Talk:Lion Capital of Ashoka
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"The small details and the high-level narrative"
@Fowler&fowler: I think we are moving in the right direction, but... my edits today are simply meant to balance, on the same level of detail actually, your sentence "Wheeler did suggest that free-standing pillars had not appeared in Europe before the advent of the Roman empire" (which is a factually doubtful claim), by showing that other authors do claim precedents from Ancient Greece or even Egypt. "Collaborative editing", to which we both agreed and signed, supposes a certain level of tolerance towards the edits of the others, i.e. you are not alone writing this article (or any article). You might have notice I never (almost never?) delete your content, but only try to balance it, or tweak it if necessary. I would expect the same from you. This is how we build an article together. Please. पाटलिपुत्र Pat (talk) 15:03, 25 August 2022 (UTC)
- I think the article is already too chock full of details. New additions yours, mine, or anyone else's should be presented on the talk page first. Otherwise, it will begin to look more disjointed. In the collaborative spirit, please present it here. And we can both look into what is the best way forward. Fowler&fowler«Talk» 15:08, 25 August 2022 (UTC)
- @Fowler&fowler: Please no, Fowler&fowler, this is not what collaborative editing is about. You get to put everything you want (60k!), but now everything new should be discussed first? This is not possible. Let's edit reasonnably as we go: my two or three lines are not going to "kill" the article (far from it I believe). "Collaborative editing" is in our agreement and what we both signed for, so we have to edit collaboratively per normal Wikipedia procedure.... पाटलिपुत्र Pat (talk) 15:15, 25 August 2022 (UTC)
- That is not the point. Everything I have added is at a high level. In other words, Irwin is mentioned only when he is mentioned by Partha Mitter. Boardman is mentioned only when he is first mentioned by Richard Stoneman. Agrawala is mentioned only when he is by first mentioned by Bopearachchi or Guha or Irwin. In that form of tertiary editing we cannot add secondary sourcing unless it offers a vignette of the tertiary edit. (It is only in the last couple of days, in order to accommodate your sources that I added a few lines directly from the Irwin or Agrawala about something.)
- If you don't observe that principle, the narrative soon descends into undue. If you have a proper secondary source that discusses the work of Arora, then we can add it, and if need be add something from Arora shedding more light on it. But the direction of the example or counter example has to come from the tertiary edit. So summing up: if Asher or Irwin in their review begin with Vincent Smith, John Marshall, and Mortimer Wheeler, we cannot counter them by a counter example offered directly in a paper by Arora, especially not when the narrative is chronological. We can only do so when someone else cites Arora's counter-example, thereby giving it notability, and then use a sentence or two from Arora shedding more light on it. And we can only do that at the proper time in he chronology. If Wheeler's work is from the 1950s and Arora's from the 1990s, then obviously those references will be discussed at different periods. That is a basic principle. Collaborative editing, yes. But there are ground rules of narrative and high level writing that underlie the collaboration. Fowler&fowler«Talk» 15:40, 25 August 2022 (UTC)]
- @WP:OWN)… Do I have to call off the deal? पाटलिपुत्र Pat (talk) 15:49, 25 August 2022 (UTC)]
- There is no bargain if it involves contradicting the basic principles of narrative high level prose which is:
- a) Use a textbook, a review article, or a review of sources in a secondary source, or a reference to another secondary source (in that order of preference) to establish the general backbone of the narrative. So, again: we can't summarize a secondary source; the summarizing has to be done by another tertiary or secondary source, preferably as a part of a review (e.g. Asher's or Irwin's on the sequence of the debate about foreign influence.)
- b) Once that is established a source that is summarized in a) can be fleshed out with an illustrative example directly from the source.
- c)If a source that has been summarized in a) has a counterexample, then it has to come from the summary of another source summarized in a) and then we can again illustrate that with an example directly from that source. But we cannot contradict a summary in a) by an example that is not in a) Fowler&fowler«Talk» 15:55, 25 August 2022 (UTC)
- It has nothing to do with WP:OWN All the big articles I have written, the FAs India and Darjeeling. The articles British Raj, Company rule in India, Dominion of India, Partition of India, ... all follow the same pattern. Fowler&fowler«Talk» 16:03, 25 August 2022 (UTC)]
- @WP:OWN). As I contribute, please just tweak my edits, or raise issues on the Talk Page if you have to, this is the normal way to do it. If your argument makes sense, I will naturally remove or correct my text. पाटलिपुत्र Pat (talk) 16:11, 25 August 2022 (UTC)]
- Well, then please tell me where is Arora's claim contradicting Wheeler summarized? Fowler&fowler«Talk» 16:21, 25 August 2022 (UTC)
- In other words, we cannot ourselves read Arora, decide that something there contradicts Wheeler and summarize it. The summarizing has to be done by another source, and at the last resort by Arora him/herself mentioning Wheeler's argument. Fowler&fowler«Talk» 16:24, 25 August 2022 (UTC)
- @
- @
- @Fowler&fowler: Please no, Fowler&fowler, this is not what collaborative editing is about. You get to put everything you want (60k!), but now everything new should be discussed first? This is not possible. Let's edit reasonnably as we go: my two or three lines are not going to "kill" the article (far from it I believe). "Collaborative editing" is in our agreement and what we both signed for, so we have to edit collaboratively per normal Wikipedia procedure.... पाटलिपुत्र Pat (talk) 15:15, 25 August 2022 (UTC)
- But isn't this called WP:BALANCE? i.e. "describe both points of view and work for balance." As far as I know, we do not need a source that balances in order to balance sources... पाटलिपुत्र Pat (talk) 16:28, 25 August 2022 (UTC)]
- Not at different levels. Take any article from Britannica. If we do not follow the principle, I can within a day reduce it to shambles. For every major assumption I can find a non-notable counterexample, i.e. one not summarized in other sources. Fowler&fowler«Talk» 16:39, 25 August 2022 (UTC)
- In this specific case, the sources used for balance are very high level as well (Boardman, Irwin, Arora...). I don't see any contradiction with WP:BALANCE. Can you give me your arguments based on Wikipedia policy? पाटलिपुत्र Pat (talk) 16:41, 25 August 2022 (UTC)]
- No, Boardman is used to illustrate something that is mentioned in Richard Stoneman. Irwin is used to illustrate something summarized in Partha Mitter. Arora has not been summarized anywhere that I can find in the context of Wheeler. Fowler&fowler«Talk» 16:45, 25 August 2022 (UTC)
- In this specific case, the sources used for balance are very high level as well (Boardman, Irwin, Arora...). I don't see any contradiction with
- Not at different levels. Take any article from Britannica. If we do not follow the principle, I can within a day reduce it to shambles. For every major assumption I can find a non-notable counterexample, i.e. one not summarized in other sources. Fowler&fowler«Talk» 16:39, 25 August 2022 (UTC)
- But isn't this called
Policy: Reliable tertiary sources can help provide broad summaries of topics that involve many primary and secondary sources and may help evaluate due weight, especially when primary or secondary sources contradict each other. Fowler&fowler«Talk» 16:48, 25 August 2022 (UTC)
- Again, as far as I know we do not necessarily need a source that balances, in order to balance sources. We present various view points according to their notability and we "work for balance". We do not necessarily need a source that does the balancing for us. Sure, tertiary sources can help, per policy, but they are not a prerequisite to presenting various notable sources. पाटलिपुत्र Pat (talk) 16:53, 25 August 2022 (UTC)
- They are in controversial pages. Balancing in Wikipedia is not that achieved by editors; it is that achieved by sources. Fowler&fowler«Talk» 16:59, 25 August 2022 (UTC)
- Not true I'm afraid, and the points in question are not particularly controversial either anyway (just minor academic divergences). Let me take an example: highly notable source A affirms a theory. Notable source B affirms the contrary. But if no source mentions their dispute, then you're saying we cannot present source A's theory, and balance it with source B's theory?? Or worse, F&F happens to have presented theory A in an article, but then no other editor would be allowed to can balance it with theory B?... and theory A is the only theory we would ever get to read about? This would be absurd and anti-encyclopedic... Sorry, I have to go for now. पाटलिपुत्र Pat (talk) 17:10, 25 August 2022 (UTC)
- WP:BALANCE says, "Neutrality assigns weight to viewpoints in proportion to their prominence. However, when reputable sources both contradict one another and also are relatively equal in prominence, describe both points of view and work for balance. This involves describing the opposing views clearly, drawing on secondary or tertiary sources that describe the disagreement from a disinterested viewpoint." So, I'm asking which secondary or tertiary source summarizes Arora's disagreement with Wheeler? Fowler&fowler«Talk» 17:06, 25 August 2022 (UTC)
- I think it is quite obvious from the combined policy statements above that policy never makes it an imperative to have secondary/tertiairy sources in order to WP:BALANCE). So clearly, when notable sources have diverging opinions, we should strive to present them, in a balanced manner, possibly relying on secondary and tertiary soures as we do so. It would be much more detrimental to the encyclopedia if we were blocked from presenting various notable viewpoints, or worse, if only a single viewpoint could be presented in an article, simply because a tertiary source doing the balancing is not available. पाटलिपुत्र Pat (talk) 17:56, 25 August 2022 (UTC)]
- I suggest we stop here, and we resume our normal editorial activities. Best पाटलिपुत्र Pat (talk) 17:59, 25 August 2022 (UTC)
- WP:BALANCE:
- For Wheeler we have a clear source. It is:
- 'Aśokan' Pillars: A Reassessment of the Evidence Author(s): John Irwin Source: The Burlington Magazine , Nov., 1973, Vol. 115, No. 848 (Nov., 1973), pp. 706-720 Published by: (PUB) Burlington Magazine Publications Ltd. Stable URL: https://www.jstor.org/stable/877526
- Irwin begins his summary of the history of the topic on page 706 with
"The story begins with James Prinsep who, between 1834 and 1837, placed the study of Indian history on a scientific footing by being first to decipher the ancient Brahmi and Kharosthi script."
- By page 713, he's reached: "All this brings us up to 1911 when Vincent Smith, after twenty years research on the subject of 'Asokan' pillars, published conclusions which have since provided the background of all debate" (clearly notable).
- Below on the same page after he has discussed John Marshall, he has,
"The next leading Indologist to give considered thought to the subject was Sir Mortimer Wheeler. Like Marshall, Wheeler reasoned within the framework of Vincent Smith's basic assumptions. He maintained that up to the time of the Mauryan dynasty, India had achieved nothing better than a kind of folk-art, and that the sudden appearance of the pillars was inconceivable without the intervention of foreign sculptors 'trained in the Perso-Hellenistic tradition.'30 On this basis, he conjectured that two or three generations after the collapse of the Achaemenid empire, descendants of the Hellenistic craftsmen employed at Persepolis had been engaged by Asoka in India. However, in his last discussion of the subject, Wheeler pointed out (surprisingly) that free-standing pillar-architecture was unknown in the West before the Romans. He was therefore careful to leave the door slightly ajar, warning us that perhaps after all, the last word on Asokan pillars had not yet been said."
- Footnote 30 says: 30 SIR MORTIMER WHEELER: Flames over Persepolis, London [1968], pp.127-45. His earlier views, which are substantially in accordance with his final ones, were published in a lecture entitled 'Iran and India in Pre-Islamic Times' Ancient India, Bulletin of the Archaeological Survey of India, No. 4 [1947-48], pp. 85–101
- So this establishes step (a) above
- Step (b) At this stage if we have to illustrate Wheeler some more, we can summarize an example from him from either source in footnote 30, but briefly
- Fowler&fowler«Talk» 18:03, 25 August 2022 (UTC)
- Per WP:BALANCEThis involves describing the opposing views clearly, drawing on secondary or tertiary sources that describe the disagreement from a disinterested viewpoint." So, I'm asking which secondary or tertiary source summarizes Arora's disagreement with Wheeler?
- If you are unable to find such a source and cite directly to Arora, I will be forced to comment out your edit, as you will be deliberately violating WP policy and adding edits of undue weight. Fowler&fowler«Talk» 18:06, 25 August 2022 (UTC)
- user:पाटलिपुत्र noted above. Fowler&fowler«Talk» 18:08, 25 August 2022 (UTC)
- Per my above statement [1], I do not think policy makes it imperative to have balancing secondary or tertiary sources in order to present various viewpoints of notable sources. It is not written this way, and it would be absurd if it were so. If you want to claim any imperative character, please go to the relevant Policy Helpdesk to obtain clarification. पाटलिपुत्र Pat (talk) 18:18, 25 August 2022 (UTC)
- Let us not edit this page for the next several days, a week perhaps, until these issues are worked out Fowler&fowler«Talk» 18:53, 25 August 2022 (UTC)
- user:पाटलिपुत्र Let's make it a full week. We can present our ideas on the talk page, even summaries, proposed edits and so forth. Or we can ask some admins to lock the page for a week or two as was done in the Buddhism article and you and I and others can resolve the differences gradually on the talk page. Luckily we have a half-way decent page in place. What say you? Fowler&fowler«Talk» 18:57, 25 August 2022 (UTC)
- Let us not edit this page for the next several days, a week perhaps, until these issues are worked out Fowler&fowler«Talk» 18:53, 25 August 2022 (UTC)
- Per my above statement [1], I do not think policy makes it imperative to have balancing secondary or tertiary sources in order to present various viewpoints of notable sources. It is not written this way, and it would be absurd if it were so. If you want to claim any imperative character, please go to the relevant Policy Helpdesk to obtain clarification. पाटलिपुत्र Pat (talk) 18:18, 25 August 2022 (UTC)
- user:पाटलिपुत्र noted above. Fowler&fowler«Talk» 18:08, 25 August 2022 (UTC)
- I think it is quite obvious from the combined policy statements above that policy never makes it an imperative to have secondary/tertiairy sources in order to
Hi @
Shape of the spokes
@Fowler&fowler: You make above an interesting remark about the spoke fragments and their thickness in the Sarnath Museum photograph from Huntington p.90 (you say: "The three spoke fragments are too thick for tapering down from where they are placed to where they are destined to end at the inner wheel; if not that, they are too thick for expanding upward and fitting between the little knobs.") Although the precise positioning of the fragments in the Sarnath Museum is debatable, my understanding is that the spokes were probably diamond-shaped (or kite-shaped to be more precise), and positionned quite close to one another, as shown in various reliefs, on in Agrawala's reconstruction, which is then broadly coherent with the thickness of the spoke fragments in the museum. The fragments don't fit if you hypothesize that the spokes were wedge-shaped (oblong triangular). It seems also that the spoke holes along the inner periphery of the rims were quite small, which too tends to confirm a kite shape. पाटलिपुत्र Pat (talk) 11:32, 26 August 2022 (UTC)
- पाटलिपुत्र That's a very good point.
- I have thought about it, but it is still not adding up. Was the wheel carved from a single block of sandstone such as the late Gupta age image seems to be (and shows some signs of the rhombus shaped spokes you posit), or were the rim, the hub, and the spokes carved separately and were fitted together to form the wheel? If the former, then it would be near impossible for none of the stubs—the broken off spokes' ends—to remain on the rim, i.e. some jagged ends, or not so jagged ends, should be visible on the inner perimeter (as are visible on the hub in the late Gupta image). The inner perimeter, however, seems to be smooth in the pictures. (I had first thought those little "buttons" were the spokes' ends, but they are some form of ritual or conventional design to serve as markers between which the spokes fit.) If the latter, then the same inner perimeter should have evenly spaced holes in which the spokes fit. But no one mentions any holes. Its surprising that there are no pictures.
- Fowler&fowler«Talk» 14:57, 26 August 2022 (UTC)
- @Fowler&fowler: Agrawala does draw the holes of the inner periphery [3], but not the knobs, which is a bit disapointing. But if you look at the Sarnath Museum photograph very closely (you'll have to download) [4], you will see the neat rounded and regular intercalary knobs all around very clearly, and on the most exposed rim portion (the one at the bottom), you can almost see some of the holes between the knobs. In all probability the intercalary knobs and the rim were carved from one block, but the spokes were carved individually and then inserted, which indeed explains why (almost) no spoke fragments remain on the rim, and why the wheel was easily disassembled when broken. I think I read this somewhere too, but can't find where at this point. पाटलिपुत्र Pat (talk) 15:10, 26 August 2022 (UTC)
- Well, Agrawala does draw the intercalary knobs in profile (together with the outwardly tapering section of the rim) in 7c [5], but 7b is clumsily drawn really... पाटलिपुत्र Pat (talk) 15:26, 26 August 2022 (UTC)
- Thank you पाटलिपुत्र for that.
- In my version, I do see what appears to be a clear hole, 1/6 inch across (if the diameter of the wheel is 2 ft 8 in as Agrawala states, and there is no reason to doubt him as he measured it in 1946 as superintendent of the ASI attached to the Central Asian Museum in New Delhi). So, the spaces between the intercalary knobs are approx 1 inch apart and the two filled in spaces to the right of the hole are approximately 3/4 inch wide. If these are the end of the spokes, how were they fitted into the holes? Was the securing pin carved out of the ends of the spokes? This could explain why there is no hole visible in the two spaces to the immediate right of the clear hole; otherwise a metal pin and/or a hole would have been visible, as the stubs barely rise above the rim.
- But if that is the case, then how were the spokes fitted in a one-piece rim with pre-made holes? It would be impossible. In the absence of a hub, this is becoming too conjectural. Fowler&fowler«Talk» 16:54, 26 August 2022 (UTC)
- More generally, पाटलिपुत्र, Agrawala 1964b's Figure 6a showing thin chariot-like spokes and a small hub does not look realistic as the spokes would need to be pinned at the other end as well and they would have very little room if the holes were 1/6 inch wide; and if they weren't what stability would they have at 47 feet height? We are talking 100 degrees summer days, followed by monsoon storms, followed by winter cold waves from Nepal, year in and year out, not to mention earth tremors if not occasional full-blown earthquakes. Agree, all this is conjecture in turn, but questions obviously remain. We are talking about stability for a period of 1500 years if we are going to look for the common reasons (Muslim iconoclasm) for the fall.
- Also, I am not seeing why one asymmetric direction would be favored in Agrawala's or for that matter Irwin's reconstruction. If Agrawala can write pages and pages about the meanings of the horse (which is the same as a rhino) and the lion (the same as a tiger) and so forth—which it is possible the culture of 2250 years ago, without access to modern genetics might have identified in some fashion—why is there nothing about why one of the two orientations (i.e showing bull and horse together on one side of the wheel and the lion and elephant on the other, or the bull and elephant on one side and the lion and horse on the other) have been favored. Surely in all the speculative writings on symbolism someone should have worried about this if the reconstruction was widely accepted. Agrawala 1964b is too full of wild conjectures and unreasoned assertions (per Irwin and others) for it to be reliable much beyond the dimensions of the capital. Fowler&fowler«Talk» 17:18, 26 August 2022 (UTC)
- @Fowler&fowler: In all probability there is one hole between each pair of knobs, as drawn by Agrawala [6], some holes having filled up with concretions during their nearly 1000 or so years buried in the ground. The rim was likely in one piece, and the spokes were inserted one by one from the inside, gathering neetly at the level of the hub. Then the hub would only have to be in two parts, the cover being secured by a pin. It would be all very neat and beautiful, and rather sturdy actually if manufactured precisely, except in the case of a catastrophic fall, which would project all the pieces far and wide. As for orientation, I think nobody really knows, except for the near-contemporary reliefs (more or less 2 centuries after the erection of the pillar) showing examples of wheels on top of animal pillars. पाटलिपुत्र Pat (talk) 17:39, 26 August 2022 (UTC)
- पाटलिपुत्र That's good construction, but that will explain the stability in the plane of the wheel. It will not explain stability in the direction of the normal (perpendicular) direction at the hub. The spokes experience torque at the rim end from the perpendicular pressure at the hub and vice-versa. If a child had to take such a wheel apart, they would alternately pull and push the hub and loosen the arrangement. That is because the hub is like a doorknob, at the farthest end of each spoke where the moment is the maximum and only a little pressure is needed to loosen (or to open the door) With even ordinary winds blowing in the face of a wheel 32 inches wide with 32 spokes secured in such fashion would feel a large torque, let alone in storms. And there is no reason that monkeys would not be tempted to do the same. Are there examples of wheels secured in such fashion that have survived in the open air for a long time? Fowler&fowler«Talk» 18:39, 26 August 2022 (UTC)
- @Fowler&fowler: Just my personal opinion, but I think tight and precise handcrafting of hard sandstone, with the spokes finely and deeply inserted inside the rim on the outside, and strongly anchored through the hub at the center, could hold any kind of natural torsion. The shaft too would have to be sturdy. But Mauryans have shown how precisely they can handle hard stone (or even granite: Barabar Caves!), if necessary through ultra-fine grinding and polishing, so a very high level of precision in assembly is indeed possible... Of course, the lions had much more inherent sturdiness then the wheel itself, and would have lasted much longer in any circumstance. Quite impressive nonetheless... पाटलिपुत्र Pat (talk) 18:53, 26 August 2022 (UTC)
- पाटलिपुत्र I have no doubt they were expert stone cutters and arrangers, but there are some mechanical limitations we are dealing with. The spokes at the rim end are 3/4 inch wide. At the hub end, they can't be much narrower than half an inch (1.25 cm) for a 1/6 inch hole to be drilled safely. At that dimension, and assuming the tightest fit, you will need a hub of 16-inch circumference, which means a diameter of 5 inches. If it is a disk without holes, it will experience quite a bit of normal pressure. You could assume holes, or make the hub much bigger, say 9 inches in diameter, or even a foot, then although there would be more pressure, it would also be more stable. But all the reconstructions show a smallish hub. Perhaps if some structural-, mechanical-, material-, and chemical engineers at one of India's institutes of technology were rounded up they could shed more certain light on it, working with archaeologists and art historians. New methods are needed. I did find one book chapter on spokes and their significance in Thai Buddhist art. It cites Irwin for the usual pre-Buddhist influences. Perhaps you might find some nuggets there:
- Indorf, Pinna. "Dvaravati Cakras: Questions of Their Significance". In Revire, Nicolas; Murphy, Stephen A. (eds.). Before Siam: Essays in Art and Archaeology. Bangkok: River Books and The Siam Society. pp. 272–309. ]
- @Fowler&fowler: In my personal opinion, the hub should only work as a "cover plate", and actually the smaller the better. In this case, the resistance to the wind only has to be considered individually for each spoke (imagine there is no hub and the spokes are independent from one another, simply inserted into the rim). The surface of one spoke was roughly 2.5cmx30cm at worst (0.0075 m2). Even in winds of 50 meters per second (about 110 miles per hour, which generate around 170kg of pressure per square meter [7]), the pressure on a single spoke would be around 1 kilogram only (the weight of a bottle of water!), spread on the whole length of the spoke. This is a very manageable for a thickish hardstone spoke firmly inserted into the rim. If the hardstone spoke is structurally sound, I don't think it would risk breaking until at the very least 20kg of pressure (a small kid sitting on it. Even the wooden spokes of a pole ladder will handle much more.)... At 111 miles per hour, the whole wheel taken globally would have to sustain around 70kg of wind pressure (32x1kg for the spokes + 40kg for the rim), something a properly set 8" sandstone shaft would also be able to handle ... पाटलिपुत्र Pat (talk) 05:46, 27 August 2022 (UTC)
- पाटलिपुत्र That's a clever suggestion, but it brings up new issues. As you've seen at the other end, we can see that the spokes are 3/4 inch thick. Assuming they narrow to 1/2 inch, they would need a hub of diameter 5 inches, as I have explained. If you suppose that the spokes can be narrowed further somehow and the hub is correspondingly smaller across and in the limiting case it is a point, the spokes will fit so tightly, that there will be a virtual disk of a diameter of five inches, and there will be turbulence inside the disk. You can't assume that a spoke exists independently of all the others, and then sum the pressures. Fluid dynamics is highly nonlinear. It will be easier to see this if you imagine a metal boat with a one-meter-wide hole in its flat bottom. If you attach one metal strip 1/2 inch wide across the hole and set the boat afloat, it will sink like a rock. If you take a large number of 1/2 wide strips and space them 1/16 of an inch apart, the boat will take a while to sink, and you will see turbulence as the water wells up. Fowler&fowler«Talk» 11:57, 27 August 2022 (UTC)
- @Fowler&fowler: Yes, viscosity/turbulence is harder to evaluate, but I don't think it changes the equation fundamentally. To further the approximation, even if you took maximum viscosity for the air (no air manages to get through the spokes of the wheel), the whole surface of the wheel would still be 0.78 m2, hence a global wind pressure of about 132 kilograms maximum (winds of 110 miles per hour). If you take out the pressure on the rim and divide by 32, you would still be at 3kg per spoke maximum (maximum viscosity, or no space for air between them). I think what is happening is that we have a relatively small object actually (about 1 meter in diameter), manufactured with a very strong, rigid and heavy material (sandstone), and handcrafted and assembled to high precision (the rim/spoke assembly alone can be very sturdy). It was probably capable of sustaining very tough weather conditions, and for a long period, since this material does not deteriorate with time (contrary to wood, limestone or even metals). But beyond that, I'm afraid only specialists could tell us! Best पाटलिपुत्र Pat (talk) 12:34, 27 August 2022 (UTC)
- पाटलिपुत्र That's a clever suggestion, but it brings up new issues. As you've seen at the other end, we can see that the spokes are 3/4 inch thick. Assuming they narrow to 1/2 inch, they would need a hub of diameter 5 inches, as I have explained. If you suppose that the spokes can be narrowed further somehow and the hub is correspondingly smaller across and in the limiting case it is a point, the spokes will fit so tightly, that there will be a virtual disk of a diameter of five inches, and there will be turbulence inside the disk. You can't assume that a spoke exists independently of all the others, and then sum the pressures. Fluid dynamics is highly nonlinear. It will be easier to see this if you imagine a metal boat with a one-meter-wide hole in its flat bottom. If you attach one metal strip 1/2 inch wide across the hole and set the boat afloat, it will sink like a rock. If you take a large number of 1/2 wide strips and space them 1/16 of an inch apart, the boat will take a while to sink, and you will see turbulence as the water wells up. Fowler&fowler«Talk» 11:57, 27 August 2022 (UTC)
- @Fowler&fowler: In my personal opinion, the hub should only work as a "cover plate", and actually the smaller the better. In this case, the resistance to the wind only has to be considered individually for each spoke (imagine there is no hub and the spokes are independent from one another, simply inserted into the rim). The surface of one spoke was roughly 2.5cmx30cm at worst (0.0075 m2). Even in winds of 50 meters per second (about 110 miles per hour, which generate around 170kg of pressure per square meter [7]), the pressure on a single spoke would be around 1 kilogram only (the weight of a bottle of water!), spread on the whole length of the spoke. This is a very manageable for a thickish hardstone spoke firmly inserted into the rim. If the hardstone spoke is structurally sound, I don't think it would risk breaking until at the very least 20kg of pressure (a small kid sitting on it. Even the wooden spokes of a pole ladder will handle much more.)... At 111 miles per hour, the whole wheel taken globally would have to sustain around 70kg of wind pressure (32x1kg for the spokes + 40kg for the rim), something a properly set 8" sandstone shaft would also be able to handle ... पाटलिपुत्र Pat (talk) 05:46, 27 August 2022 (UTC)
- पाटलिपुत्र I have no doubt they were expert stone cutters and arrangers, but there are some mechanical limitations we are dealing with. The spokes at the rim end are 3/4 inch wide. At the hub end, they can't be much narrower than half an inch (1.25 cm) for a 1/6 inch hole to be drilled safely. At that dimension, and assuming the tightest fit, you will need a hub of 16-inch circumference, which means a diameter of 5 inches. If it is a disk without holes, it will experience quite a bit of normal pressure. You could assume holes, or make the hub much bigger, say 9 inches in diameter, or even a foot, then although there would be more pressure, it would also be more stable. But all the reconstructions show a smallish hub. Perhaps if some structural-, mechanical-, material-, and chemical engineers at one of India's institutes of technology were rounded up they could shed more certain light on it, working with archaeologists and art historians. New methods are needed. I did find one book chapter on spokes and their significance in Thai Buddhist art. It cites Irwin for the usual pre-Buddhist influences. Perhaps you might find some nuggets there:
- @Fowler&fowler: Just my personal opinion, but I think tight and precise handcrafting of hard sandstone, with the spokes finely and deeply inserted inside the rim on the outside, and strongly anchored through the hub at the center, could hold any kind of natural torsion. The shaft too would have to be sturdy. But Mauryans have shown how precisely they can handle hard stone (or even granite: Barabar Caves!), if necessary through ultra-fine grinding and polishing, so a very high level of precision in assembly is indeed possible... Of course, the lions had much more inherent sturdiness then the wheel itself, and would have lasted much longer in any circumstance. Quite impressive nonetheless... पाटलिपुत्र Pat (talk) 18:53, 26 August 2022 (UTC)
- पाटलिपुत्र That's good construction, but that will explain the stability in the plane of the wheel. It will not explain stability in the direction of the normal (perpendicular) direction at the hub. The spokes experience torque at the rim end from the perpendicular pressure at the hub and vice-versa. If a child had to take such a wheel apart, they would alternately pull and push the hub and loosen the arrangement. That is because the hub is like a doorknob, at the farthest end of each spoke where the moment is the maximum and only a little pressure is needed to loosen (or to open the door) With even ordinary winds blowing in the face of a wheel 32 inches wide with 32 spokes secured in such fashion would feel a large torque, let alone in storms. And there is no reason that monkeys would not be tempted to do the same. Are there examples of wheels secured in such fashion that have survived in the open air for a long time? Fowler&fowler«Talk» 18:39, 26 August 2022 (UTC)
- @Fowler&fowler: In all probability there is one hole between each pair of knobs, as drawn by Agrawala [6], some holes having filled up with concretions during their nearly 1000 or so years buried in the ground. The rim was likely in one piece, and the spokes were inserted one by one from the inside, gathering neetly at the level of the hub. Then the hub would only have to be in two parts, the cover being secured by a pin. It would be all very neat and beautiful, and rather sturdy actually if manufactured precisely, except in the case of a catastrophic fall, which would project all the pieces far and wide. As for orientation, I think nobody really knows, except for the near-contemporary reliefs (more or less 2 centuries after the erection of the pillar) showing examples of wheels on top of animal pillars. पाटलिपुत्र Pat (talk) 17:39, 26 August 2022 (UTC)
- I've magnified Huntington's image five times, but I don't see any substantive traces of the spokes' ends or of holes. Fowler&fowler«Talk» 15:10, 26 August 2022 (UTC)
- Sorry that was an ec. Will look at the museum image next. Fowler&fowler«Talk» 15:12, 26 August 2022 (UTC)
Measurements
user:पाटलिपुत्र I respond to your post above later, but we first need to establish that this was a high-precision construction. The wheel, I mean. I'm not convinced that the wheel and the capital were crafted by the same craftsmen. In any case, The measurements according to Agrawala are:
- height of the chakra = 2ft 8 in.
- internal diameter of the chakra = 2 ft 5 inches to 2 ft 1 inch.
What do you make of this measurement? As far as I can tell, the internal rim was not a perfect circle, and it is unclear whether the external was either. The inner arcs formed by the different wheel fragments did not define circles of the same radii. I can actually check this later this weekend on Agrawala's own image. Fowler&fowler«Talk» 13:23, 27 August 2022 (UTC) Updated Fowler&fowler«Talk» 13:44, 27 August 2022 (UTC) Fowler&fowler«Talk» 13:47, 27 August 2022 (UTC)
- I'm attaching a rough reconstruction of what we've been talking about (a reconstruction based on the exact archaeological remains, and the kite-shaped spokes accomodating the exact size of the 3 spoke remains. You can click on it to see it without the red circle). All reconstructions by Agrawala also show a perfect circle [8], so I'm not sure what he means by the two internal diameters of the chakra...Here's a possible explanation. 2ft 8 inches is indeed for him the diameter of the complete wheel (outside perimeter). 2ft 5 inches does correspond to the diameter of what we would call the inner perimeter of the rim (the one where the intercalary knobs are positionned). But 2ft 1 inch would correspond closely to the diameter of the circle defined by the lateral summits of the kite-shaped spokes (red circle on my drawing, attached)... a kind of geometrical inner diameter which would be useful for any reconstruction (it actually defines the reconstruction to a large extent). It seems very improbable that there would be so much variation in the inner diameter otherwise, as it would vastly contradict all his reconstructions. This notion would also be completely incompatible with the quite perfectly regular arc of the four large rim fragments of our archaeological remains. In all likelihood the editor of his book did not really understand what this second inner diameter was about... पाटलिपुत्र Pat (talk) 14:24, 27 August 2022 (UTC)
- user: पाटलिपुत्र Please acknowledge by signing anew here that you had made an error above, that 2 ft one inch is where the rim is. Best, Fowler&fowler«Talk» 18:08, 29 August 2022 (UTC) Updated Fowler&fowler«Talk» 18:10, 29 August 2022 (UTC)
- @Fowler&fowler: Yes you're right, the 2.1feet circle is too small, I don't know how I obtained that (probably got the feet/cm conversions wrong). Here's a proper layout of the 2ft8ins, 2ft5ins and 2ft1in circles. Thanks for pointing this out! पाटलिपुत्र Pataliputra (talk) 18:32, 29 August 2022 (UTC)
- user: पाटलिपुत्र Please acknowledge by signing anew here that you had made an error above, that 2 ft one inch is where the rim is. Best, Fowler&fowler«Talk» 18:08, 29 August 2022 (UTC) Updated Fowler&fowler«Talk» 18:10, 29 August 2022 (UTC)
- I just checked all three (museum, agrawala, and your schematics) using the perfect circle tool. All three arcs form circles of different curvature. The perfect circles are fitted to the upper rim. There may be some distortion in these pictures depending on the camera angle, but these are quite a bit more than that. You might not be able to see the upper rim as the colored circle cover them entirely. Fowler&fowler«Talk» 15:14, 27 August 2022 (UTC)
- Your inner circle for example, dotted on the right, fits the upper rims of two with the lower rim of one. Fowler&fowler«Talk» 15:24, 27 August 2022 (UTC)
- That's Agrawala's own book. It has an older picture different from the Sarnath museum's. He made the measurements when the was the Superintendent of the Archaeological survey of India attached to the Central Asian Antiquities Museum in New Delhi in 1946. He would have received all the help available. Also, it says inner diameter from 2 ft 5 in to 2 ft 1 in. That's not the kind of error an editor or a typesetter would make. 29 inches/25 inches = 1.16
- The blue and the green circles are about the same radius. But the bottom one (red) is bigger. If you assume some distortion in the camera by the way in which the rims are configured, the ratio in my image is not much different. Fowler&fowler«Talk» 15:47, 27 August 2022 (UTC)
- I have to go now. I'll check late tonight or tomorrow AM. Best, Fowler&fowler«Talk» 16:01, 27 August 2022 (UTC)
- Interesting... I did the same exercise on the Sarnath Museum photograph of the original archaeological remains [9], and indeed the top left and top right rims appear to have an identical, slightly smaller, curvature, while the bottom rim appears to have a slighly wider curvature, giving a diameter about 10% larger. But I am afraid this is due to the lighting: there is a very strong top-down lighting in the photograph, which pushes the shadow of the rim's inner edge downward for the portions closest to the light, and produces a characteristic visual deformation, giving at the top (on both sides) the impression of an unnatural, extra-curvature towards the inside (in other words, the over-exposed, bright surfaces at the top of both left and right rims seem to "bend" inside)... but this is an optical illusion (shadow displacement on a slightly curved surface). A concomitant side-effect is that the inside band of the rim also gives the impression of being thinner in these top areas. Once you take this into account, you will see that the inside curvatures are identical. You can also refer to the photograph of the reconstruction by Agrawala [10], because he worked on casts of the archaeological remains, and visibly had no problem at all adjusting the curvatures, which are clearly all identical. पाटलिपुत्र Pat (talk) 19:15, 27 August 2022 (UTC)
- user:पाटलिपुत्र The reason that the inner rim is narrower above than below is that it is closer to eye (camera) level which is a little above the point where the blue and the green circles intersect. Its the foreshortening I was talking about upstairs, for the same reason that the space between the dark tiles in File:HK Hung Hum Station Corridor.jpg keeps decreasing as the tiles move away to the horizon or eye level.
- Edges in an images are discontinuities of the image intensity, or the zero crossings of David Marr. Lighting does not substantially affect edges, but viewpoint or camera angle does.
- (More technically you can convolve the image to offset the lighting disparities in a nonlinear fashion, but the discontinuities don't change—the old edges are still discontinuous but at different values of image intensity)
- But there ís some foreshortening as you insightfully point out (similar to holding up a coffee mug and turning it so you can look in. At eye level, the (b)rim and the bottom will both be circles, concentric ones, i.e. have the same center. If you lower the mug a little, the two circles will no longer be concentric; there will be more room between them below than above.
- But these effects affect the (b)rim as well. If you keep lowering it, it will look more like an oval or ellipse than a circle. The problem here is that the outer rim of all three pieces, more or less, fit in a proper circle (the brown one I have added), which means that the perspective/foreshortening effects are not significant.
- That is why Agrawala has one diameter for the outer rim, but two for the inner. I suspect that of these three pieces, either one (the bottom) did not belong to the same wheel, i.e., to another wheel (bespeaking previous mishaps) or the wheel itself had this feature/defect. A fuller discussion will have to await the appearance of another picture, with the camera held lower. Fowler&fowler«Talk» 10:37, 28 August 2022 (UTC)
- Fowler&fowler«Talk» 10:54, 28 August 2022 (UTC)
- Interesting... I did the same exercise on the Sarnath Museum photograph of the original archaeological remains [9], and indeed the top left and top right rims appear to have an identical, slightly smaller, curvature, while the bottom rim appears to have a slighly wider curvature, giving a diameter about 10% larger. But I am afraid this is due to the lighting: there is a very strong top-down lighting in the photograph, which pushes the shadow of the rim's inner edge downward for the portions closest to the light, and produces a characteristic visual deformation, giving at the top (on both sides) the impression of an unnatural, extra-curvature towards the inside (in other words, the over-exposed, bright surfaces at the top of both left and right rims seem to "bend" inside)... but this is an optical illusion (shadow displacement on a slightly curved surface). A concomitant side-effect is that the inside band of the rim also gives the impression of being thinner in these top areas. Once you take this into account, you will see that the inside curvatures are identical. You can also refer to the photograph of the reconstruction by Agrawala [10], because he worked on casts of the archaeological remains, and visibly had no problem at all adjusting the curvatures, which are clearly all identical. पाटलिपुत्र Pat (talk) 19:15, 27 August 2022 (UTC)
- I have to go now. I'll check late tonight or tomorrow AM. Best, Fowler&fowler«Talk» 16:01, 27 August 2022 (UTC)
- Nice to see you back! I think, it is too strong and sudden to be foreshortening only. There is also a strong effect due to the intense top-light, which warps the shadow line and induces you to mesure a shorter curvature. I am attaching an explanatory drawing. Additional care should also be taken to the fact that the top left and right rims are in effect reconstructed from 2 pieces each (5 rim pieces in all per Agrawala), and their alignement is visibly not perfect, tending to further bend inside. Best पाटलिपुत्र Pat (talk) 11:02, 28 August 2022 (UTC)
- You are describing shading effects. If you change the lighting on Venus de Milo, yes the edges you see will change, but the edges here are ridges. Lighting will not create new ridges. Agrawalla, btw, in his 1964 book has only two pieces. Fowler&fowler«Talk» 11:11, 28 August 2022 (UTC)
- Even if you light the edge lower, i.e. with the bulb, right next to the edge, you will still see the old edge (or an edge detector will in software). This is because the faces on either side of the edge, being at different angles with respect to the light, will have different gradients of intensity. Good simulation by the way. Fowler&fowler«Talk» 11:19, 28 August 2022 (UTC)
- I mean there are more pieces in the museum picture than in Agrawala's 1964 book. There is a third piece in the museum picture. Fowler&fowler«Talk» 11:25, 28 August 2022 (UTC)
- You are describing shading effects. If you change the lighting on Venus de Milo, yes the edges you see will change, but the edges here are ridges. Lighting will not create new ridges. Agrawalla, btw, in his 1964 book has only two pieces. Fowler&fowler«Talk» 11:11, 28 August 2022 (UTC)
- Nice to see you back! I think, it is too strong and sudden to be foreshortening only. There is also a strong effect due to the intense top-light, which warps the shadow line and induces you to mesure a shorter curvature. I am attaching an explanatory drawing. Additional care should also be taken to the fact that the top left and right rims are in effect reconstructed from 2 pieces each (5 rim pieces in all per Agrawala), and their alignement is visibly not perfect, tending to further bend inside. Best पाटलिपुत्र Pat (talk) 11:02, 28 August 2022 (UTC)
- Yes, but the ridges are visibly not sharp but rounded, which is sufficient to create a shading effect. As to Agrawala's reconstruction, he definitely used the top left rim block (made of 2 pieces) and the top right one (made of 2 pieces) (positions as seen in the Sarnath Museum photograph), but they are reversed, which means we are seeing the back of the wheel (or that the photograph in his book was reversed). There is a third fragment at the top in his photograph, which can only be our bottom rim fragment (the last remaining one, the 5th rim fragment), but probably seen from the back, ie partially, if it was damaged on that side. Hard to tell for sure... पाटलिपुत्र Pat (talk) 11:33, 28 August 2022 (UTC)
- Only parts are rounded. On the two top pieces, only the one on the right is rounded toward the top, not the lower half. You can fit the circle to just that and the problem remains. In Agrawala 1964, btw, the pieces together do not make a semi-circle. In the museum picture they do. Fowler&fowler«Talk» 11:52, 28 August 2022 (UTC)
- It is unlikely Agrawala would not show a big piece if most of it was damaged on one side. He would indicate what its extent was. Fowler&fowler«Talk» 11:55, 28 August 2022 (UTC)
Listen, you can keep arguing ad infinitum, butthe bottom line is- Agrawala's measurement:
- height of the chakra = 2ft 8 in.
- internal diameter of the chakra = 2 ft 5 inches to 2 ft 1 inch.
- It is impossible that an editor or typesetter could have made an error such as this. Fowler&fowler«Talk» 11:58, 28 August 2022 (UTC)
- Sure, I know what the books says, and I know it contradicts Agrawala's own reconstruction, and, in my opinion, the pieces in the Sarnath Museum. Just trying to reconcile the facts. Thanks for the exchange... पाटलिपुत्र Pat (talk) 12:05, 28 August 2022 (UTC)
- It is unlikely Agrawala would not show a big piece if most of it was damaged on one side. He would indicate what its extent was. Fowler&fowler«Talk» 11:55, 28 August 2022 (UTC)
- Only parts are rounded. On the two top pieces, only the one on the right is rounded toward the top, not the lower half. You can fit the circle to just that and the problem remains. In Agrawala 1964, btw, the pieces together do not make a semi-circle. In the museum picture they do. Fowler&fowler«Talk» 11:52, 28 August 2022 (UTC)
- Yes, but the ridges are visibly not sharp but rounded, which is sufficient to create a shading effect. As to Agrawala's reconstruction, he definitely used the top left rim block (made of 2 pieces) and the top right one (made of 2 pieces) (positions as seen in the Sarnath Museum photograph), but they are reversed, which means we are seeing the back of the wheel (or that the photograph in his book was reversed). There is a third fragment at the top in his photograph, which can only be our bottom rim fragment (the last remaining one, the 5th rim fragment), but probably seen from the back, ie partially, if it was damaged on that side. Hard to tell for sure... पाटलिपुत्र Pat (talk) 11:33, 28 August 2022 (UTC)
Apologies, user:पाटलिपुत्र for the impatient tone. I have now fitted circles to the farther of the two inner rim edges, i.e. the ones closer to the wall. There the shading effect would be minimal. But you still get the same disparity. Fowler&fowler«Talk» 12:21, 28 August 2022 (UTC)
- @Fowler&fowler: OK. Just to make sure: for your circles, are you working from my schematic drawing, or are you working from the Sarnath Museum photograph? Because I am working on the museum photograph, and I do not see anything near your variations (after adjustment for shading effect -about one thickness of the circle worth- and slight positioning issues, especially the top right rim fragments which has to be redressed)... Here are roughly the variations I am seeing after these adjustments (attached). It's basically all within the drawing margin of error... पाटलिपुत्र Pat (talk) 12:31, 28 August 2022 (UTC)
- I have worked with both images. In the museum picture. I first applied the Canny edge detector to it and then fitted circles to all three edges (avoiding the top right, i.e. fitting the third circle to only the lower portion of the fragment on the right. The fitted circles for the left fragment and the right, which are similar, easily fit inside the circle for the lowest fragment, i.e. with lots of room to spare. Later today, I'd be happy to upload a non-free image to the article for showing this. Fowler&fowler«Talk» 13:12, 28 August 2022 (UTC)
- I'm sending you my image by e-mail. पाटलिपुत्र Pat (talk) 13:16, 28 August 2022 (UTC)
- Sure. The problem is not the upper two fragments, but the lower one. Its inner and out rims do not form concentric circles, not even close. The outer rim matches the outer rims of the other two, more or less. The inner does not. Fowler&fowler«Talk» 13:33, 28 August 2022 (UTC)
- Doesn't seem to be working. Actually, you can just use my drawing above and superpose it to the Museum image. It should even be the same dimension. "Its inner and out rims do not form concentric circles" I do not see that either... never mind. I have to go. Please check my post above [11] about WP:BALANCE. Best पाटलिपुत्र Pat (talk) 13:51, 28 August 2022 (UTC)]
- @Fowler&fowler: If you are using the Canny edge detector for your circles, I think it probably gets thrown off by the over-exposure of the inside of the lower rim fragment [12], again due to the intense light from above. You would indeed get a significantly wider inner rim than for the other rim fragments (just as a result of the light pushing the shadow of the roundish ridge downward), at least by 3-4mm I would guess. Maybe you should work manually instead, allowing for these light effects.... From a lighting standpoint, it is a very asymetrical photograph, and a program wouldn't see that. पाटलिपुत्र Pat (talk) 14:21, 28 August 2022 (UTC)
- Modern edge-detection in machine vision, based on the work of John Canny, David Marr, Berthold K.P. Horn, Jan Koenderink, David Mumford and many others has been used on complex images for many years. I have now fitted to the circles to the raw image at the museum you refer to and they show the same result as Canny. I'm happy to upload the image to this article using the non-free format. It shows the same disparity between the lowest segment and the other two. You don't even need the top right. The remaining two themselves point to it. Fowler&fowler«Talk» 15:35, 28 August 2022 (UTC)
- @पाटलिपुत्र: Fowler&fowler«Talk» 15:38, 28 August 2022 (UTC) Updated. Fowler&fowler«Talk» 22:20, 28 August 2022 (UTC)
- Thanks WP:BALANCEd with his own reconstructions (and, frankly, the whole literature on the subject), which never takes into account nor mentions any such variations in inner diameter (as far as I'm aware...). In effect, that specific statement by Agrawala seems a bit fringe, and not even supported by the rest of his own research, nor anything that has been published on the subject: this is why I think it is probably some sort of typo or misunderstanding by the editor. It would be really interesting if there were Secondary sources discussing this issue, I'll keep my eyes open. Best पाटलिपुत्र Pat (talk) 05:10, 29 August 2022 (UTC)]
- Let me address a few contradictions in that model too... You state that the rim fragments all have roughly the same outside diameter (2.8 feet per Agrawala, which we can see in the photograph, I agree to that), but you suggest that the two dimensions given by Agarawala for the inner diameter (2.5 and 2.1 feet) would point to the fragments belonging to two different wheels. The problem is that this is not logically possible: the two wheels under such specifications would have to be vastly different objects (see attached diagram), which is not at all what we are seeing in the photograph of the remains [14]. Also the width of the rims would have to be vastly different (3 and 7 inches respectively), which not only is not visible at all in the photograph, but contradicts Agrawala's precise statement that the rim is 3.65 in width, and of course his reconstruction [15]. Again I cannot see this statement ("internal diameter 2.5 to 2.1 feet") as anything other than a typo or a misunderstanding of some sort... I'm afraid it cannot be taken at face value, given all the contradictions that it, alone, generates. Best पाटलिपुत्र Pataliputra (talk) 08:03, 29 August 2022 (UTC)
- Thanks
- @पाटलिपुत्र: Fowler&fowler«Talk» 15:38, 28 August 2022 (UTC) Updated. Fowler&fowler«Talk» 22:20, 28 August 2022 (UTC)
- Modern edge-detection in machine vision, based on the work of John Canny, David Marr, Berthold K.P. Horn, Jan Koenderink, David Mumford and many others has been used on complex images for many years. I have now fitted to the circles to the raw image at the museum you refer to and they show the same result as Canny. I'm happy to upload the image to this article using the non-free format. It shows the same disparity between the lowest segment and the other two. You don't even need the top right. The remaining two themselves point to it. Fowler&fowler«Talk» 15:35, 28 August 2022 (UTC)
- @Fowler&fowler: If you are using the Canny edge detector for your circles, I think it probably gets thrown off by the over-exposure of the inside of the lower rim fragment [12], again due to the intense light from above. You would indeed get a significantly wider inner rim than for the other rim fragments (just as a result of the light pushing the shadow of the roundish ridge downward), at least by 3-4mm I would guess. Maybe you should work manually instead, allowing for these light effects.... From a lighting standpoint, it is a very asymetrical photograph, and a program wouldn't see that. पाटलिपुत्र Pat (talk) 14:21, 28 August 2022 (UTC)
- Doesn't seem to be working. Actually, you can just use my drawing above and superpose it to the Museum image. It should even be the same dimension. "Its inner and out rims do not form concentric circles" I do not see that either... never mind. I have to go. Please check my post above [11] about
Arbitrary break (continuing the "Measurements" thread)
- Another hypotheses. I tried to scale the three measurements by Agrawala (2ft8ins, 2ft5ins, 2ft1in) on top of my schematic drawing of the archaeological remains in Sarnath Museum (attached), and actually the circle with the 2ft1in diameter exactly defines the inner perimeter of the Sarnath reconstruction. The second inside diameter (at 2ft5ins) remains a bit puzzling although it could correspond to the depth to which the spokes were inserted... it would be rather exactly the diameter of the circle defined by the spokes seen alone, without the rim (a "Dharma-Chakra" making abstraction of the rim, the "radiating sun" seen alone... definitely another important "internal diameter"). पाटलिपुत्र Pataliputra (talk) 09:26, 29 August 2022 (UTC)