The idea was strongly suppressed by the Church for centuries. Reviving it took more than a little courage from the early followers of Copernicus .

Plutarch (c. 45-125) reports that Seleucus of Seleucia (born c. 190 BC) was championing the heliocentric system and teaching it as an established fact, in the second century BC ( Seleucia was an important Greek city in Mesopotamia, on the west bank of the Tigris River ). At that exact same time, however, Hipparchus of Rhodes (190-120 BC) reverted to the geocentric belief and was instrumental in killing the heliocentric idea altogether [cf. Thomas Little Heath (1861-1940)].

Copernicus (1473-1543) himself credits Aristarchus of Samos (c.310-230 BC) for the idea of an heliocentric system. This heliocentric idea is not explicited in the only surviving work of Aristarchus, where the distances and sizes of the Moon and the Sun are estimated . However, Aristarchus makes it clear that he estimated the Sun to be much bigger than the Earth (although he still underestimated its true size). This may indeed have suggested to him that the smaller body ought to be revolving around the larger one. Actually, the heliocentric views of Aristarchus are precisely known to us from the short account given in " The Sand Reckoner " by his illustrious (younger) contemporary, Archimedes of Syracuse (287-212 BC).

Although Heraclides of Pontus (387-312 BC) deserves credit for suggesting that the Earth rotates around an axis, he did not yet place the Sun at the center of the Solar system (in spite of what some reports are still stating).

— Tell me, why do people always say it was natural for Man

to assume that the Sun went round the Earth,

rather than that the Earth was rotating?

— Obviously, because it just looks

as though the Sun is going round the Earth.

— Well, what would it have looked like,

if it had looked as though the Earth was rotating !?

Ludwig Wittgenstein (1889-1951)

(in TED talk by Richard Dawkins July 2005)

The legendary experiment, which allegedly took place at the Leaning Tower of Pisa , consisted in dropping two different weights simultaneously from the top of the Tower and supposedly recording their simultaneous arrivals on the ground... Well, one of Galileo's assistant, Vincenzio Viviani (1622-1703), did play a major role in this, but not in the way you might expect, as Viviani was not even around to witness the event, if it ever occurred!

No. Galileo died 361 days before the birth of Newton . The death of one and the birth of the other occurred in different Julian years (1641 and 1642) and in different Gregorian years (1642 and 1643). The year is the same (1642) only when the death of Galileo is recorded in the Gregorian calendar (then prevalent in Italy) and the birth of Newton is recorded in the Julian calendar (still prevalent in England at the time).

Other problems exist when conducting such experiments with the "technology" of Galileo's time, including a curious systematic error (due to muscle fatigue) when people are attempting to release simultaneously balls of different weights. A tribute to the observational skills of Galileo was that he recorded negative results to similar experiments which could be explained this way... So much for the simplicity of legendary "experiments".

For the record, such experiments only "work" properly in a vacuum , where a feather and a ball of lead do fall at the same rate. (Otherwise, a given shape, size and speed imply a certain value of the air resistance which does constitute a lesser percentage of the weight of an heavier object.) Astronaut David R. Scott successfully performed Galileo's experiment (using a feather and a hammer) on the lunar surface, on August 2, 1971 [see video ]. The same result is routinely demonstrated [at a much lesser cost] with an evacuated sealed tube containing two very different objects, usually a feather and a coin...

Three years earlier, in 1586, the Dutch engineer Simon Stevin had already accomplished the key experiment by releasing simultaneously, from a height of 30 feet, two very different pieces of lead (1 pound and 10 pounds) and observing that the sounds of their impacts "could not be separated".

Galileo's "famous experiment" at the Leaning Tower of Pisa probably never took place. Galileo himself never claimed to have performed the deed, and the fantastic decorum described by Viviani is even more unlikely. The experiment would have been largely inconclusive anyway, except to disprove the gross misconception [wrongly] attributed to Aristotle , according to which the speed of falling objects ought to be proportional to their weights (this much is easily proven wrong by less dramatic experiments which Galileo did perform). Galileo may have meant to do the grand experiment, but the idea probably occurred to him at a time when it could not be conveniently carried out, because he no longer lived next to the Tower: Galileo moved from Pisa to Padua in 1591. He had began to study falling bodies only two years earlier, in 1589.

What the Italians call " la Torre pendente di Pisa " is a bell tower, whose seven bells were used until 1950. The architect Bonnano Pisano began its construction on August 9, 1173 in the Campo dei Miracoli (Pisa's "Field of Miracles"). When the building reached the 3rd level (about 10 years later), its leaning was already pronounced, and construction stopped for 90 years. The main tower was completed between 1275 and 1284 by Giovanni Di Simone , who compensated for the tilt by giving the building a slight banana shape. The architect Tommaso Pisano (son of Andrea Pisano) finally added the top belfry between 1350 and 1372. In Galileo's times, more than two centuries later, the Leaning Tower of Pisa was pretty much what it is today: A building of about 14 700 000 kg rising 58.363 m above its foundations, with a 4 m overhang that would increase steadily (at a rate of about 1.2 mm per year) if it was not for regular heroic countermeasures...

When Torricelli died in 1647, Viviani suceeded him in the position Galileo had occupied only a few years earlier. In 1654, a dozen years after Galileo's death, Viviani began writing the first biography of Galileo. He clearly embellished things a little... In particular, the colorful narration of the experiment at the Leaning Tower of Pisa is a fiction invented by Viviani...

When Galileo died in the evening of January 8 of 1642, he was surrounded by only three people: His own son, Vincenzio Galilei (1606-1649), his junior assistant Vincenzio Viviani and his famous new senior assistant, Evangelista Torricelli, who had joined him only weeks before:

When he became Galileo's assistant in October 1638, Viviani was only a 16-year old youth from Florence, whose promising aptitude for mathematics had earned him the commendation of Galileo's patron, the Grand Duke Ferdinand II of Tuscany. By that time, the ageing Galileo had already lived under house arrest for 5 years in Arcetri. He had lost his eyesight in 1637 and he welcomed the live-in presence of the devoted Viviani, who wrote and read for him.

Another complication may arise for Julian dates between January 1 and March 24 (included) recorded in England before 1752. The legal year in England, under the old [Julian] calendar, changed on March 25. In other words, Newton was 6 days old on December 31, 1641 and clearly 7 days old on the following day, which was legally January 1, 1641. On the other hand, Gregorian years have always been incremented on January 1. To disambiguate the relevant dates, it's customary to specify either "O.S." (Old Style) or "N.S." (New Style) after the year number. For example, the birthdate of Joseph Priestley is properly given as: Wednesday, 13 March 1733 (O.S.) Priestley himself would have said that he was born in 1733. Nevertheless, any consistent chronological list of scientists should indicate 1734 as the year of Priestley's birth (the exact Gregorian date was 24 March 1734 ). About calendars... Primitive Roman calendars evolved into a somewhat variable system which featured 12 short months and, on some years, a thirteenth month (called either Intercalaris or Mercedonius) whose length was ultimately decided politically... This dubious system was replaced by an early form of the Julian calendar, introduced by Julius Caesar in 45 BC. After a rough start and too many leap years, the Julian calendar was given its final form by Augustus, and every fourth year was made a leap year starting with AD 8. Our current calendar is only a slight modification of the latter Julian calendar. It's known as the Gregorian calendar because it was introduced under the authority of Gregory XIII, né Ugo Boncompagni (1502-1585), who was Pope from 1572 to 1585. The Gregorian reform of the calendar was actually engineered by the astronomer Christopher Clavius (1538-1612) after preliminary work by Luigi Lilio (c.1510-1576). The aim was to make seasons correspond permanently to what they were under the Julian calendar in AD 325, at the time of the First Ecumenical Council of the Christian Church, the First Council of Nicea, when rules were adopted for the date of Easter (usually, the first Sunday after a full moon occurring no sooner than March 21). 10 days were dropped in 1582 (October 15 followed October 4) and new rules were devised to have only 97 leap-years in 400 years (instead of 1 in 4). Various countries adopted the "new" calendar only much later. In particular, the earliest valid Gregorian date in England (and in what was then known as the American Colonies) is September 14, 1752, which followed September 2, 1752 (the discrepancy had grown from 10 to 11 days by that time, because the year 1700 was not a leap year in the Gregorian calendar). This happened more than a century after Newton's birth, which was thus still recorded as Christmas day of 1642, although the year in Italy was already 1643. On the other hand, it is correct to remark that Stephen Hawking was born (January 8, 1942) exactly 300 years after the death of Galileo (January 8, 1642) since both events were recorded in the same Gregorian calendar.

(2003-11-03) The Lorenz Gauge [ not due to H.A. Loren t z ]

The 1867 addendum to Maxwell's equations of electromagnetism (1864)

This is the following relation between the vectorial and scalar potentials A and f , which would otherwise be defined with more leeway. In a classical context, this equation has some aesthetic appeal, as it makes the d'Alembertians of A and f respectively proportional to the density of current and the density of charge... In a quantum context not anticipated by Lorenz at the time, the potentials have a real significance of their own, which is happily consistent with that gauge : div(A) + 1 ¶ f = 0 [ In SI units, or Giorgi's MKSA system.] c2 ¶ t The thing is very often misspelled "Lorentz Gauge" (with a "t") because of a fallacious attribution to Hendrik Antoon Lorentz (1853-1928; Nobel 1902). The relation was published in 1867 by the Danish physicist Ludwig V. Lorenz (1829-1891). The Danish spelling is Ludvig Valentin Lorenz. At the time, the future Dutch physicist H.A. Lorentz was only 14 years old. Ironically, it turns out that Ludwig Lorenz is best remembered for the relation he established in 1880, building on earlier work (1878) by the young H.A. Lorentz about the theoretical index of refraction of a dielectric substance. This result is now known as the Lorentz-Lorenz relation... Spelling bee, anyone? As the Internet grows, are authors getting it right ? Date Lorenz Gauge Lorentz Gauge Both Correct 2003-11-16 368 2650 12.2 % 2008-03-10 5930 24000 19.8 % 2018-03-03 50600 44500

93500 1540 54.1 %

35.5 % 2019-07-07 28900 60700 2270 33.9% Inclusion-Exclusion : Before 2008, I was assuming that nobody used both spellings in the same page, which is not quite true. Some Internet authors either discuss both spellings (like I'm doing here) or they think it's a good idea to let people discover their pages with either spelling... (Others simply make an occasional involuntary typo.) All told, that remark increases slightly the percentage of "correct" pages (i.e., the ratio of pages containing the correct spelling to pages containing either spelling) as given by the following formula, where R, W and B are the numbers of pages containing the right spelling, the wrong one and both (respectively): R / (R + W - B) = 1 / [ 1 + (W - B) / R ) The right-hand-side is just a trick to enter each number only once... It also goes to show that B merely acts as a deduction from W. If we counted as correct just the pages which have only the right spelling, B would be like a deduction from R instead.



Different numbers are for different Google snapshots taken on the same day. They indicate that the quantitave result of Google queries is to be taken with a grain of salt.



If we assume that the pages which quote the wrong spelling have remained a fixed portion (3%) of the pages which properly discuss the Lorenz gauge, then we can estimate that there were only about a dozen such pages back in 2003. The present page was one of the happy few!

(2002-10-08) On the Origins of the Special Theory of Relativity

Was Einstein the first to formulate the (Special) Theory of Relativity?