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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@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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OK, I may be guilty of a DoS attack attempt on mathematicians' brains here, so lest anyone waste too much precious brain time decoding this deliberately cryptic statement, let me do it for you. •1/15


First, as some asked, it is to be parenthesized as: “∀x.∀y.((∀z.((z∈x) ⇒ (((∀t.((t∈x) ⇒ ((t∈z) ⇒ (t∈y))))) ⇒ (z∈y)))) ⇒ (∀z.((z∈x) ⇒ (z∈y))))” (the convention is that ‘⇒’ is right-associative: “P⇒Q⇒R” means “P⇒(Q⇒R)”), but this doesn't clarify much. •2/15

Maybe we can make it a tad less abstruse by using guarded quantifiers (“∀u∈x.(…)” stands for “∀u.((u∈x)⇒(…))”): it is then “∀x.∀y.((∀z∈x.(((∀t∈x.((t∈z) ⇒ (t∈y)))) ⇒ (z∈y))) ⇒ (∀z∈x.(z∈y)))”. •3/15

Maybe a tad clearer again by writing “P(u)” for “u∈y” and leaving out the quantifier on y, viꝫ: “∀x.((∀z∈x.(((∀t∈x.((t∈z) ⇒ P(t)))) ⇒ P(z))) ⇒ (∀z∈x.P(z)))” [✯]. Now it appears as an induction principle: namely, … •4/15

… “in order to prove P(z) for all z∈x, we can assume, when proving P(z), that P(t) is already known for all t∈z∩x” (n.b.: “(∀z.(Q(z)⇒P(z)))⇒(∀z.P(z))” can be read “in order to prove P(z) for all z, we can assume Q(z) known when proving P(z)”). •5/15
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The main problem with "Lift All Voices" as a justification for the Black National Anthem is the word "All." In order to achieve "All," the Woke are going to have to cook up more different unique national anthems than they have gender pronouns.

Mathematically speaking.

1/

And why would the Black community be the first to get their own anthem over the American Indians? The Indians used to have all the land, and they still do have some of it.

(use of "American Indian" here is intentional, as that's what they prefer to call themselves)

2/

This "inclusion by division" game is just the "separate but equal" logic for 1950s segregation reskinned, but when the Woke self segregate, they self segregate based on Krenshaw's Intersectional Matrix of Oppression, which in Theory is necessarily near infinite in size.

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When the Woke did this with gender pronouns we went from 2 genders to 37 genders to infinite genders in the span of about 5 years, but the trans folks discovered this really didn't help them out on Tinder, so they pivoted back to "trans women are women" to try and get dates.

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The only people left doing the "gender pronouns" game are the ones signaling their Wokeness on Twitter to their in-group, the trans women in the dating community aren't even doing it anymore. They've gone back to 2.

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Algebra Etc.
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@AlgebraFact
How to mentally compute the cube root of the cube of a two digit number.

Thread (1/10)

In base 10, the last digits of the cubes of digits are distinct.

If d = 0, 1, 4, 5, 6, or 9, then d^3 ends in d.

If d = 2, 3, 7, or 8, then d^3 ends in 10-d.

(2/10)

So if you're given the cube of an integer, you can figure out the last digit of the cube root.

For example, if 50653 is the cube of an integer, it's the cube of a number ending in 7.

(3/10)

Let n = 10a + b be a two-digit number, with a and b single digit numbers.

Then 10a <= n <= 10(a+1), and so n^3 is between (10a)^3 and (10(a+1))^3, i.e. between 1000 a^3 and 1000 (a+1)^3.

(4/10)

So suppose x is the cube of a two-digit number n = 10a + b.

Chop off the last three digits of x.

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Riuji
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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.

(3/23)

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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