https://machinelearning.subwiki.org/w/index.php?action=history&feed=atom&title=User%3AIssaRice%2FErgodicity
User:IssaRice/Ergodicity - Revision history
2026-10-23T22:05:15Z
Revision history for this page on the wiki
MediaWiki 1.41.2
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2895&oldid=prev
IssaRice at 04:05, 13 February 2020
2020-02-13T04:05:31Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 04:05, 13 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Line 11:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://www.greaterwrong.com/posts/gptXmhJxFiEwuPN98/meetup-notes-ole-peters-on-ergodicity</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://www.greaterwrong.com/posts/gptXmhJxFiEwuPN98/meetup-notes-ole-peters-on-ergodicity</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*** the point of my example is that there is an additive dynamic with positive growth rate, but where log-wealth utility doesn't take the bet. another question to ask is, is there an additive dynamic with negative growth rate where log-wealth utility ''does'' take the bet -- this seems to be impossible.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)? what if <math>a_n = (-1)^nn</math>?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)? what if <math>a_n = (-1)^nn</math>?</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2894&oldid=prev
IssaRice at 23:13, 12 February 2020
2020-02-12T23:13:34Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:13, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14">Line 14:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)? what if <math>a_n = (-1)^nn</math>?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)? what if <math>a_n = (-1)^nn</math>?</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* is maximizing time-average the same thing as maximizing growth rate? does one imply the other?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* is maximizing time-average the same thing as maximizing growth rate? does one imply the other?</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* is maximizing time-average the same as maximizing your wealth in the limit as time goes to infinity?</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2893&oldid=prev
IssaRice at 23:11, 12 February 2020
2020-02-12T23:11:17Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:11, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td>
<td colspan="2" class="diff-lineno">Line 13:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)? what if <math>a_n = (-1)^nn</math>?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)? what if <math>a_n = (-1)^nn</math>?</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* is maximizing time-average the same thing as maximizing growth rate? does one imply the other?</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2892&oldid=prev
IssaRice at 23:10, 12 February 2020
2020-02-12T23:10:17Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:10, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12">Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)?</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <math>a_n \to \infty</math>? if <math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)<ins style="font-weight: bold; text-decoration: none;">? what if <math>a_n = (-1)^nn</math></ins>?</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2891&oldid=prev
IssaRice at 23:09, 12 February 2020
2020-02-12T23:09:16Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:09, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12">Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if math>a_n \to \infty</math>? if math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)?</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if <ins style="font-weight: bold; text-decoration: none;"><</ins>math>a_n \to \infty</math>? if <ins style="font-weight: bold; text-decoration: none;"><</ins>math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)?</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2890&oldid=prev
IssaRice at 23:09, 12 February 2020
2020-02-12T23:09:00Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:09, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12">Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* understand the difference between <math>\lim_{n\to\infty} a_n</math> and <math>\lim_{n\to\infty} \frac1n\sum_{i=1}^n a_i</math>. What happens if <math>a_n \to a</math>? if math>a_n \to \infty</math>? if math>a_n</math> doesn't converge to any number but doesn't go off to infinity either (e.g. it oscillates between 1 and -1)?</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2889&oldid=prev
IssaRice at 23:06, 12 February 2020
2020-02-12T23:06:30Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:06, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Line 11:</td>
<td colspan="2" class="diff-lineno">Line 11:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://www.greaterwrong.com/posts/gptXmhJxFiEwuPN98/meetup-notes-ole-peters-on-ergodicity</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://www.greaterwrong.com/posts/gptXmhJxFiEwuPN98/meetup-notes-ole-peters-on-ergodicity</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">** code up models of both multiplicative and additive environments, where different organisms exist and can take or refuse bets. Here's my result https://gist.github.com/riceissa/08cdf34f999ff3cc84be8e84373e47e7 (there isn't any evolution going on here; it's just a single generation that consists of a large number of timesteps)</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2888&oldid=prev
IssaRice at 23:03, 12 February 2020
2020-02-12T23:03:26Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:03, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Here's my suggested path to learning about this, assuming you just know basic probability and statistics and calculus but you know nothing about ergodicity<del style="font-weight: bold; text-decoration: none;">:</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Here's my suggested path to learning about this, assuming you just know basic probability and statistics and calculus but you know nothing about ergodicity<ins style="font-weight: bold; text-decoration: none;">. It took me around two days to go through all the things here, but i think you can do it much quicker or much longer depending on your interests. (also i was fumbling around because i didn't know what i was doing, so you will save some time probably.)</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read http://squidarth.com/math/2018/11/27/ergodicity.html and http://squidarth.com/math/2019/04/13/ergodicity-animated.html</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read http://squidarth.com/math/2018/11/27/ergodicity.html and http://squidarth.com/math/2019/04/13/ergodicity-animated.html</div></td></tr>
</table>
IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2887&oldid=prev
IssaRice at 23:00, 12 February 2020
2020-02-12T23:00:41Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:00, 12 February 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8">Line 8:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf sections 1.1, 1.2, 2.1, 2.2, 2.3, 2.4, 2.5. something like that.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf sections 1.1, 1.2, 2.1, 2.2, 2.3, 2.4, 2.5. something like that.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2011.0065</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2011.0065</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">** code up a model of the iterated st petersburg game and play around with it. My own result was https://gist.github.com/riceissa/f0679ff2f032ca16d46ba539e40b6623</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://www.greaterwrong.com/posts/gptXmhJxFiEwuPN98/meetup-notes-ole-peters-on-ergodicity</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://www.greaterwrong.com/posts/gptXmhJxFiEwuPN98/meetup-notes-ole-peters-on-ergodicity</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** don't miss comments by abram demski and me</div></td></tr>
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IssaRice
https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Ergodicity&diff=2886&oldid=prev
IssaRice at 22:57, 12 February 2020
2020-02-12T22:57:17Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:57, 12 February 2020</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Really understand the 1.5x/0.6x game</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Really understand the 1.5x/0.6x game</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Try to formalize the game using random variables</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Try to formalize the game using random variables</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>** Come up with a formal expression for the time-average winnings vs ensemble winnings. I think you come up with something like <math>\sum_{k=0}^n \binom nk 1.5^k 0.6^{n-k} \frac1{2^n}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>** Come up with a formal expression for the time-average winnings vs ensemble winnings. I think you come up with something like <math>\sum_{k=0}^n \binom nk 1.5^k 0.6^{n-k} \frac1{2^n}</math><ins style="font-weight: bold; text-decoration: none;">. Can you prove this is always greater than 1?</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** figure out what percentage of flips need to be heads in order for you to have positive winnings. you want <math>1.5^k 0.6^{n-k} > 1</math> so the break-even value of k is <math>k = -n\log0.6/\log(1.5/0.6)</math> so the fraction of heads is <math>k/n \approx 0.557</math>. Understand that by law of large numbers, your fraction of heads will be super close to 0.5 in the long run, so you will almost never get anywhere close to having 56% of your flips be heads, so you almost certainly lose.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** figure out what percentage of flips need to be heads in order for you to have positive winnings. you want <math>1.5^k 0.6^{n-k} > 1</math> so the break-even value of k is <math>k = -n\log0.6/\log(1.5/0.6)</math> so the fraction of heads is <math>k/n \approx 0.557</math>. Understand that by law of large numbers, your fraction of heads will be super close to 0.5 in the long run, so you will almost never get anywhere close to having 56% of your flips be heads, so you almost certainly lose.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf sections 1.1, 1.2, 2.1, 2.2, 2.3, 2.4, 2.5. something like that.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* read https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf sections 1.1, 1.2, 2.1, 2.2, 2.3, 2.4, 2.5. something like that.</div></td></tr>
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IssaRice