R' Feldman brings this claim as one of his proofs that Chazal's science is Torah M'Sinai.
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” 2 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.
Let us examine each one of his proofs and see if they hold water.
1. How were they so precise in their calculations of the New Moon?
Were they really anymore precise then the scientists of their time? I don't think so. Ancient civilizations were able to calculate the movement of the moon quite well. Here is a quote from Wikipedia:
The calendar is based on mean lunar conjunctions called "molads" spaced precisely 29 days, 12 hours, and 793 parts apart. Actual conjunctions vary from the molads by up to 7 hours in each direction due to the nonuniform velocity of the moon. This value for the interval between molads (the mean synodic month) was measured by Babylonians before 300 BCE and was adopted by the Greek astronomer Hipparchus and the Alexandrian astronomer Ptolemy. Its remarkable accuracy was achieved using records of lunar eclipses from the eighth to fifth centuries BCE.
We see clearly that the Babylonian and Greek astronomers (who lived around the same time as Chazal) were able to make the same precise calculations
Chazal (Hillel II) set up the calendar that we use. This calendar is very accurate but not 100% accurate. Again from Wikipedia:
However, the assumption that 19 years exactly equal 235 months is wrong, so the average length of a 19 year cycle is too long (compared with 19 tropical years) by about 0.088 days or just over 2 hours. Thus on average the calendar gets further out of step with the tropical year by roughly one day in 216 years. If the intention of the calendar is that Pesach should fall on the first full moon after the vernal equinox, this is still the case in most years. However, at present three times in 19 years Pesach is a month late (as in 2005). Clearly, this problem will get worse over time
If R' Feldman is right, the calendar should not lose any days after all they got this knowledge Torah M'Sinai.
2. How did they know that hemophilia is transmitted by the mother’s DNA, a fact discovered relatively recently?
The answer to this is very simple. Chazal in Niddah write
איש מזריע בו לובן שממנו גידים ועצמות ... אשא מזרעת אודם שממנו עור בשר ודם
The man provides the white from which the bones and sinews grow ... the women provides the red from which the skin, meat, and blood come
Chazal thought that the blood comes from the women and therefore it made sense that a blood disease would go through the mother. However this has nothing to do with DNA. They believed this due to a mistaken idea that the blood of a person comes from his mother. Coincidentally, this mistake about the blood coming from the mother allowed them to get things right by hemophilia.
3. How did they know that “a drop exudes from the brain and develops into semen” 2 without having known that the pituitary gland, located at the base of the brain, emits a hormone which controls the production of semen.
Their statement was actually incorrect. Nothing exudes from the brain and develops into semen. The pituitary gland release hormones which stimulate the production of semen, but the hormones from the pituitary gland do not themselves turn into semen.
In short, I believe that I have shown that none of these proofs are proofs whatsoever.
On the other hand there is a whole list of statements Chazal that do contradict science. I will mention just one here and I leave it to the reader to decide what is more compelling.
The gemara in Bava Basra 25b has a dispute between R' Eliezer and R' Yeshoshua about the movement of the sun. The gemara has a similar dispute in Pesachim 94.
R' Eliezer says that the world is like a three-walled building; the north side is not covered; The sun travels along the inside of the building during the day. When the sun reaches the northwest corner, it goes above the building (therefore we can't see it, and goes eastward overnight, and rises in the northeast in the morning).
R. Yehoshua says, the world is like a box, the north side is covered;
1. When the sun reaches the northwest corner, it goes (through a window) in back of the box.
2. "Holech El Darom v'Sovev El Tzafon" - the sun (always) travels along the south by day, and circles around the north side by night.
It is absolutely clear that the above is incorrect. We know that the world is not covered by anything and the sun doesn't go behind it. We know that there is no window that the sun goes out at night. We know that the Earth spins and this is what causes the Sun to rise and set and we know that the Earth revolves around the Sun. These are not theories, they are facts and they are undisputable.
Some will try to answer that the gemara was talking allegorically and wasn't describing reality. That is clearly not true for 2 reasons:
1. The gemara in Pesachim brings a dispute between the Chachamim and the non-Jews about where the sun goes at night. They were clearly arguing with the non-Jews about reality and not about some deep concept in kabbala.
2. The Rishonim when they discuss shitas R' Tam about Tzeis Hakochavim, all bring this gemara down and they all mention the sun going out the window. They clearly held that Chazal were describing reality.
I am still waiting for a pshat in this geamra other then Chazal were mistaken in science. So far, I haven't heard or seen a single pshat that comes close to explaining the sugya.
The above is only a drop in the bucket of the conflicts. I could easily bring at least 10 more, obvious contradictions.
To sum up, I believe that I have refuted all of R' Feldman's proofs, however, I have not yet seen anyone explain how the gemara in Pesachim and Bava Basra does not contradict the scientific facts that we know.