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"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",
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"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": [
"
\n",
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\n",
" \n",
" \n",
" | \n",
" u_n | \n",
" u_x | \n",
" p_n | \n",
" p_x | \n",
" min_p_d | \n",
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\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 1 | \n",
" 1E+5 | \n",
" 0.999999 | \n",
" 0.000001 | \n",
" 0.00000999999 | \n",
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" \n",
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"text": [
" u_n u_x p_n p_x min_p_d\n",
"0 1 1E+5 0.999999 0.000001 0.00000999999"
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"prompt_number": 2
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{
"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": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" u_n | \n",
" u_x | \n",
" p_n | \n",
" p_x | \n",
" min_p_d | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 1 | \n",
" 1E+2 | \n",
" 0.9999999999 | \n",
" 1E-10 | \n",
" 0.009999999999 | \n",
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\n",
" \n",
" 1 | \n",
" 1 | \n",
" 1E+10 | \n",
" 0.9 | \n",
" 0.1 | \n",
" 9E-11 | \n",
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\n",
" \n",
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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"
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"prompt_number": 6
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{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Notes"
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},
{
"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."
]
}
],
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}