BC MATHS
Saved by @CodyyyGardner

It is trying when mathematicians declare condescendingly that there is no point doing things because their models tell them so. Well maybe some of the assumptions don't hold up. How did that work out for the no additional risk from large events and no point in border controls...

 During wave 1 cases fell very fast, faster than I think most people were expecting. Particularly in Scotland. Rt was probably ~0.5 until we started easing off.
This was despite a constant leak of cases coming out of hospitals and LTC facilities as we were rationing PPE and are policies were nowhere near ideal. There was insistence from infection control that droplet protections were sufficient. We have all learned a lot since then.
Not to mention we have learned to avoid the shit show of actively importing cases into care homes. We've learned not to repeat that. Other sectors have learned too.
We've learned a lot and there's no reason we can't control this new variant. But we will not manage if we don't try and act with clarity of purpose.
We also learned from wave 1 not to abandon contact tracing and to test people as early as possible to prevent transmission chains. I.e. TTI. That still holds true. Let us not repeat the mistakes.
In fact, in March we got Rt down to that level with effectively no targeted support from TTI because we were only testing on admission (way too late). And we had so little testing capacity.
In addition, in March there was approximately zero prior immunity. Now there is a non-zero amount and that helps eat into some of the increase in transmissibility.
We have light at the end of the tunnel with vaccines and can target vaccines at those who cannot isolate (essential workers) with more scope to do this the less urgently we need to vaccinate the vulnerable. This helps psychologically and practically.
Practically, for example, having vaccinated workers in LTC and vaccinated people support the elderly is a game changer for isolation.
Rapid testing is another tool we now have that could help alongside TTI and vaccines. We have lots more at our disposal to work with.
Chasing down every case is still going to become *more* not less important. It is perfectly possible that if vaccine evading strains don't arise in the UK we will import them at some time. Will need TTI then. Goes without saying that this will also not be the last pandemic.
I suspect one reason why the TTI is constantly underestimated is that it is in practice just naturally much better at finding cases in high transmission events than no/low transmission cases. And maybe this is hard to model.
For very many human reasons that are just intuitively apparent to anyone who has trained in taking a history from a patient: you have a shared agenda to get to the most important information about the most important events. And you build a shared understanding of what those are.
Perhaps the cases missed are much much more likely to be in the 80% or so of people who don't infect someone else.
For all the obsession with overdispersion of SARS2 and HIT, I actually think this is where it makes the most difference. I think its why many mathematicians seem baffled or underenthused by the East Asian response... sure it works in practice, but it makes no sense in theory.
In addition, just because something doesn't solve the problem on it's own doesn't mean it doesn't help solve the problem.
I don't mean to single out @BristOliver for this rant, so sorry for that. I find your takes on the whole very interesting so hope you don't block me. This just really bugged me on the back of a recent chat with a friend who is a public health trainee.
She has been working very hard on TTI all year and feels drained, and, I think, underappreciated. And I feel strongly that we have not championed this essential work enough. So much so that, I'm told, it is now increasingly common that when contacting people they get vile abuse.
A bit less of this: "there's no point in doing that thing that has been the backbone of every competent outbreak response for over 150 years and that WHO insists is key and that all Covid-controlling countries have invested in" would be nice. (Paraphrasing no-one in particular.)
Even if only out of respect for all the people working their asses off to get it done in incredibly difficult circumstances.

More from Maths

Sleepless in Broadacres \u26d4\ufe0f
Sleepless in Broadacre...
@tesssulaman
IS HISTORY ALL TRUE SERIES: when even the #Calendar isn’t❓

THE REAL ACTUAL SOLAR CALENDAR:
*Based on the noble science of #Astronomy; the sister science to #Geometry, #Mathematics and the “almost” lost numerical science mysteries. Which was mastered in

“ancient” times, but is close to forgotten, in these “modern” days. Go figure❗️😄☦️

Navigation of the oceans was man’s first real great step of personal evolution, here on earth. The earliest of discovered sciences; #astronomy; allowed men to navigate through

routes to known territories; or to discover new ones, by the endlessly reliable positions of the stars and constellations, in the night sky. Hence; much diligent study, over who knows how many epochs, and great civilizations; was an esteemed scholarly pursuit. And led to a vast

understanding of the mechanics of our solar system, as well as the natural cycles of our planet, that even we; in this so-called Information Age “high civilization, don’t often know even exists any longer. A decay of common knowledge, in our “modern” educations, actually.

#Calendars have come and gone In the last few thousand years; motivated apparently by the politics of the day, or personal whim even, by the rulers of the moment; which somehow stuck, from there, and has hardly ever been questioned again.
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Algebra Etc.
Algebra Etc.
@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.

Then a, the first digit of n, is the largest number whose cube is no greater than what's left of x.

(5/10)
MATHS
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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/
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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
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

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