Memes Are Digital

Lo those many moons ago, vain and ignorant, I spake thus: MemesArentDigital. And a lot more MemesShmemes kind of talk. Well, isn't time grand? Don't we all change? Here we are again and here I am to tell you: MemesAreDigital.

You just have to loosen up a little bit on what you mean by a digit. Now, WhatsaDigit?? Well, it's an element of a CombinatoriallyComplete representation. No, I'm not smoking anything, it's just that kind of time of day. The moon is in the seventh house and jupiter aligns with ... wait a minute, that's got nothing to do with this.

Imagine a great white empty space proceeding in all possible directions and dimensions, all alike, and no place in it marked, bounded, or distinct. I don't mean some kind of infinite universe because finity is not a distinction we've represented here. And I only call it white because otherwise I have to call it black - also not an attribute - and then you'll come over all claustrophobic. I want you agoraphobic instead.

So afraid of all that non-existent non-anything at all whiteness that you'll close your eyes. Not in a PsychoActive way, but just to make yourself a nice dark little cubby in there. A spot. Avoid large spaces, stick to small. And there you are. Distinct. Outside there's a great formless uncarved blockiness. And inside, tight and snug against your face, the very surface of that terrifying universe. Perfectly contained.

Outside that surface looms agoraphobically the empty set. Terrifying, ain't it? Hush now, you're all right. You're right here in womb land. We tossed a lasso round that terrible remarklessness and that's a set. Empty. Set. Get it?

So now we have 0 and we have 1. 0 being the empty and 1 being the universe contained in a nutshell. Oh, I told you it was outside the nutshell, didn't I? Well, inside and outside don't make any difference here because we have no way to represent them. So we can invert em without trouble. Whatever makes you comfy - we're not all agoraphobes I guess. So long as we're copacetic on the numbering I don't care.

So guess what? The empty is a meme, and that meme is zero. The universe is another meme, and that meme is one. Now to make all the other memes into digits we just subdivide the 1.

How we do that? You gotta make it more precise. Well, frankly, I don't gotta. I've shown you some memes and I've shown you how they're digital. You wanna enumerate more of 'em, that ain't my problem. You tell me MemesArentDigital, however, and I'm gonna call you on it - they sure are and you show me one that ain't. -- Pete

Tangent moved to TheAdjunct's WhatDoesMemeMeme?

It isn't a tangent if the term "meme" is used incorrectly here.

Elaborate example extracted to MemesModelProposal.

Erm... I see. I'm afraid I'm left with an overwhelming sense of "Huh?" -- DaveVoorhis

Another meme! Ambiguity ... let's number it "2". Using the usual ZermeloFraenkel? construction, we get that as a set including the empty set and the set of the empty set ... power sets are ways of chopping smaller sets up recursively you see ... LogicIsaFractal? ...

Here's a riddle.

    Pattern language is to pattern
 as Wiki is to wiki page (or perhaps as wiki roadmap is to wiki page)
 as DNA is to gene
 as _____ is to meme

I'm a little confused about this ... a pattern language is a collection of interdependent patterns. Likewise, a wiki is a collection of interdependent wiki pages. A chromosome, GenesShmenes notwithstanding, may be thought of as a collection of interdependent genes. But DNA is an alphabet of which these so-called genes are composed. Not a collection of them. So I don't know if you're asking about the constituents of memes, or about what to call a collection of interdependent memes. Clarify?

The latter. I was referring to DNA as in the coloquial expression "a person's DNA", which to us average "CSI: Crime Scene Investigation" [an American TV show] watchers means the whole thing - all genes and chromosomes lumped together. But we CSI watchers admire clear insight and careful detective work, so thank you for pointing out this discrepancy.

And now I'm confused - I don't know how technically correct I want to be here. To be honest, I want to try to extend the analogy to the "combination" and "sharing of elements" of these collections. I don't usually think in terms of chromosomes combining - I think of DNA combining (then again, what do we CSI watchers know). I suppose wikis and pattern languages don't usually combine. But civilizations and cultures do combine and mix traits (and memes are supposedly units of culture - for example culture today still seems to have most of those Sumerian Mes your above link mentions). So I don't know...

Don't be technically correct. This page got off on the wrong foot in that regard by defining digital as countable instead of discrete in both when it can change and what values it can take. -- MartinShobe?

It actually refers to CombinatoriallyComplete, not countable. Unless you're saying countable == CombinatoriallyComplete?

"But WhatsDigital?? Apart from a defunct equipment corporation? Well, that's a bit more conventional. Digital means to most of us, convertible into binary." Something is convertable into binary if and only if it's countable. -- MartinShobe?

I only said "means to most of us", that being a fillip to convention. I claimed CombinatoriallyComplete, not countable. Relations between CombinatoriallyComplete and RecursivelyEnumerable being an artifact of Turing/Post, I don't regard as a given. -- Pete

Is the definition of CombinatoriallyComplete you are using the same as the one on that page? If so, would the standard model of real numbers in ZFC be CombinatoriallyComplete? It appears to me that it would, but after my misunderstanding here, I would prefer not to rely on that. -- MartinShobe?

You ask good questions Martin! I'd agree the reals are CombinatoriallyComplete as that page defines it; all the information represented by a real is explicit in the representation. I gave the graph example on the CombinatoriallyComplete page to emphasize that this as an attribute of representation. But I am glossing; combinatorial completeness is an attribute of FunctionalProgramming with a well worked out theory beginning with Church, continuing with Curry/Schonfinkel. I'm no expert on this and I don't know just how much violence my gloss does the the formalism. I'd be curious to find out, though. -- Pete

I not an expert there either, but I'd be mildly surprised if there wasn't something else going on. As it stands now, it allows too much (almost all of mathematics, and therefore just about anything that can be modelled by it). Additionally, I'm more used to the definition of CombinatoriallyComplete used in hardware testing, which is almost, but not completely, unlike the definition here.

To be fair, I should state my own views on the "Are Memes Digital" question. It seems to me that the question makes about as much sense as asking whether music (as a whole) is digital. While there is such a thing as digital music, the digital is referring to how it is stored/processed/transmitted instead of to the music per se. -- MartinShobe?

[It seems to me that the question makes about as much sense as asking whether music (as a whole) is digital.] Maybe thats exactly the point. There are quite dome sciences, that do usually not encode the items under consideration. Take philosophy, you usually don't encode the different subjects, but approach each of them individually or all of them together. You e.g. do not simulate a lot of them. The whole point of MemesAreDigital seems to be, that memes are not just a fancy name for a philosophical concept, but something, that could very well be encoded and simulated or be analysed mathematically. -- .gz

Are we taking this analogy (these analogies) too far?

Of course we are. We as humans take all analogies too far. Just like a sixteen-year-old boy with his date - we are compelled to keep groping.

JuneZeroSix