Visualizing a Very Large Number

I mentioned in another post on the Powers of Ten a visualization of the number of combinations of 52 playing cards, taken from a Vsauce video at The number is 8.06 times 10 to the 67th power, and the example counted that number of seconds.

  1. Stand on the equator for a billion years
  2. Take one step, and wait another billion years
  3. At this rate, walk around the earth – this gets you to about 2 x 10 to the 23rd power, which is about a third of the number of atoms in a half ounce of carbon (Avogadro’s number, 6.022 x 10 to the 23rd power))
  4. Every time you complete a trip, remove a drop of water from the Pacific Ocean
  5. When you have drained the ocean, lay a piece of paper on the ground This gets you to 9 x 10 to the 48th power.
  6. Keep refilling and draining the Pacific, adding a sheet each time until the pile reaches the sun. This gets you to about 2 x 10 to the 63rd power.
  7. Do this 40,000 times (he says 1,000 times but I think he is mistaken)

I think this powerfully illustrates how big this big number is. Science articles throw powers of ten around without anchoring them in experience, which distorts our perception..

Life in a Bubble

Norwalk boatyard

I see four fundamental characteristics of all living things: they process resources from the environment and return waste products (i.e. they metabolize); they reproduce; they evolve; and (the focus of this essay) they are separated from their environment by some kind of membrane.

The origin of the chemical processes that make life possible, and the place or places of their origin, are the subject of active research. But all agree that these processes need to be concentrated so they don’t dissipate into the outer environment. Even if life processes can arise in an open environment that is rich with the necessary energy and chemical resources, evolution is not possible until there is some kind of “it” to evolve.

The key component required to contain life is a “lipid bilayer” that forms a membrane. This remarkable structure surrounds each living cell. It is formed of a double layer of molecules packed side by side, with other molecules embedded in the membrane that act as gates for passing chemicals through the membrane. You can learn about them in the Wikipedia article on lipid bilayers at

Because of this need to be separated from its outer environment, a cell is its own mini-universe. Whatever behavior it exhibits results from processes occurring within that universe, informed by information and chemicals from outside. This in turn requires the cell to form a model of what is both inside and outside its boundary.

Information and chemicals pass through the membrane in both directions, informing the cell of what is going on outside its membrane; internal machinery tracks what is going on within the cell. Each cell is specialized to process only certain kinds of chemicals and information.

Assemblies of specialized cells can process a great deal more information and chemicals than a single cell. A single-cell bacterium can configure itself as a lens to focus light on the inside of its membrane, allowing it to move toward the light. But a human’s eye and brain can form incredibly more elaborate models of what is visible.

Yet the principle is that same: only certain kinds of information and chemicals can get through the barriers surrounding individual cells and the vast collections of cells forming a complex organism, and only certain processes within the cell are monitored. It is impossible for a living organism to form a perfect model of itself or its outer environment.

Each organism’s model of its self in its environment is created out of a rich and constantly changing stew of inheritance and experience – “nature versus nurture” is entirely void of meaning. The model is volatile; what astonishes is not its malleability, but its apparent stability. If a human brain decides every tenth of a second what its brain-body is to do next, which seems to be approximately the case, the model created by a person my age (80) must have been updated 25 billion times through exceedingly complex neural transformations. This is either a miracle, or we are kidding ourselves regarding the stability of the model.

I leave you with two take-aways. One is that indeed our sense of self and our memories are transient and inaccurate, something science is probing with unsettling consequences. The other is that the organism must have some sort of criteria to decide on the appropriate next behavior. Without such criteria, no consistent model could be formed, and therefore no consistent behavior.

I feel that not enough attention is being paid to the subtleties of these criteria, and that art is a way of laying bare at least some of them. This leads me to believe that art can be a window into the workings of human brains, a subject I will pursue in other essays.