|A very short work (two-pages long!) in
which two angels discuss the divine implications of our ability to
mathematically determine the future consequences of an action, especially
wave propagation. Like
Lagrange in his famous discussion of the determinism of Newtonian physics,
these angels explain the role of mathematical predictability in the creation of the universe:
|(quoted from The Power of Words)|
AGATHOS. Let me endeavor, my Oinos, to lead you, step by step, to the conception I intend. You are well aware that, as no thought can perish, so no act is without infinite result. We moved our hands, for example, when we were dwellers on the earth, and, in so doing, gave vibration to the atmosphere which engirdled it. This vibration was indefinitely extended, till it gave impulse to every particle of the earth's air, which thenceforward, and for ever, was actuated by the one movement of the hand. This fact the mathematicians of our globe well knew. They made the special effects, indeed, wrought in the fluid by special impulses, the subject of exact calculation- so that it became easy to determine in what precise period an impulse of given extent would engirdle the orb, and impress (for ever) every atom of the atmosphere circumambient. Retrograding, they found no difficulty, from a given effect, under given conditions, in determining the value of the original impulse. Now the mathematicians who saw that the results of any given impulse were absolutely endless- and who saw that a portion of these results were accurately traceable through the agency of algebraic analysis- who saw, too, the facility of the retrogradation- these men saw, at the same time, that this species of analysis itself, had within itself a capacity for indefinite progress- that there were no bounds conceivable to its advancement and applicability, except within the intellect of him who advanced or applied it. But at this point our mathematicians paused.
OINOS. And why, Agathos, should they have proceeded?
AGATHOS. Because there were some considerations of deep interest beyond. It was deducible from what they knew, that to a being of infinite understanding- one to whom the perfection of the algebraic analysis lay unfolded- there could be no difficulty in tracing every impulse given the air- and the ether through the air- to the remotest consequences at any even infinitely remote epoch of time. It is indeed demonstrable that every such impulse given the air, must, in the end, impress every individual thing that exists within the universe;- and the being of infinite understanding- the being whom we have imagined- might trace the remote undulations of the impulse- trace them upward and onward in their influences upon all particles of an matter- upward and onward for ever in their modifications of old forms- or, in other words, in their creation of new- until he found them reflected- unimpressive at last- back from the throne of the Godhead. And not only could such a thing do this, but at any epoch, should a given result be afforded him- should one of these numberless comets, for example, be presented to his inspection- he could have no difficulty in determining, by the analytic retrogradation, to what original impulse it was due. This power of retrogradation in its absolute fulness and perfection- this faculty of referring at all epochs, all effects to all causes- is of course the prerogative of the Deity alone- but in every variety of degree, short of the absolute perfection, is the power itself exercised by the whole host of the Angelic intelligences.
implication, as I see it, is that the biblical reference to God creating
the universe through statements such as "let there be light" is to be taken
literally to mean that he had worked out mathematically precisely what
vibration (created by his voice) would lead to the creation of the universe
as we know it. In addition to this suggestion that God needed "algebraic
analysis" to create the universe, mathematicians might be interested in the
logical paradox that apparently keeps God happy. According to the angels,
God could not know everything and be happy. So, to solve this problem, he
only knows almost everything. In particular, he knows everything
except whether he knows everything. (But wait, if he knows that he
knows everything except whether he knows everything then he must know that he
doesn't know everything....!)
Wait! I'm very confused.... I first found this story in a book of plays by the Italian playwright Luigi Pirandello. I posted it here under the name "The Tight Frock Coat". An anonymous visitor wrote and corrected me, saying that it was actually Poe's "Power of Words". That does seem to be true. What I read in the Pirandello collection was obviously a copy (perhaps translated into Italian and retranslated back into English). But, how did that happen? Did Pirandello actually attempt to copy Poe? Was it just a mistake on the part of the person who created that collection? If you know the answers to these questions, please write me! Thanks, Alex.
John C. Konrath|
A cerebral work about the nature of existence and the power of the mind to create.
I have a little comment to make, which I think resolves the paradox: according to the story the way I understand it, it's not that God "knows that he knows everything except whether he knows everything"; God knows everything except that he knows everything, which means that God is certain that he doesn't know everything. Like a good scientist, God presumes his own ignorance. Therefore, God is happy, as his pursuit for knowledge continues, although it must be a fruitless, and therefore frustrating, pursuit. But perhaps it need not be frustrating. Perhaps God simply enjoys the pursuit, regardless of success.