Justin Attempts to Understand Part of “The Fabric of Reality”, Part 1

This post is part of my attempt to understand the discussion of Godel’s incompleteness theorem presented in The Fabric of Reality by David Deutsch (DD).

See part 2 here

In Chapter 10 of The Fabric of Reality, DD says:

Godel proved that if a set of rules of inference in some (sufficiently rich) branch of mathematics is consistent (whether provably so or not), then within that branch of mathematics there must exist valid methods of proof that those rules fail to designate as valid. This is called Godel’s incompleteness theorem. To prove his theorems, Godel used a remarkable extension of the Cantor ‘diagonal argument’ that I mentioned in Chapter 6. He began by considering any consistent set of rules of inference. Then he showed how to construct a proposition which could neither be proved nor disproved under those rules. Then he proved that that proposition would be true.

So my attempt to understand DD’s discussion of Godel’s incompleteness theorem will begin with a review of the relevant portion of Chapter 6, presented below:

DD opens the chapter with the question of whether we will be able to build a fully universal virtual reality generator which can render any environment the human mind is capable of experiencing.

DD clarifies that he’s talking about a virtual reality generator which could be programmed to generate all logically possible environments, and not something that would already contain within itself the specific instructions for generating the environment.

DD says we can imagine a virtual reality generator as having an effectively unlimited memory capacity for storing a given VR environment by imagining that it can read any number of disks.

DD says we can’t imagine unlimited computation speed like we can unlimited memory capacity. So what happens if the VR generator can’t render stuff fast enough??

DD says the answer is basically the VR generator would need to be able to control the equivalent of the brain’s “CPU clock” to keep it in sync with what the VR generator can generate. DD notes that this slowing down would be invisible from the user’s perspective within the simulation, though if their brain needs to be slowed down a bunch to make complex environments, more time will elapse in reality.

DD asks if there is anything outside the repertoire of a VR generator.

Would its repertoire be the set of all logically possible environments? It would not. Even this futuristic machine’s repertoire is drastically circumscribed by the mere fact of its being a physical object. It does not even scratch the surface of what is logically possible, as I shall now show.

DD says the basic idea of the argument he will use, which is called the diagonal argument, has had various other applications, like proving that there are infinite quantities greater than the infinity of natural numbers, and to prove Godel’s Incompleteness Theorem.

DD says that each program for the VR generator has to have some particular, quantized set of values for any variables, and therefore “the set of possible programs must be discrete.”

Question: What’s the alternative here? Like what would a non-discrete set of possible programs mean?

DD says each program has to be expressible as a finite sequence of symbols in a computer language.

There are infinitely many such programs, but each one can contain only a finite number of symbols. That is because symbols are physical objects, made of matter in recognizable configurations, and one could not manufacture an infinite number of them.

Question: Is this similar to how there’s an infinite number of books that could be written but a finite length to any given book, cuz books are made up of sequences of letters represented in some physical objects (in ink on pages, or in a hard drive and then displayed on a screen) and you can’t have infinite actual letters?

DD says the requirements he’s been talking about — “that the programs must be quantized, and that each of them must consist of a finite number of symbols and can be executed in a sequence of steps” — are a big deal that “impose drastic restrictions on the repertoire of any physically possible machine.”

DD asks us to imagine the infinite possible programs in an infinitely long list, numbered Program 1, Program 2, etc. You could also list them by VR environment they generate, so it’d be like Environment 1, Environment 2, etc.

DD says programs could vary a lot in how long they run for but let’s “consider only programs that continue to run for ever” to keep his proof simple.

DD says we can call the class of logically possible environments Cantgotu environments. He defines Cantgotu environments in the following way:

For the first subjective minute, a Cantgotu environment behaves differently from Environment 1 (generated by Program 1 of our generator). It does not matter how it does behave, so long as it is, to the user, recognizably different from Environment i. During the second minute it behaves differently from Environment 2 (though it is now allowed to resemble Environment i again). During the third minute, it behaves differently from Environment 3, and so on.

The “and so on” means that it behaves differently than all the Environments on our infinite list of programs the VR generator can run at some point.

Questions: How can we reason about these Cantgotu environments at all? What makes them logically possible? Do they necessarily contradict one or more of the requirements DD mentioned about programs being quantized in a finite number of symbols, etc? So the idea is these are programs which are physically impossible but which we don’t have any criticism of on logical grounds?

DD says that there’s a ton of Cantgotu environments possible, because the only constraint is that during some minute they behave differently than something in the list of programs the VR Generator can run.

DD says his argument shows that we can only run an infinitesimal fraction of the set of all logically possible environments.

Left vs. Facts

Check out this tweet:

Knowledge of a fact which is conceded as true is being used to delegitimize someone’s views. I think this is extraordinary and scary.

Normally, debate over facts involves things like discussion over whether a factual claim is true, or an argument that the fact isn’t really that important, or a claim that there’s additional context which you need to understand the fact.

Those are all fine.

But here we see someone conceding a factual claim and then being like “Ah ha! The fact that you know that puts you on the side of the White Nationalists!”

Honestly, wtf do you do with that?

There’s already so many nasty ways the left delegitimizes disagreement.

It attacks people as not having the right sort of experience to have a valid opinion because they are white/male/etc.

It attacks people as insufficiently educated and elite to understand complex topics.

It attacks people for being religious.

It attacks people as racist, sexist, homophobic, xenophobic, islamophobic, etc., for having the wrong opinions on certain topics.

These are all evil and destructive.

We shouldn’t allow them to add factual knowledge to the list.

Patreon Tries to Explain Its Lauren Southern Ban

Patreon banned conservative political commentator Lauren Southern and thus deprived her of a big chunk of her income. Patreon CEO Jack Conte has made a video trying to explain this decision. The reasoning presented in the video is mistaken.

A fundamental mistake in the video is a reliance on a concept called “Manifest Observable Behavior.” As described in the video (my transcription below):

Content policy and the decision to remove a creator page has absolutely nothing to do with politics and ideology and has everything to do with a concept called Manifest Observable Behavior. The purpose of using Manifest Observable Behavior is to remove personal values and beliefs when the team is reviewing content. It’s a review method that’s entirely based on observable facts: what has a camera seen? What has an audio device recorded? It doesn’t matter what your intentions are, your motivations, who you are, your identity, your ideology; the trust and safety team only looks at Manifest Observable Behavior.

This seems like the primary description Patreon offers for this concept, as I couldn’t find one on their site.

The emphasis on looking at behavior is kind of odd. How would you judge another person’s intentions other than by their behavior? What else is there to go on besides their behavior?

Also, what behaviors are considered good or bad depends on a person’s values. The person judging has to judge behaviors he sees as good or bad. So you can’t make value free judgments about behaviors. It’s impossible.

The idea that one makes judgments based directly on observations and free from one’s values and beliefs is a refuted mistake. As explained at the link:

[Karl] Popper was giving a lecture and at the start he said, “Observe!” People said, “Observe what?” There is no such thing as emptying your mind and just observing and being guided by the data. First you must think, first you must have ideas about what you’re looking for.

Despite their claim to the contrary — that they’re just judging value-free according to the contents of video and audio recordings — it’s literally impossible for Patreon to do what they’re claiming to do. The observations involved in “Manifest Observable Behavior” will involve ideas about 1) what to observe, i.e. what is significant or meaningful behavior 2) interpretations as to what the observed behavior means, 3) value judgments as to the morality of the behavior.

And sure enough, what is presented in the video is an argument involving value judgments and particular interpretations of facts in politically controversial matters (presented below). So “Manifest Observable Behavior” fails on its own terms.

What is Patreon’s argument for banning Lauren? From the video (my transcript):

From a high level, we removed [the pages of Lauren Southern and the members of Defend Europe] because they directly obstructed a search-and-rescue ship in the Mediterranean. And they made a variety of statements and outlined plans to obstruct similar rescue ships in the future. And that’s a violation of a section of our content policy that prohibits creators from threatening to take or from taking action that could lead to harm or loss of life.

Then Jack shows Lauren disputing that she’s part of Defend Europe. Jack continues:

Questions like “Is Lauren Southern an activist or is she a journalist?” “Is she a member of Defend Europe or is she not a member of Defend Europe?” … those sorts of binary questions, turns out they just matter less than Manifest Observable Behavior. You can’t use Manifest Observable Behavior to say who someone is. That’s just a more nebulous claim. You can use Manifest Observable Behavior to say what someone did or didn’t do, and whether or not those things are or are not against your content policy.

If you judge Lauren’s actions and decide she was participating in Defend Europe’s activities, you are in essence saying she was an activist and not a journalist, whether you make that claim explicitly or not. The Patreon guy is trying to make judgments while avoiding responsibility for making them by hiding behind a buzzphrase. This is ridiculous and should not fool anybody.

Patreon accuses Lauren of doing stuff likely to cause harm:

So what are these ships doing? Who is Lauren stopping, and why is that bad?

Bad?? Sounds like a value judgment! 🤔 Continuing:

They are search-and-rescue ships that save people attempting to cross the oceans to Europe.

Jack then claims the ship Lauren & Defend Europe stopped was a response to stuff like refugee kids drowning.

Lauren disputes the characterization of the ships being stopped as rescue ships:

See also this video explaining the mission and discussing the NGO ships:

The nature of the activities of the alleged “search-and-rescue” ships is a controversial matter, and getting more information on what the NGO ships were doing was part of the stated purpose of the Defend Europe mission. Patreon chose one side in a controversy according to their political and ideological values, and then wants to pretend they just watched some video and saw the Clear Truth.

Whether Lauren was doing anything that could cause people harm is an issue that should have gotten discussed and sorted out by an objective, non-biased third party before her income got taken away. Despite the fact that Jack acknowledges that “the authority to take away a human being’s income is a sobering responsibility,” he does not appear serious. If Jack and Patreon were really sobered by this responsibility, they’d incorporate elements of due process into their review process, like the opportunity to argue why an account ban shouldn’t occur, the right to present evidence and witnesses, etc.

These are well known elements of due process that our society has been developing and refining for centuries. But Jack/Patreon aren’t actually serious about the responsibility they have; they just want to virtue signal that they are responsible and serious because that plays well with their audience. Their communications with Lauren made it clear they would not consider an appeal. Their after-the-fact, incoherent explanation, and a vague commitment to implementing some sort of “appeals process” that won’t apply to Lauren, doesn’t come close to meeting their responsibility.