Abstractions on Inconsistent Data

[I’m not sure this makes any sense – it is mostly babble, as an attempt to express something that doesn’t want to be expressed. The ideas here may themselves be an abstraction on inconsistent data. Posting anyway because that’s what this blog is for.]

i. Abterpretations

Abstractions are (or at least are very closely related to) patterns, compression, and Shannon entropy. We take something that isn’t entirely random, and we use that predictability (lack of randomness) to find a smaller representation which we can reason about, and predict. Abstractions frequently lose information – the map does not capture every detail of the territory – but are still generally useful. There is a sense in which some things cannot be abstracted without loss – purely random data cannot be compressed by definition. There is another sense in which everything can be abstracted without loss, since even purely random data can be represented as the bit-string of itself. Pure randomness is in this sense somehow analogous to primeness – there is only one satisfactory function, and it is the identity.

A separate idea, heading in the same direction: Data cannot, in itself, be inconsistent – it can only be inconsistent with (or within) a given interpretation. Data alone is a string of bits with no interpretation whatsoever. The bitstring 01000001 is commonly interpreted both as the number 65, and as the character ‘A’, but that interpretation is not inherent to the bits; I could just as easily interpret it as the number 190, or as anything else. Sense data that I interpret as “my total life so far, and then an apple falling upwards”, is inconsistent with the laws of gravity. But the apple falling up is not inconsistent with my total life so far – it’s only inconsistent with gravity, as my interpretation of that data.

There is a sense in which some data cannot be consistently interpreted – purely random data cannot be consistently mapped onto anything useful. There is another sense in which everything can be consistently interpreted, since even purely random data can be consistently mapped onto itself: the territory is the territory. Primeness as an analogue, again.

Abstraction and interpretation are both functions, mapping data onto other data. There is a sense in which they are the same function. There is another sense in which they are inverses. Both senses are true.

ii. Errplanations

Assuming no errors, then one piece of inconsistent data is enough to invalidate an entire interpretation. In practice, errors abound. We don’t throw out all of physics every time a grad student does too much LSD.

Sometimes locating the error is easy. The apple falling up is a hallucination, because you did LSD.

Sometimes locating the error is harder. I feel repulsion at the naive utilitarian idea of killing one healthy patient to save five. Is that an error in my feelings, and I should bite the bullet? Is that a true inconsistency, and I should throw out utilitarianism? Or is that an error in the framing of the question, and No True Utilitarian endorses that action?

Locating the error is meaningless without explaining the error. You hallucinated the apple because LSD does things to your brain. Your model of the world now includes the error. The error is predictable.

Locating the error without explaining it is attributing the error to phlogiston, or epicycles. There may be an error in my feelings about the transplant case, but it is not yet predictable. I cannot distinguish between a missing errplanation and a true inconsistency.

iii. Intuitions

If ethical frameworks are abterpretations of our moral intuitions, then there is a sense in which no ethical framework can be generally true – our moral intuitions do not always satisfy the axioms of preference, and cannot be consistently interpreted.

There is another sense in which there is a generally true ethical framework for any possible set of moral intuitions: there is always one satisfactory function, and it is the identity.

Primeness as an analogue.

Atemporal Ethical Obligations

[All the trigger warnings, especially for the links out. I’m trying to understand and find the strongest version of an argument I heard recently. I’m not sure if I believe this or not.]

Edit: This was partly a hidden argument ad absurdum. I thought it was weird enough to make that obvious, but I forgot that this is the internet (and that I actually have people reading my blog who don’t know me IRL).

It is no longer enough just to be a “good person” today. Even if you study the leading edge of contemporary morality and do everything right according to that philosophy, you are not doing enough. The future is coming, and it will judge you for your failures. We must do better.

This may sound extreme, but it is self-evidently true in hindsight. Pick any historical figure you want. No matter their moral stature during their lifetime, today we find something to judge. George Washington owned slaves. Abraham Lincoln, despite abolishing slavery in the United States, opposed black suffrage and inter-racial marriage. Mary Wollstonecraft arguably invented much of modern feminism, and still managed to write such cringe-worthy phrases as “men seem to be designed by Providence to attain a greater degree of virtue [than women]”. Gandhi was racist. Martin Luther King Jr abetted rape. The list goes on.

At an object level, this shouldn’t be too surprising. Society has made and continues to make a great deal of moral progress over time. It’s almost natural that somebody who lived long ago would violate our present day ethical standards. But from the moral perspective, this is an explanation, not an excuse; these people are still responsible for the harm their actions caused. They are not to be counted as “good people”.

It’s tempting to believe that today is different; that if you are sufficiently ethical, sufficiently good, sufficiently “woke” by today’s standards, that you have reached some kind of moral acceptability. But there is no reason to believe this is true. The trend of moral progress has been accelerating, and shows no signs of slowing down. It took hundreds of years after his death before Washington became persona non grata. MLK took about fifty. JK Rowling isn’t even dead yet, and beliefs that would have put her at the liberal edge of the feminist movement thirty years ago are now earning widespread condemnation. Moral progress doesn’t just stop because it’s 2020. This trend will keep accelerating.

All of this means that looking at the bleeding edge of today’s moral thought and saying “I’m living my life this way, I must be doing OK” is not enough. Anybody who does this will be left behind; in a few decades, your actions today will be recognized as unethical. The fact that you lived according to today’s ethical views will explain your failings, but not excuse them. Thus, in order to be truly good people, we must take an active role, predict the future of moral progress, and live by tomorrow’s rules, today.

Anything else is not enough.

Self-Predicting Markets

The story of Hertz has fundamentally changed how I view the stock market. This isn’t a novel revelation – now that I understand it, I’ve seen the core insight mentioned elsewhere – but it took a concrete example to really drive the point home.

The short version of the Hertz story is that the company went bankrupt. They have nearly $20 billion in debt, and as far as anybody can tell, no path to recovery; they’re bankrupt because their business model has been losing money for years despite several attempts to turn things around. The twist? Their stock is still trading, and at time of writing they have a market cap of $900 million.

I notice I am confused.

On any intuitive understanding of the market this shouldn’t be possible. The company is literally worthless. Or really, worse – it’s less than worthless given its debt load. People are paying positive money to own negative money. On a naive view this is another nail in the coffin of the Efficient Market Hypothesis.

After noticing that I was confused, I tried to generate hypotheses to explain this story:

  • Maybe the EMH really is wrong and the markets are nonsense.
  • Maybe bankruptcy laws are so complex and tangled that the expected value of the company really is positive after all is said and done.
  • Maybe the markets expect Hertz to get a government bailout for some reason.

Some of these are plausible (in particular the second), but none of them were particularly satisfying, so I tried asking myself why I, in a hypothetical world, would buy Hertz stock in this situation. I gave myself the standard answer: because I expected the stock go up in value in the future. Then I realized that this answer has nothing to do with the value of the company.

I had been making the mistake of viewing the stock market as a predictor of company value over the short-to-medium term, but this isn’t true. The stock market is a predictor of itself over the short-to-medium term. If people think the stock will go up tomorrow, then the stock will go up today – it doesn’t matter what the value of the company does at all. The company can be literally worthless, and as the Hertz story proves, people will still buy as long as they think the stock will go up tomorrow.

Now in practice, there are a bunch of traders in the market who trade based on the expected value of the company. As long as these people have a majority or at least a plurality, then everybody else is destined to follow their lead. If the expected value of the company goes up, then the expected value of the stock goes up, as long as enough people are trading based on company value. But in cases like Hertz, the expected value of the company is nothing, so value-based traders exit the market entirely. This leaves only the “shallow” stock-based traders, whose rational move is now to trade based on the expected value of the stock being completely divorced from reality.

The market is really weird.

The Stopped Clock Problem

[Unusually for me, I actually wrote this and published it on Less Wrong first. I’ve never reverse-cross-posted something to my blog before.]

When a low-probability, high-impact event occurs, and the world “got it wrong”, it is tempting to look for the people who did successfully predict it in advance in order to discover their secret, or at least see what else they’ve predicted. Unfortunately, as Wei Dai discovered recently, this tends to backfire.

It may feel a bit counterintuitive, but this is actually fairly predictable: the math backs it up on some reasonable assumptions. First, let’s assume that the topic required unusual levels of clarity of thought not to be sucked into the prevailing (wrong) consensus: say a mere 0.001% of people accomplished this. These people are worth finding, and listening to.

But we must also note that a good chunk of the population are just pessimists. Let’s say, very conservatively, that 0.01% of people predicted the same disaster just because they always predict the most obvious possible disaster. Suddenly the odds are pretty good that anybody you find who successfully predicted the disaster is a crank. The mere fact that they correctly predicted the disaster becomes evidence only of extreme reasoning, but is insufficient to tell whether that reasoning was extremely good, or extremely bad. And on balance, most of the time, it’s extremely bad.

Unfortunately, the problem here is not just that the good predictors are buried in a mountain of random others; it’s that the good predictors are buried in a mountain of extremely poor predictors. The result is that the mean prediction of that group is going to be noticeably worse than the prevailing consensus on most questions, not better.


Obviously the 0.001% and 0.01% numbers above are made up; I spent some time looking for real statistics and couldn’t find anything useful; this article claims roughly 1% of Americans are “preppers”, which might be a good indication, except it provides no source and could equally well just be the lizardman constant. Regardless, my point relies mainly on the second group being an order of magnitude or more larger than the first, which seems (to me) fairly intuitively likely to be true. If anybody has real statistics to prove or disprove this, they would be much appreciated.

The Law of Cultural Proximity

[Not my area of expertise, but I would be surprised if the core thesis was wrong in a significant way. Probably not as original as I think it is. Based on a previous blog post of mine that went in a very different/weird direction.]

Introduction

Currently, different human cultures have different behavioural norms around all sorts of things. These norms cover all kinds of personal and interpersonal conduct, and extend into different legal systems in countries around the globe. In politics, this is often talked about in the form of the Overton window, which is the set of political positions that are sufficiently “mainstream” in a given culture to be considered electable. Unsurprisingly, different cultures have different Overton windows. For example, Norway and the United States currently have Overton windows that tend to overlap on some policies (the punishment of theft) but perhaps not on others (social welfare).

Shared norms and a stable, well-defined Overton window are important for the stable functioning of society, since they provide the implicit contract and social fabric on which everything else operates. But what exactly is the scope of a “society” for which that is true? We just talked about the differences between Norway and the U.S., but in a very real sense, Norway and the U.S. share “western culture” when placed in comparison with Iran or North Korea. In the other direction, there are many distinct cultures entirely within the U.S. with different norms around things like gun control. The categories were made for man, not man for the categories.

However blurry these lines are, it might be tempting to assume that they get drawn roughly according to geography; it’s certainly reflected in our language (note my use of “western culture” already in this post). But this isn’t quite right: the key factor is actually interactional proximity; it’s just that in a historical setting geographical and interactional proximity were the same thing. Time for an example.

Ooms and Looms

Back in the neolithic era, the tribe of Oom and the tribe of Loom occupied opposite banks of their local river. These two tribes were closely linked in every aspect: geographically, linguistically, economically, and of course, culturally. Because the Ooms and the Looms were forced into interaction on such a regular basis, it was functionally necessary that they shared the same cultural norms in broad strokes. There was still room for minor differences of course, but if one tribe started believing in ritual murder and the other didn’t, that was a short path to disagreement and conflict.

Of course, neolithic tribes sometimes migrated, which is what happened a short time later when the tribe of Pa moved into the region from a distant valley. Compared to the Ooms and the Looms, the Pas were practically alien: they had different customs, different beliefs, and spoke a different language altogether. Unsurprisingly, a great deal of conflict resulted. One day an amorous Oomite threw a walnut towards a Pa, which was of course a common courting ritual among both the Ooms and the Looms. Unfortunately, the Pa saw it as an act of aggression. War quickly followed.

Ultimately, the poor Pa were outnumbered and mostly wiped out. The remaining Pa were assimilated into the culture of their new neighbours, though a few Pa words stuck around in the local dialect. Neolithic life went on.

In this kind of setting, you could predict cultural similarity between two people or groups purely based on geographic proximity. It was possible to have two very different peoples living side by side, but this was ultimately unstable. In the long run, such things resulted in conflict, assimilation, or at best a gradual homogenization as memes were exchanged and selected. But imagine an only-slightly-different world where the river between the Ooms and the Looms was uncrossable; we would have no reason to believe that Oom culture and Loom culture would look anything alike in this case. The law that describes this is the law of cultural proximity:

In the long run, the similarity between two cultures is proportional to the frequency with which they interact.

More First Contact

Hopefully the law of cultural proximity was fairly self-evident in the original world of neolithic tribes. But over time, trade and technology started playing an increasing role in people’s lives. The neolithic world was simple because interactions between cultures were heavily mediated by geographic proximity, but the advent of long-distance trade started to wear away at that principle. Ooms would travel to distant lands, and they wouldn’t just carry home goods; they would carry snippets of culture too. Suddenly cultures separated by great distances could interact more directly, even if only infrequently. Innovations in transportation (roads, ship design, etc) made travel easier and further increased the level of interaction.

This gradual connecting of the world led to a substantial number of conflicts between distant cultures that wouldn’t have even know about each other in a previous age. The Ooms and the Looms eventually ran into their neighbour the Dooms, who conquered and assimilated them both in order to control their supply of cocoa. The victor of successive conflicts, the Dooms formed an empire, developed new technologies, and expanded their reach even farther afield. On the other side of a once-uncrossable sea, the Dooms met the Petys; they interacted infrequently at first, but over time their cultures homogenized until they were basically indistinguishable from each other.

The Great Connecting

Now fast-forward to modern day and take note of the technical innovations of the last two centuries: the telegraph, the airplane, the radio, the television, the internet. While the prior millennia saw a gradual connecting of the world’s cultures, the last two hundred years have seen a massive step change: the great connecting. On any computer or phone today, I can easily interact with people from one hundred different countries around the globe. Past technologies metaphorically shrank the physical distance between cultures; the internet eliminates that distance entirely.

But now remember the law of cultural proximity: the similarity between two cultures is proportional to the frequency with which they interact. This law still holds, over the long run. However the internet is new, and the long run is long. We are currently living in a world where wildly different cultures are interacting on an incredibly regular basis via the internet. The result should not be a surprise.

The Future

[This section is much more speculative and less confident than the rest.]

The implications for the future are… interesting. It seems inevitable that in a couple of generations the world will have a much smaller range of cultures than it does today. The process of getting there will be difficult, and sometimes violent, but the result will be a more peaceful planet with fewer international disagreements or “culture wars”. A unified world culture also seems likely to make a unified world government possible. Whether the UN or some other body takes on this role, I expect something in that space to grow increasingly powerful.

While a stable world government seems like it would be nice, homogeneity has its pitfalls. There’s a reason we care about ecological diversity so much.

Of course in the farther future, human culture will fragment again as it spreads into space. The speed of light is a hard limit, and while our first Martian colony will likely stay fairly connected to Earth, our first extra-solar colony will be isolated by sheer distance and will be able to forge its own cultural path. Beyond that, only time will tell.