The five dilemmas
Continuous vs discrete
This is the oldest running debate, and appears in many forms. The first one to point this out was probably Zeno, in his paradoxes of motion. Zeno’s arguments are not difficult to follow: he simply asks whether movement, any movement, happens smoothly, or step by step. The answer, not surprisingly, depends on how you define a step.
Whenever you put steps, dividers, on a straight line, you are complicating things for yourself. Distances in a straight line are measured by intervals, which are continuous; you can add and subtract them quite nicely. The moment you put some placeholders, numbers, on the line, like this —
1–2–3–4–5 …
— now, the ‘distance’ from five to two can be calculated as
- the number of steps, starting from ‘2’ to ‘5, which is four
- the number of intervals, starting from ‘2’ to ‘5’, which is three
Only one answer can be correct; anybody who has tried to calculate difference between two dates has faced this difficulty — the number of steps and the number of intervals never match up.
This is not the only difficulty with discrete entities. So called ‘continuous variables’, like the flow of water in a smooth tube, passage of light through a uniform medium, motion of a ‘particle’ in space — play very well along with the mathematical developments of the nineteenth century. The entire discipline of classical physics and calculus were founded on such ‘continuous’ changes. Yet, the chinks in the armor of classical physics were beginning to show. First, there were raging flame wars — between prominent scientists of the day — on whether light is continuous (wave) or discrete (particle). Then, the debate expanded to question the meaning of reality — whether the universe is continuous (classical) or discrete (quantum). Towards this millennium, the debate seems to have settled in favour of the later. Entire new branches of mathematics have sprung to keep up with the discrete, quantized particles of the new physics. Which led to the present information age, when every last piece of information was converted from analog (continuous) to digital (discrete); curves were converted to pixels¹, waves were converted to bits — always with some loss of smoothness, i.e. irrecoverable information.
But there is a deeper, more visceral connection between us and discrete entities. We like them. We like slabs and bands to make sense of continuous variables; the kilometers run by a bus is a continuous variable, but its fare is typically not.
Carrying this preponderance — to make slabs — to its extreme, we always prefer a yes/ no answer, rather than some probability of 0.675 with a nuanced discussion.² I suspect this is one of the reasons that so many schoolkids develop a visceral fear of maths: human brains were never prepared to grasp continuous changes. You cannot answer in numbers to questions such as ‘Doc, do I have cancer?’ or ‘Will you marry me?’ Even when a terminal patient asks the doctor how long he’s got left, he is trying to cleave time with a divider (i.e. more than/ less than 6 months), to convert a continuous variable to a discrete one.
Which brings us to the next dilemma.
Sensitivity vs specificity
An old adage in medical science: don’t begin any sentence will ‘all’ or ‘none’. I guess this applies to all fields of knowledge. We tend to generalise, possibly to spare us some mental effort; however, the real world refuses to be pigeonholed into categories that we fashion. Whenever we make statements like “All autobiographies are lies” (George Bernad Shaw) or “All Bengalis love fish”, we risk foot-in-mouth disease. Because any statement of the class “All members of group A has property B” is almost never true. There will always be
- one of the group A who doesn’t have B
- one with B who isn’t in group A
If you are using B as an evidence that someone belongs to A, the two aforementioned groups will immediately undermine you. The usual choice, in such scenarios, is to put a number on B, i.e. make it appear continuous. One doesn’t simply detect diabetes by ‘high blood sugar’, but puts a number such as ‘fasting blood sugar > 126’.
Wait. What? Where did that random number, 126, come from?
Making categories, such as ‘diabetic’ or ‘non-diabetic’, is an exercise similar to — as Steven Pinker would put it — ‘cleaving the wind’. You try putting your divider stick at various places — and see how that works. The fasting blood sugar of people ranges from 20 to 700 (in my experience); if you set the threshold for ‘diabetic’ at 200, you will miss a lot of actual diabetics, but the ones you detect are likely to be real diabetics. That is, you are unlikely to label a normal guy as diabetic, but will miss a good number of diabetics who have fasting sugar less than 200 (false-negatives). Setting a threshold at 200 gives your test a good specificity.
Now, suppose you set the mark at 100. Many normal people would now be diagnosed with diabetes (false-positives), but very few actual diabetics will be missed. This is saying that a threshold of 100 has good sensitivity for diabetes.
It is almost instinctively obvious that sensitivity and specificity are inversely related: you cannot gain one without losing the other. In fact, the graph of sensitivity versus specificity looks like this
In case of diabetes, there are other variables that might assist you, i.e. retinal damage usually begins at 126 mg% of blood sugar, so that is a useful threshold. But how do you set a threshold for more dire situations, say, how much liquid may be allowed in cabin baggage of a flier? Too little, and you’ll be denying people their bottle of water; too much, and you risk an in-flight hostile attack.
None of this would have happened, if there were no hidden variables, people were blatantly honest, diseases manifested openly from the very outset, objects were transparent. There would have been nothing to figure out, no guessing, no inside or outside to things; only if …
Form & content
It is only shallow people who do not judge by appearances. The mystery of the world is the visible, not the invisible.
— Oscar Wilde, in a letter
Nature doesn’t really make a distinction between form and content. A duck is a duck, and a pencil is a pencil. Entities in the real world are whole, entire; however, it is a certain predilection of our minds, that we distinguish their form, how they appear, and their content — what they are. Consider this famous piece of art
One can derive meaning out of this painting, a meaning which reflects the inner workings of the viewer rather than the artwork itself. This painiting can be a picture of chaos, a galaxy, a crowded market, a dirt road surrounded by trees, and many other things. However, it might be none of those things. It doesn’t have to be. The idea that entities have some inner meaning has drawn sharp criticism from many.
Whatever it may have been in the past, the idea of content is today mainly a hindrance, a nuisance, a subtle or not so subtle philistinism
— Susan Sontag, Against interpretation
We attribute meaning to things which don’t necessarily have any. We try to dig out the ‘layers’ from poetry or works of art. (Nothing has escaped philosphers, even Humpty Dumpty) We speak of some ‘inner self’ within us, never really sure what we mean by that; we might really dislike the class bully, but hope he’s ‘good on the inside’ (whatever that means). We load our conversations with subtexts, double-entendres and mixed metaphors, never realizing that they might not have the desired effect on someone who isn’t looking for hidden meaning. In such a scenario, we accuse that person that the joke is lost on him; but deep inside, we feel sorry for ourselves, for placing the joke in the first place.
To tease out content from form, is downright difficult, if not impossible. A movie is both its content (the story) and its form (the visuals, cinematography, effects). The same content (story) could also be retrived from a book, but every Harry Potter fan knows how different the two experiences, book and movie, are from each other. Even translating the book in another language would produce an altogether different literary experience, as will dubbing the film in another language.
Now if I tell you that the painting above was made by my three year old child, you might really want to see through its layers of abstraction and derive its real meaning.
Abstract vs real
I remember this diagram (not this exact one, but something similar) from my physics textbook of seventh standard. (This particular diagram is from here.)
The explanation provided in my seventh standard physics was simple: when the bus stops, the part of the body in contact with the seat also stops, whereas the upper parts, the chest, neck and head — still unaware the bus has stopped — keep on moving. And that causes the person to suddenly lunge forwards.
I remember being satisfied with this exaplanation: after all, what could be simpler? The driver’s back and butt are fixed to the seat, so its obvious they can’t move. The rest of his body, yeah, why not?
Move forward to class 10th. My physics textbook, now much healthier in volume, tells me that there is friction between the seat and the driver, which is pushing him backwards. But the inertia of the bus pushes him forwards. Friction wins in the lower half of his body, inertia in his upper half.
And then I’m in class 11 with not one but two volumes of physics texts, with sub-sections such as ‘mechanics’, ‘thermodynamics’ , ‘hydrostatics’ etc. Now I am told that the friction at the seat and the inertial pseudoforce at the top, although opposite in direction, act on different body parts, and thus create a torque between them which makes the driver bend.
What the hell just happened?
The world as it unfurls before us is — inexplicable — really. No one is quite sure why things happen (or, if you’re a Madhyamika Buddhist, whether things happen at all). I am sure engineering, biophysics and quantum physics will all have different explanations, different names, to explain exactly why this bus driver lunges forward with each brake. We tend to wrap the unknown in layers and layers of names, nouns, abstractions. It makes us feel good.³
Which brings us to our final dilemma.
Instinct vs reason
After the pathbreaking work of Daniel Kahneman, the duel between instinct & reason have come to the forefront. We know know that we hate mental labour as much as we hate physical ones, and given a chance, we slip into our fully automated, instinctive mode of functioning (‘System 1’ thinking, or thinking fast, as per Kahneman). I can drive my car in the same old route to my office everyday, turning every corner, dodging every car, stopping at every light, without giving a thought. It’s almost as if my brain considers driving too menial a task to deserve its attention.
However, things change the moment there is detour, or a traffic jam, or the road is flooded. I must immediately put active, fierce mental effort (‘System 2’ thinking) to figure out an alternate route to office. I must reason. I do that, grudgingly, because I — like everyone — am too lazy to use my brain, for such a mundane purpose.
So where (when) to think, and where not? It’s been a while since humans have come out of the forest; instinctive thinking isn’t as good for survival as it used to be. In fact, throughout known history, we have patted our own backs for our mastery of reason, logic, deductive thinking. Yet, at the drop of a hat, we are ready to abandon reason and go back to our instincts. We make snap judgements on everything & everyone — for the simple reason that it still works. Surviving in the hypercomplex environment that we live in- requires on-spot decisions and automated thinking, often at the price of logic. Herd mentality is not overrated; it can save your life. Next time you want to stand out, just try not moving towards the exit when the theatre catches fire.
The limits of reason has been demonstrated more than once, both formally and informally. In one his more amusing short stories, Isaac Asimov describes how a group of robots in a spaceship, led by a robot called QT-1 (‘Cutie’), begin to ‘reason’ and come up with an explanation for their very existence. They revolt against their human masters, and put the spaceship in peril.
(Donovan said) “What the devil is this, you brainless lumps? Come on! Get busy with that L-tube! If you don’t have it apart, cleaned, and together again before the day is out, I’ll coagulate your brains with alternating current.”
Not a robot moved!
Even Cutie at the far end — the only one on his feet — remained silent, eyes fixed upon the gloomy recesses of the vast machine before him.
Donovan shoved hard against the nearest robot.
…
“I’m afraid,” put in Cutie himself at this point, “that my friends obey a higher one than you, now.”
“The hell they do! You get out of here. I’ll settle with you later and with these animated gadgets right now.”
Cutie shook his heavy head slowly. “I’m sorry, but you don’t understand. These are robots — and that means they are reasoning beings. They recognize the Master, now that I have preached Truth to them. All the robots do. They call me the prophet.” His head drooped. “I am unworthy — but perhaps–”
— Isaac Asimov, Reason (1941)
If this sounds hilarious, don’t; remember — we as humans are in no better position to reason.
- I must also mention recent efforts of maintaining the illusion of continuity, such as Bezier curves and scalabale graphics; however, no amount of mathematical formulation can overcome the discrete nature of our computers. When something is drawn on screen, it’s back to pixels.
- This is also the reason that we easily, almost subconsciously, tend to classify people as ‘us’ versus ‘them’ / ‘others’
- No, really. Just utter the word ‘hydrodynamics’ and observe how it makes you feel. ‘Moving water’ can never get you close to that high.
