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41

Ralbag (Gersonidies) has the earliest known use of a proof by mathematical induction in his mathematical work Maase Hoshev (1321 CE). Source: Rabinovich, N. L. (1970). Rabbi Levi Ben Gershon and the Origins of Mathematical Induction. Archive for History of Exact Sciences, 6(3), 237-248. Available in JSTOR here. (For comparison, the prevalent thought before ...


29

I would say the biggest explanation ahead of its time was not by the rabbis, but by the Torah, steadfastly defended by even the most rational rabbis in the face of prevailing secular thought. Up until 1929 (and perhaps even as late as 1949), the leading view in astronomy was that we lived in a steady-state universe with no beginning and no end. People often ...


21

This is from the Babylonian Talmud. Shabbat 135b says that we don't break Shabbas to save the life of a baby born in its eighth month of gestation. The idea was that there are 7-month babies and 9-month babies, and an 8-month baby was either an early 9-monther or a late 7-monther and if it were an early 9-monther, it probably wasn't going to make it. ...


19

Dr. Jeremy Brown, in a post on his Talmudology blog on science in the Daf Yomi, points out that Rava, quoted in Yevamot 97a, provides the first published claim that boys' puberty can be delayed by their being either overweight or underweight. כי אתו לקמיה דרבא אי כחוש אמר להו זילו אבריוהו ואי בריא אמר להו זילו אכחשוהו דהני סימנין זמנין דנתרי מחמת כחישותא ...


19

Based on Jewish law, a person's Jewish status (for a non-convert) is determined through matrilineal descent. This means that one is only Jewish from birth if their mother was Jewish. And their mother was only Jewish if their mother was Jewish. Based on this, a person can have seven out of eight great-grandparents who are Jewish, and still not be Jewish from ...


17

Rabbi Y.L. Rapaport suggested that R' Yehoshua Ben Chananiah's statement (כוכב אחד לשבעים שנה עולה ומתעה את (הספינות (בבלי מסכת הוריות דף י עמוד א) This is thought to refer to the periodicity of Halley's comet, about 1500 years before Halley discovered this. In regards to comments suggesting that this claim is unfounded, I note that several reputable ...


16

First, you should remember how bad infant mortality was in those days. So what it says about how some infants were considered not viable (and thus could not be touched on Shabbos), no longer applies today when infant mortality is much lower. You should talk about the change in infant mortality with your students. The way you phrased your question implies ...


15

See also this letter by the Lubavitcher Rebbe on this subject, in which he states: It is my firm belief that the sun revolves around the earth, as I have also declared publicly on various occasions and in discussion with professors specializing in this field of science. He also explains why he believed this way based on the Theory of Relativity.


13

R. Yosef Albo, Sefer ha-Ikkarim 3:1, writes: Coral is intermediate between inanimate matter and plants. We also find the sea sponge, which only has the sense of touch, and is an intermediate between plant and animal stages. We also find the monkey to be intermediate between animals and man. This idea is repeated, for example by R. Moshe Isserles (the Rema) ...


13

If we're counting mathematical comments by rishonim (Medieval Scholars), then in addition to @DoubleAA's reference to Ralbag (Gersonidies) who has the earliest known use of mathematical induction, other Jews have made some strides here as well. R. Avraham bar Chiyya has an interesting proof that the area of a circle is equal to half its radius times ...


12

According to Halacha we follow Rav Sheishes's view (bechoros 7b) who holds like Rabbe Yaakov (the Tannah) that the reason honey is kosher (even if the bee extracts part of its flesh into the honey as part of the process - Rabeinu Gershom) is a Gzeiras Hakosuv (by Hashem's command) and not like the opinion who says that the reason for its permissiblity is '...


12

At the core of your question is the assumption that the flood and its fallout was natural, and was subject merely to the laws of nature as we see them today. For the purposes of this answer I will not accept that premise, however I think that one can still reconcile the evidence we see nowadays with the flood in a cogent way that draws upon the natural ...


12

In the translation of Michtav M'elyahu (Strive for Truth vol. 4 p 355), R' Carmell quotes R' Dessler that halacha does not change even if the reason given for the law seems to be untrue. He says that there may be other reasons other than the one given for the said halacha, and only the most obvious reason was the one stated, so the halacha stands without ...


11

R' Eliezer Melamed, in an essay about this blessing and a related one for Torah scholars on the Beit-El Yeshiva website, formulates the standard thus: חכם מחכמי אומות העולם שידוע כחכם וגאון באחד מן המדעים, כלכלה, מתמטיקה או אחד ממדעי הטבע, ובעבודתו תרם תרומה נכבדה למדע ולאנושות One of the scholars of the [other] nations, who is known as a scholar and a ...


11

Apparently Rambam said: בבוקר אכול כמלך, בצהריים כבן מלך ובערב כאביון eat breakfast like a king, lunch like the son of a king and dinner like a pauper. among his other advice for health which seems to have stood the test of time. I read about this study last year which seems to confirm the wisdom of the above advice: High caloric intake at ...


11

The Rambam himself addresses your question. He writes the following in Moreh Nevuchim regarding the science in the Gemara: Moreh Nevuchim (3:14): אל תדרוש ממני להתאים את כל ענייני האסטרונומיה שהם ציינו אל המצב כפי שהוא, כי המתמטיקה היתה לקויה באותם זמנים. והם לא דנו בזאת מבחינת שהם מוסרים אמרות אלה מפי הנביאים, אלא מבחינת שהם היו חכמי אותן תקופות במקצועות ...


11

There is no special Talmudic dispensation regarding oats. The Mishna lists a grain called שבולת שועל as able to become Chametz. Most Rishonim don't identify that grain with what we call oats. Some Rishonim do identify that grain with what we call oats. Your point is one very strong proof for the former position, according to which indeed oats can't become ...


11

I believe it is referring to Ha'amek Davar to Bereishit 7:23, although note that he ultimately rejects this view and believes that the fossils are of antediluvian creatures belonging to our "world", rather than from previous "worlds".


10

This article from Dr J Menczer indicates that although there is a significantly lower incidence of cervical cancer amongst Jews it is not due to family purity laws, as even Jews who do not observe these laws have a lower incidence of cervical cancer.


10

The Ramban, in his commentary on Bereishit, writes that there were only two actual "creations" and the rest were more of "formations". He says that the two things that were actually "created" were light (and the resulting difference between that and darkness) and a "small point that had no substance" (נקודה קטנה שאין בה ממש). This seems to be a reference to ...


10

The Baal HaTanya writes: והיינו הגוף שלהם גדול כ"כ שהוא בבחי' מקום ומאחר שהם בבחי' מקום הרי הם ג"כ בבחי' זמן שהמקום והזמן שניהם הם נבראים בבחי' א So in other words, time cannot exist without space, and space cannot exist without time, they are one type of creation. Although I'm not sure the exact date of this Maamar, given the style it would seem to be ...


10

It seems that Rambam anticipated certain aspects of Einstien's General Relativity. The traditional view was that time is absolute and constant: "Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external." Issac Newton However, in the Guide to the Perplexed, Rambam sees time as ...


10

First of all, the whole point of the 'river turning to blood' was that it was supposed to be a miracle, an event showing that superiority of a force over the natural world (i.e. science). So, if anything, your example proves that the Jews DO believe in modern science, as they believe that there's no natural way to turn water into blood without divine ...


10

The Seforno (c.1500) writes this in is commentary to Genesis (8:22): עוד כל ימי הארץ זרע וקציר וקור וחום וקיץ וחורף ויום ולילה לא ישבותו. "לא ישבותו" מלהתמיד על אותו האופן בלתי טבעי שהגבלתי להם אחר המבול, וזה שילך השמש על גלגל נוטה מקו משוה היום, ובנטיתו תהיה סבת השתנות כל אלה הזמנים, כי קודם המבול היה מהלך השמש תמיד בקו משוה היום, ובזה היה אז תמיד עת ...


10

There is no Halachic issue SA YD 201.7 Rema הגה: מותר לעשותו על הגג ובלבד שלא יהיה תוך כלי או אבן אחת שחקקו ולבסוף קבעו אבל חבור אבנים הרבה לא מקרי כלי (תשובת הרשב"א סימן ת"ת):‏ Its allowed to make it on the roof, but not in a container or a stone that was already inground before to be fixed. However stone assembly is not a utensil.


9

I don't expect to have this marked as the correct answer, because my ability to recall and quote sources is abysmal. How many other people accept what I write as theologically sound is going to depend on the assumptions you are working with. We are always too happy to call other strains of thought as being heretical. I think the main problem that you are ...


8

The Rambam says that the details of the chapter of the Creation (I suppose, Gen. 1 and 2) should not be taught to the masses lest they misunderstand or twist what it means (Guide to the Perplexed, 2:17). An implication may perhaps be drawn that the literal reading is not all that there is to the story of Creation and that, perhaps, it should not be taken as ...


8

R' Aryeh Kaplan z'l teaches as follows: R' Nehunia ben Hakana brings in Sefer Temuna that there are larger shmita cycles of 7000 years each, of which we are now in the 6th, putting the age of the earth at 42,000 years old. Midrash states that a "Divine day" is like 1000 years. Therefore a "Divine year" is 365,250 years. R' Yitzchak of Acco - who ...


8

Bamidbar 22:23 mentions how Bilam's donkey saw an angel which Bilam could not see. Rashi ad loc. implies that this was not a unique case: there are at times things that an animal can perceive which a human can not.


8

the quote about what Rav Saadia Gaon believed regarding literal vs. non-literal interpretation is correct but incomplete. After he writes "it is a well known fact that every statement found in the Bible is to be understood in its literal sense" - he then lists four cases when it is forbidden to take the Torah at literal understanding. They are (this can be ...


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