Volume 16 Number 42
                       Produced: Tue Nov  8  6:36:24 1994

Subjects Discussed In This Issue: 

Age of the Universe, the earth, and refuting science.
         [Sam Lightstone]
Mathematical induction & formal logic in the Gemara
         [Leora Morgenstern]
Rarest Shmoneh Esreh
         [Mike Gerver]


From: <light@...> (Sam Lightstone)
Date: Mon, 31 Oct 94 17:20:55 EST
Subject: Age of the Universe, the earth, and refuting science.

Regarding this on-going discussion about the age of the Universe, I
thought I would contribute my own twisted philosophy on the matter.

There is little question in my mind that our universe is several
billions of years old, and that our earth is likewise several billions
of years old.  I am disturbed (philosophically) by the opinions of those
who suggest that this belief is incorrect by six or seven orders of
magnitude for the following two broad reasons:

My first concern is with those people who refute any evidence that appears
to contradict their belief that the earth is less than 6000 years old as a
matter of faith.  Such people use arguments like: "G-d could have created
the earth old if he wanted to".  "Fossils of 'ancient' creatures could have
been planted in the earth by G-d during creation".  To these people I can
say simply that they should observe that we live in a world in which nature
seems to follow due course.  The rules of nature seem not to have changed
with time.  We base our philosophies, beliefs and faith largely on
deductions that we make about the world (universe) around us.  If it were
true that nature was not nearly so sensible as it appears, if the rules by
which nature governs us today were just as likely to change tomorrow, then
we would have a very hard time choosing right from wrong and left from
right.  Every thing we know and everything we believe seems to have been
built up on the cumulative understanding of the world around us.  Even
those divine bits of information which were revealed to us through the
Neviim are only accepted after they pass basic tests of integrity.  If one
says that nature is not as it appears to be -- e.g.  "it's all an
illusion", or "G-d created the world old", then they state emphatically that
they do not accept that things are as they appear.  How do they rationalize
then that their mother is their mother, or that the world was not created
yesterday?  After all, we could have been created "old" yesterday.  If you
don't accept that "nature is as nature was" since the end of the first day
of Beraishit, then the age of the universe would seem to be the least of
your problems!

The second reason relates to the scientific evidence.  The conflict between
the age of the earth as described in the Torah (taking only the simple
understanding of 6 24 hour days) is undeniably in conflict with what nature
would dictate to our powers of reason.  The age of the earth and the
universe is verified by science in not one but rather many number of ways.
You can't refute the scientific argument by simply refuting Carbon-14
dating methods.  Rather, you'd have to refute most of 19th and 20th century
physics and chemistry!

Some examples:

1) The speed of light is a very well measured constant.  (more constant
even than time , according to Einstein).  There are stars that we can see
in the sky that are billions of light years away.  That means that the
stars are so far away that travelling at the speed of light it would take
you billions of years to reach them from here.  The fact that we can see
them now, today, means that they must have been radiating light billions of
years ago.  If the universe were only a few thousand years old, then the
light from these stars would not yet have reached us!

2) A similar argument as in 1) can be used for many forms of cosmic

3) it is known and measured that the crust of the earth floats on a "sea"
of magma.  The continents floating on this magma are drifting.  This causes
the movement of the continents, volcanos etc.  Most mountain ranges are
actually formed when continents collide (smush).  Likewise, it is no
coincidence that when looking on a map you observe that North America seems
as though it fits with Europe like pieces of a puzzle.  This is the model
known as Plate Techtonics.  We know that today the continents are drifting
at a rate of about 1 inch / year.  Using this model, and assuming the rate
of drift is somewhat constant then the age of the earth can be calculated
at around 4 billion years.  Even if the rate of drift were not constant, it
is unreasonable to estimate an age value of the earth using this model that
was less than a billion years.

4) If the world was created with sea water being pure H2O, which salinized
over time, the approximate number of years before the sea reached its
current level of salinization before reaching equilibrium would be about 4.5
million years.

5) Then there's the old C-14 dating thing.  Nuff said about that.

6) The magnetic core of the earth changes polarity with regular intervals.
By examining the magnetic residue in ore we can see roughly how many times
the polarity has change in the history of the earth.  The rate of change of
this polarity is also fairly constant.  Using this measurement to age the
earth also establishes an age of over 4 billion years.  Even if the rate of
change of the polarization is severely off, there's no way to come anywhere
near 6000 years.

7) Finally, the most overwhelming argument is the fact that so many
independent means all agree to an estimated age of the earth of 4.5 billion
years, in a universe at least 10 billion years.  A single theory alone is
suspect.  Numerous supportive models, validated through experimentation,
are very convincing.

These are just some means that I am aware of which place the age of
the earth scientifically at far beyond the age indicated by the
Torah. I'm sure there are many more.

Personally I prefer one of two possible explanations:

1) We don't have all of the scientific and theological knowledge
   we need to resolve this seeming contradiction.

2) The answer lies in the kind of relativistic model proposed by
   Dr.  Schroeder in his book "Genesis and the Big Bang".  A theory
   which many people have referred to in this discussion.  The basic
   idea of this theory being that the story of the fist six days is
   told from the frame of reference of its implementer (G-d), who
   observes the story of creation from a point outside the universe.
   Using an estimated size an mass of the universe it can be shown
   that what would pass as some 15 billion years in our galaxy would
   only be 6 days for an outside observer (rate of passage of time is
   affected by gravity).  After the story of creation, the remainder
   of the Torah is told from the frame of reference of the beings that
   are involved in the history therein: human beings. Hence after
   the 6th day, the passage of time as related in the Torah is the
   same as what we perceive in our lives.

   Sam Lightstone
   Toronto, Ontario


From: <leora@...> (Leora Morgenstern)
Date: Sun, 6 Nov 94 01:52:09 EST
Subject: Mathematical induction & formal logic in the Gemara

Sharon Hollander, in vol. 16 no. 22, asked for references on the use of
induction in the Talmud (I assume she means mathematical induction) as
well as a classification of valid arguments in the Talmud.

Sam Juni, in v16n27, answered that someone had given a talk at the last
AOJS convention that gave "a computerized classification of all
arguments in Talmud."

Well, I'm assuming that Sam is referring to me, since as far as I know,
I'm the only person who gave a talk at that meeting on the connections
between the reasoning used in the Gemara and formal logic.  But I most
certainly did not give a "computerized classification of all arguments
in Talmud."  (What does that phrase mean, anyway?  What is a
computerized classification?)

What I did was to explore the possibility of formalizing certain
arguments in the Gemara within a formal logic.  Indeed, even relatively
straightforward Talmudic arguments need a lot of work before they can be
recast as formal logical proofs.  The terseness of the Gemara and the
vast background knowledge that is assumed mean that many assumptions
must be made explicit and many intermediate steps supplied before the
argument can be read as a formal proof.  (One can view the work of many
Rishonim -- such as Rashi -- as doing exactly that.)

But in fact, most Talmudic arguments *cannot* be recast as proofs in
classical logic.  This phenomenon is not limited to Talmudic reasoning;
it is true of generic legal reasoning, medical diagnosis, and garden
variety commonsense reasoning.  Even arguments that seem to us to be
valid aren't so in the classical first-order-logic sense.  This has been
noted by researchers in Artificial Intelligence (AI) (which seeks to
formalize intelligent behavior) since the 1960's and 1970's: one of the
reasons is that concepts like "typically" and "usually", which cannot be
formalized in a meaningful sense within classical logic, abound in most
sorts of reasoning -- including Talmudic reasoning.  (Abduction and
analogical reasoning also abound.)  AI researchers have developed
different types of logic -- extensions of classical logic -- to handle
this sort of reasoning (this is still ongoing work); the best known
family of such logics is known as default logic.

Many seemingly universal statements -- that is, statements that purport
to be about *all* members of a class -- are really statements that are
true only of *most* members of that class.  So they are really best
captured within a default logic.  For example, the statement "Kol
hat'valin mefigin ta'aman" -- all spices lose their flavor after
grinding -- (Beitza 14a; discussion on permissibility of grinding spices
on Yom Tov with and without a shinui) really means that *most* spices
lose flavor, as is made clear a few lines later when the Gemara notes
that saffron retains its flavor (see Rashi).  Similarly, there are many,
many seemingly universal principles that are really default principles
or "typically" statements, that can be captured within a default logic.
For example, the principle that a person does not repay a loan before it
is due (Bava Batra 5b) is not a universal principle; it is a statement
that is typically true, and in an individual case, it is considered to
be true, unless there is evidence to the contrary.  This is just one
example of a chazaka (presumption), a concept underlying default logic.
Of particular interest are cases of chazaka demei'ikara -- a statement
that is presumed to be true at time t+k, because it was known to be true
at time t, and especially cases where two chazakot conflict in a
particular situation.  The parallel phenomenon is known as the "multiple
extension problem" in default logic.  I discussed connections between
the solutions to the multiple extension problem in default logic and
resolutions to conflicting chazakot in various sugiyot in the Gemara.

In any case,
1.  Recasting arguments in the Gemara as arguments in classical
logic can be done in only a small number of cases
2.  When it can be done, it takes a lot of work to turn such
an argument into a fully formal proof
3.  Non-classical logics are needed for many other arguments
4.  Lots of arguments in the Gemara are analogical or abductive
in nature, and current extensions to classical logic can't handle
these at all.

Back to Sharon's original question on mathematical induction in the
Talmud: one good place to look is Gideon Ehrlich's "Mathematical
Induction in the Talmud" (Higayon, v.1 pp.44-68) which discusses the
various places in the Gemara in which mathematical induction is
(implicitly) used; his bibliography gives some good source material for
historical discussions of the principle of mathematical induction.

As Jeff Mandin has pointed out (mj16v34), Sam Juni's examples are of
scientific induction as opposed to mathematical induction.  While this
sort of induction is a useful way of learning about the world, it's not
a valid rule of inference: you may see white swans all your life, and
conclude that all swans are white, but the fact remains that there are
black swans in Australia.  Mathematical induction, on the other hand, is
a valid method of proof.

--Leora Morgenstern


From: <GERVER@...> (Mike Gerver)
Date: Tue, 8 Nov 1994 1:11:55 -0500 (EST)
Subject: Rarest Shmoneh Esreh

A couple of months ago, I pointed out that on Dec. 3 this year, at
Ma'ariv of Motsei Shabbat, those of us who are living chutz l'aretz will
say a shmoneh esreh with a combination of brachot that has not been said
in 95 years and will not be said for another 95 years, namely 1) atah
chonantanu, because it is Motzei Shabbat, 2) Ten brachah, because it is
still before Dec. 4, 3) ya'aleh veyavo, because it is Rosh Chodesh, and
4) al hanissim, because it is Chanukah. 

I just realized that in addition to this, on the morning of Dec. 3, we
will be saying the second rarest shmoneh esreh for Musaf. In addition
to saying the Musaf for Shabbat Rosh Chodesh with al ha-nissim, we will
also add "ul'khaparat pesha" because it is a leap year. Furthermore,
the rarest shmoneh esreh is always preceded the previous morning by the
second rarest shmoneh esreh. This happens because, at least for the next
few centuries, the only way Rosh Chodesh Tevet can occur before we
start saying "ten tal umatar" is if Chanukah is very early that year
(relative to the solar calendar), and such years are always leap
years. And it is not possible for Kislev to be only 29 days long on a
year when Rosh Chodesh Tevet falls out on Motzei Shabbat, since Kislev
is 29 days long only in years when Marcheshvan is also 29 days long, and
in that case the previous Yom Kippur would have had to be on a Friday,
which is impossible. So the Shabbat before that Motzei Shabbat must also
be Rosh Chodesh (viz. 30 Kislev), and we would say Musaf for Shabbat
Rosh Chodesh.

Several centuries from now (I haven't figured out how many centuries),
as the solar calendar (which determined the day we start saying "ten
tal umatar" outside Israel) drifts relative to the lunar calendar, a
time would eventually come when we would start saying "ten tal umatar"
after Rosh Chodesh Tevet even when it is not a leap year, and then we
would no longer say the second rarest shmoneh esreh on the morning
preceding the rarest shmoneh esreh. Such an event, when it first happens
and for a few thousand years afterwards, would be the Rarest Combination
of Shmoneh Esrehs is a 12 Hour Period, and would occur much less often
than the Rarest Shmoneh Esreh itself. However, long before that time,
Moshiach will have come, we will no longer use the fixed calendar, and
in any case we will not be living chutz l'aretz.

Mike Gerver, <gerver@...>


End of Volume 16 Issue 42