I'm sure I've "bent" this a bit, but I *think* I remember from a Sci-Fi book, "Contact" (?), the idea that some ancient, incredibly advanced, space-faring culture was able to "bend" the universe just a tiny amount so that they could fudge the value of pi, way down there in the zillionth digits or so, so that they could imbed a message in pi itself...

Spot false dilemmas now, ask me how!
(If you're not on the edge, you're taking up too much room.)

Bert Bates wrote:I remember from a Sci-Fi book, "Contact" (?), the idea that some ancient, incredibly advanced, space-faring culture was able to "bend" the universe

Yep, it was Contact.
Although I think the message was that the trillionth through trillionth and 300 bits were all zero. Which is perfectly acceptable in a random number, no matter that the probability of it happening is vanishingly low.

Pat Farrell wrote:Although I think the message was that the trillionth through trillionth and 300 bits were all zero. Which is perfectly acceptable in a random number, no matter that the probability of it happening is vanishingly low.

Well, the probability (2^300 or 2^301 depending how I read the above) of it happening randomly on the trillionth to trillionth and 300 bits would be vanishingly low , but the probability (again 2^300 or 2^301 depending how I read the above) of it happening at some point is a virtual certainty.

In fact if the digits were truly random, the string of 300 (or 301) zeros would appear an infinite number of times. The problem is that the digits are not truly random; they just don't have a pattern.

Sure, any arbitrary pattern can be expected to appear eventually for a random (or sufficiently pseudo-random) sequence of digits. But in the book, they also make the point that they can calculate how likely it is that such a distinctive subsequence (a 'message') would appear within the first N digits - and then compare with the value of N at which a message is actually found. They'd only get excited if an interesting message showed up well before it was statistically likely to do so. Where "well before" means by many, many orders of magnitude.

In the book it's implied that the more advanced aliens are in the process of discovering a number of different messages, in various transcendental numbers (not just pi). They don't know what it all means - they're just excited to try to figure it out.

The end of the book has Ellie finding one apparent message in pi. It occurs at an unspecified position in the digits of pi - and in fact, it really shows up best in base 11. It appears as a long sequence of nothing but zeroes and ones. When rendered as a raster image (dimensions unspecified, but a square), it forms the image of a perfect circle. (Cue 'The Twilight Zone' theme music here.)

Bert Bates wrote:...the idea that some ancient, incredibly advanced, space-faring culture was able to "bend" the universe just a tiny amount so that they could fudge the value of pi, way down there in the zillionth digits or so, so that they could imbed a message in pi itself...

Well, this is where I had a problem with it really. The way it's described, it's got nothing to do with bending of the universe in an Einsteinian space-time sense. They're calculating pi in the classic Euclidian sense, using mathematical formulas that are independent of any actual space-time curvature. There are other aliens out there with the ability to warp space in various ways, true. But that would have no effect on the computed value of pi, which can be defined in purely mathematical terms. In relatively simple mathematical terms, compared to the complexity of the messages alluded to in Ellie's discussions with the aliens. To me, this seems to require a far greater suspension-of-disbelief than the idea that some entity could create an entire universe to specific physical parameters.

In other words, in my opinion, a god-entity might embed arbitrary messages in, say, the fine structure constant. Or various other physical constants (preferably the dimensionless ones). Create a whole universe to spec. Great. But in pi? Ummm, no. I don't buy it.

But it did make for a memorable idea.

Bert Bates
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Hey Mike,

I didn't say that I *believed* it, just that I thought it was an interesting idea.

In yet another display of my vanishing memory, I recall a book from several years back that discussed six(?) constants in physics that ALL have to be within certain tight tolerances, or the universe couldn't exist as it does now. What I recall is that the author's point was that it's pretty darned interesting that all six are in place here, and also that perhaps there are other universes in which some of these constants are a "bit off".

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Bert Bates wrote:Hey Mike,

I didn't say that I *believed* it, just that I thought it was an interesting idea.

Oh, sure, that's all I thought you meant. Sorry if it appeared otherwise. I thought it was interesting too.

In yet another display of my vanishing memory, I recall a book from several years back that discussed six(?) constants in physics that ALL have to be within certain tight tolerances, or the universe couldn't exist as it does now. What I recall is that the author's point was that it's pretty darned interesting that all six are in place here, and also that perhaps there are other universes in which some of these constants are a "bit off".
Sounds like Martin Rees, Just Six Numbers: The Deep Forces That Shape The Universe. The idea of other universes with other constants is common in string theory today - you may want to look at Leonard Susskind's The Cosmic Landscape: String Theory and the Illusion of Intelligent Design . I haven't read that one, but it looked interesting.

Bert Bates wrote:...the idea that some ancient, incredibly advanced, space-faring culture was able to "bend" the universe just a tiny amount so that they could fudge the value of pi, way down there in the zillionth digits or so, so that they could imbed a message in pi itself...

Well, this is where I had a problem with it really. The way it's described, it's got nothing to do with bending of the universe in an Einsteinian space-time sense. They're calculating pi in the classic Euclidian sense, using mathematical formulas that are independent of any actual space-time curvature. There are other aliens out there with the ability to warp space in various ways, true. But that would have no effect on the computed value of pi, which can be defined in purely mathematical terms. In relatively simple mathematical terms, compared to the complexity of the messages alluded to in Ellie's discussions with the aliens. To me, this seems to require a far greater suspension-of-disbelief than the idea that some entity could create an entire universe to specific physical parameters.

In other words, in my opinion, a god-entity might embed arbitrary messages in, say, the fine structure constant. Or various other physical constants (preferably the dimensionless ones). Create a whole universe to spec. Great. But in pi? Ummm, no. I don't buy it.

That movie had many other issues. It wasn't disbelief that made it a bad movie.

Um, we're talking about the book. I don't think the movie got into the stuff about pi. Anyway, the pi stuff is kind of a coda that can mostly be considered on its own. I don't remember lots of other stuff in there, but I remember the bit about pi.