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
179 karma · joined September 9, 2019
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.
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.
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.
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.
Perhaps it is. Perhaps it isn't. It just depends on how much you trust their methodology.
> "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."
> "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/
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!
What are you talking about?
Once again, I'm no expert but I think that's at least helpful.
EDIT: Just finished reading both and I can say the Quanta publication doesn't add anything except a short tangent about the history of self-play. Seriously, go read the openAI publication. It has great reactive visualizations and is much more put together.
Having to deal with dongles for a couple years while the rest of the market catches up isn't a reason to push against the best port standard in decades.
Everyone seems to be forgetting that this is a 100% opt-in service. Why do we get to say what FB is obligated to do and to what standards they have to keep their website at?