Saturday, February 11, 2017

convergence

Last time, inspired by Sean Carroll's big picture look at philosophy, I repeated the big picture which I've expressed here before. As described by information theory, ideas in the loosest sense are symbolic arrangements of matter and energy flows. Brain matter has evolved accordingly to act as a flexible channel for the reception, assembly, modification, and storage of ideas.

Countless energy-consuming actions in the brain link ideas together. The links enable the ideas to be "hints" for one another. I'm not the first to suggest the analogy of a crossword puzzle. Each's answer's written clues might be vague, but the intersections of the words are crucial clues too. A strongly certain answer reinforces (or negates) the correctness of the answers that reuse its squares. The importance of context shouldn't be underestimated.

Through these linking actions, people will inevitably identify some linked ideas, endpoints, which should be relevant in some way to external actions. By "external" I merely mean that the actions don't happen solely inside the brain. The absorption of information via eyes and ears would be enough to qualify. Actions lead to outcomes, and outcomes are deeply affected by realities. Afterward, people can judge the level of agreement between the outcomes and the endpoints. But this isn't the whole effect. Based on the already mentioned links, their revised judgments of the endpoints' accuracy should revise their judgments of the linked ideas' accuracy. Ideas, actions, and outcomes are shaped by a triangle of mutual relationships.

I recognize that this big picture will provoke complaints. It grants a disappointingly mundane status to ideas and then it pairs this demotion with a sizable role for error-prone people. Wouldn't it be preferable if ideas were said to be unchanging and independent? That way, at least a few ideas exist "out there" by themselves, apart from relying on squishy, messy humans. This alternative is to insist that ideas are sturdy things

My view is that the sturdy-thing notion of ideas does have a diminished counterpart...but only through accepting a subtle redefinition. Instead of an idea having a quality of sturdiness, it can be evaluated by the number and intensity of the convergences it's involved in with other ideas. When a swarm of small easily-checked endpoint ideas have been tested as highly accurate (facts), and all these align well with a single general idea, it's like these ideas are converging on the single idea. The single idea represents a valuable summary, trend, or explanation. Brain actions such as deduction might produce convergences as well: if several axioms and proofs yield a single idea, then it's a valuable theorem. The ultimate result, after tallying an idea's convergences, is to situate it on a relative continuum. A hub idea involved in a multitude of convergences of various kinds is precious. But an isolated idea that's diverged from is suspect. 

Unfortunately, raw convergence isn't irrefutable. It carries its own inherent risk: it isn't necessarily universal. Its scope is possibly limited, even when it's quite dominant for ideas in its scope. Survey responses gathered in Connecticut could converge to an idea, but it might differ nonetheless from the idea that survey responses gathered in British Columbia converge to. Paying close attention to scope is just a price of replacing sturdy-thing ideas with convergent ideas.

But before fixating on the perceived inadequacies of ranking ideas by convergence, my advice is to methodically take an inventory of what it gives up by comparison. An idea that has been converged to many times, in many ways, is an idea that is very likely to be converged on once more. So it's probably beneficial for planning on the outcome of future actions. An idea that hasn't contradicted high-quality ideas is an idea that is very likely to not flatly contradict additional high-quality ideas. So it's probably beneficial as a lens for comprehending proposed ideas. An idea that has succinctly captured the pertinent similarities in a series of repetitive events is an idea that is very likely to echo the pertinent similarities in upcoming events in the series. So it's probably beneficial as a prediction or model of hypothetical events in its scope.

I'd say that the list of drawbacks is looking insignificant. For most purposes, a heavily convergent idea and a sturdy-thing idea are alike. The reason is that convergence is part of the original concept of a sturdy-thing idea in practice. On the assumption that an idea itself is a sturdy thing, then ideas/actions/outcomes would be expected to converge on it. The difference is whether convergence is interpreted as secondary to the idea or interpreted as defining its actual extent. Particular actions can't distinguish between the two interpretations. Perhaps the situation is reminiscent of a (positive) bank account balance. The account's owner can take the action of withdrawing currency from the bank account no matter what the account "really" consists of. For withdrawals the bank account is like a stack of currency in a locked drawer—although the equivalency doesn't work at a failing bank.

The prospect of agreeing to humble ideas could spur the forgivable question, "If not ideas, then what is considered sturdy?" And the answer is lots and lots of real stuff. The milk in my refrigerator is a sturdy thing. My idea that the milk has soured isn't. This idea is linked to the endpoint idea that in the near future I open the milk container, hold it close to my nostrils, inhale deeply, and experience a sensation of odor. The idea of the sour milk is linked to more endpoint ideas such as requesting that someone else sniff so I can watch their reactions. Depending on the outcomes of these endpoints, the idea of the sour milk might be a convergent idea or not. The milk's reality is gratifyingly sturdy. It affects the amount of convergence which my ideas about it have. The same may be asserted about a more "existential" idea about the milk: is it still in the refrigerator, or did some obnoxious household member empty it without telling me? My ideas about the milk, presently occurring in my brain, don't dictate whether the milk is now elsewhere. The actions I take won't imply that I'm finding the idea that the milk is elsewhere but that I'm thinking the ideas associated with realizing that I'm not finding the milk.

If ideas regarding soured milk seem far too frivolous, Sean Carroll's writing contains a fitting candidate which is definitely not. His "Core Theory" is an immensely convergent collection of ideas. Moreover, as he painstakingly explains, its confirmed scope is immensely broad. People's typical lives are within it. In effect researchers and engineers are rechecking it repeatedly as they act. It's not a sturdy thing...but nonetheless we're metaphorically leaning on it all the time.

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