{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dieses Notebook enthält die Begleitrechnungen zum Vortrag:\n",
    "\n",
    "“Die Grenzen des Wachstums – Nachhaltige Entwicklung aus systemdynamischer Perspektive.”, im Rahmen der Umweltringvorlesung https://tuuwi.de/vorlesungenseminare/umweltbewegungen/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ipydex.displaytools extension is already loaded. To reload it, use:\n",
      "  %reload_ext ipydex.displaytools\n"
     ]
    }
   ],
   "source": [
    "%load_ext ipydex.displaytools\n",
    "from numpy import log, exp, linspace\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1.02\n",
      "2 1.0404\n",
      "3 1.0612\n",
      "10 1.219\n",
      "20 1.4859\n",
      "40 2.208\n"
     ]
    }
   ],
   "source": [
    "# Zinsrechnung\n",
    "K0 = 100\n",
    "p = .02\n",
    "\n",
    "for n in [1, 2, 3, 10, 20, 40]:\n",
    "    print(n, round((1 + p)**n, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "T_verdopplung_2 := 35.002788781146499"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "T_verdopplung_5 := 9.0064683420005878"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.08**40  := 21.724521496799902"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "___\n"
     ]
    }
   ],
   "source": [
    "\n",
    "T_verdopplung_2 = log(2) / log(1.02) ##:\n",
    "T_verdopplung_5 = log(2) / log(1.08) ##:\n",
    "\n",
    "\n",
    "1.08**40 ##:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Schachbrett-Märchen\n",
    "\n",
    "Links:\n",
    "* https://de.wikipedia.org/wiki/Sissa_ibn_Dahir\n",
    "* http://www.uni-weimar.de/projekte/oil/hw03_reis2.html → 30mg / Korn\n",
    "* https://de.statista.com/statistik/daten/studie/180685/umfrage/produktionsmenge-von-reis-weltweit-seit-2008-09/\n",
    "    *  Im Erntejahr 2017/2018 wurden laut dieser Prognose aus dem Herbst 2017 weltweit rund 483 Millionen Tonnen Reis erzeugt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "N_exakt := 9223372036854775808"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "N_approx := 8000000000000000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    }
   ],
   "source": [
    "# Körner auf dem letzten Feld\n",
    "N_exakt = 2**63 ##:\n",
    "N_approx = 1000**6 * 2**3 ##:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mass_in_kg := 2.4e+17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "mass_in_t := 240000000000000.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "mass_bez_welternte := 496894.4099378882"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    }
   ],
   "source": [
    "mass_in_kg = N_approx*30e-3 ##:\n",
    "mass_in_t = mass_in_kg / 1000 ##:\n",
    "mass_bez_welternte = mass_in_t / (483e6) ##:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"Josephspfennig\"\n",
    "Links: \n",
    "\n",
    "* https://de.wikipedia.org/wiki/Josephspfennig\n",
    "* https://www.goldpreis.de/\n",
    "* https://de.wikipedia.org/wiki/Erdmasse\n",
    "* http://www.bpb.de/nachschlagen/zahlen-und-fakten/globalisierung/52655/welt-bruttoinlandsprodukt\n",
    "    *  Welt-BIP ca. 8000 Milliarden US-Dollar (extrapoliert)\n",
    "* https://www.finanzen.net/devisen/dollarkurs: 1.22 Dollar/Euro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "K2 := 2265408968753215.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "K2 / 1e15  := 2.2654089687532153"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "___\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "K2/BIP_Welt  := 28.317612109415194"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "___\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "K4 := 2.3619935369839827e+32"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    }
   ],
   "source": [
    "K2 = .01*(1+.02)**2018 ##:\n",
    "\n",
    "# in Billiarden (Millionen Milliarden)\n",
    "\n",
    "K2 / 1e15 ##:\n",
    "\n",
    "\n",
    "# Bezogen auf das BIP der Welt\n",
    "BIP_Welt = 80e12\n",
    "K2/BIP_Welt ##:\n",
    "\n",
    "\n",
    "K4 = .01*(1+.04)**2018 ##:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "K_in_kg_gold := 7.346508498081281e+27"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Erdmasse := 6e+24"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1224.418083013547"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Umrechnung in Gold\n",
    "Goldpreis_pro_unze = 1000 # Durchschnitt von 2008-2018: ca. 1000 Euro\n",
    "Masse_unze = .031103 # Feinunze wiegt 31.103g\n",
    "\n",
    "K_in_kg_gold = K4 / Goldpreis_pro_unze * Masse_unze ##:\n",
    "\n",
    "Erdmasse = 6e24 ##:\n",
    "\n",
    "K_in_kg_gold / Erdmasse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Grafik Exponentialfunktion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f746c58db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tt = linspace(0, 40, 1000)\n",
    "xx1 = 100*1.02**tt\n",
    "xx2 = 100*1.08**tt\n",
    "\n",
    "plt.rcParams['font.size'] = 16\n",
    "plt.rcParams['axes.labelsize'] = 16\n",
    "plt.rcParams['figure.subplot.top'] = .995\n",
    "plt.rcParams['figure.subplot.bottom'] = .14\n",
    "\n",
    "plt.plot(tt, xx1, lw=3)\n",
    "plt.plot(tt, tt*0+xx1[0], 'k--', lw=0.5)\n",
    "plt.axis([0, 41, 0, 230])\n",
    "plt.xlabel('$t$ in y')\n",
    "plt.savefig('expfkt1.pdf')\n",
    "plt.plot(tt, xx2, lw=3)\n",
    "plt.axis([0, 41, 0, 2300])\n",
    "plt.savefig('expfkt2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.125"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}