<story><title>Is Probability Real?</title><url>https://www.arameb.com/blog/2020/11/22/probability</url></story><parent_chain><item><author>st1x7</author><text>&amp;gt; the probability of that coin toss being 50% does not talk about the coin; it talks about you, and about your partial knowledge of the universe.&lt;p&gt;But it does talk about the coin - a weighted coin would have a different probability. Same in the example with the white&amp;#x2F;black balls - if they weren&amp;#x27;t 5 white and 5 black but 6 white and 4 black, the probability you would assign to the top one would be different. Again, the probability is a way to describe the balls themselves, not just our knowledge.&lt;p&gt;I get the general idea of representing probability as uncertainty and partial knowledge but your statements strike me as just straight up incorrect.</text></item><item><author>enriquto</author><text>A simple sentence that I&amp;#x27;ve found useful for pedagogy:  &amp;quot;the probability of that coin toss being 50% does not talk about the coin; it talks about &lt;i&gt;you&lt;/i&gt;, and about your partial knowledge of the universe.&amp;quot;&lt;p&gt;You can add:  &amp;quot;The coin toss itself is deterministic and the result can be computed if you know the  initial position and speed.&amp;quot;  They will inevitably bother you about the physical impossibility to measure the starting position and speed exactly, and then you say &amp;quot;ok, forget about the coin.  You have 5 white and 5 black balls inside this opaque cylinder.  What&amp;#x27;s the probability that the top ball is white?  This does not talk about the balls (the color of the top one is already determined) but about your partial knowledge of them&amp;quot;.&lt;p&gt;(EDIT: formatting)</text></item><item><author>EbTech</author><text>Since this topic isn&amp;#x27;t so well-known, I wrote the case arguing that frequentist interpretations don&amp;#x27;t work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!</text></item></parent_chain><comment><author>samatman</author><text>Thought experiment: you&amp;#x27;re presented a jar, and offered the chance to bet ten bucks on drawing a white ball. You know nothing about the content of the jar. What odds would you take?&lt;p&gt;Now, you see ten white balls get added, then are blinded while other balls are added (maybe). You estimate the jar can&amp;#x27;t hold more than about a hundred balls. What odds would you take?&lt;p&gt;Now, you see ten white and ten black get put in, and saw it was empty before. What odds?&lt;p&gt;Now, you see ten white and fifty black, but the whites are larger, and you get to draw a ball. What odds?&lt;p&gt;The difference between the second-to-last and the last is the missing information we usually think of when we talk about randomness being missing information.&lt;p&gt;And you&amp;#x27;ll see that the previous scenarios don&amp;#x27;t change anything about that.</text></comment>
<story><title>Is Probability Real?</title><url>https://www.arameb.com/blog/2020/11/22/probability</url></story><parent_chain><item><author>st1x7</author><text>&amp;gt; the probability of that coin toss being 50% does not talk about the coin; it talks about you, and about your partial knowledge of the universe.&lt;p&gt;But it does talk about the coin - a weighted coin would have a different probability. Same in the example with the white&amp;#x2F;black balls - if they weren&amp;#x27;t 5 white and 5 black but 6 white and 4 black, the probability you would assign to the top one would be different. Again, the probability is a way to describe the balls themselves, not just our knowledge.&lt;p&gt;I get the general idea of representing probability as uncertainty and partial knowledge but your statements strike me as just straight up incorrect.</text></item><item><author>enriquto</author><text>A simple sentence that I&amp;#x27;ve found useful for pedagogy:  &amp;quot;the probability of that coin toss being 50% does not talk about the coin; it talks about &lt;i&gt;you&lt;/i&gt;, and about your partial knowledge of the universe.&amp;quot;&lt;p&gt;You can add:  &amp;quot;The coin toss itself is deterministic and the result can be computed if you know the  initial position and speed.&amp;quot;  They will inevitably bother you about the physical impossibility to measure the starting position and speed exactly, and then you say &amp;quot;ok, forget about the coin.  You have 5 white and 5 black balls inside this opaque cylinder.  What&amp;#x27;s the probability that the top ball is white?  This does not talk about the balls (the color of the top one is already determined) but about your partial knowledge of them&amp;quot;.&lt;p&gt;(EDIT: formatting)</text></item><item><author>EbTech</author><text>Since this topic isn&amp;#x27;t so well-known, I wrote the case arguing that frequentist interpretations don&amp;#x27;t work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!</text></item></parent_chain><comment><author>e12e</author><text>I like the balls in container better - the mechanics of determinism is more obvious - and the contrast between perfect and partial knowledge.&lt;p&gt;And there&amp;#x27;s another interesting point - you could view &amp;quot;there&amp;#x27;s five white and five black balls&amp;quot; as your model. If in reality, there&amp;#x27;s one white ball and nine black - then your math is still right, but your model is wrong.&lt;p&gt;If you do experiments with the wrong model (assuming 50&amp;#x2F;50, getting samples from 1&amp;#x2F;10) - your best conclusion would be the model is wrong.&lt;p&gt;But for many settings, you&amp;#x27;d end up declaring your container or the hand used to pull out balls has magical powers. (and to borrow from Douglas Adams go on to prove that black is white, and get killed in the next zebra crossing).</text></comment>