Bounds, Hurdles and Progress

Bounded/limited systems/things always have small potential when you compare to an unbounded/unlimited things. Unbounded means infinite potential. A bounded system never has similar potential to an unlimited system. Limits make a huge difference; they totally transform a system into a much, much lesser system in terms of its capabilities/potential.

Unbounded systems don’t always outcompete bounded systems by a large margin in practice. Why? They often interact with some bounded system which limits their use. Or people use the unlimited system in limited ways. (In other words, the limited system is interacting with a bounded system of human rules/policies for how humans act.)

Bounded Progress

Bounded progress is a little like doing math with a “no even numbers allowed” rule. It’d be really hard to do math if you weren’t allowed to think about or use even numbers. Bounds are a big deal that get in the way everywhere.

There can also be superficial bounds that have workarounds and make no fundamental difference, so some systems appear bounded but are actually unbounded.

So basically there are two types of bounds: the ones that don’t matter (and often aren’t even counted as bounds), and the ones that matter a huge amount.

The reason for this binary dichotomy is because of the jump to universality (credit to David Deutsch for that idea, and for his discussions of infinity and unbounded progress in his book The Beginning of Infinity, which I helped with for six years).

One way to look at the jump to universality is that, due to the ability to work around small bounds with powerful tools (so they aren’t really bounds), all bounds are large bounds that exclude some giant category of stuff. A bound has to be really powerful or it won’t be able to block workarounds and therefore won’t do anything. This applies when we’re looking at the theoretical capabilities of systems. Workarounds can be a lot of extra work, but that doesn’t change what is possible or impossible to accomplish. When we think about universality and look at possibility and impossibly, we’re typically ignoring time and resource use. So we’ll consider questions like “Can this system multiply 8 digit numbers?” but not “Can this system multiply eight digit numbers in less than 3 seconds?” We look at whether it can do the job at all, not whether it can do it within an arbitrary time limit (or within an arbitrary budget). It does need to be able to finish the multiplication before it gets worn out and breaks though (otherwise it actually wouldn’t figure out the answer), so spending centuries on a task is unrealistic for systems without robust self-repair features.

There are generally many ways to accomplish the same thing, so a small bound on one way (or even blocking ten thousand ways) wouldn’t stop you from accomplishing something – bounds have to be giant, fundamental handicaps to make much impossible.

If there’s a roadblock, you can go around on a different road. It’s not a bound on where you can travel to. It just makes some destinations more expensive to travel to. Increased cost of some goals is different than a bound on capabilities. To prevent travel to a specific city, instead of a roadblock it would take blocks on an entire category of roads (e.g. all roads going east) as well as blocks on air travel, sea travel, off-road driving, walking, etc.

The reason for a jump to universality – to a system being able to do anything in a domain instead of just a few things – is because when you get some powerful tools then you can work around virtually any obstacle, so everything is possible. This happens all at once. You add one new tool and now everything is possible instead of hardly anything. The best known example of this is with universal computers but I won’t go into detail because this article is going to focus more on bounds.

Bounds vs. Hurdles

A bound is some major blocker that means you can’t go there or you can’t do that. It’s making something off limits, out of the question. Bounds are common in discussions – people simply won’t discuss some topics (there are many ways to discuss those topics, but they won’t do any of them). If the questions go on certain tangents, they won’t talk about it. Bounds are also common from the government – they make laws that you cannot do X (by any means whatsoever).

Note: Many bounds have some way to deal with that we don’t know. E.g. when people won’t discuss a topic, there is probably some stuff you could say that would fix it. Super wise people from thousands of years in the future could probably figure out a solution. Many things act like bounds for us because they are well beyond our abilities to pass, but they aren’t implied by the laws of physics so they aren’t literally impossible to pass.

Hurdles are different than bounds: they just mean something is harder to do, but you can still do it. Hurdles have workarounds; they’re just an inconvenience. Hurdles are finite, limited, small. Bounds are big and block workarounds.

Bounds are really bad. Hurdles are just a routine part of life that isn’t a big deal. With hurdles, you just have to consider resource efficiency. Is it better to go over the hurdle or around? Which way around? But you aren’t stuck. Removing a hurdle – e.g. building a road where previously there was only a path – costs resources so you have to figure out which hurdles are efficient to change at this time.

Unbounded Progress

Unbounded progress is easier than bounded progress. It’s like freeway driving vs. city traffic with tons of stoplights. On the freeway, you drive faster and it’s easier because there’s nothing in your way.

Unbounded progress means following the truth anywhere. Bounded learning means you are limiting yourself in big ways which are going to screw you over when the truth is off limits. You’ll get stuck.

There are always going to be hurdles but you can deal with them. There don’t have to be bounds that make stuff off limits.

All Problems Are Soluble

What’s to stop a problem from being solved? Not knowing how to solve it (lack of knowledge), not wanting to solve it (morality), or the laws of physics. (Credit, again, to Deutsch.)

Learn more (get more knowledge) and you’ll find a solution, or find out why it’s a bad problem and you’d prefer to solve some other problem (morality), or find out it violates the laws of physics. It’s OK if a goal violates the laws of physics: you can do something else and have a great life within the laws of physics. You don’t have to suffer over being unable to e.g. travel faster than the speed of light.

And you can always act, in your life, in time, without being conflicted or upset about it. You can make a rational decision that isn’t a compromise, and doesn’t involve fracturing yourself into warring factions. How? If you don’t know a solution, consider what should you do in the meantime to limit the fallout of your ignorance, to learn more, to avoid the matter, to find a workaround, etc. That can be answered without knowing the thing you don’t know. Do that. (If you don’t know how, ask what you can do given that ignorance as well, and there is an answer that doesn’t require the knowledge you don’t have. Repeat as needed – ask what to do given your ignorance of a list of things you don’t know – and solve that problem, and act accordingly. That will not be a compromise, and you will have no criticism of it and see nothing wrong with it.)

You can always act on non-refuted ideas – ideas with no known flaws or criticisms.

What if, instead of doing all this problem solving, we stopped problems from happening before they happened. Would that be a good approach? Not exactly. We can prevent some problems in the first place, but some problems will happen no matter what our preventative measures are. Many preventative measures are good, and we should pursue them. They can work for specific problems we foresee, but can’t work for all problems. There are always going to be unprevented problems which need solving, so we need to be good at solving problems. (The ideas that problems are inevitable and problems are soluble are from Deutsch.)

As we get better we can get rid of lots of types of problems we don’t like and prevent them. Like cholera. More cholera isn’t inevitable. But there will always be new problems of some sort, even if they are more subtle and are better problems to have, so we’ll always need problem solving.

Sustainability vs. Ongoing Progress

Sustainability is a misconception about having a life where you aren’t making progress, so you just go in circles. This can’t work (it’s unsustainable – again credit to Deutsch). Problems and errors always come up. If you have limited power (knowledge, wealth, resources, etc.) and a problem comes up, you might fail, and you might even be destroyed, depending on how big the problem is. Sustainability means waiting around to be destroyed – by a plague, a meteor, or something entirely unforeseen. (There’s also the problem of dying of aging and trying to count some of your relatives (or just any human beings) being alive, at any given time, as success. There’s a problem of low expectations when personally dying is seen as fine and compatible with “sustainability” – dying means your life was not sustained.)

“Sustainable” lifestyles have finite resources which they don’t expand beyond some limit or boundary. They aren’t making ongoing, unlimited, unbounded progress to get more resources. Since problems are inevitable, but a sustainable society has limited/finite capacity to deal with problems, there will inevitably one day be a problem that a sustainable society can’t deal with. (Problems being inevitable doesn’t just mean small problems. It means problems of all types and sizes. For example, meteor could come hit the Earth, or there could be a really deadly plague. Those are examples of big problems that can wipe out civilizations that don’t keep making progress to get more resources and control over nature.)

The only reasonable thing to do about a succession of unpredictable problems (and lots of partially predictable ones too) is to try to make progress: increase your ability to deal with problems. Don’t seek a problem-free life where you (and your descendants) just repeat the same lifestyle forever. That’s impossible (some problem will come along and disrupt it) and also it’d be boring. It requires suppressing the creativity of your children so they don’t innovate. Instead, you should focus on rapid progress. The only defense against things going disastrously wrong is to get better and better at dealing with problems, because it’s impossible to prevent all problems in the first place no matter how repetitive, circular and boring your lifestyle is (which, itself, sounds like a problem).