This is what people who care about data sound like
NY Magazine ran a far better than average article about how to analyze the Omicron news coming out of South Africa and the UK. I got all the way through it without receiving the irritating impression that either the interviewer or his subject were trying to wrench the story in either direction: neither "Wake up, it's worse than you thought!" nor "Go back to sleep, it's nothing." They're just trying to figure out how to make sense of confusing data and make useful predictions.
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How many *people who care about data" ARE there in today's world, today's America?
Many of the posts I see about Covid and vaccination...from whatever point of view...are borderline insane.
The discussion reminds me of a general problem about infection modeling that has been bothering me since this all began. At first we were told that viruses spread exponentially; that turned out to mean only that it was possible to model the kind of waves they express using exponents, provided that you were free to change the values of the exponents to fit the data. Now it sounds like, in fact, exponential models may not really work at all; they can't capture things like what he's calling 'the network effect' in which chains circle back on those already infected, and thus don't spread as the model would predict they ought.
It looks like an honest discussion, with a lot of admission that there are good questions and that there's still much we really don't understand.
'Monte Carlo simulation' was invented to analyze nuclear fission; individual simulated neutrons were introduced on random courses and traced through the materials until they either hit an atom or left the relevant space. When they hit an atom, other 'neutrons' were released and tracked.
Originally done by hand on some kind of board, with the randomness introduced IIRC by drawing cards, then transitioned to the Army's ENIAC computer. Worked pretty well, apparently. There seems to be a pretty good analogy with the spread of covid, or any virus, through a population. (although there is a lot more non-uniformity in a population than in a nuclear material)
ENIAC, which was originally built to model artillery trajectories, as also used for non-Monte-Carlo simulation of the initiator for the planned hydrogen bomb...this was the occasion for the first political dispute about simulation results. Edward Teller claimed the results verified his proposed design for the initiator; Stan Ulam asserted that the simulation (which was greatly constrained by the limited capacity of the machine) proved no such thing. Ulam was right, and the design had to be modified.
Grim, I feel embarrassed that I was part of misleading my readers about exponential functions. I got other things confused with that and asserted them quite strongly. And I was wrong. And I knew better, if I hadn't just plowed ahead and pretended that since I was a math whiz in high school, I was an authority. An exponential function means that it is highly volatile. It can poke along going slightly up or slightly down and not affect things much. When you see references about covid and contagion that include things like R=1, or R=1.1, or R=0.9, that's what is behind it. While we figure out what each variant has for an R value, we hope we are in a narrow range for predictability's sake. But external factors can mask the true value of R. The quality of medical care, the accuracy of testing (perhaps the CDC's biggest failure was not its statistics, which were pretty good all along, but its absolutely fucked-up tests, which the FDA doubled down on and said no one can use any others. Devastating.)
But a relatively small change in the exponent truly is huge. R=1.2 is horribly worse than R=1, but we don't notice it as it goes by. It's a little bit like the "trick" question for high school math about the lily pads covering a pond. It they double in size daily and the pond was covered on day 48, when was the pond 25% covered? Day 46. And on day 40 you could barely detect lily pads. It get away from you fast.
So I was thinking of geometric growth and arrogantly told people it was potentially bad, without giving a clue as to how bad, because I didn't know myself. I was doubly embarrassed because it was Zachriel who pointed it out, and was right. Contagion is multidimensional, and so a single individual can at least possibly affect many, even if most others, because of their caution, infect none.
When there are even small differences in the externals it can affect the R value. Masks ain't much and schoolchildren ain't much and distancing in the 12-items line in the supermarket ain't much, but if they all go together, everything can explode. We have sort of seen that around the indoor/outdoor split north and south in different seasons. The rules have been the same in a place for months, but suddenly everyone is indoors sharing air, or outdoors no longer sharing air and it can change fast. But we don't change fast. We remain in the mindset of last month.
So, very sorry.
AVI,
I certainly accept your apology, although I am not sure you owe one. You were always acting in good faith according to your current understanding, which is evident to me and I think to everyone. (Z's good faith is never in evidence, which is why he's not allowed around here. But it was in one of those discussions that I learned, from him, that epidemiologists actually meant something very different by 'viruses spread exponentially' than I would have understood those words to mean when used by an ordinary person or even a mathematician. Arithmetic growth, geometric growth, and exponential growth are usually intended to convey conceptual differences more similar to how your lily pad example differs from other more ordinary experiences.)
In any case I only really began to learn math at all when studying philosophy, when and as it proved necessary to grapple with problems for philosophy. It's always been subordinate and secondary, in other words, even when I've studied it seriously. My real concern was not learning how to graph special relativity but in learning to think about what relativity might mean in terms of the structure of reality; or I learned the Ancient Greek way of approaching some math problems in geometry as a way of understanding what Plato was getting at here or there. I never had any pure interest in math, and therefore am far from good at it myself.
Speaking of the Greek approach, I think it some ways it is better than our own at dealing with problems like the ones you mention. We'd tend to say that our system was always better, being more functional, and probably that is true most of the time or even all of the time for the best mathematicians among us. Nevertheless, I do think that the Greek approach can sometimes instill a more intuitive understanding of the relationship between numbers and physical reality. Socrates claimed he could make an ordinary slave 'remember' these truths, since they were obviously too complicated to teach and especially to someone with no baseline education. Thus, we must have some ability to remember things; perhaps from past lives, or from a higher self.
Perhaps; or maybe the illustrations were so much better that even an ordinary person without an education could rapidly grasp the claim.
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