Extrapolations and Crowdfunded Research (Experiment) | Two Minute Papers #44
98What is extrapolation? Extrapolation basically means continuing lines (or connecting dots, if you like this intuition better). A good example is when we have data for something from the last few days or years, and would like to have a forecast for the future.
We will do some linear and nonlinear extrapolations (and learn what they mean) and try to find out the amount of money Experiment will
raise for open research. Experiment is a cool new startup that is trying to accelerate progress in research by crowdsourcing it.
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Logarithmic growth examples from the comments:
- athletic training - at first, you make great improvements, then as you approach the limits of your endurance, progress slows down, and eventually stops (Morten Eriksen),
- The approximate number of Olympic records on the men's 100 m sprint (RelatedGiraffe),
- Bacterial growth. At first, there is a lot of sugar to feed bacteria but there simply aren't that many bacteria and they split as fast as they possibly can, roughly doubling each time step. But eventually the limits of the available sugar become apparent and newly born bacteria either don't find enough nutrition to split again or they outright starve. Inevitably you run into a balance where about as many bacteria die as are born and thus the population growth runs flat (Kram).
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Experiment, crowdsourcing research:
https://experiment.com/
Links to Wolfram|Alpha to reproduce the experiments (
Linear fit: http://www.wolframalpha.com/input/?i=linear+fit+52700,+527197,+766924,+3856542
Quadratic fit: http://www.wolframalpha.com/input/?i=quadratic+fit+52700,+527197,+766924,+3856542
Logarithmic fit: http://www.wolframalpha.com/input/?i=logarithmic+fit+52700,+527197,+766924,+3856542
Plot ALL the functions! http://www.wolframalpha.com/input/?i=plot+sqrt%28x%29+and+x+and+x%5E2+and+e%5Ex-2+where+x+%3D+0..5+y%3D0..4
One more great image to explain the concept of sublinear and superlinear:
http://deliveryimages.acm.org/10.1145/2720000/2719919/figs/f1.jpg
The good old xkcd: https://xkcd.com/605/
The thumbnail image background was created by NIAID (CC BY 2.0): https://flic.kr/p/rg1p9H
Animation at the start (MIT license): https://www.shadertoy.com/view/llXSD7
Pregnant lady image by Tobias Lindman (CC BY 2.0): https://flic.kr/p/nhZ7Yh
Splash screen/thumbnail design: Felícia Fehér - http://felicia.hu
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