I Am a Strange Loop

by Douglas R. Hofstadter

(some of my readers will recognize this as a quintessential example of Hofstadter’s Law, which states, “It always takes longer than you think it will take, even when you take into account Hofstadter’s Law”),

believe most people understand abstract ideas most clearly if they hear them through stories, and so I try to convey difficult and abstract ideas through the medium of my own life. I wish that more thinkers wrote in a first-person fashion.

Saying that studying the brain is limited to the study of physical entities such as these would be like saying that literary criticism must focus on paper and bookbinding, ink and its chemistry, page sizes and margin widths, typefaces and paragraph lengths, and so forth.

The macroscopic world as experienced by humans is, in short, an intimate mixture ranging from the most predictable events all the way to wildly unpredictable ones.

Librarian Berry, after ruminating about the subtle nature of the search for ever shorter descriptions, came up with a devilish characterization of a very special number, which I’ll dub b in his honor: b is the smallest integer whose English-language descriptions always use at least thirty syllables. In other words, b has no precise characterization shorter than thirty syllables. Since it always takes such a large number of syllables to describe it, we know that b must be a huge integer. Just how big, roughly, would b be?

A creature that thinks knows next to nothing of the substrate allowing its thinking to happen, but nonetheless it knows all about its symbolic interpretation of the world, and knows very intimately something it calls “I”.

Just as we are convinced that ideas and emotions, rather than particles, cause wars and love affairs, so we are convinced that our “I” causes our own actions. The Grand Pusher in and of our bodies is our “I”, that marvelous marble whose roundness, solidity, and size we so unmistakably feel inside the murky box of our manifold hopes and desires.

many neuroscientists’ great familiarity with the low-level aspects of the brain makes them skeptical that consciousness and free will could ever be explained in physical terms at all.

The moral of the story is that being a professional neuroscientist is not by any means synonymous with understanding the brain deeply — no more than being a professional physicist is synonymous with understanding hurricanes deeply.

But at some point, when Alan Turing’s abstract theory of computation, based in large part on Gödel’s 1931 paper, collided with the concrete engineering realities, some of the more perceptive people (Turing himself and John von Neumann especially) put two and two together and realized that their machines, incorporating the richness of integer arithmetic that Gödel had shown was so potent, were thereby universal.

Likewise, an operation on an integer that is written out in binary notation (for instance, the conversion of “0000000011001111” into “1100111100000000”) that one person might describe as multiplication by 256 might be described by another observer as a left-shift by eight bits, and by another observer as the transfer of a color from one pixel to its neighbor, and by someone else as the deletion of an alphanumeric character in a file.