A Scratch on the Wall

According to the Midrashim quoted by Rashi, Yitzchak was born precisely a year after the angels visited Avraham and Sarah, on the first day of Pesach. (According to the gemara Rosh HaShanah 11a the angels visited on Sukkos.) Rashi (21:2) writes that HaShem gave Avraham a sign. On the day the angels visited, HaShem made an etching in a wall and told Avraham, "When the sun reaches this point again next year, you will have a son." This sign requires some clarification. How exactly did this work?

An object that is standing upright in the path of the sun will form a shadow on the ground. The exact direction of the shadow depends on the position of the sun in the sky. As the sun moves through the eastern sky in the first half of the day, the shadow will be pointing westward and vice versa for the second half of the day. However, the exact direction of the shadow, i.e., its northerly or southerly bearing, will constantly change. As well, the size of the shadow is dependent on the north/south position of the sun as well. These are the principals behind the sundial. All of the factors change throughout the day and the daily patterns change throughout the year as a result of the change in direction of the earth's tilt. However, one thing is certain. At midday, the sun is not in the eastern sky or the western sky. Rather, it is either due north or due south, depending on where you are in the world. What is relevant to us is that since Eretz Yisroel, at approximately 31^o North, is above the Tropic of Cancer (23.5^o North), the sun will always be in the southern sky at midday. The size of the shadow depends on the angle of the sun in the sky which depends directly on the time of year.

Any sign involving a shadow would surely have been simplest to arrange at midday. It is therefore most noteworthy that the gemara (.ברכות כ"ז) infers from the words (18:2) "kechom hayom," in the heat of the day, that the angels visited in the sixth hour. After the food was prepared and served and the angels conversed with Avraham, it seems altogether plausible that it was exactly midday. It seems that the sign that was given was that at that moment, the southern wall (or other standing object) was casting a shadow on the northern wall. The scratch that was made on the wall indicated the end of the shadow. When the shadow reached the exact same point at midday sometime in the next year, it would indicate that a complete year had passed.

With all this considered the Midrash is quite troubling. All these details are specific to the solar year. However, Yitzchak was born precisely one year later by the lunar calendar, not the solar calendar. What significance could any sun-related sign have to the passing of a lunar year?

I particularly enjoyed the answer that Pi offered in the comments:

On pasuk 18:10, Seforno says: שוב אשוב אליך - למועד המילה כפעם בפעם.‏ This suggests that the time the angels would return a (solar) year later was not the exact day of Yitzchak's birth, but rather some time later. The book קונטרס די שמיא by Alexander Shutz on pages 18-19 claims that the ריב"א asks your question, and that ר' צבי יודא פריידמאן suggests the following answer: The angel Rephael would come back three days after Yitzchak's bris mila to heal him, which would be (about) 11 days after his birth, so that could have been the occasion when the sun reached the line that was marked on the wall.

Witnesses to Sedom's Destruction

Rashi on 19:24 notes that the destruction of Sedom happened at day break, when the sun and moon were in the sky at the same time. This was because they used to worship the sun and moon. HaShem therefore brought the destruction when both were out as a proof to all the sun and moon worshipers that the sun and moon are powerless. Had the destruction taken place when they were not in the sky, one could have argued that they were not "there" to save them. This is a rather simple statement by Rashi but the astronomical basis for it is quite interesting.

 

It is not always that the sun and moon are out together at day break. It is also not always that it is the only time that they are out together. The moon rises and sets approximately 49 minutes later each day. This is a result of the moon orbiting the earth. Just as the moon's position is reset at the end of every month, so are its rising and setting times. (The math is as follows: Every full moon cycle (month), moonrise and moonset make a full circle of 24 hours such that the times are as they were precisely one month previous. The figure of 49 minutes is achieved by dividing 24 hours by the duration of the lunar cycle, 29.5 days, 44 minutes, 3 and a third seconds. More precisely, the figure is 48 minutes, 45.5 seconds.)

At the beginning of the month, the moon follows a very similar schedule to the sun. The moon rises at the beginning of the day and sets at sundown. As the month progresses, the moon rises and sets later and later. At the middle of the month, the moon has virtually the opposite schedule to the sun. It rises when the sun sets and sets when the sun rises. As we enter the second half of the month, the moon begins to rise later in the night and thus, becomes visible at the beginning of the day.

The Midrash (Bereishis Rabba 50) teaches that Sedom was destroyed on the 16th of Nissan. As explained above, at that time of the month, the moon would have risen shortly after sunset and set very shortly after sunrise. Therefore, the only time in the entire day that both the sun and moon were out at the same time was very early in the morning and that is why the destruction took place specifically at the very beginning of the day. [Nevertheless, it is puzzling that Rashi uses the term "Alos HaShachar" which refers to a time before sunrise.]

The World's First Boat?

For 100 years Noach toiled and endured much ridicule from his neighbours as he built the ark. Sure enough, Noach had the last laugh when the flood finally came and wiped out everyone else on the planet. Having completely denigrated Noach and ignored his warnings, the people were completely unprepared. However, the ark was nothing more than a large boat. Didn’t anyone have a boat of their own to escape the destruction of the flood?

This fascinating question was asked of me by R’ Sander Goldberg of Baltimore and he followed it up with a fascinating answer from his sefer נחל חיים (Page 30.) There is some discussion regarding the general climate and environmental conditions before the flood and how they were changed forever by the flood. One of the principal catalysts for these theories is the first reference to seasons after the flood (8:22) which seems to imply that there were no seasons beforehand.

מלבי"ם writes that before the flood planet Earth was not on the 23.5 degree tilt on which it finds itself currently. The tilt was as direct consequence of the environmental havoc wreaked by the flood. When the earth is not tilted the climate conditions throughtout the world are at complete equilibrium. That is to say that weather conditions are completely uniform throughout the world and throughout the year. There is simply no reason for conditions to be any different in one place from another. Cloud cover as we know it did not exist either. After all, a partially cloudy sky means that there are clouds over one part of the land and not over the other. Rather, the skies slowly became saturated with moisture uniformly and once every forty years, writes מלבי"ם, the entire earth would be drenched with rain and the process would begin anew. (This explains why the people were not overly taken aback by the flood when it began.) מלבי"ם also attributes the longer lives lived before the flood to the consistency of the climate.

(Now THAT's climate change!)

Another condition that would result from a world climate in equilibrium is uniform atmospheric pressure. Without varying pressure, there can be no wind. Wind is a result of air moving from a high pressure area to a lower pressure area like the air flowing out of a balloon. Before the age of the motor, all large boats relied on wind to move. If there were no wind, there would have been no boats. This explains why Noach’s project appeared so strange and also explains why no one else had any means to survive the flood.

(He goes on to explain that due to this extreme difference in global climate fermentation was something that did not happen before the flood and that explains how Noach could go so terribly wrong afterwards getting drunk - alcohol hadn't existed either.)

Emunah in Time and Space

The advances in modern science over the years have allowed us to learn much about the history of the world. Scientists have been able to establish a pretty clear picture of all that preceded us. However, the instant of creation is a point beyond which no discoveries may be made. Even the most prominent of scientists, such as Stephen Hawking of the University of Cambridge, have come to the realization that "the creation lies outside the scope of the presently known laws of physics." What existed before the creation of the world is beyond human understanding. The simple explanation for this is that before the world was created, whatever it was that existed lacked the basic components necessary for human conception.

All the matter in the universe exists in three dimensions - length, width and height. We do not live in the two-dimensional world of comics and cartoons, nor can our minds conceive of something physically consisting of more than three dimensions. When a cube of a given volume is removed, it leaves behind a space, filled with air, of identical volume. However, before the creation of the world, there was nothing. The second pasuk of the Torah asserts that before creation, the world was "tohu vavohu." Rashi explains "vohu" as emptiness and void. He writes that "tohu" denotes astonishment and wonderment, as one would have been astounded by the emptiness that existed. Indeed, we are astonished to the point of incomprehension at the very idea of nothingness. It is beyond the grasp of human thought and will never be understood. An integral component of creation was the establishment of the infrastructure necessary for the existence of the world as we know it. On the second day, the waters are divided into the upper and lower waters. This is the first evidence of a dimension in creation. However, there was only one. Left, right, forward and backward did not yet exist - only up and down. The next day the waters were collected to form the oceans and reveal land. The three dimensions were now in place.

Although a physical object may be comprised of no more than three dimensions, there is another dimension commonly included as the fourth - time. Before the creation of the world, time did not exist either. In fact, the word "before" is probably a misnomer. Before implies that which preceded in time. If there is no time, there can be no precedence. This, too, is beyond the comprehension of the human mind. With the first day of creation, the concept of time was implicitly infused into the universe.

Perhaps, these ideas are directly pertinent to one of the central laws of Keriyas Shema. The essence of Shema is the acceptance of HaShem’s kingship upon us. One is required to include this concentration with the recitation of Shema or he does not properly fulfill the mitzvah (Shulchan Aruch OC 60:5). Ideally, this is accomplished with specific focus on the "ches" and "dalet" of "echad," as explained in 61:6. The ches corresponds to HaShem’s rule over the earth and the seven levels of Heaven. This is a one-dimensional focus in concurrence with the events of the second day of creation. The dalet corresponds to the four directions, essentially, the other two dimensions, over which HaShem rules. This coincides with the events of the third day. Hence, HaShem’s dominion over the three physical dimensions. The Mishnah Berurah (63:11), in the name of Levush and Magein Avraham, writes that "Baruch Sheim Kevod, etc." is subject to the same concentration requirements as the first pasuk. In this pasuk, as the words clearly indicate, we assert the eternity of HaShem’s kingship. In essence, we are declaring HaShem’s rule over the fourth dimension, time.

It also occurred to me that perhaps the requirements set forth in 61:6 regarding the specific כוונות should be augmented for modern times. The שולחן ערוך declares that we are to (mentally) proclaim השם's kingship on the heavens and earth and the four directions of the world. But in those times, that was the extent of what your average Yosef could fathom. The average layman knew little about the celestial bodies and what lies beyond our earth. However, nowadays, when all young school children are taught about the extent of our universe and are aware of the planets that make up our solar system, perhaps it is incumbent on us to have this in mind and proclaim השם's kingship on all of the universe as we know it.

The Two Luminaries

Pasuk 16 refers to the sun and the moon as "shnei hame'oros hagedolim", the two large luminaries but concludes by referring to the sun as the "maor hagadol" and the moon as the "maor hakaton". On this pasuk there is the well-known Rashi, quoting the Midrash, that the moon and the sun were created equal but the moon complained that "two kings cannot share one crown". Therefore, it was reduced to a smaller luminary. However, this is certainly an allegorical understanding of the pasuk. What, then, is the simple understanding?

In In the Beginning: Biblical Creation and Science, a fascinating book reconciling the Biblical account of creation with modern science, Professor Nathan Aviezer offers an eye-opening interpretation. An astronomical body is measured both by its true size and by its apparent size or angular diameter. The apparent size specifies how large it appears to an observer on Earth. This figure is the ratio of the true size of the object to its distance from the Earth. This figure is expressed as the angle that the object subtends from the position of an observer on Earth. That means, if you were pointing to the bottom of the object, the apparent size is the number of degrees you must rotate your arm to be pointing at the top of the object. The sun is 400 times bigger than the moon. It is also exactly 400 times further away from Earth. As a result, the apparent size for the sun and moon are identical at 0.53 degrees! Now we can understand the pasuk as follows: The first part of the pasuk is referring to the point of view of an Earth observer. From our point of view, the sun and moon are the biggest heavenly bodies and in fact, appear identical in size. The second part of the pasuk refers to the true size of the sun and moon.

Please see Pi's comment below with some nice alternative understandings of this פסוק.

The Uncountable Stars

In this week's parsha (15:5) HaShem brings Avraham Avinu outside and tells him to observe the uncountable stars and tells him that his progeny will be likewise uncountable. Rashi there quotes a Midrash that states that HaShem removed Avraham from the atmosphere and placed him above the stars to observe them. R' Chaim Kanievsky questions, why was this necessary? Why was it not sufficient to simply look at the stars from where he was?

He answers that we are taught in the adjacent commentary to Rambam's Hilchos Yesodei HaTorah (3:8) that there are a finite number of stars visible from Earth, 1022 to be exact. Beyond the scope of our vision there exists an abundance of stars which are too many to be counted. Being shown the stars from Earth was simply not impressive enough. Avraham had to be removed from Earth in order to appreciate the true extent of the berachah.

Ari S.said...

The number 1,022 is also seen in Ibn Ezra's Reishis Chachma (on astrology). He cites Ptolemy just like the Rambam mentions in a few places (i.e. hilchos kiddush hachodesh) that his knowledge of astronomy comes from the Greek sources. Ptolemy (in the Almagest) does have this number. It is pretty clear that he (and the rishonim) were aware that there were many more. In fact, the way Ptolemy and Ibn Ezra cite it is to show how the constellations are formed. It seems that this number refers to the bigger and brighter stars.

The average person can see approximately 3 - 4,000 stars (the faintest being about magnitude 6). Perhaps, another idea expressed in the pasuk could be that it is impossible to count them at once. Some are below the horizon at times and others seasonal. Some are only seen at northern latitudes and others at southern. Maybe Avraham had to go high above in order to get an angle above them to see them at one time.

Jewish people have been dispersed throughout many countries during our exile. This is often to our benefit because it provides a defense mechanism. It is much more difficult for an enemy to ever annihilate us because of this. Maybe we are being taught that you will never be able to see all the Jews in one spot to count because they will be dispersed. In the ensuing pesukim of the covenant, there are many references to the exile.

Like the Stars

In this week's parsha we read about Hashem's promise to Avraham Avinu that his children will be like the stars. (Bereishis 15:5) There are many beautiful explanations that uncover some of the depth of this fantastic blessing. One of these can be found in the writings of Rav Yehonasan Eibshitz zt"l.

Rav Eibshitz mentions that the comparison to stars includes the aspect of individuality that one can see amongst the stars. The nightly stellar display is something both gorgeous and awesome. Part of the beauty is due to the fact that each brilliant star stands alone. Each star, just like each member of Klal Yisrael, has a radiance that shines forth and allows it to stand alone and shine. While each one may not appear to touch the others, still it is the display in its enitrety that creates the breathtaking sight. Each individual of Klal Yisrael follows in his path just as each star follows its prescribed path, but it is when one sees all of Klal Yisrael working together that the true beauty can be seen.

The Miracle of שבת

In this week's parsha, the Aseres HaDibros are repeated. When I was younger, a guest at our Shabbos table offered me one sticker for every difference I could find between the Yisro version and the Va'eschanan version. I found ten.

In the fourth commandment, the mitzvah of Shabbos, we find a reference to the subjugation in Mitzrayim that was not mentioned in parshas Yisro. We are told (5:14) "And you shall remember that you were a slave in Mitzrayim and HaShem, your God, took you out from there with a Mighty Hand and Outstretched Arm. Therefore, HaShem, your God, has commanded you to make a Shabbos day." Rashi writes that this is simply a reminder that HaShem brought us out of Mitzrayim in order to perform his mitzvos, of which this is one.

There seems to be an intrinsic connection between the mitzvah of Shabbos and the exodus from Mitzrayim. There is no reason to assume that the Egyptians gave us a day off on Saturday. Rather, a more conceivable assumption would be that we had a full seven-day work week. With the exodus from the enslavement in Mitzrayim came the freedom and autonomy to set our own weekly schedule. We are thus commanded to set aside Shabbos as a way of reminding us of this great gift.

When immigrants first came over to the United States, they were forced to work on Shabbos and the Egyptian subjugation was felt once again. But the society has changed and now, even in exile, we are free to take Shabbos off from our work. The very concept of a seven-day week in the secular world is itself a miracle. The week is the only calendrical component with absolutely no astronomical significance. A day represents one full rotation of the earth on its axis. A year is one full revolution of the earth around the sun. But a week is nothing more than a group of seven days. The secular world could easily have chosen a six or eight-day week and that would have spelled eternal trouble for the Jews. On the day of Shabbos these miracles must be realized, in combination with the miracle of Yetzias Mitzrayim.

Ramba"m, in Moreh Nevuchim, seems to concur with this idea. He writes that the two mentions of Shabbos in the Aseres HaDibros teach us two separate aspects of Shabbos. In parshas Yisro, we are taught why HaShem chose to sanctify the day of Shabbos and its significance in the days of creation. Here, in Va'eschanan, we are taught why it is that we must keep the Shabbos, namely, to remember the enslavement in Mitzrayim when we had no days off and appreciate HaShem's great deliverance of us from there.