Changing the Year

[Notate bene: this post is based on one that originally appeared on 30 June 2012.]

Pope Paul III, as played by
Peter O'Toole in "The Tudors"

In 2012, June 30th had one extra second added to it. This is only the latest in a long list of calendar corrections. We'll avoid the modern arguments about what actually constitutes a "year" (a problem resolved by designer of the Jalali calendar) and go back to a simpler time.

Readers of this blog are probably familiar with the pope's work to "fix" the calendar when he realized that the Julian calendar was "off" by several days. Sure, the Julian took into account that a "year" is actually 365 and a quarter days, but it wasn't exactly a quarter-day off, and so adding a day every four years wasn't sufficient to even things out. Every 131 years, the solstices and equinoxes would be off by a day. This was a real problem for the Church, because over the centuries Easter started shifting to summer, rather than spring.

Pope Paul III (1468-1549) saw the problem and gathered several astronomers to develop reforms.* Then Paul III died, five popes came and went, and in 1572 Pope Gregory XIII was elected and found himself faced with a growing problem and several possible solutions. He mulled it over for a few years, and then declared to the world:

• The Leap Day would move to after February 28 (it had been tucked in before February 25).
• The date of Easter would be calculated differently.
• A Leap Year that is divisible by 400 will not have a Leap Day.
• Ten days needed to be omitted from the calendar, to bring it back into alignment with the solstices. Accordingly, in 1582, the day after Thursday, October the 4th, was Friday the 15th....and then everything was fine. Except when it isn't, like when we have to add an extra second here or there. (And can you imagine trying to explain to someone 1000 years ago that the year gained about 45 seconds every 10 millennia because the Earth's rotation was slowing?)

The 1582 change gave rise to a slight oddity for historians, because technically, every date prior to October 4th, 1582 is a Julian date, but also has a corresponding Gregorian date that is several days different. How you count it depends on whether you consider the date to be just a label given by those who were there at the time, or a certain number of days prior to the present day. Or it's important if you want to declare the anniversary of an event.

Anyway, the extra second was added just before midnight. You may not have noticed it, but you can say you lived at a time when a minute was 61 seconds long!

*Copernicus had dedicated his work De revolutionibus orbium coelestium [On the Revolutions of the Celestial Spheres] to Pope Paul III, hoping it would save him from potential hostility for his radical thoughts. Had Paul called him, Copernicus probably would have come running to join the team of calendar reformers; alas, he had died in 1542.

How far are the stars?

Rabbi Levi ben Gerson, also known as Gersonides, lived from 1288-c.1344. He was from a family of scholars: his father, Gerson ben Solomon of Arles, was the author of the Sha'ar ha-Shamayim, an encyclopedia of natural science, astronomy, and metaphysics.* Levi is credited with first mentioning, and possibility inventing, Jacob's Staff. (He references Genesis 32:10 when he describes the device; this is likely the origin of the name.)

At a time when religion, philosophy, astronomy, astrology and science were overlapping (and in some cases, interchangeable), Gersonides' greatest work, which was philosophical, contained his greatest contribution to astronomy. He put twelve years (1317-28) of effort into the Milhamot Adonai ("Wars of the Lord"), whose six books dealt with 1) the soul, 2) prophecy, 3) & 4) god's knowledge of facts and providence, 5) astronomy/astrology, and 6) creation and miracles. Gersonides firmly accepted astrology and the celestial hierarchy of powers inherited from neo-Platonists and pseudo-Dionysius (far too complex to go into here), but he also brought mathematics and observation to his work with extraordinary results for the time.

Postage stamp honoring Gersonides.

Gersonides rejected the Ptolemaic system of epicycles to explain the erratic motion of planets affixed to their crystal spheres surrounding the Earth. According to Ptolemy, epicycles explained the changing size of planets; he said, however, that Mars varies by a factor of six; Gersonides' observations told him that Mars's apparent size varies only two-fold. Gersonides used the Jacob Staff and a camera obscura (pinhole camera) to make careful observations over several years. For Gersonides, 48 crystalline spheres were needed to explain the apparent motion of various heavenly bodies. This expansion of the "physics" of the Ptolemaic model was nothing, however, compared to the actual physical expansion he proposed.

Careful observation with the Jacob Staff, the camera obscura, and math made Gersonides declare heavenly objects to be much farther away than previously calculated. Ptolemy claimed the distance to Venus was 1079 Earth radii; Gersonides estimated it to be 8,971,112 Earth radii away. Ptolemy said the fixed stars were 20,000 Earth radii away; Gersonides estimated them to be at a distance 10 billion times greater.

Pope Clement VI had the "Wars of the Lord" translated into Latin in 1344, making it available to the west. Its impact was minimal, however; we know of a few scholars who were influenced by it, and Kepler asked a friend to send him a copy in the 17th century. But it took Copernicus two centuries later to "confirm" to Western civilization's satisfaction that Gersonides was on the right track.

*As I have mentioned about medieval encyclopediæ before, they were often compilations of previous works; this one drew from Claudius Ptolemy's Almagest and the Morah Nebukim, or "Guide for the Perplexed" of Maimonides. A 1547 edition of ben Solomon's work can be had from Kestenbaum & Company.

Changing Time

Since today will have one extra second added to it, I thought it would be a good time to talk about calendar corrections in history. We'll avoid the modern arguments about what actually constitutes a "year" and go back to a simpler time.

Readers of this blog are probably familiar with the pope's work to "fix" the calendar when he realized that the Julian calendar was "off" by several days. Sure, the Julian took into account that a "year" is actually 365 and a quarter days, but it wasn't exactly a quarter-day off, and so adding a day every four years wasn't sufficient to even things out. Every 131 years, the solstices and equinoxes would be off by a day. This was a real problem for the Church, because over the centuries Easter started shifting to summer, rather than spring.

Pope Paul III (1468-1549) saw the problem and gathered several astronomers to develop reforms.* Then Paul III died, five popes came and went, and in 1572 Pope Gregory XIII was elected and found himself faced with a growing problem and several possible solutions. He mulled it over for a few years, and then declared to the world:

• The Leap Day would move to after February 28 (it had been tucked in before February 25).
• The date of Easter would be calculated differently.
• A Leap Year that is divisible by 400 will not have a Leap Day.
• Ten days needed to be omitted from the calendar, to bring it back into alignment with the solstices. Accordingly, in 1582, the day after Thursday, October the 4th, was Friday the 15th.

...and then everything was fine. Except when it isn't, like when we have to add an extra second here or there. (And can you imagine trying to explain to someone 1000 years ago that the year gained about 45 seconds every 10 millenia because the Earth's rotation was slowing?)

The 1582 change gave rise to a slight oddity for historians, because technically, every date prior to October 4th, 1582 is a Julian date, but also has a corresponding Gregorian date that is several days different. How you count it depends on whether you consider the date to be just a label given by those who were there at the time, or a certain number of days prior to the present day. Or its important if you want to declare the anniversary of an event.

Anyway, enjoy your extra second; it will be added just before midnight, so feel free to stay up so you can say you remember the time when a minute was 61 seconds long!

*Copernicus had dedicated his work De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) to Pope Paul III, hoping it would save him from potential hostility for his radical thoughts. Had Paul called, Copernicus probably would have come running to join the team of calendar reformers; alas, he had died in 1542.

Nicholas of Cusa

American History has a charming anecdote that the head of the US Patent Office once declared there was nothing left to invent. The background for this fable is explained here. Someone in 2010 said that we create as much data in 2 days as in all of 2003. Our ability to find and learn new things looks like it will never match the things there are to learn.

With the amount of knowledge being gained rapidly accelerating, why don't we know everything yet? Will we know everything?

Nicholas of Cusa (c.1400-1464) had an opinion on this. He outlined the problem in the opening remarks of his De Docta Ignorantia (On Learned Ignorance):

It so far surpasses human reason, however, to know the precision of the combinations in material things and how exactly the known has to be adapted to the unknown that Socrates thought he knew nothing save his own ignorance, whilst Solomon, the Wise, affirmed that in all things there are difficulties which beggar explanation in words;

He argued, however, that every living creature is

endowed with suitable faculties and activities; ... there is in them a discernment that is natural and in keeping with the purpose of their knowledge, which ensures their natural inclination serving its purpose and being able to reach its fulfillment.

If that is true, he says, then limits to our ability to know things must be built-in by our Creator for a purpose. And that purpose is that, at the end of our reasoning, when reason fails, we must turn to faith for the ultimate answers.

For this, Nicholas has been declared an anti-intellectual by at least one prominent modern scholar. But this misses his point: until we reach the limits of what we can figure out, we must travel as far as we can with reason. Just how far Nicholas of Cusa let his reason take him (and in ways that were appreciated by men like Bruno, Copernicus, Galileo and Kepler) I will explore this week.