A constructive argument for memetic complexity.

I’ve taken a bit of a break from covering meme theory recently, mostly due to focusing on NOPE and the exciting world of options-induced illiquidity. If you want to check out my prior posts on meme theory, I would suggest my series Trading Salience.

That said, I’ve had a nagging concept in the back of my mind since writing it about quantifying various concepts that I imply in the series. As captivating as it is to define taxonomies and observe trends, it tends to be a different job than actual proofs, and a harder sell to launch a sound argument from. In this post, I’m going to focus on defining some basic inferences I have about memetics, stemming largely from complexity theory, game theory, and analogous representations in linguistics and virology.

What is a meme?

I think most of us think of memes in the internet sense, like:

While this is of course a meme and ties to humor, it isn’t a unique example of the concept. In general, we can fall back to the Dawkinsian definition of a meme, which defines it simply as a unit of cultural transmission, or a unit of information that can self-replicate. By this much broader definition, we can analogize our internet memes to other cultural hearthstones, including:

• Language

• Religion

• Politics

• Identity

And many more.

However, this tends to be a very abstract notion, and like the biologist Dawkins most of us see memetics in large part analogous to phenomena we’re familiar with. Most of us know the idea of a viral meme - a meme that spreads with impunity online. The phrase is more apt than most realize.

Viruses and viroids

In the late 1800s, Adolf Mayer noted that the tobacco mosaic infection could be transmitted between plants, similar to a bacterial infection (also a fairly new concept at that time). A few short years later, Dmitri Ivanovsky employed incredibly fine filters (called Chamberland filters) which were porous to a size smaller than most bacteria, and noted the tobacco mosaic infection would still spread, indicating the existence of an infectious agent smaller than a bacterium (at least, as was known at the time).

It took until the 1930s to conclusively prove the existence of the virus, one of the most interesting lifeforms to ever arise.

Many biologists argue that viruses are not, at least by classical definitions, alive. This is because unlike bacteria, viruses are essentially balls of genetic material (whether DNA or RNA) with a sugar coating, and don’t have independent means to replicate or maintain homeostasis. While they possess the genetic ingredients to be alive (the process of replication), they are not considered alive, since they require another organism (whether a bacterium, a unicellular eukaryote, or a multicellular organism like us) to survive. More interestingly, as we’ve zoomed in on the depths of life, we’ve found that viruses can also infect other viruses. It’s tortoises all the way down.

Not even joking about tortoises. About half a century after viruses were conclusively observed, we observed the Potato spindle tuber viroid, which was even smaller than the smallest known virus! In fact, it solely consists of a nucleic acid (RNA for all known found ones). These little non-lifeforms replicate solely based on the biochemical mechanisms afforded by their hosts, and present many interesting properties.

For viruses and viroids, there’s an inherent tradeoff between simplicity and complexity. As viruses become simpler, they can propagate more effectively, simply due to the rate of mutation. RNA, which tends to also be smaller than DNA, is significantly more error-prone, due to biochemical factors. While uni- and multi-cellular organisms invest a ton of energy and materials into building error-correcting mechanisms, this does not occur in viruses and viroids for two reasons:

1) Evolutionary saddle point/metastability - To put this simply, complexity rarely arises out of a vacuum. To put it analogously, if you buy the ingredients to make a cake, they almost certainly will not re-arrange themselves to make a cake without you getting off the couch. When you apply it to evolutionary strategy, the implication here is a trade-off between “bad” and “good enough”, not “best”. This is one of the reasons you end up with vestigial organs and traits; it isn’t that they are required for evolutionary survival, it’s simply that having them wasn’t detrimental enough. The more mathematical explanation for this is borrowed from optimization problems. Many machine learning methods tend to focus on taking some function and maximizing or minimizing the value it spits out. This tends to be well-behaved in a lot of cases, and can be seen graphically like:

We call these solutions convex simply because of the shape of the graph (we’re not a terribly creative bunch). These are lovely and more stable in practice, and to go back to our argument on viruses these tend to be the optimal outcome (the best choice one could make, or the global optimum).

Evolution, on the other hand, does not usually have the luxury of convex optimization. This is due to a lot of biochemical and real-world factors (I could talk for an hour about phylogenetics and homoplasy), and it tends to follow the non-convex outcome shown above. Sometimes you will get the best possible outcome, like for example creating a kitten from an an amoeba (actually the common ancestor of both). Most times you get weird stuff like humans with vestigial tail bones or extra nipples. It’s because the genetic information tends to be retained since it does not really reduce fitness, but doesn’t improve it either.

We call these outcomes non-convex, because a saddle point (the upper blue dot on the graph) exists—an outcome which isn’t the best, but isn’t the worst either. This tends to be the path evolution follows, and viruses are not an exception.

2) Natural selection and mutation - In general, viruses have strong pressure to simplify over time for several reasons:

• Error prone media — DNA and RNA are not perfect copy machines, for various reasons (homopolymer slippage, exposure to outside elements, and many others). In all organisms, there tends to be a baseline mutation rate, which is of course critical for evolution itself. However, lifeforms tend to try to improve fidelity of genetic code, because well, otherwise you get cancer or super-cancer or your chicken eggs birth Godzilla. Evolution has created many, many different mechanisms for error-detection and correction, but the fundamental truth underlying all of them is requiring energy. Unlike the passive lifecycle of the virus, life tends to be able to collect and use energy. Viruses can’t. They can only really infect cells and hijack their energy sources to do their bidding.

• Stability in transmission — Simple viruses can transmit more easily. This is intuitive. A simple virus weighs less, and can travel by air or sea or any other mechanism to bring it into contact with a host cell. More complicated viruses by themselves may be more (individually fit) - for instance, a single virus may improve its fitness by coding for gigantic chainsaws which destroy the host immune system. The issue though is that when it wants to replicate, in general there are errors, and chainsaws are complicated things. If you code accidentally for part of it wrong, it won’t work, and will be worse than useless.

• Evolutionary arms race — Why does it become worse than useless? We can take a look at the case of COVID-19 for an example. COVID-19, or rather the viral quasispecies SARS-CoV-2 that causes it, is a fairly simply constructed pathogen:

  

  It’s literally a ball of shit (the RNA inside, the squiggly purple line) with an envelope protein (literally an outer coating) with pointy bits outside (the spike protein). Ignoring the obvious (the genetic material), the remaining components serve pretty intuitive functions:

  • Envelope protein - This helps the virus survive outside where raw genetic material (like the viroid) would be destroyed (aka stuff like sunlight).

  • Spike protein - This is the most nifty and interesting. This is literally a spike which allows it to bind to the human ACE2 receptor, hijacking the cell to spread its chewy goodness—I mean, infection. This is a uniquely designed protein specifically to help the virus infect and therefore propagate. And this works fantastically, except for evolution (or human intervention).

  We can borrow an interesting concept from game theory called evolutionary game theory. Viruses and viroids spreading infection to hosts can simply be modeled as a game with two players, player 1 (the host) and player 2 (the viroid).

  Without delving into matrix notation or the mathematics, we can see that pathogenic agents (whether viruses, bacteria, or viroids) are playing a game over many, many different intervals (called an iterated game in game theory) against the host. Despite common belief, there is rarely an inherent need for agents to evolve pathogenicity—in fact, each agent here (the host cell and the pathogen) are simply trying to maximize their own utility (they’re trying to survive and propagate). It’s actually a more optimal strategy for the pathogen and the host to co-exist with minimal damage to either, because if—for example—a virus is too pathogenic, it provokes the host to spend a lot of energy on combating it, reducing its fitness. On the converse, an infectious agent which actually helps the host tends to win out and spread the most. If you don’t believe me, read about the hypothesized origin of the cell nucleus.

  That being said, most of the time, even benign infectious agents cost energy and reduce the fitness of the cell. So there’s a strong incentive for the cell to remove the invader, which it does most often by targeting the invader with various yummy traps. Or, in the case of humans, we do it by targeting parts of the virus or bacteria that are unique to that entity and not us (for example, we target bacteria due to the differences of eukaryotic and prokaryotic ribosomes).

Now let’s take a step back from biology. I’m going to end this post shortly because I’m sure half of you are asleep by now, and I went too far into the weeds, but I do have a point—eventually. Viruses and ideas have more in common than most are comfortable with. While most ideas don’t rack up a multi-million body count (well, some do), ideas tend to require the following ingredients to survive:

1. Information

2. A means to propagate

This occurs for any idea, and for the more philosophical of my readers, one could argue ideas, much like viruses, only exist when they can be propagated. After all, if an idea is squelched out of existence (and not recorded), could you say it existed at all? Information may or may not be an objective concept (one could argue that a ball is spherical regardless of observation), but the idea of a spherical ball only exists because it can be observed and understood (that it has an effect on the host).

I was really hoping to not make this a multi-part series, but there’s a bit too much information density here (ha) to keep in just one post. I’m going to release this one for free, but as mentioned in my prior articles, I’m hoping to spin up a paid subscription service to raise money for charity. If you’re interested, please subscribe! I’m going to publish all the money raised transparently and the charity it is going to (for this and probably next month, 75% of subscription income will go to the Berkeley Chess School— the remaining 25% I will reserve for potential taxes on it).

In the next posts, I’m going to introduce Kolgomorov complexity and my lemma on memetic fitness, as well as talk about potential use cases for this in finance and other fields.

Cheers, and have a lovely weekend.