The authors correctly calculate the probability distribution of tip
displacements under the assumption of classical spring constants in
each dimension. This approximation is appropriate for a system
involving stiff bonds and moderately large displacements. For another
system, such as a biopolymer, the entropic contribution could be more
important.
Assuming that passage through the transition state of the intended
reaction is rapid compared with the classical spring-mass vibration
period of the tool arm, the probability of the tool being in a position
unacceptably far from the intended position when the reaction is
intended to take place, as estimated by this method, gives an estimated
failure probability per operation. I don't think the authors intended
this calculation as anything more than an estimate to show that under
reasonable assumptions the error rate due to mislocation can be kept
very small.
Toby Kelsey wrote:
> I have just read "Design and Analysis of a Molecular Tool for Carbon Transfer
> in Mechanosynthesis"
> by Allis and Drexler (J. Comput. Theor. Nanosci. 2, 4555, 2005), available
> online at
> <http://e-drexler.com/d/05/00/DC10C-mechanosynthesis.pdf>, and it seem to me
> that there is a
> basic error in their calculations. In section 4.4 they compute the
probability
> of thermal
> displacement of the tool tip causing errors. To do this they use Hooke's Law
> with a calculated
> spring constant to determine the energy of a displaced position, and apply the
> Arrhenius equation
> to calculate the probability of a displacement sufficient to cause an error
> occurring compared to
> the undisplaced position, which they determine is 10e-24 for a displacement of
> 0.15 nm at T=300K.
>
> This is fundamentally wrong. The calculation effectively compares one
displaced
> configuration with
> one unique undisplaced one and determines their relative probability, but in
> reality the displaced
> configurations hugely outnumber the undisplaced. Conservatively assuming the
> tool requires 1000
> atoms, there are 3000 degrees of freedom and an enormous number of possible
> configurations, the
> vast majority of which have displaced tips. The authors completely forget the
> configurational
> entropy and this renders their numbers nonsensical and misleading.
>
> To add to their mistake, they then arbitrarily assume the calculated
> probability represents the
> probability of the error "per operation". It would be a stretch to infer the
> more reasonable
> position that this could be the probability per vibration. In fact the
> calculation takes no
> account of time, which is another measure of how bogus it is.
>
> I am surprised that the referees missed these errors.
>
> To calculate the actual probability of thermally caused errors would require
> molecular dynamics
> or Monte Carlo simulations, but the authors do not even estimate the RMS
> displacement and do not
> appear to understand the simple statistics which invalidate their approach.
>
> For calculating the spring constant they reference Drexler's Nanosystems book
> (1992). I would
> not be surprised if the same basic error infects that as well.
>
> Perhaps the authors could respond in this newsgroup, if they have something to
> add.
>
> Toby
.
Error in Allis and Drexler paper ... In section 4.4 they compute the probability...displacement of the tool tip causing errors. ... The calculation effectively compares one displaced ...configurations hugely outnumber the undisplaced. ... (sci.nanotech)
Re: What is Intelligent Design? ...probability of given object or 'information system' as they like to ... I have never seen an advocate of ID propose a calculation... a given object as a product of evolution....randomly assembling entirely new genomes from scratch? ... (talk.origins)
Re: What is Intelligent Design? ...probability of given object or 'information system' as they like to ... characteristics of a rock to determine if a rock was chipped for use as ... I have never seen an advocate of ID propose a calculation... a given object as a product of evolution.... (talk.origins)
Re: Coin flips and probability of range of heads ... For 10,000 coin flips, the permitted range is 4,900 to 5,100. ... How is this calculation done? ... The formula is the probability mass function,... (sci.stat.math)
Re: What is Intelligent Design? ...probability of given object or 'information system' as they like to ... characteristics of a rock to determine if a rock was chipped for use as ... I have never seen an advocate of ID propose a calculation... a given object as a product of evolution.... (talk.origins)
