Wednesday, April 02, 2014

God is a Mathmagician

It seems to me that if existence is to exist, there are certain things that even God cannot know about it. This would necessarily follow from his own infinitude.

In short, if God is infinite, then he cannot be known, even by himself, because to know something is to render it finite, and God cannot be something other than God, i.e., infinite.

Take for example, number. Does God know the last number? Of course not. Numbers go on forever. There is no end and therefore no boundary in which to enclose them.

To exist requires boundaries, which is why it is proper to say that God doesn't "exist" to begin with. Creatures exist. The Creator does not. "Existence" is a property of, or analogy to, something else.

Schuon defines matter as "the sensible manifestation of existence as such." This implies that there are insensible manifestations of existence, which indeed there are. That is to say, all matter in existence is suffused with boundaries which are the effect of ideas.

Or in other words, as Schuon writes, "form is the manifestation of an 'idea,'" or "of a particular possibility." Thus, both form and substance, idea and matter, are limitations on possibility, rendering the infinite finite.

Even so, there is always nonlocal unity beneath the local diversity, which one might say is a shadow of the Absolute.

For example, although number goes on forever, there is no conceivable number that could be so far out as to become "detached" from the rest. Underneath the diversity of mathematics is always a continuum of unity; math is just multiples of one, or the endless variety of One-ness: unity prolonged. Even a fraction -- i.e., less than one -- must still partake of oneness, or it couldn't be defined.

Ah, but what about irrational numbers such as pi? Pi has "no solution." It has no end and therefore no boundary. As such, even God cannot know it, since it trails off into infinity, just as he does. So, does pi exist?

I don't know. I've never thought about it before. I would say that this only goes to show that there exist truths that cannot be proved with strict logic. In other words, we know that there must be a constant ratio between the diameter and circumference of a circle, even if it cannot be reduced to a fully rational expression.

Maybe the problem is that circles don't actually exist, any more than points or lines do. Rather, these are mental abstractions, pure forms that are never seen in matter. Or to plagiaphrase Benoit Mandelbrot, clouds aren't spheres, mountains aren't cones, coastlines aren't circles, and bark isn't smooth.

Speaking of Mandelbrot, one of his bestest ideas is that -- and I'm expressing this in my own way -- the immanent is just as infinite as the transcendent. For example, a coastline is not actually a finite boundary, but rather, is infinite. Thus, Tonga, for instance, is actually "enclosed in infinity."

How can that be, since infinity by definition cannot be closed? Well, let's say you are tasked to measure the coastline(s) of Tonga. Now, we all know that Tonga consists of 176 islands. Forget about that. We just want you to measure one of them. How would you begin? With a big tape measure? What about all the little nooks and crannies along the coastline, all the individual grains of sand, not to mention the molecules, atoms, and subatomic particles?

It turns out that nature is such a rough place that even the toughest Tongan couldn't possibly measure it, because

"the measured length of a stretch of coastline depends on the scale of measurement. Empirical evidence suggests that the smaller the increment of measurement, the longer the measured length becomes. If one were to measure a stretch of coastline with a yardstick, one would get a shorter result than if the same stretch were measured with a one-foot (30cm) ruler.

"This is because one would be laying the ruler along a more curvilinear route than that followed by the yardstick. The empirical evidence suggests a rule which, if extrapolated, shows that the measured length increases without limit as the measurement scale decreases towards zero" (Professor Wiki, emphasis Professor Wacky).

Wo. Let's pause here for a moment so as to allow you to assimilate this wonderful orthoparadox: the more accurately we measure something, the longer it is, to the point that perfect measurement equates to infinity?

CIBSPFY! (Can I buy some pot from you?)

This truth can be depicted visually via fractals. Magnify the itsiest bitsy of a fractal and you will see another beautiful fractal. There is no "last fractal," any more than one could find the last snowflake before they start repeating themselves. Or write the last poem. Or compose the last melody. Or bleat the last blog post.

(Which reminds me a line from the Wake that sez When a part so ptee does duty for the holos we soon grow to use of an allforabit.)

Again: the infinitude proceeds both up, into transcendence, and down, into immanence. And I would suggest that the same principle can assist us in thinking about God, who overflows and spills into and out of everything, just as Meister Eckhart claimed.

What exactly did he claim? Oh, for example, "Every single creature is full of God and is a book about God. Every creature is a word of God. If I spent enough time with the tiniest creature -- even a caterpillar -- I would never have to prepare a sermon. So full of God is every creature."

Or "Earth cannot escape heaven. Flee it by going up, or flee it by going down, heaven still invades the earth..."

Or "God forever creates and forever begins to create, and creatures are always being created and in the process of beginning to be created."

I guess that's the "end," even if no such thing is possible...


julie said...

the measured length increases without limit as the measurement scale decreases towards zero

I'm reminded of the one about the arrow that never reaches its target, because however close it gets, it still has half the remaining distance to go. Or something like that. Or more to the point, when you go down small enough, the distance between one atom and the next is greater and greater, and never to be breached.

On the one hand, molecularly speaking, it's impossible to distinguish where one thing ends and the next begins, such that everything is a part of everything else. On the other, at the same time, everything is separated from everything else. And somehow, between those two realities, everything is.

Gagdad Bob said...

It's definitely not an updated version of Zeno's Paradox. More like counting the notes between two octaves, or the colors between red and violet. "Intensive infinity," you might say, instead of the usual extensive infinity. I think it also explains how the brain can be infinite.

julie said...

Off topic, but train-wreck fascinating, the original sin of pale skin:

"I came to higher ed to study. What is this problem that I'm scared of? I don't know what to do. My principal is scared of this. Where do I point? Who's at fault? My white body is at fault," she said. "My racial identity, as a white person who believes that I am somehow better or more deserving, is the problem. The white supremacy, the structure is the problem."


Another topic of discussion was how white people's actions, like donating to charity or helping a family in need, are inherently racist. A white attendee of the conference told a story about how her family donated school supplies to one of her classmates when she was in first grade because the family could not afford them.

The receiving family had moved from India, according to the attendee. While she was happy to be helping when it happen years ago, she was now questioning her family's motives.

The irony here is that this woman is racist - but not in the way she thinks she is. To decide that all your students are failing because of the color of your skin is so over-the-top condescending, one hardly knows whether to laugh or cry.

Also, Madison taxpayers must be thrilled to know their money is being spent on conferences demonizing the majority of Wisconsin citizens.

julie said...

And thanks - I couldn't think of whose paradox it was. I didn't mean to suggest that's what the post meant, only that the one reminded me of the other.

Van Harvey said...

"Take for example, number. Does God know the last number? Of course not. Numbers go on forever. There is no end and therefore no boundary in which to enclose them"

A better and more complete knowledge of those boundaries is to be found in Number itself, which is in no way dependent upon the quantities of numbers there might possibly be, or might infinitely 'be'.

And I don't think it means Plato's forms and an imperfect reality, but a third option, the perfect unity of both, which existence is.

Which is the answer poor Zeno could never reach, stuck as he was between on those two options.

Context is King.

Van Harvey said...

BTW, have we gone through the Tongan coastline here before, or are my contexts blurring something else into memory?

USS Ben USN (Ret) said...

To infinity and beyond!

John said...

Bob, Julie;
Have you heard of ethno mathematics? This component of Agenda 21 popped up in la Nacion, San Jose, Costa Rica, yesterday.
"“Es necesario hacer consciencia en la sociedad de la existencia de estos grupos y de la importancia de tomar en cuenta sus conocimientos. ¿Por qué el indígena siempre tiene que aprender del blanco y no a la inversa?”, cuestionó." - Domingo Yojcom, coordinador de Red Latinoamericana de Etnomatemática en Guatemala . . . and
"‘Las matemáticas son un producto social y cultural, resultado de la interacción en la sociedad’ - Mariel Gavarrette

Google -" Ethnomathematics: a Multicultural View of Mathematical Ideas"
In our socialist innumeracy, even taxi drivers have their own maths. What does He have to do with it?

julie said...

Hi John,

I'm not sure I quite understand the question.

Mathematical concepts are a tool by which we may deepen our understanding of the world and how portions of it relate to each other.

Assuming, of course, that the way we have been taught reflects true principles presented with clarity. Here in the States, the new "Common Core" standards are apparently designed to make even the simplest math concepts as incomprehensible as possible, so that each student will graduate high school with the same depth of understanding as our vaunted intellectual leaders. Thus, when future generations are told that "there is no inflation" or that "the chocolate ration has been increased," they will feel confident that they are getting more for their money. No matter what the bank says.

As to the Indigenous of Costa Rica, if they understand "white" but not "black" (if that's what the coordinator's question meant; my Spanish is very rusty and not Costa Rica-specific), I can only presume that they were never taught that there is something about black to be understood.

1+1=2. This is true whether or not there is anybody to understand the concept. I'm not sure why the Indigenous should feel as though having to learn math is unfair. Perhaps because it is European? It is what it is. It works just as well with an abacus as with a calculator, and factors into the understanding of weather patterns and basket weaving as much as into medicine and computer science.

julie said...

As to your final question, "What does He have to do with it?" - I assume you mean God. In which case, you might also find a good answer by asking the Jews. I get the impression that the written Hebrew language plays as much with numbers as it does with words. And clearly, the Jews have not been harmed by their grasp of mathematical concepts.

Socialism, on the other hand, harms them just as much as it does everyone else.

julie said...

Perhaps a more relevant question regarding math and various groups of people in Costa Rica is, "what does Socialism have to do with it?"

The answer is, "as little as possible," since any genuine understanding of math reveals Socialism for the lie that it is. If each group has their own version of "math" which doesn't translate to any other, then there can be no common understanding, nor a common realization that they are being had.