The Ayurveda of Ecology

The Year, Measured: Saṃvatsara

Suśruta has the Sun, by his motion alone, mark out every division of time, and gives time the year for a body. Part of the measure of Part One is made of the Sun’s light and of the wind, and the rest, the ground, is wet or dry as the rain comes and goes. So it has the year in it without anything being added. As the sun goes north the light at a northern place grows, what the place does with the light changes, and the ground dries or is soaked.

The texts name the two halves of the year for what the sun does in them. The northward half is ādāna, the taking: it takes away a little of people’s strength each day, as sun and wind, grown sharp and hot and dry, wear down what is cool and moist in the earth. The southward half is visarga, the giving back, when cloud, rain and cool wind quiet the heat of the ground.^[3][4] And Suśruta says in one verse that the three doṣas do in the body what moon, sun and wind do in the world.

That is Caraka’s likeness of world and person, stated for the doṣas, and the measure of Part One is the world’s side of it. The sun takes, and what it takes is water: the heat spent lifting it comes to 45 parts for every hundred of sunlight that reach the ground.

To read a calendar from the measurements I need one more idea, and it is a physician’s. A doṣa is in season when it stands above its own measure, not when it is the largest thing present. Pitta is the largest of the three over 71 parts in a hundred of the open sea in every month of the year, and that says nothing about seasons. So for each box I take its three weaves over the whole year as that place’s own measure, and in each month I ask of each doṣa whether it stands above its measure there or below. Two may stand above at once, and in some months none does. Where the sea is deeper than the ground is counted, kapha has no measure at all, since no earth is found there, and so it has no calendar. For the ground of a month I use that month’s rain against that month’s drying sun, as Part One did for the year, which gives the soil no memory of the month before; I say what that costs below. The months are the average of the ten years 2009 to 2018.

Run the year and watch the land turn from one colour to another and back. Over land between thirty and fifty degrees north, where most of the people who will read this live, forty boxes averaged together give this year. Vāta stands above its measure from April to August and is highest in June. Kapha stands above its measure from October to February and is highest in December. Pitta stands above its measure from September to February, beginning a month before kapha, and is highest in November. In March none of the three does. At its height vāta stands 36 parts in a hundred above its measure, kapha 54 and pitta 18.

So the measured year on temperate land has two seasons and not three. The reasons can be read from the five. In summer the light is strong and the ground is dry: in June the soil is 19 parts water in a hundred, against 44 in December. Space and the warming of the air stand high, and they are vāta’s. In winter the light is weak and the ground is soaked. Water and earth stand together with little else, and that is kapha. Pitta is fire with water. On this land it is the water that swings through the year, from 9 parts in a hundred to 30, while fire stays between 18 and 25. So pitta goes where the water goes: into the winter. Nobody teaches a winter pitta, and I do not think the measurement has found one. It is the fault met in Part One. Nothing in the five is cold, and fire, which is heat leaving, does not fall away in winter as far as warmth does. The end of this section tries the cure.

South of the equator, on land between twenty and forty degrees, the two halves blur. Vāta is again the bright season’s, highest in December. But much of the rain there comes with the sun, and kapha and pitta stand above their measures from January on, through most of the southern autumn, and are highest in May.

The sea in the temperate north has a year too, and a quieter one. Its ground does not change with the months, so everything that moves there is the light and the wind. None of the three strays far from its measure. Vāta keeps between 0.84 and 1.17 of it through the year, pitta between 0.76 and 1.10, and kapha between 0.93 and 1.10, where on the land beside it vāta goes from 0.49 to 1.36 and kapha from 0.66 to 1.54. Vāta at sea is highest in March, at the windy end of winter, three months before it is on land.

Now the teaching.

Count the seasons off and vāta gathers in summer and is roused in the rains, pitta gathers in the rains and is roused in autumn, and kapha gathers in late winter and is roused in spring. Suśruta teaches the same three in the same order, on a calendar of his own made for this purpose, in which each season falls a month or so otherwise and the year has two rainy seasons and no late winter.^[1] Both are calendars of a monsoon country, and the box to set beside them is a monsoon one. I use the box at twenty north and eighty east, in the middle of the subcontinent.

On vāta the instruments and the texts agree by half. The measured vāta stands above its measure from February to June and is highest in May, in the hot season, which is where both texts have it gathering. Suśruta’s reason for the gathering is the land’s own state: in the hot season the plants are sapless, dry and light, and bodies are dried by the sun.^[1] Then the monsoon arrives, and between June and July the measured vāta falls from 1.21 of its yearly measure to 0.42, and it stays low until the rains are over. In the teaching the rains are exactly when vāta is roused. Vāgbhaṭa says it gathers in the hot season and is not roused then because of the season’s heat;^[3] Suśruta says that when the ground is soaked and bodies are wet, the gathered vāta is stirred up by cold, wind and rain.^[1] That is an account of what a change of weather does to a body that has spent the summer drying out. The measured land does not show it. Whether anything in the world does is taken up at the end of this section.

On pitta they also agree by half, and it is the same half. The measured pitta is highest from June to September, the months of the rains, and it is in the rains that both texts have it gathering. Even then it stays just short of its yearly measure, at 0.98 of it in June, and it does not last: by October it has fallen to 0.76 and by November to 0.44. The texts have it roused in autumn. Vāgbhaṭa gives the reason in his chapter on the seasons: pitta, gathered in the rains, is roused when bodies used to the cool of the monsoon are suddenly heated by the sun’s rays.^[3] Suśruta adds the sky and the ground: the cloud thins, the mud dries, and the gathered pitta is liquefied by the sun.^[1] On the measured land, when the mud dries the pitta goes with the water.

On kapha they disagree. The measured kapha stands above its measure from June to September, in the rains, when the ground is soaked, and is highest in July. In the cold season and the spring, where the texts have it gathering and then roused, it is at its lowest, between 0.20 and 0.30 of its measure from January to April. The teaching’s kapha is laid down in the body in the cold months, when food and water are heavy and unctuous and the sun is weak, and is melted in spring by the returning sun.^[3][1] The ground of central India in those months is dry.

All of that is one box, read at one point. A second monsoon country says the same. Across the Sahel, five boxes of land at ten degrees north, vāta stands above its measure from February to June, pitta from June to September and kapha from June to October: the dry season is vāta’s, and the rains are pitta’s and kapha’s together.

The fourth row of the table is my teacher’s calendar. Vasant Lad carried the science from India to New Mexico, far from the monsoon, and the year he teaches is a temperate one.^[8] Set beside the measured year of temperate land it fares no better. His kapha runs from January to May and the measured kapha from October to February; they share two months. His pitta runs from May to August and the measured from September to February, with no month in common. His vāta is the autumn, September to December, and the measured vāta is spring and summer; they share no month. I do not take the instrument’s side in this. The measured calendar is the calendar of the ground. His is the calendar of the people standing on it. The texts build their whole account on what the season’s plants, waters and weather do in a body, and on the interval between a doṣa’s gathering there and its being roused, and an instrument that reads the ground has no way to see either.

So the plain result is this. The measured ground has a dry bright season that is vāta’s and a wet season that is kapha’s and pitta’s together, and it has them in the temperate north and in both monsoon countries: winter and summer in the one, the rains and the hot weather in the others. Where the rain comes with the sun, as on the southern continents, the two run together. Against the texts that gives two agreements, both about gathering: vāta gathers in the hot season, and pitta gathers in the rains. It gives no agreement about rousing, for any of the three, and none about kapha. I had hoped for better, and I think the lesson is in the shape of the failure. Everything the texts say about a doṣa being roused is about a body meeting a change of season, and the regimen of the seasons, ṛtucaryā, is written for that body. The land’s year and the body’s year are two years. So it stands with the measure as it is. Two of the measure’s faults can be mended in trial, and one of its choices made the other way, and between them they take back a part of this.

Two faults and a choice

Two things about these calendars are faults of the measure and not findings, and both can be tried. A third thing, which is a choice and not a fault, is tried after them. The first was met in Part One: nothing in the five is cold. The second belongs to this part. The wetness of the soil in a month is reckoned from that month’s rain and that month’s sun, with nothing carried over, and real soil remembers. Ground soaked in April is still damp in May whether or not it rains.

For the cold, I let fire know the temperature. The fire of a place in a month is still the heat it radiates away, but it is counted by how warm the surface then is: for nothing at freezing or below, once at the planet’s mean, which is 15 degrees, and twice at 31. For the memory, I gave the soil a store. It holds up to 150 millimetres of water, which is the figure Manabe gave the land in the first models of the whole climate.^[10] Rain fills it, what overflows runs off, the sun dries it at full power while it is more than three-quarters full and in proportion below that, and what is left is carried into the next month. Neither is part of the measure on these two pages. Both are run beside it, to see which of the calendar’s quarrels with the teaching belong to the land and which to my arithmetic.

The warmth mends the winter pitta, and little else. On temperate land, the forty boxes taken together, pitta leaves the cold months, falling to 0.26 of its measure in midwinter. It stands above its measure in August and September only, and by 9 parts in a hundred at most, when the ground has begun to wet again and is still warm. Kapha keeps its months, October to February, and vāta begins a month earlier, running from March to August. So under this fire the temperate year has a slight third season, a pitta at the turn of summer into autumn. It is hardly nearer my teacher’s calendar for that. His pitta is the summer’s, and this one shares one month, the last, with it. In India, where the ground does not freeze, the warmth changes little: vāta gains January, and pitta just reaches its measure in June and in September.

The store does two things, and they should be kept apart. The first has nothing to do with memory. It changes what a year’s wetness is. The main count reckons the year from the year’s whole rain against the year’s whole sun, and that credits the downpours of July to the dry ground of March. Month by month, with or without a store, central India’s soil is on average 22 parts water in a hundred. Reckoned by the year it is 42. So the yearly measure that pitta and kapha were held against was set too high there, and that is most of why pitta in the table above never quite reaches its measure. Take the year as the mean of its months and nothing else, and pitta stands above its measure from June to October.

The second is memory proper. With the store, the soil of central India is still 37 parts water in October and 20 in November, where the month-by-month reckoning has it at 24 and 7. Pitta, which is fire with water, does not go when the rain stops. It stands above its measure from July to November, a month later at both ends than with the year re-reckoned and no store. In October it is at 1.32 of its measure, and in November at 1.00, which is only just above. With a store of half the size the months are June to October, the same as with no store at all, and with twice the size August to November. So October holds however the store is sized, and November comes and goes with it. Across the Sahel the store gives June to October, against June to September as measured.

October lies wholly inside the season in which Vāgbhaṭa has pitta roused, and it is the month in which Suśruta has the gathering end and the rousing begin. So with the year reckoned as the mean of its months, and more firmly with a store, the land’s pitta runs from the rains into the autumn, as the texts’ does. Most of that is owed to the reckoning of the year and the lesser part to the memory. Memory alone, with the store’s months held against the year as the measure reckons it, leaves pitta short of its measure in every month, as it was, and does no more than move kapha a month later.

What the store does not do is as plain. Kapha in India stays in the rains, June to October, and nothing brings it to the cold season or the spring. On temperate land the store gives kapha one more month, so that it runs from October to March, and leaves pitta in the winter beside it. And vāta does not shift at all, in either country. It cannot, in this trial, which leaves the warming of the air as it was measured. Vāta is woven of air and space, and neither is reckoned from the soil. With both mendings together the temperate year is vāta from March to August and kapha from October to March, with pitta nowhere above its measure and nearest it in August; and India is vāta from January to June, pitta from June to October and kapha from June to October. November is lost again there, and October kept.

That leaves the vāta of the rains, which no mending of the ground could reach, and here the choice comes in. Part One counts the air of a place by two things, the warmth the ground hands to it and the wind, half and half. In central India the two pull opposite ways. The warming of the air is greatest in May, at 82 watts on the square metre, and all but stops in July, at 3, when the sun’s heat is going into wet ground. The wind is strongest in July, at 3.5 metres a second against 1.9 in the still months, because over India the monsoon is a wind before it is a rain. Count the air by its wind alone, and vāta in central India stands above its measure from May to August and is highest in July. That is the span the texts give vāta, falling between Suśruta’s reckoning and Vāgbhaṭa’s: from its gathering in the hot season through its rousing in the rains.

It is India’s agreement and not a law of monsoons. In the Sahel the wind does the opposite. It is strongest in January, at 3.2 metres a second, when the dry wind blows off the desert, and weakest in October, at 1.9, as the rains end. Counted by the wind alone, vāta there stands above its measure from December to July and falls below it in the rains. The texts were written in the one country and not the other.

The measure does not show it, and I have not made it show it. Counted half and half, the fall of the warming swamps the rise of the wind, and vāta drops when the rains come, as it does in the table above. The air would have to be counted nineteen parts in twenty by its wind before July came near May, and Part One shows what counting by the wind alone costs: vāta in the dry land falls by nearly half, to 19 in a hundred. On temperate land the wind alone would give a vāta of the winter and spring, December to May, which is not my teacher’s autumn. So the vāta of India’s rains is in the world after all, in the movement that is air’s own mark, and it is the half of the measure that sees dryness that hides it. It would be easy to write it down as the body’s. In India it is the wind’s.

So the tally against the texts changes, by something less than two. Under every reckoning that takes a year’s wetness as the mean of its months, the pitta of central India stands through October, which is inside the season where Vāgbhaṭa has it roused. That is an agreement about rousing where the measure had none. It is one box, with the Sahel beside it, and it rests on how a year’s wetness is taken. And in central India vāta is roused in the rains if air is its movement, and not if air is also its dryness. Kapha is no nearer under any of them. I have not made any of the three the measure. The warmth takes fire out of the plain account of where the sunlight goes, brings in a zero and a unit, and buys by construction the agreement about heat that Part One had to report as failing. The store needs a size, and though 150 millimetres has a history, it is one more number. The wind alone halves the vāta of the desert. And the store knows nothing of snow, which holds a winter’s water back until the thaw. I have not built that.

It may be said that all this undoes the premise. If the person is commensurate with the world, the two years ought to be one. I do not think the sentence requires it, and I cannot show that from these files. What I can say is narrower. The texts put an interval inside the body’s year. A doṣa gathers in one season and is roused in another, and the seasonal regimen is written for the passage between. A reading of the ground has one value for each month, and cannot show a thing gathered and waiting. In the one place where the ground was given something to carry from month to month, pitta moved a month further into the teaching’s autumn; and the one rousing that looked beyond any reading of the land turned out, in India, to be in its wind. I have not measured a body, and this is not a demonstration.

How much the year matters. At an average place, an average month differs from that place’s own yearly mix by 7 points in a hundred. Two places on the same circle of latitude differ from each other by 22. Caraka calls time weightier than place because it is harder to escape, and I do not think the two numbers contradict him. But by the plain size of the difference, on this measure, place counts for more than season. And the leading doṣa, as distinct from the one in season, holds through all twelve months over 80 parts in a hundred of the open sea and 27 of the land. The sea is very nearly one thing all year. The land is not.

The Dial Turned by Chance: A Chain Run in Reverse

The record stops at 1979. To go further back from the present something has to be assumed about how the patient changes, and the lightest assumption available is a chain of chances. Suppose that what a place is next year depends only on what it is this year, by fixed odds. Mathematicians call that a Markov chain. The odds can be counted straight from the record: of all the places in a given state in one year, what share were in each state the year after? And a chain can be read backward as well as forward. Given what a place is now, the rule of Bayes turns the forward odds into the odds of what it was the year before, and the year before that, as far as one likes.^[11]

I built two chains, and the difference between them is the whole of this section.

The chain of constitutions fails

The first takes the state of a place to be its leading doṣa. It is the chain one gets by counting changes straight off the maps, and I did not expect it to hold. I count it because the way it fails is exact, and names the distinction the second chain needs. Counted over the 39 steps from one year to the next, each place weighted by its area, the odds are these.

A place led by vāta has 71 chances in a hundred of being led by vāta next year, and so on. Run forward, or backward, a chain like this forgets. Its memory fades by a factor of 0.97 each year, which is to say that it loses about two-thirds of what it knew every 34 years, and after 137 years it gives the same odds, to within a point, for the past of every place: 2 for vāta, 57 for pitta and 42 for kapha, whatever the place is today. Dialled back that far, the eastern Sahara has 57 chances in a hundred of having been pitta, which on this map mostly means deep sea, and 42 of having been kapha.

That is false, and the record is long enough to show it. The chain says that of all places, 84 in a hundred should have the same leading doṣa as they had ten years before, and 69 in a hundred the same as thirty years before. The record has 97 and 97. After one year it is 98. In thirty years the agreement has fallen by less than a point.

Places do not wander among the doṣas. The chain reads the boundary boxes changing back and forth, takes that for travel, and concludes that every place will in time go everywhere, the deserts out to sea. The mistake is the one a physician is trained not to make. Vāgbhaṭa says where a constitution comes from.

Prakṛti, constitution, is settled at the beginning, and the tradition treats it as lasting for life. What rises and falls afterwards is the condition of the doṣas against that constitution, and a patient’s good and bad years are not steps on a road from one constitution to another. A place has both as well. The eastern Sahara’s constitution is vāta. Whether this was a year when its vāta stood higher or lower than usual is a separate question, and it is the only one a chain of chances can fairly be asked.

The chain of conditions is nearer, and short

So the second chain takes each place against itself. For every box I take out of its record its own forty-year average of each doṣa and its own slow drift, and divide what is left by that doṣa’s usual swing at that place, so that a doṣa which always moves a great deal does not always win. The state of the box in a year is the doṣa that stands furthest above its usual level, counted in its own swings. This is near to the measure of section one applied to years, and it is not the same: the two name the same doṣa 77 times in a hundred. It can be read only where all three doṣas are present and vary, which leaves out the sea too deep for the count to find a floor, where there is no kapha: 86 parts in a hundred of the surface are read, 100 in a hundred of the land and coast and 76 of the open sea. The odds are these.

This chain comes much nearer the record than the first one did. It predicts that 34 places in a hundred will be in the same condition two years apart, 34 three years apart and 33 five years apart. The record has 36, 36 and 34. The two never differ by more than three points, out to thirty years. It errs the same way as the first, and by far less. The first chain forgot the constitution of a place, which the record keeps. This one forgets its condition a little too soon. A chain knows only last year, and has forgotten by the second step. The record keeps something a little longer.

How little is the point. If conditions were dealt afresh every year, a place would be found in the same one two years running 33.4 times in a hundred. The record has 39.8. So this year’s condition raises the odds on last year’s by 6.4 points, on the year before by 2.8, and on the year before that by 3.0. By the fifth year the advantage is 0.7, and by the seventh it is gone. Read apart, the land with its coast remembers more than the open sea: 6.8 points after one year against 5.3, and 3.4 after two against 1.6. From the seventh year on the record wanders within two or three points of chance, now above it and now below. That wander is as large as the advantage at two and three years, and at sea it is larger. So I lean on the first year, allow the second and third with less confidence, and read nothing beyond.

If the slow change in each box’s own record is left in, and the plain measure of section one is used, there is more memory and it lasts longer: 45 in a hundred after one year, 40 after five and 37 after ten, against 35 by chance, and it is gone by fifteen. The extra is whatever changes slowly in a box: a run of wet or dry years, or the reanalysis’s changing sources. I cannot tell the two apart.

Month by month there is more to remember, and no chain that fits it. Taking each box against its own calendar, between sixty south and sixty north, wherever all three doṣas can be read, a place is in the same condition from one month to the next 41 times in a hundred against 34 by chance. The advantage is 4 points at three months and 2 at six. A chain counted from one month to the next does not reproduce that. It forecasts 34 in a hundred at two months, and the record has 39. A condition lasts longer from month to month than one step of chance allows. At twelve months the advantage is still 2 points, which is the year-to-year memory seen from the other side.

One more thing can be read from the chain of conditions, and I did not expect it. Reversed by Bayes’ rule, its table of odds is the same table, to within 0.003. The odds of going from a year of high vāta to a year of high kapha are the odds of having come from one. By this test, which sees only three states and pairs of neighbouring years, nothing in the yearly wobble says which way time runs. A finer test might find a direction. I found nothing in the forty years that has one.

So this is as far as the dial turns. From what a place is today, its constitution can be read back with confidence across the whole record, and I see no sign in forty years of how much further it would hold. Its condition can be read back one year with a small advantage, a second and a third with a smaller, and not at all beyond. The chain adds nothing to the forty years I could turn by hand. It was worth building for what it refused to do.

The Horizon

Three dials, then, and where each one stops.

The constitution of each place is not on the list, because none of the three dials turns it. It hardly moved in forty years. The chain that tried to move it was wrong. I cannot say from these files how long it has stood, only that the record is too short to see it change.

That is not a statement that it has always stood. The Earth’s constitution has changed many times. Its surface has been some twenty degrees warmer than it is now and a few degrees colder; the reconstruction of Judd and colleagues follows the temperature back four hundred and eighty-five million years, between eleven degrees and thirty-six.^[12] There have been long ages with no ice at either pole. But that history is known because it was written down at the time, in rock and shell and ice, and has been read. None of it can be had by starting from today and working backward, by any method that forgets, and every method on this page forgets. The present is evidence about the recent past only. For the deep past one needs the deep past’s own evidence.

A physician knows this. The examination, by looking and touching, establishes how the patient is. It does not establish how the patient came to be so, and that is why the third member of the triad is questioning: darśana-sparśana-praśnaiḥ.^[2] The history has to be asked for. A planet cannot be asked, and its strata are the nearest thing to an answer that there is.

What the present does give, and gives firmly, is the distinction the whole of this part has turned on. A place has a prakṛti, and the measurement of Part One is a map of it. Against that it has a year, large and regular, in which the doṣas take their seasons, though not the seasons the body keeps. Against the year it has a small condition, different each year and forgotten in two or three. A model that confuses the three will make the mistake my first chain made, and send the Sahara wandering.

How It Works

The five at each box are computed as in Part One. The light’s three are space, the sunlight thrown back; air, which is half the sunlight handed to the air as warmth and half the wind, the wind being counted against the planet’s mean wind in units of the planet’s mean warming; and fire, the heat radiated away; all in watts, each divided by the planet’s mean sunlight at the ground. The ground’s two are water and earth as shares of a column counted from the surface down to 3,700 metres. Land is earth less the water in it, which is half of the lesser of one and the ratio of the period’s rain to the sun’s drying power over the same period. The sea and the lakes are water down to their floor, and the ice is water 2,000 metres thick; whatever of the column lies below them is soaked ground, half water and half earth. The five are those three and those two, divided by their sum. The doṣas are the weaves of Part One in the proportions counted from Caraka: vāta three parts air to one of space, pitta one part fire to one of water, kapha two parts water to one of earth.

The year. Monthly shares are made from the sums over 2009–2018 for each calendar month, of the light and of the rain and drying power alike. A doṣa’s strength at a box in a month is its weave of that month’s shares; the box’s own measure is its weave of the ten-year shares; the doṣa stands above its measure when the first exceeds the second. Since the measure is woven from the year’s pooled shares, the twelve months do not average to it, and a doṣa may stay below it all year. For a region the strengths of its boxes are averaged by area, month by month, and set against the average of their measures. Land and sea are told apart as in Part One. In a month with no sun a place is its ground and its wind; with no space there is then no vāta.

The three trials. For the air counted by its wind alone, the half that is warming is given no weight and the wind all of it, which leaves the planet’s total air as it was. For the fire that knows cold, each month’s fire at each box is multiplied by (T − 273.15)⁺ / (T₀ − 273.15), with T the surface temperature of that month from the same reanalysis and T₀ the planet’s mean over 2009–2018, before anything is summed. For the soil that remembers, a store of capacity c = 150 millimetres is run through all 40 years at thirty steps to the month: at each step it gains the rain, loses the drying power times min(1, s / ¾c), and is held between nothing and c. The record is run through once to set the starting state. The wetness of the soil in a month is half of the mean of s/c over that month, and the year’s wetness is the mean of its twelve months. Months are taken as equal in length.

The forty years. Yearly shares are made from the sums over the twelve months of each year from 1979 to 2018. Distances between two maps are half the sum of the absolute differences of the five shares, averaged over places by area. Drifts are least-squares lines through the forty planet-wide values, with the usual standard error of the slope.

The chains. For the chain of constitutions the state of a box in a year is its leading doṣa. For the chain of conditions, each doṣa’s strength at a box has its forty-year mean and its straight-line drift removed and is divided by its own standard deviation; the state is the doṣa with the largest result. A box is read only if all three have some swing, which leaves out the sea deeper than the column. Transition counts are summed over all boxes and all pairs of consecutive years, weighted by area, and each row is divided by its total. The reversed chain is P*_ij = π_j P_ji / π_i, with π the chain’s own resting frequencies. A chain’s forecast of agreement after k years is Σ f_i (P^k)_ii, with f the frequencies of the states in the record, and chance is Σ f_i²; the record’s agreement is the area-weighted share of boxes in the same state in years k apart, averaged over every such pair of years. The variant with the drift left in takes the state to be the doṣa with the largest ratio of the year’s strength to the box’s forty-year mean. The monthly chain does as the yearly one does, with each calendar month of each box given its own mean, drift and swing, between sixty south and sixty north, in the months where all three have some swing; that is 84 in a hundred of the box-months, the deepest sea again left out.

The backward game. The game is integrated by fourth-order Runge–Kutta with a time step of 0.05, forward with the step positive and backward with it negative. The measured planet’s five shares are divided among the seventeen subcomponents in the proportions of the game’s own resting mix. They are the pooled shares of Part One’s third section; the game in Part One’s own plate starts from the average of its globe’s places, which differs from them by a few points. The trip out and back is made twice, once with the engine’s floor of one part in a billion and once with the same step written out without it. What is held at the floor on the way out is human combustion, which the Earth system rule shuts out almost from the start. On the sphere the same is done with Heun’s method and a step of 0.1; the run is counted as failed when any value has grown past ten times the whole or has ceased to be a number.

The scripts

The first is Python and needs numpy and xarray. The rest is plain JavaScript and runs under Node.