What is abstraction, really?

Power of two

Imagine yourself an ancient tribesman. You are sitting on a dull rock in a hollow cave, surrounded by family, sitting by a fire whose crackle punctuates the howling air deeper into your temporary resting place.

Another night of idle thought. Then warmth.

Struck by a curious feeling, you see fire as if for the first time. You ask: “Whence fire? What is this that sustains us through the night?”

If you were the sort for whom details are paramount, you’d think: “Fire comes from rubbing sticks. Fire comes from wood. When lightning strikes wood, fire also comes.”

You treasure these facts like you treasure your axe and your dagger. In time, your collection will grow, and you will feel that you have put your question to rest.

But imagine yourself a different sort. A sort of mind perhaps closer to the Thales and Pythagoras than perhaps Archimedes. A different line of thought, you ask, “What else is fire? Which of the things I see is also fire?” Then perhaps you will be led to consider that all substances must come from a single source. A single essence underlying all things1.

Mathematics is borne of these two cultures. The first mathematician collects facts in the universe and finds himself splitting them into more and more groups. He assembles a catalogue and finds satisfaction in the particular patterns emerging from his arrangement.

The second mathematician conserves his categories. He asks not what million things one can say about a specific fire, but of the single thing-that-all-fires-are. He looks at fire not as it is, but as a member of a general class of fire-like things. And to him, it is in this class where all fires are the same.

Tim Gowers is a ‘functional combinatorialist’. He won the Fields medal in 1998 for connecting functional analysis and combinatorial analysis, two fields sharing the property that their problems are relatively easy to formulate, but are extremely hard to solve.

In his article, The Two Cultures of Mathematics, he opines that mathematicians can be put on a single spectrum: on one end the problem-solvers and on the other the theory-builders. This is not merely fanciful myth-making: one can roughly predict the sort of fields a mathematician will eventually do her work in by knowing where she lies on this axis.

Now, for thousands of years, the first mathematician dominated the activity of mathematics. From the Babylonians who collected particular relationships about particular triangles (but apparently never bothering to generalise to the Pythagorean theorem) to the machinations of geometers and arithmeticians in Ancient Greece and China, the search for more and more elaborate patterns became tied to the growth of civilisations. And this makes sense, for you need particular mathematics to plot and divide land. You need particular mathematics to engineer trebuchets and build aqueducts. You need a catalogue of mathematical results in order to advance your king’s military and economic agendasometimes under penalty of death!

But what do you do, once you have a collection too big to fit in your head? And how do you transfer your showpieces to other heads?

For that you need the second mathematician.

Buffon’s buffoon

It is easy to doubt that the practice of mathematics has such a divide in the first place. To help assuage this skepticism, let me treat a problem in the two different ways I mentioned.

The Buffon’s needle problem goes like this: suppose we have a floor of tightly-spaced wooden slats of equal width. If I drop a needle of some length onto the floor, what is the probability that it will intersect the one of the dividing lines?


  1. And if you were indeed Thales of Miletus, you would consider that ultimate substance to be water, ironically. 
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The Eightfold Path to the Calculus of Constructions

Has a dog Buddha-nature?

This is the most serious question of all.

If you say yes or no,

You lose your own Buddha-nature.

— from Chapter 1 of the Gateless Gate

In the beginning, there was nothing.

Then Alonzo Church came and said, “Let there be:”

variable [x]
a symbol or string of symbols that represents a particular value
λ-abstraction [(λx.E)]
a function on the λ-term E, with the variable x bound to E
application [(E F)]
applying the λ-term E to the argument F

And thus all three and only they attained λ-nature (i.e., are valid λ-terms).

Whence cometh these λ-terms?

Consider the noble function f(x) = x^3 + 1. We note that the name f is illusory and thus we can rewrite the same function as x \mapsto x^3 + 1. A λ-abstraction then is simple another way of writing this expression:

(\lambda x\;.\;x^3 + 1)

This is not a trivial transformation, however, as this also binds the variable x to the λ-term x^3 + 1. Their destinies are forever intertwined within their confining parentheses and hence the expression (\lambda y\;.\;((\lambda x \;.\; x^2)\; y+1)) is equivalent to (\lambda x\;.\;((\lambda x \;.\; x^2)\; x+1)) even though the variables have the same names.

To keep the expressions as elegant as possible, we shall adopt the following rules:

  1. Application is left-associative: (E \; F \; G) is equivalent to ((E \; F) \; G)
  2. The outermost parentheses are omitted: write \lambda x . x over (\lambda x . x)
  3. The term in a λ-abstraction extends up until a same-level closing parenthesis is found: (\lambda x . (\lambda y.E) \; F) is equivalent to \lambda x.((\lambda y.E) \; F), not (\lambda x . (\lambda y.E)) \; F
  4. Successive λ-abstractions can be combined under a single λ: \lambda x.\lambda y.\lambda z.E is equivalent to \lambda xyz.E.

Meditation: Which of the following do not have λ-nature?1

  1. \lambda x.x
  2. \lambda x^2.x
  3. \lambda x . 1
  4. \lambda xy . (\lambda zx . z^2 + x^2) \; y

Any λ-term may be further transformed according to the following reduction rules:

α-conversion
from \lambda x . E to \lambda y.F, where F is the same as E but with all instances of x replaced by y; only bound variables may be replaced in this manner
β-reduction
application to arguments leads to substitution by those arguments, e.g., (\lambda x.x^2) \; 3 is equivalent to the λ-term 3^2
η-conversion
functions are completely determined by their arguments, i.e., \lambda x . (f \; x) is equivalent to f iff all instances of x in f are bound

We are now ready to contemplate the truth2. Consider the following definitions:

  1. \text{TRUE} := \lambda x . \lambda y . x
  2. \text{FALSE} := \lambda x . \lambda y. y
  3. \text{AND} := \lambda p . \lambda q . p \; q \; p
  4. \text{OR} := \lambda p . \lambda q . p \; p \; q
  5. \text{NOT} := \lambda p . p \; \text{FALSE} \; \text{TRUE}

Meditation: Show that OR FALSE TRUE evaluates to TRUE3.


Do not be fooled: the simplicity of our system hides a profound strength. For instance, contemplate the following:

  1. \lambda fx.x
  2. \lambda fx.f \; x
  3. \lambda fx.f \; (f \; x)
  4. (etc.)

What do they do with f and x? What happens if I apply the two-argument λ-abstraction \lambda xyf.x \; (y \; f) to (2) and (3)? To (3) and (3)? To (1) and any of the succeeding λ-abstractions in the list?

Indeed, we have defined an operation that behaves like multiplication on a list that behaves like numbers. We have:

0 := \lambda fx.x
1:= \lambda fx.f \; x
2 := \lambda fx.f \; (f \; x)
(etc.)

And in general these numerals (called Church numerals) repeat the functions to which they are arguments. So for instance, if we rename our multiplication λ-abstraction above to \text{MULT} := \lambda xyf.x \; (y \; f), then:

\begin{aligned}  \text{MULT} \; 2 \; 1 &= (\lambda x y z . x \; (y \; z)) 2 1 \\  &= (\lambda z . 2 \; (1 \; z)) \\  &= (\lambda z . 2 \; (\; (\lambda f x . f \; x) \; z\;)) \\  &= (\lambda z . 2 \; (\lambda x . z \; x)) \\  &= (\lambda z . 2 \; (\lambda \alpha . z \; \alpha)) \\  &= (\lambda z . (\lambda f x . f \; (f \; x)) (\lambda \alpha . z \; \alpha)) \\  &= (\lambda z . (\lambda x . (\lambda \alpha . z \; \alpha) \; ((\lambda \alpha . z \; \alpha) \; x))) \\  &= (\lambda z . (\lambda x . (\lambda \alpha . z \; \alpha) \; (z \; x))) \\  &= (\lambda z . (\lambda x . z \; (z \; x))) \\  &= (\lambda zx . z \; (z \; x)) \\  &= (\lambda fx . f \; (f \; x)) \\  &= 2  \end{aligned}

Note: it may be best if you do this calculation by yourself using only the reduction rules above.

We may now describe the machinations of any sort of calculating apparatus by defining what “computability” is:

Computability
a function f on the natural numbers is computable if, for all its outputs, there is a corresponding λ-term that β-reduces to the output’s Church numeral

Or in the Platonic realm of mathematics, if I can find a λ-expression F \; x' =_\beta y' that is equivalent to f(x)=y where x' and y' are the Church numeral representations of x and y respectively, and by E =_\beta F we mean you can get F from E by a series of β-reductions and vice versa.

Or in plain English, if anything I can do using f in the world of math, I can also do using a corresponding F in the world of λ-calculus.

However, our symbolic excursion hides an uncomfortable truth. Can you guess what it is? (Hint: it involves the operator NOT.)

 

Consider the following derivation:

Let k := \lambda x.(\text{NOT} \; (x \; x)).

\begin{aligned} k \; k &= \lambda x.(\text{NOT} \; (x \; x)) \; k \\ &= \text{NOT} \; (k \; k)\\ \end{aligned}

We have just demonstrated a paradox, an inescapable death knell to our naïve λ-calculus.

Wither our quest to bring forth computation? Is computer science a vacuous discipline after all?

Stay tuned for the next in this series.


  1. Answer: (2), which is only valid if you consider “x^2” a string; note that (4) evaluates to a function and can still be applied 
  2. I’m just gonna follow the exposition on Wikipedia here. 
  3. Just use β-reduction until you arrive at \text{FALSE}

Smorgasbord (Aug 2018)

Chain-linked fences

Noahpinion gives three examples of proto-rationalist movements from three different places in three different periods. Someone ought to make a rationalist genealogy one of these days.

A Rationalist Tumblr classic: Ragged Jack Scarlet gives a binary model of why communities have heroes and grunts: because some people follow the idealised values of the community and some people are just there for the company. Precursor discussions to this divide include Geeks, MOPs, and Sociopaths and the classic Gervais Principle.

Something’s afoot in the Bay Area Rationalist community and people are going nuts. Granted, the last post was written two months ago but I haven’t seen any sort of comprehensive response from Bay Area rationalists.

A hilarious and Kafkaesque story about a Forgotten Employee, written in the early 00’s.

And for my last link for today, a 5-page post-mortem of the 2011 Portal 2 ARG from Gamasutra.

Wild Machine Guns

A way to break out of the whole “all stories are human stories” thinking in writing: roleplay an alien writer with blue-orange morality [WARNING: TVTropes]. E.g., an alien averse to resolution? An alien for whom love and conflict are one and the same? Someone whose ideaspace boundaries are inherently different due to a difference in biology and evolutionary history?

Can you craft heroes for propaganda purposes? (One of my classes mentioned how Americans erected statues of a local academic, nonviolent propagandist in every town in Country X, major or minor, so that they can set up bases with minimal conflict. Wasn’t enough, it turns out.)

Leadership in almost every human group requires strong precommitment skills. People follow certainty and consistency, even to the point of discarding new and contradicting evidence. This may or may not eventually doom us all.

Pen exercise: My Feelings on Grothendieck

Constraint: write about what you feel when you read excerpts about The God of Abstraction.


I’ve been a physics student for seven years now, and if you include my youthful incursions into the subject, even longer. In my journey I have seen a lot of clues, a lot of suggestions from a variety of sources: the motion and push and pull of things I can see, the way our experiments (or what I would like to think of as ‘penetration tests’ of reality) resolve themselves in particular ways, even the solutions we get from the idealised world in our problem sets. There’s a unity behind all those things, a vantage point from which everything becomes simple, or if not as simple as possible then a vantage point from which all have their own natural places, at least.

Whereas The God of Abstraction has bequeathed us a unifying worldview for the discrete and the continuous (and indeed a proof-by-example that abstraction, or rather the right abstraction, can be used to resolve confusion), the situation in physics is not as fortunate. We live in only one of many possible realities, whereas mathematics is a vast ocean that extends infinitely in all directions and suggests an incomprehensible depth we can only sense in vague ways via computational complexity considerations.

Where then is the conception of reality that is simple, true, calculable, and inevitable? We express our models in austere equations yet they stumble from even minute deviations from the idealised case. We attempt to explain reality by introducing small deviations from our ideal models, and in a particular way where we can ignore higher-order effects? Two days ago I was confronted with a humongous equation describing in full analytic glory the dynamics of a (2+2)-body system, by which one can take to mean two Earth-Moon systems orbiting each other. This equation filled many pages and I daresay no mortal can ever hope to understand it if only on its own terms. And this is okay? So long as it reduces to nearby ideal cases?

Models of equivalent explanatory power are interchangeable, hence we are free to choose whichever suits our human preconceptions the best. If we cannot take in the most accurate map of reality in our minds (and we cannot, for the only truly accurate model is reality itself), then perhaps we can get away with a simpler model with simple boundaries and simple regions. And there are only very few things which are simple to us, conceptions which we can take for granted a priori by virtue of being a species forged from the dry African savannah. Barry Mazur gives us an incomplete list, with a particular emphasis on our mathematical cognitions (really they aren’t as specialised and as particular to mathematics as they seem):

First, our physical intuition. Our understanding of causes and effects, of push and pull, of movements and their causes as we see them in the world. It is what enables us to take objects or phenomena out of reality and into our heads and run them as if in a computer simulation.

Second, our computational intuition. Processes, algorithms, counting, our counterargument to the Halting problem. It is what we use to anticipate the completion of processes and induct from a laughably few examples (really, an impossibly huge number of examples obscured only by our unawareness of our own sensory data).

Third, our geometric intuition. To build from basic notions a specific thing, like a bird building its nest from humble twigs. The fuel that powers our engineering marvels and the metaphorical fuel that will (eventually) bring us to the stars.

Lastly, our algebraic intuition. Our capacity for abstraction, to sense the essence of things, or in the spirit of one of its greatest possessors, to see the vantage point from which things in consideration appear easy and most natural. This is our capacity to compress our models of reality and draw simple boundaries along its joins.

Four intuitions from a single cluster in mindspace. The task to win, to survive until the last black hole evaporates and perhaps a little longer.

Physics brands itself as the fundamental vantage point from which everything can be understood (in principle). Really, there is no ‘physics’, no ‘chemistry’, no ‘biology’, no ‘philosophy’. There is only reality, the vast swaths of which we are yet bereft of an explanation, let alone of control. To our children we shall seem blind and deaf. To our children’s children, a mere higher-order effect they can handwave away, impossibly small and weak, like motes of dust in a sandstorm. But this future is not guaranteed. It is but one of many, one where we do not fail in our inexorable march towards winning this race towards the natural chaos where all things eventually go (and perhaps a bit further).

So unity. We have so many toy models, submodels, barely compatible pockets of coherence in our best-possible-map-of-reality we call our ‘physics’. Rare are those who simplify and compress: the last great practitioner of this lost art was Maxwell, and even then he failed to utilise the simplest possible formalism available in his time. Now there is no one. A tradition in dire need of resurrection. A true resurrection, not the goings-about by textbook authors who seem more concerned with imitation and deference to Nobel Prize-winning authorities than with a genuine presentation (really, the charitable interpretation is that it’s difficult to write down our best-possible-model at all rather than a conscious attempt at copying).

But how will this resurrection be made possible? A clue is found in both the youth of the God of Epistemic Rationality and the God of Abstraction. The former arrived at and extended Quinean naturalism by himself, the latter reinvented Lebesgue integration by himself. It is therefore this brave and arduous act of independent cartography, of seeing what is out there and making the map yourself which produces the quality of thinking needed to even begin at the task of simplification and generalisation of our best-possible-map.

This then is our crossroads. Of the people who have the physiological capacity think independently for extended periods of time, there are very few who get the corresponding (and it seems, necessary) period of isolation in which they would be able to practice this capacity in full. The opportunity for a Lebesgue-integration moment is not available to all, especially at a time when it is most needed (i.e., during one’s formative years).

If one has missed this fertile period of one’s intellectual development, can one still compensate by undergoing such an activity at a later date? Perhaps, but it should be noted that the fertile ground available to a would-be cartographer recedes in proportion to one’s schooling, for it might happen that one exhausts cursory familiarity with all fields accessible to a beginner, thus forever tainting the independence of one’s work.

Still, I believe reality is sufficiently large that we are not yet, in these modern times, at the point where such an exhaustion of fields can take place. There will always be fertile ground for an aspiring rationalist-empiricist, and if that ground recedes unreachable for everyone it shall be our duty as a society to enforce a temporary ignorance in special institutions in order to allow such an important activity to those who shall need it.

Coddle our cartographers. They are our only hope for sanity in this vast and lonely universe.


Definitions

The God of Abstraction
Alexander Grothendieck
The God of Epistemic Rationality
Eliezer Yudkowsky, since E. T. Jaynes is dead

Gabriel’s golden-plated horn

Note: I was originally going to publish this around March or April this year but life got in the way.


(I)

This year, I decided to give in.

I know I’m not alone when I say that I feel I’ve been deprived the chance to express myself musically since childhood. Unlike very fortunate young boys and girls with overbearing Asian parents, my journey into music has been an uphill battle ever since. My earliest musical memory was when I was being commended for having played by ear ABBA’s “Dancing Queen” on a keyboard at three or four years of age1. And then, silence. For a considerable number of years.

Fig. 1: Can I just say how much I DIG Chris Potter?

I belonged to a semi-musical extended family. Being of Race X, I lived with all my aunts and uncles and their sons and daughters and dogs (no one owned a cat in our little village) and I remember my cousins being frequently chastised by their mothers for having formed high school bands. It will “ruin their lives”, they said. So my cousins had all these instruments lying around: keyboards, guitars both wood and electric, perhaps even a drum set (I have to verify this with them next time), and so it was both exciting and aggravating for me as a kid to hear them perform in their bedrooms. Exciting, because hey, it’s music (though not necessarily good music) but aggravating, because as a kid I wasn’t really allowed to touch any of their instruments2.

Years passed until I got my first guitar when I was in sixth grade. An $80 wooden guitar coated with black (as black as my feelings at the time (yes, I had an amazingly embarrassing teenage period: a story for another time however)). I loved every single bit of it, of course, down to the painful calluses on my fingertips, but by then it wasn’t the music which led me to buy it. It was puberty.

Discipline was never my strong point. But when I wanted something, I got it. Within a month I was attempting to imitate Sungha Jung’s rendition of More than Words. This wasn’t as impressive as it sounds, ’cause really I haven’t any conception of high standards then. What constituted an “I can play Sungha Jung.” then was being able to evoke the idea of being able to play the thing. Heck, in my circle of friends then, being able to fingerstyle was the peak of achievement. I hadn’t yet the sense that more is possible.

But then again, it wasn’t really about the music. I had two girls to impress. And I convinced them to have lessons with me under our resident music teacher.

Okay, I’m fibbing a bit. The reason why I got my guitar that late in the game was that I was better as a singer. The reason why I didn’t actively pursue a singing career was that singing was for “faggots” in my school. I’m sorry.

(II)

Let’s go back to our original topic. With abject failure in leadership and people management staring me in the face, I decided to try my hand at something that isn’t a uphill battle for me, which is, well, music. I like to think that my strengths lie in my senses. I have perfect color vision (according to the Farnsworth-Munsell 100 hue test). I can smell when people are hungry3. My cooking has (almost) never failed my friends of supposedly exacting tastes4. And I was surprised to hear that hearing multiple independent voices à la Bach is still something of a marvel (to be fair, I can only hear up to three voices simultaneously (with perhaps a fourth voice if I cheat and whistle) whilst Bach could, in theory, hear six).

Fig. 2: Yep. Six voices indeed.

So yeah, it seems my world is vibrant and colorful and loud and it’s fascinating how The Lottery of Fascinations led me to virtual reality — anyway, I decided to pursue something that I am actually maybe naturally good at for once and it has been quite a ride. Having a healthy dose of impatience has led me to a double-prong strategy to my “self-induced musical masturbation”: I am picking up FL Studio and the saxophone at the same time, learning a hell of a lot of theory and technique and all about this wonderful intersection of expertise and aesthetics along the way.


Definitions

Race X
my ethnicity
University X
my university
FL Studio
a digital audio workstation (DAW) that until recently was considered a toy by producers because of its intuitive interface

  1. So it is very possible that my recollection of this is just a false memory.
  2. There was this one time my dad threw a birthday party for me when I was six or seven and I distinctly recall two new experiences for me that day: eating mutton for the first time, and being reprimanded for fiddling with the drums of the band my dad hired (which was doubly worse ’cause, well, it was MY birthday after all).
  3. It actually isn’t as difficult as it sounds. People’s breaths smell different when they’re hungry (see this r/AskScience post) and I sincerely used to believe this is something that anyone can notice once known, but I’ve been proven wrong about it enough times to change my mind.
  4. This born of University X being situated near Maginhawa Street, one of the most intensely competitive concentrations of food businesses in Country X, where the six-month survivability of your concept restaurant is made or broken by the opinions of your first few college-aged customers.

Smorgasbord (Jul 2018)

Note: Every month from now on, I’m going to collect all the dust and cobwebs in my head, sweep them into one big pile, and sell them to you. Isn’t that great? Oh, and quotations. And links. A lot of them.


 

Nodules galore

I’m currently drafting a Zen-themed post on type theory and kōans still make me chuckle in confusion. Here’s a sample from The Gateless Gate:

Gutei raised his finger whenever he was asked a question about Zen. A boy attendant began to imitate him in this way. When anyone asked the boy what his master had preached about, the boy would raise his finger.

Gutei heard about the boy’s mischief. He seized him and cut off his finger. The boy cried and ran away. Gutei called and stopped him. When the boy turned his head to Gutei, Gutei raised up his own finger. In that instant the boy was enlightened.

When Gutei was about to pass from this world he gathered his monks around him. “I attained my finger-Zen,” he said, “from my teacher Tenryu, and in my whole life I could not exhaust it.” Then he passed away.

(By the way, Sacred Texts is a huuuuge repository of mythology and folklore from all over the world and they’re selling a $127 flash drive that contains their entire archive to help cover hosting costs. I think digital archiving is a noble goal and I’d buy one if I weren’t so poor. But maybe you aren’t. So yeah, if you can, have a look.)

Even though I’m aware of the size distortion problems of the Mercator projection, it still surprises me to play around and see for myself the actual sizes of different countries.

Science writing has this weird, formal dress code that doesn’t really help sell its usefulness to outsiders. Sometimes, we just want to smash stuff together and see what happens. I think lolmythesis really captures this innocent, naïve curiosity that really underlies the best science, y’know, the really awesome kind.

I have a thing for manifestos, even those written by the supposedly disturbed. There’s just something so transcendent and admirable about holding yourself to a higher standard (or in some cases, holding others to a higher standard) even if it isn’t a necessarily morally defensible one. Who knows? Maybe I’ll write one someday (though I sincerely hope becoming violent, suicidal, hopelessly ironic or kooky aren’t strict requirements!)

I took a Russian class under a conspiracy theorist. Or rather, a conspiracy connoisseur, who dabbled in Rothschild hating, 9/11 truthing, moon landing denial, gravity skepticism, and flat-earthing. It seems his criterion for belief amounted to “believe whatever is the opposite of mainstream”. It was a fun class, all things considered, and it led me to some really good music.

Wild Mass Guessing

Music is much closer to a language than a mathematical structure in that it’s much easier to generate than to analyse. Inasmuch as you will find it difficult to predict what a “good” sentence is, it will also be hard to predict what a “good” song will be.

Rationality (in particular, x-rationality) is needed in science because it replaces “genius intuition” with “systematic winning”. It can tell you to stop fiddling with your pen-and-paper formulas and consider alternative formulations. It can tell you to when to call it quits and when to persist. It allows you to become strategic in your pursuit of knowledge, to places where your internal “scientific” feelings might balk at due to impurity.

There is causal knowledge unencodable using algebraic equations alone. Hence, the apparent problem of the arrow of time may only be a problem of the unnecessary symmetry in physics equations.

Explorable explanations (cf. Bret Victor) fail because they only eliminate accidental complexity (whereas learning, say, new math contains core essential complexity you can’t abstract away). Furthermore, they are one-off explanations: you can’t compose them like you could with the essential parts of actual ideas.

 

 

Pen exercise: Diseases of the Scientific Discipline

Note: this was an essay I wrote as homework for one of my experimental physics classes (in Institute X, they bend over backwards to drill scientific integrity into students).


Constraint: react to On Being a Scientist: A Guide to Responsible Conduct in Research, by various authors.

First and foremost, the job of a scientist is to uncover the truth. His measure is the clarity and novelty of his thought. If he is exacting and thorough, lining every table, checking every decimal point, but in the end writes only echoes of his teachers, then he is no greater for it. If he becomes head of his department by a curious doggedness but in doing so neglects to pursue new ideas, then he is no closer to the business of science than pedestrians on the street. A scientist should keep his identity small: in doing so he avoids the rituals and inauthentic behaviour to which science is no less immune.

The Atomic Age thrust science in the public’s view. No longer were scientists seen alone in their labs, concocting various mechanisms to demonstrate in cramped classrooms. We started writing letters to governments, affecting foreign and economic policies. We began dominating intellectual circles for better or for worse: in the 1920s it was customary to apply “relativity” to the world’s moral dilemmas [insert citation here]. This narrative is not new, but herein lies an important distinction: all science is a set of tools. If these tools are used for nefarious goals, if they are used for the betterment of humanity, they are still truthful knowledge. The responsibility lies in the person who finds their use. It is because of this that we must distinguish the scientist from the human: we hold ourselves culpable for consequences of our research because we are human, not because we sought dangerous knowledge that must not be sought.

To this end, I shall call ‘scientist’ that who seeks knowledge for knowledge’s sake and ‘science-practitioner’ the scientist with human faults and foibles. The science-practitioner in today’s world faces two main challenges: to collect citations, and to secure funding. Immediately this brings us to various conflicts of interest that may hamper the progress of scientific research. The first one is the maligned focus on credit. We are extremely protective of our ideas. It is as if the conception of an idea in one’s mind (particularly if one has reason to claim priority) leaves us with the same psychological imprint as finding a coin in the street. This is evident in the well-known rivalry of Isaac Newton and Gottfried Leibniz on the discovery of calculus, where what could have been a fruitful correspondence turned into a 20-year-long state-backed superiority contest no better than the red-team, blue-team bickering often seen in sports or politics. The scientist, in his pursuit of knowledge, must learn to avoid this pitfall lest this primal need for social status overwhelms his path to his original goal.

This issue of credit is such an important point that it warrants a longer discussion. Aside from priority, scientists also bicker about authorship. A great importance is placed on the relative order of authors in a paper. First authorship implies a bulk of the intellectual contribution to the paper; a project is after all never equally divided. More issues arise when advisors and researchers with higher administrative positions demand inclusion in the list of authors of a study, regardless of their intellectual contribution to it. Thus, a scientist is never alone. In his pursuit of knowledge, he is haunted by the spectre of his heroes, he must walk briskly keep pace with his highly competitive peers, he must let students trail behind him to carry on when he falls by the wayside, and he must carry the ever-increasing burden of administrative responsibilities on his back.

A more subtle issue on authorship arises when different parts of a paper are written by different authors. A broth is spoiled by many cooks, so why should a paper be any different? The coherence of such a multi-authored paper is rarely apparent, and problems arise when one of the authors is involved in an academic scandal. The case of Jan Hendrik Schön, an experimental physicist who was found to have fabricated semiconductor data, is now a classic warning to budding scientists. The larger question, however, is the culpability of his co-authors. Are they as guilty as the fraudulent physicist by having signed off the paper for publication? What about the people who peer-reviewed his papers? How apt is it to fault them for Schön’s career to have lasted as long as it did?

A naive attempt to cut the Gordian knot would lead one to express culpability for all those involved. “Everyone gets the whip” is a common sentiment for those who would like to get on with their lives after scandals such as these. However, a brief pause would lead one to conclude that this undermines the foundation of trust that the scientific community puts on its members. The pure scientist demands empiricism in everything, but practicality compels the science-practitioner to leave the replication to others in their respective fields and focus on extracting the pieces of information relevant to his problem. To say that we must check and double-check our co-authors for fraudulent behaviour undermines this web of trust and wastes precious hours that could have gone to research.

Of course, it is lunacy to suggest that checks and balances be done away with. That web of trust only works if it can be trusted (and this is not a trivial tautology). What I am advocating rather, is for the community to spend some of its research-hours into building automated verification systems. The advance of machine learning has increased steadily in previous years. Everywhere, we are experiencing the fruits of breakthroughs in recognition systems, from self-driving cars to a cleaner inbox. There is no physical law that prohibits spam classifiers to be aimed at scientific papers instead. Perhaps, it would even be possible to automatically rate the credibility of a researcher and possible conflicts of interest. Science may be methodical, but it need not be manual.

This brings me to my next point. Science, as a profession that defines itself in how it prods and tests the borders of human knowledge, is strangely resistant to alternative systems. There is a huge pressure to converge on professional standards detailing and constraining the various aspects of one’s work. Strange, that we extol empiricism in everything but our own practice, that we so easily peer outside the public window of discourse yet fail to see more efficient research processes. Science may pride itself on being methodical, but it need not be slow.

Consider how a random civilisation would develop its scientific community. Would you imagine that it would start with lone individuals speaking out against the mores of society, like our Grecian philosophers of old? Would you imagine mathematics intertwined with the practicalities of business and war and the economy, until its parts are distilled one by one? A Galileo perhaps, waging a public battle against old institutions. Then guilds and universities. Then the Industrial Revolution. If so, then one must work to broaden one’s horizons. It is a fallacy to suppose that societies will converge to our own, an implicit assumption of the superiority of one’s culture. If not, then you understand: there is a vast number of paths our science could have taken to get to this point. Therefore, there is also a vast number of scientific processes that could have gained foothold by the arrival of global communication. Our science is the conglomeration of different ways of expressing empiricism, some more affected by extenuating socioeconomic goals than others. It is therefore a curious and frightening prospect that our science was grown, not designed.

The second aspect of a science-practitioner’s career centers on funding. Money is the prime mover. It directs the actions of humans much more so that it is polite to admit. Its main use to the science-practitioner is in the procurement of devices necessary to conduct research. Computer systems, laboratory equipment, technicians and operating crew for heavy apparatuses: the list goes on and on. Money buys tools for the toolmaker, and as tools are said to multiply forces, so do they expand the range of phenomena within reach. A scientist without tools is left to use only his mind, and the mind can only carry so much.

What compels science-practitioners to spend an inordinate amount of hours writing grant proposals? The production of tools for toolmakers is an economy unto itself. There is a huge variety of laboratory equipment accessible to research institutions, if they have the money. Always there is a drive to purchase better and better equipment, and this is not entirely unreasonable: all the eyes in the world could never have guessed the existence of microbes without having seen one for itself. As the phenomena we investigate get more and more exotic, so must our sensory capabilities expand.

By virtue of interacting with the economy, however, this procurement process gains its own incentives. A pure scientist will whittle away everything he has to spend on furthering his research. A science-practitioner, by having to exist in reality, must treat his money as a resource and strategically place his bets on lines of study that to him would prove most fruitful. Immediately, this wrests control from the scientist to pursue his own research directions and gives it to the ebbs and flows of the economy.

There is no problem with this picture: usually we do not have perfect knowledge of what we must know (if we did, it would not be called research). This foible more than makes up for the efficiency we would otherwise gain from giving complete control to the scientist.