Mentor

Was the second originally defined in terms of the size of the Earth and c?

 Quote by uart BTW. The second of the two "coincidences" is equivalent to $g = \pi^2$. As pointed out previously, that fact that these two numbers are even close is just happenstance.
Not quite happenstance. The French seriously considered defining the meter (not the second) so that the numerical value of g would have been exactly equal to $\pi^2$ at the Paris Observatory.

 Also the sea level value of g varies depending on your position on the globe, but as far as I know it's not exactly pi^2 anywhere.
On the surface of the Earth, that is correct. Inside the Earth, that is incorrect. g increases with increasing depth to over pi^2, then decreases with increasing depth below the transition zone (but does not drop below pi^2), then increases again at some point within the lower mantle. It reaches a global maximum at the mantle/core boundary, dropping toward zero at the center of the Earth. There are two surfaces inside the Earth where $g=\pi^2$, exactly.

Recognitions:
 Inside the Earth, that is incorrect.
Yep, that's why I was talking about at sea level.

 The French seriously considered defining the meter (not the second) so that the numerical value of g would have been exactly equal to π2 at the Paris Observatory.
I didn't know that. You've got me googling "meter history" right now. :)

 Recognitions: Science Advisor Quote from wikipedia. Code: Timeline of definition 1790 May 8 – The French National Assembly decides that the length of the new metre would be equal to the length of a pendulum with a half-period of one second. 1791 March 30 – The French National Assembly accepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of the Earth's meridian along a quadrant through Paris, that is the distance from the equator to the north pole. 1795 – Provisional metre bar constructed of brass. ... So there goes that "coincidence" out the window.

Mentor
 Quote by uart So there goes that "coincidence" out the window.
Not really out the window.

That the length of a human stride and the length of a human arm are more or less the same is pretty much coincidental. What if intelligent velociraptors rather than intelligent apes had become the intelligent species on this planet?

That the length of a seconds pendulum is roughly equal to those human-based standards is even more coincidental. What if the length of a day was something different than it currently is? What if the Earth's composition was something different than it is? After all, the length of a day has varied by quite a bit since the formation of the Earth, and the value of g depends heavily on the makeup of the Earth.

That 1/10,000,000 of 1/4 of the polar circumference of the Earth is roughly equal to any of the above is yet more coincidental. What if the average human hand had four or six digits? Our infatuation with powers of 10 is just a consequence of humans having 10 fingers. What if the Earth had formed slightly differently? That this is anything but coincidence means that life/intelligence can only arise on a planet that is almost exactly the same size as the Earth, and that such life will have the same infatuation with powers of 10 as do we.

 Recognitions: Science Advisor Numerical coincidences are sometimes fascinating though. There was a guy here once who was posing a whole alternate theory of physics based on the fact that the number of seconds in a Lunar year (approx 354.37 days) times "g" was "exactly" (his words) equal to the speed of light. The interesting thing about that one is that the units actually agree, m/s = m/s^2 * sec, and numerically it was only out by about 0.1%. Too bad his alternate theories didn't stand up to any scrutiny at all.

Mentor
Blog Entries: 1
 Quote by uart Numerical coincidences are sometimes fascinating though. There was a guy here once who was posing a whole alternate theory of physics based on the fact that the number of seconds in a Lunar year (approx 354.37 days) times "g" was "exactly" (his words) equal to the speed of light. The interesting thing about that one is that the units actually agree, m/s = m/s^2 * sec, and numerically it was only out by about 0.1%. Too bad his alternate theories didn't stand up to any scrutiny at all.
That kind of reminds me of the (bad) film 23. For a long time after seeing that film as a teen me and my friends would parody it by point out "amazing" coincidences e.g.

"Hey guys! The house we just passed was number 63! If you add up our ages, times them by the number of eyes I have, divide it by the fraction if us that is currently speaking and add the number of us there are it comes to EXACTLY 63!!!11!1!!111!"

More realistically numbered coincidences are a brilliant example of conformational bias. We ignore the vast majority of relations we see and attribute arbitrary meanings to patterns we judge to be important. The arm span/height fallacy is a great one because no one ever points out the the circumference of a head =/= the length of a leg or that the size of the stomach is unrelated to the number of fingers on one hand etc

 Speculation on the seconds-pendulum and the eventual choice to define the metre/meter as one ten-millionth part of the quarter-meridian is fine, but there is a good paper on the topic on the 'Istituto Nazionale di Fisica Nucleare' web-site:- 'Why does the meter beat the second?' by Paolo Agnoli and Giulio d'Agostini (ref: arXiv:physics/0412078 v2 25 Jan 2005). It is perhaps unfortunate that the French revolutionary state did not impose the decimal-second with the same vigour it imposed the metre. If it had the 'coincidences' and 'happenstances' referred to in this thread would not exist. However, the introduction of decimalisation throughout the new system of weights and measures was only one of the design criteria set for the system, as Agnoli and d'Agostini's paper describes. Given the other design criteria, and the level of scientific and technological development attained by the 1790s, it is at least an interesting academic exercise to hypothesise how the French scientific rationalists of the period might have gone about designing a new unit of time.

Mentor
 Quote by RadioTech It is perhaps unfortunate that the French revolutionary state did not impose the decimal-second with the same vigour it imposed the metre.
Had the French Academy mucked with the definition of time, they would have made the day the base unit rather than the second.

In fact, the French Academy initially did muck with the definition of time (http://www.gefrance.com/calrep/decrtxt.htm): Le jour, de minuit à minuit, est divisé en dix parties, chaque partie en dix autres, ainsi de suite jusqu’à la plus petite portion commensurable de la durée.. (The day, from midnight to midnight, is divided into ten parts, each part into ten others, so on until the smallest measurable portion of duration.) This proposal took off like a lead trial balloon; the French abandoned the concept of decimal time less than two years after this mandate.

Unlike standards for length and mass, which varied incredibly from place to place at the time of the French Revolution, time and angle had pretty much the same representation across all of western Europe and beyond. While those representations were not decimal, they were very standard.

 If it had the 'coincidences' and 'happenstances' referred to in this thread would not exist.
Some other coincidences and happenstances would have existed instead.

However, the following observations are matters of fact:
1. that one second is virtually identical to one half the period beat by a simple pendulum of length one metre and;
2. that one second is virtually identical to 30 times the period that light takes to travel the length of the quarter meridian.
These are surprising coincidences that are not explicable by reference to the laws of physics alone.
Your paper is going along the path of numerology from the onset. This is in general a bad path to follow. Let's look at those coincidences:

That one second is virtually identical to one half the period beat by a simple pendulum of length one metre
This coincidence is rooted in two widely-used, human-based standards for a unit of length are coincidentally nearly equal to one another and that both are coincidentally nearly equal to the length of a seconds pendulum. That the number 360 holds a special place in pre-scientific numerological thinking is one of the key reasons we still subdivide angle and time the way we do.

That one second is virtually identical to 30 times the period that light takes to travel the length of the quarter meridian.
This coincidence is rooted in the coincidence that the speed of light in metric units happens to be close to a nice, round number and that the distance between the equator and the pole happens to be about ten million meters. What if the Indians (the source of our number system) had counted their fingers and toes rather than just fingers? Our ten million would be something like 32A000 in base 20, which isn't near as nice a number as 10,000,000. That part of the coincidence would have just vanished. The remaining coincidence is just that, coincidence.

 Given the other design criteria, and the level of scientific and technological development attained by the 1790s, it is at least an interesting academic exercise to hypothesise how the French scientific rationalists of the period might have gone about designing a new unit of time.
I gave you a link showing exactly what they did: They chose the day as the base unit for time. If those French rationalists had had their way the 1/86,400 day second would have been history. That there are 86,400 seconds in a day is anything but an arbitrary choice. It is deeply rooted in pre-scientific Egyptian and Babylonian mythology, which placed undo importance on the numbers 6, 12, 60 and 360.

The French concept of a day as the unit of time lasted less than two years. The metric system did not have an official unit for time for another 150 years. The cgs system of course had a unit of time, as did the MKS system. That unit, the second, did not become a part of the official, treaty-bound metric system until 1960.

 Mentor The Babylonians did not "have the meter". They, like many other societies, had a unit in length about the size of an arm's reach. Like the yard or the bu. 86400 has been explained before; it has a lot of factors. There's really nothing here.

 Quote by RadioTech [...] in one second light travels a distance equal to 30.0 times the distance between the north pole and the equator [..]
 Quote by Ryan_m_b Eh? With a little research I convinced myself that this was not true. Distance from north pole to equator - 10001.965km x 30 - 300058.95km 1 light second - 299792.458km http://en.wikipedia.org/wiki/Earth http://www.google.com/search?q=light+second
Rounded to the implicitly stated precision, you thus found:
299792.458 / 10001.965 = 30.0

Of course, it very much appears to be numerology as D H already mentioned.

 Quote by RadioTech [..] The Babylonians had been around for 2,000 years, and one way or another they had devised an 86400-second day such that: light travels 30 quarter-meridians in 1 second;[...]
OK it's a little more interesting than I expected. Do you merely suggest that it's not a coincidence? "one way or another" isn't much to go on.

 Mentor This is just numerology crackpottery. Thread locked.