<story><title>How to fit any dataset with a single parameter</title><url>https://arxiv.org/abs/1904.12320</url></story><parent_chain><item><author>cs702</author><text>Fun read. But if we allow ourselves as much precision as we need, we don&amp;#x27;t even need a parameter. Any &lt;i&gt;constant&lt;/i&gt; that is a &lt;i&gt;normal number&lt;/i&gt; should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset.&lt;p&gt;EDIT: I replaced &amp;quot;transcendental&amp;quot; with &amp;quot;normal&amp;quot; after reading  Scarblac&amp;#x27;s comment below: &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=28699622&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=28699622&lt;/a&gt; -- many important transcendental numbers, including π (Pi), are thought to be (but have not been proven to be!) normal.</text></item></parent_chain><comment><author>KerrickStaley</author><text>It&amp;#x27;s not true that any transcendental number would work. A transcendental number is a number which isn&amp;#x27;t the root of any polynomial with rational coefficients. This property doesn&amp;#x27;t imply that it contains all number sequences.&lt;p&gt;It hasn&amp;#x27;t even been proven that pi contains all number sequences.&lt;p&gt;See &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;math.stackexchange.com&amp;#x2F;questions&amp;#x2F;216343&amp;#x2F;does-pi-contain-all-possible-number-combinations&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;math.stackexchange.com&amp;#x2F;questions&amp;#x2F;216343&amp;#x2F;does-pi-cont...&lt;/a&gt; for more details.</text></comment>
<story><title>How to fit any dataset with a single parameter</title><url>https://arxiv.org/abs/1904.12320</url></story><parent_chain><item><author>cs702</author><text>Fun read. But if we allow ourselves as much precision as we need, we don&amp;#x27;t even need a parameter. Any &lt;i&gt;constant&lt;/i&gt; that is a &lt;i&gt;normal number&lt;/i&gt; should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset.&lt;p&gt;EDIT: I replaced &amp;quot;transcendental&amp;quot; with &amp;quot;normal&amp;quot; after reading  Scarblac&amp;#x27;s comment below: &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=28699622&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=28699622&lt;/a&gt; -- many important transcendental numbers, including π (Pi), are thought to be (but have not been proven to be!) normal.</text></item></parent_chain><comment><author>Scarblac</author><text>I don&amp;#x27;t believe just being transcendental is sufficient for that property.&lt;p&gt;E.g. I can&amp;#x27;t imagine that pi with all the &amp;#x27;1&amp;#x27; digits replaced by &amp;#x27;2&amp;#x27; isn&amp;#x27;t transcendental, but it clearly doesn&amp;#x27;t contain every sequence of digits.&lt;p&gt;I think you mean normal numbers.</text></comment>