Re: Wrapping my mind around the neutral gap "problem".

On 18 Jan 2006 10:06:04 -0800, "The Last Conformist"
<andreasj@xxxxxxxxx> wrote:

>
>r norman wrote:
>> On Wed, 18 Jan 2006 10:11:21 -0700, dkomo <dkomo871@xxxxxxxxxxx>
>> wrote:
>>
>> >Frank Sullivan wrote:
>>
>> >> 3. "Sequence Space" can be thought of as a 2D plane, with all of the
>> >> possible sequence combinations arranged in some sort of graph.
>> >
>> >A sequence space is not a plane. It's an n dimensional hyperspace.
>> >Each nucleotide in a gene of length n has its own axis, with the letters
>> >G, C, A and T being values along that axis. A particular gene therefore
>> >is a single point in that hyperspace. The space consists of 4^n points.
>> >
>>
>> There is no reason to think of dimensionality and coordinate axes in
>> the sequence space. It is simply a set of points, each one
>> corresponding to a unique string of length n on a 4 character
>> alphabet. Two points are connected by a line if they differ in only
>> one location. That forms a connected graph. How you choose to draw
>> or embed that graph in an n-dimensional Euclidean space is quite
>> irrelevant.
>
>Is this supposed to be a defense of the claim one can think of it as 2D
>plane? (non-rhetorical question).

I am not defending anything in particular, just stating the
mathematical facts. If you draw the set of points in two dimensions,
the lines connecting them will intersect but you just ignore that.
The space is merely a set of points with lines connecting them.

You seem to be thinking that, in two dimensions, the x and y
coordinate axes must have some meaning. Even in n-dimensions, one for
each nucleotide, the axes have no meaning. Somebody, I don't remember
just who, said that each axis would have four points corresponding to
A, G, C, and T but that doesn't make sense mathematically. And there
is no rhyme or reason to ordering those four points in any way along a
single axis.

It is just distinct points with connecting lines. That is enough for
graph theory.


.

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