23 Matching Annotations
  1. May 2021
    1. 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.

      Here's the beginning of the digital example of Isaac Newton's Waste Book.

    1. 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.

      I've annotated something about Isaac Newton's Waste Book for calculus before (possibly in Cambridge's Digital Library itself, but just in case, I'm making a note of it here again so it doesn't get lost.

      In my own practice, I occasionally use small notebooks to write temporary notes into before transferring them into other digital forms. I generally don't throw them away, but they're essentially waste books in a sense.

  2. Nov 2020
    1. 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

      Great explanation of why \(i=\sqrt-1\)

    2. 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 explained in plain-english

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

      Imaginary numbers Another graph:

  3. Oct 2020
  4. Sep 2020
  5. Jul 2020
    1. 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
  6. Jan 2020
  7. Aug 2019
    1. We won’t need these facts much over the next couple of sections but they will be required on occasion

      Nonetheless, they should be thought as an important method of mathematics.

    1. 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.

      This reminds me of the exercise we had this morning in class.

    2. 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.

      A visual representation of a Tangent Line is very useful, I honestly wasn’t visualizing what a Tangent Line was, in my head.

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

      Will the L’Hospital method be explained in this chapter?

  8. Apr 2019
  9. Aug 2018
    1. 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.”

      aka, we could bleed too much here because of the small deltas... Here's a good example of where, if you can aggregate things, the total seems much larger from afar compared with smaller injustices which are all appropriately accounted and then tallied. Think calculus...

  10. Apr 2018
    1. 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.”

      It's curious that the Calculus teacher didn't recognize Katie's excitement about the problem or that different types of careers using Calculus were not part of the classroom discussions.

  11. Feb 2018
  12. Feb 2014
    1. 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.

      The conditions and process described here mirrors the process many organizations go through in an attempt to cut costs by trying to cut through what is perceived as marketing-hype. The cost differences are compelling enough to continually tempt people down a path to considerably reduce costs while believing that they've done enough due-diligence to avoid raising the risk to an unacceptable level.