IN PRAISE OF THE CUMULATIVE, Roald Hoffmann is the Frank H. T. Rhodes Professor of Humane Letters, Emeritus, at Cornell University, USA.I used to like my energies big. What I mean is that I looked for preferences in chemistry the difference in the thermodynamic stability of two molecules A and B, the energy barrier to A converting to B that were large. I was suspicious of smaller energies, mainly because my calculation methods were lousy. In time my theory got (a little) better, but hardly up to predicting the level of control nature exercises. But even if I am unable to calculate energies exactly, Ive grown to appreciate the cumulating logic of the small, responsible even for marvelous structures, such as a cell membrane.Lets get the energy scales into focus. Energies in chemistry are measured per molecule, or per mole = 6.0223 x 1023 molecules. A common energy unit is that of kilocalories (kcal)/mol. It is easy to understand what a kilocalorie since we need daily the equivalent of ~2,000 kcal produced if that food were burned. Another calibration: to heat a liter of water from room temperature to boiling requires ~80 kcal.Here I want to tell you a short but impressive story of the power of accumulated small energies, that question our prejudices.Paint Brushes, or Esther Williamss hairSee the picture below, which shows a very familiar phenomenon. A dry paint brush typically shows all the fibers separated. When, the paint brush is dipped into water, you can see the fibers separated. And not only a paint brush, but also the hair of the marvelous actress Esther Williams, sadly no longer with us, under water in a swimming pool. However, as the paint brush emerges from water, all the fibers are fully stuck together.Figure 2. Paint brushes dry, in water and immediately after dipped in water and Esther Williams in her favorite mediumThis simple phenomena shows the magnificent power of the accumulative effects of hydrogen bonding at the molecular level, or surface tension in a macro scale at work. The driving force for aggregation, so-called hydrophobic bonding, is qualitatively understood, but the details are... complicated. Clearly it has to do in part with the balance of like-like and like-unlike forces (both small, hydrogen bonding for water, dispersion forces for all participants), and in part with another balance connected to the size of the aggregate formed (the energetics of cluster formation depend roughly on the volume, but the interface between cluster molecules and surroundings depends on the surface area). For small clusters, <1 nanometer in diameter, the entropy of mixing water and oil-like molecules overwhelms any mutual attraction, so clustering is unlikely. For larger arrays, clustering or segregation is driven by the unfavorable energetics of the interface.Small gobs of energy, not easy to understand. All power to the petiteEsther Williams or the paint brush emerges from water with all the hair stuck together. This is the net result of the effect of the petite: Dispersion forces, hydrogen bonding, multipole interactions, hydrophobic bonding these are all essential small structure-determining factors called noncovalent interactions, to