...and the concepts generated by someone two levels above you are beyond reach.
Interesting, but this second part isn't mentioned in the original post. And the added constraint makes the whole system seem less likely to be useful to me, never mind mathematical rigor. YMMV, I suppose.
This can just as well be "X did happen, but the mainstream has been convinced it did not." The theory that an extraterrestrial spacecraft crashed near Roswell, New Mexico comes to mind.
Or creationism can be seen as a combination: "Genesis 1-2 (X1) literally happened, but the atheist scientists invented evolution (X2) and tricked people into believing it."
Level is obviously antireflexive. It is a tautology that I will never generate an idea I am incapable of generating.
And of course it's probabilistic in nature anyhow - on occasion I generate ideas my friend couldn't, and he can on occasion generate ideas I couldn't.
Manfred points out that this level concept may not be antisymmetric. Others have pointed out that level may depend on the topic of expertise. For that matter, I'll claim that the concept of level can be applied to artistic pursuits like music, painting, and dancing, not just rational pursuits like math, physics, and programming.
So what if we say: A is higher level than B at topic X if the "value" of ideas per unit time which A generates but B could not is greater than the "value" of ideas per unit time which B generates but A could not. Now we have something antisymmetric.
So now, is this relation transitive? Inversely, is it possible that Alice is higher level at math than Bob, Bob is higher level at math than Carol, and Carol is higher level at math than Alice?
Right. I for one happen to believe the theory that al Qaeda conspired to execute deadly attacks on Sept. 11, 2001. That is literally a conspiracy theory. Is the process by which I came to believe that relevant to the discussion here? (If yes, I'd be happy to give more information.)
But the phrase "conspiracy theory" commonly implies (like the faked moon landing) that relatively few people believe it, generally because the evidence against the theory is fairly convincing. (Conspiracists may answer that additional evidence is not available or widely known to the public.)
I assume Systems 1 and 2 here refer to this Elephant and Rider article.
I suspect this is one of those things where both ways are true. I do believe that at least to some extent, social skills are hard-wired into human brains, and spending too much conscious thought on social actions can actually impede them.
For a bit of anecdotal evidence, I fairly often experience difficulty finding the "right" moments to insert a comment into a conversation among several people. But at other times, in a very similar conversation I can easily join in the conversation in a way that feels natural and doesn't appear to startle or annoy anyone.
One obvious factor correlated to the difference is familiarity with the group. So possibly my Mind 1 / Elephant knows more about their particular cues for attention-sharing, and/or they know more about my own semiconscious signals for having something to say. But I can also experience different degrees of ability to speak in conversation among the same group of people. A second factor which correlates to that ability is whether I feel comfortable, or anxious. I would describe the effects of anxiety (at least on my mind) as preoccupying the Mind 2 / Rider with unproductive thoughts. So it seems this might be a simple example of overthinking interfering with social skills I do have. (Though sadly, I can't "switch modes" at will, nor easily take precise measurements of what happens when I am doing it "right". And yes, these two "factors" are themselves very correlated.)
On the other hand, many social skills can only be learned. The ones we don't get for free with our brains, we can train with conscious effort, and with luck engrain them into the semiconscious "System 1".
My instinct was to ignore this reply, but I recently read a suggestion that among sufficiently rational people there is never simply a need to agree to disagree. Do you folks on this site have some sort of standard disclaimer that questions are grounded in curiosity, and are not meant to belittle anyone's experience or opinion? In any case, I'm just curious. These questions are directed to Cyan and/or Normal Anomaly and/or anyone else with a similar reaction.
Suppose that within a given domain of knowledge, Alice can create concepts that Bob can understand but not generate, and Bob can create concepts that Carol can understand but not generate. Does this imply:
I'm also confused about what it means for a concept to be beyond someone's reach. The closest experience I can think of is a mathematical theorem I cannot understand. But usually the cause of that is that I do not understand one or more of the definitions or theorems involved in the statement of the theorem itself, and enough study could presumably resolve that.
Or maybe the concept of a concept beyond someone's reach is beyond my reach.