Has anyone tried using any pattern recognition or decryption algorithms on pi (3.14…)?
Newsweek says
So I’d certainly guess they’ve tried as many algoriths as they could find. The prize for figuring that there IS a pattern woud be a coronation as King of Geeks.
or algorithms.
Well, depends what you mean by pattern. There are now algorithms for producing the k’th hexadecimal digit of pi without knowing all the intervening digits. Sadly, it doesn’t work for base 10, and as far as I know a base 10 equivalent has not been found.
Nevertheless, this constitutes a ‘pattern’ in the sense that you can work out what the next digit is.
In fact, most means of working out pi to any number of decimal places constitutes ‘a pattern’ in the sense that it is mechanically deterministic that you can work out further and further digits, regardless of numeric base.
So what is meant by ‘pattern’? Something ‘pretty’? (What is ‘pretty’?) Something that ‘repeats’?
How? Link/brief description please.
I was just wondering what would happen if someone used a code breaking algorithm on it, and if anyone has ever tried it.
The numbers “following 3.141592…” do NOT occur randomly. Randomly means that nobody can tell which is coming in any particular position, and that is definitely not the case.
What is true is that the succession of numbers does not seem to follow any particular order, or pattern, and in that respect Pi is not unique: there are plenty (infinite) of numbers with that characteristic.
Numbers that have a “pattern” belong to the RATIONAL set of numbers (those that can be expressed as the ratio of to integers), and those that not are IRRATIONAL numbers (they can’t). Both sets comprise the REALS.
The media’s use of random seems to be here: are the digits in pi’s expansion normally distributed?
Pi good. Like pi. More pi, please.
What?
Except, of course, that [symbol]p[/symbol] is irrational, and it has a pattern (just not a simple one).
There are various notions of having a pattern. There are rationals, and constructibles, and algebraics, and computables, and then some.
The current claim is that [symbol]p[/symbol] is absolutely normal. This means that, in any base b, the number of times you see a particular sequence of length k will approach 1/b[sup]k[/sup].
So in the base 10 representation of [symbol]p[/symbol], as you keep looking at more digits, you would expect to see, say, 314 about 1 in every 100 sequences of three digits–assuming that [symbol]p[/symbol] is absolutely normal.
Here’s something interesting: we know that most real numbers are absolutely normal, but we don’t know of any specific ones that are.
We have had this discussion several times and it boils down to semantics. Tell me what you mean by random and I’ll tell you if pi is random.
Imagine this: I have a device, a random number generator, and it generates digits from 0 to 9 randomly, all with equal probability. We start the machine and start recording the digits: 2458623571245896321458795632153325687441256368421691587736919725483. . . . . We can say the series was random as it came out as we could not predict the next digit. But now that we have it, is it “random” any more? After all, we do know what digit comes after ech previous digit. Now it is not random any more. In the same way, pi is random in the measure that it is unknown.
btw, when we say that some quantity is distributed “at random”, that’s generally taken to mean that it’s uniformly distributed over some set.
.12345678910111213141516. . . has a pattern, but it’s not a rational number.
The idea is mentioned in Carl Sagan’s novel Contact; the unknown, long-gone, all-powerful aliens who created the transit system also manipulated the universe in such a way as to leave a message encoded in the decimal digits of pi.
I would hope they were uniformly distributed, not Normally.
Ultrafilter declared:
Indeed, we know that almost all real numbers are normal. However, we know that
0.12345678910111213…
is normal, though the proof is harder than one might suspect.
One reason the Chudnovsky brothers gave for building a computer to find the first billion or so digits of pi was to see if any pattern emerged. So far, no one has seen any. And yes it seems to be normally distributed so the sequence 314 will occur once every 1000 (not 100) times you look at three consecutive digits. And a sequence of a 1000 consecutives 0s will occur about once in every 10^1000 consecutive digits. That said, it is not random in the formal sense since you can transmit as many digits as you like in a couple handsful of words (“Compute the first 1,000,000 digits of pi.”)
Just for the record, rationals are characterized by having indefinitely repeating sequence of digits. Irrationals are the other kind. Quadratic irrationals are characterized by having indefinitely repeating continued fractions, which have the form
n + 1
--------------------------------------
m + 1
----------------------------
p + 1
----------------------
q + .
.
.
AFAIK, there is no such way of characterizing higher degree algebraic numbers.
AAgh. The editor completely screwed up my nice continued fraction. I give up, but what was posted made no sense.
Um… whoops!
I thought it odd that pi has many occurrences of aba where a and b are digits - in other words, a digit repeats with something else thrown in between.
3.14159265358979323846
1 then 5 then 9 then 3
or at least it looks that way in the beginning.
I asked Mathematica for Pi to maybe 100,000 places, then tested for this - and tested for other quantities of intervening digits besides 1. But no pattern - it’s just that way in the beginning.
Mangetout: Thats what I was thinking when I posted this.
Originally posted by William_Ashbless
Once again, how? Link/brief description please.
BTW in my 12th grade math class I discovered a repeating pattern in pi. My teacher had pi to the 500th digit on the top of the walls, going all around the room. I forgot what I did, but it was a repeating pattern. I showed my teacher, she looked it over and said that I had found a pattern. Unfortunatly I discovered that the pattern was there because the posters were the mass produced kind and the teacher had put them up wrong with no overlapping, but they were supposed to be overlapped by one number on each side.