Exponential growth and epidemics
8分57秒
再生速度:1倍速
説明
A good time for a primer on exponential and logistic growth, no?
Home page: https://www.3blue1brown.com
Brought to you by you: http://3b1b.co/covid-thanks
Excellent visualization of this kind of growth from Minutephysics and Aatish Bhatia:
https://www.youtube.com/watch?v=54XLXg4fYsc
Data source: https://www.worldometers.info/coronavirus/coronavirus-cases/#case-tot-outchina
Some have (quite rightfully) commented on how you shouldn't look at the R^2 of linear regressions on cumulative data since even if the changes from one day to the next are completely random, the totals they add up to wouldn't be independent of each other. Since the derivative of an exponential should also be an exponential, we could instead run the same test on the logarithms of the differences from day to day, which in this case gives R^2 = 0.91.
While this video uses COVID-19 as a motivating example, the main goal is simply a math lesson on exponentials and logistic curves. If you're looking for a video more focused on COVID-19 itself, I'd recommend taking a look at this one from Osmosis: https://youtu.be/cFB_C2ieW5I
Extrapolation xkcd: https://xkcd.com/605/
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These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Home page: https://www.3blue1brown.com
Brought to you by you: http://3b1b.co/covid-thanks
Excellent visualization of this kind of growth from Minutephysics and Aatish Bhatia:
https://www.youtube.com/watch?v=54XLXg4fYsc
Data source: https://www.worldometers.info/coronavirus/coronavirus-cases/#case-tot-outchina
Some have (quite rightfully) commented on how you shouldn't look at the R^2 of linear regressions on cumulative data since even if the changes from one day to the next are completely random, the totals they add up to wouldn't be independent of each other. Since the derivative of an exponential should also be an exponential, we could instead run the same test on the logarithms of the differences from day to day, which in this case gives R^2 = 0.91.
While this video uses COVID-19 as a motivating example, the main goal is simply a math lesson on exponentials and logistic curves. If you're looking for a video more focused on COVID-19 itself, I'd recommend taking a look at this one from Osmosis: https://youtu.be/cFB_C2ieW5I
Extrapolation xkcd: https://xkcd.com/605/
------------------
These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
タグ
# exponential function
# linear regression
# inflection point
# 3b1b