The Ancient Monuments Saluting the Winter Solstice

Newton and Leibnitz get credit because they placed calculus as a general technique that is immensely broadly applicable not just to extrapolate the tangent function or the some function but to any function that's smooth in some sense. They worked out the details that do not depend on the specifics of the function especially how to push the differential and integral operators through +,-,×,÷ and function composition sign. It did not matter what the function was as long as it was built up from those operations.

I am familiar with the work of Kerala school and also of Aryabhatt's work on using differential coefficients to extrapolate the sin function (this being much before Kerala school), his work on difference equations.

Rather than getting caught up with us versus them narratives , spend some time learning about the beauty of math and how different cultures have thought about them in such creative ways. Otherwise you risk sounding uneducated, ignorant and rageful.

Enough with this bullshit please? There are genuine reasons why the knowledge of the calculus of ancient Kerala didn't travel outside India during the late middle ages.

It is a fact that Madhava a mathematician and astronomer from the late middle ages, came up with calculus, and established the Nila School of Mathematics in Kerala. For some reason, the book (Yuktibhasa) that discusses this math is written in the local language Malayalam. Most scholars at the time only understood Sanskrit, including later Western scholars who were unable to find good Malayalam book. Because of this, it was difficult to have the works translated, especially since the works describe formal proofs of concepts like series expansion, which was not even known in the Northern India at the time.

Kerala was also under Portuguese rule at the time and was frequently faced with wars, so the school gradually declined and the math culture sort of died out.

The Mathematics of India by P.P. Divakaran discusses these themes.

P.S: Most of what I've said here is taken from this Numberphile video of another mathematician discussing the life and work of P.P. Divakaran (who recently passed away) https://www.youtube.com/watch?v=G23Jx0kPCSI

By the way, Wolfram’s website has an interesting summary of the history of this formula.[0]

[0]: https://mathworld.wolfram.com/QuadraticEquation.html

Biased coverage is unfortunately rather widespread in more general media. And rise of nationalisms don't help in the matter. Which is true for western and eastern countries by the way.

Regarding a case of several millennia of prior art, there is Pāṇini, who employed metalanguage long before the idea become of interest in western side.

https://en.wikipedia.org/wiki/P%C4%81%E1%B9%87ini

I started doing astrophotography about three years ago. I'd always been interested in 'space' but never really spent hours upon hours out at night over the course of months actually just studying the night sky. I remember wondering as a kid how people even thought about planets or came up with these wild stories with the constellations...to me it just kind of looked like a bright field of randomly twinkling lights.

Well, when you're out every night from 10pm to 2am looking up, it all just kind of comes alive. You see everything. The motion of the planets, the elliptic upon which they travel, the gradual shift of the entire field as the seasons change, the undulations of the moon and it's varied trajectory across the sky. The shifting of the sun's set and rise and the ebb and flow of day vs night. Everything. Your mind just starts to harmonize with the rhythm of it all. It's pretty wonderful.

You and I personally may not have kept track, but our local religious leader did, and maybe the even staged a ceremony at the winter solstice to ask the sun to make the days longer.

After you notice that, if you want more precision, it's the day the Sun rises and sets most on the North/South. It's also the day things cast the largest shadow at noon. You will need some special device to get very precise on the sun raising position (like a pair of stones or something with a hole), and you won't be able to get precision on the shadow thing.

For more modern people, starting about only half a dozen millennia ago, it's the hour the Sun stops moving North/South within the stars and starts moving the other way around. You will need to look at it and take notes many times, and average things out to get any precision. Even more because you can't see the Sun and the stars at the same time, so you have to model them.

Solstice is a small thing they figured long ago, there are things they managed that are much more complex than that. In India there are whole temples dedicated to astronomy and built to align with different celestial geomentries.

However if you live in the open, or have daily access to the open sky, after a while you are bound to notice.

We are so used to having a ceiling above us, so used to constructions blocking our view of the sky that this seems a feat.

I was the same till I got access to the sky. Then ... oh wait ... the sun set is shifting towards those landmarks every day. Oh wait, now its turning around to go the other way.

The total span of movement is so large, that its hard to miss unless you are on a featureless landscape or in the open sea.

They didn't like go out on Dec 21st, and look where the sun was and mark it. They didn't even have calendars like that. They watched the sun every day, and waited until it stopped being lower in the sky at it's highest point in the day, and marked that angle and built whatever viewport they wanted (a door, tunnel, etc).

Then they could just go wherever they built the thing that pointed at that point in the sky, and go, oh, okay, the solstice is soon, or just happened, or whatever and plan accordingly.

It actually wasn't really accurate to the day, anyway. There are a few days on either side of the solstice where the effect is basically the same for the viewer.

https://en.wikipedia.org/wiki/Solstice#Solstice_determinatio...

https://en.wikipedia.org/wiki/Manhattanhenge

today - 07:18:59 → 16:24:29 = 9:5:30. yesterday - 7:18:23 → 16:23:53 = 9:5:30

You can use an js SVG animation to have it run in real time: https://tomchen.github.io/animated-svg-clock/clock.svg

I have no idea why we stuck with the 12 hour clocks once we stopped using sundials and variable hours: https://en.wikipedia.org/wiki/Unequal_hours

I first saw this idea at https://jmw.name/projects/linear-clock/ and then later I wrote a TUI version for myself

I had tickmarks for stuff (when to go to bed to sleep for 7.5h and wake up near sunrise, things like that). I was working on adding a config file format.

Then I lost the project due to a mishap with a pipx flag... https://github.com/pypa/pipx/issues/1324#issuecomment-211885... ;_; o7

One day maybe I'll come back and do it in Rust.

0. https://drive.google.com/file/d/1FB3Ofl4mUvOO4gGqARro9cO_kjJ...

December: https://www.timeanddate.com/sun/uk/kirkwall?month=12&year=20...

June: https://www.timeanddate.com/sun/uk/kirkwall?month=6&year=202...

Now if you disclose your local time offset from GMT, say, Palantir can send a drone carrying roses.

They aren't "all over the place" in the US, and I certainly don't have a local archaeologist that I can just call up.

FWIW: The Northeastern US is quite recent with human presence. It wasn't settled until after the last ice age. Pretty much anything old is celebrated because there is so little of anything old.

The article talks extensively about how these monuments were used for timekeeping. Marking the seasons allowed people to predict animal migrations and plan agricultural activities.

It seems that you are the one who has forgotten the practical uses of these artifacts.

In the northern latitudes, doubtful. It would be cool enough year round.