4 ms·

If people are unwilling to do the math themselves, then it becomes a question of what can you trust? Something physical (an abacus, say) could potentially be m

If people are unwilling to do the math themselves, then it becomes a question of what can you trust? Something physical (an abacus, say) could potentially be manipulated by slight of hand or optical illusion. Something digital (an iPhone app) could silently do the same. But what if you make it really easy for the user to do the math themselves, by explicitly breaking down the calculation into a video of smaller steps where the numbers move to show the calculation. E.g. $19 + $25 + $28 on such an app: 19 25 +28 --- 10 20 14 +28 --- 10 20 10 20 +12 --- 30 10 20 +12 --- 40 20 +12 --- 60 +12 --- 72

catalogia 7y ago
> "Something physical (an abacus, say) could potentially be manipulated by slight of hand or optical illusion." That's true, but people often overestimate their ability to see through such ploys. That's why the shell game (https://en.wikipedia.org/wiki/Shell_game https://en.wikipedia.org/wiki/Shell_game) is thousands of years old and still going strong, across the world.
judge2020 7y ago
I think they need some registers that print receipts.
nkrisc 7y ago
In my head, 19+25+28 becomes: 20 + 25 + 30 - 3 = 72 Works well with multiplication too. 12 * 13 = 10 * 13 + 2 * 13 = 130 + 26 = 156. or 19 * 15 = 20 * 15 - 15 = (10 * 15) * 2 - 15 = 285 There's no simple rule I know for multiplying by 19, but for 20 you just add a zero and double it. It's all about transforming the numbers into ones that are easier to work with in your head, and just accounting for your transformations at the end. Even if you forget to account for your padding, you're still in the right ballpark and have a rough idea of what the answer should be near.
papln 7y ago
Essentally, you are saying that a calculated result is a theorem, and the calculator shouold provide a proof. As always, course the standard of a commnicated proof depends on what axioms and theorems the verifier knows.

catalogia 7y ago

> "Something physical (an abacus, say) could potentially be manipulated by slight of hand or optical illusion." That's true, but people often overestimate their ability to see through such ploys. That's why the shell game (https://en.wikipedia.org/wiki/Shell_game https://en.wikipedia.org/wiki/Shell_game) is thousands of years old and still going strong, across the world.

judge2020 7y ago

I think they need some registers that print receipts.

nkrisc 7y ago

In my head, 19+25+28 becomes: 20 + 25 + 30 - 3 = 72 Works well with multiplication too. 12 * 13 = 10 * 13 + 2 * 13 = 130 + 26 = 156. or 19 * 15 = 20 * 15 - 15 = (10 * 15) * 2 - 15 = 285 There's no simple rule I know for multiplying by 19, but for 20 you just add a zero and double it. It's all about transforming the numbers into ones that are easier to work with in your head, and just accounting for your transformations at the end. Even if you forget to account for your padding, you're still in the right ballpark and have a rough idea of what the answer should be near.

papln 7y ago

Essentally, you are saying that a calculated result is a theorem, and the calculator shouold provide a proof. As always, course the standard of a commnicated proof depends on what axioms and theorems the verifier knows.