The way it works for me is this:
First I come up with a sketch of the proof and try to formalise it and find holes in it. This is fairly creative and free and fun. After a while I go away feeling great that I might have proven the result.
The next day or so, fear starts to creep in and I go back to the proof with a fresh mind and try to break it in as many ways as possible. What is motivating me is that I know that if I show somebody this half baked proof it's quite likely that they will point out a major flaw it. That would be really embarrassing. Thus, I imagine that it's somebody else's proof and my job is to show why it's broken.
After a while of my trying to break it, I'll then show it to somebody kind who won't laugh at me if it's wrong, but is pretty careful at checking these things. Then another person... slowly my fear of having screwed up lifts. Then I'm ready to submit to publish.
So in short: I'm motivated to get proofs right (I have yet to have a published proof corrected, not counting blog posts) out of a fear of looking bad. What motivates me to publish at all is the feeling for satisfaction that I draw from the achievement. In my moderate experience of mathematicians, they often seem to have similar emotional forces at work.
Related to: Humans are not automatically strategic, The mystery of the haunted rationalist, Striving to accept, Taking ideas seriously
I argue that many techniques for epistemic rationality, as taught on LW, amount to techniques for reducing compartmentalization. I argue further that when these same techniques are extended to a larger portion of the mind, they boost instrumental, as well as epistemic, rationality.
Imagine trying to design an intelligent mind.
One problem you’d face is designing its goal.
Every time you designed a goal-indicator, the mind would increase action patterns that hit that indicator[1]. Amongst these reinforced actions would be “wireheading patterns” that fooled the indicator but did not hit your intended goal. For example, if your creature gains reward from internal indicators of status, it will increase those indicators -- including by such methods as surrounding itself with people who agree with it, or convincing itself that it understood important matters others had missed. It would be hard-wired to act as though “believing makes it so”.
A second problem you’d face is propagating evidence. Whenever your creature encounters some new evidence E, you’ll want it to update its model of “events like E”. But how do you tell which events are “like E”? The soup of hypotheses, intuition-fragments, and other pieces of world-model is too large, and its processing too limited, to update each belief after each piece of evidence. Even absent wireheading-driven tendencies to keep rewarding beliefs isolated from threatening evidence, you’ll probably have trouble with accidental compartmentalization (where the creature doesn’t update relevant beliefs simply because your heuristics for what to update were imperfect).
Evolution, AFAICT, faced just these problems. The result is a familiar set of rationality gaps:
I. Accidental compartmentalization
a. Belief compartmentalization: We often fail to propagate changes to our abstract beliefs (and we often make predictions using un-updated, specialized components of our soup of world-model). Thus, learning modus tolens in the abstract doesn’t automatically change your answer to the Wason card test. Learning about conservation of energy doesn’t automatically change your fear when a bowling ball is hurtling toward you. Understanding there aren’t ghosts doesn’t automatically change your anticipations in a haunted house. (See Will's excellent post Taking ideas seriously for further discussion).
b. Goal compartmentalization: We often fail to propagate information about what “losing weight”, “being a skilled thinker”, or other goals would concretely do for us. We also fail to propagate information about what specific actions could further these goals. Thus (absent the concrete visualizations recommended in many self-help books) our goals fail to pull our behavior, because although we verbally know the consequences of our actions, we don’t visualize those consequences on the “near-mode” level that prompts emotions and actions.
c. Failure to flush garbage: We often continue to work toward a subgoal that no longer serves our actual goal (creating what Eliezer calls a lost purpose). Similarly, we often continue to discuss, and care about, concepts that have lost all their moorings in anticipated sense-experience.
II. Reinforced compartmentalization:
Type 1: Distorted reward signals. If X is a reinforced goal-indicator (“I have status”; “my mother approves of me”[2]), thinking patterns that bias us toward X will be reinforced. We will learn to compartmentalize away anti-X information.
The problem is not just conscious wishful thinking; it is a sphexish, half-alien mind that distorts your beliefs by reinforcing motives, angles or approach or analysis, choices of reading material or discussion partners, etc. so as to bias you toward X, and to compartmentalize away anti-X information.
Impairment to epistemic rationality:
Impairment to instrumental rationality:
Type 2: “Ugh fields”, or “no thought zones”. If we have a large amount of anti-X information cluttering up our brains, we may avoid thinking about X at all, since considering X tends to reduce compartmentalization and send us pain signals. Sometimes, this involves not-acting in entire domains of our lives, lest we be reminded of X.
Impairment to epistemic rationality:
Impairment to instrumental rationality:
Type 3: Wireheading patterns that fill our lives, and prevent other thoughts and actions. [3]
Impairment to epistemic rationality:
Impairment to instrumental rationality:
Strategies for reducing compartmentalization:
A huge portion of both Less Wrong and the self-help and business literatures amounts to techniques for integrating your thoughts -- for bringing your whole mind, with all your intelligence and energy, to bear on your problems. Many fall into the following categories, each of which boosts both epistemic and instrumental rationality:
1. Something to protect (or, as Napoleon Hill has it, definite major purpose[4]): Find an external goal that you care deeply about. Visualize the goal; remind yourself of what it can do for you; integrate the desire across your mind. Then, use your desire to achieve this goal, and your knowledge that actual inquiry and effective actions can help you achieve it, to reduce wireheading temptations.
2. Translate evidence, and goals, into terms that are easy to understand. It’s more painful to remember “Aunt Jane is dead” than “Aunt Jane passed away” because more of your brain understands the first sentence. Therefore use simple, concrete terms, whether you’re saying “Aunt Jane is dead” or “Damn, I don’t know calculus” or “Light bends when it hits water” or “I will earn a million dollars”. Work to update your whole web of beliefs and goals.
3. Reduce the emotional gradients that fuel wireheading. Leave yourself lines of retreat. Recite the litanies of Gendlin and Tarski; visualize their meaning, concretely, for the task or ugh field bending your thoughts. Think through the painful information; notice the expected update, so that you need not fear further thought. On your to-do list, write concrete "next actions", rather than vague goals with no clear steps, to make the list less scary.
4. Be aware of common patterns of wireheading or compartmentalization, such as failure to acknowledge sunk costs. Build habits, and perhaps identity, around correcting these patterns.
I suspect that if we follow up on these parallels, and learn strategies for decompartmentalizing not only our far-mode beliefs, but also our near-mode beliefs, our models of ourselves, our curiosity, and our near- and far-mode goals and emotions, we can create a more powerful rationality -- a rationality for the whole mind.
[1] Assuming it's a reinforcement learner, temporal difference learner, perceptual control system, or similar.
[2] We receive reward/pain not only from "primitive reinforcers" such as smiles, sugar, warmth, and the like, but also from many long-term predictors of those reinforcers (or predictors of predictors of those reinforcers, or...), such as one's LW karma score, one's number theory prowess, or a specific person's esteem. We probably wish to regard some of these learned reinforcers as part of our real preferences.
[3] Arguably, wireheading gives us fewer long-term reward signals than we would achieve from its absence. Why does it persist, then? I would guess that the answer is not so much hyperbolic discounting (although this does play a role) as local hill-climbing behavior; the simple, parallel systems that fuel most of our learning can't see how to get from "avoid thinking about my bill" to "genuinely relax, after paying my bill". You, though, can see such paths -- and if you search for such improvements and visualize the rewards, it may be easier to reduce wireheading.
[4] I'm not recommending Napoleon Hill. But even this unusually LW-unfriendly self-help book seems to get most points right, at least in the linked summary. You might try reading the summary as an exercise in recognizing mostly-accurate statements when expressed in the enemy's vocabulary.