The reason many people do not understand Lisp but prefer murky syntaxes where the edges are intuited instead of made explicit is also related to this lack of natural ability to deal with explicit edges. We seem to prefer the wrong kind of simplicity naturally, or find the wrong kind of simplicity too rewarding at too early an age, and people who refuse to think about things tend to go very wrong.
For instance, people generally think that 2+2 is 4. But it is not. It is only when this expression is explicitly delimited from side-effects that the simple folk understanding holds. (+ 2 2) is always 4. In 3*2+2, 2+2 is definitely not 4, and it would be wrong to think about 2+2 to begin with. Most people wil recognize that the edges have moved in this expression, but fail to understand the power of explicit edges because they think they can always see them, just like stupid people for ages (not just after computers arrived on the scene) have thought that they could omit the century in dates because nothing would ever last longer than 100 years. Old and ancient works of art often contain the day, month, and year of the century, but you have to make some highly educated guesses as to which century because stupid people have thought the edges of the century needed not be specified.
The objection is on the face strong, but I have a lot of trouble when trying to analyse it. For instance : it is true that 2 + 2 is ambiguous as stated, for the reasons stated. However, (+ 2 2) is also ambiguous, for a plurality of possible reasons that weren't stated but still exist. Suppose the (+ 2 2) lives on a fortran machine wherein four has been redefined. Is it ambiguous now ? Perhaps not, because whosoever redefines four deserves anything he gets. But then, by the same token, perhaps 2 + 2 is not unambiguous, because whosoever truncates a string idem deserves anything he gets ?
The problem of edges, limits and boundaries is not a small matter in anthropology, incidentally. The most common failure mode of the brain, by very far, is clearly boundary related. Ever had your brain totally fart, completely forget what it was you were doing and why ? Just as you walked through an arch or door or otherwise boundary ? So go back past the boundary and be amazed at the sudden rescue of a broken frame! Because yes, the brain does this anchoring of its own frame on the visualii and it sometimes doesn't manage to frameswitch cleanly (ie, import all the old data and all the old running processes into the new space) over a boundary.
But this aside, how do you specify a margin ? Mind that this is not nor does it reduce to the much easier problem of specifying a difference, which is to say specifying the boundary between two equally given things. No, the margin is essentially trying to specify the difference from inside a given thing, with the other thing ungiven. It is asking you to know what you don't know, so to speak, just like you're required to know that there's more to the string and so Polish notation may be a good idea, you're equally required to know that you're running on a Fortran machine and just make sure that 2 = .. 4 = .... before proceeding with 2 2 + (except of course should you be stuck on php, in which case any number of consecutive = may - or may not - suffice).
What are the geometric boundaries of the Universe, while we're at it ? Is it really a Klein Bottle ? You see, clearly, we seem to prefer the wrong kind of simplicity naturally. Or maybe it's that we find the wrong kind of simplicity too rewarding at too early an age. In any case, how is it that you can go about your daily shopping without knowing whether the earth is flat or round ? Wait, you can't, can you. But before it was known to be round, you also could. Of course, back then it was known to be flat. And before that round again, and before that it was just a half lemon atop a turtle. Turns out you always knew what the geometric boundaries of "the world" aka this planet were. The only problem being that they weren't quite as invariant over time as it'd behoove some boundaries, especially as long as the thing they bound is not changing.
So how about the Universe altogether ? Because you do realise it changes things, whether it's flat or not. Things you will probably never know aboutiii, perhaps because you simply don't live that long, or travel that far.
It is true that since we've launched satellites, our idea of Earth's geometry is no longer that of worms, bound by it. We've integrated it instead into our mental space by regarding it from both sides, and consequently the Earth's shape is no longer a boundary but merely a difference, say between a submarine and a space station. And in becoming a difference rather than a boundary, it became a proper and comfortable subject of thought, with predictable and verifiable results. Something it didn't enjoy back when it hurled through the voids atop an endless pile of turtles.
People living in the middle ages did not live in a time bubble wide enough to make the century count a difference to them. The century was then a boundary, and so uncountable. For the people living before them, with better "health care"iv the century was not a boundary, and so they breached it, ab Urbe condita (which was then the boundary). People living today mostly still live in a narrow time bubble, which is why they keep reinventing well known things as "their own"v, but for the happy minority that actually uses computers and the Internet, time itself is somewhat of a porous boundary. And so yes, even if times past start off as this indistinct pizza, they're rapidly digested into mere differences rather than rock wall.
It makes sense to us few to see through millenia count, but imagine for a second the paralyzing overhead if no discussion could proceed for as long as any boundary anywhere still stood, undigested. Why, we'd have to drop everything and freeze, the notion is not disimilar to the proposition that "while evil goes unpunished, the state does not exist". Sure, why not, let's forget everything else and chase goats around Broadway all day long, we've got nothing better to do.
In short, I think it is at best naive to molest people for whom differences were in fact boundaries for their inept handling of what's plainly seen as a mere difference. But then again, it is at best naive to preserve people's imaginary right to their own boundaries, instead of properly raping them into their final shape. So then... what exactly is left here ?
I have no idea.———
- The general principle is, "link directly to the source", and for very good reasons. Yet here I much prefer this indirect linking because it seems to me to greatly enrich the conversation, let alone provide proper credit. Credit is important not for some sort of vanity or pecuniary benefit considerations, but because meaning is impossible without source, as amply discussed say here and here.
At any rate, if anyone wishes to argue the point please do, I want to hear it. [↩]
- More properly said, the perceptible, which is why music works in the first place. [↩]
- By definition, because if you did know about them then they'd be differences, not boundaries anymore. [↩]
- This specifically and strictly means they had working sewers. [↩]
- Do you know what random derp around here did recently ? Why, he "came up" with things! [↩]