Reach + parameterisation of reach

Date: 2020-11-02

I wrote this as part of a post on reach + IGCs. This was 95% of the post at the point I copied it out; it seems better as a stand alone post.

I think reach is parameterised over infinite domains. I explain what I mean by that below. I don’t know if this is right, but I would be surprised if it were wrong, so I would like to know if anyone disagrees.

When an explanation has reach, it means the explanation is general over many problems or situations. The exact nature of this generality is particular to the explanation.

One example of reach is theories which are time-independent and/or space-independent; maybe a theory works everywhere and at all times (at the beginning of the universe, and now, and we expect it will in 100 billion years and onwards), like general relativity or quantum theory; or maybe a theory works regardless of the time of day (‘if I dial the emergency number someone will pick up, but only if people commonly have and use phones’, ‘leaving food on the stove will heat it, then cook it, then burn it, and then set fire to it’)

Reach can be mundane and fantastical. All explanations have some level of reach.

It’s hard (or impossible) to compare explanations’ reach without a common phenomena to use as a basis. Does a theory of housing in post-GFC North America have more or less reach than a theory of sodium’s role in the ionosphere? I don’t know if that question has an answer. What about newtonian gravity and general relativity? It’s reasonable to say that GR has more reach because GR explains phenomena which newtonian gravity does not, and the reverse is not true; GR is an explanatory superset.

Reach has a size, but it’s hard to be exact besides ‘zero’ and ‘infinite’. It doesn’t really make sense for reach to be ever be completely zero (b/c the explanation would not account for anything). If an explanation has little reach then it only accounts for very specific things (it’s parochial). Explanations can also have unbounded reach. Sometimes it might seem like explanations have near-unbounded reach (e.g. newtownian gravity seemed unbounded except for the orbit of Mercury). In reality, we can’t reliably tell the difference between ‘near-unbounded’ and ‘parochial’ without a superior understanding of what’s going on (which requires additional explanations).

Reach is parameterised over infinite domains. That’s because those domains correspond to–a least–levels of emergence. Some domains are subsets/supersets of other domains, but they can be incomparable too. Example: natural selection has some domain like ‘all life on earth with a genome’ (it might be even more specific than this, though). natural selection also has some domain in time and space; we expect natural selection will work in many other contexts too, like some alien life, provided it meets certain conditions. It’s possible that alien life might not meet those conditions, like hyper-advanced bioengineered AGIs. It’s not clear how natural selection would work here, and we can recognise that b/c we know something about the bounds of it’s reach. We can reason about what domains of reach an explanation has by exploring the explanation (thoughts, experiments, predicts, etc).

We don’t care that explanations have zero reach in some domains. General Relativity doesn’t really have anything to do with housing prices in the USA. So even though GR has some universal reach WRT time and space (AFAIK; galaxy rotation rates aside), it has 0 reach WRT housing prices. (It does have reach when it comes to houses themselves; you still experience gravity when building houses and when inside houses etc, and need to take it in to account.)

If an explanation has reach over some complete domain we say it has universality. I don’t know if the domain needs to be infinite, but it seems like many important universalities have an infinite domain. Some universalities are special and some seem like they’re not special. Some important domains of universalities are: all matter at all points in space and time, all computable programs, all programs, all real numbers, all people, all alphabets, all ideas, etc.

curi once said:

X is a universal Y if it can do any Z that any other Y can do.

I could say: This turing machine is a universal computer because can compute any program that any other computer can compute. The universality is all computable programs.

Or: Paths Forward is a universal discussion methodology because it can lead to a successful conversation for all conversations that any other discussion methodology can lead to success in. (I don’t know if this is actually true yet, but I suspect it is and would be surprised if it were false)

short reflective post script

I think I have used terminology correctly but there are parts I’m not certain about. An example: When I talk about domains and universalities I’m reasonably confident the terms are close-to-right (or actually right / okay / clear), but wouldn’t be surprised if there were minor issues. I would be surprised if there were major issues.

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