An “isthmus” and a “bottleneck” are opposites. An isthmus provides a narrow but essential connection between two things (landmass, associations, causal chains). A bottleneck is the same except the connection is held back by its limited bandwidth. In the case of a bottleneck, increasing its bandwidth is top priority. In the case of an isthmus, keeping it open or discovering it in the first place is top priority.
I have a habit of making up pretty words for myself to remember important concepts, so I’m calling it an “isthmus variable” when it’s the thing you need to keep mentally keep track of in order to connect input with important task-relevant parts of your network.
When you’re optimising the way you optimise something, consider that “isthmus variables” is an isthmus variable for this task.
Quick update: I suspect many/most problems where thinking in terms of symmetry can be more helpfwly reframed in terms of isthmuses[1]. Here’s the chain-of-thought I was writing which caused me to think this:
(Background: I was trying to explain the general relevance of symmetry when finding integrals.)
In the context of finding integrals for geometric objects¹, look for simple subregions² for which manipulating a single variable³ lets you continuously expand to the whole object.⁴
The general feature to learn to notice as you search through subregions here is: shared symmetriesfor the object and its subregion. hmmmmm
Actually, “symmetry” is a distracting concept here. It’s the “isthmus” between subregions you should be looking for.
WHEN: Trying to find an integral
THEN: Search for a single isthmus-variable connecting subregions which together fill the whole area
FINALLY: Integrate over that variable between those regions.
or said differently… THEN: Look for simple subregions which transform into the whole area via a single variable, then integrate over that variable.
Hm. This btw is in general how you find generalizations. Start from one concept, find a cheap action which transforms it into a different concept, then define the second in terms of the first plus its distance along that action.
That action is then the isthmus that connects the concepts.
If previously from a given context (assuming partial memory-addresses A and B), fetching A* and B* each cost you 1000 search-points separately, now you can be more efficient by storing B as the delta between them, such that fetching B only costs 1000+[cost of delta].
Or you can do a similar (but more traditional) analysis where “storing” memories has a cost in bits of memory capacity.
This example is from a 3B1B vid, where he says “this should seem promising because it respects the symmetry of the circle”. While true (eg, rotational symmetry is preserved in the carve-up), I don’t feel like the sentence captures the essence of what makes this a good step to take, at least not on my semantics.
An “isthmus” and a “bottleneck” are opposites. An isthmus provides a narrow but essential connection between two things (landmass, associations, causal chains). A bottleneck is the same except the connection is held back by its limited bandwidth. In the case of a bottleneck, increasing its bandwidth is top priority. In the case of an isthmus, keeping it open or discovering it in the first place is top priority.
I have a habit of making up pretty words for myself to remember important concepts, so I’m calling it an “isthmus variable” when it’s the thing you need to keep mentally keep track of in order to connect input with important task-relevant parts of your network.
When you’re optimising the way you optimise something, consider that “isthmus variables” is an isthmus variable for this task.
Quick update: I suspect many/most problems where thinking in terms of symmetry can be more helpfwly reframed in terms of isthmuses[1]. Here’s the chain-of-thought I was writing which caused me to think this:
(Background: I was trying to explain the general relevance of symmetry when finding integrals.)
“An isthmus is a narrow piece of land connecting two larger areas across an expanse of water by which they are otherwise separated.”
This example is from a 3B1B vid, where he says “this should seem promising because it respects the symmetry of the circle”. While true (eg, rotational symmetry is preserved in the carve-up), I don’t feel like the sentence captures the essence of what makes this a good step to take, at least not on my semantics.
I like the word and I like the idea of an opposite to “bottleneck”