{ "metadata": { "name": "", "signature": "sha256:e9556f053b45966da8ae9a60c6da2cb2651f44e5b0921f31492ff8b296a6b1b7" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Author: HoverHell" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Any non-astronomically-small increase in chance of having an astronomically long life is worth more than anything in a normal-duration life." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Definitions an assumptions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " * $p^x$: base probability of an extended life (\u201cxlife\u201d)\n", " * $p^n$: probability of a normal-length-only life (\u201cnlife\u201d)\n", " * Approximation:\n", " * $p^o$: probability of \u201csomething else\u201d\n", " * Assumption: $p^o \\approx 0$\n", " * Therefore $p^n = 1 - p^x - p^0 \\approx 1 - p^x$\n", " * $p^\\Delta$: expected possible change of the probability of xlife.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " * $u^n$: base utility of nlife\n", " * $u^x$: utility of xlife\n", " * $length(xlife) \\gg length(nlife)$ (by definition)\n", " * Assumption: utility $U(time) > 0$ on average\n", " * \u201cCognitive capabilities should allow for better-than-random outcomes in an influencable system\u201d\n", " * Therefore $u^x \\gg u^n$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Actions:\n", " * $A^x$: assisting, \u201cwork on increasing the probability of xlife\u201d\n", " * $A^n$: unassisting, \u201cenjoy the nlife\u201d\n", "* $u^A$: utility of nlife with $A^x$\n", " * $u^A = u^n + u^\\Delta$\n", " * Assumption: $u^\\Delta$ < 0\n", " * Approximation (for simplicity): $u^A \\approx 0$" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " * $U(A^n) = p^n * u^n + p^x * u^x + p^o * \u2026$\n", " * $U(A^n) = p^n * u^n + p^x * u^x$\n", " * $U(A^x) = (p^n - p^\\Delta) * u^A + (p^x + p^\\Delta) * u^x$\n", " * $U(A^x) = (p^x + p^\\Delta) * u^x$\n", " * $U(A^x) - U(A^n) = p^x u^x + p^\\Delta u^x - p^n u^n - p^x u^x$\n", " * $U(A^x) - U(A^n) = p^\\Delta u^x - p^n u^n$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " * Condition (of preferability):\n", " * $C(A^x): U(A^x) - U(A^n) > 0$\n", " * $C(A^x): p^\\Delta u^x > p^n u^n$\n", " * $u^x > 0, p > 0$,\n", " * $C(A^x): p^\\Delta / p^n > u^n / u^x$\n", " * $C(A^x): p^\\Delta > p^n * u^n / u^x$" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## Infrastructural\n", "from decimal import Decimal as D\n", "import pandas as pa\n", "DF = pa.DataFrame" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "u_n = D(\"1\") # utility of nlife # arbitrary constant here\n", "u_x = u_n * D(\"1e5\") # utility of xlife # very humble low guess\n", "p_x = D(\"1e-6\") # base probability of xlife # also somewhat low\n", "\n", "p_n = 1 - p_x # probability of nlife # see assumptions\n", "\n", "columns = 'u_n u_x p_n p_x min_p_d'.split()\n", "c_a_x = lambda: p_d > p_n * (u_n / u_x)\n", "min_p_d = p_n * (u_n / u_x)\n", "\n", "DF([(u_n, u_x, p_n, p_x, min_p_d)], columns=columns)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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u_nu_xp_np_xmin_p_d
0 1 1E+5 0.999999 0.000001 0.00000999999
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ " u_n u_x p_n p_x min_p_d\n", "0 1 1E+5 0.999999 0.000001 0.00000999999" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "values = [\n", " # u_x, p_x\n", " [D(\"1e2\"), D(\"1e-10\")],\n", " [D(\"1e10\"), D(\"1e-1\")],\n", "]\n", "DF([[u_n, u_x, 1 - p_x, p_x, (1 - p_x) * (u_n / u_x)]\n", " for u_x, p_x in values], columns=columns)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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u_nu_xp_np_xmin_p_d
0 1 1E+2 0.9999999999 1E-10 0.009999999999
1 1 1E+10 0.9 0.1 9E-11
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ " u_n u_x p_n p_x min_p_d\n", "0 1 1E+2 0.9999999999 1E-10 0.009999999999\n", "1 1 1E+10 0.9 0.1 9E-11" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Notes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " * The whole model assumes that life extension gives time to do more life extension, making scenarios between nlife and xlife improbable.\n", " * If $p^x$ is close to 0, $p^\\Delta \\approx u^n / u^x$.\n", " * Probability values of 1e-3 are below noise level; conclusions of that for the relevant estimated situations are unclear.\n", " * Life extension paths and technologies can vary; from cyborgisation to mind-uploading.\n", " * Whether there can be more-than-current-civilisation-stable dystopic economies given life extension technologies is an open question." ] } ], "metadata": {} } ] }