100-meter pace over the course of a whole kilometer. We're arguing linearly , but actually, we shouldn't be. We should be thinking that actually, this is a nonlinear relationship.
It turns out that in these curves, the curvature of the torsion evolved linearly . Both of them evolve linearly along the curve. And therefore, we could prove that they satisfy several properties that are
Why? Because I feel like I'm getting knowledge every time I buy one. That is not thinking linearly .
Why? Because I feel like I'm getting knowledge every time I buy one. We think linearly . And I said, if you turned that money dial up, maybe you shop at a different brand.
Why da, da, da? In humans it scales linearly .
Why da, da, da? So it scales linearly .
make it even stronger. I'm going to assume that the consumer has linear utility, which means that prices in equilibrium are going to be constant. labor factors that produce financial services linearly out of labor. Okay.
But Kimi K2 Thinking and Kimi K2 is a model that is very popular. People say that has very good creative writing and also in doing some software on making the attention mechanism scale linearly with inference token prediction. So there was Qwen2-VL, for example,
And in our heads, if we're subject to exponential growth bias, we think that quantity is going to grow like the dashed line. It's just going to grow linearly , continuing to change at the same slow rate as it currently is. And actually, what's happening is the full black curve here, where it's just going to take off, and it's going to grow exponentially and get
Or there are specific areas that we designate it to. But technology has been created very linearly . Mainstream technology in the last like 15 years has been created linearly .
It is faster and faster and faster, Moore's law and all these things. And the human brain thinks linearly , and so does organizations. You don't necessarily get into that, but we'll try and get ahead of that.
If you graph this angle as a function of distance to the optical axis, you'll see that it can be approximated as linear. The problem is that the magnetic field doesn't scale linearly . It's much stronger near the edges of the magnet.
We should be thinking that actually, this is a nonlinear relationship. The distance that you cover doesn't scale linearly with the time that you can cover your 100 meters. OK, so that's a type of pseudo-linearity question.
Ideas grow like this too. These ideas and many others grow kind of non-linearly , and that is why we have a very hard time judging them and judging their potential, especially at the beginning. All these ideas and many others have been rejected by people with lots of experience in their beginnings.
But technology has been created very linearly . Mainstream technology in the last like 15 years has been created linearly . It's come from one place.
because they are the implications of exponential growth are startling but it's is not just in the future we've already seen this uh if I take 30 steps linearly 1 2 3 4 5 I get to 30 if I take 30 steps exponentially 2 486 I get to a billion it makes a huge difference and
They administered a few other drugs in an attempt to revive him, but Tusko died shortly thereafter. The mistake they made was to assume that safe drug dosage scales linearly with mass. It does not. And it turns out there are a lot of things like this that don't scale in the way you'd expect.
Well, it comes in when we're thinking about pizza and the value for money for pizza. So I'm going to posit that the price of a pizza scales linearly with the diameter. And this is true, and I'll show you some data to back that up in a second.
means you get better value for money with your pizzas the bigger the pizza that you buy. Just to double-check that it is true that the price of the pizza scales linearly with the diameter, this is data that was collected by a "New York Times" journalist, a guy called .
That was to differentiate it from linear access memory as in old magnetic tapes. Well, you could only access it linearly . They came up with this new thing where you could address any-- you could ask any address.
You're more like just separating the molecules from each other. But if you instead kind of pull it in such a way that it stretches linearly and becomes kind of more like a fiber, there's a very specific point as you're stretching it-- it deforms.
This discovery was purely by accident. Bully for you. Super glue polymers are almost all single chains running linearly between the surfaces. They have a directionality to them, kind of like wood grain.
most bullish aggressive models, we found that hurricanes don't strengthen linearly . Like they're not just steadily
But he found the prices of 75,000 pizzas, and he plotted them on a chart, which looks like this. And you can see that roughly, the diameter of the pizza does scale linearly with the price. But remember that the area scales as the square of the diameter, so the more you pay for the pizza or the bigger the pizza
And this is what exponential curves can look like sometimes. They can look like they're growing very slowly, and linearly almost at the start. And then very quickly, they can take off and get out of control.
We looked at a problem that hadn't yet caused a kind of a catastrophe. We hadn't experienced a huge problem, but we saw something growing non-linearly quite kind of steep. And then we decided to curb it-- ozone-depleting substance emissions.
independently by Bernoulli, by Euler, and by Talbot to use them to design railway trucks. OK? And the nice property of this curve is that the curvature evolves linearly along the curve. There is some psychological research that claims that these curves are very good for the human eye.
And this curve, we defined it to be the curve that penalizes for the change, both in curvature and in torsion. It turns out that in these curves, the curvature of the torsion evolved linearly . Both of them evolve linearly along the curve.
Why? Because I feel like I'm getting knowledge every time I buy one. What I really loved about your answer is-- what most people do when they answer the "quadruple" question is they think very linearly .
start going up. It's going up almost like linearly , right?
policies that we have are not well structured for this type of reality. We still think linearly .
It's just a massively complex computer science problem. And so we just gotta bring every technology to bear. Otherwise, we scale up linearly or we
So all of these things, almost like a chemical reaction, you know, you have three ingredients in the chemical reaction, and you need to linearly scale up the three ingredients.
If you wanted to get the same area of pizza, you would need four of those 8-inch diameter pizzas, which would cost you 40 pounds, not 20 pounds for the 16th diameter pizza. So the fact that there's this nonlinear relationship, that the area scales as the square of the diameter while the price scales linearly with the diameter, means you get better value for money with your pizzas the bigger the pizza that you buy.
It means that people who suffer from this bias don't tend to invest for the future because they tend to undervalue the value of their savings in the future, because they don't appreciate that it's going to grow exponentially, and they think it's just going to grow linearly . The flip side of that is that they also take on more debt than they should do because they undervalue the value that that debt is going to cost them to service
Yeah. But then when you go to the 50 to 100 years, we grossly underestimate the progress because we tend to think linearly .
When we think about what Google is doing specifically in education and talking about things like literacy, talking about students being pushed linearly
And what you see is that, at least at the lower-mass end, we're pretty much proportional to this plot, which is the star formation rate just growing linearly with the mass.
Why five steps? Because I'm a number cruncher, I think linearly .
But our mindset, as I mentioned before, is only increasing linearly .
It's got near the stiffness of a solid part, but because of how this lattice structure is created, a lot of the stresses are translated linearly
and I love the immediacy of getting that e-book. Right? Um, and it works for me with fiction, 'cause I really read linearly in fiction. But I'm noticing like I, I also