Posted on 04/02/2013 6:57:24 PM PDT by BenLurkin
Well, the same is true for any irrational number, and there are an infinite number of irrational numbers between any two rational numbers. The exceptional thing about our DNA, though, is not that it contains information, but that it contains systematically organized information structures. The decimal form of an irrational number, though, doesn’t provide much if any useable information, much less anything like the purposeful structuring of a DNA code. The infinite decimals are simply an artifact of performing a mathematical operation in a number system unable to render the result with precision. If we use fractions, they all vanish into thin air :)
I always felt that there being four letters in the name of God, and four letters in the genetic “alphabet” was no coincidence.
Very interesting!
That was the plot of one of the Star Trek Movies.
Yes, and this massively sophisticated molecular machinery simply arose spontaneously after bombarding mud puddles with lightening for a few hundred million years.
Just like a Panasonic CF-53 laptop computer with Windows 7 would arise spontaneously if we filled a beaker full of the elemental powders from which it is formed, put some sea water in,and then bombarded the laptop soup in the beaker with lightening for a few hundred million years. Or maybe, we initially only get a chip to form in the beaker and the chip eventually EVOLVED all by itself into the laptop (with operating system) after being bombarded by cosmic rays for a long time.
Right?
That’s the plot from and old Star Trek TNG episode.
Star Trek TNG actually. Picard manages to retrieve and decode the message.
Yep.... Seriously... a person has to be a complete idiot not to recognize intelligent design.
“On a related note, Prometheus was such a disappointment. It held so much promise only to fall apart. And I had been really looking forward to it as well! “
Prometheus could have been/should have been mind-blowingly fantastic. Instead, it was little more than a pathetic, hackneyed, shoot-em-up replay of the original Alien script, not even really a prequel.
Prometheus was a complete failure from an intellectual or philosophical point of view.
introns are the comments of the genetic code.
Exactly.
I remember a Science Fiction story with this theme. Not only were the protagonists able to determine that human DNA contained a coded message, they also discovered that the message had already been delivered.
“It’s the fifth day, and I’m bored.”
I hear ya but I disagree. There is a Star Trek continuity. It’s pretty consistent and holds together.
What I think is a travesty is the last Star Trek movie where they went back to the early days of Kirk at the Academy and they just changed the future. And wiped out the entire continuity. It was just wrong.
The young Kirk movie was a travesty.
(Do like the new Uhura though...)
I bought that years ago when I was in grad school, and in line with a lot of critiques, I think, I found it really shook up my thinking, even if I wasn’t willing to go the whole way with his thesis. I was particularly impressed with his discussion of hearing voices, and his assertion of how common it was. This led me to make certain inquiries, as he more or less suggested IIRC, and it was as he said. So you know, if you hear a kid say, “The puppy said ‘Hi’ !”, ... believe it.
I can’t find it right now, of course ... “Maybe I loaned it to somebody.”
It is actually an open problem whether every finite sequence of digits occurs in the decimal expansion of pi (and likewise open for expansions in any other base).
But it is most assuredly not the case that all irrational numbers have every sequence of digits, for instance the number with decimal expansion
.54544544454444544444....
there being n 4’s between the n-th 5 and the (n+1)-st 5 is irrational, but only contains a very restricted set of finite digit sequences — in particular having only 4’s and 5’s as digits, but even more restricted than that: any sequence with a single 5 and any number of 4’s before and after will occur, but once two 5’s occur (necessarily non-adjacent) the first can be preceded by at most one fewer 4’s than occur between the left-most 5 and the next 5, the number of 4’s between successive 5’s must increase by one and the number of 4’s after the right-most 5 must be at most one more than the number of 4’s between the two right-most 5’s.
Actually, like my example, pi is a very tame irrational number: though less obviously so than for my example, its decimal expansion can, in principle, be generated by running an algorithm. Like the rational numbers, the set of real numbers, both rational and irrational, whose decimal (or binary or base b) expansion can be generated by an algorithm is countable, so there are uncountably many “non-algorithmic” irrationals (my favorite being the “oracular number for FORTRAN”, defined by listing all valid FORTRAN programs ordered by total number of symbols and within each number in lexicographic order by the standard ordering on ASCII symbols, the i-th digit right of the binary point is 1 if the i-th program would halt in finite time when run on an machine with infinite memory, and 0 otherwise). That, and its friends, other binary, decimal and base b oracular numbers for various and sundry ways of describing algorithms, are some of the very few non-algorithmic irrationals one can describe at all.
I assume you are alluding to CONTINUED fractions? Many irrationals have a simple repetitive continued fraction representation, and even 'e' has a regular pattern, even though it doesn't actually repeat. And of course any finite continued fraction is a simple fraction, and can be represented by a repeating decimal.
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