Doubling Time

couldn’t agree more.

James Ferguson was rejoicing in the insights to the universe that one can derive from The Principles of Natural Philosophy, Sir Isaac Newton’s seminal work published seventy years earlier. This masterpiece established a joint foundation in physics and mathematics that enabled the birth of the Industrial Revolution and the modern age of cosmic discovery.

By any measure, we are living in the golden age of astronomy. The rate at which research papers are being published is the highest ever. The number of astrophysicists in the world is fifty percent more than just a decade ago. And the power of the world’s telescopes—peering in all wavelengths of light—has allowed astronomer’s to see more objects at greater distances than ever before. Not a week goes by when a newspaper headline doesn’t reveal a newly discovered fact or feature of the universe—no greater nightmare exists to disturb the sleep of a textbook author. Not long ago, new editions of astronomy textbooks came out more often than absolutely necessary, just to short-circuit the lucrative secondary market for used books. Now, the release of new editions can be justified almost monthly, simply to stay current with the pace of discoveries in the field.

But let’s stop and think for a moment. How often do people in the modern history of science ever write anything like, We hardly know anything about anything or Gee, I wish we were not living in such backward times. It seems whenever scientists or writers talk about our knowledge of the natural world, they wax poetic about how far they’ve come, and how much they know. Actually, a famous party-pooping remark of Thomas Edison’s holds that we don’t know one millionth of one percent about anything. But in general, praise of the depth and breadth of contemporary knowledge is the rule rather than the exception. The Preface to The Universe Revealed, a college textbook published in 2000 agrees:

Astronomy is the oldest science, but it is also tremendously active right now. Discoveries are being made by large new telescopes on high mountaintops and by sophisticated new observatories in space.

But so too does the preface to The System of the Stars, a treatise on the known universe written one-hundred and ten years earlier in 1890 by the prolific astronomy popularizer Agnes Clerke. She was sure that she was living in the golden age of discovery:

Now, in the history of the human intellect, there is no more astonishing chapter than that concerned with the sidereal researches of the last quarter of a century.

Thirty years earlier, in 1860, Professor Elias Loomis mused with similar emotion in the Preface to his highly acclaimed An Introduction to Practical Astronomy,

The rapid advance in the cultivation of Practical Astronomy which has recently been made in the United States is one of the most encouraging features of the age.

One could analyze the decade-by-decade political, social, and cultural forces at work that promoted cosmic discovery, but astronomy did not have unique favor with the political funding of the time and was simply one of many fields enjoying an explosive growth of knowledge. The editor’s preface to the Annual of Scientific Discovery 1852 contained hyperbolic praise.

The progress of invention and discovery, of improvement and application, is so rapid, unceasing and continuous, that it would require a volume many times the size of the present to record, even in a summary manner, all that transpires of scientific interest in the course of a single year.

The editor was convinced he knew why:

One fact must be apparent to all, that is, that the number of persons now engaged in contributing to the advance of every department of natural and physical science is greater than at any former period. The evidence of this is to be found in the… greatly increased publication and circulation of scientific books and journals.

When a field of research grows exponentially, every generation perceives itself as living in a special time. A quantitative analysis reveals this as well. Recently, while browsing the stacks of Princeton University’s astrophysics library, I paused by the wall of shelves containing the Astrophysical Journal, the leading research journal in the field, which has been around since the birth of modern astrophysics. With all copies on display, from Volume 1 in 1895 to the most recent publication, the middle of the wall (and hence, the halfway point of the Journal’s record of research) was easy to find. Adjusting for increases in page size over the years, the halfway point fell among the journals dated fifteen years ago. Yes, half of all research papers ever published in astrophysics have been published in the past fifteen years. But fifteen years ago, others strolling past the same wall could have made the identical statement. As they could fifteen years before that. And fifteen years before that. And fifteen years before that. My colleagues in other sciences share similar tales.

Are scientists today more verbose than yesterday? Are we writing more research papers just to survive the proverbial paradigm of publish or perish? I think not. There have always been verbose scientists and there have always been more papers written than substance demanded. One way to calibrate the rate that important research gets published is to assess how quickly you fall behind for not reading the journals regularly. During my own professional career this time interval has dropped from years to months.

Gordon Moore, co-founder of the Intel Corporation, recognized as early as 1965 that the growth of the electronics industry enabled computing power (and associated trappings of computer technology) to double every eighteen months. This now-famous Moore’s “law” for computing, with a much shorter doubling time than for science in general, has held remarkably true for the past thirty-five years, with no sign of losing its relevance to the information revolution. My first electronic mail account was up and running in 1982, back when a few thousand scientists and engineers were the principal users of this new fangled technology. Moore’s law made it inevitable that today, twelve doubling times later, my friends and family, would be online with fresh email accounts.

Our minds seem poorly equipped to grasp the consequences of exponential growth. Consider the following example. If you came upon a small lake where a particular form of fecund algae was doubling its population every day, and if you returned after one month to find the algae covering half the lake, then how much longer would you have to wait before the entire lake was carpeted with algae? Answer: One day. Exponential arithmetic such as this enables half of all the algae (at all times) to declare they were “born yesterday,” and that the population growth of their era was like none that preceded it. My favorite “doubling” experiment is the one where somebody gives you a penny a day, doubled, for every day of a 31-day month. That is, one cent the first day, two cents the second day, four cents the third day, eight cents the fourth day, and so on. How much money is your friend handing you on the last day of the month? Answer: $10,737,418.24

To sustain exponential growth, modern science requires (as a minimum) the free exchange of ideas. Where this does not happen, science flounders. We saw it in the 1600s, when Galileo was tried and his writings were banned by the Inquisition. But it also happened recently. The idea that characteristics acquired during life are genetically transferable to your offspring is traceable to one of the four “laws of evolution” put forth by the eighteenth century French biologist Jean Lamarck. This notion was adopted by the twentieth century Russian biologist T. D. Lysenko and resonated with the political agenda of the Central Committee of the Communist Party, who passed a resolution denouncing mainstream Mendelian genetics. A resolution from the USSR Academy of Sciences followed closely, which outlawed the study and teaching of Mendelian genetics altogether. The politics of it all began in 1938, when Lysenko was appointed head of the Lenin Academy of Agricultural Sciences

Big mistake.

For three decades, right up until the death of Khrushchev, Russian biology moved backward just by standing still. Russian agriculture suffered the most by not reaping the benefits of the world’s ongoing genetic research as applied to crops and their yields. While “Lysenkoism” in Russia was being praised by Stalin and then by Khrushchev, biology in the rest of the world enjoyed two doubling times in research and productivity, including the Nobel prize-winning discovery of the DNA molecule.

There’s no crime in being wrong; most scientists are wrong most of the time. In this case, however, the unholy mix of science and politics perverted the process of self-correction, which is so crucial to the discovery of scientific truth. Science advances quickest wherever and whenever it can stay clear of religious dogma, prejudice, and political agenda (unless of course the political agenda itself is to advance science). In Europe and in America, these conditions have largely been met—especially in the physical sciences—ever since the dawn of the industrial revolution in the 1700s. It’s no accident that Europe and America have become the most powerful economic and industrial forces the world has ever seen.

Not all intellectual or creative enterprises are in their golden age. While I’m no expert in the liberal arts, nor do I claim knowledge beyond that gleaned from conversations at cocktail parties, I have never heard anyone claim that we are in the golden age of art or sculpture or music or film or poetry or novel-writing. For many, the golden age was far away and long ago. This rearward-looking posture may simply be the consequence of one’s inability to know for sure whether the praise of new art (in any form) will survive the critique of time. In the sciences, however, if an idea is demonstrably wrong, it will not one day be proved correct, which enables us to discard such ideas in the spirit of simply tidying up around the house.

People sometimes look longingly rearward at times when to do so is, in fact, unwarranted. Consider what is widely described as the golden age of space travel—the Mercury, Gemini, and Apollo programs of the 1960s leading to the first moon landing in 1969. No doubt those were special times. But are they more special than today. Not really. We are now building a space station with a class of reusable space vehicle that we launch multiple times per year. We have launched space probes that, at this moment, are orbiting Mars, are on their way to Mars, are intercepting a comet’s tail, are orbiting and asteroid, are orbiting Jupiter, and are on their way to Saturn. We also maintain hundreds of communication satellites (in low- and high-Earth orbit) as well as a dozen space-based telescopes. Just because we do not have Moon bases and other unrealized dreamscapes, it doesn’t mean that our presence in space has not in fact grown exponentially.

One can rightly ask how it is still possible for scientists to sustain an exponential pace of discovery. Back in the 1960s, the Jurassic days of computing, a research paper was written by hand, given to a typist, and typed on a manual typewriter—complete with added typos. All the special math characters were hand-drawn in place. Figures and diagrams were plotted by hand on graph paper and then farmed off to a graphic artist. The research paper was then mailed off to the journal, with carbon copies kept for your records. Background research for the paper required a trip to the library. You would read there anything you needed to know. You would also take copious hand-written notes, for photocopiers were not yet a common feature of the office environment.

Nowadays, using the internet, you can search for key-words and subjects related to your own research in every published paper for any year in nearly every astrophysics journal. And it can be done in a minute or two. You can download any (or all) of these papers to your laptop computer and read them at your leisure, without your computer getting heavier for having done so. You observe the universe from telescopes that are controlled in real time by a user-friendly interface on your desktop computer. Your data are plotted and formatted within seconds while you “typeset” your manuscript using simple software tools provided by the journal’s publisher. You send the paper to an online service so that your colleagues all around the world can read the entire contents of your submission to the journals before the next day’s morning coffee.

All exponential growth must end somewhere. It ended with our algae when there was no lake left to take over. There may be a quantum limit to computing speeds. And there cannot be more scientists on Earth than people on Earth. But the end is not otherwise in sight. I cannot imagine what another forty or fifty years will bring—three scientific doubling times and thirty Moore’s law doubling times of computing power. If Moore’s law continues to hold, the early 21^st century will look like a primitive culture in which research moved like molasses and the “real” potential of the infant internet had not yet been realized. Our Golden Age of discovery flows not from a particularly prodigious rate of research, but by the consistency with which we have maintained the exponential growth of this research. By that measure, our golden age has lasted since the industrial revolution gave birth to it, with no sign of letting up. And there will be no rest for the weary textbook writers, who must continually rewrite new editions as they chase the cosmic frontier, just as they did a hundred years ago.