The question Dyson was responding to (What do you believe is true even though you cannot prove it?) is similar to this very interesting thread:<p>What's the craziest or weirdest thing in your field that you suspect is true but is not yet supported fully by data?<p><a href="http://www.reddit.com/r/AskReddit/comments/1kqtgy/serious_scientists_of_reddit_whats_craziest_or/" rel="nofollow">http://www.reddit.com/r/AskReddit/comments/1kqtgy/serious_sc...</a>
<i>"But the assumption that digits in a big power of two occur at random"</i><p>That may not be the best of assumptions, but it doesn't hurt his argument. Benson's law learns us that the initial digits of 2^n tend to be low (empirically, but in this case, also mathematically. See <a href="http://www.johnderbyshire.com/Opinions/Diaries/Puzzles/2004-09.html" rel="nofollow">http://www.johnderbyshire.com/Opinions/Diaries/Puzzles/2004-...</a>). Less than 8% of powers of two begins with the digit '5'. Also, fewer powers of five begin with an even digit than with an odd digit.<p>The argument that there <i>is</i> no deep mathematical reason why it has to be true, though, I find more belief than math. We don't know such a reason, but that doesn't mean it doesn't exist.