one is unable to understand everything from within a system, is as follows. A system is complete when all statements (or their negations) can be proved from within that system. Systems can be proved to be consistent, i.e. free from contradictions, but only by involving a larger frame of reference, which then requires an even larger system to prove its consistency, and so on. In short, we require information that is only available from outside of our universe to determine the accuracy of any answer to any question that can be raised within the universe. In other words, we can never know the answers to questions like, “does God exist?” or, “what is the universe’s purpose in existing?” because we cannot obtain information about what exists beyond the boundaries of our universe.
In effect, Gödel is saying that we can never know anything fully and completely. Thus, even the very best of our scientific understanding is ultimately unverifiable.
Some might say that if this is true, then what is the point of doing anything. Why bother to develop a universal religion, for instance? The answer, of course, is that we need one just as much as we need an understanding of how things work, because both improve the quality of our lives. Time enough to stop doing our best after we are dead!
General Systems TheoryEdit
The basic concepts underlying General Systems Theory are simple, once the terms employed are recognized and their meaning understood. The theory’s power stems from its generalisability, for all systems (whether living or non-living, small or large) demonstrate the same principles.
General Systems Theory can be summarized as follows.
A system is a processing complex of interrelated parts that acquires supplies and turns them into something else. Thus, a person can be called a system, for each individual takes in oxygen, nutrients and water, processes them, and turns out movement, growth, and bodily waste. A factory can be called a system, for it takes in raw materials and energy, carries out operations, and turns out manufactured goods and waste.
Physical and biological systems exist everywhere; they range in scale and form from primitive Archaean life to galactic clusters, and the same systems terminology applies to all.
No system within our universe is “closed.” In other words, there is no system within the universe whose boundary is impermeable to everything. For example, the Earth receives and processes energy from the Sun; the Sun was formed from earlier Milky Way galactic dust, and radiates energy that interacts with the galaxy’s particles; all galaxies exert gravitational pulls upon one another (so their motions are interdependent), and so on. An alternative way of expressing this property is to state that all systems are “open.”
Thus, all systems (except, possibly, the universe itself) are subsystems of larger supersystems, and, in particular, the biological system is a subset of the physical system. In other words, life is a subsystem of the universe.
We cannot tell if our universe is a subsystem of a larger universe. If there is no linkage to anything external, if the universe is entirely self-contained, and neither takes in nor gives out any form of material, then it is closed. If our universe is somehow related to (i.e., exchanges information, energy and/or matter with) a larger Universe, then it is open.
Systems are dependent upon, and thus controlled by, their various supersystems. This fact becomes readily apparent when a system can no longer obtain needed resources from its environment (its supersystem) and shuts down. It is also demonstrated when a system’s outputs are so excessive or aggravating that its supersystem (its environment) can accept no more, and the resulting back-pressure (a.k.a. feedback) shuts down the system’s operations.
The criteria that determine what we can do, or what we are able to produce, are all to be found in the way our supersystems react to our behaviour. Our supersystems can reject (partially or fully) or accept (partially or fully) our outputs. (For example, a rejection by family, friends, employer or society can soon effect our welfare.) Conversely, supersystem acceptance creates the demand for more of the same output and thus encourages more of the same processing activity.
General Systems Theory terminology can be used to increase our understanding of the problem-solving and decision-making processes described in Solving Problems and Making Decisions. Thus, the supersystem (earlier termed the environment) provides the criteria that determine the success or failure of its subsystems’ behaviours. Physically existing supersystems exhibit and enforce many real criteria, and we make practical decisions successfully by knowing and respecting these. Similarly, mentally existing supersystems (i.e. major constructs) exhibit and enforce many abstract criteria, and we make moral decisions successfully by knowing and respecting these.
The Conservation LawsEdit
As the Conservation Laws have been referred to several times in the text, it might be useful to say a little more about them.
Conservation Laws state that, amid all the changes that occur throughout the universe, certain quantities and qualities (for instance, the total amount of energy/mass, momentum, charge, spin, parity, etc.) are always conserved. The value of each (although not necessarily the form) after an interaction is always the same as the value of each before. These laws explain why, for instance, a perpetual motion machine cannot be built. (Interacting system-parts generate heat which is lost to the surrounding environment. Thus the machine loses energy and eventually stops.) Conservation laws explain why there is a property we call inertia. (We feel a force termed inertia when, for instance, we push an object to start it moving. Accelerating an object in this way changes its velocity, and this means we have added to its momentum. Since momentum must be conserved, it must be taken from somewhere; in this case from our hand and body, and, ultimately, from the Earth, reducing its spin (i.e., its angular momentum) a tiny fraction. The inertial force we feel is our body’s reaction [Newton’s Third Law of Motion] to the force that transfers momentum from the Earth to the object.)
The several Conservation Laws are likely to be sub-manifestations of one comprehensive law that we have not yet discovered. Superstring theory may soon be able to tell us more, not only about the Conservation Laws, but also about why certain physical constants are just right for our universe to exist and to create and nourish life. Superstring theory, in Witten and Townsend’s M-theory version, can now account for the existence of the known forces (gravity, electromagnetic, strong and weak nuclear), showing that they may all be derivatives of minute vibrating strings 10-35 meters or less in length, and existing in either 10- or 26-dimensional hyperspace. Superstring theory exercises the minds of many physicists and cosmologists (the first group, because it may be the elusive TOE/GUT [Theory Of Everything or Grand Unified Theory] long searched for, and cosmologists, because it predicts and allows for the existence of other universes.)
Some seemingly inexplicable phenomena (such as the behaviour of virtual particles, or the instantaneous transmission of quantum states, as well as time-travel and teleportation [both recently demonstrated to exist]) might represent a window through which we may glean a little knowledge about the possible existence of any such super-universes.
Our universe may be just an adjunct of a larger Universe, with the larger Universe retaining ultimate control. Control by a super-Universe could be rigid, creating nothing more than a fully deterministic sub-universe if the connections between the two were entirely inflexible. However, this seems not to be the case. Wave/particle duality and the laws of conservation allow minuscule events unlimited freedom to act, as long as conglomerate activities obey the conservation constraints (see also the earlier discussion on free will).
Alternatively, our universe’s existence could be simply a manifestation of nothing, just as branches of mathematics can be created from definitions rather from actuality. All that is needed is for the whole to sum to zero, and that sum to be maintained regardless of how its parts manifest or become manipulated (a condition maintained by causality and described by the Conservation Laws).
- Ludwig von Bertalanffy, General Systems Theory: Foundations, Development, Applications (New York: George Braziller, 1968).
F. Kenneth Berrien, General and Social Systems (New Brunswick: Rutgers University Press, 1968).
- Pairs of “entangled” photons (i.e., identical entities that share common origins and properties) have been separated and sent along optical fibres in opposite directions a distance of ten kilometres before being made to randomly choose and take one of several, equally possible, paths. The two photons always make identical decisions, even though the distance separating them when this decision is made greatly exceeds the distance any form of radiation could travel in the time available to make the choice. In fact, identical random decisions are apparently made instantaneously. (This behaviour is already being discussed as the possible basis for an uncrackable encryption code that the military or banks might use.) Although predicted by quantum mechanics, the phenomenon has yet to be understood. An external Universe might be just what’s involved, with information that controls supposedly random behaviour being instantly passed through to our universe, in a way that makes this information appear to us as being in two places at once. If this is the case, then our universe is actually (although possibly restrictedly) open.
A team of Australian scientists have recently teleported a laser beam; that is, they destroyed it in one location then reconstructed its identical copy in a new location, one meter distant.
(Also see Anton Zeilinger, “Quantum Teleportation,” in Scientific American, April 2000, 50-59.)
- It is intriguing to recognize that causality and the Conservation Laws implies that our universe is always retaining the ability to return to any of its earlier forms.