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Amusingly enough, I got into the conference this year early. This seems to be a small piece of evidence for my hypothesis that these sorts of applications often work as lotteries.

I was able to get a copy of this via interlibrary loan some time ago, after finding much better citations.

Got this from a website that sells copies of Russian dissertations.

I definitely pulled out all the stops on this dissertation, and learned a fair amount in the process. If you're not living in Russia, and looking for a Russian dissertation, I would be a good person to contact. I can't get you the dissertation but I can put you in contact with people who can.

I don't see how that would be a problem. Perhaps I'm missing something, so if you could explain I'd be appreciative.

Usually the problem is that wavelengths smaller than the grid size obviously can't be resolved. A class of turbulence modeling approaches can help with that to a certain extent. This class of methods is called "large eddy simulation", or LES for short. You apply a low pass filter to the governing equations and then develop models for "unclosed" terms. In practice this is typically done less rigorously than I'd like, but it's a valid modeling approach in general that should see more use in other fields. (Turbulence modeling is an interesting field in itself that a rational person might be interested in studying simply for the intellectual challenge.)

You'd be more likely to get some kind of waves that propagate at fixed speed along the grid, giving you a privileged rest frame, like in the old discredited theories of aether.

I'll try to steelman Florian_Dietz.

I don't know much anything about relativity, but waves on a grid in computational fluid dynamics (CFD for short) typically don't have the problem you describe. I do vaguely recall some strange methods that do in a Lagrangian CFD class I took, but they are definitely non-standard and I think were used merely as simple illustrations of a class of methods.

Plus, some CFD methods like the numerical method of characteristics discretize in different coordinates that follow the waves. This can resolve waves really well, but it's confusing to set up in higher dimensions.

CFD methods are just particularly well developed numerical methods for physics. From what I understand analogous methods are used for computational physics in other domains (even relativity).

I only skimmed this post, but I want to point out that most computational physics (and engineering) uses discretized space and time much as you've described. This is not new, just how things are often computed in practice.

Whether or not reality is discrete in this sense is beyond my knowledge as an engineer, but I have had conversations with physicists about this. (As I recall, it's possible, but the spatial and temporal resolution would be very small.)

Also, there are some exact solutions for discretized physics like this, but in general it's harder to do. Plus, because physical laws tend to be written in continuous form, very few people look for exact solutions like this.

makes all the contradictions go away

Not really. In computational fluid dynamics, converting to discrete equations can introduce major problems. One important problem is conservation. Depending on how you formulate your discrete equations, mass, energy, etc., may be no longer conserved and might not even be approximately conserved. "Equivalent" continuous equations would not have the same problem. And I would not say solving this problem is trivial by any means, though I know at least one way to do it.

I can see that I misremembered the lecture. Seems to be an application of Bayes as Lumifer suggested for the basic approach. Other more complex approaches were also discussed.

While I don't have my notes in front of me, I do recall from the decision analysis class I recently took that log score is related to the weight one would give to one forecaster among several when combining forecasts. Unfortunately it does not appear that the professor uploaded the slides on ensemble forecasting, so I can't provide any more right now. I am emailing the professor. Thought this would help in the meantime.

Thanks for pointing out that post by nostalgebraist. I had not seen it before and it definitely is of interest to me. I'm interested in hearing anything else along these lines, particularly information about solving this problem.

  • Citation: Богданович И. И. Влияние подготовки топлива в форсунке на тонкость распыла. Дисс. канд. техн.наук. М., 1948, 136 с. (Bogdanovich I. I. Influence of fuel preparation in the nozzle on the spray fineness. Diss. cand. Technical Sciences. Moscow, 1948, 136 pp.)

  • library URL:

Old Russian dissertation. As far as I can tell, this is only available at the Russian State Library. If anyone could visit that library and scan the dissertation, I'd be appreciative.

I'd be more than willing to fulfill a similar request of anyone who could visit this library and get a good quality scan.

What I have tried: Google, Worldcat, Libgen, and other search engines have not returned this dissertation. My university interlibrary loan office participates in a special program to obtain foreign dissertations (usually on microfilm). They were unable to get a copy of this. I have also tried purchasing this dissertation on disserCat, but there is no scan of the dissertation available at present, so it is not for sale. I also emailed another Russian website which claimed to be able to sell the dissertation, but I never received a reply.

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