can be factored uniquely into primes. So if you have a number of that form, then you can just factor it, and that tells you the exponent on 3 and the exponent on 5. And so you know exactly which person it was, which car they came from, and which seat they came from.- And prime factorization is every single number can be decomposed into the atoms of mathematics, which is the prime
world on brains that aren't fully developed yet. Yeah, there's been these like exponential rises in anxiety, depression, um, you know, young women and girls have fallen off a cliff almost with the rise of social media.
But actually, that's not the technical definition of exponential growth. Exponential growth is something which grows in proportion to its current size. So the money in your bank account, if you leave it there long enough, it is growing exponentially.
that really launched a thousand ships that really got this field going and marked the beginning of the phase of exponential growth that we are in today. So what is interesting about this is not only that it's an exoplanet, but the amplitude of the signal here is larger
OK, again, what's this got to do with anything? exponentially fast, it turns out.
get a chance to read the book Intel's Engineers to try to explain to people once the power of the exponential of microchips doubling every 24 months once did a back of the envelope calculation just for fun they said what if a 1971 VW Beetle improve improved at the same rate microchips had
You see not only uh lighting efficiency rising very quickly, but also the cost of a bulb falling. So, there's a double exponential trend on LED efficiency. May not seem like a big deal, but this will save a hundreds of billions of dollars
and 13 years. So, US dollar output of manufacturing never stopped going up and it followed that same parabolic exponential curve. But jobs are fewer. And that's where the problem is because well, what are these people going to do?
Now this plot can be extended into the future, and we see all sorts of predictions of climate increasing, the temperature increasing exponentially throughout the next 50 years to 100 years. Of course, this is not the first time in Earth's recent history that the planet has experienced a really rapid increase in temperature.
It's worth just examining for a moment the difference between linear progressions, which is our intuition, and the reality of information technology, which is exponential. So linear goes one, two, three, four. Exponential, which is information technology, goes to two, four, eight, siexteen.
exponential. So linear goes one, two, three, four. Exponential, which is information technology, goes to two, four, eight, siexteen. Is that really so different?
that worked just fine so we have built-in linear predictors but the nature of Information Technology is exponential and that causes an acceleration in technology because uh each technology Builds on the last so technology uh gets more powerful and the Paradigm shifts occur more rapidly uh
Pace it's an axiom that uh changes is a constant but actually it's not a constant it's a it's an exponential and that's why the future is surprising uh halfway through the general project the Skeptics were still going strong saying I told you this wasn't going to work I mean here are halfway through the project and only 1%
brain scanning they form trajectories that are amazingly predictable and what is predictable is that they're exponential and and it's a it's a simple comparison but people really don't get it uh and the biggest criticism of these ideas I call the criticism from
And they could just barely do it with natural, with the natural things that are in the environment. An exponent . I mean using the classic thing an exponential curve is self-similar.
into the appliance, right? What why would you ever have an unintelligent appliance, right? At this point, when it gets exponentially cheaper. We used to get in traffic accidents. Right? Like like the big reveal, right?
It's called exponential growth. So exponential growth has multiple meanings in different contexts. In the media, it's often used to mean fast or to mean big, something that's big or growing quickly.
much bigger than we think. So exponential growth bias has a number of problems. 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
But then very quickly, as we saw both in the first wave and indeed in the second wave, things can get out of hand if you don't take action. So exponential growth bias can damage our responses to things like pandemics. So that's the end of the first bit of the talk about nonlinearity.
um that I don't think existed anywhere close to you know where we are now 30 years ago 20 years is very kind thank you um but yeah I I think that astronomy as a field has really sped up um exponentially as with has has a lot of other stem Fields um with the Advent and and development of sort of Cutting Edge technologies that make it possible for us to manage big data and you know perform simulations expeditiously and I think really um capitalize on on the enormous amounts of data that we're getting from our telescopes
So this is the number of objects launched into space in the past few years. an exponential growth here in the number of objects launched into space, so really reaching a new era where a lot more things are being put up in space.
To me, it means taking early and decisive action to address a problem, before the problem becomes an exponential one and before the problem outstrips our capacity to address it without terrible suffering. And so this is probably a graph you've all seen before.
An exponential increase in all of them.
For exponentially declining prices, people can build measles, smallpox, et cetera, put it in a drone, and fly it down our streets.
and exponential growth of this energy and so on.
So exponential growth of untreatable disease has already begun.
The exponential curve of DNA sequencing price fall is faster than Moore's law.
increases exponentially. So that is something that makes it very hard to replicate a network once the network gains scale, something that Googlers
distributed exponential models of scaling are what's important again I won't go into it too much but it's
is exponentially more fun but also harder than print or television
or exponential pace. Those of us in the real world, if you can think about how you adapt to change, it's not exponential.
But the exponent wasn't one, it was about 0.8.
In the exponent is the sum of three primes minus N, but adding in the exponent is the same as multiplying exponentials together.
These are the scaling exponents WBE theory predicts, including many that are not multiples of a quarter, but all follow from the same theory.
The exact exponents vary a little, but overall, as cities grow larger, you systematically get more of each.
- So there's this exponential decay in frequency of earthquakes of a given magnitude and an exponential increase in the amount of energy released
So an exponential increase of access to creativity.
that the transformation creates exponential growth as a result of the transformation in an unexpected way. So, growing up, my mom worked in newspapers
This is a very specific example of a positive feedback loop, which many people will be familiar with. It's called exponential growth. So exponential growth has multiple meanings in different contexts.
It's not fast-growing. It doesn't seem very big in my bank account anyway. So it is an exponential growth process, but it's not big or fast, and that can surprise people, I think. And this is what exponential curves can look like sometimes.
So it is an exponential growth process, but it's not big or fast, and that can surprise people, I think. 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.
They have more debt compared to their income, so it controls somewhat for educational attainment there. The other thing about exponential growth bias, going back to the pandemic, is that people who exhibit higher levels of exponential growth bias were also less likely to comply with non-pharmaceutical interventions, things like mask-wearing, social distancing, test-taking, contact tracing,
There's lots more in the book. But things like exponential growth, square laws. There's cube laws. There are feedback loops, both positive, which give us these growth processes which grow unexpectedly quickly like exponential growth,
time have increased exponentially but our ability to extract Insight from that meaning from that has only grown
to predominate or the exponential difficulty of the problem we're going to crack is going to predominate?
It is exponential. And as per law, it's double exponential.
If it's exponential, the sooner you can act, the more effectively you can shut it down.
Seed dispersal falls off exponentially as you go away from the tree.
It's like exponential. Thank you.
"Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist." This is a quote I had in my office on the wall.