{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(unknown)=\n", "# Unknown\n", "\n", "> *From the point of view of form, the type of all the arts is the art of the musician - Oscar Wilde* \n", "\n", "Missingness of one or all of the principle components of data, code, server, models, weights, and profiles is what is at stake (but perhaps migration represents redefining home?): \n", " - $f(t)$ I\n", " - $S(t)$ ii-V-I\n", " - $h(t)$ iii, IV, vi, vii, alterations\n", " - Δ7 \n", " - m or min\n", " - ° or dim\n", " - ø or m7♭5, -5\n", " - `+` or aug, ♯5 or +5\n", " - sus\n", " - ♭9, ♯9, ♯11, ♭13\n", " - $(X'X)^T \\cdot X'Y$ tension & release (e.g. Aiim7/E (GΔ) - iim7♭5/E Em)\n", " - $\\beta$ m7♭5 > 7♯9 > 7♭9 > °7 > 7, etc \n", " - $SV'$ BWV 846 Prelude in C Major, Op 28 Prelude No. 4\n", "\n", "While Tyler Perry's work captures the collective unconscious via tension (bad marriage) & release (church music), the characters he creates don't have individually compelling arcs that subsume many of the parameters of life\n", "\n", "This is equivalent to their $SV'$ being a vector of mostly $zeros$ and the barriers, challenges, diversions, sirens, misfortunes, obstacles, courses, \"chains\" within which Tyler Perry is supposed to \"dance\" aren't rich, leaving a basic ii-V-I redemption arch with perhaps one or two straightforward insersions of, say, iii and IV." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", " 1. f(t)\n", " \\\n", " 2. S(t) -> 4. y:h'(t)=0;t(X'X)X'Y -> 5. b -> 6. SV'\n", " /\n", " 3. h(t)\n", "\n", "\n", "### `ii`: Departure 1, 2, 3\n", "- Sensory acuity: vision, hearing, smell, balance, glucose\n", "- Memory & cognitive: integrity, decline, tests\n", "- Physical activty: sarcopenia, brisk, dynamometer\n", "\n", "### `V`: Struggle 4\n", "- Frailty: loneliness, isolation, usefulness\n", "\n", "### `I`: Return 5, 6\n", "- Independence: ADLs, IADL\n", "- Hard-outcomes: shuffling, reflexes, falls, hospitalization, organ-failure, death\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "\n", "\n", "\n", "> *[Letters to Abigail](https://www.masshist.org/digitaladams/archive/doc?id=L17800512jasecond)*\n", "\n", " 1. Pessimism\n", " \\\n", " 2. Beyond Good & Evil -> 4. Dionysian -> 5. Science -> 6. Morality\n", " /\n", " 3. Robustness\n", "\n", "![](https://upload.wikimedia.org/wikipedia/commons/4/49/%22The_School_of_Athens%22_by_Raffaello_Sanzio_da_Urbino.jpg)\n", "\n", " 1. Chaos\n", " \\\n", " 2. Frenzy -> 4. Dionysian -> 5. Algorithm -> 6. Binary\n", " /\n", " 3. Energy\n", "\n", "### Activation Function, $Q$: 1st, 3rd, 5th, [♭♭7th](https://en.wikipedia.org/wiki/Chord_notation#Chord_quality), 9th \n", "- Hunter-gatherer/`War`: [humanism](https://www.uuftc.org), spiritual teachings (I)\n", "- Peasant/`Economics`: judeo (B)\n", " \n", "### [Biases](https://www.youtube.com/watch?v=lAcYahc74o8), $U()$: 11th, 13th\n", "- Farmer/`Calculus`: christian (G)\n", "- Manufacturer/`Philosophy`: world religions (Y)\n", " \n", "### Weights, $\\frac{dU()}{dQ}$: ♯9,♭9,♯11,♭13 \n", "- Electricity/`Musick`: prophetic utterances ([O](https://www.youtube.com/watch?v=1aM1KYvl4Dw))\n", "- Railway/`Leisure`: individual experience ([R](https://www.youtube.com/watch?v=fu-3WN9TJNI)) \n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Define the total utility function U(Q)\n", "def total_utility(Q):\n", " return 100 * np.log(Q + 1) # Logarithmic utility function for illustration\n", "\n", "# Define the marginal utility function MU(Q)\n", "def marginal_utility(Q):\n", " return 100 / (Q + 1) # Derivative of the total utility function\n", "\n", "# Generate data\n", "Q = np.linspace(1, 100, 500) # Quantity range from 1 to 100\n", "U = total_utility(Q)\n", "MU = marginal_utility(Q)\n", "\n", "# Plotting\n", "plt.figure(figsize=(14, 7))\n", "\n", "# Plot Total Utility\n", "plt.subplot(1, 2, 1)\n", "plt.plot(Q, U, label=r'Total Utility $U(Q) = 100 \\log(Q + 1)$', color='blue')\n", "plt.title('Total Utility')\n", "plt.xlabel('Quantity (Q)')\n", "plt.ylabel('Total Utility (U)')\n", "plt.legend()\n", "plt.grid(True)\n", "\n", "# Plot Marginal Utility\n", "plt.subplot(1, 2, 2)\n", "plt.plot(Q, MU, label=r'Marginal Utility $MU(Q) = \\frac{dU(Q)}{dQ} = \\frac{100}{Q + 1}$', color='red')\n", "plt.title('Marginal Utility')\n", "plt.xlabel('Quantity (Q)')\n", "plt.ylabel('Marginal Utility (MU)')\n", "plt.legend()\n", "plt.grid(True)\n", "\n", "# Adding some calculus notation and Greek symbols\n", "plt.figtext(0.5, 0.02, r\"$MU(Q) = \\frac{dU(Q)}{dQ} = \\lim_{\\Delta Q \\to 0} \\frac{U(Q + \\Delta Q) - U(Q)}{\\Delta Q}$\", ha=\"center\", fontsize=12)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running this code will generate a visual demonstration of diminishing marginal utility with appropriate calculus notation and Greek symbols.\n", "\n", "Here is the generated image:\n", "\n", "![Diminishing Marginal Utility](https://abikesa.github.io/johnadams/diminishing_marginalutility.png)\n", "\n", "> One needs challenges, a worthy adversary, the embrace of more remote overtones of the harmonic series - ***Q**ualities*\n", "\n", "- Westmalle Dubbel, $7$ %\n", "- Duvel, $8.5$ %\n", "- Truth, $8.7$ %\n", "- Westmalle Tripel, $9.5$ %\n", "- St. Bernardus `Abt 12`, $10$ %\n", "\n", "![](https://abikesa.github.io/belgian/craft.png)\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.4" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 4 }