[Avodah] A God who knows the future

[Micha Berger]

On Fri, Aug 05, 2011 at 12:19:52PM -0400, Hankman wrote:
: Btw, there is no reason you could not get from Miami to NY in a weird
: world with only discrete points, so I am not understanding your need
: for the continuum to get from Miami to NY.

That weird world may be ours. There are theories of quantum gravity,
the possible unification of Quantum Mechanics and General Relativity,
in which space is quantized. The granularity is very small (Planck
length is 1.6 * 10^-35 meter), but as long as it's not infintesimal,
it avoids Xeno's paradox.

Also, Xeno's paradox uses infinity in the Aristotilian
conception. "Parallel lines meet at infinity" and "Parallel lines don't
meet" are considered equivalent in classical thought, because you could
never have an infinity of anything.

The early versions of the calculus avoided this problem by invoking
limits. IOW, as we get closer to infinity, we get ever closer to this
point. Thus, it doesn't actually discuss sums of an infinite series.

However, since Cantor's transfinite math, the notion of taking a real
sum of an infinite number of infintesimals can be modeled mathematically,
and we don't shy away from it.

Also, the amount of time it takes to make this sum of infinite points
of space is also subject to the same halving and rehalving. So, it
takes a finite time to cover that finite distance.


Pulling things onto topic for Avodah...

Inifinity is the one topic of math that has theological, and thus Torah
implications.

I've argued here a number of times in the past 13 years that this is one
of the things the Rambam is addressing with his Negative Theology. An
Aristotilian can't have a conception of Infinite Power. But the Rambam
doesn't define Omnipotence that way -- he defines it in the negative:
there is nothing Hashem can't do because of a lack of Power.

Similarly, Cantor's algebra distinguishes between kinds of infinity.
Alef-null (written: alef subscript 0) is the number of integers (counting
numbers). C, which may or may not be alef-1, is the number of numbers,
including integers, ratios, and irrational numbers. IOW, an infinitely
long ruler has alef-null 1 cm marks in it, and C infintesimal points
along its length.

Here's from something I wrote on Birkhas Avos
<http://www.aishdas.org/asp/1998/08/avos.shtml>:
    ...
    Rabbi Yochanan (Megilah 31a) said, "Where ever you find G-d's
    greatness, that is where you find His humility". Perhaps we can
    understand this apparent paradox by comparing G-d's properties to
    those of humans. Schools have a problem of overcrowding. There are
    just so many students a teacher can adequately pay attention to. As
    the number of students grows, each one can only get less and less
    attention. Not so Hashem. His infinity is not just that He is a
    "Kel", G-d over all, but also "Gadol", great enough to give personal
    attention to each person.
    ...

And on berakhos in general
<http://www.aishdas.org/asp/2005/12/what-is-berakhah.shtml>:
    ...
    Hashem Elokeinu -- There is a contrast between these two names
    of Hashem and their implication. This topic alone would require
    multiple essays, so I will simply sketch a couple ways of viewing
    this contrast:
    ...
    2- The very remoteness of the name Havayah also implies Divine
    Mercy. This is not intuitive, however, the need to create law comes
    from a person's limited ability to deal with many individual cases. A
    teacher with few students is effective, one with more students,
    less so. To manage a country, we need laws and policies, since we
    do not have infinite time and attention to cover every decision on a
    case-by-case basis. Therefore, it is only because Hashem is Infinite
    that Divine Mercy is possible. Therefore, this expression can be
    seen as a declaration of the unity of G-d, despite the different
    appearances of Mercy and Strict Justice.
    ...

And in <http://www.aishdas.org/asp/2009/02/infinity-and-thought.shtml>:
    ...
    This difference is a good METAPHOR for explaining a common theological
    error.

    Many wonder how G-d, in charge of the entire universe, could possibly
    be interested in an individual person out of billions on a little
    backwater planet out in one galaxy among who knows how many...

    This is viewing G-d like alef-null. It's a huge set. But there are
    gaps between its members.

    G-d's infinity is beyond that. I'm not saying it's C, or anything
    along those lines (which is why I wrote the word "metaphor" in bold
    at the beginning of this digression), just that it's greater than
    alef-null. And just as the real number line as an infinite number
    of points between zero and one (in addition to comprising an infinite
    number of such intervals), G-d has an infinite amount of attention
    to bestow on each of us.
    ...

-Micha

-- 
Micha Berger             Zion will be redeemed through justice,
micha at aishdas.org        and her returnees, through righteousness.
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