Following both jimrandomh and MixedNuts, I think perhaps the disagreement could be expressed in terms of resource normalized learning curves.
A learning curve can be generated for a single domain and a single person, and the datasets that support them allow one to compare different people’s ability to learn and the ease or difficulty of different domains. Here are good examples. I’ve actually seen these produced and compared in a startup and used to identify whose process should be mined for lessons to teach other analysts, and seeing the graphs was kind of surprising to me because I had expected them to be noisy and abstract, but using a moving average to smooth things out (or looking at day to day performance over several weeks) but they showed S curves as people exponentially got the hang of things with early insights allowing greater insights and then hit diminishing returns as the marginal utility of insights started to decrease. Also, there were obvious and visible between-person differences in the curves themselves.
Implicitly, all of those curves were assumed to have the same X-axis which was “human-brain-hours” or something like that. Human brains were assumed to be equivalent (at least they had the same startup burn rate per hour...) and so only the hours and days spent learning were being considered.
So imagine we work out a way to normalize processing power in terms of theoretically inter-convertable input to a physical computing process like transistors or joules or some such. You might be able to normalize learning curves between different systems using something relatively universal, like total energy expended on learning so far, or computing-element-gram-seconds or some such.
With such a measure you might be able to vividly see that a trillion joules spent learning a very hard task would produce vastly better results for any fixed resources you allocated to a “fundamentally smarter” process (assuming a task where the learning curve wouldn’t flatten out too fast to make learning differences moot). At a certain point, especially if you’re comparing processes with different starting points on the curve at “time=0″, it might be pointless to allocate learning jobs to certain learning systems given time and resource constraints, and then we might say that the learning systems that weren’t “worth” assigning a learning task were “categorically different”… but figuring out this categorical difference in practice would involve a lot of features of the context, like the opportunity costs implied by the number and quality of alternatives, the task you’re considering, hard deadlines, and perhaps “throttling issues” where each system in the learning economy’s performance per resource per time may become sub-linear in resources beyond a certain point. On throttling issues, JacobCannel has interesting thoughts based on the physics of computation.
Following both jimrandomh and MixedNuts, I think perhaps the disagreement could be expressed in terms of resource normalized learning curves.
A learning curve can be generated for a single domain and a single person, and the datasets that support them allow one to compare different people’s ability to learn and the ease or difficulty of different domains. Here are good examples. I’ve actually seen these produced and compared in a startup and used to identify whose process should be mined for lessons to teach other analysts, and seeing the graphs was kind of surprising to me because I had expected them to be noisy and abstract, but using a moving average to smooth things out (or looking at day to day performance over several weeks) but they showed S curves as people exponentially got the hang of things with early insights allowing greater insights and then hit diminishing returns as the marginal utility of insights started to decrease. Also, there were obvious and visible between-person differences in the curves themselves.
Implicitly, all of those curves were assumed to have the same X-axis which was “human-brain-hours” or something like that. Human brains were assumed to be equivalent (at least they had the same startup burn rate per hour...) and so only the hours and days spent learning were being considered.
So imagine we work out a way to normalize processing power in terms of theoretically inter-convertable input to a physical computing process like transistors or joules or some such. You might be able to normalize learning curves between different systems using something relatively universal, like total energy expended on learning so far, or computing-element-gram-seconds or some such.
With such a measure you might be able to vividly see that a trillion joules spent learning a very hard task would produce vastly better results for any fixed resources you allocated to a “fundamentally smarter” process (assuming a task where the learning curve wouldn’t flatten out too fast to make learning differences moot). At a certain point, especially if you’re comparing processes with different starting points on the curve at “time=0″, it might be pointless to allocate learning jobs to certain learning systems given time and resource constraints, and then we might say that the learning systems that weren’t “worth” assigning a learning task were “categorically different”… but figuring out this categorical difference in practice would involve a lot of features of the context, like the opportunity costs implied by the number and quality of alternatives, the task you’re considering, hard deadlines, and perhaps “throttling issues” where each system in the learning economy’s performance per resource per time may become sub-linear in resources beyond a certain point. On throttling issues, Jacob Cannel has interesting thoughts based on the physics of computation.