Wednesday, July 15, 2009
On Infinite Division and Codes in DNA
Snippets from the June 2009 edition of BBC Focus magazine...
'In 1924, two Polish mathematicians proved that a solid ball can be cut into pieces, which, when rearranged, form not only the original ball, but an exact copy as well. The proof of this amaizing result, called the Banach-Tarski paradox, assumes it's possible to cut things up indefinitely finely, which isn't really possible.' p. 48.
In other words, the assumption that a concrete object is composed of an actually infinite number of discrete parts leads to the conclusion that you can cut up 1 ball and end up with 2 balls identical to the original ball. Since this is plainly ridiculous, this is a reductio of the assumption of infinite divisibility. This would have application as an counter-example to the actual infinity of the past in discussion of the kalam cosmological argument (in addition to the now standard Hilbert's Hotel example).
Also...
'Deinococcus radiodurans, is the most radiation-resistant organism in the world... the fact that its DNA is packed in a tight ring and that the cells contain high levels of manganese seem to be contributing factors... Scientists from the Pacific Northwest national Laboratory in the US have even argued that it could be used to store valuable information in the event of a nuclear catastrophe. To prove it, they encoded the words It's a Small World into its DNA. A hundred bacterial generations later, the words were still there.'
Any post nuclear holocaust scientist who stumbled across this particular organism and discovered that its DNA encoded the sentence It's a Small World in its DNA might be tempted to attribute this fact to intelligent design. But, of course (and note the sarcastic tone here), making such a design inference a) would not be science, b) would explain nothing (because it leaves the origin of the designer unexplained), c) would be unconstitutional in America, d) would mean he was trying to take us back to the dark ages and establish some sort of a theocracy, etc...
'In 1924, two Polish mathematicians proved that a solid ball can be cut into pieces, which, when rearranged, form not only the original ball, but an exact copy as well. The proof of this amaizing result, called the Banach-Tarski paradox, assumes it's possible to cut things up indefinitely finely, which isn't really possible.' p. 48.
In other words, the assumption that a concrete object is composed of an actually infinite number of discrete parts leads to the conclusion that you can cut up 1 ball and end up with 2 balls identical to the original ball. Since this is plainly ridiculous, this is a reductio of the assumption of infinite divisibility. This would have application as an counter-example to the actual infinity of the past in discussion of the kalam cosmological argument (in addition to the now standard Hilbert's Hotel example).
Also...
'Deinococcus radiodurans, is the most radiation-resistant organism in the world... the fact that its DNA is packed in a tight ring and that the cells contain high levels of manganese seem to be contributing factors... Scientists from the Pacific Northwest national Laboratory in the US have even argued that it could be used to store valuable information in the event of a nuclear catastrophe. To prove it, they encoded the words It's a Small World into its DNA. A hundred bacterial generations later, the words were still there.'
Any post nuclear holocaust scientist who stumbled across this particular organism and discovered that its DNA encoded the sentence It's a Small World in its DNA might be tempted to attribute this fact to intelligent design. But, of course (and note the sarcastic tone here), making such a design inference a) would not be science, b) would explain nothing (because it leaves the origin of the designer unexplained), c) would be unconstitutional in America, d) would mean he was trying to take us back to the dark ages and establish some sort of a theocracy, etc...
