Is that physics?
In my article Information reduction 5: The classic glass of water, I drew upon the example of a glass of water to illustrate the principle of information reduction. In this example, the complex and detailed information about the kinetic energy of water molecules (micro level) is reduced to simple information about the temperature of the water.
Of course, a physicist might criticise this example – and quite rightly so, because the glass of water is actually much more complicated than this. Boltzmann’s calculations only apply to the ideal gas, i.e. one whose molecules do not interact except when they collide and exchange their individual movement information.
An ideal gas
The ideal gas is an idealisation you won’t find anywhere in the real world. Other forces exist between individual molecules than the purely mechanical ones, and the situation in our glass of water is no different. Because water is a liquid not a gas and because much stronger bonds exist between molecules in liquids than between gas molecules, these additional bonds complicate the picture.
Water
Moreover, water is a special case. The water molecule (H2O) is a strong dipole, which means it has a strong electrical charge difference between its two poles, the negatively charged pole with the oxygen atom (O) and the positively charged pole with the two hydrogen atoms (H2). As a result of this strong polarity, multiple water molecules join together. If such agglomerations were to be maintained, the water would be a solid (such as ice) rather than a liquid. But since they are only temporary, the water remains a liquid, but a special one that behaves in a very particular way. See, for example, the current research of Gerald Pollack.
Physics and information science
A glass of water probably isn’t the example a physicist would have chosen, but I’m not going to change it. It’s as good an example as any to explain the ratio of information at the micro and macro levels. Boltzmann’s calculations are only approximately correct, but his thesis holds: the temperature of an object is the macro-level information that summarises the many data points about the chaotic movements of the individual molecules at the micro level.
The glass of water may be a bad example to a physicist. For our consideration about micro and macro states, however, it makes no difference whether we are considering an ideal gas or a glass of water: there is always a huge information gap between the macro state and the micro state, and that is the salient point. In a glass of water, the micro state contains billions of times more information than the macro state. And, interestingly, although the micro state is richer in information, it is the macro state that is of greater interest to us.
The transition
How does the transition from micro to macro state take place in different cases? Clearly, this transition is slightly different in the glass of water than in the ideal gas due to the special properties of the H2O molecule. And the transition from the micro to the macro state is completely different in our other examples of classification, concept formation and framing that are not drawn from the physical world. We will now go into these peculiarities. See the posts to come.
This is a page about information reduction — see also overview.
Translation: Tony Häfliger and Vivien Blandford