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I'd push that it isn't just statistics. It is finding a way to overcome any learned experience and expectations. I remember people having a hard time understa

by taeric 3y ago

I'd push that it isn't just statistics. It is finding a way to overcome any learned experience and expectations. I remember people having a hard time understanding that the reason things fall behind the car when you toss them out the window is 100% air friction. To the point that many in my college classes would get that basic question wrong. Or, for fun, show an image of someone spinning a rock on a string overhead, ask what happens when they let go of the string with an arrow for where the rock will go. Nevermind how many of us (myself included) have a hard time with the idea that .9999.. equals 1. Even more amusing when you consider few have trouble with .3333... * 3 doing so. Yes, statistics can be particularly difficult to really internalize. I'm not entirely convinced it is uniquely difficult.

bertil 3y ago
Probably. I just happen to have had the most incredible physics teachers, and I know elite engineering schools do too: Feynman, that Eastern European lady who is way too loud and excited about science, the “let’s see if conservation of movement works, or if that bowling ball will crush my skull” guy. Every school had more than one. Steve Mould is a gift from above, but not a unique one… On the other hand what Randal Monroe from xkcd and Grant Sanderson from 3blue1Brown have alluded to, that felt like witchcraft unlike anything I’ve seen in class. I went to what should be one of the most demanding schools for statistics and it took me years to make sense of it. Re-opening my notes after things clicked was earth-shaking. And it wasn’t specific to the school: we also had economics teacher, and they were incredible: hilarious, terrifying, unforgettable. “Our task is to forecast inflation. We have tried many approach, mainly macroeconomics and bone reading. Bone reading was more accurate, but the minister didn’t think it involved enough suffering.” How do you forget that?
- taeric 3y ago
  Love the suffering joke! I do think that most physics benefits from the empirical nature of being able to test ideas. Statistics is tough because you can't really empirically test a lot of distributions. And then a ton of us (again, myself included) have a hard time seeing the subtle differences introduced with some framings. The Monty Hall one is hilarious for just how upset so many people get on being wrong on it. Note that I think with modern computers, you can start to test more distributions in simulations than you could dream of in the past. Has some of its own problems, of course, and it is a shame that we lose a lot of symbolic manipulation in the process. So, I still largely think it is getting people past their experiences. I think that is ultimately compatible with your point. I think I'm just calling into question how rosy the rest of the landscape isn't, in the learning environment.
burnished 3y ago
I think the .999 repeating thing has more to do with how we teach limits, people struggle to understand how two things that look definitionally different are the same because the rationale isn't well motivated. I had a professor that framed the whole process as an argument which was much easier to grasp, and I can easily imagine most people just getting a lecture or two on the equations and the implications. Plus phrasing it as 'equals' or 'are the same' sort of puts the challenging part right in the front. Focusing on the difference more naturally leads you to the same conclusion.
- taeric 3y ago
  It isn't a limit thing, though? It is a textual representation thing. You are not confused that 01 is the same as 1. Similarly, you are ok that .33... is the same as .3... In fractions, you are ok with the idea that 1/2 is the same as 2/4. And that you are often supposed to work in reduced form, such that you will probably never put 2/4 down as an answer to any problem. We work with "regular" numbers for so much of our life that it is odd to consider how to write them to that level.
  - burnished 3y ago
    Its not a textual representation thing, there are other repeating sequences that do not converge. I mention limits because that was the context in which I learned about this, others have pointed out you can demonstrate this with just algebra (which makes me wonder if I just wasn't paying attention when that lesson came up).
- Clamchop 3y ago
  It can be proven that it equals 1 using basic algebra.
  - gpm 3y ago
    Sure, but if your "basic algebra" includes the popular inconsistent axiom that "numbers have a unique decimal representation (up to leading and trailing zeros)" you can equally well just disprove any of the rules of algebra that you used to reach the conclusion. When people have (accidentally) been taught that, and then they're presented with a case where it's false, it's perfectly reasonable that they wonder whether it's that thing that they were taught, or something else that they were taught, that is wrong. You don't have to look very far to find cases where it was the other laws of algebra that they believed were wrong, for example the popular proof that 1 + 2 + 3 + ... = -1/12. Even a mathematically sophisticated alien who comes from a culture that somehow never used the rationals or reals the way we do might at first think that this is a fact that leads to a proof that no object that obeys your rules of algebra exists, rather than a proof that 0.999... = 1. Most people, even most university students, don't have the benefit of a formal mathematical education that actually clarifies these kinds of riddles.

by taeric 3y ago

bertil 3y ago

Probably. I just happen to have had the most incredible physics teachers, and I know elite engineering schools do too: Feynman, that Eastern European lady who is way too loud and excited about science, the “let’s see if conservation of movement works, or if that bowling ball will crush my skull” guy. Every school had more than one. Steve Mould is a gift from above, but not a unique one… On the other hand what Randal Monroe from xkcd and Grant Sanderson from 3blue1Brown have alluded to, that felt like witchcraft unlike anything I’ve seen in class. I went to what should be one of the most demanding schools for statistics and it took me years to make sense of it. Re-opening my notes after things clicked was earth-shaking. And it wasn’t specific to the school: we also had economics teacher, and they were incredible: hilarious, terrifying, unforgettable. “Our task is to forecast inflation. We have tried many approach, mainly macroeconomics and bone reading. Bone reading was more accurate, but the minister didn’t think it involved enough suffering.” How do you forget that?

taeric 3y ago
Love the suffering joke! I do think that most physics benefits from the empirical nature of being able to test ideas. Statistics is tough because you can't really empirically test a lot of distributions. And then a ton of us (again, myself included) have a hard time seeing the subtle differences introduced with some framings. The Monty Hall one is hilarious for just how upset so many people get on being wrong on it. Note that I think with modern computers, you can start to test more distributions in simulations than you could dream of in the past. Has some of its own problems, of course, and it is a shame that we lose a lot of symbolic manipulation in the process. So, I still largely think it is getting people past their experiences. I think that is ultimately compatible with your point. I think I'm just calling into question how rosy the rest of the landscape isn't, in the learning environment.

burnished 3y ago

I think the .999 repeating thing has more to do with how we teach limits, people struggle to understand how two things that look definitionally different are the same because the rationale isn't well motivated. I had a professor that framed the whole process as an argument which was much easier to grasp, and I can easily imagine most people just getting a lecture or two on the equations and the implications. Plus phrasing it as 'equals' or 'are the same' sort of puts the challenging part right in the front. Focusing on the difference more naturally leads you to the same conclusion.

taeric 3y ago
It isn't a limit thing, though? It is a textual representation thing. You are not confused that 01 is the same as 1. Similarly, you are ok that .33... is the same as .3... In fractions, you are ok with the idea that 1/2 is the same as 2/4. And that you are often supposed to work in reduced form, such that you will probably never put 2/4 down as an answer to any problem. We work with "regular" numbers for so much of our life that it is odd to consider how to write them to that level.
- burnished 3y ago
  Its not a textual representation thing, there are other repeating sequences that do not converge. I mention limits because that was the context in which I learned about this, others have pointed out you can demonstrate this with just algebra (which makes me wonder if I just wasn't paying attention when that lesson came up).
Clamchop 3y ago
It can be proven that it equals 1 using basic algebra.
- gpm 3y ago
  Sure, but if your "basic algebra" includes the popular inconsistent axiom that "numbers have a unique decimal representation (up to leading and trailing zeros)" you can equally well just disprove any of the rules of algebra that you used to reach the conclusion. When people have (accidentally) been taught that, and then they're presented with a case where it's false, it's perfectly reasonable that they wonder whether it's that thing that they were taught, or something else that they were taught, that is wrong. You don't have to look very far to find cases where it was the other laws of algebra that they believed were wrong, for example the popular proof that 1 + 2 + 3 + ... = -1/12. Even a mathematically sophisticated alien who comes from a culture that somehow never used the rationals or reals the way we do might at first think that this is a fact that leads to a proof that no object that obeys your rules of algebra exists, rather than a proof that 0.999... = 1. Most people, even most university students, don't have the benefit of a formal mathematical education that actually clarifies these kinds of riddles.