yes it does. that’s exactly what it is you’re describing. all of it adding up. as always people struggle with exponential growth because it’s not very intuitive.
my favorite way to demonstrate the unintuitive nature of exponential growth is this question:
there’s a pond, and a lily pad on it. the number of lily pads double every day on the pond. so on day 1 there’s one, day 2 there’s two, and on day 3 there’s four… etc.
if it takes 120 days for the pond to get completely covered in lily pads, what day was only half of it covered?
I mean sure it would? That’s rhe whole point is that exponential growth quickly reaches massive quantities. Like literally after 120 days I doubt that many lilypads would fit on earth.
they wouldn’t, but it’s not a real pond, and not real lily pads. i was going to say 20 but went for 120 to make the ratio more extreme, not to make it realistic.
I don’t disagree with your explanation of exponential growth or how it does answer for the speed at which we went from, say the magnifying glass to the hubble space telescope.
However, the exponential growth alone model does have a floor: it presumes that there was some kind of push, drive or want for progress. Like, as if there was a destination we’re supposed to end up at and its just a case of how long it took to get there. It excludes the idea that people might not have wanted to.
People didn’t want to toil all day in someone else’s farm. In smaller numbers, on good land, people didn’t have to do very much to get the food they needed. Its only when farming became developed and consistent enough that those living there had the numbers to go kill the people who lived on the good land.
Once we’d been, for all intense and purpose, domesticated by grain, “progress” was inevitable.
Another example would be the industrial revolution. People ask why it was so much faster here in the UK than France. It wasn’t because of a desire for progress. Its that French people had a natural aversion to being worked for 12 hours a day in hell-like factories and workhouses. I mean, British people did too but they had mostly just been kicked off the common land they had lived on for centuries. So, they had no other place to go and begging and not having a job for more than three days was made illegal, punishable by being sent to to workhouses. At one points, they had more British soldiers fighting the riots at home than they had fighting napoleon.
my comment referred to knowledge more than anything. the more you know, the more you have to go from to learn new things. incredibly simplistic summary for very complex phenomena, but I wasn’t going to go through the entire human history. there are breaking points and regression stages, but generally speaking it makes sense that the more you progress, the faster you can progress further. you have more tools.
“something doesn’t add up”
yes it does. that’s exactly what it is you’re describing. all of it adding up. as always people struggle with exponential growth because it’s not very intuitive.
my favorite way to demonstrate the unintuitive nature of exponential growth is this question:
there’s a pond, and a lily pad on it. the number of lily pads double every day on the pond. so on day 1 there’s one, day 2 there’s two, and on day 3 there’s four… etc.
if it takes 120 days for the pond to get completely covered in lily pads, what day was only half of it covered?
The standard story is “One Grain of Rice” https://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Martin/instructional unit/day4.exponential/excel/grainofrice.html
thanks, i love that story.
If it takes 120 days to be covered thats a huge fucking pond.
that is purposeful. it wouldn’t make much of a point if it took 10 days.
I mean sure it would? That’s rhe whole point is that exponential growth quickly reaches massive quantities. Like literally after 120 days I doubt that many lilypads would fit on earth.
I’m not sure what lily pads so I went with the largest which have around 7.069m2 of surface area or 0.0000007069km2 surface area.
Earth has a surface area of 510,064,472km2
After 120 days of doubling we have
6.64614x1035 * 7.069x10-6 = 4.6982Ex1030
So you are correct but it’s also around 23x the surface area of the sun.
I love how their goof helped further show how humans suck with exponential numbers
I think the lilypads might need to be smaller than an atomic nucleus? Someone check my math. But still larger than a Planck length, so it is fine.
they wouldn’t, but it’s not a real pond, and not real lily pads. i was going to say 20 but went for 120 to make the ratio more extreme, not to make it realistic.
The pond is the Pacific Ocean.
Let’s see…2^120 is 1.329•10^36 lily pads. Say 15cm diameter for a lily pad, that’s got an area of 177cm^2. That’s 10.3•10^38 cm^2.
The surface area of the Pacific Ocean is only 1.652•10^18 cm^2.
We’re boned.
Nah just really small Lily pads
I don’t disagree with your explanation of exponential growth or how it does answer for the speed at which we went from, say the magnifying glass to the hubble space telescope.
However, the exponential growth alone model does have a floor: it presumes that there was some kind of push, drive or want for progress. Like, as if there was a destination we’re supposed to end up at and its just a case of how long it took to get there. It excludes the idea that people might not have wanted to.
People didn’t want to toil all day in someone else’s farm. In smaller numbers, on good land, people didn’t have to do very much to get the food they needed. Its only when farming became developed and consistent enough that those living there had the numbers to go kill the people who lived on the good land.
Once we’d been, for all intense and purpose, domesticated by grain, “progress” was inevitable.
Another example would be the industrial revolution. People ask why it was so much faster here in the UK than France. It wasn’t because of a desire for progress. Its that French people had a natural aversion to being worked for 12 hours a day in hell-like factories and workhouses. I mean, British people did too but they had mostly just been kicked off the common land they had lived on for centuries. So, they had no other place to go and begging and not having a job for more than three days was made illegal, punishable by being sent to to workhouses. At one points, they had more British soldiers fighting the riots at home than they had fighting napoleon.
my comment referred to knowledge more than anything. the more you know, the more you have to go from to learn new things. incredibly simplistic summary for very complex phenomena, but I wasn’t going to go through the entire human history. there are breaking points and regression stages, but generally speaking it makes sense that the more you progress, the faster you can progress further. you have more tools.