<story><title>The bunkbed conjecture is false</title><url>https://igorpak.wordpress.com/2024/10/01/the-bunkbed-conjecture-is-false/</url></story><parent_chain></parent_chain><comment><author>tsimionescu</author><text>This is an interesting case of a conjecture holding true for small objects but breaking down for huge ones, without specifically adding that size in somehow.&lt;p&gt;Sometimes we tend to have this intuition that if a rule applies to all low numbers, than it must apply to all numbers, that there can&amp;#x27;t be some huge number after which it breaks down (unless of course it explicitly includes that huge number, such as the rule &amp;quot;all numbers are smaller than a billion billion billion&amp;quot;).&lt;p&gt;This is such a powerful intuition, even though it&amp;#x27;s obviously wrong, that rules that break it are even seen as a problem. For example there is the so-called &amp;quot;hierarchy problem&amp;quot; in physics, which states something like &amp;quot;there is no reason why the weak force is so much stronger than gravity&amp;quot;. As if 2 times as strong is somehow fundamentally different than it being 10^24 times as strong from a mathematical perspective. And this has ended up being called a major problem with the standard model, even though it&amp;#x27;s completely normal from a mathematical perspective.</text></comment>
<story><title>The bunkbed conjecture is false</title><url>https://igorpak.wordpress.com/2024/10/01/the-bunkbed-conjecture-is-false/</url></story><parent_chain></parent_chain><comment><author>andrewflnr</author><text>While I wouldn&amp;#x27;t accept a probabilistic &amp;quot;proof&amp;quot; of a theorem like this, it does seem clear to me that those results are important for directing the focus of research, especially in cases where they go against intuition. Given that most of the math community was barking up the wrong tree, even if these guys only had the probabilistic result, surely that would eventually help someone find the right proof? That&amp;#x27;s at least worth publishing as a letter or something, right?&lt;p&gt;Ed: reflecting on my first sentence, I guess I tend to think of proofs as being at least as important a product of math as the raw truth of a statement. A fact is a fact, but a proof represents (some level of) understanding, and that&amp;#x27;s the good stuff. Experiments are potentially good science, but usually not math.</text></comment>