Current video status + A couple lectures

Hey there, love what you do so far but i have some constructive criticism today : One thing i love about your videos is that you make everything clear and justified (and neatly visual) but i wouldnt say that of this video. Why? well, the physics calculation are.. a whole subject, I've been in physics for 4 years and its something i have big gaps in my understanding so I would be really interested to see them explained. Specifically, when you're doing you're first reasoning, you're thinking in terms of Delta t and Delta x then, you isolate a factor of Delta X squared over Delta t, and you say we can consider it is constant... but why is that justified? what even is Delta X or its "limit" dX ? mathematically ? Its like in physics you can say "why wouldn't it be justified?" but honestly, I get arithmetic , i get calculus, I dont get physics. I don't understand in what context you're saying what you're saying, why is it allowed, why is it clever. I don't get the rules at play here, I can't understand why its rigorous... is it? Still, love what you do, take care and <3

In chemistry lab we had a horizontal, cylindrical glass tube in the ends we inserted cotton balls soaked in chemicals that reacted making a white powder (I forget exactly which chemicals they were). We measured the time it took for a white ring to appear on the inside of the tube and we measured where that ring formed. Somehow we calculated the relative mol-masses of the chemicals and their diffusion through air.

Gregor Shapiro

It's still coming, that was another one where I struggled more than I care to admit on finding a script I was happy with. Hopefully not too long after this one, though I might take a refreshing break with a topic I find easier to write about quickly.

3blue1brown

It's a good question, you can derive that it's related to the RMS velocity of each molecule, which is fairly fundamental and connected to other statistical mechanical properties of a gas. But off the top of my head, I'm not sure of the best way to measure diffusivity empirically.

3blue1brown

It's a good point. I actually chose those as deliberately weak symptoms which could come from lots of causes. Even if it's only 1 in 100 people who both have those symptoms and have covid (in this fiction population where true covid prevalence is as high as 1 in 1000), the test described is accurate enough that this prior will be updated to be well above the lowest category offered in the choices. The point then is that even weak symptoms play a meaningful role in the takeaway that a prior is not necessarily the prevalence. In your tweet, you suggest the prior should be 1 in 285, but in that case, your posterior would be around 24%, still outside that bottom-most 0-15% category.

3blue1brown

EDIT: I was wrong! Took me a while to figure out the source of my confusion though, I had to do it this way to get it: d_t(u) ~ (u_t)dt d_x(d_x(u)) ~ ((u_x)dx)_x)dx = (u_xx)dx^2 so (u_t)dt = (1/2) (u_xx)dx^2 ---> u_t = (dt/2dx^2) u_xx = D*u_xx ... as you have, with D = dt/2dx^2 ... I had taken a course in computational methods for PDEs, and D was used for the diffusion number in the discrete case when translating from the continuous case, not the other way around, haha. Either way, my blunder is below for all to see! Hey Grant, Great video here. It's really interesting that you've gone from the finite difference equation to the partial differential equation as opposed to the other way around, but I think you've got the diffusion number D wrong in your notebook explanation. You've multiplied by (dx)^2/dt when this wasn't necessary (I'm using a small d instead of delta here). Normally the continuous diffusion equation would be u_t = a*u_xx; in your case, a = 1/2. When you make a finite difference approximation of this, the equation becomes [u_(i+1) - u_i]/dt = a*[(u_(n+1) - u_n) - (u_n - u_(n-1))]/(dx)^2 You would then rearrange the equation to get [u_(i+1) - u_i] = (a*dt/(dx^2))*[(u_(n+1) - u_n) - (u_n - u_(n-1))] With your diffusion number D being equal to (a*dt/(dx^2)). In this case, I think the confusion stems from the fact that you need two indices for your density -- one for space and one for time. And of course, you could add in the fact that if you want more spatial dimensions, you add more indices. Cheers PS: Not sure how I feel about seeing your face in the video -- more educating but less dazzling -- obviously the education is better, but the dazzling feels good!

I'm an architect interested in vapor diffusion in concert with other moisture transport physics. The diffusion lecture is a very exciting peek into what I'm trying accomplish in an analysis of a peculiar encapsulated attic situation. I would really love to be pointed in the direction of a good starting point to analyze a 2D slice through my theoretical project space. The ideal output would be very visual (architects being the audience). It's been a long time since I acheived my physics degree, but I'm game to learn or "re learn" the necessary content. Please advise as you're able!

Yes please on any and all stats/probability videos! Arguably the most important societal math and often the most subtle and counter-intuitive (the math that can surprise you). I've been looking around for a "beta" video you posted earlier demonstrating the updating of the posterior iteratively and am not seeing it. Do I need to look harder or has it been removed? Thanks again for your excellent work!

About your diffusion video: I find it very enlightening, thanks. But there is one detail that I'm wondering about now: How do you find the diffusion constant in the real world? The way you explained it it's an arbitrary constant that I just have to set in order to make the limit well defined, but in reality we observe particular diffusion constants that are related to material constants, temperature, ..., and it would be nice to see whether there is a good explanation to that. Maybe something like "Atoms aren't infinitely small, so delta x is actually a fixed term, and neither is the time step if we look at the typical time an atom needs to travel to its neighbour given a particular temperature."

Rion Boom Crabhands Keon

Grant did a video on Bayesian priors a while back. I think he was playing around with that same theorem in the tweet. Maybe check out his Bayes Theory video if you haven't seen it

Heavens, I would *love* to see the follow-on video about likelihood ratios and odds. Count this as a vote for that proposal!

Burt Humburg

I'm not buying the relevance of "sore throat and fatigue" as a prior: https://twitter.com/gabrielweymouth/status/1333502893161373704 This doesn't mean the odds won't be slightly higher than if you felt in the peak of health, so your point is still valid even if the change is small. However, I think the the point would be more clear, more in line with medical advice, and less likely to sound like you are inviting self-diagnosis if you used example symptoms that were actually well correlated with COVID-19.

Gabe

I'll use the telepathy analogy, next time I hear about false positive, thanks for the trick, it's helping making things intuitive!

Oltarus

That tweet was very interesting. I got initially to quite confusing results until I understood what you meant with the "prior". I am totally looking forward to seeing that further explained in a video :)

Boudewijn Redeker