Here are some 17 base π Mma timings: In[55]:= tim[RealDigits[17, \[Pi], 69]] During evaluation of In[55]:= 0.000157 Out[55]= {{1, 2, 0, 2, 2, 0, 0, 2, 1, 1, 0, 1, 0, 2, 0, 2, 3, 0, 0, 2, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 2, 0, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 0, 1, 2, 0, 0, 1, 2, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 0, 1}, 3} In[56]:= tim[RealDigits[17, \[Pi], 512];] During evaluation of In[56]:= 0.000851 In[57]:= tim[RealDigits[17, \[Pi], 1024];] During evaluation of In[57]:= 0.002248 In[58]:= tim[RealDigits[17, \[Pi], 2^11];] During evaluation of In[58]:= 0.006922 In[60]:= Table[Timing[RealDigits[17, \[Pi], 2^n]][[1]], {n, 12, 18}] Out[60]= {0.020484, 0.106171, 0.556247, 2.749796, 14.463928, \ 79.579053, 367.510315} --rwg Dan Asimov <dasimov@earthlink.net> wrote: The thing I mainly recall about Contact is that a message is sent by somehow *altering* the digits of pi. Keith Lynch>You are misremembering. There's no implication that pi had ever had a different value. (At least not in the paperback. Does anyone have a first edition hardback they can check?) Dave Dyer <ddyer@real-me.net> wrote: On the other hand, since PI has an infinite number of nonrepeating digits, such finite patterns MUST exist. Keith Lynch>That doesn't follow. Last I heard, nobody had ever proven pi normal. Normality, despite its name, is very weird. It's known that "nearly all" numbers are normal, i.e. non-normal numbers are of measure zero, but, to the best of my knowledge, nobody has ever proven any particular number to be normal. (Some numbers contrived for the purpose have been proven normal in one base, but not in all positive integer bases at once.) If pi *is* normal, as it probably is, then it's true that pi in binary must contain all possible bit strings, including copies of every book and DVD -- and the complete archives of this list, including posts that haven't been written yet. But of course all of these are buried enormously deep. Finding anything "interesting" in the first trillion digits would be, well, interesting. Also seehttp://www.netfunny.com/rhf/jokes/01/Jun/pi.html which is apparently the best known thing I've ever written. If pi is normal, does it necessarily contain ASCII text of a proof that pi is normal? :-) James Propp <jamespropp@gmail.com> wrote: I wonder whether Sagan was falling prey to the confusion about whether pi is a mathematical constant or a physical constant. Keith Lynch>Possibly. But he was obviously aware that it could be calculated, not just measured. A dimensioned physical constant such as the speed of light could be made to contain any desired message by a choice of how our system of units is set up. A dimensionless constant such as the fine structure constant or the proton-to-electron mass ratio would be the same number in any system of units. But those are of course measured, not calculated. They're both only known to about nine significant digits, and it would be an enormous amount of work to learn each additional digit, so there's no possibility of storing lengthy messages in them that we could read even if someone had write access to them. Anyhow, a message in a physical constant would merely prove that the writer is cleverer or more powerful than us, not that he is infinitely clever or powerful. A message in pi would prove the latter. Except that we could never rule out the possibility that our computers which "found" the message had been hacked. And that's a logically preferred hypothesis, since it would require only a finite amount of cleverness and power. Similarly for *any* alleged proof of a being's omniscience or omnipotence. JPropp>Personally, I think we should look for a message from God in the digits of seventeen. I mean, everyone says that after the decimal point there's just a whole lot of 0's --- but how far out have they looked? Keith Lynch>No, the digits of seventeen *in base pi*, 120.220021101020230020003... This of course never repeats or terminates. And I'd bet that nobody has ever checked it for hidden messages. :-) As an aside, half the time this list seems to be more about Mathematica than about math. To how many digits can Mathematica calculate 17 in base pi? (I calculated the above digits using plain old C. It took me all of ten minutes to write the code.)