Volume 25 Number 10
Produced: Sun Nov 10 16:55:08 1996
Subjects Discussed In This Issue:
Administrivia
[Avi Feldblum]
Administrivia - Moderator in Pasadena for Shabbat
[Avi Feldblum]
Can G-d Generate a random number? (2)
[Robert Israel, David Charlap]
G-d and Paradoxes
[Micha Berger]
Random numbers (2)
[Joshua W. Burton, Richard K. Fiedler]
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From: Avi Feldblum <feldblum@...>
Date: Sun, 10 Nov 1996 16:21:15 -0500
Subject: Administrivia
Hello All,
Welcome back to Mail-Jewish! Thank you to all those who emailed, called
and otherwise tried to check up that all was well with me and why
mail-jewish was not coming out. I hope that I have gotten work back
under control and mail-jewish will resume being the high caliber mailing
list it has been for the last several years. I still am working on
catching up with all the mail sent - there were about 1400 new messages
when I finally logged on again late last week after being off the net
for almost a month. I've narrowed that doen to about 450 messages that I
need to read and move either to one of the mail-jewish lists, to update
the kosher Restaurant database or to respond to individually.
I'll probably have a number of Administrivia postings over the next few
days, as I work my way through the messages. In the meantime, if you
sent me mail to be dropped from the list or postponed, address changed
etc over the last month, I should be getting to it during the next few
days.
Avi Feldblum
Shamash Facilitator and mail-jewish Moderator
<mljewish@...> or feldblum@cnj.digex.net
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From: Avi Feldblum <feldblum@...>
Date: Sun, 10 Nov 1996 16:25:51 -0500
Subject: Administrivia - Moderator in Pasadena for Shabbat
Hi,
I will be in Pasadena, California this coming Shabbat. I think that there
is not much there in the way of Orthodox shul etc, but I do think that
someone had emailed me that they lived in Pasadena and kept kosher
etc. If you could email again I would greatly appreciate it. I will be
at a course held at CalTech, which ends late on Friday. I get the
feeling that the Jewish section of LA is not a short drive from
CalTech. Any leads or invites greatly appreciated.
Avi Feldblum
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From: Robert Israel <israel@...>
Date: Thu, 3 Oct 96 09:06:45 -0700
Subject: Re: Can G-d Generate a random number?
Dick Fiedler ( <dfiedler@...>) wrote:
| I would like to know if G-d knows all which would imply that he can not
| generate a random number and thus is limited by his own complete
| knowledge or if it is possible that G-d can generate a random number and
| not know what this number will be before hand.
There is no such thing as "before hand" for God. This is similar to the
old chestnut "can God make a stone so big he can't lift it?" There is
no such thing, but that is not a limitation on his power. Similarly, God
can't make a four-sided triangle, and again that is not a limitation - it
is just that "four-sided triangle" is a description that could not possibly
apply to anything.
| Furthermore does G-d know the value of pi or is it as irrational for H-m
| as it is for us mortals.
Every mathematician knows "the value of pi". It is the ratio of the
circumference and diameter of a circle, one of the values of -i ln(-1),
twice the integral of sqrt(1-x^2) from -1 to 1, etc., etc. "Irrational" does
not mean "unknowable", it just means "not the ratio of two integers".
That is just as true for God as it is for us.
Now for a more interesting question, does God know the following statement:
"God does not know this statement"
| And lastly can G-d be surprised?
Certainly not in the way that people can. As Rambam notes in the Guide
for the Perplexed, any attribute that is ascribed to God and also to people
has quite different meanings in the two cases. "Surprised" is not one of
the list of attributes he discusses, and I can't imagine a scenario in which
it would apply.
Robert Israel <israel@...>
Department of Mathematics (604) 822-3629
University of British Columbia fax 822-6074
Vancouver, BC, Canada V6T 1Y4
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From: David Charlap <david@...>
Date: Thu, 3 Oct 1996 13:58:25 -0400 (EDT)
Subject: Can G-d Generate a random number?
<dfiedler@...> (Richard K. Fiedler) writes:
>
>I would like to know if G-d knows all which would imply that he can not
>generate a random number and thus is limited by his own complete
>knowledge or if it is possible that G-d can generate a random number and
>not know what this number will be before hand.
This sounds like a variant on the "can God create a rock so heavy He
can't lift it". The very nature of the question is self-contradictory.
You may as well ask "can God create black which is white?"
>Furthermore does G-d know the value of pi or is it as irrational for H-m
>as it is for us mortals.
The answer is yes and yes. This is not really a question. The value of
pi is not unknown. It can not be represented using our number system,
but it is an exact value and it is known even by us mortals.
Do you want to draw a line of exactly pi units long? Draw a circle
whose radius is exactly one unit long. The length of that circumference
is exactly twice the value of pi.
The "irrational" property of the number is simply the fact that it can
not be precisely represented using our number system. It does not
have anything to do with the number itself.
>And lastly can G-d be surprised?
You enjoy asking questions that seem to have no answer, don't you?
The answer is obviously "no". To be surprised, you have to witness
something you did not expect to see. Something that knows everything,
including the future, obviously can not ever be surprised.
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From: <micha@...> (Micha Berger)
Date: Thu, 3 Oct 1996 12:57:58 -0400 (EDT)
Subject: G-d and Paradoxes
On the question if G-d could pick a random number, or catch a cold, or
create a rock so heavy even He couldn't lift it, or in general, show
weakness.
I can see a number of resolutions:
1- The Rambam writes (Guide, II) that G-d can not do the paradoxical. His
example is that Hashem couldn't create a circular square. In that case,
we'd have no problem saying no to any of the above.
2- The Ramchal disagrees by insisting that logic itself is a creation,
and therefor Hashem is not subject to it. However, this also robs us
of the ability to apply our reason to the problem, which is our only
way to analyze the question.
3- The Rambam (Guide, I), also asserts that when we call G-d infinite,
such as Omniscient, Omnipotent, etc.. we are really describing the
absense of limitations. (The Rambam probably followed Aristotle's
belief that only infinity only exist in potential -- that you would never
stop -- and not as a "completed infinity" such as Cantor's transfinite
numbers. Aquinus' philosophy is subject to a number of the flaws that
Aristotle found in the idea of the completed infinite.) This is
because we can't understand Him, and can only discuss his behavior,
and what he is not. So, Omnipotent means "not limited by something
else's strength or mass".
In this sense, there would be no problem saying that He is limited by
Himself, His own strength (in the case of the rock), or his own
knowledge.
Micha Berger 201 916-0287 Help free Ron Arad, held by Syria 3626 days!
<micha@...> (16-Oct-86 - 19-Sep-96)
<a href=news:alt.religion.aishdas>Orthodox Judaism: Torah, Avodah, Chessed</a>
<a href=http://aishdas.org>AishDas Society's Home Page</a>
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From: Joshua W. Burton <jburton@...>
Date: Thu, 3 Oct 96 10:24:47 -0500
Subject: Random numbers
> I would like to know if G-d knows all which would imply that he
> can not generate a random number and thus is limited by his own
> complete knowledge or if it is possible that G-d can generate a
> random number and not know what this number will be before hand.
The flippant answer is that God made (generated) ALL the numbers,
including the random ones. But which ones are those?
The concept of randomness is deep and rather slippery. Bill Vetterling,
in a wonderful textbook called "Numerical Recipes", recalls that he was
working on an IBM mainframe back in the '70s, and discovered that their
built-in algorithm for pseudo-random numbers had self-correlations, such
that if you took successive triplets of such numbers and plotted them in
three-dimensional space, they all showed up on a small number of
distinct planes, rather than randomly through the space. He complained
to the tech rep, and was told that he was misusing the random number
generator. "We guarantee that any ONE number will be random. We don't
guarantee that more than one together will be random."
If that didn't strike you as hysterically funny, the point is that it
is meaningless to call one number in isolation "random". The most you
can say is that it was chosen by some algorithm that is uncorrelated
with the problem you plan to use it on. Working with digital computers,
which (barring cosmic rays and other glitches) are deterministic, the
best we can do is to start with a seed (like the exact current time)
and create from it a number which _looks_ random. However, if for
some reason we always ask for a random number at a predictable time
of day, we may find unexpected correlations. Similarly, if the routine
was written by an incompetent, as in the case Vetterling cites, we will
see correlations between successive numbers drawn from the same seed.
(Since no string of numbers generated deterministically is truly random,
there are always such correlations, but a good algorithm will hide them
so they are unlikely to bite the user in so obvious a way!)
Within the context of quantum mechanics, there are some measurements
whose results are provably random---that is, uncorrelated with any
other observable in the universe. An example would be the timing of
clicks in a Geiger-Mueller counter, or the horizontal spin of an
electron whose vertical spin has just been measured. This, of course,
is the origin of Einstein's famous whine that "Der Herrg-tt wuerfelt
nicht" (God doesn't throw dice). Nowadays, very few people disbelieve
quantum mechanics on these grounds, and in fact we now believe that
the evaporation of black holes creates true randomness by "throwing
dice" behind a curtain that we cannot observe even in principle.
Probably the best answer ever given to Einstein's protest was Bohr's
well-known rejoinder: `Albert, stop telling Him what to do!'
In that spirit of humility before the Unknowable, here is my own
editorial slant. A computer can make numbers that are "random enough"
for many practical purposes. Quantum systems can make numbers that
are truly random, from the point of view of any one observer. Some
quantum gravitational systems involving event horizons can make
numbers which are random from the point of view of _any_ observer
in the outside universe. Using these expedients, or others of which
we have not yet conceived, God can make numbers which are random from
the point of view of His creation, truly and for all time. Whether
such numbers are random from His own point of view is not a question
to which I can assign any operational meaning, so I hastily decline to
step in it. Does God know about such numbers "beforehand"? G-d knows!
> Furthermore does G-d know the value of pi or is it as irrational
> for H-m as it is for us mortals.
This question hangs on a misunderstanding of the word "irrational",
I think. Even we mortals know the exact value of pi: it's pi. What
I imagine you are groping towards here is a question about whether the
decimal representation of pi is uncomputable for God. (All rational
numbers have computable representations, but the converse is not true.)
The answer is clearly no. Here is how to compute an exact decimal
representation of pi:
Add 4(-1)^n/(2n+1) to infinite precision, for all nonnegative integers n.
This shows that pi's decimal representation (unlike that of many
numbers of interest to theoretical CS people) is computable, and in
countably infinite time. God has plenty of that, at the very least.
By the way, is "H-m" some weird politically correct unisex thing, or
are there poskim who seriously hold that the masculine object pronoun
in English has kedusha when capitalized?
> And lastly can G-d be surprised?
Fooled, no. But I like to think He is always surprised.
``Even those who see stars ask, +----------------------------------------+
`What is a star?', because to see | Joshua W. Burton (847)677-3902 |
merely with one's eyes is to see | <jburton@...> |
very little.'' -- Yury Manin +----------------------------------------+
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From: Richard K. Fiedler <dfiedler@...>
Date: Thu, 3 Oct 1996 11:25:41 -0500
Subject: Re: Random numbers
I appreciate your response.
Actually I was skirting for me what the real issue is.
I fail to understand why God must be outside of time itself.
I understand that if God exists outside of time then he must know
everything that was or will be. And if this is so I smart at the idea the
we really have free choice.
But perhaps God does have a basic attribute of time albeit a very different
one then ours. When the "Big Bang" occured wasn't that an exchange of time
and energy for matter?
From God's point of view creation only has existed for a few days but
none the less there is a time factor and God doesn't know the outcome.
If Choas really means that the would is indeterminent perhaps this is for
God as well.
Thus we would have free choice though God would effect his creation through
his ability to do tikun.
Dick Fiedler <dfiedler@...>
Skokie Il (708) 329-9065 Fax (708) 675-6033 /\
Efrat Israel (02) 932706 Fax (02) 932707 \--/--\--/
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End of Volume 25 Issue 10
