6 ms·

I'd say memorization and building expertise are orthogonal. Expertise is lossy intuitive reasoning. It's pattern recognition based on practice and experience.

I'd say memorization and building expertise are orthogonal. Expertise is lossy intuitive reasoning. It's pattern recognition based on practice and experience. Then there is logical reasoning based on memorized facts, which is a fallback mechanism people use when they don't have the necessary skills. It usually fails, because it's inefficient, it doesn't scale, and it doesn't generalize. Sometimes memorization is necessary, but it's often not the actual point. When kids are asked to memorize the multiplication table, they are not really supposed to memorize it. They are supposed to build a mental model for multiplying numbers without resorting to first principles or memorized answers. Then if your model can calculate 7 * 8, you can also use it to calculate 7e10 * 8e11, even if you haven't memorized that specific fact.

brigadier132 2y ago
> It's pattern recognition based on practice and experience This is arguably another form of memorization. Magnus Carlson is the best Chess player in the world because he memorizes everything without effort.
- jltsiren 2y ago
  It's memorization in the same sense as an LLM is a database. You can think like that if you prefer, but I don't find it a useful perspective.
iwsk 2y ago
When kids are asked to memorize the multiplication table, they are actually supposed to memorize it.
tsimionescu 2y ago
The multiplication table doesn't have patterns, or it only has a few. You really do need to remember all of the 100 results. I know what 7*8 is, and I know the rules for exponents, so I can compute 7e10*8e11. But I can't "deduce" what 7*8 is by any rule, it's just a fact I remember. I have certainly not added 7 to itself 8 times in decades.
- LouisSayers 2y ago
  > I can't "deduce" what 7*8 is by any rule But you can break this into a different problem knowing that 2^3 = 8, and doing 7*2*2*2. This isn't as fast but is in a way more useful because while 7*8 is fairly easy to remember you're not going to remember 17*8 etc but you can problem solve it fairly quick. There are other ways of seeing the multiplication table as well. For example 9 times something can be thought of as 9*x = 10*x-x. I never learnt these, but simply realised over time that there are different approaches to doing calculations.
  - Dylan16807 2y ago
    > But you can break this into a different problem knowing that 2^3 = 8, and doing 7*2*2*2. Doing that multiplication all the way through is super slow. When they said "can't" they meant in an effective sense, since they did mention repeated addition as an option. And that's not an effective way to get there. > There are other ways of seeing the multiplication table as well. For example 9 times something can be thought of as 9*x = 10*x-x. Yes, you can do that one. But that's just about the only fast trick there is.
    - wizzwizz4 2y ago
      Multiplication and division by 2 and 5 correspond to each other. Multiplication by 11 is shift-and-add. There are many such tricks.
      - Dylan16807 2y ago
        The first one doesn't help with remembering times tables. The second one is outside the 1-10 times table we were talking about.
        wizzwizz4 2y ago
        6 is 2×3, so 6×5 = 30. Likewise, 17 = 2×8 + 1, so 5×17 = 85.
    - 2y ago

brigadier132 2y ago

> It's pattern recognition based on practice and experience This is arguably another form of memorization. Magnus Carlson is the best Chess player in the world because he memorizes everything without effort.

jltsiren 2y ago
It's memorization in the same sense as an LLM is a database. You can think like that if you prefer, but I don't find it a useful perspective.

iwsk 2y ago

When kids are asked to memorize the multiplication table, they are actually supposed to memorize it.

tsimionescu 2y ago

The multiplication table doesn't have patterns, or it only has a few. You really do need to remember all of the 100 results. I know what 7*8 is, and I know the rules for exponents, so I can compute 7e10*8e11. But I can't "deduce" what 7*8 is by any rule, it's just a fact I remember. I have certainly not added 7 to itself 8 times in decades.

LouisSayers 2y ago
> I can't "deduce" what 7*8 is by any rule But you can break this into a different problem knowing that 2^3 = 8, and doing 7*2*2*2. This isn't as fast but is in a way more useful because while 7*8 is fairly easy to remember you're not going to remember 17*8 etc but you can problem solve it fairly quick. There are other ways of seeing the multiplication table as well. For example 9 times something can be thought of as 9*x = 10*x-x. I never learnt these, but simply realised over time that there are different approaches to doing calculations.
- Dylan16807 2y ago
  > But you can break this into a different problem knowing that 2^3 = 8, and doing 7*2*2*2. Doing that multiplication all the way through is super slow. When they said "can't" they meant in an effective sense, since they did mention repeated addition as an option. And that's not an effective way to get there. > There are other ways of seeing the multiplication table as well. For example 9 times something can be thought of as 9*x = 10*x-x. Yes, you can do that one. But that's just about the only fast trick there is.
  - wizzwizz4 2y ago
    Multiplication and division by 2 and 5 correspond to each other. Multiplication by 11 is shift-and-add. There are many such tricks.
    - Dylan16807 2y ago
      The first one doesn't help with remembering times tables. The second one is outside the 1-10 times table we were talking about.
      - wizzwizz4 2y ago
        6 is 2×3, so 6×5 = 30. Likewise, 17 = 2×8 + 1, so 5×17 = 85.
  - 2y ago