Curry-Howard for Non-Dummies – Part 3

In Part 2, we considered the implication A → ⊥, saw that in the logic of the original formulation of Curry-Howard (known as Intuitionistic Logic for those who care) it was equivalent to asserting that A had to be an empty type. We also speculated that in some other interpretation, A → ⊥ might be the type of a program that never terminates. We’ll see if we can make this idea useful in a moment.

Double Negation

But first, let’s consider the type ¬¬A, which, using the formulation described in Part 2, expands out to (A → ⊥) → ⊥.

In the normal Boolean logic that most programmers will be familiar with, if you negate a false value, you get a true value. (This kind of logic is Classical Logic.) One way to define this property is to say that there is a program with this type: ¬¬A → A in whatever programming language corresponds to Classical Logic.

But in the logic we have been using so far this won’t quite work. As mentioned at the end of Part 2, we need to show that A comes from some place on the left side of the arrows. Since it isn’t made clear in this type, it won’t work for us. We can fix this by rearranging the expression so that A appears on the left side, which means that we can build a program of the type A → (A → ⊥) → ⊥.
To see that this is so, there are two cases to consider.
The first is if A is an empty type. Then we are back to a case like ⊥ → B;, where the program is never going to get any input and so it doesn’t really matter what is on the right side. If A is a type with members, then we already know that the type A → ⊥ is empty, so the second part of the program is just the same as the ⊥ → B; case. So either way, we can build this program using the rules we were already using.
Now let’s consider what we need to add in order to make the Classical Logic rule work.

Classical Logic

In order to get the behaviour we expect from Classical Logic, we need to be able to do something that we just showed is not possible for our previous programming rules. We need to be able to build a program that fits the description of the proposition type ¬¬A → A, which expands to ((A → ⊥) → ⊥) → A.
To be able to build such a program, we need to have a typing scheme that is a little bit less strict than the one we’ve been using – one that is willing to “wait and see how things turn out” before fully assigning type. It needs to be able to risk that the program might not terminate and, to really fulfill the proposition type, it needs to be able to make sure that we always end up with a definite value regardless of what actually happens.
In this sense, Classical Logic is the logic of perfect information, where you always have enough knowledge to see what is true and what is false, and you can always stop things when they go awry to make sure they turn out in the end.
There are two ways to ensure that you have this kind of knowledge and power: the first is to always deal with a world that is “small enough,” so that you can always find out the truth of things in a reasonable amount of time. For example, if we restrict our purple unicorn-finding program to looking for it in the room we happen to be in at the moment, then we can be sure that we will either find a purple unicorn or definitely not find a purple unicorn in a finite amount of time.
The second way to ensure the Classical Logic rule is to work in a “arbitrarily big world” with “magic powers” that allow you to find out the truth of things even when they are impossible. An example of this would be to have a “Halting Oracle”, a magic detector that will tell us whether our program will eventually terminate or not.
It turns out that there is a particular type of program that meets the description of the proposition type ¬¬A → A. It falls somewhere between the “small enough” and “magic power” solutions and is known as a “continuation”. This kind of program basically allows you to abort a program and return a value anyway. You can think of a “return” statement or an exception as a poor-man’s continuation. In principle, the program that you abort could have been non-terminating, but you get to see this and abort it to make sure it turns out anyway. The “seeing this” part is outside of the system itself, so it is sort of a magic power, but in practice we rely on the fact that we are working with a small enough world that the programmer can see what would happen and choose to abort the computation.

Searching for Purple Unicorns

Let’s return to our program that uses a spy satellite to search for purple unicorns.
Will it run forever or will it terminate? If we stick with our constructive method of building facts, then it will only terminate if in fact purple unicorns exists and it finds one. Unfortunately, there are ways that purple unicorns could in fact exist, but our program still won’t terminate: for example, if during the day purple unicorns hide in caves and at night when they come out it is too dark for our satellite to spot their particular shade of purple. Unfortunately, in this case our program doesn’t really fulfill its type and it doesn’t really prove anything at all, one way or the other.
If we avail ourselves of the Classical approach to things, we can make our program terminate even if there aren’t any unicorns by, say, allowing the satellite to do one orbit and then just assume that we were right to begin with that they don’t exist and abort the program with a negative result. This basically forces truth into a box we find convenient and doesn’t really prove anything either. It is just a fancy form of axiom.
Another option is to not worry about being able to reify our ideas and proofs as programs, assume that purple unicorns exist and develop elaborate theories about their habitat, physiology and behaviour. These might be interesting theories and some of them might be true and consistent with the real world because, by the way we have defined them, we know quite a lot about them. For example, we know that unicorns very horse-like, so many things that are true about horses can be comfortably said to also be true about purple unicorns. We can also assume that their characteristic purple is a known shade of purple. In this way, theories of purple unicorns might we’ll be perfectly compatible with existing zoological studies, or colour theory. Assuming the impossible does not necessarily produce inconsistency.
Medieval scholastics were able to do some good logic, rhetoric and philosophy by contemplating things that most of us think are impossible, such as angels dancing on the head of a pin.

Implications for Mathematics

Curry-Howard gives us a possible definition for truth in mathematics linked to computation. At this point in time, most mathematicians don’t seem all that interested in this possibility, since they are fond of studying purple unicorns, such as the kind known as “uncountable sets”. I don’t really want to dissuade them from this study, anyway. Purple unicorns are fun to think about, and can sometimes provide inspiration for useful things. (See continuations above.)
However, both mathematicians who work with computer science and computer scientists who have Classical mathematical training need to be very careful how they think about computational truth: it doesn’t work the way they are used to.

Implications for Logic

Curry-Howard gives us a reason to explore logics that are subtler or more complex than Classical logic. Computation requires us to incorporate a notion of uncertainty into our thinking, and logics that can handle this might offer new vistas of useful thought to explore. Lots of great work has been done this way.

Implications for Computer Science

Curry-Howard reminds computer scientists that we are not afforded the luxury of either believing in purple unicorns or being too certain that purple unicorns don’t exist. Infinity is a big place after all, and our programs can’t explore all of it.
Curry-Howard also gives us a tool to draw inspiration from what logicians and mathematicians are doing to better understand how to think about computation. We need all the tools we can get.

I hope that any brave soul who worked all the way through to the end of this has gleaned an understanding of Curry-Howard, and an appreciation for the rich, cross-pollination of disciplines that it enables.

Curry-Howard for Non-Dummies – Part 2

In Part 1, I described the “Curry-Howard” principle in very simple terms. I culminated with the explanation that a program can be seen as a proof of the implication represented by A → B, where A is the type of its inputs and B is the type of its outputs. Moreover, A → B is itself both a type and a proposition in a simple implicational logic.
And that’s all well and good, but now it’s time to see some wrinkles in this idea in preparation for exploring the consequences of Curry-Howard upon mathematics, computer science and logic in Part 3.

What Happens When a Program Doesn’t Terminate?

In Part 1, you may have noticed that I made a bold assumption about my programs. The rationale for considering the program to be a proof of the implication was that I was able to run the program by consuming a thing that met the description of an A and produce a thing that met the description of a B. My program is a proof by construction.

But what happens if I made a mistake and wrote a program that doesn’t terminate for all inputs that meet the description of an A?

Let’s return to the example where the description of A is “a purple unicorn” and the description of B is “a horse-race winner”. Let’s say I decide that what I’ll do is create a new program whose input C has the description “a spy satellite in orbit” and I conceive a program for the implication C → A that says that I’ll have the satellite orbit the Earth, checking every square inch of it until it finds a purple unicorn, at which time it will let me know its location, and I’ll go capture it. Once I have this purple unicorn, I will immediately pass it to my previous program as input and will then be able to produce a horse-race winner. We can think of the composition of these two programs together as a new program that is a proof of the implication C → B. But are we sure this works?
It could be that there is such a thing as a purple unicorn after all, and that it just so happens that no one has ever seen one and that our spy satellite, which is very thorough, will do its job and find a purple unicorn that was previously missed. In this case, we would have a proof of C &arr; B. But maybe there really is no such thing as a purple unicorn (on the surface of the Earth, anyway), and our satellite will just circle the Earth forever.
In this latter case, I have a fully described program that would take a spy-satellite and produce a horse-race winner, but if I try to run it, it basically hangs up on the first step and never completes. So merely having a description of a program is not sufficient to have a proof. What I really need is the description of a program that is guaranteed to terminate for all its allowable inputs.

So does this mean that a potentially non-terminating program has no place in a Curry-Howard view of things? Is there not still some value to having some well-defined program that witnesses an implication, as opposed to having no proof at all of the implication, except perhaps “because I said so?”.
To tackle this, we must expand our repertoire of concepts a bit.

Negation

In Part 1, I covered how we can define the truth of the proposition represented by a type as the existence of a thing that meets its description. If the description of A is “purple unicorn” and I can present a purple unicorn, then A is true, and if there is no purple unicorn to be found, then A is false.
So any type that is false must have no possible members. If you think about this a moment, then you realize that any two types that are false must share the same list of members, i.e. none. This means that they share the same extensional definition. And by the same token, the members of both types will all meet the description “a thing that is impossible”. So they also share an intensional definition.
In this sense, all empty types are equivalent to a single basic empty type, which we will give as a name the symbol ⊥. This symbol can be pronounced a number of ways, but we can continue to think about it as “the empty type”.
Is there a way to use this type in an implication to produce interesting types of programs?
An obvious possibility is to put the empty type on the left side of an implication: ⊥ → A. As a program, this would be a program that takes members of the empty type as input. This is very much like our “purple unicorn produces a horse-race winner” program. It is a program that (if we are correct that there are no such thing as purple unicorns) will never get any input (since there are no instances of the input type to pass to it), and therefore it will never produce its output. This doesn’t mean that the type of its output is necessarily empty, just that this function can’t be used to prove anything definitely, or, looking at it from the other end, you could say that this kind of program could prove anything, since a program that isn’t going to run can promise anything you like, since it will never have to deliver. (Just like a politician who knows he won’t be in the next government…)
The next obvious possibility is to put the empty type on the right side of the implication: A → ⊥ . This one is a little bit trickier to make sense of. At first glance, this one might be a good match for our C → A implication, the “take a spy satellite and find a purple unicorn” program. And that has some interesting possibilities. But normally this form of implication is interpreted to mean ¬A, which is an assertion that A is empty and false. To explain how this works, we need to explain a little bit more about the original formulation of Curry-Howard.

The Original Curry-Howard

To understand the original formulation of Curry-Howard, you must understand some basic facts about a couple of things, which have been known to get quite complex but for our purposes are extremely simple. The first is the Lambda Calculus, which is really just the world’s simplest programming language. There are basically two “commands” in this programming language. One allows you to define a program that takes an input, and the other allows you to pass input into a program that has been defined by the first “command”. There are some technical details if you are really interested, but seriously, that is all there is to this.
The amazing thing about this simple programming language is that it is as powerful as any other programming language you could invent. The thing that makes this language so powerful is that you are allowed to pass a program to itself as input. Under certain circumstances, if the program gets applied as part of its own execution, the program might never finish. This is exactly like defining a function that contains only a call to itself: it will just go in circles forever.
Now, there is a limited form of the Lambda Calculus known as the Simply Typed Lambda Calculus, which basically works like the implication types we’ve been talking about. The important thing to know about the types in this programming language is that the description of the inputs and outputs of a program must be simpler than the description of the type of the implication itself. This ensures that you can’t pass a program to itself as input, and this means that all programs in this language always terminate.
To illustrate, consider a simple program that has the type A → A. Since its input is of type A, and since its own type is A → A, which is more complex than simply A, it can’t possibly get itself as input.
The amazing thing about this language is that, despite giving up the most important trick of the full Lambda Calculus (recursion), you can still do quite a lot with it, including a significant portion of arithmetic.
Another important attribute of this language is that it is strictly constructive, which is another way of saying that you can only output on the right side of the implication things that are built up from things supplied on the left side. This ensures that we don’t pull any conclusions out of thin air, and that we can always trace the origins of a particular conclusion from what we started with through the well-defined building steps along the way.
A consequence of this fact means that the implication A → ⊥ can only exist if A is in fact an empty type. This means that the only type allowed to have ⊥ on the right is ⊥ → ⊥. This explains why saying A → ⊥ is the same as saying ¬A., i.e. A is empty and false.

We now understand enough about Curry-Howard to think about some of its consequences, which we will explore in Part 3.

Curry-Howard for Non-Dummies – Part 1

(Anyone who wants to learn is not a dummy)

At the risk of alienating the (small) audience who is used to me writing about not-too-technical topics, I would like to take a crack at an important but technical topic in theoretical computer science. This topic is often known as the Curry-Howard Isomorphism, though there are variations on its name. Despite the forbidding name, the principle it represents is useful to understand for anyone who is interested in logic, computation or programming languages, which would obviously include programmers of all skill levels. I hope to provide an introduction that anyone in this wider audience can understand.

Programs are Proofs

The very basic idea of Curry-Howard is that you can think of a program as a proof. A proof of what? A proof that if you provide certain inputs to that program you can produce the corresponding output.
Another way to think about this is to understand that both programs and proofs are series of rule-following steps that allow you to transform what you started with into a new result.
We often take this generating capacity of programs for granted, but the very nature of programming requires a deep understanding of the structure of inputs, the structure of outputs and the details of the relationships between them. This is exactly the same kind of activity as creating a proof in math or science.

Programs are Implications

In logic, the simplest way to state a proposition that captures this inputs-to-outputs behaviour of programs is as an implication: A → B, ( read as “A implies B”). This means that if I already know that A is true then I will also know that B is true.
To see the parallel to a program, I have to understand that “A is true” is equivalent to “I can find a thing which fits the description of A”.
This last step is perhaps not quite so obvious, so let me give an example. Let’s say that A stands for “a purple unicorn” and B is “a horse race winner”, then A → B could mean that “if I had a purple unicorn I would run it in a horse race, and since purple unicorns are magically fast, I would be sure to win”.
You can see that this is a kind of program: give me a purple unicorn as an input, and I can follow a series of steps to produce a horse race winner.
While this may be a good program, it can’t be run, since purple unicorns don’t exist. And since purple unicorns don’t exist A can’t be true.
If I change my program to match C → B, where C is “a well-bred horse”, I’m back in business: my program can now be run again, when I run it (or rather run the well-bred horse in the race) and produce a horse race winner, I will have proved the correctness of the implication.
To return to a slightly more programmatic example, let’s say that A is “a number” and B “a number greater than A”, and my program adds one to its input. I then feed it “1” as input, my program produces “2”, which is indeed greater than 1, and I’ve proven that, given the number “1” I can produce a higher number.

Types are Propositions

However, we aren’t quite done here. I just showed that for a particular thing that met the description of an A (“a number”) I could get a particular B (“a number greater than 1”), but what I really need to do is show that any thing which meets the description of an A can always be used to produce a B using my program. In order to do this, I need to think a bit more about what it means to be a “thing which meets the description of A or B”.
There are basically two ways to define “things that meet the description of A”: by listing all the individuals that meet the description (this is called an extensional definition) or by proposing a rule (typically an inductive rule) that allows me to produce or recognize an A at will (this is called an intensional definition).
It so happens that we already have a concept in programming languages that does this definitional work for us: types. Types can be defined by an exhaustive list. For example, the character type is typically defined by a list of ASCII or Unicode characters that is fully known already. Types can also be defined by a rule. For example, a number type might be defined as any sequence of digits. You wouldn’t have to list all the numbers (there are probably too many) – you just have to check the simple formation rule to determine membership in the type.
Based on this, we can see that any type can be construed as a logical proposition that can be verified by lookup or by rule: just produce an individual item that meets the description and we know that our proposition is “true”.

The Type of Programs

We now have enough machinery to show that our program works for all of its inputs. We showed that A and B are both types and propositions. We now have to see that the implication A → B is also both a type and a proposition. To meet the description of the proposition A → B we have to show that our program will take any A and produce a B. As with our simple propositions, we need either an exhaustive list or a rule that allows us to cover all the bases. The easiest way to do that is to start with our definition of A. When we look at the structure of our program, we will have to see that there is either an exhaustive list of the elements of A or some rule that follows the rule for A to cover all the possible values of A, and then for each path that results from this rule or lookup, show that a B will result.
This can be very complicated for complex programs but it is often possible to break a bigger program up into smaller bits, each of which can be checked in this manner. Generally programming languages and type systems are designed so that the compiler can verify the type of a program automatically.
When we have completed the process of verifying our program, we will know that our program fulfills the description of the proposition A → B, that it conforms to the corresponding type, and that it is also a proof of that proposition.

If you have followed this far, you have grasped the basic idea of Curry-Howard. It is, I hope, a surprisingly simple idea, but with profound consequences for logic, mathematics and computer science. In Part 2, I hope to expand a bit on some of the elementary consequences.

Truth, Sales and Leadership

Salesmen, politicians and chief executives are all cut from the same mould. Their fundamental job is to impress and make others feel good about buying what they have to sell.
As someone who has spent his career in product delivery, and who is sceptical by nature, I’ve had a mixed relationship with the sales and presentation types. I have all too often ended up on the hook when one of them sold unicorns when what we had in the barn was donkeys.
But, unlike many technically oriented delivery specialists, I have a deep appreciation for the value and necessity of presentation and sales. I understand the symbiotic nature of our separate disciplines. In the end, things only work out well when both roles are filled competently, and both sides need to remember their dependence on the other if they want to succeed.

To Impress or to Be Impressive

If at this point you aren’t sure which side of this proposed divide is your natural home, let me propose a simple way to decide: which do you think is more important, to impress or to be impressive? If you don’t understand this distinction, let me rephrase: would you rather be famous and admired for something that you didn’t put a lot of effort or skill into, or be amazingly accomplished at something that no one knew about you?
Now some of you are I’m sure objecting that these are always or usually the same thing: accomplishment and skill, and recognition for that accomplishment and skill generally go hand in hand.
But the truth is that it is rarely the case that the two go together naturally. Are the best singers and actors the biggest stars, and vice versa? Are the most successful politicians most often the smartest and most qualified decision-makers? Is your average CEO the biggest expert in the business he is running?
This isn’t a complaint that the world isn’t fair. On the contrary, I think there is a good reason why things work this way. Impressing people requires that you present yourself in terms that they can understand, evaluate and appreciate. Being impressive requires honing your abilities and understanding beyond the experience and comprehension of most people, to make distinctions and to have perceptions beyond what is evident to a non-expert.

When Sales or Fulfillment Goes Bad

Each of these sides has its obvious pitfalls, and to understand these, all you have to do is think about the negative stereotypes of these two groups.
The bad salesman or politician is full of hot air, with plenty of promises that never get kept. The bad salesman is convinced he could “sell snow to the Eskimos”, the bad politician certain that he could finesse over the most egregious scandal and get away with breaking every promise.
The bad expert (let’s use software developer as an example) is disdainful of the buying public, mystified that they don’t see the deep technical skill that went into solving several difficult and subtle challenges but are instead impressed or put off by trivial details, such as the colour choices on the main screen. The bad software developer is convinced that good software will always sell itself, and sales and marketing are clueless bozos who soak up money and accolades that rightfully belong to the technical geniuses.
Both of these stereotypical bad guys are wrong: they desperately and inseparably need each other.

Commanding Officer and Executive Officer

To illustrate the symbiosis of these two callings, I will draw on an example that has literally been battle-tested over centuries. It is traditional in the military for there to be two command roles for every unit: Commanding Officer (CO) and Executive Officer (XO).
The CO is the external face of the unit. It is his job to represent the skills of his unit up the chain, to convince the command hierarchy to give his unit more resources, and to cheerlead and praise his men for their accomplishments. Ideally, he should be loved by his men, and they should feel proud and honoured to serve under him.
The XO is the internal manager and disciplinarian of the group. It is his job to push, prod, terrorize and manhandle his men to improve their skills and achieve their mission goals. He must be the first to observe and criticize any short-comings and ruthlessly punish any breach of discipline. He is the expert in building the best possible soldiers. Ideally, he should be respected and feared, at best grudgingly liked, and made fun of when the men are absolutely, positively certain that he can’t hear them.
With such radically different profiles, you would expect that these two officers should not work together very well, right?
But the truth is that, if both men actually understand their roles, they should be working in perfect collusion with each other. The XO should be feeding the CO with good things about the men that can be praised, and let him know when the men are achieving their best and can’t be expected to give anymore. The CO will let the XO know if any bad reports are coming in from outside the unit and share his fears of how the unit might fail in upcoming missions.
The two roles are distinct, and require different focuses, but they must be done in perfect concert to achieve maximum effectiveness in the situation. Such dual leadership roles can and often are performed by a single person in non-military leadership situations, but there is something to be said for the collaborative specialization of individuals dividing up the areas of responsibility. Even if you find yourself with both roles, you have to find some way to separate them in the minds of others so that they don’t contaminate and undermine each other.

Truth and Presentation

I think we would all agree that the ideal situation is the one where things both seem good and are good, but where the downside is also known and managed. Being aware that some aspects of the truth (possibly not the most important ones) need to be highlighted for the sake of presentation is important for experts to understand. Keeping in mind that finding and fixing negatives is essential for quality products and that it is in everyone’s interests to not diverge too far from the truth in presentation is vital for sales to understand.
A well-packaged truth can only come about when both perspectives work together and respect each other.

On Being an Amateur Academic — Part 3

The Pros of Being an Amateur Academic

While I’ve already pointed out that there are some real problems and downsides to being an amateur academic, there are some distinct bonuses over being one of the professionals. I will discuss the three most important ones, in my opinion.

Free to Wander

There was a time when I was seriously considering going to grad school and becoming a professional academic. The biggest difficulty I had, other than how to support myself if I took that route, was choosing a focus for my studies.
My interests have always been wide-ranging, and in order to be taken seriously for graduate studies, I would have had to focus down to a tiny sliver of one conventionally defined discipline out of all the ones that seemed interesting.
To make this worse, in practice what you have to do is find an advisor who will tell you what to do, preferably quite closely aligned to their interests. (More on that later.)
Ignoring the fact that you can get caught in a dead-end area of focus that is on the verge of going out of fashion, from the point of view of sheer intellectual curiosity you need to accept that, for many years at least, you will have to stick to something pretty close to your chosen topic if you want to have any hope of finishing your degree and getting a job. (Two huge and separate hurdles.)
Once a professional academic has established their career, they can and do branch out, but you have to be able to stay devoted to one thing for longer than I can manage.
To give you an idea of the range of interests I’ve been free to explore, mentioning only fields that I have spent a non-trivial amount of time studying over the last ten years (the time it can take to finish a PhD and get an appointment), and including only topics I think I could have a sensible discussion with a pro about at, say, an intellectual dinner party, or in an online forum: computer science (programming language theory, type theory, finite model theory; mathematical logic), mathematics (foundations of mathematics, category theory, abstract algebra, model theory, proof theory), linguistics (syntax, phonology, sociolinguistics, historical, computational), ancient languages (Classical Greek, Classical Arabic, Classical Chinese), music (Middle Eastern music theory), as well as various topics in history, philosophy, political science, and the arts.
This is an impossibly diverse list by most academic standards, and to be honest I’m not sure how or if I’ve managed to grasp all these, except that I tend to go through periods of weeks or months focused on one or two them, and over time I revisit old topics to refresh my memory and learn the next increment.
How well do I know these areas? Some of them well enough that I think I could probably write a decent paper in the field, given the time. Many of them well enough to deliver a coherent introductory lecture, mostly from memory with some notes. None of them do I know as well as I’d like (or as well as true specialist), but again, that is one of the trade-offs I’ve made for breadth versus depth, which I’m only free to do as an amateur academic.

No Pressure or Competition

Professional academia can be a ruthlessly competitive arena. There are many more graduates than positions. Everyone in your field is trying to stake out their intellectual turf and achievements, and unless you come from money, most people starting out are strapped for cash.
To be able to succeed in this environment you need to be able to produce quality papers in some profusion and also work the circuit to develop contacts with and the favourable opinion of those in a position to advance your career.
To be honest, competitiveness is present in any professional environment, but the advantage to being, say, a starting programmer, is that you can make an acceptable living right of the gates, and, so long as you aren’t too obviously lousy, you can manage to build an okay career without being a star (except perhaps only in your own mind).
No matter how well you understand something or what great idea you have, writing a good paper that is not vulnerable to being shot down in flames within five minutes by a rival is a surprisingly difficult thing to do. Technical fields can be especially hard, since marshalling all the details so that they are both correct and convincing can be a monumental juggling task. People who can regularly pull it off are in my opinion under-lauded rock stars. (I won’t mention any names here, lest I start to gush and bore the last remaining reader to tears. ;-) )
This is a huge advantage of being an amateur academic: I only ever have to convince myself that I understand something (still rather challenging sometimes), rather than proving it to the world, and thus risk potentially making an ass of myself in the process (I still get to do that on the internet, so all is not lost. ;-)).

True Intellectual Freedom

The last benefit of being an amateur academic I want to discuss is also the only one that I think is a benefit to the world at large, not just for the amateurs themselves. It is the main reason that I would encourage someone to take this path for a reason that is other than just “to thine own self be true”.
As an amateur academic I’m not beholden to anyone for my learning or position in the academic world. I don’t know the players personally, nor have any tribal allegiance to one school of thought or another. If, after studying an area for some time, I decide that “the emperor has no clothes”, I don’t stand to lose any professional standing by abandoning the field. I risk nothing in breaking ranks from prevailing trends or fashions or taking on a heretical position that I sincerely hold.
As an amateur, I long ago realized that if I had any chance of making an original contribution to one of my fields of interest, it was going to be because I was freer to cross-pollinate disciplines that are normally considered distinct, or by calling BS on a field-wide group-think stemming from professional allegiances and lineages.
All disciplines (especially as they grow more specialized and esoteric) need more outsiders to take an interest in them, even if they dissent with their prevailing positions, and even if some of us who dissent are cranks.
For a professional academic, intellectual inquiry inevitably must be tinged with realpolitik, but an amateur academic is free to engage in a genuine dialectic of ideas, in the tradition of Socrates.
In any field of endeavour, to advance in skill and knowledge it is helpful to have good opponents, ideally people who share your values and interests, but with different methods and perspectives.
I think that the amateur academic is well suited to this role, and I hope that others will embrace it, and make a contribution to the intellectual health of our society, as I have tried to do in my own humble and questionably effective way.

On Being an Amateur Academic — Part 2

The Cons of Being an Amateur Academic

There certainly are some drawbacks to being an amateur academic (as there are with any undertaking). I will discuss the three I think are the most important.

Takes Lots of Time with No Obvious Payoff

This is the most obvious problem with being an amateur academic. Keeping up with one field (let alone several as I do) requires a big time commitment that is hard to juggle with an unrelated (or distantly related) full-time job. To be fair, professional academics have this problem too, in the sense that they typically also have to teach courses, grade papers and assignments, serve in administrative positions and committees, write grant proposals, and a whole bunch of other tasks that don’t relate directly to their research interests in order to make their living. They probably still get a bit more time to do it during work hours and they also can get paid sabbaticals to be able to devote full time to a particular project.
Aside from the time and energy costs of full-time professional employment, the biggest challenge for the amateur in this regard may be explaining to friends and family why you spend so much time on something that doesn’t provide any remuneration or social standing. Most people will just think you are strange. (My family and friends are mostly pretty tolerant about this, but then again not all of them know how much time I spend on this stuff, and they have independent reasons to think I'm strange. ;-) )

Not Taken Seriously

In some of the fields I’m interested in (notably mathematics and linguistics) there are many honest-to-goodness cranks out there. You know, the kind that are trying to prove how some aspect of the field is related to alien visitations, or who have some pet racial or political theory they want to promote.
Especially in such fields, but also in most other academic fields, not having graduate and publication credentials in that field is a real handicap to being taken seriously, especially if you have modestly controversial opinions about some important topic.
On internet forums, it is easy to fall afoul of the academic-purity police and look like a crank. (I’ve noticed that this is particularly true if you post while sleep deprived ;-) ) By contrast, I could name some well-known academics with credentials left and right who I would argue are certifiable tinfoil-hats, but who routinely get a free pass from other posters because of their apparent standing.
If as an as an amateur academic you take it in your head to get published in respectable academic journals, good luck to you. Aside from the fact that you would be competing at a disadvantage with worthy graduate students and post-docs who desperately need to get published for professional advancement, and who have the more established sponsors to put in a good word for them, the easiest cut off for a time-strapped editor is to reject you based on lack of credentials and sponsors.
You can rail against the injustice of this, but many of the cranks take this approach too, so I wouldn’t recommend it.
Better to accept this limitation and, if you really want to make a contribution to a field, don’t worry about credit, but involve yourself in online communities of interest where you can explain your ideas. If someone steals them and advances their career with them, so much the better; you shouldn’t go into amateur academia for glory any more than for money.
I would also recommend being respectful of those with the credentials. They have given their blood, sweat and tears to their discipline, and have had to jump through hoops that an amateur academic hasn’t had to, so they are likely to know what they are talking about in some meaningful way, even if you disagree with them. This can be tricky, since nobody likes to be disagreed with by a nobody, and without credentials, that's how you look to them, at least initially. (You may want to try flattery as an opening gambit. ;-))

Lack of an Intellectual Community

Professional academics have colleagues, rivals, advisors, conferences, and other means to form communities of shared interest in the same field. The amateur academic must resort to regaling bored but tolerant spouses and friends with their latest fascination.
Personally, I think this is the greatest hardship of being an amateur academic, since it is a passion for learning that drives you to be one, and any passion wants to be shared.
The internet helps with this, since there are all kinds of blogs, mailing lists and other forums that can be used to connect the like-minded, but my own experience is mixed here. It is hard to find a community that is at exactly the right level for whatever state of mastery you have reached, and in many forums people with less knowledge resent the explanations they get of how they are off-base, no matter how gently presented, and people with more knowledge, or more credentials often resent hearing from the “peanut gallery” about their specialty (see the previous section).
The amateur academic can be a lonely fellow. (But hey, you wouldn’t spend so much time in solo study if you couldn’t handle being alone, now, would you?)

On Being an Amateur Academic — Part 1

When I started this blog, I decided to add the description “amateur academic” after “professional software developer” in my "About Me". I thought it was a useful addition to explain not only the range of stuff that I intended to talk about, but also to explain my activities around the web for people who Google me and are trying to figure out why I’m posting somewhere about some pretty esoteric topics that are not obviously related to get-it-out-the-door software development.

What is an “amateur academic”?

Since the very concept of “amateur academic” will be unfamiliar to many, perhaps even oxymoronic, or maybe even quaint in a 19th-century English gentleman sort of way, I’ve always meant to explain what I mean by this description. More importantly, I also want to share my experience of the pros and cons of being an amateur academic with others of like persuasion. (I think there are more of us than you might think, especially among technically inclined people.)

The term itself is, I hope, a self-explanatory composition of the two individual words that make it up.

“Academic” means that I am interested in topics that most people consider esoteric, theoretical, and in the sole domain of professors. It means I spend a significant amount of my time reading books, papers and online materials related to these topics. Most of the latter are in fact the professional academic literature of those fields of study, and are produced by the professors and grad students we normally identify with the term “academic”.

“Amateur” is an even simpler term to explain in this context: it just means that I study these topics and materials only for fun rather than with the intention to also make a living at it.

Are you crazy?

Studying purely for fun is likely to make me seem off my rocker to lay people and professional academics alike, neither of whom may be able to imagine how such challenging material could be enjoyable to work through without the incentive of remuneration. (Graduate students, on the other hand, may relate to this more directly, though many of them may still be optimists who have hopes of cashing in on their knowledge some day.)

Whether I’m off my rocker or not, this is how I am, and I long ago accepted it and have been making life choices that make my proclivities possible. Aside from the existence of the internet, with its multitude of resources and public access to material and forums which used to be private and hidden, the most important ingredient to succeeding as an amateur academic is to be realistic about the pros and cons. For this reason, I will expand on these pros and cons for the next couple posts.