I don’t think there can ever be a mathematical theory of intelligence, it’s just too complex a trait. Mathematics works well applied to systems simple enough to have a precise specification, whereas a complex neural network of 10^14 synapses doesn’t strike me as like that.
Interesting... We know that reaction time is significantly slowed in old age, but IQ is not usually diminished as much. What happens to the correlation when comparing people at 20 with people at 70?
I'm curious about something, here. I was educated as a scientist and engineer. In those disciplines, if one wants to "do math" with a measurable quantity - especially if one wants to use something measurable as one factor in a complex mathematical model, one just "normalizes" the variable. x' = [x-x(0)]/[x(1)-x(0)]; where x is that thing you are measuring, x(0) is the lowest value one can conceivably observe, and x(1) is the highest realistic value. x' is "normalized" x, and will always vary between 0.00 and 1.00. Even though the Kelvin scale has an absolute zero, there are a LOT of mathematical models involving temperature that do not use T as a simple scalar - for the purpose of what is being modeled, one still normalizes T. Not always, but frequently. For some things, Kelvin temperature can be a useful parameter, as-is, without normalizing. There are some variables one "normalizes" in a different way, mathematically, that makes the normalized variable go from o to infinity, or from 1 to infinity. Kelvins, un-normalized, is a 0 to infinity type variable, as-is. One normalizes in the way that will best serve the "needs" of the model one is trying to develop, of course.
There is both art and science in choosing x(0) and x(1) for any variable, of course. One is modeling a phenomenon as closely as possible, not actually discovering some absolute law of the universe, when one normalizes a variable in a model equation.
Do intelligence researchers, who have a measurement instrument whose output they'd like to incorporate into a more complex model, really NOT do this? To me, as a chemist / chemical engineer with an academic background, not even trying to normalize whatever measurable(s) I had at hand would seem almost like malpractice!
Perhaps comparing human intelligence to temperature is misleading. Intelligence might be a bundle of mental abilities, measured in different ways, that do not have 100% correlation; so that a person might be excellent at problem-solving but mediocre at memorization. A better comparison might be to the measurement of physical fitness. So, for example, simply measuring handgrip is not a satisfactory way of measuring overall physical fitness; because it does not have 100% correlation with other measures like endurance or cardio-vascular efficiency.
"Intelligence might be a bundle of mental abilities, measured in different ways, that do not have 100% correlation; so that a person might be excellent at problem-solving but mediocre at memorization."
And that is acknowledged as such.
To me, the term intelligence means the ability to use logical reasoning to solve complex problems, to have original thought, to think critically, abstractly, and imaginatively. Information or knowledge should not be considered intelligence. Indeed, intelligent people usually have a high degree of knowledge or information, but intelligence is the ability to discover beyond current information or knowledge.
I don’t think there can ever be a mathematical theory of intelligence, it’s just too complex a trait. Mathematics works well applied to systems simple enough to have a precise specification, whereas a complex neural network of 10^14 synapses doesn’t strike me as like that.
Interesting... We know that reaction time is significantly slowed in old age, but IQ is not usually diminished as much. What happens to the correlation when comparing people at 20 with people at 70?
Interestingly, Der and Deary found that it increases with age:
https://www.sciencedirect.com/science/article/pii/S0160289617300636
—NC
Very interesting article...
"Perhaps devising a mathematical theory of intelligence is beyond human intelligence."
...and a very interesting conjecture.
The question is whether it's human intelligence now or a future enhanced intelligence.
I'm curious about something, here. I was educated as a scientist and engineer. In those disciplines, if one wants to "do math" with a measurable quantity - especially if one wants to use something measurable as one factor in a complex mathematical model, one just "normalizes" the variable. x' = [x-x(0)]/[x(1)-x(0)]; where x is that thing you are measuring, x(0) is the lowest value one can conceivably observe, and x(1) is the highest realistic value. x' is "normalized" x, and will always vary between 0.00 and 1.00. Even though the Kelvin scale has an absolute zero, there are a LOT of mathematical models involving temperature that do not use T as a simple scalar - for the purpose of what is being modeled, one still normalizes T. Not always, but frequently. For some things, Kelvin temperature can be a useful parameter, as-is, without normalizing. There are some variables one "normalizes" in a different way, mathematically, that makes the normalized variable go from o to infinity, or from 1 to infinity. Kelvins, un-normalized, is a 0 to infinity type variable, as-is. One normalizes in the way that will best serve the "needs" of the model one is trying to develop, of course.
There is both art and science in choosing x(0) and x(1) for any variable, of course. One is modeling a phenomenon as closely as possible, not actually discovering some absolute law of the universe, when one normalizes a variable in a model equation.
Do intelligence researchers, who have a measurement instrument whose output they'd like to incorporate into a more complex model, really NOT do this? To me, as a chemist / chemical engineer with an academic background, not even trying to normalize whatever measurable(s) I had at hand would seem almost like malpractice!
Perhaps comparing human intelligence to temperature is misleading. Intelligence might be a bundle of mental abilities, measured in different ways, that do not have 100% correlation; so that a person might be excellent at problem-solving but mediocre at memorization. A better comparison might be to the measurement of physical fitness. So, for example, simply measuring handgrip is not a satisfactory way of measuring overall physical fitness; because it does not have 100% correlation with other measures like endurance or cardio-vascular efficiency.
"Intelligence might be a bundle of mental abilities, measured in different ways, that do not have 100% correlation; so that a person might be excellent at problem-solving but mediocre at memorization."
And that is acknowledged as such.
To me, the term intelligence means the ability to use logical reasoning to solve complex problems, to have original thought, to think critically, abstractly, and imaginatively. Information or knowledge should not be considered intelligence. Indeed, intelligent people usually have a high degree of knowledge or information, but intelligence is the ability to discover beyond current information or knowledge.