Volume 19 Number 93
Produced: Wed Jun 7 23:38:02 1995
Subjects Discussed In This Issue:
Akudim Nekudim U'vrudim
[Gilad J. Gevaryahu]
Goedel and Eilu Va'Eilu
[Micha Berger]
Yacov, Lavan, Sheep, and Genetics
[David Neustadter]
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From: <Gevaryahu@...> (Gilad J. Gevaryahu)
Date: Fri, 19 May 1995 16:49:46 -0400
Subject: Akudim Nekudim U'vrudim
My friend, Eddie Goldberg, was kind enough to allow me to post a summary of
his article on the issue of "akudim nekudim u'vrudim". The original article
appeared in Segulah Le'Ariella, Jerusalem, 1990.
Gilad J. Gevaryahu
==============
This is an updated version of the note about Jacob and Laban's sheep. I
will try and state the main points briefly. Note, probably only goats
are spotted (and the sheep are hum, i.e.brownish instead of the dominant
white) but I use the phrase "spotted sheep" for those that Jacob gets
for simplicity of explication, even though this is not the designation
in the Bible either.
1. Jacob's family were professional herders. Evidently Laban's was not.
However Laban's family were not complete fools. It is clear that both
sides knew that there was a genetic factor in the deal and for this
reason their flocks were separated by 3 days travel (Breshit 30:36).
Furthermore, Laban's sons accused Jacob of cheating (fooling) their
father. Of course it was also true of Laban.
2. There are two stories of what Jacob did. The first story is about
the peeled sticks. If you read Hazal, especially in the midrash, you
will see that almost none of them believed that "babameise" either.
They ascribe it to either ahizat einayim (a form of sorcery), switching
of fetuses (by God) or to pregnancies due to fertilization by the sheep
drinking at the trough and backing up and sitting in the trough from
whose waters they were fertilized (if I remember, the sperm came in hail
[from heaven?]). (I guess this is not so far from Rashi's explanation
to 30:39). Nor in my estimation could any professional shepherd have
believed this, no less pass it on orally until the time of Moshe
Rabbeinu. In fact, I think, as you will see at the end, this was a
funny story that they told themselves about how Jacob was able to
outsmart and belittle Laban.
3. The second story comes when Jacob calls his wives to the field to run
away and he tells them of his dream. A messenger of God shows him that
the spotted ram is mounting the non-spotted ewe and this is how to get
even with Laban. (By this we know that Jacob understood Mendel's laws
of random assortment of chromosome pairs, at least as it applied
practically to his sheep and goat herds.) I contend that Jacob mated
all the ewes with spotted rams before making the deal with Laban. How
did Jacob know that Laban would let him set the terms of the deal? When
Jacob first came, and Laban wanted him to work, he asked Jacob what his
terms were. Jacob gave him an offer he couldn't refuse: no cash,
nothing up front, just your daughters when I have finished . When Jacob
asked Laban for Rachel (after his marriage to Leah), Laban set the terms
of 7 more years and even gave Jacob a prepayment, Rachel, so that Jacob
wouldn't refuse. So when Jacob wanted to leave, he knew that Laban
would want him to stay and would ask to state his price. He made a deal
that Laban wouldn't refuse. Since Jacob was in a position similar to an
indentured servant (Devarim 15:12) Laban has certain obligations which
he admits. Jacob, being a "nice guy", tells him: actually you don't
have to give me anything if you agree to the following deal....
4. How did Jacob enrich himself? He started his compound interest stake
(his spotted flock) by using insider knowledge as well as utilizing
Laban's capital (Laban's flocks) without Laban's knowledge. By the
pre-deal matings, he got not the small number of spotted sheep due from
random matings, but somewhere between 25-50% of all the sheep born
during the next birthing season. In addition he greatly enriched the
remaining herd with the recessive spotted gene. I assume from the
story, that spotted is the recessive trait and non-spotted the dominant
trait. Spotted sheep are homozygous (both chromosomes have the gene for
spotted). When a spotted ram is mated with a spotted ewe, all of the
offspring are spotted. This is why Jacob says that any non-spotted
sheep that you find in my flocks are stolen. Non-spotted sheep were of
two kinds: heterozygous and homozygous, which are ndistinguishable.
However a good, professional shepherd could distinguish them by test
matings; the heterozygotes can sire or give birth to spotted offspring.
1) Non-spotted heterozygous sheep have one gene of each kind.
When a spotted ram is crossed with a non-spotted heterozygous ewe, half
the progeny will bespotted (homozygous recessive) and half white
(heterozygous);
2) Non-spotted homozygous dominant sheep (with two genes for
non-spotted).
When a spotted ram is crossed with a non-spotted homozygous ewe, all of her
new offspring will be non-spotted heterozygotes (i.e. they will have one
spotted and one non-spotted chromosome).
In the ensuing years, Jacob must remove the spotted sheep at birth and
cross only white ones. However he knows which rams are heterozygous
from previous crosses and uses them to mate with all the ewes (until he
has sufficient opportunity to test for new heterozygous rams) thus
getting the maximum number of spotted offspring. Mating a heterozygous
ram with heterozygous ewes yields 1/4 spotted sheep, 1/2 non-spotted
heterozygotes and 1/4 non-spotted homozygotes. Mating a eterozygous ram
with homozygous ewes yields all nonspotted progeny, 1/2 heterozygous and
1/2 homozygous dominant.
5. How do we know that the deal was made after the mating season? After
I told my wife, Ariella my idea, she told me that I could only be sure
if it was written in the text. She then read the text with me and found
that in the story most of the verbs are in the vav hamehapechet (passe
simple - narrative past) tense of the story: vayasar, vayiten vayasem,
..., vayehemu, vateladna, and all of a sudden: vehakesavim hifrid
Yaakov! This is the plu-perfect, before the time of the story. If you
want another example you will find it in Genesis 26:18ff. Incidently,
my daughter who had been listening said that he was called Lavan as a
shem gnai (a bad name) because that was how they tricked him. Also, in
Hebrew there is no distinction between the sheep of Lavan and the white
sheep (another double entendre).
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From: Micha Berger <aishdas@...>
Date: Mon, 22 May 1995 08:37:33 -0400 (EDT)
Subject: Goedel and Eilu Va'Eilu
Ari Belenky (<belenkiy@...>) writes:
> Micha Berger continued my thought, *misrepresenting* it: he repeated
> familiar "ellu ve'ellu divrei elochim hayim" (which was firstly
> pronounced to resolve the machloket between schools of Shammai and
> Hillel. Even they both argued Halakhicly flawlessly, Halakha follows
> Hillel's opinion. Why - it is another story.)
I didn't intend to misrepresent a continuation of your thought. I was
trying to accurately represent my own thought, which was similar to
yours. I appologize if I didn't make that clear.
You MUST distinguish between the arguments of Beis Hillil and Beis
Shammai, with those of Hillel and Shammai. The teachers only disagreed
three times, all of them on dirabbanan's (Rabbinic legislation).
The schools argues alot more often, the gemara writes, "because they
did not properly serve their teachers", and Torah was lost in the
transmission. The debate did NOT start with Hillel and Shammai
themselves.
I'm saying this not for Ari's edification, but because this issue is
a big peice of the debate between Graetz's "History" and Rabbiner Hirsch,
and has since become a major part of the debate between Conservativism
and Orthodox.
(In the conservative mythos, Hillel invents the middos shehaTorah nidreshes
bahem [hetmeneutical principles]. Shammai resists all innovation, and
rejects the midos for "strict tradition", providing thesis and antithesis
for Graetz's novel about the history of the Talmudic era.)
> All this is well-known and I did not discuss it because the solution
> that "Halakha follows Hillel" is perfectly legitimite solution on the
> syntaxis level and nobody has problems with it.
For similar reasons, your should be clear that halachah follows BEIS Hillel.
Again, in Graetz's view, a vindication of innovation in halachah; and in
C view, a vindication of their phylosophy.
I was trying to distinguish between two ideas, which I will call
Divrei Elokim Chaim (DE"C -- the words of the Living G-d / G-d of
Life) and halachah. My not making this distinction earlier probably
lead to Ari's misunderstanding of my idea. (Based on R. Tzadok
HaCohen -- it MIGHT even be what R. Tzadok was trying to say.)
I wrote:
: When two opinions argue, both are teaching Hashem's word.
: Halachah, on this level, contains paradoxes. Abayei could say assur,
: and Rava could say mutar, and both are within halachah.
Both schools were teaching DE"C. So, the level of DE"C does include
contradiction. (Or maybe, to be more exact, the logic used by DE"C does
not include Aritotle's law of contradiction.) By not being consistent,
DE"C stands outside the class of systems subject to Goedel's analysis.
: 2- On a different level, halachic rulings are made. We can not follow
: both Abayei and Rava.
This is the level I'm now titling "halachah". To convert DE"C to practice,
we must get a p'sak. In the case of Abayei and Rava, these psakim have
already been determined. As new situations and problems arise, the psak
does not yet exist. Such a system isn't closed, and therefor also may
not be Goedelian.
> The statement about "non-finitness" is merely non-true. In each moment
> Halakha is definitely finite: all rules are known and finite, all
> letters (things in the world known to us) also. We can multiply new
> sentences infinitely, the basis is still finite.
This seems to be saying that R. Mosheh's teshuvos could have been produced
algorythimcally. Are piskei halachah merely geometry like: applying a set
of ules iteratively to a collection of verses (and halachos liMosheh
misinai - laws given ascripturally to Moses at Sinai).
My point was that it wasn't. I was trying out the idea that the conversion
from a pluralistic DE"C in R. Tzadok's thought-logic, to a usable p'sak
halachah was a creative, and therefor system enlarging process. In fact,
I was insisting that Goedel seems to imply the idea of getting a singlular
p'sak halachah from the iterative application of a finite set of rules to
a finite collection of givens is not always possible.
R. Tzadok gives us an out. The iterative application gives us DE"C, which
allows contradiction. A creative, and therefor non-closed, system of p'sak
gives us halachah, which must be distinct.
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From: David Neustadter <david@...>
Date: Tue, 6 Jun 1995 20:46:18 +0300
Subject: Yacov, Lavan, Sheep, and Genetics
For me, the issue of explaining the story of Yacov and Lavan's sheep
using genetics was compounded by another question that bothered me about
the story.
Yacov basically tells his wives that he did not try to get rich off of
Lavan, but that Hashem just kept causing Lavan's sheep to give birth to
whatever type of offspring was assigned to be yacov's wages. If Yacov
was indeed taking advantage of Lavan, then he is also lying to his
wives. Somehow, based on Yacov's previous actions, I can accept that he
would take advantage of Lavan, but I would rather not accept the fact
that he lies to his wives. For this reason, I was driven to look for an
explanation of the whole story whereby Yacov is not purposely taking
advantage of Lavan, but rather even he sees the results as a miracle of
God (which he did not ask for).
The explanation goes like this:
Lavan has solid colored sheep and multicolored sheep. Obviously the
multicolored are the minority, otherwise Yacov wouldn't have asked for
them as his wages. Now, if you didn't know genetics, and didn't pay
particular attention to which of your sheep mated with each other, you'd
probably assume that if two solid sheep mated, the offspring would be
solid, and if two multicolored sheep mated, the offspring would be
multicolored, and that if a solid and a multicolored sheep mated, the
offspring would have a 50-50 chance of being solid or multicolored.
Based on this assumption, Yacov told Lavan that he wanted the
multicolored sheep, the minority, as his wages. He then SEPARATED these
sheep from the solid colored sheep. The reason that he chose his wages
this way is quite clear from the text - he tells Lavan that he will
later prove his honesty in that any solid sheep among his sheep will be
considered stolen. He obviously expected that his multicolored sheep
would have only multicolored offspring.
Now in order to claim that Yacov wasn't lying to his wives, all we have
to assume, is that Yacov also expected that the solid sheep left for
Lavan would have only solid offspring. This is a very fair assumption,
according to the logic described above.
However, neither Yacov nor Lavan knew that genetics doesn't work that
way. Obviously the gene for multicolored is recessive. Therefore,
Yacov was correct in expecting that his multicolored sheep would have
only multicolored offspring. However, among the remaining solid sheep,
some of them had one gene for multicolored. If these solid sheep with
one gene for multicolored mated with each other, then one in four of
their offspring would be multicolored. In this way, Yacov, in addition
to getting an initial flock and all of its future offspring, which is
all that he intended to get, got some of Lavan's offspring each mating
season.
I found this explanation of the story to be reasonably satisfying. The
one point I haven't mentioned yet is the issue of the sticks. Well, I
have an answer for that one too, but I admit that it's not quite as
satisfying as the rest of the theory. If you look closely at the text,
it doesn't say that the sticks caused the sheep to have multicolored
offspring. It only says that the sticks caused the sheep to become
sexually active. In fact, it seems from the text that that is why Yacov
put them there. He wanted his sheep to be more sexually active than
Lavan's. If Yacov actually thought that the sticks caused the sheep to
have multicolored offspring, why would he not have put them there for
all of the sheep?
Any comments?
David
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End of Volume 19 Issue 93
