Jeff Jacobs

@jpj

Assistant Teaching Professor, Georgetown University

Joined on Jan 27, 2023

  • I'm stuck trying to figure out what it means, economically (and what we're trying to demonstrate with it), for the employer to have three possible wage levels to choose from, rather than two... For the two-wage-level case, we have: Worker Work Home Employer
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  • Web apps without rolling your own server • Most basic: GitHub Pages (web app must be rendered to html, hence quarto) • Streamlit map -- benefits: write directly in Python without worrying about compilation to html via quarto; using GSheets as DB, but also many many drawbacks of streamlit • Live coding: make the basics of the map app [sidebar, main window, sl.Map(), Geocoding API • Vercel + Next.js: Pre-caching views • ^For those, talk about pre-loading all of the possible views -- for example, if they're visualizing 50 states, they can pre-render those 50, at urls like /al, /az, etc
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  • Part 1: Working Backwards from Extended Labor Market Game I'm starting from the Extended Labor Market Game, from page 33, and trying to work backwards. The Extended Labor Market Game as it is on that page looks like: Worker $\textsf{Work}$ $\textsf{Home}$ Employer $W^C$
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  • Introduction: Metaphors We Die For For those hoping to understand society from a soicolinguistic or intellectual-historical standpoint, the title of Lakoff and Johnson's 1980 Metaphors We Live By make it seem as if it should be shelved alongside Newton's Principia Mathematica, Darwin's Origin of Species, or Marx's Capital in a "Widely Cited, Rarely Read" section. However, unlike the religious-secular and political-revolutionary rifts engendered by these works (whether intended/desired by the author, as in Marx's case, or not, as in Newton's), the most striking fact about the content of Lakoff and Johnson's work is its blandness, its failure to connect the dots between the metaphors discussed and the exciting political or social contexts out of which they emerged. In this sense, the blandness of the work contrasts sharply with Raymond Williams' Keywords, a work in more or less the same genre, published only four years earlier. Williams' short, etymological explorations of politically-charged terms immediately catalyzed further waves of linguistic-historical studies within the broader program of the Birmingham School of Cultural Studies. From its publication to the present, socially- and politically-minded authors and publishing houses have explicitly drawn on the tradition of Williams' book as a framework for understanding political-rhetorical concepts: Martin Jay's Cultural Semantics: Keywords of Our Time (1998), Bennett et al.'s New Keywords (2005), Andrew Levine's Political Keywords (2009), John Patrick Leary's Keywords: The New Language of Capitalism (2019), Keywords in Policing, Keywrods in Australian Politics, and so on, not to mention an entire book series, Keywords in Literature and Culture, published by Wiley-Blackwell with the following editorial summary: Indebted to the work of Raymond Williams, the series identifies and documents keywords as cultural analysis, taking the reader beyond semantic definition to uncover the uncertainties, disagreements, and confrontations evident in differing usages and conflicting connotations. Metaphors We Live By meanwhile, despite its comparable subject matter (a subject matter that, we argue, is in fact even more fertile for this kind of socio-political analysis) and sociolinguistic approach, did not give rise to a similar wave of context-aware cultural studies of metaphorical-linguistic meaning. In this work, therefore, we aim to combine the political and cultural awareness of Williams' approach with the linguistic-analytic rigor of Lakoff and Johnson's, to shed light on how metaphor can be used to clarify but also to obfuscate meaning within political rhetoric.
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  • I'm not sure exactly what to say about it, since I feel like... maybe it helps me to have a topic (like Algerian Rev) as "point A" and then another thing that's "point B" and then I figure out how to get from point A to point B but, here goes... Before the rev Algeria was officially only a French colony from 1830 to 1848, because then the 1848 revolution happened and it was pretty radical so they gave all Algerians the same rights (citizenship, voting, etc.) as metropole French people. Meaning, Algeria was literally an official département of France just like Paris was[^departement] So like, in that sense it was p different from all the other colonial powers: people in India never had British citizenship, for example. This "specialness" was kind of a big part of why the revolution was so bloody, though: on the one hand, in theory, it could have been a good experiment in cross-cultural exchange and whatnot, if France had truly embraced Algerians as equals in practice (like, in their day-to-day norms) to the extent that they made Algerians equal to them legally... To put it another way, the British made it obvious both legally and culturally that British ppl were "above" people in India, but in France it was more subtle, so that the revolutionary grievances were about the attitude that French ppl had towards Algerian ppl, not about the legal structure as such. So, that's why it makes sense that Fanon, as the "theorist of the revolution", gave this very psychological account of French colonialism---if you read the Indian "equivalents" of Fanon, for example, they weren't psychiatrists and their anticolonial theories weren't really about the psyché of the colonized so much as... like concrete grievances about laws and taxes and economics, etc... The part of all that which made it really bad, though, was also that unlike India, Algeria was France's main settler colony: by the time of the revolution there were about 1 million French settlers in Algeria, who were called pieds noirs[^pieds]. This is where the Palestine metaphor starts to enter in obviously, bc yeah settler colonialism.
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  • Multiple Hypothesis Testing It's a bit messy to try and fit all of the pairwise hypothesis tests you have to do into one statement like this, but to overthink everything like I usually do :stuck_out_tongue_winking_eye: here is the full-on logic statement for the hypotheses you would have. In words, from what I understand: The null hypothesis $H_0$ is that all the artists are "the same", in terms of the Spotify features that can be obtained for all their songs, and then The alternative hypothesis $H_A$ is the logical negation of this: that it is not true that all the artists are "the same" in this sense. Mathematically, since in this class we have only learned pairwise tests (and going beyond pairwise tests can actually be quite tricky, because of corrections you need to make when using the same dataset to test multiple hypotheses), you'd want to write out the individual hypotheses as follows: Let $A = {\text{Weeknd},\text{TaySwift},\text{Bad Bunny},\text{BTS},\text{Drake}}$ be the full set of artists you want to consider, let $F$ be the full set of features you want to consider, and let $\mu_{f,a}$ represent the mean of feature $f$ for artist $a$. Then the null hypothesis is
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  • What We're Given $D \in {0, 1}$ = has disease $T \in {0, 1}$ = test result (In the real world, however, we cannot observe $D$, only $T$) 99% accuracy:$\Pr(T = 1 \mid D = 1) = 0.99$ $\Pr(T = 0 \mid D = 0) = 0.99$ Rare disease: 1 in 10000 people has it $\Pr(D = 1) = \frac{1}{10000}$
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  • There are two potential choices for the normalization term, that is, the denominator in the interference and arbitrariness measures which makes them invariant to affine transformations of payoffs: $$ \begin{align*} \widehat{\mathcal{I}}{A \rightarrow B} &= \frac{\pi_B(s^*) - \pi_B(\widetilde{s})}{\max{s \in S}{\pi_B(s)} - \min_{s \in S}{\pi_B(s)}} \ \widehat{\mathcal{A}}{A \rightarrow B} &= \frac{\pi_A(s^*) - \pi_A(\widetilde{s})}{\max{s \in S}{\pi_A(s)} - \min_{s \in S}{\pi_A(s)}} \end{align*} $$ The idea is, what should we choose for the set $S$ of possible strategy profiles over which the min and max are taken?
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  • Domination Measure: Invariance to Scaling Specific Case: Invisible Hand Game The original Invisible Hand Game looks like Corn Tomato Corn 2, 4 4, 3
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  • Normalizing the Capacity to Dominate Original Version The original, overall measure is $$ \mathcal{C}{A \rightarrow B} = f({\mathcal{C}{A \rightarrow B}(\widetilde{s}) \mid \widetilde{s} \in (S_A \setminus s^*)}), $$ i.e., a function of the strategy-specific capacities, where $\mathcal{I}$ stands for "Interference" and $\mathcal{A}$ stands for "Arbitrariness"
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  • Axioms and Theorems of Republican Liberty Let $S_i$ be the set of strategies available to an agent $i$. Keeping in mind that our measure of the absolute capacity of an agent $A$ to dominate another agent $B$ is given by $$ \mathcal{C}{A \rightarrow B} = f({\mathcal{C}{A \rightarrow B}(s) \mid s \in S_A}), $$ and similarly for the absolute capacity of $B$ to dominate $A$. This also gives us a measure of the relative capacity of $A$ to dominate $B$, that is, the difference between $A$'s capacity to dominate $B$ and $B$'s capacity to dominate $A$:
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  • Advanced Algebra: The Magic if Logs and Sequences (Why you only need to memorize the geometric sequence/sum formulas!) Log Rule Recap $$ \begin{align} \log(m \cdot n) &= \log(m) + \log(n) \tag{1} \ \log(m^n) &= n\log(m) \tag{2} \end{align} $$
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  • Advanced Algebra: Sequences and Sums Quick Cheatsheet Secret-Shortcut Sum Formulas $$ \begin{align*} \sum_{i=1}^n i ; &= \frac{n(n+1)}{2} \ \sum_{i=1}^n i^2 &= \frac{n(n+1)(2n+1)}{6} \ \sum_{i=1}^n i^3 &= \frac{n^2(n+1)^2}{4} \end{align*} $$
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  • Precalculus: The Unit Circle Quick Preliminary I'll be referring to this unit circle diagram throughout: I like to think of the coordinates for the 3 points in each quadrant as follows: $$ \frac{\sqrt{3}}{2} = \textbf{long}, \frac{\sqrt{2}}{2} = \textbf{middle}, \frac{1}{2} = \textbf{short} $$
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  • Factoring by Grouping The problem: Simplify $$ \frac{3x^3 - 3x^2 + 7x - 7}{27x^4 - 147} $$ The tricky thing about this one is that you have to group the numerator into $(3x^3 - 3x^2) + (7x-7)$, and then notice that the first group contains multiples of $3$, and the second multiples of $7$, so that for the rest of the problem you're looking for places where you can use one of your "factoring tricks" to find hidden $3$s and $7$s. So, let's start by factoring out as much as we can from the two groups in the numerator:
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  • Simplifying Polynomials and Compound Interest Simplifying Polynomials: Overview The basic goal that you have, throughout all these problems, is to take a scary-looking, complicated expression and simplify it into a form where someone could look at it and immediately see what the solutions are. For example, if you show someone the expression $$ x^3 - 6 x^2 + 11 x - 6 = 0 $$ they're going to have no idea what values of $x$ make this true... BUT, if you do the work to factor this, it turns out to be just
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  • Trig Identities Cheatsheet First, let's remember our negative angle rules (N for Negative), since it turns out you can always use these rules to derive any of the identities below from any of the other ones! (N1: Negative Angle Negates $\sin$) $$ \sin(-\theta) = -\sin(\theta) $$ (N2: Negative Angle Doesn't Change $\cos$)
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  • Advanced Algebra Practice: Log Rules and Inverses Logarithms Definitions First and foremost, we recall our spiral rules for converting exponents to logs and logs to exponents: (D1) Log $\rightarrow$ Exponent $$ \log_a(b) = c \iff a^c = b $$ (D2) Exponent $\rightarrow$ Log
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  • Precalc, March 1, 2023 Test 3 What is the bearing of $\mathbf{W}$ from the origin? Answer: $S$ $26^\circ$ $W$ $$ \cos^{-1}\left(\cos \frac{9 \pi}{8} \right) $$ $$ f(x) = \cos\left(\sin^{-1} x \right) $$
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  • Installing the TI-84 Emulator (So you never have to worry about having your calculator ever again!) Download the emulator program here (it says that it supports Windows and Mac, so it shouldn't matter which one you have) It will ask you for a "ROM file" --- no need to worry about what that is, you could copy that file over from a physical calculator to your computer but it's a headache so instead just use mine here: ti84se.rom The TI-84 Silver Edition image should pop up, and then yeah you can just use it the same way you use a regular calculator!
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