In light of my tweet thread about the category of finite sets and commutative monoids (https://t.co/jnY0wZZbxq), I thought I might try to say what the analogue is for braided monoidal things (although much of this is still somewhat hypothetical).
So okay, here's a thread on the category of finite sets and a way in which it controls algebraic structure in symmetric monoidal categories. I think it's some really pretty stuff.
— Jonathan Beardsley (@JBeardsleyMath) December 6, 2020
![](https://pbs.twimg.com/media/EpGdTRmW8AAMzRa.png)
![](https://pbs.twimg.com/media/EpGdUfrXIAAcYkF.png)
![](https://pbs.twimg.com/media/EpGdUy1XIAAp7l-.jpg)
T.G.
He also showed that every vine decomposes as a braid followed by a planar tree.
![](https://pbs.twimg.com/media/EpGdWJPWMAAKN2H.jpg)
![](https://pbs.twimg.com/media/EpGdWo6W8AIceYm.jpg)
![](https://pbs.twimg.com/media/EpGdW_7XMAE9rm3.jpg)
More from Maths
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.
Oh for crying out loud. I don't know anyone who thinks we can get R below 0.9 with this new variant. It's 22 virus generations to even get from 50,000 cases to 5,000 at R=0.9 - that's 4 months. TTI is a complete fantasy right now: spend the money on the vaccine rollout. https://t.co/MyeBt8tC1w
— Oliver Johnson (@BristOliver) January 3, 2021
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.
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A brief analysis and comparison of the CSS for Twitter's PWA vs Twitter's legacy desktop website. The difference is dramatic and I'll touch on some reasons why.
Legacy site *downloads* ~630 KB CSS per theme and writing direction.
6,769 rules
9,252 selectors
16.7k declarations
3,370 unique declarations
44 media queries
36 unique colors
50 unique background colors
46 unique font sizes
39 unique z-indices
https://t.co/qyl4Bt1i5x
PWA *incrementally generates* ~30 KB CSS that handles all themes and writing directions.
735 rules
740 selectors
757 declarations
730 unique declarations
0 media queries
11 unique colors
32 unique background colors
15 unique font sizes
7 unique z-indices
https://t.co/w7oNG5KUkJ
The legacy site's CSS is what happens when hundreds of people directly write CSS over many years. Specificity wars, redundancy, a house of cards that can't be fixed. The result is extremely inefficient and error-prone styling that punishes users and developers.
The PWA's CSS is generated on-demand by a JS framework that manages styles and outputs "atomic CSS". The framework can enforce strict constraints and perform optimisations, which is why the CSS is so much smaller and safer. Style conflicts and unbounded CSS growth are avoided.
Legacy site *downloads* ~630 KB CSS per theme and writing direction.
6,769 rules
9,252 selectors
16.7k declarations
3,370 unique declarations
44 media queries
36 unique colors
50 unique background colors
46 unique font sizes
39 unique z-indices
https://t.co/qyl4Bt1i5x
![](https://pbs.twimg.com/media/DrIk2JhU8AAjf_m.jpg)
PWA *incrementally generates* ~30 KB CSS that handles all themes and writing directions.
735 rules
740 selectors
757 declarations
730 unique declarations
0 media queries
11 unique colors
32 unique background colors
15 unique font sizes
7 unique z-indices
https://t.co/w7oNG5KUkJ
![](https://pbs.twimg.com/media/DrIk3TjU0AAhf3D.jpg)
The legacy site's CSS is what happens when hundreds of people directly write CSS over many years. Specificity wars, redundancy, a house of cards that can't be fixed. The result is extremely inefficient and error-prone styling that punishes users and developers.
The PWA's CSS is generated on-demand by a JS framework that manages styles and outputs "atomic CSS". The framework can enforce strict constraints and perform optimisations, which is why the CSS is so much smaller and safer. Style conflicts and unbounded CSS growth are avoided.
Great article from @AsheSchow. I lived thru the 'Satanic Panic' of the 1980's/early 1990's asking myself "Has eveyrbody lost their GODDAMN MINDS?!"
The 3 big things that made the 1980's/early 1990's surreal for me.
1) Satanic Panic - satanism in the day cares ahhhh!
2) "Repressed memory" syndrome
3) Facilitated Communication [FC]
All 3 led to massive abuse.
"Therapists" -and I use the term to describe these quacks loosely - would hypnotize people & convince they they were 'reliving' past memories of Mom & Dad killing babies in Satanic rituals in the basement while they were growing up.
Other 'therapists' would badger kids until they invented stories about watching alligators eat babies dropped into a lake from a hot air balloon. Kids would deny anything happened for hours until the therapist 'broke through' and 'found' the 'truth'.
FC was a movement that started with the claim severely handicapped individuals were able to 'type' legible sentences & communicate if a 'helper' guided their hands over a keyboard.
For three years I have wanted to write an article on moral panics. I have collected anecdotes and similarities between today\u2019s moral panic and those of the past - particularly the Satanic Panic of the 80s.
— Ashe Schow (@AsheSchow) September 29, 2018
This is my finished product: https://t.co/otcM1uuUDk
The 3 big things that made the 1980's/early 1990's surreal for me.
1) Satanic Panic - satanism in the day cares ahhhh!
2) "Repressed memory" syndrome
3) Facilitated Communication [FC]
All 3 led to massive abuse.
"Therapists" -and I use the term to describe these quacks loosely - would hypnotize people & convince they they were 'reliving' past memories of Mom & Dad killing babies in Satanic rituals in the basement while they were growing up.
Other 'therapists' would badger kids until they invented stories about watching alligators eat babies dropped into a lake from a hot air balloon. Kids would deny anything happened for hours until the therapist 'broke through' and 'found' the 'truth'.
FC was a movement that started with the claim severely handicapped individuals were able to 'type' legible sentences & communicate if a 'helper' guided their hands over a keyboard.