Exponential Growth in Computation How about computation? In 1971, Intel put out its first computer chip, the Intel 4004. It had 2,300 transistors on it, at $1 each. Intel no longer actually tells you how many transistors are on their chips, but the recent Core i9 had 7 billion transistors at less than a millionth of a penny each. This represents a 27-billion-fold increase in price performance in forty-five years.

How small can you make the whole gadget?" "Hyper-relays can be had micro-size … wiring … chips — Space, you've got a few hundred circuits there.

A modern economic system is of extraordinary complexity. Imagine a three-dimensional jigsaw puzzle, consisting of roughly 100 million parts. Some parts touch against, let us say, 1,000 other parts. (That is, each family deals at one time or another with that many employers, banks, retail stores, domestic servants, and so on.) Other parts touch—let us be conservative—50,000 other parts (firms that sell to retailers and buy from other firms and hire laborers and so on). It would be enough of a task to fit these 100 million pieces together, but the real difficulties have yet to be mentioned. The pieces change shape quite often—a family has twins; a firm does the next best thing and invents a new product. The economist has the interesting task of predicting (in the aggregate) each of these movements. Meanwhile a busy set of people—congressmen, members of regulatory bodies, central bankers, and the like—are changing the rules on who or what the jigsaw pieces will be and how they are shaped. And of course there are other jigsaw puzzles (foreign economies) of comparable complexity, and these other puzzles are connected at literally a million points with our puzzle.

In 1965, Gordon Moore, the founder of Intel, noticed the number of integrated circuits on a transistor had been doubling every twelve to twenty-four months. The trend had been going on for about a decade and, Moore predicted, would probably last for another.9 About this last part, he was off by a bit. All told, Moore's law has held steady for nearly sixty years. This relentless progress in price and performance is the reason the smartphone in your pocket is a thousand times faster and million times cheaper than a supercomputer from the 1970s. It is exponential growth in action.

Simplicity in a system tends to increase that system’s efficiency. Because less can go wrong with fewer parts, less will. Complexity in a system tends to increase that system’s inefficiency; the greater the number of variables, the greater the probability of those variables clashing, and in turn, the greater the potential for conflict and disarray. Because more can go wrong, more will. That is why centralized systems are inclined to break down quickly and become enmeshed in greater unintended consequences.

By 2020, a chip with today's processing power will cost about a penny," CUNY theoretical physicist Michio Kaku explained in a recent article for Big Think,23 "which is the cost of scrap paper. . . . Children are going to look back and wonder how we could have possibly lived in such a meager world, much as when we think about how our own parents lacked the luxuries — cell phone, Internet — that we all seem to take for granted.

Just three or four decades ago, if you wanted to access a thousand core processors, you'd need to be the chairman of MIT's computer science department or the secretary of the US Defense Department. Today the average chip in your cell phone can perform about a billion calculations per second. Yet today has nothing on tomorrow. "By 2020, a chip with today's processing power will cost about a penny," CUNY theoretical physicist Michio Kaku explained in a recent article for Big Think,23 "which is the cost of scrap paper. . . . Children are going to look back and wonder how we could have possibly lived in such a meager world, much as when we think about how our own parents lacked the luxuries — cell phone, Internet — that we all seem to take for granted."

Just three or four decades ago, if you wanted to access a thousand core processors, you’d need to be the chairman of MIT’s computer science department or the secretary of the US Defense Department. Today the average chip in your cell phone can perform about a billion calculations per second. Yet today has nothing on tomorrow. “By 2020, a chip with today’s processing power will cost about a penny,” CUNY theoretical physicist Michio Kaku explained in a recent article for Big Think,23 “which is the cost of scrap paper. . . . Children are going to look back and wonder how we could have possibly lived in such a meager world, much as when we think about how our own parents lacked the luxuries — cell phone, Internet — that we all seem to take for granted.

We see that each surface is really a pair of surfaces, so that, where they appear to merge, there are really four surfaces. Continuing this process for another circuit, we see that there are really eight surfaces etc and we finally conclude that there is an infinite complex of surfaces, each extremely close to one or the other of two merging surfaces.

I do not think we can build systems that are large with large components.

If you were building a chip company and you were taping out a chip, the tapeout of a chip is around $100 million, just the tapeout. Not to mention the tools, which are probably another $100 million, and not to mention all the engineers, all the systems you’re bringing up, things like that. In order to build one of our chips, it’s a few billion dollars. And we’re just one chip company. There’s a whole bunch of chip companies. When they tape out a chip it’s no less than $25 million. Writing, developing a large language model–taping out a chip these days, what the software industry is learning is that building these large language models is kind of like taping out a chip.

I would define complexity, not really as genetic complexity because if you take it purely as genetic complexity, E. coli... a single cell may have 4,000 genes but the metagenome, the pool of genes in E. coli around the place may be on the order to 30,000 or more... [T]hat's the level of complexity equivalent to the human genome, or even more complex than the human genome, but it's organized and structured in a different way. ...You might say that it's structured in a similar way to an ... but I think an ant colony has taken that level of Eusocial behavior a long way beyond anything you would see in E. coli. So I would define it as morphologically complex, meaning cells are larger and have a lot of stuff in them.

The more things you have, the more things you have to manage.

Simplicity isn't merely cheaper, it's easier.

The emergence of computer technology in World War II and its rapidly growing power in the second half of this century made it possible to deal with increasingly complex problems, some of which began to resemble the notion of organized complexity. Initially, it was the common belief of many scientists that the level of complexity we can handle is basically a matter of the level of computational power at our disposal. Later, in the early 1960s, this naive belief was replaced with a more realistic outlook.