Hierarchy of Ideas

The Hierarchy of Ideas

Feynman described it like this in a lecture at Cornell, titled "The Character of Physical Law: The Distinction of Past and Future" (edited for clarity):

“We have a way of discussing the world . . . at various hierarchies, or levels. Now I do not mean to be very precise, dividing the world into definite levels, but I will indicate, by describing a set of ideas, what I mean by hierarchies of ideas.

For example, at one end we have the fundamental laws of physics. Then we invent other terms for concepts which are approximate, which have, we believe, their ultimate explanation in terms of the fundamental laws. For instance, "heat." Heat is supposed to be jiggling, and the word for a hot thing is just the word for a mass of atoms which are jiggling. But for a while, if we are talking about heat, we sometimes forget about the atoms jiggling, just as when we talk about the glacier we do not always think of the hexagonal ice and the snowflakes which originally fell.

Another example of the same thing is a salt crystal. Looked at fundamentally it is a lot of protons, neutrons, and electrons; but we have this concept "salt crystal," which carries a whole pattern already of fundamental interactions. An idea like pressure is the same.

Now if we go higher up from this, in another level we have properties of substances, like "refractive index," how light is bent when it goes through something; or "surface tension," the fact that water tends to pull itself together, both of which are described by numbers. I remind you that we have got to go through several laws down to find out that it is the pull of the atoms, and so on. But we still say, "surface tension," and do not always worry, when discussing surface tension, about the inner workings.

On, up in the hierarchy. With the water we have waves, and we have a thing like a storm, the word "storm" which represents an enormous mass of phenomena, or a "sunspot," or "star," which is an accumulation of things. And it is not worthwhile always to think of it way back. In fact we cannot, because the higher up we go the more steps we have in between, each one of which is a little weak. We have not thought them all through yet.

As we go up in this hierarchy of complexity, we get to things like muscle twitch, or nerve impulse, which is an enormously complicated thing in the physical world, involving an organization of matter in a very elaborate complexity. Then come things like "frog."

And then we go on, and we come to words and concepts like "man" and "history," or "political expediency," and so forth, a series of concepts which we use to understand things at an ever higher level.

And going on, we come to things like evil, and beauty, and hope . . .

Which end is nearer to the ultimate creator, to God, if I may use a religious metaphor? Beauty and hope, or the fundamental laws? I think that the right way, of course, is to say that what we have to look at is the whole structural interconnection of the thing.”

All the intellectual efforts man makes, according to Feynman, proceed at different levels of explanation and understanding. What he in particular finds fascinating is to see the connections between levels in the hierarchy—for example, how beauty connects to history, and how history connects to man’s psychology, and how man’s psychology connects to the workings of the brain, and how that connects to the neural impulse, the neural impulse to the electrochemistry of the neuron, that electrochemistry to the movement and behavior of molecules, which connects to the expression of subatomic particles, and so on down to the strangest levels of quarks and gluons, or perhaps strings . . . and of course the connection goes “both ways.”

We can examine the world at any level, to any depth, and also extend the breadth of our inquiry in any direction. We might like to study the brains of all kinds of animals (remaining on the biological level, but expanding the breadth of that view to encompass many kinds of brains), or we can find one phenomenon, like the flash of electrochemical energy in the brain, and follow that upward (to things like consciousness) or downward (to things like the behavior of sodium-gated channels in neuron cells).

Feynman didn’t claim that either end was “closer to God.” He said that continuing right off the edge in either direction is actually a mistake, if one hoped to find all the big answers that way. That means that dwelling solely in concepts like “beauty, hope and evil” or solely in “the fundamental physical laws” is not sensible. It’s especially not sensible for those who specialize at either end of the pole to argue with one another! Instead, he thought we ought to focus on the amazing connections that could be made—in fact, to discover the connections that already exist—in and between these levels.

Different fields investigate connected aspects of reality, often with different questions and methods. Physical laws constrain biological processes, for example, but a useful biological explanation may concern an organism’s behavior or environment. Here, “hierarchy” describes levels of organization and explanation, not a ranking of legitimacy or importance.

Science works at many levels; a fundamental description is not automatically the most useful one. Assuming that one could derive the “meaning of life” by understanding quantum electrodynamics is no different from saying that attaining nirvana at a meditation retreat would allow you to figure out how to fix a broken washing machine. That’s perhaps why Feynman said of science, "Knowing all the fundamental laws as we know them today doesn't give you a good understanding of much right away."

According to Paul Davies in God and the New Physics (1983):

“The distinction being made here is sometimes referred to as 'holism versus reductionism.' The main thrust of western scientific thinking over the last three centuries has been reductionist. Indeed the use of the word 'analysis' in the broadest context nicely illustrates the scientist's almost unquestioning habit of taking a problem apart to solve it. But of course some problems (such as jigsaw puzzles) are only solved by putting them together—they are synthetic or 'holistic' in nature. The picture on a jigsaw puzzle, like the speckled newspaper image of a face, can only be perceived at a higher level of structure than the individual pieces.”

A maxim often attributed to Einstein expresses the idea: “one cannot solve a problem at the same level of thinking that created the problem.” In other words, you cannot continue to think of individual puzzle pieces and how they fit into one another and expect to have any insight into where those pieces should go. To answer the question “Where should this piece go?” you need to look up from one level to the next and, literally, see the bigger picture. If you examine the subatomic world and don’t find evil or beauty or God there, it doesn’t mean you have proven they don’t exist any more than examining the nonsensical marks on a single puzzle piece proves there is no bigger picture that is or could be formed.

The account describes a universal hierarchy of abstraction (UHA): a framework for relating parts and wholes across scales. It is a way to organize questions, rather than a demonstrated single ordering of every possible concept.

As you learn a subject, ask how its concepts connect with explanations at other scales. A model of neural activity and a psychological account of attention may address related questions without being interchangeable.

Different questions call for maps at different scales. So, if you’re in your house one day and you’re looking for a needle, you might like to have a thorough understanding of where all your furniture is, how to operate a drawer, and a detailed list of the contents of those drawers, so you can locate this tiny object.

But if you wanted to travel to outer Mongolia, you would need a much bigger map to help you coordinate movements and actions at a larger magnitude. Your house and the tiny needle inside the drawer would still be as real as they ever were, but for the purposes of traveling to outer Mongolia, they are omitted from your map. Likewise, when at home and looking for a needle, you do not need to start by locating yourself in your universe, then in your galaxy, then on your planet, continent, country, and so on. It’s okay to forget that all that even exists and use a “map” that only contains your house.

There is a Buddhist parable in which Gautama “preaches” to a crowd by simply holding up a single flower and not saying a word. Because he was silent and pointed directly at reality, one of his disciples is said to have attained enlightenment at once. The author draws a parallel with Matthew 6:28–29, quoting: “Behold the lilies of the field: they neither labor nor spin. Yet I tell you that not even Solomon in all his splendor was dressed like one of these.”

Gautama was “saying” something profound about saying: He chose a clever way to indicate reality without indicating it at all, like pointing to the moon without needing to use a finger. Wordlessly, without gesture or symbol, he conveyed the mystical and astonishingly profound idea that “it is.” We can imagine that this is the extreme far end of the universal hierarchy of ideas—so abstract it is beyond abstraction. And yet, the Buddha could access this level of comprehension via the mundane, i.e., the level of a simple flower growing in a field.

Jesus, likewise, was not really talking about botany or the historical king Solomon. He wasn’t even talking about money or the nature of work or what the self really is underneath the socially constructed artifice of clothing. He, too, was pointing to reality, and used one level of understanding (clothing, flowers) to point to another.

Consider which level your question concerns and what an adjacent level might reveal. Specialization remains useful; connections to other fields can help when your current explanation leaves something important out.

Think about depth but also breadth. Make connections. Become curious about what your problem looks like on different levels.

You can also compare the questions on your “twelve favorite problems” list. Some may share a mechanism or a useful analogy. Look for a connection you can explain or test, rather than assuming that every pair must have a practically useful link.

If you want to know more about the way things are, then the hierarchy of ideas can help you navigate your way through and keep your inquiry organized. If you are attempting to learn to solve some particular problem, the hierarchy can help, too. It reminds you that the appropriate level of inquiry is the one that helps you solve the problem you currently have. For example, if you walk into a psychiatrist’s office and ask them why you’re anxious all the time, they wouldn’t start by saying, “Well, in the very beginning was the big bang . . .” Rather, the right level of abstraction is a bit like the setting on a magnifying glass—the best one is the one which allows you to see the object you’re interested in most clearly.

Changing levels can help when a problem remains stuck. If you’re stuck and can’t find a way out, try to zoom in or out one level of abstraction. If your perspective itself is a tool, then realize that some points of view are like scalpels, some are like enormous industrial cranes, and some are like supercolliders. Sometimes you feel like you’re encountering a problem when really you are just using the wrong tool, i.e., looking at things from the wrong perspective. If trying to find a resolution at your current level on the hierarchy isn’t working, try to find ways to step out of that level.

For example, someone anxious about work might examine both their response to a difficult task and the expectation that they should never feel uncomfortable. Questioning that expectation may ease one source of pressure. It is a change in framing, not a reason to assume that persistent anxiety will disappear or that psychological care is unnecessary.

Applying the idea

• Explaining a concept to someone else can reveal gaps in your understanding. The learning method commonly called the Feynman technique uses this approach.
• Write down what you know, then explain it in plain language to a beginner. Identify gaps and check them. You can “tell a story” to make an explanation easier to follow, while checking that its analogies preserve the relevant relationships.
• Choose a level of explanation that helps answer the question at hand. If it does not, examine a broader context or a more detailed mechanism, and ask what the change lets you explain.