The Ayurveda of Ecology

What the Game Leaves Open

Part One said, by way of a caution about the word “game,” that wind does not choose and rock has no strategy. That sentence claimed more than the method needs, and I want to take the surplus back.

The mathematics used here holds for players that never decide anything. That was the point of citing Maynard Smith and Price. But it holds equally for players that do. It asks one thing only, that whatever fares well should increase, and it is silent on whether anything is experienced in the faring. So the model does not require the elements to be inert, and it does not show that they are. It has no opinion.

The tradition does not speak with one voice on this either, and I see no need to make it. Caraka, sorting substances for the purposes of medicine, calls sentient what has sense faculties and insentient what has none: sendriyaṃ cetanaṃ dravyaṃ, nirindriyam acetanam.^[5] That is a physician’s working line, and it is drawn at faculties. The same Caraka counts six constituents of the world where we have been counting five, the sixth being the unmanifest brahman, and says that the same six make the person.^[5] And the Chāndogya Upaniṣad, telling how fire, the waters and food came to be, has being look before it brings forth fire, fire look before it brings forth the waters, and the waters look in their turn: tat teja aikṣata, bahu syāṃ prajāyeyeti; tad apo ’sṛjata — “that fire looked: let me be many, let me bring forth. It sent out the waters.”^[8]

Whether there is awareness in fire and in water is a real question and a very old one. It is not this essay’s question. Nothing below depends on answering it either way, and nothing below should be read as having answered it. Where I write that a player gains a place, or holds one, or is shut out, I mean what Part One meant by vṛddhi and kṣaya: there is more of it, or less.

A Doṣa Is a Weave

Part One read this as arithmetic. Vāta was space plus air, pitta was fire, kapha was water plus earth, and I said at the time that a doṣa is more than that. Two things are wrong with the sums.

The first is that a sum cannot tell a mixture from a heap. Open ocean, with a great deal of water and no earth, scores as high for kapha as a marsh does. But the grammar of the sentence is against it. Vāta comes from the two, in the dual number; so does kapha. A doṣa is what two elements make together, and where one of the two is missing there is nothing for the other to make it with.

The second is pitta. “Fiery” is what the Saṅgraha says, and Part One took it to mean fire alone. Pitta’s own description will not allow that. Caraka lists its qualities in the first chapter: sasneham uṣṇaṃ tīkṣṇaṃ ca dravam amlaṃ saraṃ kaṭu, a little unctuous, hot, sharp, liquid, sour, flowing, pungent.^[5] Hot and sharp are fire’s, by the same list of the elements’ qualities that Part One used for its table. Unctuous and liquid are water’s, and fire’s own list has the opposite of the first: fire is dry. A thing that is hot and also wet is not fire alone. Suśruta asks outright whether there is any fire in the body apart from pitta, and answers that none is found: pitta is spoken of as fire because it does fire’s work of burning and cooking.^[7] So the body’s fire is never met alone. It is met as pitta, and pitta is a liquid. That is why the table on this site, and the teaching I learned, give pitta as fire and water.^[11][12]

So in this part a doṣa is a weave of two strands. It is defined by three properties. When its two elements stand in the doṣa’s own proportion, the weave is as large as their sum. As they depart from that proportion it is smaller. When either is absent it is nothing. For vāta the strands are air and space, in equal parts; for kapha, water and earth, in equal parts, the texts giving the pair and no ratio. For pitta I take three parts of fire to one of water, which keeps it fiery and leaves it liquid. That last proportion is a judgment, the fifth number of mine, and the plate lets you change it.

Two consequences follow at once, and the second is in the texts already.

Water belongs to two doṣas. Pitta and kapha are bound to each other through it, and whatever takes water from a place takes something from both.

And fire without water is not pitta. Slide the water in Fig. 2 to nothing and pitta goes with it, however fierce the fire. That sounds wrong until one reads what Vāgbhaṭa says about the hot season. In the half of the year when the sun travels north, sun and wind together, sharp, hot and dry, wear away the gentle qualities of the earth,^[3] and the doṣa that builds up in that dry heat is vāta. Pitta’s trouble comes later, and he says exactly when: in bodies used to the cool of the rains and heated all at once by the sun’s rays, the pitta gathered during the rain is roused in autumn.^[3] Pitta is roused when the sun comes back onto soaked ground. The chapter on the seasons was treating it as fire meeting water all along.

Above its own measure

One more thing has to change with the sums. Disease, in Vāgbhaṭa’s definition, is the doṣas out of proportion. Out of proportion to what? Not to one another. Caraka gives the healthy body five añjali of pitta and six of kapha, a double handful being the unit, and nobody concludes that health is a kapha disorder.^[5] Each doṣa has a measure of its own, and Caraka adds in the same passage that it is this measure that is liable to rise and fall.

So on this page a doṣa is never called high because it is larger than the other two. It is called high when it stands above its own measure, and there are two measures in use. Set against the planet’s measure, which is the weave averaged over the whole globe and the whole year, a place shows its constitution: which doṣa it has more of than the planet at large. Set against the place’s own yearly measure, a day shows its season: which doṣa is up now.

Read this way, the settled planet of Part One comes out at vāta 31, pitta 31, kapha 38 of a hundred, where the sums gave 36, 18 and 46. The sphere of section one gives 31, 33 and 36. The even proportion that Part One’s table was built to find in the elements is there in the doṣas too, once pitta is allowed its water.

The constitutions of place are on the globe in the next plate, under the view called “doṣa of the place.” Pitta stands furthest above the planet’s measure over 42 parts in a hundred of the globe: nearly everything, land and sea, within about twenty degrees of the equator. Kapha leads over 41: everything poleward of about fifty degrees, and most land well short of that. Vāta leads over the remaining 17, and all of it is sea, in a belt of each hemisphere between the two.

What is not on this map. Vāgbhaṭa’s dry open country, jāṅgala, the land he calls mostly vāta,^[2] is missing. The model has no deserts. Deserts are made by air that sinks and by rain that falls somewhere else, and nothing in the model carries anything from one place to another; it has only spreading. Its Sahara and its Congo differ by a few parts of water, and the wrong way round. Part One’s toy put its driest land on the equator, where the real planet is wettest, and so does this one, by a smaller margin. It has no land dry enough for vāta to lead. That is an honest result about what is missing, and I come back to it at the end.

The Patient’s History

The physician’s second kind of time is the stage the patient has reached, and it is learned by asking. Vāgbhaṭa’s three ways of examining a patient are looking, touching and questioning.^[2] A planet answers questions in rock. For the last 485 million years, the span over which the chemistry of fossil shells and teeth gives a continuous record, the answers have lately been put in a form that a small model can use.

The largest of them is a history of the Earth’s surface temperature in eighty-five steps, each step a geological stage, published in 2024 by Emily Judd and her colleagues. It joins those measurements to several hundred runs of a climate model, and comes with an estimate of the carbon dioxide in the air at each step.^[14] The climate runs needed a map of land and sea for every stage, and those maps exist: they are reconstructions of where the continents stood and where the shorelines ran.^[15] To these I add the brightness of the sun, which has risen by about four parts in a hundred over the span;^[16] the latitude that ice is known to have reached, from the deposits that glaciers leave;^[17] and the oxygen in the air, estimated from the charcoal of ancient fires.^[18]

Sorted by element, this is a record of four of the five. Earth is the land: how much of it there is and where it lies. Water is the sea and the ice. Fire is the temperature, which has ranged from 11 to 36 degrees. Air is the two gases. One of them is the breath, and Caraka’s gloss on air in the person is exactly that.^[5] The estimates of oxygen run from the low twenties to above thirty parts in a hundred through the age of the coal forests, against 21 now, and fire itself enters the record only when there was something on land to burn and oxygen enough to burn it, some 420 to 430 million years ago.^[18] The fifth element has no record. Rock keeps what was there, and ākāśa is the room for things to be there. What the record does keep is how much stood between the ground and the open sky, and that is the carbon dioxide again.

I should say exactly what the model is given and what it is asked. It is given three things for each stage: the map of land and sea, the brightness of the sun, and the carbon dioxide. The gas enters as it does in the simplest climate models, as a favour to fire that is the same in every place and every month, so much for each doubling. The size of that favour is the sixth and last number of mine in this part, and I fixed it by one published threshold before looking at any temperatures: with today’s continents the last of the model’s year-round ice goes when carbon dioxide passes about 790 parts per million, which is close to where a much-cited simulation has the ice of Antarctica beginning.^[19] It is a loose fit. Other climate models put that threshold elsewhere, and well before 790 the model’s ice has shrunk to a remnant. The model is then asked where the elements stand and how the doṣas read, at rest, under each stage’s conditions. The temperatures are kept back for comparison.

Press Play and the continents assemble into a single land, Pangaea, by about 300 million years ago, and come apart again. Then set beside one another what the model says and what the record says. There are five things to report, and two of them are failures.

The patient has a constitution, and it is not today’s

The record first, since this owes nothing to the model. Of the eighty-five stages, six were colder than the one we live in. Weighted by how long each lasted, the planet’s temperature over the whole span averages 24 degrees, against 14 for the last ten thousand years, and it was warmer than now for 94 parts in a hundred of the time.^[14] The model’s reading says the same thing in a physician’s terms. Among the three doṣas, pitta is the largest in 73 stages and kapha in 12, the oldest of the 12 by a hair. All of kapha’s fall either in the long ice age of the coal forests and after, between about 355 and 270 million years ago, or in the last five million years. The present stage is the fifth most kapha of the eighty-five, and the four ahead of it all lie within the four million years just behind us.

By its long history this planet is pitta by constitution. We met it in one of the two kapha ages the model finds.

The weave reads the record better than fire does

Across the eighty-five stages, the model’s share of fire rises and falls with the measured temperature, but loosely: the correlation is 0.64, where 1 would mean they kept perfect step. Pitta’s share among the three doṣas does better, at 0.74. The reason is the sea. In the model, as in Part One’s table, water quenches fire, and fire holds a smaller share at sea than on land. So the planet’s total of fire goes up and down with the area of land, whatever the heat. Take the late Ordovician, about 450 million years ago. Land was 17 parts in a hundred of the surface, a little over half of what it is now; carbon dioxide stood well above its level before coal; and the record has the planet at 28 degrees, against 14 for the present. The model’s fire for that stage is 12.9 parts in a hundred, which is less than the 14.1 it gives the present. A warm sea is not short of pitta, though. It is fire with water in it, and a world with little land is short of kapha. Pitta’s share for the same stage is 34.7, against 33.2 now: on the right side of the present, if not by much. Here the reading the texts suggest is the better instrument, by a margin that can be measured.

That is the most that can be claimed. Carbon dioxide alone, with no model at all, tracks the temperature at 0.73. The model was handed the heat, and in its doṣas it hands it back, with nothing added.

Ice comes in the right ages, and stays too small

The record has ice in three long spells: around the end of the Ordovician, from the late Devonian through the age of the coal forests, and from about 34 million years ago until now. The compilation used here also has four brief cold snaps in the Jurassic and Cretaceous.^[17] Counting a stage as icy when the model keeps year-round ice over at least one part in a hundred of the globe, model and record agree in 67 stages of 85: ice in both in 32, in neither in 35. The model has ice the record lacks in 10 stages, and lacks ice the record has in 8. Five of those 8 are the first twenty-odd million years of the Antarctic ice sheet itself, when the model’s ice is there but falls short of one part in a hundred; so the number I fixed by the beginning of that ice does not hold it once it has begun. And the model’s ice never comes closer to the equator than about 65 degrees. The real ice of the coal-forest age reached 32. In the model, cold makes ice; ice does not make cold. On the real planet it does, by throwing sunlight back, and that is how an ice sheet grows past the place where it began.

The model warms where it is already warm

This is the plainest failure. In the record, the hot ages were hot mostly at the poles. The difference in temperature between the equator and the high latitudes shrinks as the planet warms; across the stages the two move against each other with a correlation of −0.90. In the model the contrast in fire between equator and pole grows as the planet warms. The model’s contrast and the record’s run opposite ways, at −0.55. A rule in which what does well grows will always give more to the place that has most, and nothing in this model pushes back. Anything it says about which latitudes change most should be distrusted, and I will hold it to that in the next section.

Without place, the game still follows the history

Given each stage’s planet-wide conditions, the game’s fire follows the sphere’s through all eighty-five stages almost exactly, with a correlation above 0.99, while sitting about 7 points away from the sphere in its totals, and as much as 9. Deep time, it turns out, is easy for the game. A change that comes to the whole planet at once is exactly the kind it can see. What it lacks is what it lacked in Part One, and the year has made the lack plainer.

Five crises

Five times in this span a large part of the kinds of animals in the sea died out within a geologically short time. They are the triangles on Fig. 6. Vāgbhaṭa divides diseases, in the half-verse after the one that defines them, into those that arise within and those that arrive from outside, nija and āgantu.^[2] The division sorts the five cleanly, and a reading by doṣa sorts them again.

Dates, causes and the chemistry are from the review by Bond and Grasby and the studies it draws on.^[20] The differences between stages are from the temperature record.^[14] The readings in the last column are mine, made from the record.

They are not the model’s. In three of the four crises that arose within, the model’s doṣas move slightly the other way: its kapha falls into the end-Ordovician ice, and its pitta falls across both of the great heatings. The reason is in what it is given. Each stage has one figure for carbon dioxide, a median over millions of years, and those figures do not carry the pulses. The estimate for the stage of the end-Ordovician ice is higher than for the stage before it, and the estimates on the far side of the end-Permian and end-Triassic eruptions are lower than on the near side. A model that is handed its heat cannot find a fever the chart does not show. This is also why the end-Ordovician ice, which the record has, is not among the model’s kapha ages.

What the five have in common is not a direction. Two came with cooling and at least two with heating, and the planet has been as cold and as hot at other times without a comparable loss. What they have in common is pace. The end-Permian extinction, the worst of them, ran its course in about sixty thousand years, on a planet whose stages last millions.^[20] I will come back to pace, because Vāgbhaṭa has a verse about it.

One last entry in the history belongs to time itself. Corals lay down a ridge a day and a band a year, and Devonian corals have about four hundred ridges to the band.^[21] A Devonian year had about four hundred days in it. The year was no longer than ours; the Earth turned faster, and the days were shorter. Even the calendar, which the last section treated as fixed, has a history.

Game, Sphere and Time

Part One asked how a game among the five elements compares with equations on a map, and found that the game is the map with place removed. Part Two has added time to both, three times over, and the division of labour has become clearer.

The game’s blind spot has a precise shape now. It sees whatever happens to the whole planet at once, on any scale of time. It cannot see a season, because a season is time arriving differently at different places. Caraka ranked the four common factors and put time above place. The model suggests why they are hard to rank the other way round: place without time is still a map, but time without place loses the year.

The weave earned its keep in two places. It read the warm, sea-covered world of the late Ordovician as richer in pitta than the present, where fire alone read it as poorer. And it found the settled sphere nearly even among the three doṣas, where the sums have it more than half kapha. A third thing it was built to do, which is to keep dry heat out of pitta as Vāgbhaṭa’s seasons do, could not be put to any test, because the model has no dry land. None of that makes it right. It makes it a better instrument than the sum, by the test of the record and by the test of the texts, and I have changed this essay’s reading of Part One accordingly.

And the caution of Part One stands, with more behind it. The sphere on this page has been set beside eighty-five stages of the real planet’s past and a hundred years of its present, and it has failed in ways that are written down above. That is what the comparison was for. The models used to project the real climate conserve energy and mass, carry water on the wind and build ice that cools what is around it. This one does none of those things. It is a way of asking a physician’s questions of a planet and seeing which of them have answers.

How It Works

The rule of local growth is Part One’s, unchanged: the same seventeen subcomponents, the same Earth system table M, the same crowding.^[10] On the sphere the payoff to subcomponent a at place i and time t gains three terms:

π_a = v_a + c_a · M y − κ x_a + F_i(t) f_a + g [L_i e_a + (1 − L_i) w_a] − b (1 − L_i) e_a

where f_a, w_a and e_a are how much fire, water and earth the subcomponent contains, L_i is the fraction of the place that is land, g = 0.15 is the hold of land and sea on their own elements and b = 0.4 is what the open sea takes from earth. Fire’s favour is

F_i(t) = s [ℓ q(φ_i, δ(t)) − 1] + h log₂(CO₂ / 280)

with s = 0.6 as in Part One, ℓ the sun’s brightness relative to today, and h = 0.03. Here q is the day’s sunlight at the top of the air at latitude φ when the sun stands over latitude δ, divided by its average over the whole planet:

q = (4/π) (H sin φ sin δ + cos φ cos δ sin H),  cos H = −tan φ tan δ

and δ swings between 23.44° north and south once a year. The Earth’s orbit is taken as a circle. The sun’s brightness ℓ follows Gough’s formula, 1/(1 + 0.4 t/4,570) for t million years ago.^[16] A year is 48 units of model time, and the time step is 0.1 as before, by Heun’s method.

The grid is an icosahedron with each face divided in four, four times: 2,562 points, each with five or six neighbours. Spreading uses the standard cotangent form of the Laplacian on that mesh, scaled so that the mobilities of Part One (space 1, air 0.8, fire 0.3, water 0.2, earth 0.03) mean the same distance covered as they did on its map. On a test function the operator is accurate to about half of one part in a hundred on average, and is at its worst, about twelve parts in a hundred, at the twelve points that have five neighbours.

A weave of two strands a and b, with p the first strand’s share of the recipe, is

W = (a/p)^p (b/(1 − p))^{1 − p}

which equals a + b when a : b is p : 1 − p, is less otherwise, and is zero when either is zero. Vāta is the weave of air and space with p = ½, pitta of fire and water with p = ¾, kapha of water and earth with p = ½, each taken on the local shares of the five elements. A place counts as frozen at a given moment while fire’s share is under 0.02, and as under year-round ice when fire’s yearly mean is under 0.02. By the stricter test of staying under 0.02 on every day of the year, the model at this length of year has no such place.

For the deep past the model is run to a repeating year under each stage’s land, sun and median carbon dioxide, starting from the stage before, and its yearly means are kept. For the century it is run from 1925 to 2025 without a break. The figures quoted in the text are written out by the scripts and are not typed by hand.

The data

Temperature, carbon dioxide and the land–sea masks for the eighty-five stages are from the public files of Judd and colleagues.^[14] The latitude reached by ice, and the charcoal estimates of oxygen,^[18] are as compiled in the data files of the SCION model.^[17] Present-day coasts are Natural Earth’s.^[33] Yearly carbon dioxide since 1925 is from the Indicators of Global Climate Change,^[23] and yearly temperature from NASA’s GISTEMP.^[24]

The scripts

Plain JavaScript with no dependencies; they run under Node, and need engine.js and presets.js from Part One in the folder above. The archive has both, laid out to run, with a note on the order.