Pictures, Visualizations, Graphs

Pictures are said to be worth a thousand words.

Maybe. Consider Euclid, Book I, Proposition 16:

In any triangle, if one of the sides is produced, then the exterior angle is greater than either of the interior and opposite angles.

Diagram found here

Euclid is a language unto itself. The words are part of the language, but few people, it seems, can understand the words without the diagram, even if they only picture the diagram in their heads. I know I can’t – I immediately construct the picture in my mind, at the very least. Once you’ve got the picture, then the words help you walk through the proof.

But the picture itself doesn’t tell you what you are to prove from it. Those 2 dozen words in italics that describe what the picture is for do that. This picture might be worth a thousand words, but those thousand words don’t include what the picture means.

I’ve mentioned before how I was epically terrible at Greek, back in collage, yet epically great at Euclid. It’s just a knack, and I’ve done little with it, but I was that annoying kid who could just read the proposition, look at the diagram, and, 9 times out of 10, produce the proof without having to look at the text. Other people could glance at the rules for forming verbs in Greek, and just get them, while they were a plate of spaghetti to me. Just one of those things.

I watched the other students struggle their way through Euclid. I never had that experience, the glory, even, that some people had when the brilliant truth of Euclid’s modest claims broke through – but it was beautiful. Some kids had very limited ideas of what was true, and seeing how the logic of a Euclidian proof compels agreement was the dawn of a new world to them. I think I had a similar experience in 4th grade, when I first understood how the hard sciences can prove something true. Given a set of assumptions and definitions and the rules of logic, a really well-constructed experiment can really prove something, within, of course, the limitations of the observations and definitions.

But I digress. The point here: diagrams don’t speak for themselves You have to speak their language to understand them, and sometimes need many additional words of explanation. One more point: practice makes perfect. If you, like a St. John’s freshman, are working through Euclid pretty much every day, you start to get the hang of how he works, so that each successive proposition tends to make sense more quickly and easily than the last. (This is offset by the generally increasing complexity of the propositions, but you get the drift.)

I write all this to explain to myself how it is that diagrams such as the one below don’t seem to impress people:

So let’s spell it out:

  1. This chart displays deaths by age band by week per 100,000 people in that age group.
  2. The order of the lines on the graph are the inverse of the order of the ages in the list to the right. That is, the bottom group in the list is the top line in the chart, and visa versa.
  3. The y-axis scale peaks at 50 deaths per week, which the line for weekly deaths in the 75+ Years group slightly exceeds at a couple of points. This means that a little more than 50 age 75+ people per 100,000 died over a week a couple of times.
  4. Conversely, at no point are any deaths per 100,000 of those under 40 evident. Given the scale, where 1 death per week is noticeable as a slight bump, this means that, at most, something well under 1 death per week per 100,000 occurred for those under 40.
  5. For those under 50, the peak weeks might be as high as 1 per 100,000 at a couple of points. Since the under 40 are invisible at this scale, if you add them all together to get a weekly deaths per 100,000 for all those under 50, your total weekly deaths per 100,000 over the 7 age groupings added together reaches a max of about 1 at two points over the last 18 months.

But what does this all mean? It means, first, deaths among the elderly have been high, and deaths among those under 50 have been low, with deaths among those between 50 and 75 being measurable but much lower than those 75 and over. For those under 40, deaths per week doesn’t even register at this scale.

One more piece of information not presented here is the age distribution across the population. That’s not the point of this diagram, which is expressly concerned with deaths per 100,000. But to get your arms around what this means in terms of total deaths, you’d also need to consider how many people fall into the various categories.

Here’s a 2019 distribution from the Kaiser Foundation:

(aside: I can never seem to find population distributions by age expressed with the same age banding that the CDC uses. I’ve wasted time backing into the numbers, but it just seems odd that the data is most generally presented with wide age bands that one cannot easily change. So this is going to be sloppier than I’d like, but I think the point will still be clear. End gripe.)

The US population is estimated at about 332M. Almost a quarter of that population, or about 78 million people, are under age 18. Last I checked, about a week ago, 380 Americans under 18 – children – had deaths ‘involving’ COVID (that’s the CDC’s language, not mine). As Briggs points out, that’s less than half as many children as died of pneumonia over the same period. And before you go there, recall that pneumonia also can have lingering or permanent effects on those who survive it.

On the other end, 16.5% are over 65, or about 55 million Americans. Backing into the numbers on the chart above, at the two peaks in April 2020 and January 2021, it looks like as many as 75 people 65 and older died per week. Multiplying that per 100,000 number by the 550 units of 100,000 in 55 million, you get peak weekly deaths in the 65+ age groups of about 41,000 deaths. Peak weekly deaths ‘involving’ COVID for people 65 and over were about 100 times the TOTAL deaths of children over the entire 18 months of the pandemic.

Therefore, taking these CDC numbers at face value, COVID is a threat to the elderly, and not a threat to children. The overall risk of death for children is not significantly increased by the presence of COVID in the environment. Indeed, the overall risk of death for those under 50 is not meaningfully increased by the presence of COVID in the environment.

This situation was evident, as in screaming from the page, with the very first Imperial College report back in March of 2020. But do you hear about it on the news? No?

Author: Joseph Moore

Enough with the smarty-pants Dante quote. Just some opinionated blogger dude.

7 thoughts on “Pictures, Visualizations, Graphs”

  1. The graph would’ve been improved if they’d used per 10,000, as some early reports did– or let you clump it to months, or SOMETHING so that you can actually SEE most of the ages on the graph!

  2. Now do maps.

    Rand McNally is something close to pron for me and its graphic depictions of what is where and how to get there make perfect sense to my brain.

    My family? Fuggedaboutit! No innate geographical awareness. When I ask if they understand how to get from Point A to Point B, they say, “Oh, Siri will get me there.”

    I point out that SkyNet’s likely first move will be to channel the geographically ignorant into pre-planned ambushes, but my Cassandra-like warnings fall on deaf ears.

      1. Recently wound up with (due to need) a new-to-me-vehicle. Sure, the phone has GPS and all. But I made a point of buying a set of maps to stow in the ‘glove’ box, just to be sure. No built-in (and out-of-date) nav system, but the fluxgate compass? Good idea, that.

    1. Oooh, I’m no good with maps, but I’m VERY good at navigation– especially if I have a mountain or tall building to go off of.

      Dives my family NUTS when the Nuvi says “take a left” and I go right, instead, because I can see the “road closed” down a few blocks, or I know that if I go left I’ll have to cross traffic, or I take a longer route because it’s raining and I don’t want to deal with where I can see the water will be.

  3. “Seat of the pants.” Once back in college I tried a new-to-me seven mile run loop. I started out with a bunch of fellow oarsmen but because I’ve always been relatively slow managed to get separated from them. Dusk fell and I realized I hadn’t the slightest notion where I was going. Fortunately, it was a big full moon that evening. I still knew (roughly) where I was in relation to campus, so used it to navigate my way back home.

  4. I took four years of German in college. By the fourth year, all the students in the upper level German classes were either language majors, or math majors like me. Oddly, no one in my upper level math classes was a language major.

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