# Framing Practicum: Bistability

This is a [framing practicum](https://www.lesswrong.com/s/Fu7Euu3F96rKhFRWH) post. We’ll talk about what bistability is, how to recognize bistability in the wild, and what questions to ask when you find it. Then, we’ll have a challenge to apply the idea.

**Today’s challenge: come up with 3 examples of bistability which do** ***not*** **resemble any you’ve seen before**. They don’t need to be good, they don’t need to be useful, they just need to be novel (to you). 

Expected time: ~15-30 minutes at most, including the Bonus Exercise.

What’s Bistability?
-------------------

The classic picture of bistability is a marble in a double bowl:

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/0cf91be0645dce4f44349df8704353bf0b08fa36f4c39828.png)

The marble has one stable equilibrium on the left, and another on the right. Although the marble has a whole continuum of possible positions, when left to its own devices for a while it will settle down to one of just two positions.

My own head-canonical examples of bistability come from digital electronics. One is the signal buffer: it turns a sorta-low voltage (like 1 V) and into an unambiguously low voltage (like 0.01 V), or a sorta-high voltage (like 4 V) into an unambiguously high voltage (like 4.99 V). One stable equilibrium is at 5 V, the other is at 0 V, and all other voltages get pushed toward one of those two. This is crucial to building large digital circuits: without buffering, 5 V would decay to 4 V then 3 V as we pass through one gate after another, and eventually we wouldn’t be able to tell whether a voltage is supposed to be high or low.

Another electronic example is the latch, one of the standard low-level memory elements in digital circuits. You can think of a latch sort of like the marble-in-a-double-bowl, but with two extra features:

*   The state of the marble can be read out. One “bowl” represents “0”, and the other “1”.
*   An input signal can switch the “marble” from one state to the other.

So, to “write” a bit into the memory element, we push the system into the desired “bowl” (i.e. basin of attraction). It then stays in that state indefinitely, and we can read out the stored bit as many times as we like until it is “overwritten” (i.e. the state is set again).

What To Look For
----------------

In general, bistability (and multiple stability) should come to mind whenever an analogue system (i.e. a system with continuous state variables) has discrete behavior. In particular, it’s usually necessary for lossless transmission/storage of discrete information - a system with a single stable equilibrium has no long-term memory, since it always returns to the same state. 

Useful Questions To Ask
-----------------------

In the double bowl picture earlier in the post, there’s a hump between the two stable equilibria. The higher the hump, the harder it is to push the marble from one equilibrium to the other. In chemistry, we call that height the “activation energy” - the energy which must be provided to move from one stable state to another. If we want to switch the marble’s state (e.g. to write a bit into memory), we need to provide that activation energy, and a “higher hump” makes it harder/more expensive to set the bit. On the other hand, a higher activation energy makes it less likely that random noise will accidentally push the marble from one side to the other, so a higher-hump memory element can store a bit for longer.

In general, other than the usual [equilibrium questions](https://www.lesswrong.com/s/Fu7Euu3F96rKhFRWH/p/jjsXqByQWYwu5tYXq), **in a bistable system we usually want to know what’s required to change from one stable equilibrium to another**. A few ways this can apply:

*   We want to set the system into one state or another. So, we need to know what kind of “kick” will do that.
*   We want to make the system more or less likely to switch state. So, we need to know how to raise or lower the "hump" between states.
*   We see the system change from one state to another, and we want to know what caused the switch. So, we look for kicks which are large enough to overcome the hump, and ignore smaller noise.
*   We want to know how long it will take the system to accidentally change states due to random noise - i.e. how long the “memory” is reliable.

The Challenge
-------------

**Come up with 3 examples of bistability which do** ***not*** **resemble any you’ve seen before**. They don’t need to be good, they don’t need to be useful, they just need to be novel (to you).

**Any answer must include at least 3 to count, and they must be novel to you**. That’s the challenge. We’re here to challenge ourselves, not just review examples we already know.

However, they don’t have to be very good answers or even correct answers. Posting wrong things on the internet is scary, but a very fast way to learn, and I will enforce a high bar for kindness in response-comments. I will personally default to upvoting every complete answer, even if parts of it are wrong, and I encourage others to do the same.

**Post your answers inside of spoiler tags. (**[**How do I do that?**](https://www.lesswrong.com/posts/2rWKkWuPrgTMpLRbp/lesswrong-faq#How_do_I_insert_spoiler_protections_)**)**

**Celebrate others’ answers.** This is really important, especially for tougher questions. Sharing exercises in public is a scary experience. I don’t want people to leave this having back-chained the experience “If I go outside my comfort zone, people will look down on me”. So be generous with those upvotes. I certainly will be.

If you comment on someone else’s answers, focus on making exciting, novel ideas work — instead of tearing apart worse ideas. [Yes, And](https://medium.com/improv4/saying-yes-and-a-principle-for-improv-business-life-fd050bccf7e3) is encouraged.

I may remove comments which I deem insufficiently kind, even if I believe they are valuable comments. I want people to feel encouraged to try and fail here, and that means enforcing nicer norms than usual.

**If you get stuck, look for:**

*   Systems whose long run behavior can end up a few different possible ways, depending on the initial conditions
*   Analogue systems with discrete behavior
*   Long-range transmission or long-term storage of discrete information

**Bonus Exercise**: for each of your three examples from the challenge, what kinds of “kicks” could cause the system to switch state? What controls how strong the kick needs to be? Suppose you want to switch the state, or want to know what caused a state switch; what kicks could you rule out on the basis that they’re too small? Can you do a Fermi estimate for how often a kick large enough to force a state switch happens due to random noise?

This bonus exercise is great blog-post fodder!

Motivation
----------

Much of the value I get from math is not from detailed calculations or elaborate models, but rather from *framing tools*: tools which suggest useful questions to ask, approximations to make, what to pay attention to and what to ignore.

Using a framing tool is sort of like using a [trigger-action pattern](https://www.lesswrong.com/tag/trigger-action-planning): the hard part is to notice a pattern, a place where a particular tool can apply (the “trigger”). Once we notice the pattern, it suggests certain questions or approximations (the “action”). This challenge is meant to train the trigger-step: we look for novel examples to ingrain the abstract trigger pattern (separate from examples/contexts we already know).

The Bonus Exercise is meant to train the action-step: apply whatever questions/approximations the frame suggests, in order to build the reflex of applying them when we notice bistability.

Hopefully, this will make it easier to notice when a bistability frame can be applied to a new [problem you don’t understand](https://www.lesswrong.com/posts/CSZnj2YNMKGfsMbZA/specializing-in-problems-we-don-t-understand) in the wild, and to actually use it.