Is the idea also that someone two levels below me would not be able to understand some of my ideas? Because this seems like two different things, making this “level” stuff much fuzzier. 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.
I prefer to measure this stuff in years, which is a function of both experience and potential. E.g. I am about 5 years behind my boss in the sense that in 5 years I think I’ll be able to think like him in the areas I most care about, by some fuzzy measure of likeness.
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?
...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.
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:
Alice is two levels above Carol?
Nothing in particular, because this is not the intended semantic meaning of “two levels above”?
Any concept created by Alice is beyond Carol’s reach? (I doubt this.)
Alice is capable of generating some concepts (at least one) which is beyond Carol’s reach?
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.
Disclaimer: Any discussion of XFrequentist’s model in this comment is not necessarily how XFrequentist thinks of it, but rather my variant on it.
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.
The community norm is that questions are grounded in curiosity. I’ve never seen anyone take offense at an honestly asked question.
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:
Alice is two levels above Carol?
Nothing in particular, because this is not the intended semantic meaning of “two levels above”?
Any concept created by Alice is beyond Carol’s reach? (I doubt this.)
Alice is capable of generating some concepts (at least one) which is beyond Carol’s reach?
My interpretation (assuming this all takes place within one subject area) is that:
Yes iff Alice can generate concepts Carol cannot understand,
No,
No,
Probably, but not necessarily (see bullet 1).
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.
If we are talking about Immutable Levels, a concept beyond my reach is one that I will never understand no matter how much I study or how well it is explained to me. I cannot name any concepts I’ve encountered that seem to be beyond my reach in this sense, except maybe General Relativity. That one could just be a lack of math background.
If we are talking about Mutable Levels, a concept beyond my reach is one that I could not learn without further study of background material.
Is the idea also that someone two levels below me would not be able to understand some of my ideas?
No, I agree that this interpretation isn’t useful.
I don’t understand why not; it seems entirely equivalent. (Is this just an act of signaling—a manifestation of the fact that it’s impolite to acknowledge the existence of levels below oneself—or what?)
Is the idea also that someone two levels below me would not be able to understand some of my ideas? Because this seems like two different things, making this “level” stuff much fuzzier. 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.
I prefer to measure this stuff in years, which is a function of both experience and potential. E.g. I am about 5 years behind my boss in the sense that in 5 years I think I’ll be able to think like him in the areas I most care about, by some fuzzy measure of likeness.
Level is obviously antireflexive. It is a tautology that I will never generate an idea I am incapable of generating.
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?
Reminder: my original idea was
...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.
My mileage does vary. I took the added constraint as implied, and I think it makes the whole system more useful.
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:
Alice is two levels above Carol?
Nothing in particular, because this is not the intended semantic meaning of “two levels above”?
Any concept created by Alice is beyond Carol’s reach? (I doubt this.)
Alice is capable of generating some concepts (at least one) which is beyond Carol’s reach?
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.
Disclaimer: Any discussion of XFrequentist’s model in this comment is not necessarily how XFrequentist thinks of it, but rather my variant on it.
The community norm is that questions are grounded in curiosity. I’ve never seen anyone take offense at an honestly asked question.
My interpretation (assuming this all takes place within one subject area) is that:
Yes iff Alice can generate concepts Carol cannot understand,
No,
No,
Probably, but not necessarily (see bullet 1).
If we are talking about Immutable Levels, a concept beyond my reach is one that I will never understand no matter how much I study or how well it is explained to me. I cannot name any concepts I’ve encountered that seem to be beyond my reach in this sense, except maybe General Relativity. That one could just be a lack of math background.
If we are talking about Mutable Levels, a concept beyond my reach is one that I could not learn without further study of background material.
An oversight—I’ll see if I can get XFrequentist to add it in.
No, I agree that this interpretation isn’t useful.
The probabilistic interpretation is neat, that rings true.
I don’t understand why not; it seems entirely equivalent. (Is this just an act of signaling—a manifestation of the fact that it’s impolite to acknowledge the existence of levels below oneself—or what?)