Many years ago I took a course in symbolic logic. My professor was a man named Zoltan Domotor, who I remember with great fondness. In particular, I remember him once saying, “These are truths that even God can’t change,” referring, if I remember correctly, to modus ponens, and modus tollens – axioms which form the foundation of logic. If I understand him correctly, he was saying that it is possible to imagine a world with different laws of nature, but it is impossible to imagine a world without logic. I’m not sure that I quite agree with this – many Jewish authorities say that God made the world logical so that people could understand it – but the real point is that some truths are more basic than others.
Other truths, while not as basic as modus ponens and modus tollens, are so basic that they can be derived without the need of experimentation – they follow inexorably from their postulates. One such truth is the Theory of Relativity.
Einstein begins his original 1905 paper on Relativity with two simple postulates: There is no absolute state of rest, and the speed of light is the same in all frames of reference.
Examples of this sort [asymmetries in Maxwell's electrodynamics when applied to moving bodies - DB], together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.
The rest of the paper develops the Theory of Relativity step by step, without references or citations. No further information is needed – if these two postulates are true, then the theory of relativity must also be true.
Another example is evolution. Darwin spent years collecting evidence that evolution indeed accounted for the origin of species. But evolution must be true for any system in which the following two postulates are true: Descendants tend to have characteristics of their progenitor, and some characteristics are more advantageous for survival or propagation than others.
To understand the power of evolution, imagine a population in which 50% of the individuals had a characteristic that gave them a mere 1% greater chance of survival. After the first generation, their percentage of the total population will rise to 50.25% of the total population. After ten generations it will rise 52%. After a hundred generations it will rise to 73%. After a thousand generations it will rise to 92%. If this were a population of humans, and we assume an average generation of 25 years (probably too high), a thousand generations would be 25,000 years. This may seem like a long time when compared to a human lifetime, but in terms of human history it is quite short.
The real beauty of evolution, however, is that it can be applied to any system in which characteristics are inherited. In human terms, evolution acts simultaneously on the gene, the individual, the tribe, and society as a whole. Any of these (in fact, any group that persists over generations – and you can also play with the definition of generation) can be considered a “unit” of evolution.
Evolutionary theory has also been applied to economics – technologies that are more successful survive, while less successful technologies die out, and even ideas themselves – the unit of ideas being called a “meme”.
All this has been a rather lengthy jumping-off point to what I really want to explore in future posts: the nature of human nature.