Does Human Knowledge Double Every 5 Years?

U.S. Research Funding by Sector

I think the real problem with this post will be presentation. I have an Excel spreadsheet that shows U.S. federal funding for reseach by sector, and I want to show the growth rates and doubling times. However, the time series for some sectors differs, for a variety of reasons. So, please be patient with me.

I will put the figures in the extended post below, as well as some analysis, and report the topline findings here. In a later post I will do the same for subcategories. I think it will look messy. The purpose is to see what choices are being made, so we can compare funding differences to outputs--the numbers of academic publications and patents in each field.

Mathematics and computer sciences have seen the greatest growth, with a CAGR of 10.54% and a doubling time of 6.92 years. Strangely, physical sciences (including astronomy, chemistry and physics) fared second worst, with a CAGR of 5.14% and a doubling time of 13.83 years. However, it did start with the second highest base total, if that's any justification... Slowest growth in federal research funding was experienced in social sciences, with a CAGR of 4.82%, which gives a doubling time of 14.72 years.

Update: I had to recalculate all the stats to account for inflation, converting all $ figures to 2006 USD. It changes everything...

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.

So, Does Human Knowledge Double Every 5 Years?

1. No,

2. But it could

3. Because we see that it does in sectors where we pour in human and financial resources.

However, the Western world is not pouring in human and financial resources the way it used to. Students are choosing law, business and web design instead of engineering and science. Government is encouraging private sector R&D (and encouraging universities to work closely with business), but it doesn't happen enough and when it does, it is focused on very short term proejcts that improve a bottom line in the next quarter.

Absent the commitment of extra resources, it looks like human knowledge doubles every 10-15 years. I'll be showing my work in the next post, and then supplementing it with information about the commitment of resources, an unwelcome next task.

But where there is a clear incentive, such as nanotechnology or global warming (where the incentive may be just getting a project funding by slapping a green label on it), we get the output that shows that our knowledge and exploitation (via patents) of a given sector can double every five years.

Continued below--click if you want to see a bit of a rant...

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.

University Students Worldwide

The OECD charges for their statistical publications, but sometimes you can find a browsable 'Read It' version (sort of try before you buy?). In any event, I found a freebie copy of a 168 page PDF of their Focus on Higher Education document for 2005-2006.

I'm looking for numbers for enrollment, hopefully a time series. However, as I browse through I will put other relevant information here in bullet points. Bear with me--this is a work in progress.

• There are more than 17,000 higher education institutions in the world.
• 'In the past three decades, the proportion of young people enrolled in higher education has risen from 20% of the population to just over 50% on average in the OECD.(Angel Gurria, Secretary General of the OECD.)
• In 2002, approximately 3.6 million researchers were engaged in R&D in the OECD (p. 46)
• In 2003, 2.12 million students were enrolled in universities outside their country of origin (93% in the OECD) (p. 64). This has increased by 50% since 1998.

And that's all. Big disappointment. I have seen elsewhere the figure of 88 million university students worldwide--it was from a UNESCO high muckamuck, and I'll link to it when I re-find it. But what I need are annual figures... for the world... going back 1,000 years, if possible--hey, you could send me a link...

UK Higher Education Numbers

According to this website published by Universities UK, In 2004/05, there were approximately 2.3 million students in the UK (Total undergraduate and postgraduate).

This chart shows growth from 1961 through 1995, going from 200,000 to 1 million in 34 years. It's evidently more than doubled in the past eleven years. Even looking only at this period, compound growth is 7.87%, which would double every 9.85 years. Looking at the entire period, CAGR is 7.02%.

Click on the image to see a bigger version. Courtesy of University of Leeds

With the recent addition of student fees, I don't see hypergrowth kicking in any time soon. Hope the rest of the world will compensate.

Outcomes

Advances in human knowledge should make life better. That's hard to measure. However, we can measure if human life gets longer (it does), healthier, richer (if not more rewarding), etc.

The rest of this post is philosophizing--feel free to skip. And in a previous post, I talk about the Outcomes Fallacy. But if you want thinking on the issue of human knowledge and outcomes, click to read more.

University Enrollment in China

If we start with the premise that university students are destined to either become creators or transmitters of human knowledge, large increases in their total numbers would augur well for future trends in the growth of human knowledge. (Obviously there's plenty of room for contribution by non-graduates--at least I hope so, as a non-graduate myself.)

If you are interested in the background of education in The People's Republic of China, I highly recommend this article in Wikipedia.

Here's an article by People's Daily, written in 2000, about China's plans to expand university enrollment. They cite the number of 2.04 million in 2000, and projected an increase of 1 million by the end of the year. But the article is really bad and really is not useful, other than as a signpost for further research. It did however, have the huge advantage of being the first return on a Google search for Chinese university enrollment.

The China Education and Research Network published a 2001 article writing about a goal to increase China's university enrollment to 15% (of 18-24 year olds) by 2010 from the then level of 10%.

A link at the bottom of the article led me to this announcement, which is a bit hard to decipher:

• China's universities and colleges enrolled 2.6 million freshmen in 2001, 800,000 more than last year.
• Officials with China's Ministry of Education said that China plans to increase the number of university students to 16 million in the five years to 2005, compared with a total enrollment of over 11 million in the 1996-2000 period.
• According to a special plan for educational development, university students will account for 15 percent of school students in 2005. By that time, the number of postgraduates will reach 600,000.

So this supports, in a roundabout way, the first piece--2000 level of 10% with projected rise to 15%, but target date of 2005. Let's see if we can find out how they did...

In 1977, despite the fact that 5.7 million students took the uniform national examinations, there were only 278,000 university places available for them. What a waste... By 1985, (if I am reading the Wikipedia article referenced above correctly), that had risen to 560,000 places (there were also 550,000 places for professional and technical schools). And we see above that they enrolled 2.6 million in 2001. That's essentially a ten-fold increase in 24 years. Well done, China. But sadly, that's only a CAGR of 9.76%.

For science and engineering, we read that China is now putting out about 600,000 graduates per year. This does not appear to be a huge increase--Wikipedia tells us that there were more than 1 million applicants for science and engineering places in 1984, and we can kind of infer that there were about 200,000 accepted, a CAGR of 5.12%.

It very much resembles the growth in science and engineering found in the United States between 1950 and 2000. But it doesn't even replace that growth, let alone overcome the shortfall in U.S. (and OECD) science and engineering since 2000.

As so often happens, I find more relevant research after I've written all the above. (You get to see the work in progress, FWIW...)

The Chinese Ministry of Education does publish enrollment figures. I found out thanks to Wang Yibing, former UNESCO higher education specialist and part time professor at Zhejiang University. In this article (PDF), Wang shows the MOE figures for Institutes of Higher Learning from 1998 to 2006. I reproduce them below.

It shows that growth of post-graduate enrollment since 1998 (from 725,000 to 3,648,000) does show a CAGR of 22.38%. We have another winner! This is truly exciting--these are post graduates, after all. It almost makes up for the disappointment in U.S. patents found earlier in the week. Now we just have to hope that they don't get hijacked into designing toys for U.S. consumers...

Enrollment at Institutes of Higher Learning overall in China since 1998 also shows a 21.21% CAGR, again, more than sufficient to double every five years! Hooray, China! I am reluctant to carry this analysis back to 1977, because I believe my prior numbers separate universities and other institutes of higher learning, but we just have to root for another 5-10 years of growth.

Click to see the numbers.

Trends in U.S. Knowledge Workers

This is another grab bag post, where I park interesting numbers for further exploration at a later date.

• In the last 20 years of the twentieth century, the U.S. college-age population declined by more than 21%, from 21.6 million in 1980 to 17.0 million in 2000. The college-age population decline reversed itself in 2001, and will increase to 19.3 million by 2010 (a 13% increase over the year 2000 figure). Witty comment about how demography is destiny, please.
• The private, for-profit sector is by far the largest employer of science and engineering workers. In 1999, 74% of scientists and engineers with bachelor’s degrees and 62% of those with master’s degrees were employed in private, for-profit companies. So we might see an explanation of why patents grow more quickly than academic publications--at least in some sectors...
• Between 1991 and 2001, the number of jobs in the U.S. increased by less than 15% while science employment increased by more than 93%. Much of this can be attributed to the enormous growth in computer scientists. The number of computer systems analysts and scientists increased by 268%, or 1,135,000 people, during this period. The number of natural scientists increased by almost 33%. Within this category, medical scientists experienced the largest increase: 111%.
• Within engineering, as in the period from 1991–2001, electrical and electronic engineering is projected to have the biggest absolute employment gain, up by 31,000 jobs, or about 11% between 2000 and 2010. Larger relative gains are expected for biomedical, environmental, and computer hardware engineers. Further declines in petroleum engineers, as well as mining and geological engineers, are projected. Employment for all engineering occupations is expected to increase by only 9.4% over this period.
• The Bureau of Labor Statistics expects that the trends evident between 1991 and 2001 will persist. While the economy as a whole is expected to generate 15.2% more jobs over this decade, employment opportunities for scientists (excluding social scientists) and engineers are anticipated to increase by about 44%, amounting to an additional 2.3 million jobs.
• Approximately 88% of the increase in science and engineering jobs will occur in computer-related occupations. Overall employment in these occupations is projected to grow by almost 69% between 2000 and 2010, with more than 1.9 million jobs being added.
• Eight of the ten occupations expected to grow most rapidly between 2000 and 2010 are computer-related. The increasing demand for computer-related occupations reflects the rapid advances in computer technology and the continuing development of new computer applications, including the Internet and intranets.
• Overall, computer specialists, a component of computer and mathematical occupations, are projected to increase by 68.6%, for example. Five computer occupations — computer software applications engineers, computer support specialists, computer systems analysts, computer systems software engineers, and network and computer systems administrators — also are among the occupations with the largest projected numerical job growth. Computer and data processing services is the economy’s fastest-growing industry, and in almost all industries, employment in computer occupations is projected to grow much faster than average.

Well, they might want to rethink their forecasting on petroleum engineers, but there is no indication that anyone expects hypergrowth in the numbers of science and engineering workers.