Comments by "N Marbletoe" (@nmarbletoe8210) on "3Blue1Brown" channel.

  1. How about an idea of motion through the iterations. Like, take a line and iterate it to look like one side of the Koch snowflake. Start at one end, Iterate once, then take one step along the line to where it bends (at 1/3 the length). Then iterate, and take a step, etc. You'd go 1/3, then 1/9, then 1/27 length of the original line.... With this idea of motion I guess there are two degrees of freedom of motion, since you could also go backwards (except for the first step). If we imagine that instead of staying on the line, you could also jump to nearby parts of the snowflake, there might be jump distances that would give an average degrees of freedom that is not an integer. Maybe that could be done more simply, what if a particle sits on a random spot on a y shape and can move along lines to intersections or end points. If it's on an ends it has one choice of motion. If it's in the middle it has 3 choices. So on average it would have 6/4 degrees of freedom?
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  2. i guess there is not a formula, but rather an algorithm for such curves
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  3. They have those. What they don't always know is the population prevalence, since that changes over time for some things.
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  4. an ocean wave has forward momentum, even though the water particles that make the wave move in circles. idk if that helps...
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  5. You would have to do periodic random sample surveys, like the UK did (but not the US or most other countries)
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  6. You can compare vaccines, IF they are both tested with randomly selected participants. Random selection solves a great many problems...
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  7. R squared has to be between 0 and 1. It is the proportion of the variation that is explained by the model.   In this video, the R squared shown is 0.975, meaning that 97.5% of the variation is explained by fitting it to that line.
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  8. Just say, "Ten million men get tested each year, that's a lot of tests, so there will be a lot of false positives. We recommend a second test to confirm or discount the first."
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  9.  @magic_cfw  lol then Just say "Your nuts are probably fine, the first test is often wrong"
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  10. the only way to "know" is to do a random sample of the population, or else, to test everyone. indeed, if there's no random survey the denominator is highly suspect! the UK did random sample testing, but the US did not. our population prevalence numbers were off by a factor of 2x or 10x or "whatever" times.
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  11. so the coast of Britain is not self-similar in shape, but it is self-similar in fractal dimension (box-filling dimension), within some range of scales. cool.
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  12. Sensitivity: P(T+) | (D+) probability of getting a positive test given that I am positive for the bug
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  13. electricity and magnetism
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  14. Or, both?
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  15. cool story thx
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  16. "even a good test is often wrong, if it's testing for something really rare."
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  17. basically, geometrically, it is similar to the reason a car direction changes if your left hand wheels hit the soft shoulder
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  18. We're in the early, exponential part.
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  19. ran across this in the paper: https://link.springer.com/article/10.1007%2Fs15010-020-01401-y "Using a single-term exponential model, we yielded a high R2 value of 0.95. The exponent is 0.38, meaning that the infected population doubles in size around every 1.8 days. A divergence from the exponential fit is observed at the data point on the 31st January 2020, and we expect further divergence in the future, due to the effect of the new quarantine measures starting to take place."
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  20. i don't think absorption/ emission is required
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  21. that is a great example. one can reason by extremes, and see that 0% to 100% of the positive results will be false positives, even if the experimental "false positive rate" is 95%. 1. if nobody has the disease, every positive will be false. 100% false 2. if everybody has the disease, every positive will be true. 0% false So the "real world" false positive rate depends on the number of people who have the disease, as well as the quality of the test.
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  22. a thousand years, because it would have to replicate the body also
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  23.  @Fringe-ui8qf  thanks, nice explanation
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  24. brownian motion, or any other way that the electrons are accelerated such as being hit by microwaves
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  25. i think in that case the light would be stopped, absorbed.
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  26. that has been done. see papers on Superluminal propagation in gain assisted media.
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  27. right, photons have no charge. (in any theory afaik)
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  28. do you mean 1/ r^2 ?
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  29. it slows down in a media such as water, air, etc.
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  30. i think in a prism that would take very high energy light, like maybe x-rays or gamma
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  31. one example is a flourescent rock, which resonates in uv frequencies. if you shine a light with uv on it, it glows.
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  32. correct. a photon is not a particulate point. it acts like a particle in some ways, like a wave in others, but it is in fact neither one.
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  33. (neither one, meaning it is not a classical particle or a classical wave)
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  34. or they update information that we don't actually know, which is a problem
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  35.  @theespatier4456  Agree. Iceland randomly tested 10,000 people and got like 4 positives. Even assuming all were false, the false pos rate was 0.04%. Of course, Iceland may be unfairly good at things. They even jailed financial theives after 2008, unlike almost any other nation.
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  36. And if the tests were given at random among the entire population, then that positivity rate would be informative.
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  37. electromagnetic field, to be clear. and it describes an aether that is very different from the historical concept, so that's why the name aether isn't used.
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  38. the light never really slowed. it just got delayed. if you could see the light in extreme detail, the waves always traveled at the same speed, but they were combined with other waves from the material that produced a delay effect.
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  39. makes sense, but even with a near-100 specificity it is possible that most positive tests are false. (if true cases are very rare)
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  40. He wrote a book called "Ship of gold in the deep blue sea"
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  41. Say a mildew test has 90% sensitivity. Say that I take the test. It is positive. What are the odds that I actually have mildew?
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  42.  @stephenspackman5573  The answer is: D) Not Enough Information. My odds depend on both 1) how common it is and 2) my test result. Without #1 we can't estimate my odds at all. What if nobody in the country has mildew? My odds would be zero. And if everyone has it my odds would be 100%. So it is essential to know the population prevalence of the disease to interpret an individual's test result. PS I think the prevalence would be called the "prior"
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  43.  @stephenspackman5573  Yes indeed, as you said I should have said. "What were the odds going in."
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  44. i think because the light moves electrons, which create new light waves, and these combine with the original waves to delay the phase
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  45. yes
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  46. accelerate it back and forth
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  47. nice! cool experiment
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  48. maybe because the predictive value requires knowing the population prevalence, which they don't know since they aren't doing random sample surveys (except in a few countries)
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  49. it never really slowed down, it just got combined with other waves that delayed it
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  50. either one. if test doesn't match truth, it's either a false + or a false -
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