Discover and read the best of Twitter Threads about #math

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For any subset A of a topological space X, there are no more than 14 sets that can be formed from A using the closure and complement operations. The complement of B is B' = X-B. Closure C(B) = smallest closed set containing B. (Neat problem from Kelley's General #Topology.) #math
There's a lemma that helps one show this. Letting C(A) denote the closure of A, and N(A) the complement of A, we can prove:

Lemma: for all sets A, one has the equation
The result follows from the semigroup with identity I generated by 2 elements N and C such that N² = I, C² = C, and CNCNCNC = CNC. Its 14 elements are:

Should have nice matrix representation. #math
Read 4 tweets
"If I were to write a textbook on #complexity, it would be structured like this..."
- SFI Pres David Krakauer starts off this morning at #CSSS19 #CSSS at @IAIASantaFe

#error #adaptation #universality #coarsegrained #math #theory
"If you talk about #intelligence and #stupidity, you talk about #communication and #policy. That is the natural place to start."

"If you've ever written a Lokta-Volterra #equation, you've drawn a perpetual motion machine. There's no #dissipation."

- SFI President David Krakauer
"Why #God is a bad #theory: it's not because it's not true; it's because it uses an infinite-dimensional process to explain low-dimensional phenomena."

- SFI President David Krakauer at #CSSS19 on #Ockham's Razor & why #Darwin's animal breeding metaphor backfired on #evolution
Read 7 tweets
Let’s talk #MyOriginalFailure for #FailureFriday


When I was in middle school I wanted to be an astronaut, but was told women couldn’t be astronauts. #SallyRide was older than me but she didn’t let that stop her.

It stopped me.

In HS I was the top student in every #math class I took til precalc. Didn't it was ok to have to work at being good at math. No adult recognized my potential and pushed me. I lost interest in spite of my math SAT score being higher than my verbal.
#Fear #PerfectionProblems
Read 8 tweets
Trick question: Which slices of this pie would benefit most from $1,000/month?

If so many people benefit, why are the detractors obsessed with groups that don't even make a dark line on the chart?

#YangGang #BasicIncome #FreedomDividend @AndrewYang
If your argument is against #FreedomDividend or #BasicIncome because "something, something, people in the black part of this graph," then why are you willing to hold back 88% of the nation over it? It took me a while to compile this visualization, but opposition seems petty.
Clearly, I feel for the "working poor," but they are this many of us. Less than 4% work 40+hrs/week and earn below the poverty line. If a policy will benefit them ... AND another 84% of the nation significantly, then which is the better policy? #MATH
Read 7 tweets

1/11 I’m so over establishment politicians—Republican and Democrat. I want my government officials to have ONE agenda: improving citizens’ lives and making this country the best it can be. @AndrewYang has this agenda and this agenda alone. For our current...
2/11 ...politicians, the goal seems to be to always shame and destroy the other side, regardless of whether or not they have a good idea. And people actually buy into this tribal BS. Tribal republicans: you’re full of shit or just extremely ignorant if you honestly believe...
3/11 ...that Trump and the anchors at @FoxNews’ (who constantly lie and cover for him) goal is to make your lives better. Tribal democrats: you’re full of shit or just extremely ignorant if you honestly believe that Trump supporters are all evil and that establishment...
Read 12 tweets
1/13 Abro hilo de mi explicación a como hicieron el #pucherazo. Básicamente consistía en adulterar el voto por correo. Recordemos que el voto por correo luego es enviado al colegio electoral y se deposita y MEZCLA en la urna con el correo ordinario, [...]…
2/13 […] es decir NO se cuentan por separado, y así queda perfectamente escondido el fraude.

Recordemos también que Sánchez cuando llegó puso de jefe de Correos a su antiguo jefe de gabinete. Y también cambio a TODA la cúpula de correos. […]…
3/13 […] El voto por correo que llegaba a correos lo abrían, así tenían una lectura en tiempo real de la intención de voto. Y quitaban la papeleta de quién no interesa, y ponían la papeleta de quién interesaba, es decir el PSOE. […]
Read 44 tweets
Yang is on Point tonight!

#YangTownHall #YangGang #math #FreedomDividend
I love how effortlessly @AndrewYang talks about solving complex problems. #refreshing
Read 9 tweets
Sharing #MyStory as an #international #immigrant a part of @IWS_Network #Voices without #Frontiers initiative! As a #scientist and an advocate for #workplaceequality, I believe in the power of stories. #IWS #VoicesIWS #SayItForward #WomenInspire #WomeninScience #WomenInSTEM
As a child, how would you have liked moving schools in new cities with different cultures every 2-4 years?

Growing up in the #IndianArmy, I absolutely loved it! By the time I was 18, we had moved over 9 times across 9 states! #Diversity #India #TravelTuesday #IWS #VoicesIWS
My #memories of #India include sunny days, welcoming people, rich heritage, vibrant colors, abundant fruits and mouth-watering street food! #IWS #VoicesIWS
Read 39 tweets
Hello, I am Edna Matta. I was born in #Ibague, known as #Colombia’s #CityofMusic. A beautiful place near snow-covered volcanos (Ruiz, Santa Isabel and Tolima), large expanses of paramo forest, lakes and streams where a diverse array of animal and plant species coexist
My story starts with #powerful, #strong #women in my #family. I was the third of 4 children and my mom #firstMentor had to raise us practically alone, since my father had to work in a different city, 20h away by car
My mom is a very #strong #woman that taught me #values, to #workhard and to be #self-sufficient #StrongWomen #StrongFamily
@IWS_Network #VoicesIWS /1
Read 36 tweets
Fun fact: the deficit would be shockingly close to zero today with Clinton-era tax levels.
Back when we had a surplus in 2000, federal revenues were ~20% of GDP.
In 2018, feds spent ~20.3% of GDP
Deficit would have been ~0.3% GDP w/Clinton-2000-era tax $
=*<$100 billion deficit.*
After a succession of tax cuts, revenue has dropped to 16.5% GDP.
Deficit? $779 billion.
2000 arguably an anomaly - top of dotcom boom, etc
But tax cuts as scored by CBO are big part of deficit: Fiscal Cliff deal which extended most of the Bush tax cuts scored as ~$400B deficit for fiscal 2018 alone.
Trump tax law scored as $135B cut in '18; $280B in '19
Read 6 tweets
1/$TSLA #OpsMgmt101 #PoorQuality
1/ @lopezlinette, nice article. This is not surprising to me or other industry veterans. I have one rebuttal; FPY is not 14%, it is probably closer to 0%.

How did we get here? Remember this mess?:
@lopezlinette 2/ In order to meet their 5k/week commitment, Tesla put untrained interns and employee’s on the line and lowered and probably lowered their quality standards.

@lopezlinette 3/ There was no amount of QC inspection that could’ve prevented quality escapes. Actually, Tesla probably lowered their quality standards to ship more product. In industry terms, they basically “shipped shit.” Multiple twitter threads and in the forums claiming poor quality.
Read 8 tweets
I used @ProjectJupyter to investigate @NSERC_CRSNG expenditure over recent years using #opendata from @OpenGovCan. My exploration is freely available via @mybinderteam here:… 1/
According to the @OpenGovCan data, Discovery programs @NSERC_CRSNG increased in budget by 16% between 2013 and 2016. 2/
#NSERC leadership was notified of significant gaps in funding for #math and #stats #research by the math/stats Liaison Committee, by Institute Directors, and (publicly) by @NGhoussoub in May.… 3/
Read 6 tweets
1/6 Data and the Quest for Truth: A short cartoon talking about the value of data in establishing truth. First, distinguish between matters of opinion and matters of fact.

#datascience #scientificmethod #machinelearning

#think2018 #IBMPartner @ibmanalytics
2/6 You can have a preference and that’s cool. You like one thing. I like another. We run into problems when we argue about verifiable facts. Watch out for #confirmationbias

#datascience #analytics #confirmationbias

#think2018 #IBMPartner
3/6 Ignoring evidence can impact people around you… and that’s bad. We live in a #BigData in which everything is quantified. To solve our problems, we need to become data-literate.

#datascience #machinelearning

#think2018 #IBMPartner
Read 6 tweets

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