So as a very, very simple example, addition gives you the answer to the question, if I add 2 and 2, what do I get. Subtraction -- and the answer, of course, is 4.And this is the deepest thing I'll say in this whole talk.
And this is the deepest thing I'll say in this whole talk. And subtraction , of course, gives you the answer to the inverse question, which is, what do I need to add to 2 in order to get 4, the answer, of course, being 2. Now inverse deduction works in a very similar way.
And we talk in the book about something which is sort of RidicuList. It's called the subtraction game. I think I've even done the subtraction game with some teams at Google.
up there is single-digit addition. It's literally five plus seven, or one plus one. And once you get ten in a row there, it'll move you up to one digit and a double digit addition, and then single digit subtraction and then we call it very basic multiplication. Once you get ten in a row there, it keeps moving you down what we call this "knowledge map" and if you keep going down the knowledge map, you start getting into some more advanced arithmetic; some pre-algebra here. Go further down and it starts getting into algebra, a
You do it once, and then you can forget about it. And the analogy we have to-- subtraction is you have to mow the lawn. Otherwise, the weeds are going to overrun the place.
It's called the subtraction game. I think I've even done the subtraction game with some teams at Google. And essentially, what you do is you have people come up with a list of things that used to work, don't work anymore that are driving them crazy,
to be able to do this-- for there to be enough of that period for them to be able to do the calculations, And there is leftover because when the subtraction was made of this from this,
because that was eight weeks into the trip. So if you're doing the subtraction , they've only got four weeks of food left. Things start going poorly, and then they start-- they run out of food.
with the old pictures. And through the magic of digital subtraction , here's the template. Here's the new image.
So the cones are producing the brightness information as well as the color information. And they are doing it by subtraction not addition. Which makes our visual system almost insensitive to absolute brightness levels.
my cousin was a much more primitive version, but this is the same, actually some of the same basic code. It's been fancied up a good bit now. But the general principle is, it'll give you as many--this is subtraction one--it'll give you as many problems as you need until you get ten in a row. And it's a very simple--it got cut off here-- but you can have the videos here, there's hints, you can see it draws a number line for you. The Khan Academy videos can be pumped in, and itís a very simple idea; you do it until you get ten in a row,
And he said something very wise. He said, "Subtraction isn't one and done." It's like mowing the lawn. You gotta do it like pretty regularly.
I could listen to you two all day long. I wanted to go back to the addition sickness and subtraction exercises because that's such an important topic as we've been in this sort of grow at all costs sort of industry for so long. And it turns out-- I was just thinking, as you said, Slack messages, it turns out that at Google, I think the number of emails
So yeah, so certainly from NASA's perspective it's, oh, these are brilliant scientists. They can do a little bit of addition or subtraction depending on what they want and figure it out. But we can see that there is quite a bit of complexity here, even to the point where you mentioned in your book
Any mutation here is lethal to the person. So we start to discover by elimination and by subtraction fascinating parts of the genome that are worth looking at. And the other thing I might just say is it's the correlation.
but that doesn't mean you're getting better. Right. And the key to scaling is smart subtraction . So let's talk about meetings for a moment, because I think on the list of things that might be considered bad friction are meetings.
Yeah, I'm really behind on my car payments right now. For Deonna, life right now is about subtraction . What she can live without. Like I'll eat like once a day. It It's easier to buy fast food cuz a
And these calculators look really complicated, but they could do very little. They could do sort of basic addition, subtraction . Later models could do square roots.
Here's the new image. So we did that, and through digital subtraction , here's a small subset of one of those images, taken on the 7th of April, 1997.
It could not work by addition. So it doesn't. It works by subtraction . So there are basically three channels of information coming from your cones to your head.
And essentially, what you do is you have people come up with a list of things that used to work, don't work anymore that are driving them crazy, and then come up with a way maybe to reduce the burden, the subtraction target. So I was doing it with another company, not Google, a competitor.
What came out of this is in 2003, I started making the Ken Ken blocks What I created first was a 4 by 4 with only addition problems Next is a 9 by 9 with only addition problems Then next I created a mix of addition and subtraction , then multiplication and division Then I went on to create puzzles that made all four rules mixed, and with operators I went on to create these math calculation blocks
And I created KenKen with addition only, four-by-four to nine-by-nine grid size. Then I created KenKen with a variety of combinations of operations, such as addition and subtraction , multiplication only, multiplication and division, and all four operations with symbols.
Next, 4 plus 3 equals 7. But mathematics, addition, subtraction , multiplication, division, that's all.
And so maybe we can figure out how to do induction in the same way that people in mathematics figure out how to do other inverse operations. Like, for example, subtraction is the inverse of addition, or integration is the inverse of differentiation, and so forth. So as a very, very simple example, addition gives you the answer to the question, if I add 2 and 2, what do I get.
Those are the things that really hurt. That money that you didn't make, will end up being a far bigger subtraction from your theoretical end net worth, then the things that you did buy that perhaps did not work as well as you hoped it would.
for each of the group presidents, is we call the subtraction game.
And the other one is blue minus-- sorry one is red minus green and the other one's blue minus yellow. And then there's a third one, which is such a complicated function of additions and subtractions that produces brightness from the cones. So the cones are producing the brightness information as well as the color information.
People who see the dress as blue and black, they assume, their brains assume that it's lit from above and so they make no such subtraction .
Umpteen number of things he has made for children, for addition, subtraction , to give them that interest in,
And she tried to make up sand clock of three minutes for using just clock, addition, subtraction , multiples,
You keep taking the tickets, and the number remaining gives you, by subtraction , if you like, the number that you sold.
Now you do not need, once you get good at the abacus it's very easy to do additions, subtraction 'cause just by putting in the sum you've done the addition already and multiplication
sit on that bicycle as long as it takes to actually learn how to ride the bicycle. And so, that's what we wanna do here. We wanna allow you to experiment, we wanna allow you to fail, but you're not going to move on to more advanced topics until you actually, until you actually master the topic. So this is -- that is the subtraction one module. This, right here, is trigonometry. This, right here, is shifting and reflecting functions.
Why, I say, it is realistic meditation is that one is a meditation based upon subtractions .
And it's one of the things that the design team did a lot was to, instead of really concentrating on adding major new features, they looked at ways you could do subtractions the same