Instinctively my thought process goes: The dollar is the extra, then the ten cents is split, $0.05, done (plus or minus a double check). I can sense the $0.10 answer trying to be suggested instantly in the background, but it has a fraction of a second before it gets cut off, presumably because this is a kick type I’ve done 10,000 times.
Formal algebra is the very slow (in relative terms) but reliable answer.
Well yea, the processes at that timescale are not even exactly serial. When the 10 cents appears i just derail into pondering how stupid I must be to have 10 cents even pop up consciously, while 5 cents pops up.
When we were taught math at school we often had to do verification step. Then i was doing contests a fair bit and you care to check yourself there, you solve each problem and check the answer, then in the end if you solved everything you go over them again and doublecheck, triplecheck. We had few hard problems on tests instead of many easy ones. You often had to think—how do i check this?
It seems not everyone’s taught this way, some people have self esteem-boosting cultural stuff in mind, and the self doubt can be seen as worst thing ever culturally. In US movies there’s always someone who’s like, i can’t do it, i can’t do it, then the hero talks them into jumping over the gap anyway, and they do it, which is just silly.
For other example, say, I face something like monty hall problem. I think—how can i solve it so that i can be sure in the answer? Well, the foolproof way is to consider all the possibilities, which i can do rather rapidly by visualizing it. I don’t need to think in terms of probabilities. There’s other important thing here: reductionism. One need to know what things are derived, and that derived things aren’t ‘better’ or ‘right’. The probabilities are substitute for evaluating a potentially infinite number of possible worlds and counting them. If you ever have conflict between some first principles reasoning and some advanced high level reasoning, the advanced reasoning is not the one that’s working correctly, probably you’re misapplying it.
I recall many arguments over physics on some forum with some guy who just didn’t understand the reductionism. His barrels would float due to Archimedes law, not due to pressure difference; then it gets confusing when you have a barrel fall down into water (dynamical situation), and he would try to use highest level concepts he can think of. Or when you have submarine stuck to the seafloor. Or plugging your sink with a piece of styrofoam that you think would float, by Archimedes law, except it won’t, because there’s no pressure being applied to it’s bottom. The people who don’t get reductionism, they have the pressure difference first principles thing saying the styrofoam won’t float, and archimedes law that they misapply and it says it will, and archimedes law sounds advanced so they think its the one that’s right.
Instinctively my thought process goes: The dollar is the extra, then the ten cents is split, $0.05, done (plus or minus a double check). I can sense the $0.10 answer trying to be suggested instantly in the background, but it has a fraction of a second before it gets cut off, presumably because this is a kick type I’ve done 10,000 times.
Formal algebra is the very slow (in relative terms) but reliable answer.
Well yea, the processes at that timescale are not even exactly serial. When the 10 cents appears i just derail into pondering how stupid I must be to have 10 cents even pop up consciously, while 5 cents pops up.
When we were taught math at school we often had to do verification step. Then i was doing contests a fair bit and you care to check yourself there, you solve each problem and check the answer, then in the end if you solved everything you go over them again and doublecheck, triplecheck. We had few hard problems on tests instead of many easy ones. You often had to think—how do i check this?
It seems not everyone’s taught this way, some people have self esteem-boosting cultural stuff in mind, and the self doubt can be seen as worst thing ever culturally. In US movies there’s always someone who’s like, i can’t do it, i can’t do it, then the hero talks them into jumping over the gap anyway, and they do it, which is just silly.
For other example, say, I face something like monty hall problem. I think—how can i solve it so that i can be sure in the answer? Well, the foolproof way is to consider all the possibilities, which i can do rather rapidly by visualizing it. I don’t need to think in terms of probabilities. There’s other important thing here: reductionism. One need to know what things are derived, and that derived things aren’t ‘better’ or ‘right’. The probabilities are substitute for evaluating a potentially infinite number of possible worlds and counting them. If you ever have conflict between some first principles reasoning and some advanced high level reasoning, the advanced reasoning is not the one that’s working correctly, probably you’re misapplying it.
I recall many arguments over physics on some forum with some guy who just didn’t understand the reductionism. His barrels would float due to Archimedes law, not due to pressure difference; then it gets confusing when you have a barrel fall down into water (dynamical situation), and he would try to use highest level concepts he can think of. Or when you have submarine stuck to the seafloor. Or plugging your sink with a piece of styrofoam that you think would float, by Archimedes law, except it won’t, because there’s no pressure being applied to it’s bottom. The people who don’t get reductionism, they have the pressure difference first principles thing saying the styrofoam won’t float, and archimedes law that they misapply and it says it will, and archimedes law sounds advanced so they think its the one that’s right.