Read this post, with replies, on Less Wrong.

Replies to comments on my *Chains, Bottlenecks and Optimization*:

## abramdemski and Hypothesis Generation

Following the venerated method of multiple working hypotheses, then, we are well-advised to come up with as many hypotheses as we can to explain the data.

I think *come up with as many hypotheses as we can* is intended within the context of some background knowledge (some of which you and I don’t share). There are infinitely many hypotheses that we could come up with. We’d die of old age while brainstorming about just one issue that way. We must consider *which* hypotheses to consider. I think you have background knowledge filtering out most hypotheses.

Rather than consider as many ideas as we can, we have to *focus* our limited attention. I propose that this is a major epistemological problem meriting attention and discussion, and that thinking about bottlenecks and excess capacity can help with focusing.

If you’ve already thought through this issue, would you please link to or state your preferred focusing criteria or methodology?

I did check your link (in the quote above) to see if it answered my question. Instead I read:

Now we've got it: we see the need to enumerate every hypothesis we can in order to test even one hypothesis properly. […]

It's like... optimizing is

alwaysabout evaluating more and more alternatives so that you can find better and better things.

Maybe we have a major disagreement here?

## abramdemski and Disjunction

The way you are reasoning about systems of interconnected ideas is

conjunctive: every individual thing needs to be true. But some things aredisjunctive: some one thing needs to be true. […]A conjunction of a number of statements is --

at most-- as strong as its weakest element, as you suggest. However, adisjunctionof a number of statements is --at worst-- as strong as itselement.strongest

Yes, introducing optional parts to a system (they can fail, but it still succeeds overall) adds complexity to the analysis. I think we can, should and generally do limit their use.

(BTW, disjunction is conjunction with some inversions thrown in, not something fundamentally different.)

Consider a case where we need to combine 3 components to reach our goal and they all have to work. That’s:

A & B & C -> G

And we can calculate whether it works with multiplication: ABC.

What if there are two other ways to accomplish the same sub-goal that C accomplishes? Then we have:

A & B & (C | D | E ) -> G

Using a binary pass/fail model, what’s the result for G? It passes if A, B and at least one of {C, D, E} pass.

What about using a probability model? Problematically assuming independent probabilities, then G is:

AB(1 - (1-C)(1-D)(1-E)))

Or more conveniently:

AB!(!C!D!E)

Or a different way to conceptualize it:

AB(C + D(1 - C) + E(1 - C - D(1 - C)))

Or simplified in a different way:

ABC + ABD + ABE - ABCD - ABCE - ABDE + ABCDE

None of this analysis stops e.g. B from being the bottleneck. It does give some indication of greater complexity that comes from using disjunctions.

There are infinitely many hypotheses available to generate about how to accomplish the same sub-goal that C accomplishes. Should we **or** together all of them and infinitely increase complexity, or should we focus our attention on a few key areas? This gets into the same issue as the previous section about *which* hypotheses merit attention.

## Donald Hobson and Disjunction

Disjunctive arguments are stronger than the strongest link.

On the other hand, [conjunctive] arguments are weaker than the weakest link.

I don’t think this is problematic for my claims regarding looking at bottlenecks and excess capacity to help us focus our attention where it’ll do the most good.

You can imagine a chain with backup links that can only replace a particular link. So e.g. link1 has 3 backups: if it fails, it’ll be instantly replaced with one of its backups, until they run out. Link2 doesn’t have any backups. Link3 has 8 backups. Backups are disjunctions.

Then we can consider the weakest link_and_backups group and focus our attention there. And we’ll often find it isn’t close: we’re very unevenly concerned about the different groups failing. This unevenness is important for designing systems in the first place (don’t try to design a balanced chain; those are bad) and for focusing our attention.

Structures can also be considerably more complicated than this expanded chain model, but I don’t see that that should change my conclusions.

## Dagon and Feasibility

I think I've given away over 20 copies of _The Goal_ by Goldratt, and recommended it to coworkers hundreds of times.

…

The limit is on feasibility of mapping to most real-world situations, and complexity of calculation to determine how big a bottleneck in what conditions something is.

Optimizing software by finding bottlenecks is a counter example to this feasibility claim. We do that successfully, routinely.

Since you’re a Goldratt fan too, I’ll quote a little of what he said about whether the world is too complex to deal with using his methods. From The Choice:

"Inherent Simplicity. In a nutshell, it is at the foundation of all modern science as put by Newton: 'Natura valde simplex est et sibi consona.' And, in understandable language, it means, 'nature is exceedingly simple and harmonious with itself.'"

…

"What Newton tells us is that […] the system converges; common causes appear as we dive down. If we dive deep enough we'll find that there are very few elements at the base—the root causes—which through cause-and-effect connections are governing the whole system. The result of systematically applying the question "why" is not enormous complexity, but rather wonderful simplicity. Newton had the intuition and the conviction to make the leap of faith that convergence happens, not just for the section of nature he examined in depth, but for any section of nature. Reality is built in wonderful simplicity."