Scientific Techeles Gematria

I already had this on my web site before I started this blog, but I realized today that I have no link to it anymore (and I am very tired). So, rather then retype it, here is the link:

Techeles Gematria

It is an interesting gematria that I came across in yeshiva. Basically, if you combine some gematrias of the word techeles, and then convert that number (assuming it is in units of amos (~18 inch)) into nano-meters, you get the maximum absorption frequency of light of indigotin (in the visible range), which is the chemical composition of the dye from the murex trunchulus snail (and the indigo plant). Take a look!

When is the Gender of an Unborn Child Determined?

The mishnah in Berachos Chapter 9 says:

One who cries out for that which is past - this is prayer in vain. How so? His wife is pregnant, and he says, "May it be Your will that my wife give birth to a male," - this is a prayer in vain.

It would seem at first glance that this implies that the gender of the child is determined before a woman (or perhaps her husband) notices that she is pregnant. However, this seems not to be the case, for the Yerushalmi says:

The academy of Yanni say: The Mishnah was speaking about a woman on the birthing stool. But before that point, one may pray [for the gender] in accordance with "Behold, as clay in the hand of the potter...."

This implies that the gender is not set until right before birth! And further, in Midrash Bereishis Rabba 72:6 we see the opinion of R' Yehudah ben Pazi who says that even on the birthing stool the fetus can be transformed, and thus one can still pray.

Most people today go by the rule that up to 40 days, one can pray for the gender, but not after that. [I have not yet found the source for this.]

According to modern science, the gender of the child is determined at conception (although I remember seeing something to the effect that there is a possibility of gender change at the very beginning of pregnancy, but I cannot recall where I read about it). This seems to contradict the gemara's interpretation of the Mishnah in Berachos.

However, it does not necessarily. There is a concept in the gemara that one should not count his grain too much, because then G-d will not cause a miracle and give him more. Meaning, that G-d does not want to do open miracles, but hidden ones He does. Therefore, if no one has detected the gender of the child, it would seem that G-d could perform a hidden miracle of changing the gender all the way through pregnancy. (However, today, with ultrasound, it would seem we cut this time down quite a bit - once we detect the gender, a gender change would be an open miracle). This would explain the Gemara's opinion of the Mishnah, that the prayer in vain refers to the time during birth, i.e. where the gender can be observed for the first time.

However, there is a source in Chazal that gender is determined at conception. The Midrash Tanchumah, Parashahs Pekudeh, sif 3 discusses what happens during conception and says that G-d tells a certain angel to go down and protect the droplet, and cultivate it into 365 parts. After doing so the angel shows the drop to G-d and says:

"I have done just as You have commanded me, so what has been decreed for this droplet?" The Holy One, Blessed is He, immediately decrees the destiny of the droplet; if it will be male or female, weak or strong, ...

This Midrash is seemingly saying that the gender is decreed at conception! If this is the case, then perhaps (unless this goes against psak halachah) one could take this view and say that indeed gender is determined at conception, and explain the Mishnah above accordingly.

The Number of Stars in the Universe

As is mentioned in many outreach lectures, the Gemara in Berachos 32B says the following:

Hashem said to her (Israel): My daughter, 12 mazalos did I create in the rakia, and for each one I created 30 hosts. For each host, I have created 30 legions, for each legion I have created 30 cohorts, for each cohort I have created 30 maniples, for each maniple I have created 30 camps. To each camp I have hung365,000 myriads (10,000s) of stars corresponding to the days of the solar year. All of them I created for your sake.

This Gemara seems to be telling us how many stars there are in the rakia (which I have found is best defined as the view of the sky from the Earth). It is obviously rounding the number off because it was well known when this was written that the solar year is a bit longer than 365.25 days.

If you multiply out the groups, you get a total of 1.06434X10^18 stars. As many point out, this is within a few orders of magnitude of the current scientific estimates of the number of stars in the visible universe.

I thought I would add a bit to this idea as follows:

First, according to this Gemara, it is only mentioning the 12 mazelos of the zodiac. The zodiac covers a 16 degree band across the sky. Therefore for the total number in the whole sky, you must compute the surface area of the 16 degree band and apply the stars-per-degree^2 to the rest of the celestial sphere. This is pretty straight-forward, and one finds that the whole sky (assuming the same star density) yields 7.6476 X 10^18 stars.

Now, according to sceintific studies, there are anywhere from 10^21 -> 7 X 10^22 stars in the observable universe. These numbers are computed by taking a small strip of the sky, and counting the number of galaxies in that strip, and then assuming each galaxy has an average number of stars similar to our own Galaxy. They then use this to estimate the whole universe. This can be problematic for a couple for reasons.

First, besides the fact that we don't know how many stars are in earlier galaxies, we also don't know if we are seeing different galaxies to begin with. This is because through the bending of light around other galaxies, sometimes you can see two or more images of the same galaxy. This is referred to as an "Einstein Ring." Now, we can detect these, but it is entirely possible that there are other lensing effects we can't immediately detect. This phenomena reduces the number of galaxies in any view of the sky. Also along these lines are topological concerns. There is debate about the shape of the universe, but it seems that it is flat. This means that if the universe is finite (which is accepted) then the universe behaves like a pacman game in that if you fly too far in one direction, you will loop around and come back to where you started. With this in mind, it is possible that some the the most distant galaxies we see are actually the same galaxies we see elsewhere.

Second, assuming each patch of sky is equal to the others is highly extrapolative. A perfect example of why is found here. In this article it describes a huge, vast empty "hole" in the universe devoid of stars and galaxies that was not noticed previously. How many other holes there are we may never know for sure. These "holes" reduce the estimated number of galaxies in the universe even more, and if there are enough of them, could invalidate the extrapolation of one patch of sky to the next.

With all this in mind, the difference of 7 X 10^18 and 7 X 10^22, while enormous, is not conclusive. (For a quick example, say we find out that most old galaxies only have about 10^9 (1 billion) stars and that there are really only about 10 billion unique galaxies, then the number comes to 10^19.)

Scientific Confirmation of the Reason for Issur Yichud

For this post, I get off easy, since FKM posted a nice post on the topic.

Check it out here:

http://fkmaniac.blogspot.com/2008/07/research-that-vindicates-issur-yichud.html

Basically, researchers found that when a man was alone with a woman, for a few min., his testosterone levels rose about 8% even if he did not find the woman attractive...

Cool Torah and Science Movie

I found this movie on YouTube. It is a computer animated movie that deals with Torah and Science issues in an entertaining way (I think meant for children). It is made by Nathan Aviezer, author of "In the Beginning: Biblical Creation and Science", and "Fossils & Faith: Understanding Torah and Science" (both available at Amazon). "In the Beginning" is highly recommended by me, as it goes step by step through the Creation narrative and gives a possible scientific explanation of the events that are going on each "day". (He is of the opinion that each "day" was a "phase" of variable length). Anyways, that book is now an entertaining movie, where RamBam, Einstein, and Darwin fly through time in a space ship, so here it is (in 5 parts):

PART 1 of 5:


PART 2 of 5:


PART 3 of 5:


PART 4 of 5:


PART 5 of 5:


They can be found in Hebrew as well at: faithship's Videos