The “one that works out” can also give you a misrepresentation of how the world works and a false sense of how lucky one should expect to be over a long period of time. At an earlier point in my life, I had been applying to many well-known big tech companies right out of school (not a top school either). I never got a reply from any of them so I ended up accepting a local job with a non-tech company after months of searching. But I didn’t give up my hopes and kept applying to big tech, and while I did manage to get the occasional interview with some mediocre companies or the random startup, I also miserably failed all of them too. At some point during my long period of despair at never getting a better job, my very top pick (and arguably one of the best tech companies in the world at the time) reached out to me. Even more miraculously, I somehow passed their interview (the only tech interview I passed in the prior year) and accepted a job there. I really enjoyed working there. Some of the best few years of my life. And my performance reviews were great too, so the imposter syndrome from having failed so many tech job interviews sort of faded into the background. But after a few years, perhaps due to the “hedonic treadmill” mentality, I thought I could do better. So I left to join a startup. Well, the startup failed, as startups tend to do, but what I didn’t expect and what caught me off guard was that I was now back in the same situation I was in right after graduating from college. Don’t get me wrong—having “the name” on my resume now meant I could get at least one chance at an interview about anywhere. But much like the first round that I tried to forget about, I once again failed all the interviews. Unfortunately, this second time around never procured a “get out of jail free” card. So I guess my lesson is: 1) there’s a lot of luck involved in these things, 2) if life gives you a winning lottery ticket at some point, don’t throw it away for the chance to win an even bigger lottery, and 3) that famous saying about “the only actions regretted are those not taken” is absolutely, totally wrong—almost all of my regrets in life relate to taking some action I shouldn’t have rather than inaction.
To be honest I feel like I have seen much better expositions of zero knowledge proofs. The playing cards example is nice in some ways, but people are often exposed to trickery regarding playing cards. The recipient of the proof needs to verify that the deck of cards is a normal deck of cards, that no cards have been swapped out or altered, etc. These are all precisely the things that magicians are regularly able to fool people about. So really you have to make an additional assumption of "no funny business", which distracts from the mathematical core of what you are trying to demonstrate. Likewise, the example of compositeness is a bit off because even though there is knowledge about the composite number that the proof does not reveal, that knowledge is in fact not known the to person constructing the proof either! The proof is not really zero knowledge either, since it gives the reader knowledge of a specific witness to its compositeness. Even the wikipedia example of going into the cave (which used to be featured more prominently in the article) I think is terrible. Why wouldn't you just walk a loop to prove you know the way through the secret door? Also, it's clearly not zero knowledge, as it reveals some information about how quickly they can pass through the gate. In general I think avoiding physical examples is necessary, since reality is complicated, and in the real world some information always leaks. I think the best example for teaching about ZKPs is the graph isomorphism problem: Given two large graphs, you can prove that you know a isomorphism between two graphs by generating a new randomly labeled graph that is isomorphic to both of them and showing it to the provee, who can then ask you to demonstrate that this new graph is isomorphic to either graph A or graph B. Since you don't know ahead of time which one they will ask for, the only way you could consistently pass this test is if you actually do have a graph that was isomorphic to both A and B simultaneously. But since you only reveal one of the isomorphisms, it really is zero knowledge.
I've read hundreds of dust mite studies, and this is the conclusion I came to, but it's difficult to put in a direct single argument with a citation that most people would require to accept it. I also got dust mites entirely out of my home and my chronically low vitamin D was resolved without a change in lifestyle or supplementation. But I'll do my best to share some of the steps toward this conclusion: #1. There is a body of molecular research showing dust mite allergens directly damage the immune system, most importantly once you inhale their fecal pods, they cause epithelial permeability in the lungs. (this study is a good overview of several ways it directly damages the immune system, all of which are totally unrelated to type 1 hypersensitivity, btw: https://www.jacionline.org/article/S0091-6749(18)30848-0/fulltext ) #2. There are challenge studies that show dust mites directly causing eczema symptoms after inhalation, which shows that dust mite allergens can act on areas other than the respiratory system, probably by entering the blood stream. Of course there are also challenge studies for asthma. (here's a paper arguing for causal role in asthma https://www.atsjournals.org/doi/full/10.1164/rccm.200811-1756pr ) #3. All of the major allergic diseases(asthma, eczema, rhinitis, and although it is not as well studies, I believe IBS) have epithelial damage and increased allergy as a core feature of the disease. #1 and #2 are good evidence that dust mites play a causal role in these diseases #4. From asthma and epithelial permeability in the lungs you can get to worse outcomes from flu and covid etc, from rhinitis you can get to worse sleep and worse mental health etc and reach a large number of health outcomes. #5. It's true that people with allergy suffer worse from all these problems, but so much damage has already been done before you even get to Type 1 hypersensitivity, but that's another story. So basically, dust mites directly damage your immune system in the lungs, skin, nose, eyes, guts(and maybe more?), create a sustained immune response, and leads to a multitude of other bad health outcomes. And since low vitamin D is associated with dust mite sensitization(( https://www.worldallergyorganizationjournal.org/article/S1939-4551(24)00021-8/fulltext ) , it's also associated with all those other bad health outcomes that are actually caused by dust mites. People have a mental model that vitamins are at the root level of causality, and therefore don't consider that vitamin D could also be caused by dust mite exposure. IgE levels are inversely associated with vitamin D: https://www.nature.com/articles/s41598-020-77968-1 But supplementing vitamin D doesn't lower IgE: https://publications.aap.org/pediatrics/article/150/Supplement%203/S7/189978/Effect-of-Vitamin-D-Supplementation-on-Total-and?autologincheck=redirected And of course high IgE is directly caused by exposure to dust mites if you're sensitized. I don't know the specific mechanism by which they cause low vitamin d, but two possibilities are that #1: the high and sustained immune response your body runs from constant dust mite exposure consumes vitamin D and acts like a leaky bucket. #2: dust mites somehow disrupt vitamin d production in the skin(e.g. there was one study showing https://www.jacionline.org/article/S0091-6749(13)01768-5/fulltext )
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