How did Chazal know that hemophilia is transmitted by the mother's DNA?

A while back, I wrote about Rabbi Aharon Feldman's mistaken claims about the Chazal's statement about brain exuding semen, which purportedly meant that the pituitary gland emitted a hormone that controlled semen production. I think a discussion of another idea in his essay would be in order.

This time, I will cite the full paragraph {update: from this rather famous article}:

Why does mainstream opinion reject R.Avraham’s opinion? This is not because they considered the Sages greater scientists than their modern counterparts. Rather, they believed that, unlike R. Avraham’s view, the source of all the knowledge of the Sages is either from Sinaitic tradition (received at the Giving of the Torah) or from Divine inspiration. That they were in contact with such sources in undeniable. How else could we explain numerous examples where the Sages had scientific information which no scientist of their time had? How were they so precise in their calculations of the New Moon? How did they know that hemophilia is transmitted by the mother’s DNA, a fact discovered relatively recently?[1] How did they know that “a drop exudes from the brain and develops into semen” without having known that the pituitary gland, located at the base of the brain, emits a hormone which controls the  production of semen. None of this could have been discovered by experimentation.   Either they had a tradition directly teaching them these facts, or they knew them by applying principles which were part of the Oral Torah regarding the inner workings of the world. Thus they knew the precise cycle of the moon; they knew that there was a relationship between the coagulation of blood and motherhood; and they knew that there was a relationship between the brain and male reproduction.

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[1] It is forbidden to circumcise a child whose brothers have died from bleeding after his circumcision, מתו אחיו מחמת מילה, because of a danger that he too might die. Since the brothers died from what we know now as hemophilia, and we are afraid that this condition is hereditary. Since this prohibition applies only to a maternal brother, the Sages knew that hemophilia is inherited through the mother, a fact discovered relatively recently.

Firstly, he claims (along with mainstream opinion) that all of Chazal's knowledge of science either came from derashot or Divine revelation. This would be rather surprising to Rav, who studied under a shepherd. As we see in Sanhedrin 5b:

 But did not Rav himself say: I spent eighteen months with a shepherd in order to learn which was a permanent and which a passing blemish?

This would be rather surprising to Shmuel (in Niddah 47a) who, in order to learn the physical signs of female maturity, had a maidservant pose nude for him, and then recompensed her for her embarrassment:

Shmuel said: Not that the wrinkle actually arises {=appears}, but rather, when she puts her hand behind her, it appears as if the wrinkle below the breast appears.
Shmuel examined his slave and gave her four zuz as payment for her embarrassment.

This generalization, that all of Chazal's knowledge stemmed from Divine revelation or derashot, is thus demonstrably false.

Rabbi Feldman gives three proofs that Chazal knew (some) knowledge via Divine revelation or else from derashot. One I addressed in the aforementioned post, about the brain exuding semen, where not only is the pituitary gland explanation a stretch, but in fact Aristotle and the Pythagoreans made an identical statement, such that Rabbi Feldman would be forced to assert that the Pythagoreans also had Divine inspiration.

In this post, I would like to turn to consider a second of his statements, namely that:

How did they know that hemophilia is transmitted by the mother’s DNA, a fact discovered relatively recently?

In fact, the gemara makes no mention in particular of DNA. Rather, in Yevamot 64b, we have:

For it was taught: If she circumcised her first child and he died, and a second one who also died, she must not circumcise her third child; so Rabbi. R. Simeon b. Gamaliel, however, said: She circumcises the third, but must not circumcise the fourth child... 

And a later case involving maternal cousins:

Come and hear what R. Hiyya b. Abba stated in the name of R. Johanan: It once happened with four sisters at Sepphoris that when the first had circumcised her child he died; when the second [circumcised her child] he also died, and when the third [circumcised her child] he also died. The fourth came before R. Simeon b. Gamaliel who told her, 'You must not circumcise [the child]'.

And in the (setama de-)gemara's analysis a bit later, we have איכא משפחה דרפי דמא ואיכא משפחה דקמיט דמא:

In the case of circumcision, one can well understand [why the operation is dangerous with some children and not with others] since the members of one family may bleed profusely while those of another family may bleed little...

Though one would think that, had they really had good knowledge of hemophilia, they would be able to recognize the symptoms by the first child, know absolutely that it was a genetic disorder transmitted on the X chromosome, and not waited for a second or a third. That is, a statement like "if the blood is loose, then one should not subsequently circumcise a second sibling."

Now, is Divine knowledge of DNA and the X chromosome the the only way of knowing this. Rabbi Feldman rejects normal discovery of this fact. As he writes:

None of this could have been discovered by experimentation.

But is this really so? It is true that the first time we see hemophilia in a medical work is in a work by Abulcasis,  though he does not mention the maternal angle. But we do not have every medical work from the ancient world, and it may well be that someone else did recognize it.

But one can recognize this fact of maternal transmission without knowledge of DNA. Well, the fellow in fairly modern times to discover it did so:

In 1803, Dr. John Conrad Otto, a Philadelphian physician, wrote an account about "a hemorrhagic disposition existing in certain families" in which he called the affected males "bleeders."^[23] He recognized that the disorder was hereditary and that it affected mostly males and was passed down by healthy females.

He wrote:

"About seventy or eighty years ago, a woman by name of Smith, settled in the vicinity of Plymouth, New Hampshire, and transmitted the following idiosyncrasy to her descendants. It is one, she observed, to which her family is unfortunately subject, and had been the source not only of great solicitude, but frequently the cause of death. If the least scratch is made on the skin of some of them, as mortal a hemorrhagy will eventually ensue as if the largest wound is inflicted. (…) So assured are the members of this family of the terrible consequences of the least wound, that they will not suffer themselves to be bled on any consideration, having lost a relation by not being able to stop the discharge occasioned by this operation."

This was decades before Gregor Mendel (who researches genetics in plants) was born; and Mendel only published in 1865. And DNA, and its structure, was only understood much later.

How did Dr. Otto discover this? By simple observation. He traced people with the disease, see who had it, and who their ancestor was. If Chazal were indeed discussing hemophilia, then they (or contemporary Greek scientists) could have simply seen the pattern, given enough repetition. No knowledge of the internal workings of DNA is necessary!

Furthermore, there is faulty science of Chazal which works out to predict that this blood-disease should be maternal. As we see in parashat Tazria, on the pasuk Isha Ki Tazria veYalda Zachar, Ramban writes:

ובמשמעותו אמרו (שם לא א): 

אשה כי תזריע, אשה מזרעת תחילה יולדת זכר. 

ואין כוונתם שיעשה הולד מזרע האשה, כי האשה אע"פ שיש לה ביצים כביצי זכר, או שלא יעשה בהן זרע כלל, או שאין הזרע ההוא נקפא ולא עושה דבר בעובר, אבל אמרם "מזרעת", על דם הרחם שיתאסף בשעת גמר ביאה באם ומתאחז בזרע הזכר, כי לדעתם הולד נוצר מדם הנקבה ומלובן האיש, ולשניהם יקראו זרע. 

Thus, the mother contributes the blood and the man contributes the white. This, in accord with contemporary Greek science.

And we see in the gemara in Niddah (31a) that the mother contributes the blood:

Our Rabbis taught: There are three partners in man, the Holy One, blessed be He, his father and his mother. His father supplies the semen of the white substance out of which are formed the child's bones, sinews, nails, the brain in his head and the white in his eye; his mother supplies the semen of the red substance out of which is formed his skin, flesh, hair, blood and the black of his eye; and the Holy One, blessed be He, gives him the spirit and the breath, beauty of features, eyesight, the power of hearing and the ability to speak and to walk, understanding and discernment. When his time to depart from the world approaches the Holy One, blessed be He, takes away his share and leaves the shares of his father and his mother with them. R. Papa observed: It is this that people have in mind when they say, 'Shake off the salt and cast the flesh to the dog'.

Ancient Greek medicine was a well-developed system. As was Chazal's science. So is modern science. It is no wonder that, on occasion, their paths may cross. That one particular conclusion of one system is matched in a second system does not indicate that they share assumptions. For years, people went to bloodletters, or applied leeches. This because of false beliefs about the four humours of the body. Yet, in some instances, nowadays bloodletting is a good idea, and has positive effect. This does not mean that it is because those who originally recommended leeches had a deep understanding of modern science.

If Rabbi Feldman had left it as positive kiruv, we could leave well enough alone. Perhaps they reached this knowledge via some Divine source. There are a few (IIRC, about four) gemaras that present a solution of sod Hashem lireav, sometimes among other solutions. And this might even be inspirational. But to take this and insist it is the only possibility, and then to use it as a mallet to try to attack the well-established, and true, position of Rabbi Avraham son of the Rambam, but others in his camp as well, that Chazal could err in science -- well, if so, then the response has to be to critically assess whether the evidence truly indicates that, and that Divine knowledge is the only reasonable explanation of these phenomena. And it isn't.