The difference between “I can grasp this in principle but my attention span is not long enough” and “I am not intelligent enough to grasp this” escapes me. A limit is a limit; either you can actually grasp the theory or you can’t. The specific bottleneck in your intelligence, and I very much include attention span in that, is not relevant.
A certain skill set is required in order to employ mental prostheses such as written-down equations, computer programs, and the like. Without the prosthesis of writing, it would likely have been impossible to eventually prove Fermat’s Last Theorem. Without a computer program to do an exhaustive search of possible cases, it might have been humanly impossible to prove the four-color theorem. Ink on paper acts as a kind of memory, and also acts as a kind of attention span, or as an attention span prosthesis.
There may not be any upper bound on what can be remembered, on the length of one’s effective attention span, once one is using these and other prostheses.
But it requires a certain minimal skill set in order to begin to make use of these external prostheses. Many humans, especially those who are born with conditions that limit their native intelligence, may be unable to acquire that skill set.
So that threshold that Egan writes about may lie somewhere inside the human race, with some humans above the threshold, and others below. I.e., the threshold he refers to here:
I believe that humans have already crossed a threshold that, in a certain sense, puts us on an equal footing with any other being who has mastered abstract reasoning.
Abstract reasoning is built on the manipulation of symbols, so it will be limited to those humans who have the ability to manipulate symbols with some degree of reliability—enough to get them from one equation to the next. But once a human is able to get from one equation to the next, he can in principle follow (line by line) a proof of arbitrary length, even with a finite memory that can hold only a few equations at one time.
Egan is specifically addressing the in principle ability to understand something given time and inclination. He says, “I suspect that something broadly similar applies to minds and the class of things they can understand: other beings might think faster than us, or have easy access to a greater store of facts, but underlying both mental processes will be the same basic set of general-purpose tools.” A short attention span will stop a person from putting in the necessary time to understand something. If a person had the ability to learn quantum field theory but couldn’t afford to buy the textbooks, would you still say “a limit is a limit”?
The difference between “I can grasp this in principle but my attention span is not long enough” and “I am not intelligent enough to grasp this” escapes me. A limit is a limit; either you can actually grasp the theory or you can’t. The specific bottleneck in your intelligence, and I very much include attention span in that, is not relevant.
A certain skill set is required in order to employ mental prostheses such as written-down equations, computer programs, and the like. Without the prosthesis of writing, it would likely have been impossible to eventually prove Fermat’s Last Theorem. Without a computer program to do an exhaustive search of possible cases, it might have been humanly impossible to prove the four-color theorem. Ink on paper acts as a kind of memory, and also acts as a kind of attention span, or as an attention span prosthesis.
There may not be any upper bound on what can be remembered, on the length of one’s effective attention span, once one is using these and other prostheses.
But it requires a certain minimal skill set in order to begin to make use of these external prostheses. Many humans, especially those who are born with conditions that limit their native intelligence, may be unable to acquire that skill set.
So that threshold that Egan writes about may lie somewhere inside the human race, with some humans above the threshold, and others below. I.e., the threshold he refers to here:
Abstract reasoning is built on the manipulation of symbols, so it will be limited to those humans who have the ability to manipulate symbols with some degree of reliability—enough to get them from one equation to the next. But once a human is able to get from one equation to the next, he can in principle follow (line by line) a proof of arbitrary length, even with a finite memory that can hold only a few equations at one time.
Egan is specifically addressing the in principle ability to understand something given time and inclination. He says, “I suspect that something broadly similar applies to minds and the class of things they can understand: other beings might think faster than us, or have easy access to a greater store of facts, but underlying both mental processes will be the same basic set of general-purpose tools.” A short attention span will stop a person from putting in the necessary time to understand something. If a person had the ability to learn quantum field theory but couldn’t afford to buy the textbooks, would you still say “a limit is a limit”?