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.

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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
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
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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
Arthouse-Kuklite
Arthouse-Kuklite
@Miltantvibes
Algebra 1 and pre-algebra worksheets are something that all would love to have been able to dominate in high school. Sometimes they do not dominate it there and that's when it could be a bit difficult.


But after learning and doing problems of algebra and pre-Algebra and worksheets online, it will no longer be a problem. There are many cases in all the life of a person where they have to learn.
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

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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🙏🏻
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RISHI BHRINGI AND ARDHA-NAREESHWAR SHIVA

Rishi Bhringi was a devoted bhakt of Mahadev. However, in his devotion to Shiva, he ignored Mata Parvati.

Once, he visited Kailasha along with other Rishis. All the Rishis did parikrama of Shiva and Parvati both except Rishi Bhringi.


The same situation continued whenever Rishi Bhringi visited Kailasha. Mata Parvati decided to teach him that Shiva and Parvati are one and inseparable.
So on one such visit, Mata Parvati sat on the left lap of Mahadev when Rishi Bhringi came.


Seeing this, Rishi Bhringi took the form of a bee(some say bird) and did pradakshina/ parikrama only around Shiva’s head and ignored Ma Parvati.
Angered Mata took away the Shakti from his body. Rishi lost his blood and flesh and was left with a bare skeletal form.


Seeing him in such a situation where he was unable to support himself, Shiva granted a third leg to him.
Shiva then fused one half of his body with that of Ma Parvati and appeared as Ardha Nareeshwar.
Rishi Bhringi finally realised that Shiv and Shakti are one and the same.
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