Common Core math was the pinnacle of their evil genius, and low-point of our complacency... It disrupted the minds of an entire generation on how even the most basic things work.
Readin', Writin', & Rithmatic
How far did they get? Let's see.
1895 8th Grade Final Exam, Kansas:
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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).
It's also just kind of a cool combinatorial structure! I've been talking to @CreeepyJoe about this lately, as well as @grassmannian.
The first thing you have to know is that, in a braided monoidal category you can still have commutative monoids. Since a braided monoidal category C has a "twist" map for every object β(x):x⊗x→x⊗x, if x is a monoid you can ask for the following diagram to commute:
Remember that being symmetric monoidal just means that if you take the twist map above and do it twice, you get the identity map, but braided monoidal doesn't mean that. But it's okay! You can still define commutative monoids here.
But so anyway, we can talk about commutative monoids in braided monoidal categories.
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
It's also just kind of a cool combinatorial structure! I've been talking to @CreeepyJoe about this lately, as well as @grassmannian.
The first thing you have to know is that, in a braided monoidal category you can still have commutative monoids. Since a braided monoidal category C has a "twist" map for every object β(x):x⊗x→x⊗x, if x is a monoid you can ask for the following diagram to commute:
Remember that being symmetric monoidal just means that if you take the twist map above and do it twice, you get the identity map, but braided monoidal doesn't mean that. But it's okay! You can still define commutative monoids here.
But so anyway, we can talk about commutative monoids in braided monoidal categories.
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H was always unseen in S2NL :)
Those who exited at 1500 needed money. They can always come back near 969. Those who exited at 230 also needed money. They can come back near 95.
Those who sold L @ 660 can always come back at 360. Those who sold S last week can be back @ 301
Those who exited at 1500 needed money. They can always come back near 969. Those who exited at 230 also needed money. They can come back near 95.
Those who sold L @ 660 can always come back at 360. Those who sold S last week can be back @ 301
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THREAD: 12 Things Everyone Should Know About IQ
1. IQ is one of the most heritable psychological traits – that is, individual differences in IQ are strongly associated with individual differences in genes (at least in fairly typical modern environments). https://t.co/3XxzW9bxLE
2. The heritability of IQ *increases* from childhood to adulthood. Meanwhile, the effect of the shared environment largely fades away. In other words, when it comes to IQ, nature becomes more important as we get older, nurture less. https://t.co/UqtS1lpw3n
3. IQ scores have been increasing for the last century or so, a phenomenon known as the Flynn effect. https://t.co/sCZvCst3hw (N ≈ 4 million)
(Note that the Flynn effect shows that IQ isn't 100% genetic; it doesn't show that it's 100% environmental.)
4. IQ predicts many important real world outcomes.
For example, though far from perfect, IQ is the single-best predictor of job performance we have – much better than Emotional Intelligence, the Big Five, Grit, etc. https://t.co/rKUgKDAAVx https://t.co/DWbVI8QSU3
5. Higher IQ is associated with a lower risk of death from most causes, including cardiovascular disease, respiratory disease, most forms of cancer, homicide, suicide, and accident. https://t.co/PJjGNyeQRA (N = 728,160)
1. IQ is one of the most heritable psychological traits – that is, individual differences in IQ are strongly associated with individual differences in genes (at least in fairly typical modern environments). https://t.co/3XxzW9bxLE
2. The heritability of IQ *increases* from childhood to adulthood. Meanwhile, the effect of the shared environment largely fades away. In other words, when it comes to IQ, nature becomes more important as we get older, nurture less. https://t.co/UqtS1lpw3n
3. IQ scores have been increasing for the last century or so, a phenomenon known as the Flynn effect. https://t.co/sCZvCst3hw (N ≈ 4 million)
(Note that the Flynn effect shows that IQ isn't 100% genetic; it doesn't show that it's 100% environmental.)
4. IQ predicts many important real world outcomes.
For example, though far from perfect, IQ is the single-best predictor of job performance we have – much better than Emotional Intelligence, the Big Five, Grit, etc. https://t.co/rKUgKDAAVx https://t.co/DWbVI8QSU3
5. Higher IQ is associated with a lower risk of death from most causes, including cardiovascular disease, respiratory disease, most forms of cancer, homicide, suicide, and accident. https://t.co/PJjGNyeQRA (N = 728,160)