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
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@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
Michael Kinyon
Michael Kinyon
@ProfKinyon
Loops and their multiplication groups

A thread in 15 parts

(0/15)

Recall that a quasigroup (Q,*) is a set Q with a binary operation * such that for each a,b in Q, the equations a*x=b and y*a=b have unique solutions x,y. Groups are quasigroups and this property is usually one of the first things proved in elementary group theory.

(1/15)

Note that we don't assume associativity of *!

A loop is a quasigroup with an identity element. The story of why they are called loops is an interesting one and may even be true, but I will save it for another day. I am going to focus on loops in this thread.

(2/15)

Natural examples of nonassociative loops:
- The nonzero octonions under multiplication
- The sphere S^7 under octonion multiplication
- I have discussed other examples


For each x in a loop Q, define the left & right translations L_x, R_x : Q->Q by L_x(y)=xy and R_x(y)=yx. These mappings are permutations of Q. The composition L_x L_y of two left translations is not necessarily a left translation because Q is not necessarily associative.

(4/15)
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/
MATHS
P. Geerkens \u271d\ufe0f
P. Geerkens ✝️...
@pgeerkens
@GWOMaths One might say that physicists study the symmetry of nature, while mathematicians study the nature of symmetry.

1/

Observing symmetry in nature, such as noting the similarity between the symmetries of a snowflake and a hexagon, is readily comprehensible. What does it mean then to study "the nature of symmetry"?

2/

Mathematicians define a "group", G, as a set of elements {a,b,c, ...} with a binary operation ⊡ and a distinguished element e (the identity of G) satisfying these specific properties:

3/

For all a, b, c in G
1) Closure: a⊡b is in G.
2) Associativity: (a⊡b)⊡c = a⊡(b⊡c)
3) Identity: e⊡a = a⊡e = a.
4) Inverse: There exists an element a* such that a*⊡a = a⊡a* = e.

4/

Just as functions on the integers, rationals, or reals are defined as mappings, mathematicians define a *group morphism* μ as a mapping from one group to another that preserves the group structure:

5/
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

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