Avot213

12:
Equinoxes: This refers to the determination of when each of the four seasons of the year is held to commence. This the Hebrew tekufah serves to indicate both equinoxes and solstices. In the Gregorian calendar currently in civil use the solstices fall on 21st June and 21st December. These are times when the sun appears to be at its greatest distance from the earth's equator and the days are longest and shortest. The equinoxes occur on March 21st and on September 21st. As its name implies, these are times when daylight and night time are virtually equal.

13:
In ancient times the spring equinox was one of the determining factors for the sages when they had to decide whether a year was an ordinary year or a leap year – in which a whole month was added in the lunar calendar. (The fixed calendar that we use today was introduced by Hillel II, the President of the Sanhedrin, around the year 359 CE. For details see
Tractate Rosh ha-Shanah which we studied 6 years ago.) This was to ensure that the festival of Passover always fell on or after the spring equinox, because the Torah [Exodus 13:4, 23:15, 34:18, Deuteronomy 16:1] legislates that this festival must always be held when it is spring in Eretz-Israel. To this day it is this consideration that determines the date of the festival of Easter for the Christian Church.

14:
The Gemara [Sanhedrin 11b] preserves for us an example of such a 'presidential decree' in the days of the Bet Mikdash:

15:
The traditional method of determining the four astronimcal tekufot is attributed to the Babylonian Amora Shemu'el. All rabbis now know that his method is inaccurate, but it is still used for ritual purposes because it no longer has any real calendrical importance. In fact, its only use today, as far as I can recall, is in that quaint custom which obtains only in the diaspora where the wording of one of the benedictions of the Amidah changes slightly on December 5th! (In Eretz-Israel this change always occurs on Marĥeshvan 7th.) This is because it was originally intended that those living in the diaspora should ask for copious rain from 60 days after the autumnal equinox. This should be on November 20th, but, since it is based on the old Julian calendar, it is now 15 days out.

To be continued.

In Avot 210 Amnon Ronel wrote about the relationship between 'fear' and 'wisdom'. Jacob Chinitz has sent me a related comment:

Again we have proof of the fallibility of proverbs. Because truth is complicated, the simple proverb is usually, simplistic, inaccurate, or totally opposite to the truth, which may be encapsulated in another proverb. Here, we say: ignorance produces fear. On the contrary, ignorance produces complacency, as in global warming, Aids (before the connection with sex was discovered), smoking (before the Surgeon General's report came out). Another example: Ignorance is Bliss, contradicted by another proverb: Knowledge is Power. Unless we assume that Bliss and Power are themselves opposites.