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"cells": [
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"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction: Copernican Lifetime Equation\n",
"\n",
"In this notebook, we take a look at the Copernican lifetime equation, a simple method for calculating the lifetime of any phenomomenon. The original discussion of this equation is worth a read and can be found on SciHub (questionably legal) [here](https://sci-hub.tw/10.1038/363315a0). "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.441317Z",
"start_time": "2018-12-29T16:51:47.788400Z"
}
},
"outputs": [
{
"data": {
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""
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""
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Data science imports\n",
"import cufflinks\n",
"import plotly.graph_objs as go\n",
"import plotly.plotly as py\n",
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"# Display all cell outputs\n",
"from IPython.core.interactiveshell import InteractiveShell\n",
"InteractiveShell.ast_node_interactivity = 'all'\n",
"\n",
"cufflinks.go_offline()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculations\n",
"\n",
"$$(\\frac{z}{1 - z})*t_{current}\\le t_{future} \\le (\\frac{1 - z}{z}) * t_{current}$$\n",
"\n",
"$$z = \\frac{1-\\text{confidence interval}}{2}$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.449208Z",
"start_time": "2018-12-29T16:51:49.444454Z"
}
},
"outputs": [],
"source": [
"def calculate_multipliers(ci):\n",
" z = (1 - ci) / 2\n",
" return z / (1 - z), (1 - z) / z"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.464598Z",
"start_time": "2018-12-29T16:51:49.451786Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0.025641025641025664, 38.999999999999964)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
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"data": {
"text/plain": [
"(0.3333333333333333, 3.0)"
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"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
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"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"calculate_multipliers(0.95)\n",
"calculate_multipliers(0.5)\n",
"calculate_multipliers(0.99)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.470705Z",
"start_time": "2018-12-29T16:51:49.467296Z"
}
},
"outputs": [],
"source": [
"def calculate_lifetime(t_current, ci):\n",
" low, high = calculate_multipliers(ci)\n",
" return t_current * low, t_current * high"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To use this equation, `t_current` must be in years, and `ci` must be a fraction."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lifetime of Humanity\n",
"\n",
"https://en.wikipedia.org/wiki/Human_evolution#H._sapiens"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.476859Z",
"start_time": "2018-12-29T16:51:49.472916Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(5128.2051282051325, 7799999.999999993)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"calculate_lifetime(200000, 0.95)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's write a quick function to nicely display the results."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.481758Z",
"start_time": "2018-12-29T16:51:49.478850Z"
}
},
"outputs": [],
"source": [
"from datetime import datetime, timedelta"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.487123Z",
"start_time": "2018-12-29T16:51:49.483536Z"
}
},
"outputs": [],
"source": [
"def print_lifetime(t_current, ci):\n",
" low, high = calculate_lifetime(t_current, ci)\n",
" now = datetime.now()\n",
" try:\n",
" print(\n",
" f'Estimated lifetime from {(now + timedelta(days=low*365)).date()} ({low:,.2f} years) to {(now + timedelta(days=high*365)).date()} ({high:,.0f} years).'\n",
" )\n",
" except:\n",
" print(f'Estimated lifetime in years: {low:,.2f} to {high:,.0f}.')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.493339Z",
"start_time": "2018-12-29T16:51:49.489675Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated lifetime in years: 5,128.21 to 7,800,000.\n"
]
}
],
"source": [
"print_lifetime(200000, 0.95)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.499846Z",
"start_time": "2018-12-29T16:51:49.496121Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated lifetime in years: 1,005.03 to 39,800,000.\n"
]
}
],
"source": [
"print_lifetime(200000, 0.99)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Data Science\n",
"\n",
"https://hbr.org/2012/10/data-scientist-the-sexiest-job-of-the-21st-century"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.513848Z",
"start_time": "2018-12-29T16:51:49.502120Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated lifetime from 2019-02-23 (0.15 years) to 2252-11-02 (234 years).\n"
]
}
],
"source": [
"print_lifetime(2018 - 2012, 0.95)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.525728Z",
"start_time": "2018-12-29T16:51:49.519264Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated lifetime from 2020-12-28 (2.00 years) to 2036-12-24 (18 years).\n"
]
}
],
"source": [
"print_lifetime(2018 - 2012, 0.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Beowulf\n",
"\n",
"https://en.wikipedia.org/wiki/Beowulf"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.545863Z",
"start_time": "2018-12-29T16:51:49.533766Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated lifetime in years: 26.10 to 39,702.\n"
]
}
],
"source": [
"print_lifetime(2018 - 1000, 0.95)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Print Books\n",
"\n",
"https://sfbook.com/the-evolution-of-the-book.htm\n",
"\n",
"https://en.wikipedia.org/wiki/Book#History"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.568138Z",
"start_time": "2018-12-29T16:51:49.557043Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated lifetime in years: 29.49 to 44,850.\n"
]
}
],
"source": [
"print_lifetime(2018 - 868, 0.95)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Doctor\n",
"\n",
"https://en.wikipedia.org/wiki/History_of_medicine"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.579687Z",
"start_time": "2018-12-29T16:51:49.575851Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated lifetime in years: 20.46 to 31,122.\n"
]
}
],
"source": [
"print_lifetime(2018 - 1220, 0.95)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Most Likely Lifetime: t_future == t_past"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.587428Z",
"start_time": "2018-12-29T16:51:49.582230Z"
}
},
"outputs": [],
"source": [
"from scipy.stats import norm\n",
"\n",
"x = np.logspace(-3, 3, num=1000)\n",
"y = norm.pdf(np.log10(x), loc=0, scale=0.6)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"ExecuteTime": {
"end_time": "2018-12-29T16:51:49.750790Z",
"start_time": "2018-12-29T16:51:49.589834Z"
}
},
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