**From:** Johnicholas Hines (*johnicholas.hines@gmail.com*)

**Date:** Wed Feb 04 2009 - 18:27:36 MST

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I think it is valuable to specify models and make them concrete. Then

we can ask each other "Are you using THIS mental model? How exactly

does your mental model differ?".

People might, with justification, criticize me for offering models

which are simplistic. However, I hope this message spurs people to

offer countermodels in a comparably concrete and specific format.

1. Here is one model, which you might call "constant capability

increase per effort".

There is one endogenous variable "capability" (c).

There is one exogenous variable "effort" (e).

There is one parameter, "capability growth per effort" (cpe).

The single equation is that the time derivative of capability is

proportional to effort (D[c]=e * cpe).

The story for this model is something like: "Once upon a time, there

was an engineer, and she worked every day on her system. It gradually

got more and more capable."

2. Here is a second model, which you might call "constant capability

increase per capability".

There is one endogenous variable "capability" (c).

There is one parameter, "capability growth per capability" (cpc).

The single equation is that the time derivative of capability is

proportional to capability (D[c]=c * cpc).

The story for this model is something like: "Once upon a time, a

system tried to improve itself. It became more and more capable, and

was able to improve itself faster and faster."

3. Here is a third model, which you might call "diminishing capability

increase per capability".

There is one endogenous variable "capability" (c).

There is one parameter, "capability growth constant" (cgc).

The single equation is that the time derivative of capability is

inversely proportional to capability (D[c]=cgc / c).

The story for this model is something like: "Once upon a time, a

system tried to improve itself. It became more and more capable, but

each increment took more and more time."

4. You can add the first two models together.

There is one endogenous variable "capability" (c).

There is one exogenous variable "effort" (e).

There are two parameters, "capability growth per effort" (cpe) and

"capability growth per capability" (cpc).

The single equation is that the time derivative of capability is the

sum of two components, one proportional to effort, and one

proportional to capability (D[c]=e * cpe + c * cpc).

The story for this model is something like: "Once upon a time, there

was an engineer, and her system. They worked together on improving the

system's capabilities, and the system gradually got more and more

capable, until her improvements were eclipsed by its

self-improvements."

5. You can add a threshold to get a model with linear engineering,

exponential growth, and a threshold (D[c]=e*cpe + (c>ct?c*cpc:0)).

There is one endogenous variable "capability" (c).

There is one exogenous variable "effort" (e).

There are three parameters, "capability growth per effort" (cpe),

"capability growth per capability" (cpc), and "capability threshold"

(ct).

The single equation is that the time derivative of capability is the

sum of two components, one proportional to effort, and one which is

proportional to capability if capability is above the capability

theshold, and zero otherwise.

(I think this is what most AGI rhetoric uses.)

6. This last one takes a bit of motivation. Suppose the system in

question has two parts, one which is modifiable by the system and one

which is not. The total capability of the system is a combination of

the two parts. But the combination is not a simple addition or

multiplication of figures of merit. Rather, the total capability of

the system is measured in "speed", and each "elementary cycle" needs

to pass through both the modifiable part and the nonmodifiable part.

There is one endogenous variable "modifiable part's speed" (m).

There are two parameters, "modifiable part's improvement per

capability" (mpc), and "nonmodifiable part's speed" (n).

There are two equations:

The total capability of the system, the speed, is the inverse of the

sum of the inverses of the modifiable and nonmodifiable parts' speeds

(c = 1/((1/n)+(1/m))).

The time derivative of the modifiable part's speed is proportional to

the total capability (D[m]=mpc * c).

Note: ALL of these are one-dimensional models. The world of

higher-dimensional models (e.g. separate capabilities for chess and

learning to learn) is entirely open.

Johnicholas

**Next message:**Krekoski Ross: "Re: [sl4] Uploads coming first would be good, right?"**Previous message:**Charles Hixson: "Re: [sl4] Uploads coming first would be good, right?"**Next in thread:**Petter Wingren-Rasmussen: "Re: [sl4] simplistic models of capability growth"**Reply:**Petter Wingren-Rasmussen: "Re: [sl4] simplistic models of capability growth"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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