Also in physics, some steps are small (and very abstract) and don’t correspond to any very important concept.
I agree with you that in (say) the simplification of an expression, or in (say) using the chain rule to compute the derivative of a complicated function, or in any other non-pointless calculation for that matter, every step has some conceptual purpose: there’s a reason why you are doing any given step, and the reason can be explained. Each step means something.
When I said (bold added)
I didn’t intend to convey that I think the individual steps of the calculation are meaningless.
I just mean that a conceptual understanding of why you’re doing each step in the calculation doesn’t necessarily have to help much with error correction. This is pretty obvious, e.g. even with something really simple like manually adding together 100 different purchase amounts to see how much money you spent this month. Each step in that calculation has some conceptual meaning, but the ability of that knowledge to help with error correction is limited. If you know to within a $0.05 range what the final $ amount should be, you have to get to ~ the end of your calculation before it can help you know that you’ve made a mistake: It is not going to help you catch that arithmetic mistake on step 41 of your calculation where you wrote $456.28 + $1.10 = $457.28 (not until you get to the end, that is). A “conceptual understanding of what the numbers mean” doesn’t help in a situation like that: It’s a process error, or a conceptual error about arithmetic, or a physiological(?) problem (e.g. how I randomly spaced out for a millisecond), or something else.
I reached a daily edit limit :( and can’t change this. IIRC it said I’m only allowed to edit 23 times per day but that doesn’t make any sense because I haven’t edited 23 times.
Instead of this
I wanted to say this:
What I mean by saying that some of these checks don’t mean anything until you get to the end of the calculation is like, suppose you are manually adding together 100 different purchase amounts to see how much money you spent this month, and your check is that you know to within a $0.05 range what the final $ amount should be in the above situation. Then you have to get to ~ the end of your calculation before it can help you know that you’ve made a mistake: It is not going to help you catch that arithmetic mistake on step 41 of your calculation where you wrote $456.28 + $1.10 = $457.28 (not until you get to the end, that is). A “conceptual understanding of what the numbers mean” doesn’t help in a situation like that: It’s a process error, or a conceptual error about arithmetic, or a physiological(?) problem (e.g. how I randomly spaced out for a millisecond), or something else.
IIRC Feynman talked about e.g. understanding numbers and how that was important. I think it was in “Surely You’re Joking, Mr. Feynman!“ (probably in more places). Maybe checking out Feynman could be helpful.
Laughing about making a reading error is a rather different attitude than recognizing that the error is caused by a faulty automatization that should be taken seriously and fixed. The error is probably related to many other reading errors which have made conversing with you difficult.
I don’t think laughing at a situation is a “rather different attitude” than taking the situation seriously.
E.g. if I tripped over my carpet and mildly hurt myself, I might laugh about it. That wouldn’t necessarily mean I am not taking seriously the idea that I should fix my carpet to prevent myself from tripping again.
This sentence falsely implies that I have integrated Objectivism more than I actually have. It’s more of a statement about what things I think it would feel good to achieve for the ideal man, whom I aspire to be.
For me personally, there are definitely some things that I’m pretty sure are pro-life but also don’t feel good to do (and vice versa).
edit: and also some things where I’m just not sure whether or not they are good
I think everyone is capable of great things, so in some sense I think that basically everyone should be similarly ambitious.
There are a few exceptions, like if you know you’re going to die tomorrow then you should probably not be trying to do something groundbreaking (though even then, you should still be ambitious wrt how to spend your last moments).
I can think of a lot of philosophical beliefs that could cause people to be unambitious, and I don’t share those beliefs. Some examples of those anti-ambition beliefs:
the belief that there is no free will
people believing bigoted myths about the race (or sex etc) to which they belong
subjectivism: we can’t know anything anyway so why bother
people believing that smarts are determined genetically and that they simply aren’t smart enough to be better than average
a lot of religions to one extent or another say it is sinful or pointless to pursue earthly values
Environmentalism and Marxism say (roughly) that material success means you’re exploiting the earth or the proletariat respectively
an extremely common theme in popular movies/books is for there to be a character who is outwardly successful but inwardly miserable, and (unlike in FH) the explanation is given is that success and happiness are incompatible