Does Human Knowledge Double Every 5 Years?

Into The Jungle Of Research Funding

Oh, this hurts. I did not want to go into research funding. But now that it is fairly clear that the rate of progress varies significantly by sector, we have to examine the inputs.

The first relevant document found is a PDF from the European Commission. It states that it wants the EU to increase research 'efforts' to 3% of GDP by 2010. Ambitious, that. The document talks about the importance of 'basic research,' as opposed to directed, I assume, which is encouraging. It actually serves as a good basic primer on how funding is structured in Europe, the U.S. and Japan, but while it talks about funding for specific programmes, it doesn't talk about levels of funding at the national or international level. So we move on.

Curious Cat, a blog that bills itself as a Science and Engineering blog, posts research funding for U.S. academic R&D for the past few years (see below in the extended post). More importantly there's a link to the NSF where we find an Excel spreadsheet (also in the extended post below) that charts all federal spending on research for science and engineering between 1970 and 2003. There are other charts available for viewing and downloading here.

In 1970, combined spending by all U.S. Federal agencies for research in science and engineering totaled $4.9 billion (USD). By 2003, that had grown to $53.3 billion (USD). Not bad.

The compound annual growth rate for U.S. Federal funding for research into science and engineering is 7.28%, which means it doubles every 9.86 years.

However, adjusting for inflation to 2006 U.S. dollars, it reads a bit differently. In 2006 dollars, the spend in 1970 was the equivalent of $26 billion, while the 2003 spend rises on recalculation to a total of £58 billion. That provides a CAGR of 2.39%, which would double every 29.35 years. A bit sad, that.

But the spreadsheet breaks spending down by discipline, as well. I'll address that in the next post.

League Tables and Update

Here is the league table for 25 points of measurement of the growth of human knowledge. As shown, only 10 of the 25 grow faster than 14.87% per year, which is what is needed to double every 5 years.

Field                                                            CAGR                   Doubling Period (Yrs)
1. Nanotechnology patents                                  44.91                           1.87
2. Nanotechnology journals                                 42.03                           1.98
3. Global warming patents                                  38.62                            2.12
4. Prions patents                                                33.76                            2.38
5. Programming patents                                      33.53                            2.4
6. Stem Cells patents                                           26.47                            2.95
7. Prions journals                                                 25.57                            3.04
8. Global warming journals                                    24.71                            3.14
9. Epidemiology patents                                        17.37                             4.33
10. Stem Cells journals                                          16.63                             4.51
5 Year Doubling Rate                                          14.87                             5
11. Programming journals                                     12.55                             5.86
12. Alzheimers Disease patents                              11.26                             6.5
13. Oncology patents                                              10.02                             7.26
14. Alzheimers Disease journals                                9.65                             7.52
15. Oncology journals                                                9.23                             7.85
16. DeSolla Price estimate of world literature growth   7.0                             10.24
17. Epidemiology journals                                           6.22                           11.49
18. Mars journals                                                        5.78                           12.34
19. Shale oil journals                                                   5.53                           12.88
20. US patent grants                                                    5.21                           13.65
21. University enrollment worldwide                              4.85                           14.64

22. Publications in astrophysics since 1970                     4.0                             17.67
23. US patent applications                                             3.88                           18.21
24. U.S. Book publishing                                                3.65                           19.33
25. Shale oil patents                                                      2.58                           27.21

More discussion below--click if you want to see it.

That Eureka Moment--University Students Worldwide

I have been searching for this for quite a while. UNESCO had it--click here to see it on their website. I include the graph here--click on the image to see a larger version.

  The number of tertiary education students has grown from 68 million in 1991 to 132 million in 2004. That's a doubling over a 14 year timespan. That's a compound annual growth (CAGR) rate of 4.85%, which would lead to a doubling every 14.64 years. It's a third of the growth rate we would need to double every five years.

This is daunting. We see the world university student population mirroring the growth rate of India since 1947, when what I think everyone assumes is a growth rate similar to China's.

I don't think this is adequate growth to sustain a required expansion of conventional infrastructure, let alone power a Singularity.

Human Knowledge and Patents

It used to be that, when an academic found something new in her or his research, she or he would write a paper and submit it to an academic journal. And it used to be that when corporate research and development departments (or some geezer in a garage) made a discovery, they would rush to apply for a patent.

Now, academics are quite likely to file a patent, or the institution they work for might--or both, in combination. So it would not be surprising to see a growth in patent applications.

The United States Patent and Trademark Office has been issuing patents since 1790. As of March, 2006, the USPTO had issued more than 7 million patents.

And wonder of wonders, miracle of miracles, they have a statistics page that shows patent activity by year since 1790. Wow.

We'll have to juggle a bit here. The applications for patent stops at 2005 (390,733), but the patent grants time series goes to 2006 (173,771). It's kind of important which year to choose, because in 2006 patent grants returned to growth after 2 years of decline. Not coincidentally, the Patent Office hired 1,100 new patent examiners in 2006 to deal with a backlog of applications.

Going to 2006, patent grants have shown a CAGR (compound annual growth rate) of 5.21%, which would cause a doubling of patent grants every 13.65 years. Patent applications started being counted in 1840, and as I said, we don't have 2006 figures. For the 165 years available, patent applications have shown a CAGR of 3.88%, which would double applications every 18.21 years.

Well, perhaps the rate of growth has been higher recently. That's what the five-year comparison is supposed to show. We will focus on patent grants only, and statistics are in the extended post below.

There are only two five year periods where the number of patents granted is double that of the preceding five year period. After the Civil War (1867-1871), when patents climbed from 26,613 to 61,646, and between 1807 and 1811, when patents rocketed from 366 to 898.

There are many five year periods where the numbers of patents declined, the most recent being the period between 1977 and 1981.

The figures below look very much like the real world. As the population increased and the environment became more conducive to technological innovation, human knowledge grew--but not exponentially and not, indeed, in a straight line. Recent performance is good--but no better in percentage terms than many periods preceding it. The number of US patents granted has not doubled in the past 15 years, let alone the past 5. We'll take a look at other countries' patent statistics later--maybe they are making up for the U.S. shortfall.

Click if you want to see the numbers.

But This Isn't Just About The Singularity, Dammit!

The Singularitarians need an exponential growth of human knowledge to enable their theory of short term artificial intelligence.

But I submit they are not the only ones who are changing their behaviour and expectations because of this general idea floating around. The idea that human knowledge doubles every five years can become an excuse for inaction.

If people think that human knowledge doubles every five years, they may think that improved science and technology will provide a 'deus ex machina' last minute cavalry charge over the hill solution to something, meaning they don't have to change their current behaviour.

They might continue smoking, thinking that surely, by the time they're 69 (the average age of diagnosis for cancer), we will have found a silver-bullet solution for all cancers.

Their organisations don't modify damaging behaviour, thinking that we will find a way to turn pollution into ice cream and champagne, or replace depleted fisheries with genetically modified de-boned cod that jump into our nets with a smile.

I think this attitude, to the extent that it exists, is quite dangerous. If my first pass through publicly available data suggests anything (and even when I finish it will need to be approached academically), it suggests that human knowledge does not double every five years.

What we do see is that specific sectors, such as nanotechnology or proteomics, grow even faster than that for short periods of time:

• When the sector is new
• When the sector is sexy
• When government or private industry sees a short term gain resulting from it
• When intermediate goals are visible and attainable

But exponential growth then reverts to a mean, or returns to an average growth that is far slower. That growth rate varies according to the availability of inputs, such as researchers, funding and above all the availability of findings from outside the given sector--the multi-disciplinary rescue. This has rescued Moore's Law more than once, and it is applicable across fields.

Not every problem deserves the resources of a Manhattan Project, which is the prime example of how throwing money and scientists at an issue can produce results. Some problems can be solved without a Manhattan Project. But I fear that problems like lung cancer and artificial intelligence do need resources at that scale...

...and I fear even more that a general, sloppy impression that human knowledge doubles every five years without any real effort or a need to get behind the knowledge machine and push is actually harming the cause of scientific and technological progress. It relieves us of personal responsibility. Oh, the new horde of Chinese researchers will solve it, so we don't have to.

That is pernicious.

What Is The Singularity?

Okay. Here is the definition provided by the Singularity Institute for Artificial Intelligence (SIAI):

"The Singularity is the technological creation of smarter-than-human intelligence. There are several technologies that are often mentioned as heading in this direction. The most commonly mentioned is probably Artificial Intelligence, but there are others: direct brain-computer interfaces, biological augmentation of the brain, genetic engineering, ultra-high-resolution scans of the brain followed by computer emulation. Some of these technologies seem likely to arrive much earlier than the others, but there are nonetheless several independent technologies all heading in the direction of the Singularity – several different technologies which, if they reached a threshold level of sophistication, would enable the creation of smarter-than-human intelligence."

The Institute is described on Wikipedia here. I emailed the founder, Eliezer Yudkowsky, to get his thoughts on what I am doing here. He hasn't responded as yet.

For 'Singularitarians', the Singularity is a big transformative concept, one of those spectacular theories that will change human life as we know it. When we create intelligence greater than our own, we will solve problems that we cannot solve today. Furthermore, many of the technologies (and especially nanotechnology) that will be used to create artificial intelligence will be used by the artificial intelligence to help us with healthcare, energy (PDF), space travel and more. God help us if we create an artificial intelligence that wants to sit on the couch and watch the soaps.

Those who fear artificial intelligence, nanotechnology (and perhaps big transformativc concepts), manage to create a vision of some rough beast slouching towards Bethlehem waiting to be born. From fears of grey goo (nanotechnology run wild) to the destruction of human ambition, AI is a threat--perhaps the biggest outsourcing threat of all, especially if it is embodied in robots.

Authorgeddon and Book Publishing

Well, I guess we need to hope that the Singularity happens before 2052. That's the year when Authorgeddon is predicted to happen, according to Wikipedia. In case you're wondering, Authorgeddon is the moment in time when the number of books published in the U.S. is expected to surpass the number of people in the U.S. who are willing to admit having read a book in the previous year.

"A study by print on demand company Lulu.com pinpoints 2052 as the year when Authorgeddon will arrive. The study arose from statistics published by R.R. Bowker, the company that controls ISBN distribution in the U.S., which reported that the number of books published in America in 2004 hit a record 195,000 -- a 14% increase over the previous high of nearly 175,000 recorded the year earlier. Bowker reports that the average annual rise in published titles over the last three years has been 14.6%."

That 14% increase looks pretty interesting--if it held up it would mean that the number of books published in the U.S. would double every 5 years. So, how does that stack up to real publishing statistics?

From Bookwire (owned by RR Bowker):

1993: 104,124

1995:  113,589

1999:  119,357

2000:  122,108

2001:  141,703

2002:  147,120

2003:  171,061

2004:  190,078

Sadly, in 2007 the number of books published in the U.S. plummeted to 172,000 new titles (I'll bet it's that damn Internet thingie). The overall CAGR is 3.65%, which would double every 19.33 years. But even looking at statistics to 2004 only (2005 might have been a blip, after all) it gives us CAGR of 5.14%. So even by cherry-picking the time frame to include the rosiest picture of growth, we get about 1/3rd of the growth we need. The concept of human knowledge doubling every five years did not originate with US book publishing statistics, I'm afraid.

In a Knowledge Economy, Is Global GDP a Proxy for Knowledge?

Let's assume for a moment that it might be. World GDP has been growing strongly of late--above trend, and in the face of challenges that formerly may have caused it to falter. But it has not grown at anything that would resemble a doubling every 5 years--in 2000, according to the World GDP was 32 trillion US dollars, and in 2005 it was 44.4 trillion. Great growth--not doubling.

You could point out the obvious--that knowledge is not spread evenly throughout the world. But the part of the world where knowledge might be presumed to be greatest grew at a slower rate than the part of the world where it might be presumed to be lesser. No doubt much of that growth is due to increased human knowledge. But more than a little was due to more workers.

Hmm. This would not be the first time that we see indications that the more dramatic effects of knowledge occur when existing knowledge is made available to new people. Making 30-year-old call centre technology available to India, disassembling factories in England and reconstructing them in China and Indonesia, this is knowledge transfer, not creation. And, to repeat my refrain, this is great, good and wonderful--if you don't have an agenda that demands exponential growth in new knowledge.

The search continues.

It Should Be Lumpy, Right?

We wouldn't expect a uniform doubling of human knowledge within a 5-year timeframe, right? Even if this is a law as inexorable as Moore's (and that doesn't seem as inexorable as it once was, or am I reading the Dell ads wrong?), one would reasonably expect that human knowledge would advance a little in some areas and a lot in others. You with me?

Given what the world's attention has been focused on since 2002, here are some of the areas where I think human knowledge should have increased fastest:

• Epidemiology, thanks to SARS and Avian flu
• Biofuels
• Vaccines
• Proteome
• Oil extraction from rock and shale
• Mars
• Genetically Modified Organisms
• Fishery management
• Global warming
• Solar activity
• The Long Tail
• Stem cell cultivation
• Infectious diseases

I will treat this as a proxy list of subject areas to explore. I'm going to be digging around to see if we've seen dramatic advances in any or all of these. I'll probably dedicate a few posts to each of them. Got any suggestions?