by Daniel Romm
“This is all very interesting but also very confusing. Can we ever be certain of anything?”
“Not unless we acquire, perhaps through mutation or invention, a sufficient set of sensory receptors and modes of thought. At any given time there may be many hypotheses or theories that have thus far passed every test but they are and will always be only provisionally true.”
“Even quantum theory? It's so weird and distasteful to physicists that hundreds have designed experiments to discredit it. Consequently it has been exposed to far more trials than any other theory yet has passed them all with flying colors.”
“Nevertheless, there's still a chance it too will be proven wrong in some respect. Even Newton's aforementioned law of gravity, although seemingly infallible, had to be augmented by Einstein's general relativity before it could account for the perihelion of Mercury's orbit. Furthermore, although quantum theory passes all current tests, we may come up with a different theory tomorrow that also passes the same tests. Then we would have two concurrently ‘true’ theories, only one of which will prevail as more tests are performed.”
“Using Ockham's razor wouldn't we go with the simplest, the one requiring the fewest assumptions, until one or the other eventually wins out?”
“Yes but simplicity doesn't make a scientific theory any truer. Our minds can only comprehend phenomena by lumping them under as few categories as possible, so we are all reductionists by nature. We seek one inclusive label like ‘dog’ or ‘cat’ or ‘tree’ or ‘triangle’ or ‘chair’ with which to name many similar individuals, none of which are identical. Without the label we could not make sense of the boundary-less sensory input that inundates us every moment of our waking lives; everything would appear as one big blur of sensation.
“The natural tendency to simplify also applies to causes and theories but to a lesser extent. Science's search for a ‘complete unified theory of everything’ and religion's positing of one ‘ultimate cause’ i.e. God, are motivated by this same human impulse. So, as you surmise, the simplest or most convenient theory would be psychologically preferred, or in the last analysis naturally selected, since a predilection for reductionism is necessary for our survival.
“The more complex of the two will be shelved for the time being and ultimately rejected altogether. Only the favored one will persevere. This will be unfortunate if the simpler one is subsequently found wanting since the other will have probably been forgotten and may not resurface even though never having been disproved. We will then have to start over from scratch rather than have available a perfectly sound alternative that was rejected merely because of its relative complexity.”
“So there are no true theories?”
“Only in a limited sense. All ‘true’ theories have this in common — they pass all currently existing tests. But we would have to run all the tests simultaneously to provide a common set of starting circumstances, so they are still merely partial truths. Furthermore we can never be sure our test or tests have covered everything. Even were we to possess more than our meager set of sense receptors our ‘truth’ would still be ascertained by what we choose to measure, but these choices are restricted to the relatively small number of practical tests our limited minds can contrive.
“Before we can perform any experiment we must first decide which set of predictions we want to test. In this sense the ancient Greek sophist Protagoras was on firm ground when he said, ‘Man is the measure of all things.’ To top things off, we would be incapable of arbitrarily choosing what to experimentally measure without bias even if we did have the requisite inventiveness, senses and precise instrumentation.”
“How so?”
“We would still be limited by our innate inflexibility. Mankind has always studied the same basic attributes of reality using the same modes of imagination as evidenced by the congruous approaches taken in widely divergent fields of study. Compare the subject matter of various disciplines: infinite Being in philosophy, infinite spacetime in physics and Cantor's various degrees of infinity in mathematics. All of these concepts have a similar structure, which indicates we virtually pre-select reality.”
“Isn't it possible we are merely persuaded by tradition and education to follow the same path rather than being compelled by our basic nature? After all, Aristotle's influence over his European successors limited the range of fields of study and severely retarded any improvement in methods of investigation for over a millennium.”
“Yes it's possible but it's much more likely we are constrained by an inherent human trait. The Renaissance geniuses after Aristotle didn't produce new theories ‘out of the blue’. They merely furthered investigations he had already begun. ‘Truth’ tends to evolve slowly rather than arise spontaneously. I conjecture this is so because we have only a small number of modes of conceptualization, imagination and perception with which to make sense of the parts of reality we can comprehend.”
“What are they?”
“I don't recall Kant's entire list33, but it includes hierarchy (or inclusion), inversion, series (or limit), divisibility, dualism, contradiction, unity, multiplicity, eternity, causality, comparison and necessity. Compounding these with each other enables us to derive other concepts such as: freedom and will; desire, attraction and force; change, motion, quantity, number, space and time; perfection, God, goodness, virtue and purpose; similarity, commonality and difference; paradox, error, knowledge and truth; repetition, custom and habit; order, symmetry and regularity; progress, growth and evolution; and nothingness, vacuum, emptiness and death.”
“Many of these have a mathematical flavor.”
“Einstein's proclamation that ‘God must be a mathematician’ is an eloquent expression of the fact that we, but not God, can only conceive things in certain fixed ways and mathematics is the most precise language in which we do so. All of physics and probably all of philosophy can be described more concisely and accurately in mathematical symbolism than ordinary language.”
“How do you explain that Riemann ‘constructed’ differential geometry as a purely mental exercise yet Einstein later showed it perfectly described spacetime? Wouldn't this prove Riemann's work was absolutely true even though it was a product of human imagination? Perhaps reality is finite and, even though our senses are incomplete, our modes of thought alone suffice to comprehend it.”
“Like all of us, Riemann was born and raised in our world so his insights could not have been mere mental constructs; they were based on a synthesis of his earthly experience of space and time.34 Moreover, Einstein's theories don't attempt to explain how the universe works: this is beyond our grasp. They only construct models enabling us to predict future events. We analyze all new facts through the same old modal techniques. Even our analyses of the modes themselves are constrained by the selfsame modes, so we can't get outside of them through philosophical thought experiments unless we mutate new modes or senses. Without a mathematical model or an analogical pictorial representation any posited part of reality, for instance a fourth dimension, that doesn't conform to one of our inherent modes or senses is incomprehensible to us.”
“Such as ESP?”
“No. It can be easily imagined as can ghosts, déjà vu, time travel and many others. But beyond these there are attributes of and relations among space, time and causality that we can't even begin to visualize, yet whose existence lends credence to strange but imaginable old notions that haven't been disproved, like ESP. Quantum theory is an example of an inscrutable concept.”
“Are there others?”
“Several. Superstring theory is one. It may simplify and/or expand existing models for perceiving reality but won't add new modes of perception to the current collection of substance, space, time, change and a few others. New facts can expand the applicability of a given mode but can't create a new mode.”
“Didn't the concept of energy require a new mode?”
“No. We can't sense energy per se, only manifestations of it. It is merely a par
ticularly useful and economical quantification of kinds of motion and force, and these concepts are themselves derived from the old modes of substance, space, time and change.
“Without new modes we can neither envision nor create new aspects of reality. The best we can do is to apply old modes of conception to new facts, which is all we have ever done. This is why true paradigm shifts in knowledge aren't yet possible. Copernican theory merely shifted the center of the solar system's circular motion from the earth to the sun. Non-Euclidian geometry didn't create new modes for imagining shapes and distances; it merely applied the old ones differently. Even quantum theory doesn't create a new mode. It's merely an ingenious attempt to ‘explain’, using only existing modes, unperceivable phenomena such as discrete chunks of time.”
“I thought mathematics gives us a complete understanding of quantum theory.”
“Mathematics gives us a complete description of quantum theory but this isn't the same as comprehension. Mathematics is a concise symbolic language that must resort to the use of ‘mega-symbols’ to represent things like infinity (denoted by ‘∞’) or the square root of –1 (denoted by ‘i’) that we can't begin to imagine. Physics has its own special set of mega-symbols, for instance the one denoting the wavelength of ultraviolet light that represents its ‘color’. The more of these a theory requires the more incomprehensible it will be and quantum theory is necessarily suffused with them. That's why we'll never be able to intuit it at a fundamental level until we evolve new modes of conception, and no theory would be so bold as to propose it introduces us to new modes.”
“Do other philosophers share your views?”
“Many, but not all. Any philosophy of truth must also be tested. Mine is bolstered by science since it echoes the correspondence principle's criteria for arriving at truth, namely that a competing theory can survive only if it correctly expands other theories that haven't been dialectically disproved. I've given you a lot to chew on. Feel free to stop by anytime if you have questions or refutations.”
* See footnote 4
____________________
29 In his Essays
30 In The Principles of Human Knowledge
31 As related in Plato's Republic
32 In An Enquiry Concerning Human Understanding
33 In Critique of Pure Reason
34 As Dewey generally remarks in Human Nature and Conduct
Table of Contents
Cover Page
Title Page
Copyright
Contents
Part I: May 3, 2297
1 Ben's Manuscript
2 Relativity Theory in the 23rd Century
3 Jenny
4 Jim
5 Quantum Theory in the 23rd Century
6 Ben's Reverie
7 Ben's Reverie — Continued
8 A First Date
9 A Fruitful Friendship
Part II: The 24th Century
1 Are We Gods?
2 Crisis
3 The Mission
4 The Corporation
5 A Picnic
Part III: The 25th Century
1 Utopia
2 The Beginning of The End
3 A Theoretical Glimmer of Hope
4 The Time Machine
5 Our Finest Hour
Part IV: Epilogue
Part V (Appendix): Is Quantum Theory True?