Extrapolations and Crowdfunded Research (Experiment) | Two Minute Papers #44

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Extrapolations and Crowdfunded Research (Experiment) | Two Minute Papers #44

Two Minute Papers 06.02.2016 2 985 просмотров 99 лайков

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What 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. ______________________ 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). Subscribe if you would like to see more of these! - http://www.youtube.com/subscription_center?add_user=keeroyz 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 Károly Zsolnai-Fehér's links: Patreon → https://www.patreon.com/TwoMinutePapers Facebook → https://www.facebook.com/TwoMinutePapers/ Twitter → https://twitter.com/karoly_zsolnai Web → https://cg.tuwien.ac.at/~zsolnai/

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dear fellow Scholars this is 2minute papers with Caro what is extrapolation we hear the

What Is Extrapolation

term a lot so let's try to learn what's behind it despite the complicated definitions that are out there extrapolation basically means continuing lines 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'll jump right into an example just give me a second to build this up it's going to make sense in the end I promise so in many fields of science it is really difficult to get research projects funded experiment is a cool new startup that is trying to accelerate progress by crowdsourcing it doesn't get simpler than this system scientists pitch their research project plan and kind-hearted people pledge a one-time donation to help their cause it is like Kickstarter for research some of the newer funded projects include growing food in space developing an open protocol for insulin production and of course a mandatory Cat Project that includes sequencing the Genome of rare mutations crowdfunding research is such a terrific idea and I tell you these guys are really doing it right the startup has been founded in 2012 and people pledged $52,000 that year in the next year 10 times that and they have kept a steady and quite impressive growth ever since in 2015 they raised almost $4 million for open research it's amazing okay so a nice extrapolation problem how much can they expect to raise next year in 2016 before we start we have to be extremely sure to extrapolate only if we are reasonably sure about the nature of the trends and that they won't change significantly in the near future with that out of the way let's do a linear

Linear Extrapolation

extrapolation linear means that growth follows a straight line so we put these dots on a paper and try to connect them with a line now we take the mathematical description of this line and substitute something in it since we have four years of data four dots we would be interested in the location of the fifth point which is the amount of raised money in 2016 so let's do it 10 the 6 is 1 million so this says that we can expect $4. 2 million but let's be more optimistic and do a super

Super Linear Extrapolation

linear extrapolation superlinear means that the rate of growth is not a straight line but something that is accelerating in time if this assumption is true we can expect them to raise way more $7. 4 million a bit more pessimistic solution would be a sublinear extrapolation sublinear means that growth slows down in time this kind of growth is described well with for instance the logarithm function this effect is also often

Effect of Diminishing Returns

called the effect of diminishing returns a good example of this is the skill level of Google deep Minds artificial intelligence program that plays go as we add more and more computational resources the algorithm gets better and better at the game but after a point there's only so much one can learn therefore progress slows down and eventually gets close to stopping there are so many examples of this effect in our lives if you have some great examples of logarithmic growth let me know in the comment section I'll include the best ones in the video description box according to this logarithm we can expect the company to raise less than the previous estimation $3. 1 million next year sorry guys a common Pitfall in popular media is that the mathematically untrained Minds almost always assume linear growth due to its Simplicity this can lead to hilariously wrong results if you would extrapolate the size of the belly of a pregnant woman after 9 months your conclusion would be run because she's going to explode whereas we know that a baby is going to be born and she is going to get back in shape if I had zero wives yesterday and it's my wedding day today I will sure as hell have a couple dozen wives by next month many things are inherently nonlinear and doing a simple linear extrapolation often doesn't do justice to the problem at hand bear in mind that there are many different ways to connect a bunch of dots let's try to find out why we had widely varying results this is due to the fact that we only had four samples that means four dots if I plot these possible functions that we've been talking about we get the following it seems that the further we go the more they diverge however in this case if we have data only between zero and one for instance there is very little difference between a wild exponential function and a very conservative square root based growth you can also Imagine your logarithm here the more dots we have over a greater period of time the more we can distinguish the nature of our growth and an educated mind has to take into consideration that many phenomena are inherently nonlinear if you catch someone doing a linear extrapolation always ask are you sure that the process your modeling is indeed linear and do you have enough data to prove that that's all for today thanks for watching and for your generous support and I'll see you next time

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