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

More from Maths

Handwaving Freakoutery
Handwaving Freakoutery
@Freakoutery
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.

3/

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.

4/

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.

5/
MATHS
Gro-Tsen
Gro-Tsen
@gro_tsen
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
MATHS
Advertisement
Artem Chernikov
Artem Chernikov
@archernikov
Saharon Shelah and number 4, a thread.

Shelah is an incredibly prolific mathematician working mostly in mathematical logic who has (co-)authored around 1500 papers so far. His other superpower is the ability to discover number 4 where it has absolutely no reason to be. 1/32


Example 1. "There are just 4 second order quantifiers".
In first-order logic, one is allowed to form statements about structures, such as graphs, groups, fields,
etc., with only quantification over elements allowed. 2/32

So you can say "exists x, ..." or "for all x, ..." with x ranging over the elements of the structure M, but you can't say "for all subsets of M, ..." or "for all binary relations on M, ...", etc. Allowing such
quantifiers puts us in the context of _second order logic_. 3/32

It was well-known in logic and computer science that one can express more complicated properties by quantifying over binary relations on M rather than just over the unary ones. But can we say even more quantifying over ternary relations? 4/32

And how does this compare to quantifying over functions, bijections, or any other infinitely many possible types of relations on M one can think of? In his 1973 paper Shelah proved that there are exactly 4 (four) possible types of second order quantifiers. 5/32
MATHS
Yardley Yeadon
Yardley Yeadon
@MichaelYeadon3
@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...
MATHS
Riuji
Riuji
@weakconvergence
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)
MATHS

You May Also Like

Eric
Eric
@ericbahn
1/ Recently, I learned about the concept of ‘struggle porn’. This refers to the fetish of sacrificing nearly everything (health, relationships, time) for your startup. I fear that this label is creating more harm than good.

2/ @nateliason wrote a fabulous article about this topic, which first introduced me to this concept. Everyone should read it:

3/ @alexisohanian also recently spoke about struggle porn, though referring to it as ‘hustle porn.’ (as the co-founder of @hustlefundvc, obviously I take issue with this pejorative definition of ‘hustle’, but that’s another topic)

4/ Struggling in itself isn’t necessarily bad. Let’s be real here--if you’re going to start a startup, you will struggle. Founders should expect to work harder generally than employees. You will be challenged in many ways and also be super rewarded in others. This is normal.

5/ However, if you are over-indexing on hard work without clear purpose and degrading your mental health/relationships in the process--then this is very bad and we obviously should not celebrate this behavior.
STARTUPS
Katie Mack
Katie Mack
@AstroKatie
Light travels at about 1 foot per nanosecond.

Hold your hand up 12 inches from your face: you’re seeing your hand as it was a nanosecond ago. Everything you look at is, to one degree or another, in the past. The farther away in space, the more ancient in time.

You can’t see the Sun as it is now, but you can see it as it was about 8 minutes ago. You can’t see Alpha Centauri now, but you can see it 4.4 years ago. You can see the Andromeda Galaxy as it was 2.5 million years in the past. And so on.

With powerful telescopes, we can see galaxies whose light has been traveling to us for more than 13 billion years. We see them shining in a universe that’s still young, where gravity has just begun to pull matter together into stars and galaxies.

We can see something even more distant, and more ancient, than the first galaxies. If we peer out far enough, in between the galaxies, we can see parts of the Universe that are so far away, it has taken the light from that distance almost the entire age of the cosmos to reach us.
SCIENCE
Advertisement
Jaya_Upadhyaya
Jaya_Upadhyaya
@Jayalko1
NARHARI AND BHAGWAN PANDURANG/VITTHAL

Once a goldsmith by the name of Narhari lived in Pandharpur. He excelled in his craft. He had vowed not to look at Pandurang or visit his mandir ever, as he was a Shiva Bhakt.
One day, a wealthy merchant visited him.


He wanted a gold girdle studded with precious gems, to be made for Prabhu Vitthal. Narhari refused to make it as it was for Vitthal.
After many requests, he agreed to make the girdle but asked the merchant to bring the measurement from the mandir as he himself would not go there


The measurement was given n he made the girdle. When the girdle was put on Vitthal, it was loose. Narhari had to shorten it. Now the girdle became tight. So Narhari was forced to take measurement on his own. He had to go to the mandir but went blindfolded to avoid seeing Vitthal


In the Mandir, when blindfolded Narhari touched Vitthal, he felt as if he was touching Shiva with matted hair, the moon, snake in His neck and Trishul in His hand. Ecstatic with joy, he removed the blindfold to see Shiva but he found the murti of Vitthal with Rukmini there.


He realised the truth that there was no difference between Vitthal and Shiva. Narhari at once fell at the feet of Panduranga. He then took the measurement of the waist of Vitthal and this time the ornament fit the Murti perfectly.

Narayan Hari🙏🏻
ALL
Anu Satheesh \U0001f1ee\U0001f1f3
Anu Satheesh 🇮🇳...
@AnuSatheesh5
Thiruvizha Mahadeva Kshetram
#Alappuzha 
#Keralatemples 🚩

Thiruvizha Mahadeva Kshetram is located in Cherthala and it is believed that Prathishta of temple was done by Vilwamangalam Swamy. Paramashiva is Swayambhu here and is worshipped as Kalakandha which means who swallowed


Halahala visham to save the world during Samudra mathanam. 

It is a famous temple where people seek the blessings, for curing the Kaivisham. The poison given by someone to destroy a person is made to vomit here. This is removed by making them vomit the poison by a special


medicine.
The medicine for vomiting is made from a plant near temple by Palodathu family. The milk offered to Bhagwan is mixed with the extracts of the plant.

Story says that once this place was a dense forest, and a woman was looking for the presence of a tortoise in the pond


and the tip of her stick hit the bottom and it started bleeding in the pond. 
Frightened, the lady informed every one and after searching in pond people found Swayambhu Lingam inside the pond. Thus Prathishta was done here.

Om Namah Shivaye
Shambo Mahadeva
🙏🕉🙏
ALL
Ryan Caldbeck
Ryan Caldbeck
@ryan_caldbeck
1/ I am seeing more and more founder secondary in venture rounds (Secondary = founders selling some of their shares before some other shareholders are able). Series B-D. I see both as an investor and through entrepreneur circles.

2/ I like secondary for entrepreneurs. Moderation is key but in a lot of situations I think it helps accelerate the co. Lots of very smart investors disagree. Here are my thoughts.

3/ Magnitude: My basic rule of thumb from what I see is market is 4+ yrs and up to 10% of founder’s equity stake with some $ cap that makes sense given stage etc. (typically <$10m)

4/ The entrepreneurial journey is brutally hard. Giving some financial relief helps remove one piece of pressure. I don’t think that secondary in the magnitude mentioned impacts the drive/persistence of great entrepreneurs.

5/ That secondary means they will be able to just sleep knowing they can pay their kids’ tuition. Secondary will make most founders better at their jobs, thus accelerating the co.
ALL