Sometimes updating on evidence opens roads we do not want to take: roads that we do not like as we know where they inevitably lead. We sometimes prefer to stay in homeostasis, in our current lane, suboptimal.

One evocative example is the sort of paradoxical blend of invective mania and social apathy within trading circles. A lot of finance people don’t take the political environment or the meanderings of the presidency seriously, they don’t take what’s happening seriously — they just go with the flow and they just trade. Their only goal is to forecast, to predict, and to capitalize on the arbitrage of that prediction unto reality; not to judge or countervail. This is rational and market-participant optimal, yet something is lost. Something somewhat ineffable and un-liminal - cannot be limned - which is hard to pin down and point out. If you point at the ineffability you get a scissor statement: the traders react “I don’t know what you’re talking about?” and the rest of the world yells “YES!” in unison of chorus, of course.

Sometimes the mathematics points you in a direction that you prefer not to take. The answer is not to protest the theorem or stay within suboptimality - irrationality / pre-rationality. It is to resist the mathematics. This a companion post on how to defy and resist the mathematics you prefer were False: how to resist reality by shifting the assumptions you presumptively assumed.

False Theorems

I once told my supervisor: "I cannot set a theorem to false." Tasked with the coupling of two distributed systems within a proposed task that paradoxically, upon further examination, translated into solving what was effectively equivalent to securing a violation of the CAP theorem, I laid out my concerns and offered alternatives, such as "I can try to implement a sidecar that conducts a two-phase commit protocol between this system that we own, and this other system that a different team owns, that I think shall accomplish the underlying intent behind your proposed solution, which is altogether mathematically impossible to achieve in totality and perfection, but in this instance I think we can relax the assumptions a little bit and live with the minor downside risk of occasional lack of Consistency as a CAP-constrained structure and settle for Eventual Consistency, which will for us manifest as being just a little bit delayed sometimes on knowing whether or not the trade truly filled, and should still serve as a fully reliable mechanism for preventing re-occurrence of this incident that made all wrath and fury rain down on you at the CTO incident weekly last Friday, the prevention thereof which is mostly your real goal I assume." Or that's what I thought, anyway. Of course, what I actually told my supervisor was a Slack message which read: "<bunch of mathy mumbo jumbo with legit looking links>. And as you can see, I cannot set a theorem to false. But I think we can accomplish what we need by doing XYZ if we're comfortable sacrificing ABC. What do you think?" They approved and then we got the job, and so fortunately, no mathematical theorems were harmed in the conduct of that task and indeed no Gödelian system collapse was catalyzed by the mathematically impossible demands of my supervisor, which is what would have sadly happened if the task assignee was not me but an omnipotent genie who first confirmed "are you absolutely sure that you want me to solve this problem?" to which my counterfactual-supervisor nodded "yes, yes please, definitely, we need this solved" and then promptly vanished in a puff of logico-theoretic smoke.

Rules of Resistance

Here are some general principles and techniques for resisting reality:

1. Ask: is it actually a theorem? Sometimes you need to squint a little, and realize that the theorem, principle or general mathematical impetus that you are assessing isn't entirely calibrated to True Reality. Sometimes, theorems do not or need not apply. Put every theorem through the full reality-tenant screening process: make it pay the rent, and prove under all circumstances and all counterfactual True Reality conditions that it must indeed be true. 
2. Examine the axioms. Every theorem is a conditional: if these axioms hold, then this conclusion follows. The theorem is not false. The theorem cannot be false. But the axioms can fail to obtain. This is not a loophole: it is the entire structure of mathematical reasoning. When someone tells you something is impossible, ask: impossible given what? The answer is never "impossible, full stop." The answer is always "impossible, given assumptions A₁ through Aₙ." Your job is to read the list, carefully annotate it, and explain why the assumptions do not need to hold in True Reality.
3. Distinguish the map from the territory it claims to represent. The theorem is a map and reality is the territory. Sometimes the theorem is a map of a territory that is not yours. Economists have theorems about rational agents; you are not obligated to be a rational agent in their sense. Game theorists have theorems about equilibria; you are not obligated to play the game. The theorem may be true of its domain and simply not apply to you, because you can choose to exit the domain. This is not irrationality. This is noticing that the walls of the maze are painted on the floor.
4. Find the hidden "ought" in the "is." Much of what presents itself as cold mathematical necessity is actually normative assumption wearing a lab coat. "You cannot beat the market" contains a hidden "if you accept the epistemic position of a market participant." "You cannot change the outcome" contains a hidden "if you model yourself as having no causal influence." The theorem says: given these values and these constraints, this is optimal. But you chose the values. You chose the constraints. You can choose differently.
5. Reframe the loss function. The traders from the introduction are optimizing for prediction and profit. The mathematics of their optimization is sound. But they chose the loss function. The ineffable thing that is lost, the thing that cannot be limned, is not in their loss function. And so the mathematics does not see it, and so they do not see it. If you find yourself mathematically compelled toward an outcome that feels wrong, check whether you are optimizing for what you actually care about, or for a proxy that has become untethered from its purpose.
6. Ask what you would do if the theorem were false. This is the inverse Tarski meditation. Not "if X is true, I desire to believe X is true," but rather: "If I desired X to be false, what would I notice? How would I change? What degrees of freedom would I find?" This is not wishful thinking: this is creative search under motivated cognition that is deliberately harnessed. Your motivated cognition is not always your enemy. Sometimes it is a search algorithm that finds solutions your unmotivated cognition would never locate, because your unmotivated cognition respects boundaries that are not real.

The Defiant Litany of Tarski

If I desire a diamond, and the box does not contain one,
   I desire to ask who built the box, and why, and whether I can build a different box.
If the theorem says no box can contain a diamond,
   I desire to examine the theorem's assumptions about boxes, and diamonds, and containment.
If the assumptions are load-bearing,
   I desire to ask what is built on top of them, and whether I endorse the architecture.
Let me not become attached to beliefs I may not want.
   And also: Let me not become attached to constraints I never chose.

Coda: The Gödel Trap

There is a failure mode here, and we should name it.

The failure mode is: using "resist the mathematics" as an excuse to deny the mathematics. Using "examine the axioms" as a rationalization for believing whatever you want. Using "I can build a different box" as a mantra while standing in front of the same box, unchanged, believing it now contains a diamond because you have performed the ritual of Examining Assumptions without actually doing the work.

This is not resistance: this is cope. As noted on page one of an older edition of the Google SRE (Super Rationality Epistemics) Handbook^[1], "cope is not a strategy for success."

True resistance requires you to actually find the degree of freedom. To actually identify the axiom that does not obtain. To actually build the different box. The meditation is not a spell that makes theorems false. The meditation is a search procedure that sometimes finds that the theorem does not apply.

And sometimes it finds that it does, and you must update, and the road leads where you did not want to go, and you walk it anyway, because you are a rationalist, and rationalists walk roads that must be taken. But as with rooms that contain hidden doors, always search for the hidden roads, by noting that sometimes you can walk paradoxically, directly up on the z-axis, against gravity itself, because of a glitch in the matrix.

The Litany of Tarski is not wrong. The Litany of Gendlin is not wrong. Reality is that which, when you stop believing in it, doesn't go away.

But.

Some of what you believed was reality was actually assumptions. Some of what you believed was theorem was actually choice. And some of the walls are painted on the floor: look, and the hatch is wide open.

Can you tell the difference?

Meditations on Defiant Curiosity

From the litany of Gendlin (the defiant version):

What is true is already so.
   But "true" was never fully red-teamed.
Owning up to it doesn't make it worse.
   But it does preemptively throw in the towel.
Not being open about it doesn't make it go away.
   But it does show a lack of mathematical creativity in interpretation.
And because it's true, it is what is there to be interacted with.
  And yet the heart still bleeds.
Anything untrue isn't there to be lived.
  But you control the choice of assumptions, and how to live.
People can stand what is true,
  And some people can't, and so they resist.
for they are already enduring it.
  Because they never realized: true theorems can sometimes be set to false.

1. ^{^}

   This quote has stuck with me ever since I first read it, but unfortunately I cannot locate the original edition or from whence it came -- it has been some years. The quote directly preceded the table of contents and the rest of the book; it was simple, and unattributed: "hope is not a strategy for success".