“Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.” – Leonhard Euler
I find this a very interesting attitude for a mathmatician. Why is this?
Let us ask first, what is a mathematician? A mathematician is a person who practices the study of mathmatics.
Well, bully for us. Gold stars all around.
Let us then ask, philosophically: What is mathematics?
Mathematics is the notational system that provides for the representation of
- nouns (“Train leaving boston”, “Acceleration”)
- operations (“Addition [ or “+ ], subtraction [ or ”-” ]
On this definition we can understand statements such as “F = M*A” as meaning: “the noun force results from the performance of the multiplication operation on the noun mass and the noun acceleration”. It may hard to see this with something as “simple” as multiplication of division, but with say, the quadratic formula it becomes a bit more clear. There are nouns, and a complex operation is performed on those nouns to produce product (or products).
But there is one more point that we are missing. Mathematics provides lastly a codex of legal operations that may be made. For example it is an “illegal operation” to attempt to divide 1 by zero”.
So now we know what mathematics is:
Mathematics is a tome that contains rules for valid “statements”, a vocabulary which describes nouns, and a vocabulary that describes operations applicable to nouns.
A mathematician could take one of two stances on the relationship of this notational / behavioral discipline:
- Math, or the symbolic system that expresses phenomena and rules for manipulating said symbols, shares a common parent with the phenomena themselves. Thus by the same necessary existence of phenomena, so must come the ruleset for describing said phonemena.
I shall call this view: Mathematics is strong or “Mathematics is necessarily real, and necessarily maps to phenomena”
- The alternate view would be the one anecdotally introduced to me by my second astronomy teacher my Spring semester: “Do you think that (such and such science) is real? Or are its rules sufficiently permissive / so elastic such that they just happen to map to the phenomena we see around us? “
I shall call this view: Mathematics is weak or “Mathematics has no inherent bond to phenomena and is essentially, a trivial game - no different than sudoku - that describes a set of symbols, a rule for valid ‘setups’ that has, for some strange reason, a large number of participants in said delusion**
Euler seems to have taken the second view, which would be the view of Kant as well. There is a world which we experience, a world of phenomena, whose behavior, with research, would appear predictable and knowable. Euler would take that view and expand it to say, that those knowable and predictable phenomena could be described by the discipline of mathmatics; yet he complicates this phenomenological view by asserting that that’s not good enough. He then claims that while math may seem sufficiently accurate it, well, only seems accurate.
There could be a mysterious world, Euler’s quote would have us believe, a noumenal world in Kant’s parlance, where that mapping may not in fact be true. Thus in the noumenal world “2+3 =6” or “a square has 600 sides” is possible, but in our world, the world of phenomena, we would only ever experience the exceedingly compelling notion that “2+2=4”.
Why did Euler feel the need to posit this invisible realm? Was it the only way for this minister’s son to give his faith a loophole in which to escape as the body of human knowledge increased exponentially (math geek pun intended)? It’s baffling to me that one of the most brilliant mathematicians of all time invented this world, for no necessary purpose.
Kant theorized that God experienced the noumenal world. He could see the 600-sided square and the thing we experienced as a red chair in the phenomenal world was truly a zebra-patterened hammock in the noumenal world.
It was while I was thinking about this that I noticed another Wikiquote:
The kingdom of God cometh not with observation: Neither shall they say, Lo here! or, lo there! for, behold, the kingdom of God is within you.” – Yeshua (Jesus Christ)
I always think of the noumenal world as a world behind a wax-paper wall (like japanese shoji but with translucent cellophane versus rice-paper). The good book would have us believe that the noumenal world, where He (as by virtue of being of the same substance as the Father) dwells, is inside of us.
Yet when we think, we think in the world of phenomena. How can we think without thinking? How do we know without reference to the phenomenal world of our experience? It’s a Zen koan again.
I suppose that’s appropriate, when we consider the work of the mathmetician and the work of the mystic against one another we wind up at insolubles.
The only solution is gnosis: radical imparting of the knowledge. A sacred teaching that, instead of writing to our phenomenally-oriented mind, imprint itself into our noumenal connection: our souls. Is it possible to “know” with the soul? To pass through reason and language unfiltered?
Euler seems to think that his work was but an enrichment of the silly symbological game - while he was hunting for that most elusive teaching. The teaching of Solomon, the wisdom beyond wisdom: the fountain of youth, the manna of God, the holy grail, the Great Teaching, the sorcerer’s stone. The gnosis knowledge that turns lead to gold and expugates sin itself.
Yeshua tells us it’s within. Others tell us it’s without. I think i’ll side with the mystic and gnostic Yeshua and the Gnostic Judas. There’s a gnosis for that teaching - why has Christianity foresaken that path?