Monday, January 19, 2009

Math and Counting

The man who reforms society is still caught in society, being free from conditioning he will act in his own way, which will act again upon society. So our problem is not reformation, how to improve society, how to have a better Welfare State, whether communist or socialist or what you will. It is not an economic or political revolution, or peace through terror. For a serious man these are not the problems. His real problem is to find out whether the mind can be totally free from all conditioning and thereby perhaps discover, in that extraordinary silence, that which is beyond all measurement.
K, London, 17th June 1955

I was walking back home with my daughter. She has inherited very less of my physical features (which is good) but mirrors a lot of my inner being (the goodness of which I am undecided about). She is the only person on earth who readily and effortlessly connects to my thoughts and views and like a flowing river cleanses the water that was once there. Our thoughts and inner unrest cohere on such excursions into silent worlds and still paths - as paths inherently are; isn't it amazing that the path we take to go somewhere doesn't go anywhere? All the grand movement of the world has been along paths which are still there, perhaps repaired, but dustily there - where unrelated topics swerve into deep conversations.
We were discussing school - her marks in the exams weren't good - and about the education methodology that her school follows. She was not sure whether she should feel bad about her results. I wasn't sure either, so I offered that we should feel bad for about half hour and then reflective for another half before rejoicing in the results for a final half hour's duration. She was willing to try this out (and it was her indecision which helped sell this idea, else we would have debated this). We were also discussing our neighbours and about the demonstrated selfishness of the young lady of that house. We were also discussing prices of vegetables as we had to go back home and write accounts though we wondered why we did that and whether growing our vegetables was an option and so on. I think it was the latter topic which rammed the doors open to our deep pondering. Allow me to paraphrase what might have been the words we exchanged before I quote the actual discussion.
"Why do we need to write accounts?"
"So that we can keep track of how much we spend on particular things."
"So that we know where to cut down if we need to budget."
"But can we do without veggies or the rice we eat?"
"Perhaps not, but we can learn to adjust with less if a day calls for it."
"Which is something that R next door doesn't now and hence the shouting and screaming."
"Don't gossip! R's problem is beyond that. She is not really interested in living as a family and hence is more keen on wanting more than she can offer to the health of the family. One needs to better understand the motivation behind such a person wanting a family in the first place."
"S! How immature of you to call people names without knowing sufficiently well about them!"
"Anyway, I suppose keeping accounts would help me put my math education to use."
Something like what was quoted above lead to the following:

"Dad, why do we need to count?"
"In order to measure, in order to plan, in order to budget, in order to predict, in order to capture knowledge about the functioning of certain systems, in order to prevent hazards arising from miscalculation, in order to ration things out, in order to estimate and several more reasons."
"I understand, but it feels unnatural."
"It is, sweetheart. It is a creation of man, and like most of the creations in there, it is rather unnatural. Counting per se is unnatural though measuring isn't."
"How so?"
"Measuring when it is a perceivable manifestation of a sense of rightness, is natural."
"Not clear."
"Well, Nature knows how much water will evaporate when exposed to heat. Nothing more, nothing less. It is natural and not something that one can will differently. Nature doesn't allow for a sapling to flower or bear fruits and the maturity of the plant or tree is measured before allowing for that. Mountains cannot grow indiscriminately. There is a measure which is controlled by the physical attributes of the rocks composing the mountain, gravity and isostasy."
"You saw Stacy?"
"Isostasy! Something that is used to explain the point at which the mountain base turns into mush due to the increasing weight above it. Let's go home and read about it."
"Ok, so measurement and counting are two different things according to you, right?"
"For the sake of a discussion, yes."
"And keeping accounts is?"
"Aah! Good! So do we need to count?"
"On?" (and this is where I always turn to look at her and love her even more. She listens and treats words seriously unlike people who would simply nod whenever I say "Depends". She has beautiful eyes, if you would allow me an aside.)
"On where you are and where the world is."
"Dad! Are you trying to evade this conversation as I have no hassles dropping it and going back home and doing the accounts till the day when I get married and have an intelligent daughter who would ask me "Why do we need to count?"?"
"No, sweets. I am dead serious."
"Ok, then explain."
"Let me give you an analogy before I proceed. There is this world which about 100 square feet. In a corner is a little gramophone record player which..."
"We are buying the gramophone record player, right?"
"Not now, but eventually, yes. So in the corner is this little gramophone record player which continuously flowers music. People are growing deaf and then they die when they are totally deaf. You want to switch off the music so that people don't suffer, but everyone else stops you from doing so. Their only way of knowing that they are alive is the music - if they can hear it, they know they are alive. And you plan to turn it off for their benefit?"
"Hmmm. And this is related to counting, how? You are saying that if we stop counting the world as we know it will collapse?"
"Or it would require the re-birth of an entire world which consciously notes the point at which it felt the need to measure and also count."
"The former is of no use, so let's go with the latter."
"Perfect!" and I held her closer. Sometimes a pointless hug means that I am still alive. S knows that and threw her arm around my waist.
"You are going to explain, right?"
"Of course. I don't think there is a need to count in order to be alive. So, if all I am interested in is eating my fill, sleeping when I want to and waking up when I am done, performing tasks because I need to survive and not be at the mercy of the elements, because I have no fur or claws but a brain which also needs to be protected then I do not need to count. Let us take a normal day..."
"... on an island where E and his daughter S are the only inhabitants and no can enter that place."
"I wish I get to see such an island."
"Not sure you will like it. Then you will hate me for having made it so enchanting by including it in all my theories."
"You sure know how to spoil a moment, don't you!?"
"Anyway, so on this island we wake up and stretch ourselves and brush our teeth. No counting needed so far. Then we walk around and get a few coconuts and some fruits and veggies."
"No accounts so no counting."
"Well, no counting because of no accounts but also no counting because we eat to our fill. We do not pluck beyond what we know is necessary for a meal. That is measure and not counting. One might be hasty to say: Oh! You picked 2 coconuts or a handful of figs so you are counting. That would be, as I said, hasty and silly. If we walk a thousand footsteps and know that we are going to get tired soon, and then repeat that several times before we automatically know when we are going to get tired and when we are going to get hungry, then it is measure and not counting. Of course, we see only one sun. Should we call that knowledge counting? No! We can see five coconut trees in front of us and one is rotting. We don't need to know counting to realise that we should plant some more trees. There is a huge difference between intrinsic measure and contrived counting. Are we together?"
"So far, yes."
"So we don't need counting till our breakfast. We know by experience the exact amount of sea water to use to cook our veggies, and we will rub the twigs till the fire is made and not till we reach the count of 582 twirls of the stick. We eat not 134 gms of potato but the amount we need to not feel hungry. If there is only this much tomatoes we set aside some for dinner. It might turn out to be less or more but that is fine. No one is giving us Michelin stars for our culinary capabilities or our standing as restauranteurs."
"Well, it is only the two of us, so its ok."
"Well, if we extend this to any number of people, it will still be ok if we understand the philosophy behind this. Then we walk around the island, write, read, sing, plant trees, build hammocks and watch the sunset and dance after dinner. Nothing needs counting. We are alive and hopefully happy but haven't had to count. We celebrate any day we want as your birthday. We make strawberry cakes whenever we feel like. We build sand-castles and design kites out of dried leaves and coir without having to count. Essentially we live and enjoy living without having to count."
"Ok. So now we are a village of fifty people. How does it scale?"
"Everyone consumes what s/he needs and produces enough to satisfy the village's wants. How much is the want? That is known by experience and understanding. The ability to count doesn't assure accurate estimates. Estimates is still a function of experience. For the farmer to know how much land he should bring under the plough and whether the signs in the sky auger well and whether he needs to repair his barn or not and how much of the produce will typically reach the cooking pot is not something that the ability to count helps. It is experience. Like a ironsmith who says that you need to heat the rod till it is hot enough to hammer. He doesn't talk in terms of degrees celsius or other counts. He heats the rim till it just fits the wheel before rapidly cooling it. No counting there; just experience and a measure of rightness."
"What about food? Someone will want more and some less."
"But there is only so much. One could increase the land that is tilled. The want for more could be a physiological aberration or plain greed. The latter has brought us to the state of the world as it is today and the former can be treated through medicines."
"But we need to count the millilitres of medicine that we give him."
"Or have a measure of the right amount. No doctor knew the right amount of a medicine without experience. No medicine discovered came with a count as to how much of it should be administered. The measure was obtained from experience. Earlier it was tried on human beings and now on monkeys and fruit flies."
"Indeed. Human beings are inherently destructive and greedy but are also the only creatures that can save this world from self-annihilation."
"The problem and the solution."
"God and Devil."
"But aren't you just using measure as an alternative to count? Isn't that just playing with words when the act is essentially the same?"
"Not really, sweetheart and don't drag your feet. I have told you what that does to the footwear."
"Let me give you an example. You know how much milk you want. That is measure. Do you count the ml of milk you drink? Watch animals around you and you will know how measure and counting are different."
"They probably do the counting unconsciously."
"If it unconscious then it cannot be counting. If you ate a measured amount of bonbons till you felt that any more would not do well for your tummy, do you know the count of how many you ate? Definitely not. If you had kept a count and at around 20 thought that this was too high a number and probably you should stop, then it is counting and not unconscious. If you did it unconsciously and then counted the wrappers then too the initial phase was measurement and the latter was counting - one unconscious and the other conscious."
"I get what you are saying, but I am not totally convinced."
"If you were blind and I was feeding you dinner with a spoon and I was also telling you a story, would you or not tell me when you are full? Does it depend on the number of spoonsfull you had? Does it depend on the duration of the story? Does the story's import depend on the amount you ate or the minutes spent?"
"Remember R's wedding we went to?"
"Do you recall how the cooks prepared the meals? None of them used teaspoons or weighing measures to decide on the amount of salt or dal to add to the dishes, did they? They didn't use beakers to measure the water to be added. You can call it counting. I call it measuring. All things natural are measured. You cannot count happiness or fear or greed or inspiration. They can only be measured."
"Ok. Now that makes sense. So I understand that counting is not instinctive or natural, but does that mean we can do without it?"
"If we accept that counting is not natural then we automatically know that we don't need it for survival. All that we need for survival has been provided to us by Nature and nature."
"But that would mean that we live like animals."
"Which is why I said, you cannot stop the music though you know very well that the music is not needed for the people in the world to be alive."
She held me tighter and I knew she was able to realise the place that counting has in this world.
"Then we need to understand where counting is vital."
"I suppose in budgeting and planning and the other things you mentioned."
"True, but before we go there, stop to think why do we need to do them."
"Because if we don't we can run into trouble."
"So counting is essentially a means to avoid running into trouble. It is our tool to prevent miscalculation, under-planning, under-utilisation and missing opportunities to gain from the environment around us. It is essentially a means to compare and contrast which measuring can never help in. I can never say which has more right sweetness - this dish or that if they were both prepared with a measure of rightness than a count of the number of spoons of sugar. Mind you, even with your count every batch of sugar and every ounce of green chilli you buy has a different taste and you need to alter your counts to match rightness of taste. Counting is a predictable way to avoid failures and re-learning or as cynics say: re-inventing the wheel. But the point is, we are re-inventing and measuring nearly every day in so many spheres of existence. We need to know whether to run at this speed or more to catch the bus that just left the bus-stop. No, you cannot and should not do that. If it has left then you wait for the next bus or reach the stop earlier. No climbing into a running bus."
"Fine dad! I won't. God!"
"We count a lot and then we store them in our head in order to create a safe world where things are predictable. We now have manuals and guides to tell us how much of this and how much of that should be there in order to produce X quantity of that. Then something changes (ore quality, fibre content, sucrose levels, tensile strength of raw materials, brittleness, etc.) and we are upset and we count all over again. Counting has essentially cut off the sense of measuring in human beings. Somehow monkeys know that a particular fruit is going to be sour. They know with one step on a branch whether it can take their weight or not. Counting helps us be safe and cocooned with the surety of the world around us. We don't count the amount we breathe or the number of breaths. Hence, counting is not necessary."
"But is counting essentially wrong?"
"Nothing is inherently wrong or right. Counting isn't when applied to certain technological and scientific things. Do we need them for living on this earth in harmony and in peace? No. Like most other inventions of man, counting helps only this much especially where re-invention has little benefit over the invented. For instance, if I know that this much temperature is required to fabricate silicon wafers and then so much photoresist is allowed I probably do not want to discover those measures every time I make a new wafer. It is far too wasteful to do that. I could probably feed them into control panels and have a self-managing manufacturing plant."
"I didn't understand a word."
"Ok. Let's try again. Do you remember the tea tasting ceremony we went to? There they explained how tea was manufactured and the oxidation process etcetera? So there are manufacturing units which know the temperature that should be maintained and the height of the drying beds and so on. Such knowledge is not worth re-inventing at every harvest as it would lead to excessive wastage. Here, I think, counting is utile. There are similar areas where it is worth using knowledge that comes out of experience."
"How does one decide?"
"By a measure of rightness. It is so simple if only we are comfortable with simplicity. But we cannot accept simple solutions as they all expect the human being to be simple too."
"But that doesn't quite happen."
"It doesn't and it won't. Man is inherently insecure and counting is the strongest pillar he invented to build his fortress of greed and grandeur."
"Woah! That is strong."
"No, sweets, listen. He started by counting the deer he killed and the men he could defeat. He built walls and then higher ones. We count spears and the dead to decide who should rule a piece of land and then count the number of heads that bow down and the acres of land under one's seal to decide who is more powerful and hence who should be more respected. We searched new lands and burned more forests to create food for the countless. We wallowed in orgies and feasts while a poor man starved because we counted greatness by the amount we could afford to waste. We invented new ways of military murder and sought better weapons to kill more with least effort. The less blood-thirsty invented money and used counting to decide who was richer and more powerful and likewise who could be enslaved or not. Then we measured the worth of science by the lives it could take or save but never bothered about the natural balance we were disrupting leading to more consumption and more resource utilisation. We count on providing a better standard of living at the cost of a measure of better living. We would burn more forests and build taller and grander buildings without measure though we would immediately count our expenses and investments in the same.

This need to count migrated into our relationships where we became calculative and want more without a sense of giving and balancing the measure of mutual happiness. The philosophy and the need to count is essentially the same whether it is done with numbers or with greedy wants. The ability to count creates a security in taking and hoarding. One who cannot count will only take what he needs and he who can see your pile of gold as being higher than his needs to count to ensure that the total weight of his is more than yours. With the ability to count comes the possibility of comparison and with that comes the illusion that that which is calibrated is less important than the calibration itself. If you look around you, everything is a count. All of business is a count, a count for profit, more revenues with least regards to things that cannot be counted - ethics, morals, exploitation, fairness. All of relationships has become whether the husband has bought more diamonds or not and whether the wife has mothered more sons or not and whether the parents bought X clothes and gadgets every month or not. Everyone is trying to grab and take whatever they can because they count and compare with others. All of education has become grades and scores and percentages and not what one has understood and what one can apply to the betterment of life around us. All of life is a count of what we have done, seen, owned, possessed and spent."
"So I needn't worry about my Math grades?"
"You better! Forget about the scores but figure out why you didn't understand the concepts well enough to use them in the exam."
"But I can stop counting them, right?"
"If you can stop the music, yes."
We walked on for a while silently.
"I spoke too much?"
"Who's counting?"

Counting has a purpose. Recognising that, is wisdom...


  1. Drifted in here after a very long time. But who's counting *Grin* ?

    Its winter break - Very very cold. I'm recovering from a nasty flu. Had a good read.

    It is sad that the world exists in numbers and has forgotten to live by measure.

    I guess I need not tell any more :)

  2. no one can write as good as you! am an anonymous fan of your blog!!
    ps: btw even i dono who u are!

  3. Parvati10:20 PM

    You have a grouse against the products and instruments/aids of the mind and against counting too, it seems, as being one of them. I wonder why.

    You lean strongly towards life and nature as they were before man's mind came into the scene. But it is impossible to go back in consciousness - we have to be consciously natural unlike we now are - semiconscious, contrived, unnatural, unspontaneous, always in a non-smooth staccatoed movement thanks to our mind - but also unlike animals or the rest of nature, unconsciously natural and spontaneous and instinctive.

    Counting, measuring and calculating will be replaced then by an accurate innate knowledge of the exact requirement without the fumbling that mind has to go through now from ignorance to knowledge.

    Until then, "Mummy!, dont throw away my abacus!"

  4. Dear A,
    I agree, it is sad.

    Dear N,
    Welcome to this blog. Sorry for the delayed response. I am glad you find the posts so. Not many people know who I am, which is probably good!! ;-)

    Dear P,
    No, I do not have a grouse, so you needn't wonder! No I do not lean towards that state of mind before any particular time nor am I making a plea to go back to any particular state of consciousness. I just wished to explore how we create struts for ourselves and then live in conviction that what was created cannot be removed from life itself. We believe that the instruments we create our vital to life.