This reminded me of The Anasazi Sun Temple that catches the first light of the Summer Solstice in a specific point in the temple. I first discovered this watching Carl Sagan's Cosmos early this year (which I'd highly recommend, BTW)
How did ancient cultures know when the solstice was? If you didn't tell me it was the 21st, I don't know how I'd be able to tell you other than by carefully measuring the sunrise and sunset times
> How did ancient cultures know when the solstice was
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 geometries.
Honestly I bet you would have at least a reasonable intuition about it if you were among them. It's pretty remarkable how much our distractions and 'being indoors' all the time dulls our senses to nature.
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.
It seems unintuitive today because people living in cities and towns don’t usually see sunrises and sunsets from where they live. If you had a way to easily reference the sunrise and sunset points against known horizon, it’d be very easy to tell.
I’m sure you’d know that this was winter. If you line 2 sticks up with sunrise, and keep adjusting them every morning, eventually you’ll see that the sun stops rising further south and starts moving north again. You don’t need complex mathematics to work it out.
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 sunset 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.
I am super impressed by humans noticing and separating the planet's from the stars. Look at those stars they don't twinkle and they move funny. I guess the planets drew attention because of their brightness and by their lack of twinkle.
Kerala, for the curious, is also the place where the infinite series (and with it arguably calculus) was devised some 200 years before Newton's birth.
Blatant Western-centrism within academia (and the strange, almost primitive-hatred for living ancient-cultures) perhaps hasn't led either to the recognition of "ancient" monuments in India or its scientific/astronomical outputs.
The festival of Sankranti for eg. is so old that due to the Hindu Luni-Solar calendar's usage of the sidereal year, it has drifted off from the winter-solstice by 20 odd days, starting from 150 BC (amusingly as has the Julian calendar, but due to a lack of precision in arithmetic / observational accuracy).
That's regrettable yes, as any centrism. But people interested in epistemology certainly are aware of major contributions to sciences by Indian thinkers.
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.
Although western centrism is definitely a thing, the link you provided states that temple, for example, was started in the 16th century. The article link is about something from 2800BC
> Blatant Western-centrism within academia (and the strange, almost primitive-hatred for living ancient-cultures) perhaps hasn't led either to the recognition of "ancient" monuments in India or its scientific/astronomical outputs.
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
Depends on the details of how you define calculus. Archimedes was doing integration, Descartes was evaluating slopes and tangents of algebraic curves. Isaac Barrow had a good grasp of fundamental theorem of calculus -- that differentiation and integration are inverse operations. Brook Taylor did Taylor series before Newton.
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 sin 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 amd called them out as rules/results of broad apicability. 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 Aryabhatta'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 ignorant and rageful conspiracy monger.
The inaccuracies in the Hindu calendar is and was a lot more than the Julian calendar. The Julian calendar assumed that a year was 365 1/4 the day. This is slightly inaccurate and therefore there was a need to correct for the leap day that's added every 4 years by skipping it every 100 years, adding it back every 400 years. At time of Gregorian correction it was off by 10~11 days because of an error of 10 minutes in their estimate of the length of an year.
Hindu estimate of the length of an year, although remarkably accurate, was less accurate than the estimate of 365 1/4th. Usually the length of an year has been overestimated, making the Hindu calendar to lose accuracy quicker. These errors were order of a day per year versus off by about 10 minutes like the Julian calendar.
This was less of a problem historically because Ujjain observatory would correct the calendar time time using accurate observation of the Equinox. Since the fall of Ujjain observatory the Hindu calendar has been accumulating drift error for centuries.
This reminded me of The Anasazi Sun Temple that catches the first light of the Summer Solstice in a specific point in the temple. I first discovered this watching Carl Sagan's Cosmos early this year (which I'd highly recommend, BTW)
https://en.wikipedia.org/wiki/Casa_Rinconada
Where I live, I find it wild that there is a 5.75-hour difference between the summer and winter solstices, nearly a quarter of a whole day.
Where I live, the difference is almost six months!
For Orkney the difference in day length between winter and summer solstices is about 12 hours?
December: https://www.timeanddate.com/sun/uk/kirkwall?month=12&year=20...
June: https://www.timeanddate.com/sun/uk/kirkwall?month=6&year=202...
my modern equivalent(I needed last year for surfing (after i needed to cut a surf trip short as it became night))
https://daylight.franzai.com/
and yes, the maths fails when you are super super high north or south
Hey! nice little useful web page. I like the minimalism of it.
Does the math fail because of not considering (i) equation of time and (ii) oblateness of the Earth ?
How did ancient cultures know when the solstice was? If you didn't tell me it was the 21st, I don't know how I'd be able to tell you other than by carefully measuring the sunrise and sunset times
> How did ancient cultures know when the solstice was
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 geometries.
Honestly I bet you would have at least a reasonable intuition about it if you were among them. It's pretty remarkable how much our distractions and 'being indoors' all the time dulls our senses to nature.
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.
Probably easier to measure the location of sunsets and sunrises rather than the time?
Edit: Obviously somewhere like here in Scotland observing the sunrise is easier said than done - particularly at this time of year!
It seems unintuitive today because people living in cities and towns don’t usually see sunrises and sunsets from where they live. If you had a way to easily reference the sunrise and sunset points against known horizon, it’d be very easy to tell.
I’m sure you’d know that this was winter. If you line 2 sticks up with sunrise, and keep adjusting them every morning, eventually you’ll see that the sun stops rising further south and starts moving north again. You don’t need complex mathematics to work it out.
To tell it accurately of course takes work.
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 sunset 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.
I am super impressed by humans noticing and separating the planet's from the stars. Look at those stars they don't twinkle and they move funny. I guess the planets drew attention because of their brightness and by their lack of twinkle.
In India,
https://www.etvbharat.com/english/bharat/padmanabha-swamy-te...
Kerala, for the curious, is also the place where the infinite series (and with it arguably calculus) was devised some 200 years before Newton's birth.
Blatant Western-centrism within academia (and the strange, almost primitive-hatred for living ancient-cultures) perhaps hasn't led either to the recognition of "ancient" monuments in India or its scientific/astronomical outputs.
The festival of Sankranti for eg. is so old that due to the Hindu Luni-Solar calendar's usage of the sidereal year, it has drifted off from the winter-solstice by 20 odd days, starting from 150 BC (amusingly as has the Julian calendar, but due to a lack of precision in arithmetic / observational accuracy).
That's regrettable yes, as any centrism. But people interested in epistemology certainly are aware of major contributions to sciences by Indian thinkers.
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
Although western centrism is definitely a thing, the link you provided states that temple, for example, was started in the 16th century. The article link is about something from 2800BC
The article is about more than just that one monument and has a few contemporary examples as well.
> Blatant Western-centrism within academia (and the strange, almost primitive-hatred for living ancient-cultures) perhaps hasn't led either to the recognition of "ancient" monuments in India or its scientific/astronomical outputs.
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
Depends on the details of how you define calculus. Archimedes was doing integration, Descartes was evaluating slopes and tangents of algebraic curves. Isaac Barrow had a good grasp of fundamental theorem of calculus -- that differentiation and integration are inverse operations. Brook Taylor did Taylor series before Newton.
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 sin 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 amd called them out as rules/results of broad apicability. 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 Aryabhatta'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 ignorant and rageful conspiracy monger.
The inaccuracies in the Hindu calendar is and was a lot more than the Julian calendar. The Julian calendar assumed that a year was 365 1/4 the day. This is slightly inaccurate and therefore there was a need to correct for the leap day that's added every 4 years by skipping it every 100 years, adding it back every 400 years. At time of Gregorian correction it was off by 10~11 days because of an error of 10 minutes in their estimate of the length of an year.
Hindu estimate of the length of an year, although remarkably accurate, was less accurate than the estimate of 365 1/4th. Usually the length of an year has been overestimated, making the Hindu calendar to lose accuracy quicker. These errors were order of a day per year versus off by about 10 minutes like the Julian calendar.
This was less of a problem historically because Ujjain observatory would correct the calendar time time using accurate observation of the Equinox. Since the fall of Ujjain observatory the Hindu calendar has been accumulating drift error for centuries.