Path dependence of learning

https://gyazo.com/553218bb4005a3f0d57e901453ae836d

From some state S0, do action A1 to get to state S1, and from there do action A2 to get to state S2.

One day, a new action A3 was born

Doing this will put you in state S3.

This state is recognized as "S1 and S3 are the same" because S1 and X axis are the same

but on the Y-axis they are in phase with each other.

Although not depicted in the figure, the cost axis also differs, with S3 costing less, so everyone will move in that direction.

By doing action A4 from S3 we get to state S4.

S3 is not S1, so there is no guarantee that A2 can be done

Even if you do an A4 that is equal as a vector, the S4 you arrive at is not an S2.

If S4 is the same X as S2, it is unknown if there is any real harm

Yes, these ideas have been discussed in various fields, but are especially known in the following areas and concepts

Path Dependence:

A concept used in economics and social sciences, it refers to the fact that the final state of a system is highly dependent on its path and history. In other words, different paths to reach the same end point can lead to different outcomes and impacts.

I assumed this keyword would come up.

This concept is used in mathematics and physics when the order of operations affects the outcome. In your example, it is relevant in that doing actions A3 and A4 in sequence and doing the original actions A1 and A2 may not produce the same result.

When I say noncommutative, I feel that "doing A1 and then A2 is not equivalent to doing A2 and then A1".

This is another kind of path dependency.

Systems Thinking and Side Effects:

In systems engineering, ecology, and business process management, it refers to the fact that changing a part in a system may affect unexpected parts of the system.

A concept used in software engineering is that even in an abstracted system, internal details can affect the external. Even if a new action A3 looks the same as A1, internal differences may affect subsequent results.

Oh, this one.

GPT is amazing for finding this, it fits very well into the context of "learning programming" that I had in my brain, which is not described in the abstracted explanation above.

In other words, abstraction hides difficulties, which makes S3 more productive than S1, but [" All non-trivial abstractions, to some degree, are leaky.

The law of leaky abstractions means that whenever somebody comes up with a wizzy new code-generation tool that is supposed to make us all ever-so-efficient, you hear a lot of people saying “learn how to do it manually first, then use the wizzy tool to save time.” Code generation tools which pretend to abstract out something, like all abstractions, leak, and the only way to deal with the leaks competently is to learn about how the abstractions work and what they are abstracting. So the abstractions save us time working, but they don’t save us time learning.

Compatibility and Backward Compatibility:

It is used in technical design and software development to consider how new elements or changes will be compatible with existing systems and processes.

Context Dependence:

In linguistics, philosophy, and computer science, it refers to the fact that the meaning or effect of an element or action depends on its context.

Your ideas are related to concepts discussed in these areas. In particular, the concepts of path dependence and noncommutativity apply in that elements and actions in a system have different effects on multiple dimensions (x-axis, y-axis, cost axis, etc.) and their combination and order can significantly affect the final outcome.

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relevance

Thoughts triggered by reading this

I'm guessing that having had this discussion recently, the information was in an accessible part of your brain.

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