Calculus and mechanics are often taught as separate subjects. It shouldn’t belike that! If you learn calculus without mechanics, it will be boring. If you learnphysics without calculus, you won’t truly understand. The exposition in this bookcovers both subjects in an integrated manner and aims to highlight the connectionsbetween them. Let’s dig in.3

This operation will form a function if the initial movement horizontally is guaranteed to find no more than one value on the graph

There are efforts that actually do work to decrease educational gaps: these include Bob Moses’ Algebra Project, Adrian Mims’ (contact person for one of the letters) Calculus Project,  Jaime Escalante  (from “stand and deliver”) math program, and the Harlem Children’s Zone.

Frank Wilhot's: "Conservatism consists of exactly one proposition, to wit: There must be in-groups whom the law protects but does not bind, alongside out-groups whom the law binds but does not protect." https://crookedtimber.org/2018/03/21/liberals-against-progressives/

Libertarianism is notionally grounded in the idea of self-determination and personal responsibility, but in practice, powerful libertarians routinely trade off (others') freedom for (their own) tax savings.

After all, imagine we framed the problem differently, the way itmight have been fifty or 100 years ago: as the concentration ofcapital, or oligopoly, or class power. Compared to any of these, aword like ‘inequality’ sounds like it’s practically designed toencourage half-measures and compromise. It’s possible to imagineoverthrowing capitalism or breaking the power of the state, but it’snot clear what eliminating inequality would even mean. (Which kindof inequality? Wealth? Opportunity? Exactly how equal would peoplehave to be in order for us to be able to say we’ve ‘eliminatedinequality’?) The term ‘inequality’ is a way of framing social problemsappropriate to an age of technocratic reformers, who assume fromthe outset that no real vision of social transformation is even on thetable.

Newton's Waste Book (MS Add. 4004) The most cherished legacy that Newton received from his stepfather, Barnabas Smith (1582-1653), seems to have been this vast manuscript commonplace book Add. 4004. Smith was rector of North Witham, a wealthy clergyman who married Newton’s mother on 27 January 1646. The immediate consequence of this union was that the three-year old Isaac Newton had to be sent to live with his grandmother. On Smith’s death, Newton appears to have inherited his library, most of which he gave away much later in life to a kinsman in Grantham. Smith himself had made extensive use of these books, in compiling a volume of theological commonplaces. This consisted of hundreds of folios bound in pasteboard, ruled at the top and in the margin of each folio to allow space for a heading and references to each entry. Newton was not interested by the very pedestrian efforts in divinity, largely the culling of quotations, with which Smith had begun to fill the book since its inception on 12 May 1612. He wanted its paper, as the title that he wrote on its original cover in February 1664 (‘Waste Book’) suggested.

The largest collection of Isaac Newton's papers has gone digital, committing to open-access posterity the works of one of history's greatest scientist. Among the works shared online by the Cambridge Digital Library are Newton's own annotated copy of Principia Mathematica and the 'Waste Book,' the notebook in which a young Newton worked out the principles of calculus.

We say i (lowercase) is 1.0 in the imaginary dimension Multiplying by i is a 90-degree counter-clockwise turn, to face “up” (here’s why). Multiplying by -i points us South It’s true that starting at 1.0 and taking 4 turns puts us at our starting point: And two turns points us negative: which simplifies to: so

Imaginary numbers seem to point North, and we can get to them with a single clockwise turn. Oh! I guess they can point South too, by turning the other way. 4 turns gets us pointing in the positive direction again It seems like two turns points us backwards

Imaginary numbers let us rotate around the number line, not just move side-to-side.

Abby's favorite subject in high school

In logic, functions or relations A and B are considered dual if A(¬x) = ¬B(x), where ¬ is logical negation. The basic duality of this type is the duality of the ∃ and ∀ quantifiers in classical logic. These are dual because ∃x.¬P(x) and ¬∀x.P(x) are equivalent for all predicates P in classical logic

We won’t need these facts much over the next couple of sections but they will be required on occasion

Last, we were after something that was happening at x=1x=1x = 1 and we couldn’t actually plug x=1x=1x = 1 into our formula for the slope. Despite this limitation we were able to determine some information about what was happening at x=1x=1x = 1 simply by looking at what was happening around x=1x=1x = 1. This is more important than you might at first realize and we will be discussing this point in detail in later sections.

Likewise, at the second point shown, the line does just touch the graph at that point, but it is not “parallel” to the graph at that point and so it’s not a tangent line to the graph at that point.

We will be seeing limits in a variety of places once we move out of this chapter.

Facebook’s chief concern, he said, was a feature of the proposal called a “private right of action.” Unlike the Obama bill, which left most enforcement to the F.T.C., Mactaggart proposed letting consumers sue companies that violated the law. (Illinois had included such a right in its biometrics law, allowing Licata to sue Facebook.) Facebook feared that if interpretation of the new rules was left to juries, rather than regulators, it would take years just to determine what the company’s compliance obligations were. “We support more disclosure in principle,” Castleberry explained to me. “But the stakes are just much higher with the private right of action.”

So I started thinking, Where can I do this [kind of math] all the time? … I started talking to my dad and he was like, “Well engineering is somewhere where you could do this … if you want to do the math all the time, then go into engineering.”

The Backblaze environment is the exact opposite. I do not believe I could dream up worse conditions to study and compare drive reliability. It's hard to believe they plotted this out and convened a meeting to outline a process to buy the cheapest drives imaginable, from all manner of ridiculous sources, install them into varying (and sometimes flawed) chassis, then stack them up and subject them to entirely different workloads and environmental conditions... all with the purpose of determining drive reliability.