How should I go about identifying them?
Do you think I was on the right track with my own attempt, or do you think (or suspect) that I am completely missing the mark?
How should I go about identifying them?
Do you think I was on the right track with my own attempt, or do you think (or suspect) that I am completely missing the mark?
From a private DD email from 2011, about when he had a short conversation with Feynman IRL:
he [Feynman] then went on to declare that existing educational practices, mainly in universities, will ensure that “there will be no more great physicists”
btw, are you as pessimistic about academic math as you are about academic physics?
By the way, it occurred to me that this might leave more gaps in my knowledge than I realize, because profs know how dumb most of the students are and intentionally design tests that will have a B class average.
edit: in other words, this is occurring
Yeah I definitely misinterpreted your question the first time, sorry.
I thought about this for a while and I don’t have great answers.
The amount of time it takes for me to be successful @ philosophy is one proxy for my chances of failure chances. Like if it takes 50 years that’s pretty damn close to failure, and if it takes 500 years, that’s failure. All of my answers below only hold insofar as the amount of time it takes for me to be successful @ philosophy is determined by the amount of hard work I do (though I recognize that this is only one factor, so my points are very weak).
Advantages of making philosophy a secondary focus, regarding chance of success at becoming a great philosopher:
Disadvantages:
edit: made significant revisions ~30 mins after I posted this
This is the kind of error that is important to post mortem (investigate underlying causes) if trying to improve at philosophy. It’s similar to how I think investigating arithmetic errors, to understand what they are and what caused them, is important if trying to improve at math (this came up above). The similarity is that they are both (as a first guess) errors in basic prerequisite skills, possibly 5+ levels distant from what you’re actually trying to do.
It’s very hard to know what bottlenecks an error effects unless you know what the root cause error is. The root cause error often causes many other downstream errors. So you can find a visible error, investigate, find an underlying error (the root cause or at least closer to it), and then figure out what its consequences are.
With arithmetic, a way to begin is by categorizing errors – trying to understand what types of errors you are and aren’t making. This helps pinpoint what’s going on.
Do you make calculation errors with addition? Subtraction? Working with negatives? Multiplication? Division? Fractions, percents, ratios, decimals? Exponents? Some of those (which?), all or none? (This is oriented towards investigating multiple errors over time. It’s easier to investigate effectively if you can find patterns.)
Are the errors from mental math? Or do they also happen with various tools (pencil and paper, text editor, whiteboard app, various math apps)?
Do you misread numbers from the problem? Do you misread or misunderstand the words in the problem?
Do you have memory errors? E.g. you think you remember a number from the problem, and use that, but actually you misremembered and should have reread it?
Do you get a correct number in your head then output it incorrectly? Does it depend on output device like talking, hand writing, typing or calculator buttons?
Are the errors happening when dealing with long numbers? Do you lose track of intermediate steps in the calculation when doing it mentally? When there are lots of steps, do you skip writing all of them down, which results in errors sometimes?
Do you have more than one process for doing arithmetic, and if so does any process have a different error rate than another? Like do you have a “careful mode” which has a lower error rate, and if so what do you differently?
Are there any differences if any other people are involved vs. you’re working alone?
These are just examples. One could come up with many more. These are aimed to be decently accessible to figure out. If you identified some problem areas more specifically than arithmetic, then you could drill down and come up with some stuff like this that’s more specific and detailed.
Here are a few math questions:
You’re going to explain trigonometry to a student who has all the prerequisites but knows nothing about it. What do you begin with?
Do you understand mathematical induction?
Do you understand recursion?
(These are just context questions.)
Do you know any programming?
Have you worked with logic stuff like De Morgan’s laws? Please don’t look anything up. They’re the ones for converting from and to or or vice versa.
Do you have any knowledge of logic gates / basic computer hardware? Do you know about e.g. reversible gates/logic or half-adders?
Here are some advantages to philosophy as a secondary focus which are relevant to success or failure at philosophy:
Disadvantages:
This is the kind of post that I think bystanders often kinda ignore and don’t learn much from, and also don’t say anything about. But you could take it as an example of how to look into an error and try to brainstorm things in a kinda similar way for some other type of error that you want to investigate.
Just saw this math page and had an opinion about it. No context from the link is needed.
- All the numbers lying on the real number line are known as real numbers
- All the real numbers greater than zero are positive real numbers
- 25 is a real number
From the above statements, we can say that if the first two statements are true then the third one is definitely true.
What are your thoughts?
It’s very hard to know what bottlenecks an error effects unless you know what the root cause error is.
Here was my reasoning for saying that arithmetic is not a bottleneck issue for me:
For exams, I basically decide what grade I’m going to get by increasing or decreasing the amount of material I study. I don’t do this quantitatively, but I meet all my goals with respect to grades. Doesn’t this show that my bottleneck is my willingness to study?
For everything else in my career (right now at least), the main issue I seem to be facing is that I don’t know wtf to work on, and it’s very hard to see how arithmetic errors could possibly be the root cause of something like that.
A context where it sounds like arithmetic errors could potentially be a bottleneck issue for me is if I get into another situation where I need to do a whole bunch of long 30 page calculations by hand, since the main problem here is the amount of time it takes me to do them. But that’s not an issue I’m facing right now.
I wasn’t thinking about bottlenecks for getting good grades or test scores (or choosing what to work on). I was thinking about the issue of understanding math and physics well. I think arithmetic errors (or their underlying causes) could be important for that.
- Do you understand mathematical induction?
- Do you understand recursion?
Do you know any programming?
Have you worked with logic stuff like De Morgan’s laws? Please don’t look anything up. They’re the ones for converting from and to or or vice versa.
Do you have any knowledge of logic gates / basic computer hardware? Do you know about e.g. reversible gates/logic or half-adders?
Yes.
- You’re going to explain trigonometry to a student who has all the prerequisites but knows nothing about it. What do you begin with?
I guess the very first thing I’d start with is defining the sine, cosine, and tangent functions.
I guess the very first thing I’d start with is defining the sine, cosine, and tangent functions.
What definitions would you give?
I’d say
sin(theta) = length(opposite side) / length(hypotenuse)
cos(theta) = length(adjacent side) / length(hypotenuse)
tan(theta) = length(opposite side) / length(adjacent side)
I’d then have to justify my claim that these functions I’ve defined only depend on theta
Just saw this math page and had an opinion about it. No context from the link is needed.
- All the numbers lying on the real number line are known as real numbers
- All the real numbers greater than zero are positive real numbers
- 25 is a real number
From the above statements, we can say that if the first two statements are true then the third one is definitely true.
What are your thoughts
Something that jumps out at me is that the first two statements don’t actually imply the third on their own because we need to know that 25 > 0.
I’m pretty sure you’re misreading it.
oh LOL oops. I did misread it. You got me.
The second statement is unnecessary.
Maybe it’s established context that 25 is “lying on the real number line,” and so the deduction of 3 from 1 could be valid, but this is a really stupid example because why would anyone define what the real number line is before you define what a real number is?
Yeah. I wouldn’t grant them an established context. I’d say the second is irrelevant and the first does not imply the third. So it’s really bad!
Could you edit one of the bullet points to make it correct?