this post was submitted on 21 Jul 2024
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"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?
If it takes 120 days to be covered thats a huge fucking pond.
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.
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 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.
I’m not sure what lily pads so I went with the largest which have around 7.069m^2^ of surface area or 0.0000007069km^2^ surface area.
Earth has a surface area of 510,064,472km^2^
After 120 days of doubling we have
6.64614x10^35^ * 7.069x10^-6^ = 4.6982Ex10^30^
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
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.
Nah just really small Lily pads