The Fundamental Difference In Structure

THIRD EXAMPLE (LIMITS OF ACCURACY OF MEASURING)

Suspend a lightweight body by a long thin fibre in equilibrium orientation.

This is often used by physicists to measure weak forces which deflect it from that position.

The continued effort to improve the accuracy of this very commonly used device of a ’torsional balance’, has encountered a curious limit, most interesting in itself.

In choosing lighter and lighter bodies and thinner and longer fibres - to make the balance susceptible to weaker and weaker forces - the limit was reached when the suspended body became noticeably susceptible to the impacts of the heat motion of the surrounding molecules and began to perform an incessant, irregular ‘dance’ about its equilibrium position, much like the trembling of the droplet in the second example. Though this behaviour sets no absolute limit to the accuracy of measurements obtained with the balance, it sets a practical one.

The uncontrollable effect of the heat motion competes ‘To wit: the concentration at any given point increases (or decreases) at a time rate proportional to the comparative surplus (or deficiency) of concentration in its infinitesimal environment. The law of heat conduction is, by the way, of exactly the same form, ‘concentration’ having to be replaced by ’temperature’.

with the effect of the force to be measured and makes the single deflection observed insignificant. You have to multiply observations, in order to eliminate the effect of the Brownian movement of your instrument.

This example is illuminating in our present investigation.

For our organs of sense, after all, are a kind of instrument. We can see how useless they would be if they became too sensi tive.

The Vn RULE

There is not one law of physics or chemistry, of those that are relevant within an organism or in its in teractions with its environment, that I might not choose as an example.

The detailed explanation might be more complicated, but the salient point would always be the same and thus the description would become monotonous.

But I should like to add one very important quantitative statement concerning the degree of inaccuracy to be expected in any physical law, the so-called Y n law.

If I tell you that a certain gas under certain conditions of pressure and temperature has a certain density, and if I expressed this by saying that within a certain volume (of a size relevant for some experiment) there are under these conditions just n molecules of the gas, then you might be sure that if you could test my statement in a particular moment of time, you would find it inaccurate, the departure being of the order ofYn.

Hence if the number n == 100, you would find a departure of about 10, thus relative error == 10% • But if n == I million, you would be likely to find a departure of about 1,000, thus relative error == lo °10.

This statistical law is quite general.

The laws of physics and physical chemistry are inaccurate within a probable relative error of the order of I Ivn, where n is the number of molecules that co-operate to bring about that law - to produce its validity within such regions of space or time (or both) that matter, for some considerations or for some particular experiment.

An organism must have a comparatively gross structure in order to enjoy the benefit of fairly accurate laws.

Otherwise, the number of co-operating particles would be too small, the ’law’ too inaccurate.

The particularly exigent demand is the square root.

1 million is a large number.

An accuracy of just 1 in 1,000 is not good if a thing claims of being a ‘Law of Nature’.