Isaac Newton vs. Li Wenwen; Sendak advances

Today’s contestants are powerhouses! Isaac “creator of laws or rules” Newton has already defeated the #2 hitter of all time and a co-creator of the more-relevant-than-ever Three Laws of Robotics. Meanwhile Li “duplicate name” Wenwen powerlifted her way past two of the greatest musicians of our time.

What happens when the smartest man who’s ever lived meets the strongest woman ever? It’s up to you to tell us!

It would be great to invite both of them to speak, but that’s not an option. We only have the budget for one speaker in this seminar, and Newton was the director of the Royal Mint or something like that, so he’s not gonna let us get away with paying in IOUs.

Past matchup

Dzhaughn writes:

Doesn’t “Goodnight Moon” need a comma or three? What does it *mean* when she leave out those commas? With “Brown, Margaret Wise” vs. “Brown Margaret Wise” we have a paternalistic emphasis on the patronymic in the former against a strong suggestion of cannibalism in the latter. And, reallly, where do we stand on cannibalism? Soylent Green is People or the Authentic Paleo Diet? I’ll pass on both.

There also was the time I boughtlots of peanut butter cups for Halloween and there weren’t many trick-or-treaters. Maurices, Mo’ Probems. But over all a sweet memory.

This doesn’t answer who we should pick, but, wow, so much happening in such a small space! Actually, I can make it even smaller:

This kind of free association is what blog commenting is all about. Really this one comment makes the whole seminar competition worth it.

But we still need to decide who advances, and for that we turn to the concise summary from Anonymous Pigeon:

“Where the wild things are” is great but a bit of a boo hoo ending. The ending of it never happened or it did in dream or whatnot makes everything that happened so worthless. If Maurice Sendak has a poor ending to offer us, I would go with Margaret Wise Brown because her book “Goodnight moon”, ends in sleep, just as we should after a long seminar.

A seminar ending in sleep . . . all too accurate! But that’s not what we want. We want to stay awake, so the Wild Thing it is.

Again, here are the announcement and the rules

32 thoughts on “Isaac Newton vs. Li Wenwen; Sendak advances

  1. I vaguely remember that McMahon and Bonner’s excellent “On Size and Life” had a graph of the weightlifting world record for various weight divisions, which scaled as body weight ^ 2/3 or 3/4 or something like that. (I’m at a conference and so can’t look at my copy today.) Anyway, it leads to the interesting idea that what we care about shouldn’t be absolute performance, or the best in crude weight bins, but performance relative to the background physiological scaling law. How good are you *compared to * Mass^2/3 (or whatever). So, at Li Wenwen’s seminar we can all try this out.

    • If I were going to guess, I’d say that the force you can exert is proportional to the cross sectional area of the muscle, which is proportional to the muscle mass to the 2/3, so I’d guess body_weight ^(2/3) would be the overall scaling law for maximum weight lifted.

      If I were going to do a first order correction, I’d look at an adiposity measure. For whatever reason the medical field never got this right, and used a dimensional measure (weight/height^2) = BMI which can never be right precisely because it’s dimensional (unless in theory it’s part of a dimensional group in which there’s a constant pressure, which makes no sense).

      Adiposity is going to be estimatable as a function of the dimensionless group: adiposity_index = rho_muscle / (weight / (height * pi * (waist circumference / (2*pi))^2) ). This treats people as if they were a cylinder and if they’re very fat their density will decline, leading to a higher adiposity index.

      To first approximation then we can regress max weightlifting ability against body_weight^(2/3), adiposity_index, and sex, and use that as our predictor which each person can compare themselves to.

      • BMI is nonsensical, not because it’s dimensionful* but because its scaling is wrong: weight doesn’t scale as height^2. If people were isometric (same shape) it would be ~ height^3. People aren’t isometric, but if they obey any scaling at all it’s ~height^2.6 . As far as I know, hardly anyone has actually looked into what the best scaling exponent would be (one link: http://www.math.utah.edu/~korevaar/ACCESS2003/bmi.pdf) — I’ve often thought it would be fun to find some large dataset of weight and height *and* body fat measurements, to analyze. Maybe someone reading this knows of such a database?

        * I agree it would be better if it were dimensionless, but our understanding of metabolic scaling is too much of a mess to hope for this.

        • A physical process can not depend on a dimensional quantity, because the physical process must be independent of your choice of units but dimensional quantities aren’t. Now, it can depend on a dimensionless quantity in which one member of the group is some constant, in which case you can pretend it’s ok to work with a dimensional version, but it’s still wrong. For example, if you have some fluid mechanics issue and you’re always going to be working in water, then instead of the Reynolds number rho * v * l / mu you can work with v*l since rho/mu is a constant for your problem, but it’s stupid because you’ll need to specify the units you’re using and convert them between different datasets and such.

          In the case of BMI, you’d have to argue that somehow weight / height^2 which is dimensions of pressure is relevant to health perhaps because relative to some known constant pressure it measures something important, like perhaps blood pressure or some aspect of the difficulty of supporting the body or some garbage… it just isn’t the controlling factor. It’s typical of what happens when you hand some regression software to some doctors I think. I recently had a conflict with a doctor on Mastodon regarding this. I think he blocked me rapidly when I suggested that he was right that BMI was a bad measure, but that waist circumference (his proposed alternative measure) was also not a good plan. He immediately referred me to I think Neyman + Pearson about how ratio variables are terrible for modeling or some such. It was some of the worst cross-talk I’ve ever experienced in science. I’m pretty sure he banned me quickly.

          I too would love a height, weight, age, sex, body fat measurement dataset. Even better if it follows some people long enough to measure risk of adverse cardiovascular outcome, but I’d go with just the basics to get started.

          It’s clear that weight, height, and waist circumference are all relevant to your health, it’s also clear that one important mechanism is through adiposity which is related to density by virtue of the fact that fat has a different density than lean body mass. If we can’t measure density directly (because we’re looking for a cheap in-office measure) then Buckinham’s Pi theorem tells us that length, mass, and time are three independent units, so we can express the variables weight, height, waist circumference, and density = 4 variables as 4-3 = 1 dimensionless group which will completely eliminate the redundant symmetry. So we get heart_risk = f(rho_muscle/(weight/(height * pi * (waist_circumference/(2*pi))^2))) with f some likely nonlinear function… If we have a dataset we can estimate f and will find that it works well compared to other strategies using dimensional measures like waist circumference or BMI. That this has never been done and widely publicized in doctors offices is sad.

        • Raghu, if you care about this, check back tomorrow, I will post a link to my Julia repo that will do the calculations and make some graphs. It’ll be a quarto document as part of a group of documents I’m developing for Julia tutorials.

          If you just want to see the quick graphs here’s an Imgur:

          https://imgur.com/a/H7QtPrj

        • Dang it, I realized I forgot to multiply by a constant and change the label on the percent body fat one before I made the graphs, but it doesn’t change the story, the final correct version will be in the github archive. The “adiposity” index directly and essentially linearly correlates with estimated percentage body fat.

        • Knut Schmidt-Nielsen was one of the original researchers of scaling laws related to physiology. He has a very good book about it, entitled “Scaling: Why is Animal Size So Important?” It’s an excellent book, although my absolute favorite by him is “How Animals Work.” Both of these are extremely well-written and for my whole career I tried to model my writing style on his, so I would recommend these to anyone who does any technical writing even if they have no interest in scaling laws.

          As for the sorts of data you (Raghu and Daniel) are interested in, you might check out the NHANES dataset. I don’t remember exactly what is there or how often the data are updated but I think it has, or used to have, weight, height, waist measurement, and many other values. However, I don’t know whether the individual data are available, it might just be cross-tabs or other summary tables. Sorry I don’t have the patience to check, but if you have sufficient interest then maybe you do have the patience!

        • Ok Raghu and etc. Here’s the github where I’ve been putting together some modeling and data analysis vignettes using Julia. Eventually I want to walk through these in 5-15 minute YouTube videos but that’s a surprisingly large amount of overhead in recording and editing sound and etc. Still… it’s on my plate.

          https://github.com/dlakelan/JuliaDataYouTube/tree/main/Vignettes/Modeling

          In that directory you’ll find bodyfat.qmd and the html output and the bodyfat_files directory. If you clone that github and cd into the Modeling directory you can just look at the html file.

          Let me know if it doesn’t work. I wish that there was a lot better blog software than WordPress, something more like Discourse where it’s trivial to upload some images and such right here in the comments.

        • I didn’t know until reading this thread that BMI is literally

          weight / height^2

          It is amazingly bad, and trivially easy to do much better with no complexity cost just by mucking about with the exponent. It also calls into question so many common comparisons–over time, between countries. I don’t doubt that we’re getting fatter, but some of the increase in BMI over time is just people getting taller over time. Some cross-country differences is some countries being taller than others. I can’t believe this.

          Burn it all.

        • Daniel: Thanks! This looks wonderful, but I’m too swamped to give all your stuff the attention I’d like to, and for now I’m just going to make a note to myself that it’s there! I’ll point out, though, that I can’t understand why the adiposity index makes any sense to pay attention to, since it treats humans as isometric (i.e. mass / length^3 = constant), which is definitely not true.

          I did, by the way, look at the McMahon and Bonner book, and it is Mass^(2/3) for the weightlifting records, as one would guess if cross-sectional muscle area is the determining factor. This was apparently first plotted by M. H. Lietzke in 1956; I haven’t dug up the reference. I wonder if using the current weightlifting records would show the same scaling. …

        • snatch <- c(135, 145, 155, 169, 175, 187, 200)
          wc <- c(55, 61, 67, 73, 81, 96, 109)
          d <- cbind.data.frame(snatch, wc)

          plot(snatch ~ wc, data=d)

          This was pulled from wikipedia. 'wc' is weight class….I'm not sure how Olympic lifting works, but I am wondering if actually weight class should be lagged. For example, do people in the 55kg weight class actually weigh 60.9kg (just below the next class)?
          lift = mass^n, so n=log(lift)/log(mass) …doesn't seem like 2/3

        • It will make a big difference what lift it is…I just assumed weightlifting WR meant Olympic lift… but even the snatch vs clean and jerk are completely different.

        • Seems close to 1/2 with this data, but maybe the bottom of weight class isn’t the best choice, or maybe the snatch not the same lift.

          snatch <- c(135, 145, 155, 169, 175, 187, 200)
          wc <- c(55, 61, 67, 73, 81, 96, 109)
          d <- cbind.data.frame(snatch, wc)
          d$ln_snatch <- log(d$snatch)
          d$ln_wc <- log(d$wc)

          library(ggplot2)
          ggplot(d, aes(y=snatch, x=wc)) + geom_point(size=4) + xlim(0, 210) + ylim(0, 210)

          ggplot(d, aes(y=log(snatch), x=log(wc))) + geom_point(size=4) + xlim(0, 5.3) + ylim(0, 5.3)

          library(brms)

          #nonlinear
          prior1 <- prior(normal(12, 5), nlpar = "k") + #guess at k based on y-intercept for log plot above
          prior(normal(1, 0.25), nlpar = "n")

          fit1 <- brm(bf(snatch ~ k*wc^n, k ~ 1, n ~ 1, nl = TRUE),
          data = d, prior = prior1, cores = 4)
          fit1

          #linear
          fit2 <- brm(ln_snatch ~ 1 + ln_wc, data = d, cores = 4)
          fit2

        • Raghu, the adiposity index is roughly constant for people with a similar level of fat percentage, it increases when people become fatter because their belly circumference increases making the cylinder bigger but the mass doesn’t increase in the same way making their density lower. Constant density of water divided by lower density of notional human cylinder equals larger adiposity which is the goal of the index.

          At the very least the adiposity has the following desirable property… If you compare two adult people, one of whom is 20% taller, but otherwise everything about them is the same proportionally, they will have the same adiposity index. However since weight scales like length^3 in this “all proportional” hypothetical, weight/height^2 =BMI will just automatically get bigger for the taller person.

          Once humans hit their adult height, essentially the only way they can get bigger or smaller is to gain or lose muscle and fat. If they gain fat, it generally increases their belly circumference. If they gain muscle it generally doesn’t or much less. So a person who gains muscle will increase their notional density, the person who gains fat will decrease their notional density. That’s what the adiposity index measures.

        • Hi Daniel,
          You’re perhaps mis-understanding my point related to adiposity index. You write, “If you compare two adult people, one of whom is 20% taller, but otherwise everything about them is the same proportionally, they will have the same adiposity index.” This is what I’d like to see data on; I’m highly skeptical that people *even with the same body fat percentage* are isometric (i.e. have mass ~ length^3 scaling), which is required for this adiposity index to make sense. There’s a nice illustration of short and tall basketball players that I’ve shown in a class; with images scaled to the same height, it’s clear that the taller one has disproportionately thicker bones (like among animals in general). Using the wrong scaling makes adiposity index useless in the same way BMI is useless. It’s perhaps a bit less useless since L^3 scaling is closer to reality than L^2.

        • Raghu, your point is valid. I don’t deny it but I do think it’s a “second order” effect.

          First, let’s discuss the issue of **within person** comparisons at different time points. Assuming an adult, they aren’t changing the amount of bone they have (short of osteoporosis a separate issue). Therefore as people gain adipose tissue their adiposity will rise in a reliable way that will be tracked by the index. So at least this is good.

          Second, if you want to see comparisons across body fat percentages and height, the dataset might do it, so I’ll add those graphs.

          Third, let’s make some additional modeling assumptions.

          Assume cross sectional stress on the bones stays approximately constant, and that bones are a relatively small fraction of total mass (I think both of those are reasonable approximations, especially having moved skeletons around in classrooms).

          if weight scales even approximately like h^3, then bone cross sectional area should scale like h^2 and the bone lengths scale like h, so the bone volume also scales like h^3. Bone is about 1.8 times as dense as meat which is close to 1 for water, so overall mass will scale like 1 * (1-epsilon) h^3 + epsilon * 1.8*h^3 where epsilon is a typical fraction of bone volume in the middle of the range for adults. This also scales like h^3 except that epsilon itself changes from one end of the realistic scale to the other. (ie. something like 5ft tall to 6.5ft tall adults)

          if we do a taylor series for epsilon as a function of h, we could do epsilon = epsilon0 + k *h. This results in scaling of something like 0.8*k*h^4 + (1+0.8*eps0)*h^3.

          If you scale h to very large values, then the animal becomes all leg bones… but define h as a fraction of the tallest person ever (Robert Wadlow who was like 8ft 11in tall). Most people are about h = 0.55 to 0.7 on this scale. Let’s assume that k is a small number like 0.1, so 0.8*0.1*h^4 ~ .01 whereas let’s say eps0 is about 0.1 so (1+0.8*0.1)*h^3 ~ 0.32.

          now let’s look at the derivatives… d/dh for each component is 0.096 and 1.45 respectively. In other words, we really don’t expect the bone changes to have super-important components within the range of what we expect for normal adults (h = 0.55 to 0.7). If you want to include toddlers perhaps you have a different story. I will add this stuff to the Julia tutorial!

        • Raghu.

          I took the data and split it into 5 groups by height quintiles, then plotted percentage body fat vs my adiposity index and colored the points by group membership. If there were “systematic” differences among different heights, then you’d expect some kind of banding or difference in relationship across these 5 groups. Instead you see the data has a cloud like structure with all the colors pretty evenly mixed. I could go farther in the analysis but as a first pass, it definitely seems like the relationship of bodyfat vs adiposity index is independent of height.

          https://imgur.com/a/iLJX1Zx

        • I went so far as to fit a mixed model on the data

          using MixedModels

          hm = fit(MixedModel,@formula(pctfat ~ 1+adiposity + (1+adiposity | hclass)), dat)

          println(hm)

          println(“Random effect estimates for mean and slope for each group:”)

          println(ranef(hm))

          and the final result:

          Random effect estimates for mean and slope for each group:
          [[0.0 0.0 0.0 0.0 0.0; 1.3684584940218145e-7 -1.2504219206016485e-7 2.939758816911235e-7 -3.4661490549540556e-8 -2.7111804848354477e-7]]

          It decided the overall mean was exactly the same for each group, and the slopes varied only in the 7th decimal place… That’s just too close to zero, which makes me think if I wanted to rely on this I’d have to fit a Bayesian model so I understand exactly the calculation it’s doing. But I don’t expect it would show anything different, just maybe have more stable numerical calculations resulting in a more accurate uncertainty.

          But yeah, there’s no reason to think there’s an important difference in the relationship by height.

        • @jd: about current records — thanks, this is interesting! I looked at the total record lifted (snatch + clean& jerk) in those same weight categories, and it also gives an exponent around 0.57 — far from 2/3 . I wonder what’s changed since the 1950s! One possibility: the McMahon and Bonner graph goes to “Log body weight” = 2.3, which I’m guessing is log_10 of weight in pounds, so 90 kg. (https://imgur.com/a/3UQufOm) If we only plot current records to 90 kg, the scaling exponent is 0.70 +/- 0.05, like in the 1950s. Does the scaling break down for more massive lifters, or are the heavier lifters slacking off?

          This is much more interesting than the tasks I’m procrastinating on, of conference travel reimbursement and futile complaining to the provost about the steady growth of external services we spend money on (new: “Academic Impressions” — look it up, if you dare!).

        • Daniel: neat graph (height quintiles). I agree that the height dependence is weak, and it would take a lot of data to extract. I also agree that the non-isometry is not a major factor. I haven’t written out the math, but I think the adequacy of the adiposity index scaling is consequence of the true (non-isometric) scaling, to the extent it exists, being closer to length^3 than the weird BMI length^2.

        • @Raghu – Ahh ok, so they are combining 3 lifts, one of which, the press, is not an Olympic lift. So these must be powerlifters and not Olympic weight lifters. That is one difference – a difference in the type of lifter. Also, when it says press, I wonder if this is bench press or a leg press machine? That might make a big difference as the former is a chest/arm lift and the latter is legs (where as the snatch and clean and jerk are full body leg/back lifts).
          In my plots and data from Wikipedia, I left off the highest weight class because it has no upper limit to weight, so the relationship between body weight and lift is no longer linear even on the log scale. This is because the lifter can gain as much weight as they want (which also means they gain a lot of fat too) in an attempt to get as strong as possible, since they don’t have to ‘make weight’. So those points wouldn’t follow the same lean body mass to lift relationship as the other points.

  2. Haven’t we heard enough from Newton? The guy had a whole lifetime to explain the laws of motion, optics, calculus, mint operation and alchemy. He held a tenured chair at Cambridge. He’s had dozens of biographies and only god knows how many scholarly papers devoted to his every thought and practically every meal. He thought every action generated an equal and opposite reaction. Fine… my reaction to all his action is to push back. Enough already. If we need to know about Newton, we can ask James Gleick.

    Li Wenwen is untenured. She is unknown (relative to Newton, and I believe relativity is all that matters, in general.) Our seminar should explore the unknown. There is simply no stronger potential speaker.

  3. I want to hear Newton speak about the Royal Society. They were actually doing and warehousing experiments in those days, with the motto “Nullius in verba”–more or less, “take no one’s word for it”–as an expression of resisitance to institutional authorities. Seems like a long way from where we are now, but perhaps pertinent to our future.

    We can be regaled with hilarious stories of small fires and explosions and maybe practical jokes that culminated in Science as we understand it and forms the very basis of…this tournament. Among other things.

    And, I don’t really care to hear Li Wenwen talk. I won’t understand a word of it. If we have a translator, we’d have to take his/her word for it. We can invite her, with complete respect, to be the podium.

    • That’s easy to determine. Since dissatisfaction with and/or ranting about BMI is strongly correlated with BMI, just ask them whether or not they think BMI is a useful measurement.

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