Read on Twitter
[THREAD: UJJAIN — HYPE VS. FACTS]
1/82
Timekeeping is a 3,500-year-old tradition that goes back to Ancient Egypt and Babylon where they used giant stone obelisks for the purpose. We call them shadow clocks, or sundials. This is how they mostly looked.
![[THREAD: UJJAIN — HYPE VS. FACTS]1/82Timekeeping is a 3,500-year-old tradition that goes back to Ancient Egypt and Babylon where they used giant stone obelisks for the purpose. We call them shadow clocks, or sundials. This is how they mostly looked.](https://pbs.twimg.com/media/EnVN81QWEAAPuTv.jpg "[THREAD: UJJAIN — HYPE VS. FACTS]1/82Timekeeping is a 3,500-year-old tradition that goes back to Ancient Egypt and Babylon where they used giant stone obelisks for the purpose. We call them shadow clocks, or sundials. This is how they mostly looked.")
1/82
Timekeeping is a 3,500-year-old tradition that goes back to Ancient Egypt and Babylon where they used giant stone obelisks for the purpose. We call them shadow clocks, or sundials. This is how they mostly looked.
2/82
With time, these ideas were adopted and further refined by other civilizations, most notably the Ancient Greeks. Sundials started getting smaller and more accurate after the Greeks introduced trigonometry to its calculations. Here's a quick primer on how the thing works.
With time, these ideas were adopted and further refined by other civilizations, most notably the Ancient Greeks. Sundials started getting smaller and more accurate after the Greeks introduced trigonometry to its calculations. Here's a quick primer on how the thing works.
3/82
The whole idea is that things cast shadows. And depending on the angle of light, the shadow can be longer or shorter. Also, the shadow always points directly away from light. That's pretty intuitive, nothing complex to process here. That's all the physics you need.
The whole idea is that things cast shadows. And depending on the angle of light, the shadow can be longer or shorter. Also, the shadow always points directly away from light. That's pretty intuitive, nothing complex to process here. That's all the physics you need.
4/82
A sundial is nothing but a circular plate with a stick at the center. This stick runs along the plate's axis and is called the gnomon (the one who knows). The plate itself is the dial. Kept out in the sun, the gnomon would cast a shadow on the dial.
A sundial is nothing but a circular plate with a stick at the center. This stick runs along the plate's axis and is called the gnomon (the one who knows). The plate itself is the dial. Kept out in the sun, the gnomon would cast a shadow on the dial.
5/82
The shadow's angle is always aligned with that of the Sun and since the latter moves throughout the day (actually it's the Earth that does), so does the shadow. The dial is etched with hour markers at regular intervals so the shadow falling on them tells the time.
The shadow's angle is always aligned with that of the Sun and since the latter moves throughout the day (actually it's the Earth that does), so does the shadow. The dial is etched with hour markers at regular intervals so the shadow falling on them tells the time.
6/82
That was a short explanation. Here's a detailed version. Imagine the Earth as a giant sundial and its axis as the gnomon. Jaipur on the North Pole, you can see how the gnomon's shadow would move tracing a circular path with the Earth's rotation.
That was a short explanation. Here's a detailed version. Imagine the Earth as a giant sundial and its axis as the gnomon. Jaipur on the North Pole, you can see how the gnomon's shadow would move tracing a circular path with the Earth's rotation.
7/82
If a circle is taken as 360°, and the day has 24 hours, each hour would correspond to a 15° slice on the Earth dial. Remember, the entire dial is in light here because the Earth's axis isn't exactly perpendicular to its orbital plane, there's a 23° tilt.
If a circle is taken as 360°, and the day has 24 hours, each hour would correspond to a 15° slice on the Earth dial. Remember, the entire dial is in light here because the Earth's axis isn't exactly perpendicular to its orbital plane, there's a 23° tilt.
8/82
This hypothetical sundial works because the gnomon is parallel to the Earth's axis, and since the axis is perpendicular to the equator, the dial itself aligns with the latter. That's why a sundial built to this specification is called an equatorial sundial.
This hypothetical sundial works because the gnomon is parallel to the Earth's axis, and since the axis is perpendicular to the equator, the dial itself aligns with the latter. That's why a sundial built to this specification is called an equatorial sundial.
9/82
The further away you move this sundial from the pole, the more of it will fall in the shadow. At the equator, only half of it would see the Sun which means, it'd only be capable of telling the time over roughly 12 hours instead of 24. See the second image here.
The further away you move this sundial from the pole, the more of it will fall in the shadow. At the equator, only half of it would see the Sun which means, it'd only be capable of telling the time over roughly 12 hours instead of 24. See the second image here.
10/82
But there's one problem with equatorial sundials. The gnomon must always run parallel to the Earth's axis. At the pole, this is easy, just let the dial sit flat, parallel to the equator. But on other latitudes, this becomes problematic.
But there's one problem with equatorial sundials. The gnomon must always run parallel to the Earth's axis. At the pole, this is easy, just let the dial sit flat, parallel to the equator. But on other latitudes, this becomes problematic.
11/82
At non-polar latitudes, the gnomon can either be parallel to the Earth's axis, or perpendicular to the ground, never both. To keep the gnomon parallel to the Earth's axis, it must be kept on an angle with the ground. At what angle? Brace for some light geometry here.
At non-polar latitudes, the gnomon can either be parallel to the Earth's axis, or perpendicular to the ground, never both. To keep the gnomon parallel to the Earth's axis, it must be kept on an angle with the ground. At what angle? Brace for some light geometry here.
12/82
Here's how we do it. First, some labels:
BC: Equator
IM: Earth's axis
DG: A non-equatorial latitude
JL: Alignment of the gnomon (parallel to IM)
KH: Alignment of the dial (parallel to the ground)
α: Angle of the latitude DG with the equator
P.S. diagram courtesy, moi.
Here's how we do it. First, some labels:
BC: Equator
IM: Earth's axis
DG: A non-equatorial latitude
JL: Alignment of the gnomon (parallel to IM)
KH: Alignment of the dial (parallel to the ground)
α: Angle of the latitude DG with the equator
P.S. diagram courtesy, moi.
13/82
Since a latitude is defined by the angle by which it's separated from the equator, the latitude (DG) in our example is α° N.
Since DG and BC are parallel and AG forms the transversal between them, angles GAC and DGA are equal, per the theorem of alternate interior angles.
Since a latitude is defined by the angle by which it's separated from the equator, the latitude (DG) in our example is α° N.
Since DG and BC are parallel and AG forms the transversal between them, angles GAC and DGA are equal, per the theorem of alternate interior angles.
14/82
When two straight lines cross each other, opposite angle are congruent. Thus, FGE is equal to DGA which is already equal to GAC, i.e. α. Since JL and DE are mutually perpendicular, JGE must be a right angle, i.e. 90°. Which leaves JGF as 90-α.
When two straight lines cross each other, opposite angle are congruent. Thus, FGE is equal to DGA which is already equal to GAC, i.e. α. Since JL and DE are mutually perpendicular, JGE must be a right angle, i.e. 90°. Which leaves JGF as 90-α.
15/82
Since KH is tangential to the Earth's surface and AF is perpendicular to it, KGF must also be a right angle. Part of this angle is JGF which is 90-α. Thus, the remaining part, i.e. KGJ must be 90-(90-α). That reduces to α.
Since KH is tangential to the Earth's surface and AF is perpendicular to it, KGF must also be a right angle. Part of this angle is JGF which is 90-α. Thus, the remaining part, i.e. KGJ must be 90-(90-α). That reduces to α.
16/82
Since KH is the dial and JG is the gnomon, KGJ is basically the gnomon's tilt against the dial. That is α. Which also happens to be the latitude!
In short, an equatorial sundial's gnomon must be at an angle with the dial the value of which is the same as its latitude.
Since KH is the dial and JG is the gnomon, KGJ is basically the gnomon's tilt against the dial. That is α. Which also happens to be the latitude!
In short, an equatorial sundial's gnomon must be at an angle with the dial the value of which is the same as its latitude.
17/82
The Greeks has all of this figured out at least by the time of Euclid (300 BC) if not earlier. But they had already borrowed the more primitive obelisk clocks from the Babylonians as early as the 6th century BC, long before the equatorial or equinoctial sundial.
The Greeks has all of this figured out at least by the time of Euclid (300 BC) if not earlier. But they had already borrowed the more primitive obelisk clocks from the Babylonians as early as the 6th century BC, long before the equatorial or equinoctial sundial.
18/82
Do note at this point that a sundial has to be aware of its latitude since that's the value governing the gnomon's orientation. But it doesn't have to know the longitude. This is a very crucial bit that'll come in handy later down the thread.
Now let's go to Afghanistan.
Do note at this point that a sundial has to be aware of its latitude since that's the value governing the gnomon's orientation. But it doesn't have to know the longitude. This is a very crucial bit that'll come in handy later down the thread.
Now let's go to Afghanistan.
19/82
Some 285 miles north of Kabul, where Kokcha pours into Amu Darya and Afghanistan meets Turkmenistan, is an archaeological dig. Politically, the region is part of the frontier province of Takhar. At one time in the past, this is where kings would come on hunting expeditions.
Some 285 miles north of Kabul, where Kokcha pours into Amu Darya and Afghanistan meets Turkmenistan, is an archaeological dig. Politically, the region is part of the frontier province of Takhar. At one time in the past, this is where kings would come on hunting expeditions.
20/82
On one such expedition, Khan Gholam Serwar Nasher stumbled upon some artefacts that seemed ancient. Intrigued, he called upon Daniel Schlumberger the famous Princeton archeologist to investigate. By 1970, French archeologists had dug the whole place up.
On one such expedition, Khan Gholam Serwar Nasher stumbled upon some artefacts that seemed ancient. Intrigued, he called upon Daniel Schlumberger the famous Princeton archeologist to investigate. By 1970, French archeologists had dug the whole place up.
21/82
Turns out, this desolate stretch was once a bustling Graeco-Bactrian metropolis named Aï Khanūm (Uzbek for Lady Moon). The Greeks called it Alexandria after the famous Macedonian conqueror. There were many Alexandrias those days, this one was Alexandria on the Oxus.
Turns out, this desolate stretch was once a bustling Graeco-Bactrian metropolis named Aï Khanūm (Uzbek for Lady Moon). The Greeks called it Alexandria after the famous Macedonian conqueror. There were many Alexandrias those days, this one was Alexandria on the Oxus.
22/82
Aï Khanūm was pretty much the frontier of the Graeco-Bactrian territory, almost bordering the Mauryan Empire of India. To the south, Bactria reached what's today Hyderabad (Pakistan) but was then Pattala. Aï Khanūm unfortunately was completely abandoned by 145-120 BC.
Aï Khanūm was pretty much the frontier of the Graeco-Bactrian territory, almost bordering the Mauryan Empire of India. To the south, Bactria reached what's today Hyderabad (Pakistan) but was then Pattala. Aï Khanūm unfortunately was completely abandoned by 145-120 BC.
23/82
The city was named Alexandria for a reason. In 329 BC, Alexander was in the region on an eastward campaign. Aï Khanūm is where he made a pit stop. His men fatigued, his supplies running out, the emperor decided to stay on until ready to fight again.
The city was named Alexandria for a reason. In 329 BC, Alexander was in the region on an eastward campaign. Aï Khanūm is where he made a pit stop. His men fatigued, his supplies running out, the emperor decided to stay on until ready to fight again.
24/82
It's during this period of rest that he founded a city, named it Alexandria on the Oxus (ancient name for Amu Darya), and married a local Bactrian princess called Roxana.
This is the magnificent city the French Archaeological Delegation in Afghanistan had unearthed.
It's during this period of rest that he founded a city, named it Alexandria on the Oxus (ancient name for Amu Darya), and married a local Bactrian princess called Roxana.
This is the magnificent city the French Archaeological Delegation in Afghanistan had unearthed.
25/82
To the East, Bactria bordered the Mauryan Empire, not far from where Aï Khanūm stood. And the Mauryan Empire was divvied up into 4 provinces, one of them being the Western province with capital at the newly-annexed Avanti.
To the East, Bactria bordered the Mauryan Empire, not far from where Aï Khanūm stood. And the Mauryan Empire was divvied up into 4 provinces, one of them being the Western province with capital at the newly-annexed Avanti.
26/82
Avanti was so grand for its time, it was made the capital of the whole empire. Today, we know the city as Ujjain.
Ujjain has an interesting location.
Horizontally, it sat right in the middle of the Mauryan Empire. Almost vertically so too.
Avanti was so grand for its time, it was made the capital of the whole empire. Today, we know the city as Ujjain.
Ujjain has an interesting location.
Horizontally, it sat right in the middle of the Mauryan Empire. Almost vertically so too.
27/82
Even today, the longitude that runs through this city (76°38′E) is considered the "unofficial" prime meridian of India.
India, not world.
The longitude is roughly half an hour behind the one that runs through Allahabad, the "official" prime meridian of India (IST).
Even today, the longitude that runs through this city (76°38′E) is considered the "unofficial" prime meridian of India.
India, not world.
The longitude is roughly half an hour behind the one that runs through Allahabad, the "official" prime meridian of India (IST).
28/82
This astronomical trivia was first recorded in the Sanskrit treatise Sūrya Siddhānta. Even today, traditional Hindu horoscopes treat the Ujjain line as its 0°.
Sūrya Siddhānta itself goes back to between 350 and 500 AD depending on who you ask.
This astronomical trivia was first recorded in the Sanskrit treatise Sūrya Siddhānta. Even today, traditional Hindu horoscopes treat the Ujjain line as its 0°.
Sūrya Siddhānta itself goes back to between 350 and 500 AD depending on who you ask.
29/82
The practice of standard time wasn't confined to India though. Throughout antiquity, empires and kingdoms have designated their own "prime meridians." There was no universal time coordinate because the need was never felt.
The practice of standard time wasn't confined to India though. Throughout antiquity, empires and kingdoms have designated their own "prime meridians." There was no universal time coordinate because the need was never felt.
30/82
While the choice of a nation's standard/prime meridian (a local "0°," if you will) is constrained by geometry (the closer to the horizontal midpoint, the better), that of the universal prime meridian is rather arbitrary. Any given longitude can play the role.
While the choice of a nation's standard/prime meridian (a local "0°," if you will) is constrained by geometry (the closer to the horizontal midpoint, the better), that of the universal prime meridian is rather arbitrary. Any given longitude can play the role.
31/82
But ancient Indians weren't the first to have a standard meridian, or even meridians in general. Greek polymath Eratosthenes had propounded longitudes as early as the 3rd century BC. That doesn't necessarily mean the Indians learned it from him.
But ancient Indians weren't the first to have a standard meridian, or even meridians in general. Greek polymath Eratosthenes had propounded longitudes as early as the 3rd century BC. That doesn't necessarily mean the Indians learned it from him.
32/82
In fact, it's possible that astrologers in Ujjain came up with the concept of longitudes independently since they didn't measure those in degrees like the Greeks did. The first reference to this in India comes from the aforementioned Sūrya Siddhānta.
In fact, it's possible that astrologers in Ujjain came up with the concept of longitudes independently since they didn't measure those in degrees like the Greeks did. The first reference to this in India comes from the aforementioned Sūrya Siddhānta.
33/82
Sūrya Siddhānta itself claims to be from 2 million years ago. Obviously, that's just poetic liberty and the oldest it's been dated to is around 350 AD; it was done by John Bowman of Colombia University. So that makes Eratosthenes at least 550 years older than this text.
Sūrya Siddhānta itself claims to be from 2 million years ago. Obviously, that's just poetic liberty and the oldest it's been dated to is around 350 AD; it was done by John Bowman of Colombia University. So that makes Eratosthenes at least 550 years older than this text.
34/82
Eratosthenes defined a prime meridian for Alexandria in Egypt. That's because he worked there, as the librarian at the Great Library of Alexandria. After him, others Greek city-states started marking their own prime meridians. This included one at Rhodes.
Eratosthenes defined a prime meridian for Alexandria in Egypt. That's because he worked there, as the librarian at the Great Library of Alexandria. After him, others Greek city-states started marking their own prime meridians. This included one at Rhodes.
35/82
By 150 AD, Claudius Ptolemy came out with a treatise of his own in Alexandria. It was titled Γεωγραφικὴ Ὑφήγησις (Latinized as Geographia). Geographia was a rehash of an earlier work by Marinus of Tyre with additional influences from contemporary Persian cartographers.
By 150 AD, Claudius Ptolemy came out with a treatise of his own in Alexandria. It was titled Γεωγραφικὴ Ὑφήγησις (Latinized as Geographia). Geographia was a rehash of an earlier work by Marinus of Tyre with additional influences from contemporary Persian cartographers.
36/82
With this volume, Ptolemy became the first individual to propose a universal time coordinate, a single standard prime meridian for the entire world. This original prime meridian corresponds to 25° 40' 32″ W today. That's way off the line through Greenwich.
With this volume, Ptolemy became the first individual to propose a universal time coordinate, a single standard prime meridian for the entire world. This original prime meridian corresponds to 25° 40' 32″ W today. That's way off the line through Greenwich.
37/82
Ptolemy's meridian remained the global prime well into the Middle Ages. The line in Ujjain became prime for territories within the Indian subcontinent with the Sūrya Siddhānta, 200 years after Geographia. At no point in time was it the universal standard.
Ptolemy's meridian remained the global prime well into the Middle Ages. The line in Ujjain became prime for territories within the Indian subcontinent with the Sūrya Siddhānta, 200 years after Geographia. At no point in time was it the universal standard.
38/82
So thus far, here's what we have.
Sundials originated in Ancient Egypt and Babylon. The simplest kind is the equinoctial or equatorial sundial. It consists of a dial with hour markings and a gnomon. The gnomon casts a shadow which tells the time.
So thus far, here's what we have.
Sundials originated in Ancient Egypt and Babylon. The simplest kind is the equinoctial or equatorial sundial. It consists of a dial with hour markings and a gnomon. The gnomon casts a shadow which tells the time.
39/82
The angle between the gnomon and the dial must be the same as the latitude at the place of installation. Ergo, the sundial's configuration changes with a change in latitude. No dependency on the longitude whatsoever. This holds true for other kinds of sundials too.
The angle between the gnomon and the dial must be the same as the latitude at the place of installation. Ergo, the sundial's configuration changes with a change in latitude. No dependency on the longitude whatsoever. This holds true for other kinds of sundials too.
40/82
That is, two identical sundials on two different longitudes but on the same latitude will function the exact same way. They'll give different time readings but they'll both be equally accurate.
We also learned that Aï Khanūm was the Uzbek name for Alexandria on the Oxus.
That is, two identical sundials on two different longitudes but on the same latitude will function the exact same way. They'll give different time readings but they'll both be equally accurate.
We also learned that Aï Khanūm was the Uzbek name for Alexandria on the Oxus.
41/82
Alexandria on the Oxus was a pit stop developed into a functional city by Alexander the Great while on a campaign trail toward India. The city sat on the eastern frontier of Bactria, not far from the border with the Mauryan Empire of India.
Alexandria on the Oxus was a pit stop developed into a functional city by Alexander the Great while on a campaign trail toward India. The city sat on the eastern frontier of Bactria, not far from the border with the Mauryan Empire of India.
42/82
Concurrent to the founding of Alexandria on the Oxus, was the Mauryan annexation of Avanti, an ancient city corresponding to today's Ujjain. Ujjain was considered the hub of Indian timekeeping because an ancient book on the subject said so.
Concurrent to the founding of Alexandria on the Oxus, was the Mauryan annexation of Avanti, an ancient city corresponding to today's Ujjain. Ujjain was considered the hub of Indian timekeeping because an ancient book on the subject said so.
43/82
This book was Sūrya Siddhānta and it was the first to introduce India to longitudes. It also named the one through Ujjain, the subcontinent's prime meridian. This book's been dated to 350 AD or later.
The idea of longitudes was first given 550 years earlier by the Greeks.
This book was Sūrya Siddhānta and it was the first to introduce India to longitudes. It also named the one through Ujjain, the subcontinent's prime meridian. This book's been dated to 350 AD or later.
The idea of longitudes was first given 550 years earlier by the Greeks.
44/82
Eratosthenes proposed longitudes and local prime meridians in the 3rd century BC. Ptolemy proposed a single universal prime meridian for the whole world (like today's UTC) in 150 AD. This was 200 years before Sūrya Siddhānta.
Eratosthenes proposed longitudes and local prime meridians in the 3rd century BC. Ptolemy proposed a single universal prime meridian for the whole world (like today's UTC) in 150 AD. This was 200 years before Sūrya Siddhānta.
45/82
Now coming back to Afghanistan, in 1975, the French team digging up Aï Khanūm unearthed a carved slab of limestone with a large cylindrical hole through it. The slab was 45 cm high, 35 cm wide, and 15 cm thick. The hole was 22 cm across.
Now coming back to Afghanistan, in 1975, the French team digging up Aï Khanūm unearthed a carved slab of limestone with a large cylindrical hole through it. The slab was 45 cm high, 35 cm wide, and 15 cm thick. The hole was 22 cm across.
46/82
After much deliberation, this artefact was concluded to be an exotic type of sundial, one of its kind that didn't feature even in Vitruvius' list of 13 types of sundials from 25 BC.
The inner surface of the cylindrical hole had markings.
After much deliberation, this artefact was concluded to be an exotic type of sundial, one of its kind that didn't feature even in Vitruvius' list of 13 types of sundials from 25 BC.
The inner surface of the cylindrical hole had markings.
47/82
There were two sets of markings (lines), each with 13. These lines were arranged in such a way that if the surface were to be unrolled and spread flat, it'd show the two sets running parallel to each other. Each set had a long center line with 6 smaller ones on either side.
There were two sets of markings (lines), each with 13. These lines were arranged in such a way that if the surface were to be unrolled and spread flat, it'd show the two sets running parallel to each other. Each set had a long center line with 6 smaller ones on either side.
48/82
If the slab were to be laid parallel to the equator, and a rod driven through the hole's axis, this could easily become a modified equinoctial sundial. The rod would then be the gnomon. We will get to the working of this sundial shortly but first some design details.
If the slab were to be laid parallel to the equator, and a rod driven through the hole's axis, this could easily become a modified equinoctial sundial. The rod would then be the gnomon. We will get to the working of this sundial shortly but first some design details.
