Damn, I'm doing research involving partitions right now. I used crank/rank all the time -invariants that he introduced years ago. What a shame, RIP
Readit Newsfermenflo commented on Freeman Dyson Has Died nytimes.com/2020/02/28/sc... · Posted by u/ChickeNES
For the curious, do you have a link to the paper?
I don't remember if this is the exact paper but as united893 already posted, the paper was probably:
https://annals.math.princeton.edu/wp-content/uploads/annals-...
Long story short: Imagine you have an object, place an ant on the surface of the object, and then instruct the ant to walk in a straight line forever. Will the ant ever end up in the same place it started (with the same initial direction)? If so, then it has formed a closed geodesic. For some objects, the answer is obvious. For a perfect sphere, the answer is always yes. In fact, any sphere-like object (imagine warping/contorting a sphere without tearing or poking holes in it) will always have at least 3 such closed geodesics: https://en.wikipedia.org/wiki/Theorem_of_the_three_geodesics.
Miriam managed to construct an amazing formula that, when given the number of holes in an object, can give you the probability of forming a closed geodesic when starting from a random point in a random direction.
This: https://www.youtube.com/watch?v=Sx-kAlEpiZk is a great video that goes over what I explained and a couple other great achievements of hers. Worth a watch.
Mirzakhani will always have a special place in my heart.
I was an undergraduate mathematics student when I discovered her work. It was a paper on closed geodesics and there was something special about her writing. Her approaches were simple an elegant -the kind that made you, as a reader, feel accomplished for understanding such a complex subject. It wasn't long until she was placed among other grand mathematicians that I looked up to.
A year later she died. I wasn't even aware of her health. It sucked to see an idol go so young. But it's incredible what she accomplished within her lifetime. She'll always be one of the greatest.
That's also what I was taught as a best practice, but it's not always possible. Otherwise, best practice is to index the gears (ie mark a specific tooth on each). That way, when you disassemble the gearbox (it's bound to happen sometime for maintenance), you can make sure it's reassembled so that the same teeth will continue to mesh, preserving the wear pattern. Otherwise, wear is substantially increased.
That's also what I was taught as a best practice, but it's not always possible.
Isn't milk such a small part of most people's diets that it couldn't possibly have much of an effect? Especially for adults. Most people I know just put a bit in coffee and that's about it. I can't remember the last time I drank a glass of milk.
(Note I mean milk the drink, dairy is probably a big part of diets but that's not being studied here)
That was also one of my initial thoughts. But who knows. I'm sure milk consumption varies a lot in different geographies, cultural backgrounds, upbringings, etc...
I personally never drink milk. The only dairy product I regularly consume is butter. But I had a roommate who drank a glass of milk with dinner every day and occasionally had a bowl of cereal in the mornings. So It's at least a spectrum.
Okay, but let's stop and think about it for ten seconds: Of course drinking a slightly different brand of milk doesn't make you live 4.5 years longer; the headline claim is obvious nonsense. (And as I understand it, it's now thought that to the extent there is any difference, it's in favor of the high-fat milk.)
So then the conclusion seems to be that confounding factors have an extremely strong effect on the conclusion, even when the investigators have tried hard to screen them out.
Why? What went wrong with the attempts to screen out the confounding factors?
To be fair, it's a pretty large claim to just assume that something "went wrong with the attempts to screen out the confounding factors" and that the conclusion must be false.
It's a shocking conclusion, I'll give you that. And to be honest, I'm not convinced either. You might very well be right. But it's a strong claim to make agains a peer-reviewed journal publication.
It sounds like one must still assume they correctly accounted for all confounders.
Exactly. As I said, they didn't reveal much of the process that "accounted for confounding" but I just wanted to dismiss everyone's initial reaction that this is just an obvious case of confounding.
Perhaps it is. Perhaps it isn't. It just depends on how much you trust their methodology.
I know everyone's reaction (mine included) was: "No shit, people who drink low-fat milk probably live healthier lives in general"... But it looks like they really did account for other variables and found that milk-fat percentage was the only strong factor in play:
> "High-fat milk consumers may have lifestyles that are less healthy than low-fat milk drinkers. Since this possibility was recognized before the onset of the investigation, statistical adjustments were made for a dozen potential confounders. Statistical analyses determined that these variables had little influence on the milk fat and telomere relationship. Nevertheless, other variables could explain some of the relationship between milk fat intake and telomere length identified in the present investigation."
My immediate thought is, those who grab the 1% milk at the grocery store are more likely to make other healthy decisions as well. Can anyone comment on whether the study adjusted for this?
My immediate reaction as well. Seems like the perfect case of confounding. But after reading the paper, I saw this statement:
> "High-fat milk consumers may have lifestyles that are less healthy than low-fat milk drinkers. Since this possibility was recognized before the onset of the investigation, statistical adjustments were made for a dozen potential confounders. Statistical analyses determined that these variables had little influence on the milk fat and telomere relationship. Nevertheless, other variables could explain some of the relationship between milk fat intake and telomere length identified in the present investigation."
They didn't go into great detail as to what those confounders were, but it looks like they took that into account and isolated milk-fat percentage as well as they could. Source: https://new.hindawi.com/journals/omcl/2019/1574021/
> It searches until it finds a seed, then goes back to the trail, maybe using the angle of the sunlight as a guide, to return to the nest, following the stream of outgoing foragers.
I remember reading that ants counted steps to find their way home. Perhaps I'm remembering incorrectly or maybe it was false?
Either way, cool article. Emergence is a cool property that shows up everywhere!