We read in this week’s Parshah, “Hashem’s appointed festivals that you are to designate as holy callings”. And again two verses later, “These are the appointed festivals of Hashem, the holy callings, which you shall designate in their appropriate time”.
Rashi comments on this apparent repetition, “above it speaks of adding a month to the year and here it speaks of sanctifying the New Moon”. The verse is stressing the point that ‘you’ are to call i.e. designate, the Yomim Tovim. The double expression is because there are two methods that need to be employed in order to correctly designate the correct time for Yomim Tovim – the decision to make a ‘leap month’ i.e. one of 30 days, and the decision to make a ‘leap year’ i.e. a leap year with an extra month of Adar II.
Let us take a moment to contemplate the synchronisation of these two mechanisms. We are instructed to ensure that Pesach is always in the spring. A lunar year has in it only 254 days as opposed to the solar year which has 365 days. If we employed only a lunar calendar – as do the Muslims – then eventually Pesach would eventually fall out of sync with the spring season by eleven days every year. To ‘correct’ this the Beis Din would add an extra month every few years. But not only must Pesach be kept in the spring it must always be kept on the 15th of Nissan. The lunar and solar calendars have to run in complete tandem – no simple feat.
A closer look at the ability to determine the length of a lunar month will show us how great our tradition is. Prior to the Exodus we find that Moshe was told about making the calculations of the months of a lunar calendar. How was Moshe able to work out the precise time that the moon takes to do one complete cycle? Only fairly recently (1997) did NASA come up with their computerised calculation of the time between one new moon and the next as being 29.530588 days. Moshe was troubled and Hashem revealed to him the exact calculations that were necessary to set the calendar. The Gemora records that Rabban Gamliel had a tradition that the renewal of the moon took place not before 29 days and 12 hours, plus two thirds of an hour and 73 parts. Sparing the actual maths – this gives us a figure of according to our tradition of every 29.530594 days the moon is renewed.
What human mind has the ability to calculate with pinpoint accuracy the cycles of the heavenly bodies that are tens of thousands of kilometres away from us and come up with a number – one that NASA is incredibly close to matching(!) – without the benefit of modern scientific equipment? The answer is that we have a tradition that goes all the way back to Moshe who received it directly from the Divine source.
Let me end with a tangential point which can also strengthen our belief and appreciation of the Divine and infinite depth of the Torah and the words of our sages in the Talmud – even on matters of astronomy and mathematics. The Talmud discusses the relationship between the diameter of a circle and its circumference. The verse describes a circular copper tank that King Shlomo built in his palace as being, “ten cubits from its one lip to its other, circular all around….. and a thirty cubit line (קו) could encircle it all around”. Seemingly from the verse the relationship between the circumference and the diameter is 10:30; i.e. for every 1cubit of diameter we have three times that amount in circumference. The mathematicians amongst you will surely note that this is not really accurate. Really C=pD – the circumference is p times the diameter. p we know is about 3.14 and so the number 3 is inaccurate.
Ingeniously the Vilna Gaon pointed out that in this verse the word for circumference is written one way and read another way. It is written ”קוה“ but it is read ”קו“. What is behind this? The numerical values of these two words reveal something fascinating. קוה = 111 and קו = 106. If we look carefully at the relationship between these two numbers we note that they share the same relationship as do 3 and 3.14 (106/111 = 3/3.14). Here we have a hint to the magical number of p, the number that took years for mathematicians to discover.
Good Shabbos, Yaakov