Tuesday, October 26, 2010

Chazal Knew the Number of Stars!

Here's an oldie but goodie. (I have a lot of 'em, but am slow in cleaning them up for the FH blog.)

Babylonian Talmud, Berachot 32b:
Resh Lakish said: The community of Israel said before the Holy One, blessed be He: Sovereign of the Universe, when a man takes a second wife after his first, he still remembers the deeds of the first. Thou hast both forsaken me and forgotten me! The Holy One, blessed be He, answered her: My daughter, twelve constellations have I created in the firmament, and for each constellation I have created thirty hosts, and for each host I have created thirty legions, and for each legion I have created thirty cohorts, and for each cohort I have created thirty divisions, and for each division I have created thirty camps, and to each camp I have attached three hundred and sixty-five thousands of myriads of stars, corresponding to the days of the solar year, and all of them I have created only for thy sake, and thou sayest, Thou hast forgotten me and forsaken me! Can a woman forsake her sucking child?
I find this piece of aggadah especially fascinating because of what some claim is an amazing correspondence between it and astrophysical reality. I first came across this idea in the Proceedings of the Association of Orthodox Jewish Scientists (unfortunately I no longer have the article) in which S. Aranoff explains that if one multiplies to the point of "30 camps" one arrives at 2.9 x 108 galaxies in the universe. Multiply to "myriads" and one gets 3.65 x 109 stars per galaxy. Multiplying these numbers gives a value of about 1 x 1018 for the number of stars in the observable universe.

Let's now compare the Talmud numbers with current (2010) scientific estimates:

Galaxies in the known universe:
Talmud: 2.9 x 108
Science: minimum 8 x 10
Difference: 2 orders of magnitudes
Stars per galaxy:
Talmud: 3.65 x 109
Science: 4.5 x 1011
Difference: 2 orders of magnitudes
Stars in the known universe:
Talmud: 1 x 1018
Science: 3-7 x 1022
Difference: 4 orders of magnitudes
This is astounding! Resh Lakish is from the 3rd century CE, and he is passing on a tradition that is within a few orders of magnitudes from what science has estimated for the number of stars in the known universe. The fact that there was even a conception of such large numbers is absolutely amazing! This passage is used by many kiruv workers to prove that Chazal must have had a God-given mesorah. It is easy to find references on the 'net suggesting this. (When in doubt, check Aish. They claim that Chazal even knew about galactic clusters, estimating it at 30 galaxies per cluster (the Milky Way cluster contains more than 40 galaxies.) They also speculate what other groupings might mean, and suggest that another "30 grouping" might be "megasuperclusters".)

Once again, it is time to be a party-pooper. So let us now deconstruct this amazing "coincidence".

1) There is in this proof an assumption that the Talmudic passage has embedded within it a statement about physical reality. But there is no reason to suspect that this was the intention of Chazal; it is likely that they are just using hyperbole to emphasize how beloved Israel is to God, which - of course - is a major theme in the written and oral law. (As an aside, note that the actual terms used refer to Roman army units.)

2) The ancient Hebrews basically believed in the astronomy (and astrology) as developed by the surrounding cultures in which they lived, such as Assyria and Babylonia and - later - Greece. So perhaps - assuming a very old mesorah - we should give the Assyrians the credit for their understanding of the vastness of the universe??

3) Even if we were to grant the raw numbers (I don't), it works both ways: many more sources show an incorrect knowledge of astronomy. For example, regardless of the feeble attempts of "scientific" OrthoFundies to reconcile the creation story of Genesis with modern science, the much more compelling argument is that those who passed down and eventually wrote down the story believed, like other ancient peoples, that the sky was a solid dome with the Moon, Sun, and stars all embedded in it. And need we mention the myriad of old rabbinic sources (and, embarrassingly, even modern ones such as statements by the last Lubavitcher Rebbe) that insist on a geocentric universe (usually accompanied by some claptrap about relativity proving that geocentricity is "as valid" as heliocentricity.) Other examples in astronomy (and other knowledge disciplines) abound.

4) The twelve constellations are an arbitrary convenience for astronomical observations. The stars in a constellation have no relationship to one another besides an apparent proximity. 30 hosts per constellation is an implied relationship in the proof (but not necessarily the Talmud itself) and is actually a meaningless mathematical relationship. And what is the basis for "multiplying up to camps" to get the number of galaxies? What do hosts, legions, cohorts, and divisions represent, anyway? Some deep, mystical secret that our puny minds are not privy to?

5) Why is God off by even 1 order of magnitude?

6) I've saved the best for last.

From ancient India comes the Lalitavistara Sutra, a Buddhist text that recounts the miraculous deeds of Gautama Buddha. French scholar Georges Ifrah describes in an interview with Robert Krulwich how the Buddha was in a counting contest with a mathematician named Arjuna. One contest consisted of counting the "atoms" (that is, the smallest unit of matter) in a yojana (about 10 km). See the article for the specific formula which - according to mathematician Alex Bellos - shows that the Buddha determined quite accurately the size of a carbon atom! One notable difference from the Talmudic story is that the intention of the Buddhist text is to represent a very large number. (By the way, Indian culture - unlike that of Judaism and the ancient Near East - had actual words for VERY large numbers. They didn't just give up at "10,000"!)

Of course, a true fundie would probably claim that the Indian religions (and its later Buddhist offshoots) were ultimately derived from Judaism anyway and will point to the story of the children of Abraham being sent away to the East (see Rashi to Genesis 25:6). So don't expect that arming yourself with facts will win any arguments with missionaries kiruv maniacs.


MKR said...

I appreciate your patiently putting all these materials together. It's very instructive. The kiruv arguments seem to turn on the fact that even a stopped clock tells the correct time twice a day.

Skeptitcher Rebbe said...

Galaxies in the known universe:

Talmud: 2.4 x 108
Science: minimum 8 x 10
Difference: 2 orders of magnitudes

Actually doing the math gives you 2.92 X 10 ^ 8 rather than 2.4

Not sure if this was a typo on your part or just a dumb mistake on S. Aranoff's part.

Still 2 orders of magnitude at this scale is a huge number. I read on the Chabad website this:

"Doing the math: 12 x 30 x 30 x 30 x 30 x30 x 365,000 x 10,000 = 106,434 x 10^18 = approx 10^22.

But then we have to include the other non-Zodiac constellations, bringing us closer to the 24th power. Apparently, these rabbis had a higher source of knowledge."

First off their numbers are totally off, as your article shows the Talmud describes 10 ^ 18 stars comparred to the scientific 10 ^ 22. I can't believe that they made such a dumb mathmatical error. Not to mention they claim that science has claimed 10 ^ 24 stars, still putting them off by 2 orders of magnitude.

Although determining constellations is fairly arbitrary, but according to what I found online there are about 88 determined constillations. This may put them one order of magnitude closer to the total number but the number of stars per galaxy would still be off by two orders of magnitude regardless of the number of constillations. Also in order for this to work the total number of constilations would have to be at least 350,000 compared to the 88 determined constillations, in order to come to the smallest estimate provided here 3 x 10 ^ 22.

In short this isn't a close estimate at all. 4 orders of magnitude is an enourmous difference. Imagining me paying back a $10,000 loan with $1 saying that it is close, just 4 orders of magnitude a away, basically the same amount and you will see my point.

Frum Heretic said...

I fixed the typo, thanks. (Actually, my notes had the correct answer and I can't be 100% sure that the original article has 2.9)

As far as constellations, they were referring to zodiacal constellations and not the more expansive definition used by science.

The Chabad article is nonsense for that reason alone. PLUS, they are claiming that the passage in the gemara indicates some higher knowledge, but feel the need to a fudge (and a large batch at that!) factor to tweak the number??

benqish said...

I really need to read this a few times to understand the mathematics!

I still have one point to make. Why do you assume that modern scientists know the number of stars and galaxies. Just think of the size of the brain of the greatest living astronomer or the size of his largest telescope compared to the universe. The comparison is mind boggling. Do not fall into the easy trap of assuming that science is necessarily correct. The arrogance of modern scientists is very sad and that should not mean that a critical person like you - and I admire you for that - should play along with it. Science does usually have an answer for most things, maybe even the best answer, but there are other answers. Science itself is not monolithic but multi-faceted and multi-opinionated.

Frum Heretic said...

I'm not sure where scientific arrogance comes into play here. The claim that folks are making is that the gemara jives with scientific findings. The easy way out would have been to simply say that the gemara has the correct number and science is wrong. But then, of course, one is speaking to a completely difference audience.

Again, I don't believe that the gemara is making any such statement about the actual number of stars. It is using hyperbole and metaphor to convey the great love of God for the Jewish people.

Deborah Shaya said...

A person must do Teshuva to Hashem if he/she has been inside any place of idolatry.

Avodah Zarah denies the Sovereignty of Hashem, the One G-d, and Creator of the World.

e.g. a Buddist temple/Hindu temple/church/Sikh temple/Greek temple/buildings of any other kind of foreign worship. These are all places of idolatry.

Hashem, our G-d, is a very “JEALOUS G-D” who demands “EXCLUSIVE WORSHIP.” (2ND Commandment.)

Anonymous said...

haha.. damn fundies. Hinduism is one of the only ANCIENT religions that still survives today, and Buddhism is practically a direct derivative of some of hinduism's most ancient Vedanta Philosphies. I'm studying Orthodox and Ex.Orthodox Jews atm, and I'm enjoying your blog. Thank you :)

Anonymous said...

Maybe the ancient Egyptian knew that, read about ancient Egypt at http://famouspharaohs.blogspot.com