Figure 3 in DOI 10.1007/s10654-017-0316-1 ]]>

Sometimes it’s not necessary to specify such an algebra, but just to operate as if you had it available. This is the way complex-analytic functions are defined. It has been proven that if a complex-to-complex function has definite values obeying Cauchy’s differential equations throughout the domain of any simple open region of the complex plane, then every possible way of enlarging that region while still satisfying the Cauchy equations will give the same value at every domain point so reachable. If such a function is defined in the starting region as the sum of a convergent series, it’s usually possible to propagate the Cauchy equations to extend the domain of the function far beyond that of the series that originally defined it. This can be justified by going into your favorite exotic algebra and showing how, although the series adds to infinity, there is an “infinite” term that can be subtracted to get the same result the propagation gave.

The Riemann Zeta Function is a famous example.

]]>Regarding motivation for competing, I totally agree. Actually, while my school didn’t have any coaching apparatus (besides what I started and ran myself), my motivation was still social: my arch rival had qualified for camp the year before, and I’d be damned if he qualified twice without me qualifying once! My two hours per day came from studying surreptitiously during chemistry class, and during the nearly daily detentions I would get for doing that.

Demographics is always a tough issue. I think physics is special among school subjects because a lot has to go right before a student can approach a competition. For the USAPhO, they should already have calculus learned, and a full year of calculus-based physics (e.g. AP Physics C) on top of that, before the year even begins. Many schools don’t offer both, and for those that do, they’re usually capstone, senior year courses.

No matter what we do, our pool of students has to be drawn from those who understand calculus-based physics, which at the minimum means students passing AP Physics C with a 5. This group is a fraction of a percent of all high school students, and it already has overrepresentation/underrepresentation factors like 5:1 (gender), 10:1, or even more. Changing this situation requires nothing short of a complete revolution in high school education.

I’ve thought about sending selections of F=ma contest problems to high school teachers, since it nominally doesn’t require calculus. But most algebra-based physics courses, even at the best schools, stick to routine problems that boil down to mining numbers from the question text and plugging them into a pre-supplied formula. Meanwhile, many F=ma questions test deeper conceptual knowledge, often involving subtle cases where standard formulas don’t work. That’s presumably why most physics teachers we advertise to don’t allow more than a few percent of their students to even take the test — it would likely lead to more confusion than learning.

The situation just seems very difficult to change. I certainly hope it will, and I hope to have enough impact someday to play a part, but changing competition physics in a vacuum is just trickle down economics. In the end I think change will be driven bottom up by science popularizers, popular culture at large, and of course teachers themselves.

]]>ItĂ˘Â€Â™s a shame Physics canĂ˘Â€Â™t begin with creation itself, in discovering how and why everything was created, and for whom: that such things remain outside the realm of science from the beginning. And I might add, running is very enjoyable, itĂ˘Â€Â™s been my experience doing so is no less competitive, if running alone on a concrete walk verses on a track with other people; itĂ˘Â€Â™s like most everything else, itĂ˘Â€Â™s simply a matter of who youĂ˘Â€Â™re competing with and why.

Reading your paper tells me that the study of Physics has not yet revealed that children are not kids. Just as mankind are not humans. Nor does it infer anything concerning creation, or its Creator. Though IĂ˘Â€Â™m sure Physics keeps many people very busy thinking on other things, wherein they can spend theyĂ˘Â€Â™re entire lifetime learning a few comprehensive principles that have no bearing in what is truly important, truth, and the assurance of redemption; the adoption of their own bodies. Such worldly endeavors could easily consume a lifetime and achieve very little, except make truth unattainable, especially if oneĂ˘Â€Â™s mind had been corrupted from an early age.

How amusing can the concept of Physics and the minds of its beholder be; when we have people of all races and colors in the world, yet no one knows who, or what color those identified as Ă˘Â€ÂśwhiteĂ˘Â€Âť are. Which by simple observation they are translucent people, or better stated of a fair countenance Ă˘Â€Â¦ Why is that?

And perhaps itĂ˘Â€Â™s not a bad thing to encourage children of all ages to hang in there while continuing to learn things concerning heaven an earth; but first I would suggest they learn who they are, and their purpose of being here.

]]>First we should remember that mumps-infections don’t cause measles damage and vice versa, same with rubella, even if a common vaccine is used against them. So we should look at the diseases separately.

According to the source https://academic.oup.com/jid/article/189/Supplement_1/S4/823958 cited by Wikipedia, 0.3% measles fatality refers to the years 1987-2000. On the other hand https://academic.oup.com/ije/article/38/1/192/696766 gives an estimate of 0.05% for developed countrie. I assume 0.1% is an accepted estimate of magnitude for long-term effects including death and disability by measles.

The CDC page https://web.archive.org/web/20160211185233/https://www.cdc.gov/vaccines/vac-gen/side-effects.htm#mmr didn’t say that it’s an allergic reaction to measles vaccine which can cause “seizures, deafness, permanent brain damage, or other long-term effects”. Seizures are usually not a long-term effect. The problem of estimating measles vaccine risk is discussed further e.g. on https://books.google.de/books?id=Hyn0CAAAQBAJ&pg=PA67. Still, 1:1000000 seems an accepted estimate for long-term effects of MMR-vaccine. However MMR-vaccination includes two doses, so it seems we should consider 2:1000000 as risk of the overall vaccination.

Wikipedia doesn’t says that about 10% of mumps cases lead to meningitis, but rather the other way around: “before vaccination, about 10% of cases of aseptic meningitis were due to mumps”. However even if 10% is about the risk that a mumps case will lead to meningitis, this is a viral meningitis. While “permanent disability (such as hearing loss, epilepsy, learning disability, and behavioral problems)” is caused by bacterial meningitis, not associated with mumps.

While mumps can cause long-term damage in particular in adolescents and adults, measles includes a higher risk than mumps of brain damage and death, in particular for infants, adults and old people. Therefore, in the remainder of this post I only look at measles.

For USA we can assume life expectancy of about 80 years.

According to the formal model, average age of disease is 1/2*(life expectancy), but in reality measles occure earlier in life: “Median patient age was 5 years (interquartile range = 1 year to 18.5 years); 25 (4%) patients were aged <6 months, 68 (10%) 6â€“11 months, 76 (11%) 12â€“15 months, 167 (24%) 16 monthsâ€“4 years, 203 (29%) 5â€“19 years, 138 (20%) 20â€“49 years, and 27 (4%) â‰Ą50 years" https://www.cdc.gov/mmwr/volumes/68/wr/mm6817e1.htm

From these numbers we can estimate average age of measles at about 15 years; which means long term-effects will impair T=65 years of remaining lifetime.

US population is about N=327 million.

From 2010 till 2019 there have been 307 measles cases per year on the average.

I don't right understand how a number of 1200 measle-mumps- and rubella cases and non-MMR-vaccination rate of x=8% means an initial exposure of E=15000, since we also have to take into account cases created through further follow up infections which are represented by the factor 1/(1-nx).

Assuming a vaccine coverage of 92% while herd immunity apparently holds in the USA, we know that the number n can't exceed 12.5. So we may work with n=12, which is about the lower end of the spectrum cited in the literature of basic reproduction numbers for measles.

Since number of measles cases is Ex/(1-nx), we arrive at the estimate E=300*4%/8%=150.

v=vaccination damage risk/measles damage risk=2:1000

R=150*65/(330 mill.*0.002)=0.0148, which means:

Optimal collective non-vaccination rate is 7.3%.

Optimal individual non-vaccination rate is 8.2%.

Of course these numbers don't have much of a meaning, since they rely on very coarse and insecure estimates and models. Still I doubt that in reality R=70 holds for measles, and rather think that R being smaller than 1 is plausible.

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