Thursday, June 25, 2020
Tuesday, June 23, 2020
The permanent end of normal times.
Even just a few years ago, when mowing the lawn, I'd be making bees flee from their buzzing round the clover. No pesticides, no herbicides in my yard, lots of nectar-bearing flowers, clover continuing to proliferate in the lawn - but where are the bees? Oh, to be at the risk of a bee sting!
For that matter, where are the squirrels? The "green acres" behind my house are empty; and not one squirrel shows up to eye the bird-feeders. (What is new is a pair of chipmunks.).
My little pond got one froggy visitor last year. None so far this year.
I think just like people in the red states seem oblivious of the COVID-19 virus, or at best, "oh, its just like the flu", humanity is sleepwalking through an ecological crisis; but will be suddenly woken up to the unsustainability of what it is doing. Unlike our other crises, there is no November 3rd election day, or new vaccine or treatment that hold out the possibility of life going back to normal.
Posted by
Arun
at
7:05 AM
The permanent end of normal times.
2020-06-23T07:05:00-04:00
Arun
environment|
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environment
Monday, June 15, 2020
Sunday, June 14, 2020
Saturday, June 13, 2020
Friday, June 12, 2020
Thursday, June 11, 2020
Saturday, May 09, 2020
Thursday, April 30, 2020
Crime is gentler in fiction
During this long lockdown I'm reading John Sandford's "Prey" series of novels, whose protagonist Minneapolis-based criminal detective Lucas Davenport goes after the perpetrators of rather gruesome crimes. "Rather gruesome" is an understatement, and so when I read the author's introduction to "Mind Prey", quoted below, I had a resurgence of my ever-increasing desire to secede from the human race.
Sometime after I finished Mind Prey, I was invited to give a talk about crime-fiction writing at a medical examiners' convention. As part of the deal, I got to sit in on the convention, which I did for a while. I left after an FBI presentation on serial killers because, quite frankly, my stomach wasn't strong enough to look at the pictures.
I covered the crash of an L1011 airliner in the Everglades, with arms, legs and heads lying all over the place, saw perhaps a hundred or so surgeries in doing some occasional medical writing, including double amputations on accident victims and debridement of burn victims, and saw any number of shot people waiting for ambulances, without much problem. But what insane criminals do to people, especially women — that I can't look at, or write. When I deal with such subjects in the Prey series, I promise you that the violence is toned down.
Far down.
Tuesday, April 07, 2020
On Emergent Phenomena
Bee has a blog post: "What is emergence? What does “emergent” mean?" For whatever reason, 99% of my comments simply don't go through, so discussion over there seems impossible. My thoughts on the subject are newly formed, and I'm putting them down here, so that I can get unstuck, and not because these ideas are right or have any merit. So this post will likely be revised or even deleted.
This from Bee is as good a description of "emergent" as you can find:
Consider the Second Law of Thermodynamics. Pick any set of microscopic laws - the Standard Model of particle physics; or the Standard Model modified in any way, or one of the 10^500 universes of superstring theory. Or make heat a fluid (Lavoisier's "caloric" was the context in which Carnot did his work). The Second Law remains true in all these cases. While as students of physics, we are indoctrinated with statistical mechanics as underlying the Second Law of Thermodynamics, the Law actually arises from very general considerations, with no assumptions at all about the microscopic physics, i.e., from the mathematical properties of Pfaffians and some mapping of mathematical concepts into physical concepts. (Zemansky's 1965 Kelvin and Caratheodory--A Reconciliation indicates what I'm talking about).
The way I see it, the Second Law is true if heat is an invisible fluid and it is also true if matter is made of atoms and heat is simply the energy of random molecular motion. So in what sense can the Second Law of Thermodynamics be said to derived from the properties of the system's constituents? The Second Law is not only an emergent law, in some sense of the term "strongly emergent", it is so. It is a law that is true no matter what the underlying microscopic physics is, and thus can be "derived" from some axiom set including axiom A with some mapping of mathematical to physical concepts, but can equally well be derived from some other axiom set including the axiom (not A) with some other mapping of mathematical to physical concepts.
In this regard, I'm not sure the concepts of "weak emergence" and "strong emergence" are particularly useful. An example is the never-ending debate of whether the phenomenon "consciousness" is strongly emergent, or is explainable ultimately in terms of the brain and its cells. Let's imagine humans, electronic/compute devices, Fred Hoyle's solar-system sized cloud all exhibit "consciousness". Taking the Second Law of Thermodynamics as our exemplar, and assuming that a mathematical description of "consciousness" is feasible, one has to concede the possibility that such a description is rather independent of the microscopic details. If that turns out to be true, then the same problematic situation (at least to me) arises - how can such a description be said to be "derived" from the properties and interactions of the constituents of the conscious system?
The chemistry of hydrogen, carbon, etc., are a particular way because of the properties of their constituents, and would be different if e.g., the electron/proton mass ratio was different, or if the radius of the proton measured electron Compton wavelengths was much larger. Derivation of the chemistry crucially depends on these properties. That is one kind of emergence. I'd place all the things described by the Wilsonian renormalization group in this category too.
A second kind of emergence is where the behavior of the system can be described independent of its constituents, e.g., as with the Second Law of Thermodynamics. These are perhaps two useful types of "emergence", especially if we can find more laws of physics like the Second Law.
This from Bee is as good a description of "emergent" as you can find:
Something is emergent if it comes about from the collective behavior of many constituents of a system, be that people or atoms. If something is emergent, it does not even make sense to speak about it for individual elements of the system.
There are a lot of quantities in physics which are emergent. Think for example of conductivity. Conductivity is the ability of a system to transport currents from one end to another. It’s a property of materials. But it does not make sense to speak of the conductivity of a single electron. It’s the same for viscosity, elasticity, even something as seemingly simple as the color of a material. Color is not a property you find if you take apart a painting into elementary particles. It comes from the band structure of molecules. It’s an emergent property.It is in the discussion of weak and strong emergence that I drift away. I think I get stuck on the "can be/cannot be derived".
Weak emergence means that the emergent property can be derived from the properties of the system’s constituents and the interactions between the constituents.....In physics the only type of emergence we have is weak emergence. With strong emergence philosophers refer to the hypothetical possibility that a system with many constituents displays a novel behavior which cannot be derived from the properties and the interactions of the constituents. While this is logically possible, there is not a single known example for this in the real world.(Perhaps it is because I'm stuck on the notion of derivation as is done in mathematical logic.)
Consider the Second Law of Thermodynamics. Pick any set of microscopic laws - the Standard Model of particle physics; or the Standard Model modified in any way, or one of the 10^500 universes of superstring theory. Or make heat a fluid (Lavoisier's "caloric" was the context in which Carnot did his work). The Second Law remains true in all these cases. While as students of physics, we are indoctrinated with statistical mechanics as underlying the Second Law of Thermodynamics, the Law actually arises from very general considerations, with no assumptions at all about the microscopic physics, i.e., from the mathematical properties of Pfaffians and some mapping of mathematical concepts into physical concepts. (Zemansky's 1965 Kelvin and Caratheodory--A Reconciliation indicates what I'm talking about).
The way I see it, the Second Law is true if heat is an invisible fluid and it is also true if matter is made of atoms and heat is simply the energy of random molecular motion. So in what sense can the Second Law of Thermodynamics be said to derived from the properties of the system's constituents? The Second Law is not only an emergent law, in some sense of the term "strongly emergent", it is so. It is a law that is true no matter what the underlying microscopic physics is, and thus can be "derived" from some axiom set including axiom A with some mapping of mathematical to physical concepts, but can equally well be derived from some other axiom set including the axiom (not A) with some other mapping of mathematical to physical concepts.
In this regard, I'm not sure the concepts of "weak emergence" and "strong emergence" are particularly useful. An example is the never-ending debate of whether the phenomenon "consciousness" is strongly emergent, or is explainable ultimately in terms of the brain and its cells. Let's imagine humans, electronic/compute devices, Fred Hoyle's solar-system sized cloud all exhibit "consciousness". Taking the Second Law of Thermodynamics as our exemplar, and assuming that a mathematical description of "consciousness" is feasible, one has to concede the possibility that such a description is rather independent of the microscopic details. If that turns out to be true, then the same problematic situation (at least to me) arises - how can such a description be said to be "derived" from the properties and interactions of the constituents of the conscious system?
The chemistry of hydrogen, carbon, etc., are a particular way because of the properties of their constituents, and would be different if e.g., the electron/proton mass ratio was different, or if the radius of the proton measured electron Compton wavelengths was much larger. Derivation of the chemistry crucially depends on these properties. That is one kind of emergence. I'd place all the things described by the Wilsonian renormalization group in this category too.
A second kind of emergence is where the behavior of the system can be described independent of its constituents, e.g., as with the Second Law of Thermodynamics. These are perhaps two useful types of "emergence", especially if we can find more laws of physics like the Second Law.
Saturday, March 28, 2020
Dehydrated Elephants
Not Even Wrong noted the recent passing of mathematician Robert Hermann 1931-2020.
In that blog post, Peter Woit wrote:
In that blog post, Peter Woit wrote:
Being ahead of your time and mainly writing expository books is unfortunately not necessarily good for a successful academic career. Looking through his writings this afternoon, I ran across a long section of this book from 1980, entitled “Reflections” (pages 1-82). I strongly recommend reading this for Hermann’s own take on his career and the problems faced by anyone trying to do what he was doing (the situation has not improved since then).The reference is to Robert Hermann's book, "Cartanian Geometry, Nonlinear Waves, and Control Theory, Part 2", which you can read in Google Books. This is where I first encountered dehydrated elephants. To quote:
Posted by
Arun
at
3:20 PM
Dehydrated Elephants
2020-03-28T15:20:00-04:00
Arun
history|mathematics|
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Labels:
history,
mathematics
Saturday, March 07, 2020
Wednesday, January 01, 2020
Sri Dakshinamurthy
Posted by
Arun
at
9:34 PM
Sri Dakshinamurthy
2020-01-01T21:34:00-05:00
Arun
devotional|dharma|Hindu|
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Labels:
devotional,
dharma,
Hindu
Tuesday, December 24, 2019
Sten Konow: The Aryan Gods of the Mitani People
Recent findings in ancient human DNA are leading to narratives like the following, e.g., Tony Joseph in Outlook India, September 12, 2019:
The only direct evidence of language in India from that era is of the Vedic language, of the Rg Veda and subsequent works. The theory of Aryan Invasion/Migration is that these Central Asian pastoralists brought the Vedic language to India, and so the Rg Veda, if composed in India, must date to 2000 BCE - 1500 BCE or so.
The Rg Vedic hymns sing the praises of the mighty Saraswati river, and the geographical information in later texts of the drying/dried-up Saraswati plus modern science enables us to identify the ancient perennial river that the Saraswati must have been, and it last flowed 9000 to 4500 years before present.
The Rg Veda places the Saraswati along with the Ganga, Yamuna and the rivers of Punjab and so the theory that the Vedic people transferred the name of some river outside of India to the river that was already desiccated when they arrived is hardly tenable. Why they would not transfer the holy name of Saraswati to one of the great rivers they newly encountered is another mystery. Totally far-fetched is the notion that the Vedic people took an older tradition from non-Indo-European inhabitants and translated it into their hymns.
Next, we have the treaty between the Hittites and the Mitani, found in the cuneiform library unearthed at Boghazkoi in Turkey which mention Vedic gods - specifically Indra, Mitra-Varuna and the Nasatyas. The dates given via Egyptian and Middle Eastern chronologies for the Mitani treaty are 1375 BCE - 1350 BCE. The lineage of the Mitani signatory, Mattiuaza (a.k.a. Shattiwaza) is known, via the cuneiform libraries, to have extended at least four generations prior, and his ancestor, Shuttarna I, son of (legendary?) Kirta is dated to early 15 century BCE.
So how did Indra, Mitra-Varuna and the Nasatyas make their way to ancient Mesopotamia around 1500 BCE? The Aryan Invasionist postulates that these deities developed before the Aryans reached India and then some branch of the Aryans carried these gods to the Mitani lands and some other branch carried them to India.
Norwegian Indologist Sten Konow, in his paper published in 1923, argues persuasively that the Vedic gods were of Indian development. Since I found it difficult to get hold of a copy of this paper, I imagine it is the same for others, and so I present here a scan (link) and a transcript (link) of the paper.
Konow like the other Indologists of his time, believed in the Aryan Invasion Theory. His chronology seems to be an early Indo-European period, followed by a period of Aryan unity, when the ancestors of the Indian/Iranian Aryans ranged from perhaps the Volga to the outskirts of India; and lastly the Indian period, after the Aryans split into Indian, Iranian and possible other branches. Konow argues that the Vedic gods as mentioned in the Mitani treaty are developments from the Indian period, and not from the period of Aryan unity. Konow writes:
If you accept Konow's conclusion, this means there is simply not enough time for Central Asian Pastoralists to enter India between 2000 BCE and 1500 BCE, with Indo-European languages and the precursor forms of Indra, Mitra, Varuna and Nasatyas; to develop the later forms of the deities, and then carry them to the Mesopotamia by 1500 BCE."And here is an equally unambiguous and clear statement from the study published in Science a few days ago, titled: "The formation of human populations in South and Central Asia": "Using data from ancient individuals from the Swat Valley or northernmost South Asia, we show that Steppe ancestry then integrated further South in the first half of the 2nd millennium BCE, contributing up to 30 per cent of the ancestry of most modern groups".For our purposes, let us stipulate that the genetic evidence of the handful of ancient individuals has been interpreted correctly to show a migration into India of Central Asian Pastoralists between 2000 BCE and 1500 BCE. The problematic assertion is this: "who brought Indo-European languages to India, between 2000 BCE and 1500 BCE."
So it is clear, without even a shadow of a doubt, that both the studies support the migration of Central Asian pastoralists who brought Indo-European languages to India, between 2000 BCE and 1500 BCE.
The only direct evidence of language in India from that era is of the Vedic language, of the Rg Veda and subsequent works. The theory of Aryan Invasion/Migration is that these Central Asian pastoralists brought the Vedic language to India, and so the Rg Veda, if composed in India, must date to 2000 BCE - 1500 BCE or so.
The Rg Vedic hymns sing the praises of the mighty Saraswati river, and the geographical information in later texts of the drying/dried-up Saraswati plus modern science enables us to identify the ancient perennial river that the Saraswati must have been, and it last flowed 9000 to 4500 years before present.
The Rg Veda places the Saraswati along with the Ganga, Yamuna and the rivers of Punjab and so the theory that the Vedic people transferred the name of some river outside of India to the river that was already desiccated when they arrived is hardly tenable. Why they would not transfer the holy name of Saraswati to one of the great rivers they newly encountered is another mystery. Totally far-fetched is the notion that the Vedic people took an older tradition from non-Indo-European inhabitants and translated it into their hymns.
Next, we have the treaty between the Hittites and the Mitani, found in the cuneiform library unearthed at Boghazkoi in Turkey which mention Vedic gods - specifically Indra, Mitra-Varuna and the Nasatyas. The dates given via Egyptian and Middle Eastern chronologies for the Mitani treaty are 1375 BCE - 1350 BCE. The lineage of the Mitani signatory, Mattiuaza (a.k.a. Shattiwaza) is known, via the cuneiform libraries, to have extended at least four generations prior, and his ancestor, Shuttarna I, son of (legendary?) Kirta is dated to early 15 century BCE.
So how did Indra, Mitra-Varuna and the Nasatyas make their way to ancient Mesopotamia around 1500 BCE? The Aryan Invasionist postulates that these deities developed before the Aryans reached India and then some branch of the Aryans carried these gods to the Mitani lands and some other branch carried them to India.
Norwegian Indologist Sten Konow, in his paper published in 1923, argues persuasively that the Vedic gods were of Indian development. Since I found it difficult to get hold of a copy of this paper, I imagine it is the same for others, and so I present here a scan (link) and a transcript (link) of the paper.
Konow like the other Indologists of his time, believed in the Aryan Invasion Theory. His chronology seems to be an early Indo-European period, followed by a period of Aryan unity, when the ancestors of the Indian/Iranian Aryans ranged from perhaps the Volga to the outskirts of India; and lastly the Indian period, after the Aryans split into Indian, Iranian and possible other branches. Konow argues that the Vedic gods as mentioned in the Mitani treaty are developments from the Indian period, and not from the period of Aryan unity. Konow writes:
"As far as I can see, everything points to the conclusion that Jacobi was right in maintaining that the Mitani gods were Indian and not Aryan, so that we must, in fact, assume that the sphere of Indian civilization had, in the middle of the second millennium B.C., extended into Mesopotamia. The epoch of the Aryan conquest of India and the beginning of Indian civilization must consequently be relegated to a still earlier period, though we have no means of stating how long an interval we must assume between the Aryan invasion and the Mitani treaty. There is, however, one small detail which prevents us from thinking that this interval was quite short."
...
...
"I hope to have made it probable that these gods were Indian and not Aryan or even Iranian. If the conception of the Aśvins as groomsmen belongs to the later phases of the Ṛgveda period, as it seems to do, we must further draw the conclusion that the extension of Indo-Aryan civilization into Mesopotamia took place after the bulk of the Ṛgveda had come into existence. The oldest portions of the collection would consequently have to be considered as considerably older than the Mitani treaty. "
The modern Aryan invasionist/migrationist, as far as I know, conveniently doesn't address Konow's arguments. It would be interesting to see a modern response to Konow. It would also be interesting to see how the non-invasionist accommodates or dismantles Konow's arguments.
What are the possibilities that the Aryan invasions might entertain?
One could open a can of worms by casting doubt on the Mitani chronology. One could also cast doubt on Konow's (invasionist) reading and interpretation of the Vedic literature. One might argue that developments in the Vedic pantheon were being contemporaneously being transmitted from northern India to Mesopotamia -- but in that case, one would have to rethink how language and Indo-European culture was transmitted, migrations and invasions are hardly necessary.
One might argue that the ancient human DNA is wrongly dated, and the invasion/migration that the genetic evidence indicated actually occurred a thousand years earlier. But the geneticists are unlikely to have the eras so wrong. In any case, the Aryan invasionist won't want to give up the 2000 BCE-1500 BCE chronology in any case.
IMO, the most viable conclusion is that the Vedic pantheon was developed in India much before 1500 BC and migrated from India to the Mitani lands. In which case the people that genetics says were migrating into India between 2000 BCE and 1500 BCE did not introduce Indo-European languages to India, the Vedic language was already there. This is not impossible, the Sakas around 200 BCE - 100 CE, and the English, 1700-1950 CE also carried with themselves Indo-European languages to India, but did not introduce them to India. The Aryan invasionist can continue to postulate that the first entry of Indo-European language into India was via invasion or migration, but the evidence of the Mitani treaty is that this event has to be much prior to 1500 BC; and via the evidence of the Saraswati, prior to 2500 BC.
A point peripheral to the above, but of interest is that Konow argues on linguistic grounds that the dasyus/dasas mentioned in the Rg Veda as the enemies of the Vedic people were not speakers of Dravidian languages, but rather spoke in Kolarian tongues (the Austroasiatic language family in India).
Thursday, December 12, 2019
Satellite Remote Sensing Techniques to Unearth the Lost Sarasvati River & its Palaeochannels
Saturday, December 07, 2019
Is there such a thing as intelligence?
On dailykos, Nonlinear asks: Is There Such A Thing As Intelligence?
Writing about himself,
....
Writing about himself,
As I moved forward in school a pattern began to emerge. I am what is known as a three tier learner. There are subjects in which I express severe learning disabilities. ....Then there is a second tier, subjects where I am right around average. In school this was things like Social Studies, English, Art, Chemistry, Biology, Auto Mechanics, Wood Working, Drafting, Literature and Physics. I was a B student in all these things.
Then there were the things I was gifted in which included Math, Metal Work, Music and Physical Education. And once I got into an enriched High School you can add Agriculture, Ag Mechanics, Home Ec, Electronics, Plumbing, and Economics. In these I was an A+ student....
....
But depending which IQ test you administer and how you administer it I go off the conventional scoring table (over 200) or am far below average and profoundly disabled at 69. You can manipulate the test you give me to get a result anywhere in between. The smartest move I have ever made was refusing to allow them to write about me in journals and turn me into a circus freak. I am a human calculator. I honestly can’t understand why people can’t just multiply and divide large numbers in their head. I also calendar calculate. And yes I have been called an Idiot Savant, for a while that was my diagnosis.Nonlinear then takes up the case of animal whisperers of which he is one to make his point.
But being a freak has lead to me being fascinated by intelligence and how it works. I have come to conclude that there is no such thing as general intelligence. All mental activity is situational.
Posted by
Arun
at
10:23 PM
Is there such a thing as intelligence?
2019-12-07T22:23:00-05:00
Arun
cultural differences|culture|IQ|
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Labels:
cultural differences,
culture,
IQ
Thursday, October 03, 2019
India has no native religions - a summary
From Dr Pingali Gopal's book summary of Europe, India and the Limits of Secularism by Jakob de Roover.
The two important properties of religion are: first, it must make a claim about the origin and purpose of the world (the how and why of the Cosmos); and secondly, this message must be true This is the ‘metaphysical’ position of any religion.
Based on the metaphysical conditions, Indian traditions are not possibly religions. They do not properly raise the issue of origin of the Cosmos. Vedas, Upanishads, Brahmanas, Puranas, Itihaasas have multiple stories of creation and purposes of Cosmos. The ideas in the multiple stories say just about everything and everything. Depending on the context, an individual in the multiple narratives may call the question of Cosmos origin illegitimate; or consider it pure speculation lacking any truth value; or say that all claims are true; or even suggest that Cosmos has no origin and is always present. The Buddhists and the Jains have no conception of a God in the first place! Strangely, in Indian tradition and culture, a person can equally believe all the stories and may equally reject all of them. Finally, it looks almost as if the ‘origin’ question and the place of God are irrelevant.
Religion is thus impossible in a culture where the questions of origins can be an illegitimate one. The Western world is always in a grip of historicity trying to find the truth value of its scriptures. The Biblical history is right in the center of investigation with advocates and opponents on either side of the battle line trying to prove or disprove. This attitude hardly excites or disturbs their counterparts in India. It is the attitude of a culture towards the holy books that generates questions or fails to do so. Literature investigating the truth claims made by ‘religious texts’ is absent in India. To ask whether they are true or false is to exhibit a profound ignorance of the culture whose stories they are.
As another component, there must be certain sociological conditions absolutely required for guaranteeing the identity of religions. These are:
The two important properties of religion are: first, it must make a claim about the origin and purpose of the world (the how and why of the Cosmos); and secondly, this message must be true This is the ‘metaphysical’ position of any religion.
Based on the metaphysical conditions, Indian traditions are not possibly religions. They do not properly raise the issue of origin of the Cosmos. Vedas, Upanishads, Brahmanas, Puranas, Itihaasas have multiple stories of creation and purposes of Cosmos. The ideas in the multiple stories say just about everything and everything. Depending on the context, an individual in the multiple narratives may call the question of Cosmos origin illegitimate; or consider it pure speculation lacking any truth value; or say that all claims are true; or even suggest that Cosmos has no origin and is always present. The Buddhists and the Jains have no conception of a God in the first place! Strangely, in Indian tradition and culture, a person can equally believe all the stories and may equally reject all of them. Finally, it looks almost as if the ‘origin’ question and the place of God are irrelevant.
Religion is thus impossible in a culture where the questions of origins can be an illegitimate one. The Western world is always in a grip of historicity trying to find the truth value of its scriptures. The Biblical history is right in the center of investigation with advocates and opponents on either side of the battle line trying to prove or disprove. This attitude hardly excites or disturbs their counterparts in India. It is the attitude of a culture towards the holy books that generates questions or fails to do so. Literature investigating the truth claims made by ‘religious texts’ is absent in India. To ask whether they are true or false is to exhibit a profound ignorance of the culture whose stories they are.
As another component, there must be certain sociological conditions absolutely required for guaranteeing the identity of religions. These are:
- a world-view codified in a textual source called a ‘holy-book’ and must be widely known
- a standard world-view with clear boundaries and which cannot undergo changes across generations
- an authority to settle disputes in transmission and interpretation of stories and legends (thus having a hierarchy of texts)
- a source of excommunication when two interpretations collide (say Shaivism, Vaishnavism, Buddhism)
- an organization to transmit and propagate its world-views.
Sunday, September 29, 2019
Jammu & Kashmir - flashback to 1948
October 5th 1948:
(# 70 in "Towards a Ceasefire in Kashmir, British Official Reports from South Asia, 18 September - 31 December 1948", Editor: Lionel Carter).
Pakistan most certainly will not give Kashmir up in the face of Indian threats. To many Pakistani officers it seems probable that the war in Kashmir is at present essential to the existence of the Indian Union. They see it as the one common factor uniting all the different forces, which, if left to themselves, would pull the State to pieces. Without a "popular war" the Nehru Administration would have to settle the conflicting claims of its own members, satisfy the Sikhs, reconcile labour and capital, deal with the Communists and take drastic and unpopular measures to stop the drift of the national economy towards complete chaos. Hyderabad was a card which was good as long as it was held; now that it has been played there remains only Kashmir and the stakes on that card have been made so heavy in both men, money and prestige, that it cannot remain unplayed much longer. Recent speeches by Union Ministers do tend the suggest the obtrusion [sic? intrusion] of the U.N.O. into the relations between India and her State of Kashmir has been a tedious restraint on the Union's ability to manage her own affairs efficiently. Patel going so far as to remark on October 1st, that "if the Security Council releases us from that embarrassment we shall perform that operation also (i.e., Kashmir) with the least amount of danger." A singularly vacuous remark if ever there was one! Either Mr. Patel was using Hyderabad as a yard-stick to measure the Indian Army's martial prowess, or else he was completely ignorant of the military implications and the political consequences of a Union advance upto the Pakistan border.This is from Adrian Reed (Junior Staff Member, Lahore Deputy High Commission posted to Rawalpindi) to Olver (?Stephen Olver, Pakistan Foreign Service in Karachi).
(# 70 in "Towards a Ceasefire in Kashmir, British Official Reports from South Asia, 18 September - 31 December 1948", Editor: Lionel Carter).
Tuesday, September 10, 2019
The obliquity of the ecliptic
On IndiaFacts, Anil Narayanan makes the case that the astronomers who wrote the Surya Siddhanta measured the obliquity of the ecliptic to be arcsin(1397/3438) = 23.975° and not 24° as has been translated by Whitney et. al. since 1858; since 24° would be expressed as arcsin(1398/3438) or arcsin(1399/3438) and never arcsin(1397/3438).
This puts the Surya Siddhanta to some 3000 BC. Anil Narayanan promises more to support this date.
Answer to 3438 - it is the approximate radius of the circle in minutes (the exact value is 3437.74677078...).
My criticism of Anil Narayanan's article - see Aryabhatta's sine table on Wiki. 1397 comes from a linear interpolation for 24° between rows 6 and 7 of that table.
That is,
22° 30' = 1350' has jya = 1315
26° 15' = 1575' has jya = 1520
What is the angle whose jya = 1397?
The linear interpolation answer is 1350' + (1397 - 1315) * (1575' - 1350')/(1520 - 1315)
= 1350' + 82 * 225'/ 205 = 1440' (exactly!)
1440' = 24°.
This is probably how Whitney et. al. came to 24°. The question then was linear interpolation the method of calculation used? e.g., see the same Wiki article. I think to establish the point made Anil Narayana's article, we have to know how intermediate values in the R-sine table were computed.
Or, following Anil Narayanan's philosophy, that the precision of the Indian R-Sine is 1/3438, the obliquity of the ecliptic in the Surya Siddhanta is not an approximate 24°:
Using the formula here: http://glossary.ametsoc.org/wiki/Obliquity_of_the_ecliptic
or a more exactly formula one can estimate the range of times of that observation.
This is an important observation which bears repeating: The precision of the Indian R-Sine is 1/3438.
This puts the Surya Siddhanta to some 3000 BC. Anil Narayanan promises more to support this date.
We currently know of at least 3 other items in Indian astronomy that point to 3000 BC, or thereabouts.If Anil Narayanan is right, then he is also right about this:
1) The value of the Sun’s equation-of-center given in the SS indicates a time range of 3000 BC or older;
2) The ubiquitously mentioned pole-star in Indian astronomy and literature, namely Dhruva (modern name Thuban), indicates a period about 3000 BC;
3) It is mentioned in the Satapatha Brahmana text that the Krittika Nakshatra rises exactly in the East, which occurred only in ancient times, around 3000 BC. Nowadays Krittika rises between East and North-East.
We will discuss these in other articles.
The misconception, which has to do with the tilt, or obliquity, of the earth’s axis, also ranks among the most clever and successful obfuscations in Indian astronomy carried out by the European scholars of yesteryear. They skillfully achieved the difficult task of hiding the treasure in plain sight, so to speak.The two questions that I have are - how was this angle measured or inferred, and what is the origin of the Indian standard radius of 3438?
Answer to 3438 - it is the approximate radius of the circle in minutes (the exact value is 3437.74677078...).
My criticism of Anil Narayanan's article - see Aryabhatta's sine table on Wiki. 1397 comes from a linear interpolation for 24° between rows 6 and 7 of that table.
That is,
22° 30' = 1350' has jya = 1315
26° 15' = 1575' has jya = 1520
What is the angle whose jya = 1397?
The linear interpolation answer is 1350' + (1397 - 1315) * (1575' - 1350')/(1520 - 1315)
= 1350' + 82 * 225'/ 205 = 1440' (exactly!)
1440' = 24°.
This is probably how Whitney et. al. came to 24°. The question then was linear interpolation the method of calculation used? e.g., see the same Wiki article. I think to establish the point made Anil Narayana's article, we have to know how intermediate values in the R-sine table were computed.
Or, following Anil Narayanan's philosophy, that the precision of the Indian R-Sine is 1/3438, the obliquity of the ecliptic in the Surya Siddhanta is not an approximate 24°:
According to Mr. Bentley, the Hindu astronomers (unless in cases where extraordinary accuracy is required) make it a rule, in observing, to take the nearest round numbers, rejecting fractional quantities: so that we have only to suppose that the observer who fixed the obliquity of the ecliptic at 24 degrees, actually found it to be 23 and 1/2.Rather the measured obliquity of the ecliptic is bounded by arcsin(1396/3438) and arcsin(1398/3438), i.e, between 23° 59' and 24° 1' (23.983° and 24.017°).
Using the formula here: http://glossary.ametsoc.org/wiki/Obliquity_of_the_ecliptic
or a more exactly formula one can estimate the range of times of that observation.
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