BC MATHS
Saved by @SteveeRogerr

⬇️⬇️⬇️ The "Math" of Fear

As it is Thursday, I have a post for you today in anticipation of Gov. DeWine's new Maps of Fear which he has tried to phase in. I have previously discussed both the new red and blue maps and their issues -

 - but today I hope to illustrate even more clearly what level of manipulation is going on, particularly with the new blue 'ICU Utilization' map.
Attached I have two images.

The first is a hyper-simplistic (and unrealistic) but illustrative example of the calculations that the new blue map goes through to arrive at its numbers.
Instead of telling us the percent of beds occupied by COVID+ (not necessarily ill *with* COVID, but testing positive) - the governor and ODH only calculates the percentage of COVID+ out of just the *used* beds.
In the first image, I have an example of a 100 bed ICU with just two patients - one COVID positive (red) and one COVID negative (green). The other 98 beds are empty and able to accept new patients.
⭐️ Normal people would look at this situation and say that 1% of the beds in the ICU are being used by COVID positive patients.

But that's not how Gov. DeWine would present this situation to us. Instead of looking at the total available beds, they look only at the beds in use.
⭐️ In this example, there are only 2 beds *in use.* 1 of those is occupied by a COVID positive patient, making the 'ICU utilization' as defined by Gov. DeWine and ODH *50% instead of 1%.*
And if that green COVID neg patient were to be discharged and only the COVID positive patient remained, the COVID ICU utilization would be *100%* despite 99% of beds in the ICU still being available to accept patients. Now this is, again, a very extreme example and unrealistic.
In the second image, however, I illustrate the same concept with the real numbers for Region 8 (southeast Ohio). Southeast Ohio has been called out week after week now for having very high 'ICU bed utilization,' but what does that mean in real numbers?
Over the (probable) 7 days that today's blue map will be made from, there was an average of ~80 total ICU beds in the region. On average, ~29 were occupied by COVID positive patients, and ~31 by COVID negative patients, with ~20 beds empty.
⭐️For those of us using 'normal' math, we would say that 29 out of 80 beds are occupied by COVID positive patients, or 36.3%.
⭐️But using Gov. DeWine's Math of Fear, our denominator is only 60 (29+31). Meaning that his equation becomes 29 out of 60 beds are occupied by COVID positive patients, or 48.3% instead of 36.3%!

By manipulating the numbers, they have increased the real percentage by a third.
Not only does it artificially increase the apparent usage, it also creates perverse incentives (like so many of his metrics). The fewer non-COVID patients are using the ICU beds, the worse the COVID numbers look.
The worse the COVID numbers look, the more scared people will be to use the hospitals for those other procedures potentially leading to even lower non-COVID usage. Conversely, the more people using the ICU beds for other reasons, the *less used* it looks.
The games need to stop.
Note: For simplicity, I rounded the beds and the people to whole numbers so I wouldn't have to chop them in pieces for the illustration, so the specific % calculated here might be slightly off of what Gov. DeWine presents later today. But these are the real numbers for Region 8.
#InThisTogetherOhio

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Mathematically speaking.

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In light of my tweet thread about the category of finite sets and commutative monoids (https://t.co/jnY0wZZbxq), I thought I might try to say what the analogue is for braided monoidal things (although much of this is still somewhat hypothetical).


It's also just kind of a cool combinatorial structure! I've been talking to @CreeepyJoe about this lately, as well as @grassmannian.

The first thing you have to know is that, in a braided monoidal category you can still have commutative monoids. Since a braided monoidal category C has a "twist" map for every object β(x):x⊗x→x⊗x, if x is a monoid you can ask for the following diagram to commute:


Remember that being symmetric monoidal just means that if you take the twist map above and do it twice, you get the identity map, but braided monoidal doesn't mean that. But it's okay! You can still define commutative monoids here.

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When I was starting out as a grad student, I remember being frustrated with analysis problems where it didn't use DIRECTLY the things we spent so much time proving in class.

As an example, let's look at a standard real analysis problem:

(1/23)


The problem looks like it can be done using the dominated convergence theorem.

This is an important theorem and is used in a lot of places outside a grad real analysis class. A student would go through a lot of buildup leading to this theorem.

(2/23)

Now, let's see whether the conditions for DCT are satisfied.

First, for fixed 00 as n->infinity.

So we have a.e. convergence of the integrand in [0,1].

To the student, this builds a stronger case to use DCT to solve the problem.

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Finding an integrable dominating function is where the problem starts.

It would seem NATURAL (at least for me) to bound it with:

p.s. it feels "natural" to me because it is reminiscent of squeeze theorem problems, math students encounter in calculus.

(4/23)


However, 1/x^n is not integrable in (0,1) and hence cannot be (further) dominated by an integrable function.

So, what I would do is since I know it converges a.e. to 1, maybe it converges uniformly to 1?

This leads me into a BAD detour.

(5/23)
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@DesmondSwayne Sir Desmond is right. SAGE makes mathematical predictions based on flawed models.
I chose to stick my neck out almost 4mo ago here:
https://t.co/b0rT5Lq9HI
I experienced much anxiety doing this, aware that, if I was badly wrong here, I would be destroyed as a contributor.

That said, I thought the immunology so clear that I made three, specific & testable predictions which should apply if I was right.
Please examine them, on the right, under the pie chart:


In particular, I predicted that the epidemic would not reignite in London. Obviously, we have many “cases” but I urge people to disregard these & instead to look at excess deaths, on the principle that a severe (occasionally lethal) respiratory virus would show itself this way.

Here is a chart showing the trend of deaths in London alone over recent years. A prominent peak of deaths is evident as the virus swept through in spring. Also visible the August heatwave. But there are no excess deaths now.
I submit this is a striking example of herd immunity.


I’m still waiting for SAGE or indeed anyone to provide an alternative explanation for the sharp nature of the spring excess deaths peak which doesn’t involve herd immunity or otherwise removing from the pool those vulnerable to lethal outcomes (same result). Given this sharp...
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