[maro]

I think you are very confused. Current computer hardware relies on base 2. Base 2 is implemented physically as two STATES--high voltage and low voltage. From the applied math point of view, we are dealing with base 2, regardless of the implementation method. The intrinsic base 2 design of the hardware is used to represent numbers in hexadecimal, or base 16. From the machine level hex representation, other layers of software represent numbers to the users in base 10, which is the way most people represent numbers. So what? If our hardware was configured as base 4 using four distinguishable voltage states, nothing about our computer technology would change. Nothing that mathematicians do is base-dependent. That is a stunningly obvious statement--or so I thought before I read your comments. The set of integers does not assume any particular representation of integers. As far as your strange statement that there is a path from DOS to XP--do you mean that there is a progression , DOS1, DOS2, DOS3...DOSN, where DOSN is XP, where each element in the progression differs from the last by a few bitflip changes, and each intermediate program is a working program? If you do, you are quite wrong, and have never written any software.

[Nebullis]

It's okay to make a loosely based analogy of genetics using computer software. But it's invalid to turn that around by implying that the limitations of software apply to genetics as well. By definition a bitflip is a change in the value of a binary state. If the difference between DOS and Windows XP involved a change from binary to a quantum state computing, then it would be a difficult task indeed to find a bitflip path between the two. But such is not the case, the software is binary, and your tangental wordiness about how this is represented at the user interface is completely irrelevant.

In the world of genetics, mutations include crossovers, duplications, additions, and subtractions. Bitflip mutation programs include these as well. If you line up the binary code for DOS and Windows XP, you can bitflip your way from one to the other with great ease.

Your original point was that this is not true for a genetic code. Let's start with something very simple like two same sized-genomes from two different species. Can you imagine bitflip mutations that would transform one genome into the other?

[Southack]

"The intrinsic base 2 design of the hardware is used to represent numbers in hexadecimal, or base 16. ... So what? If our hardware was configured as base 4 using four distinguishable voltage states, nothing about our computer technology would change."

On the contrary, transistors and semiconductors work very well with two basic states (low voltage/ground and high voltage). To truly work at Base 4 would require hardware capable of operating effectively when FOUR voltage states were present, such as Ground, + 5 volts, + 10 volts, + 20 volts.

To imagine that NOTHING about our computer technology would change is to overlook the incredible hurdles facing multi-state electronics at their most fundamental level.

Now, can our Base 2 electronics be used to represent any Base and any state? Of course. Can they "easily" operate at their most fundamental levels in any Base or state? Not now.