If the feedback constant is less than one, intelligence growth stops.
You should distinguish between exponential and linear growth.
First, the feedback constant is different for every level of intelligence.
Whenever the constant is greater than one, the machine is limited by making the transformations involved, and the intelligence is not well characterized as being limited by its intelligence and instead should be thought of as limited by its resources.
Whenever the constant is less than one and greater than zero, intelligence growth is only linear, but it is not zero. If the constant remains low enough for long enough, whole periods of time, series of iterations, that have some places where the constant is above one also have sub-exponential growth.
The relationship between the AI’s growth rate and our assisted intelligence growth rate (including FAIs, paper and pen, computers, etc.) is most of what is important, with the tie-breaker being our starting resources.
An AI with fast linear growth between patches of exponential growth, or even one with only fast linear growth, would quickly outclass humans’ thinking.
First, the feedback constant is different for every level of intelligence.
I meant to mention that, but I didn’t. It looks like I didn’t so much forget as write an answer so garbled you can’t really tell what I’m trying to say. I’ll fix that.
Anyway, it will move around as the intelligence changes, but I figure it would be far enough from one that it won’t cross it for a while. Either the intelligence is sufficiently advanced before the constant goes below one, or there’s no way you’d ever be able to get something intelligent enough to recursively self-improve.
Whenever the constant is less than one and greater than zero, intelligence growth is only linear, but it is not zero.
No, it’s zero, or at least asymptotic. If each additional IQ point allows you to work out how to grant yourself half an IQ point, you’ll only ever get twice as many extra IQ points as you started with.
Having extra time will be somewhat helpful, but this is limited. If you get extra time, you’d be able to accomplish harder problems, but you won’t be able to accomplish all problems. This will mean that the long-term feedback constant is somewhat higher, but if it’s nowhere near one to begin with, that won’t matter much.
Were you using “feedback constant” to mean the second derivative of intelligence, and assuming each increase in intelligence will be more difficult than the previous one (accounting for size difference)? I took “feedback constant” to mean the first derivative. I shouldn’t have used an existing term and should have said what i meant directly.
I used “feedback constant” to mean the amount of intelligence an additional unit of intelligence would allow you to bring (before using the additional unit of intelligence). For example, if at an IQ of 1000, you can design a brain with an IQ of 1010, but with an IQ of 1001, you can design a brain with an IQ of 10012, the feedback constant is two.
It’s the first derivative of the most intelligent brain you can design in terms of your own intelligence.
Looking at it again, it seems that the feedback constant and whether or not we are capable of designing better brains aren’t completely tied together. It may be that someone with an IQ of 100 can design a brain with an IQ of 10, and someone with an IQ of 101 can design a brain with an IQ of 12, so the feedback constant is two, but you can’t get enough intelligence in the first place. Similarly, the feedback constant could be less than one, but we could nonetheless be able to make brains more intelligent than us, just without an intelligence explosion. I’m not sure how much the two correlate.
You should distinguish between exponential and linear growth.
First, the feedback constant is different for every level of intelligence.
Whenever the constant is greater than one, the machine is limited by making the transformations involved, and the intelligence is not well characterized as being limited by its intelligence and instead should be thought of as limited by its resources.
Whenever the constant is less than one and greater than zero, intelligence growth is only linear, but it is not zero. If the constant remains low enough for long enough, whole periods of time, series of iterations, that have some places where the constant is above one also have sub-exponential growth.
The relationship between the AI’s growth rate and our assisted intelligence growth rate (including FAIs, paper and pen, computers, etc.) is most of what is important, with the tie-breaker being our starting resources.
An AI with fast linear growth between patches of exponential growth, or even one with only fast linear growth, would quickly outclass humans’ thinking.
I meant to mention that, but I didn’t. It looks like I didn’t so much forget as write an answer so garbled you can’t really tell what I’m trying to say. I’ll fix that.
Anyway, it will move around as the intelligence changes, but I figure it would be far enough from one that it won’t cross it for a while. Either the intelligence is sufficiently advanced before the constant goes below one, or there’s no way you’d ever be able to get something intelligent enough to recursively self-improve.
No, it’s zero, or at least asymptotic. If each additional IQ point allows you to work out how to grant yourself half an IQ point, you’ll only ever get twice as many extra IQ points as you started with.
Having extra time will be somewhat helpful, but this is limited. If you get extra time, you’d be able to accomplish harder problems, but you won’t be able to accomplish all problems. This will mean that the long-term feedback constant is somewhat higher, but if it’s nowhere near one to begin with, that won’t matter much.
Were you using “feedback constant” to mean the second derivative of intelligence, and assuming each increase in intelligence will be more difficult than the previous one (accounting for size difference)? I took “feedback constant” to mean the first derivative. I shouldn’t have used an existing term and should have said what i meant directly.
I used “feedback constant” to mean the amount of intelligence an additional unit of intelligence would allow you to bring (before using the additional unit of intelligence). For example, if at an IQ of 1000, you can design a brain with an IQ of 1010, but with an IQ of 1001, you can design a brain with an IQ of 10012, the feedback constant is two.
It’s the first derivative of the most intelligent brain you can design in terms of your own intelligence.
Looking at it again, it seems that the feedback constant and whether or not we are capable of designing better brains aren’t completely tied together. It may be that someone with an IQ of 100 can design a brain with an IQ of 10, and someone with an IQ of 101 can design a brain with an IQ of 12, so the feedback constant is two, but you can’t get enough intelligence in the first place. Similarly, the feedback constant could be less than one, but we could nonetheless be able to make brains more intelligent than us, just without an intelligence explosion. I’m not sure how much the two correlate.