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Recursion

As a high school student, I remember being told that you can't, or at least shouldn't, define terms in a self-referential manner.

Having this pointed out at a young age made me realize how complex meaning can be sometimes. If not that, then at least how complex it can be to articulate concepts that at one point might've seemed to be self-evident.

You can't define time as 'the time it takes for things to happen', as the definition is, in some way or another, making reference to itself.

I know, perhaps this is not the best example to illustrate my point, but hopefully this generic example brings up better and more relevant examples of how this has happened in your own life.

Sometimes we're at a loss for words for defining things that we see every day, and feel an odd sort of gravity towards simply repeating the same word.

Probably the reason we tend to do this is due to a crutch. I think that to some extent we're delaying our responses in order to come up with an actually satisfying response. But we never do.

The reason that self-referential definitions don't tend to work in most cases is because they open an endless wormhole out of which there is no escape. If words are shorthand for their definitions (which honestly, I don't know if they are), then if a word is included in its own definition, we will keep going down into the definition over and over again. Following my not-so-good example:

'time is the time it takes for things to happen'

'time is the [is the time it takes for things to happen] it takes for things to happen'

'time is the [is the [is the time it takes for things to happen] it takes for things to happen] it takes for things to happen'

'time is the[is the [is the [is the ..... '

and so on.

This little example brings to light the fun game of recursion. In the definition of a term, this simply does not yield a usable result. Yes, we're going down an infinite wormhole, but we're also going nowhere, so it's not a satisfying result, so it's not an appropriate definition.

What about computers?

Recursive definitions get a bit more interesting when applied to computers. This is, in part, because computer languages have a different way of operating than natural languages.

Perhaps I'm just saying that due to my currently limited perspective, but certain syntactic elements of computer languages make recursion a manageable phenomena, instead of an illogical one. This is because of conditional clauses which allow us to contain the scope of self-reference.

Put in english and taking my original not-so-good example of a self-referential definition, this would look something like:

time is the time it takes for things to happen as long as you haven't defined time as a subset of time more than once.

The condition that starts after 'as long' makes sure that we don't define time as a subset of time more than once, which is the one time (no pun intended?) we're doing in the first sentence.

This might not make any sense in linguistic terms, but in computational terms, this is manifested with the usage of 'if' statements within a self-referential, recursive function.

What this means is that without an exit condition, a recursive function will simply not work. It will consume all of the computing power of a machine and it will inevitably crash. Insert reference to entropy here. For example, if we ask a computer to solve the following statement:

function x(int a) { return x(a + 1) }

Then, this would mean that when we call it, it calls itself, which it then calls itself, which it then calls itself. We can use an if statement (or any other type of conditional clause) to contain this from getting too silly.

Why does this matter? Why is this interesting?

To me, this is interesting because recursion exists in real life – in “nature”. Maybe it doesn't exist (or can't function) in our languages, but it exists in visual patterns that we see everyday: leaves, branches, cells, snowflakes. Fractals.

Language can't encapsulate self-reference in the same way that “nature” does because language is inherently limited by our human capacity to deal with reality. Perhaps language does handle self-reference in a perfectly logical way, but perhaps our brains can't conceive it. Perhaps we couldn't have come up with the idea of trees if we hadn't seen them first.

This is perhaps one of the reasons why fractals seem to be so mysterious and so fascinating. There is seemingly no hierarchy or order to guide our perspective. There is no bottom, there is no top, it just 'is'. And given that we have many limitations that contain us and most of the concepts and objects we interact with, interacting with a concept that is unbound and uncontainable is somewhat hard to fathom.