Does Human Knowledge Double Every 5 Years?

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...

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.

Sobering News

The post below from yesterday, which details the stately, rather than exponential, increase in granted patents in the U.S., has really got me thinking, and I think we'd better report on the state of play here.

Let's detail those areas where we have seen adequate growth to double human knowledge every 5 years:

Update: We have since found other areas where the CAGR is sufficient to double human knowledge every five years:

Update 2: A modest review revealed errors in my calculations regarding oncology. Its position has changed (and not for the better).

Prions, where academic journal publications have increased at a CAGR of 25.57%, and patents have increased by 33.76%

Software, where academic journal publications have increased at a CAGR of 22.83% and patents have increased by 33.53%

Post-graduate enrollment in China, which has increased at a CAGR of 22.38% (although see below for more discouraging information about the growth of tertiary education worldwide)

(All percentages are CAGR (compound annual growth rate.)

1. Nanotechnology, with a blistering growth in publications of 97.16% per year. Patents, 76.15%.

2. Global Warming publications, with a of 16.85%

3. Total Chinese patent applications, at 25% per annum

4. Chinese computing patents, 58.29%

5. Chinese telecommunications patents, 30.26%

(was oncology)

7. Epidemiology patents, 22.76%

So far, that's it.

Now let's look at where we did not find anything like doubling every five years (remembering that we need a CAGR of 14.87% to double in five years time):

Update: We have now found other areas where human knowledge does not appear to be growing at a rate that will double in five years time:

Worldwide university enrollment, which has a CAGR of 4.85%

Alzheimer's disease, where academic publications have a CAGR of 9.65% and patents a CAGR of 11.26%

Programming, where academic publications have a CAGR of 12.55% and patents a CAGR of 12.83%

Chinese university enrollment, with a CAGR of 9.76%

1. U.S. patents granted, 5.21%

2. Epidemiology publications, 8.85%

3. Shale oil extraction, publications 5.59%, patents, 2.61%

4. Publications on Mars, 5.78% (see also here and here)

5. U.S. Book publishing, 5.14%

6. Indian university enrolment since 1947, 5.51%

7. Climate Models, 12.66% (Very close to 5-year doubling rate of 14.87%)

8. Improvements in Climate Models, 13.76% (Also very close)

9. Growth in publication of scientific and technical papers, 1995-1999

             OECD 0.1%

             U.S., -1.8%

             Canada, -2.2%

             UK, -0.1%

             Netherlands, -0.5%

10. Publications in astrophysics, 4% (since 1970)

11. Growth in percentage of cancer patients surviving 5 years after diagnosis, 0.7% (1960-2005)

12. Drop in percentage of soldiers dying from wounds received in battle, 1.54% (1941-2006)

13. Projected growth in number of scientists (U.S.), next ten years, 7.18%

14. Patent filings in India, last five years, 8.45%

15. Increase in patent filings, World International Patent Office, 1 year, 6.4%

6. Oncology pubications, 9.23% (revised)

Considering I cherry picked areas that I thought would be most likely to show robust growth, this is scary.

          

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.

Chinese Papers in Nanotechnology

Well, I was going to wait before starting on nanotechnology, but I don't have a convenient place to park this information, so you get it in toto:

From PhyiscsToday.org: "A paper by Ping Zhou and Loet Leydesdorff (PDF) suggests that China is rapidly developing research expertise in nanotechnology. Six years ago, US-based scientists published 50% of the papers in the journal Nanotechnology and China accounted for zero. Today 25% of papers in the journal are from US-based scientists and 15% from China. Zhou and Leydesdorff report that between 1999 and 2005, for 85 journals in the fields of chemistry, physics and material sciences that are relevant to nanotechnology, the number of papers published by China rose exponentially to 8.34%, while papers published by other countries either remained steady or declined. China's overall world share in science journals is 6.52%, suggesting that China is aiming to be at the forefront of research into nanotechnology."

The paper this article is based on talks about a ratio between GDP and R&D, the return of overseas scholars and other factors. The paper then details research that looks like what we're trying to do here--except they're doing it a lot more... scientifically. They even call it scientometric analysis! I'm going to steal that...

Where I am using crude statistics available for free and for fun, they use "indicators like total publications, total citation rates, percentage of world share of citations, as well as the top one percent of most highly cited papers in order to measure scientific output."

Something else I'm going to have to look at--"For the input indicators, we used the OECD's Main Science and Technology Studies published online and in print (OECD 2004)." Like me, they experienced difficulty in searching large databases of publications. They found their own solution, but it won't help me going forward.

Some interesting findings:

• Between 1999 and 2004, China moved from 10th to 5th place in terms of overall scientific publications
• The overall US share has dropped from 35% to 30% between 1992 and 2004 (but if the overall number is rising, who cares?)
• Countries where English is commonly spoken (and written, obviously) appear to have an advantage when it comes to having your paper cited by others
• More than 4,400 science and technology journals were published in China in 2001
• Half a million articles are published annually in Chinese journals
• It appears that Chinese scientists read the work of scientists in other countries, but that international scientists don't read (or at least don't cite) work published in Chinese journals (with the exception of some Chinese journals that are published in English)
• The Chinese government declared nanotechnology a critical R&D priority in 2001, and a group of commissions and ministries issued a strategic plan for development of nanotechnology through to 2010
• Definitions are tough. It was hard for the researchers to find all nano-related papers, and only nano-related papers. (I know what that's like--and what it means. You actually have to read, instead of count, and that takes time)
• The paper's authors use really, really cool graphs to show their work. I am extremely jealous

Now I just have to find out where they got those numbers at the end of the news release...  they could have listed those 85 journals...

Back to Work

I'll be writing a lot more about the Singularity later. Let's go back to the basic building blocks that will educate my later writing.

We return to the numbers of people in higher education. If this number is growing exponentially, there might be reason to think human knowledge will too, in future. Specifically, in India, we find "India's provision for higher education rose from a meagre 200,000 at the time of Independence to an astronomical 5,000,000 college and university places by 1998." Those words come from Gajaraj Dhanarajan, President and CEO, The Commonwealth of Learning, Vancouver, Canada. He was speaking in August of 2000 at the 11th General Conference--Universities as the Gateway to the Future.

Let's see--India achieved independence in 1947 (right? Might be off a year--Nope. Google says August 15, 1947). If Indian university students had doubled in number every five years since then, starting from a base of 200,000, they should now have 516 million university students. So, if they have started growing exponentially, it is recently. (How many university students should India have? Using figures from Dhanarajan's speech, to have the same rate of university enrollment as Canada {5%}, for example, India should have had 50 million university students in 2000. Room for improvement here).

This is actually fairly important. The Compound Annual Growth Rate (CAGR) for the Indian university population is 5.51%. The CAGR needed to double in five years is 14.87%. A CAGR of 5.51% means the population doubles every 13 years, instead of five. We won't get where we need to be at this rate.

If you've been reading from the bottom up, you'll be able to join in the refrain--"Great growth. Not doubling."

Happy Coincidence

A chart I put up on the weblog cited Derwent's World Patents Index as a source. It is found at Thomson.com, and it has information regarding 31.66 million patent documents. (Okay, let's future proof this--in 2012, will it have information on 63 million patent documents?)

They charge to get in and look around, so I'm hovering on the periphery, seeing if I can find more meta-data about the database. For example, an article titled 'Open access to the medical literature: How much content is available in published journals?' by Marie McVeigh and James Pringle, published in 2005, indicates that about 20% of medical literature published in 174 journals since 1992 is 'open access', that is, freely available online. They estimate that a bit less than 60% of medical literature in that time period can be accessed electronically. We also find that Thomson's ISI Web of Knowledge has 20 million users from 81 countries accessing a database of 22,000 journals, 23 million patents and much more. All good supporting data for my second hypotheses, about the increasing availability of human knowledge. But I would love to see the growth rate for new data coming into that database, and I can't find it.

However, I did find this--an article called 'Eastward ho! --The geographic drift of global R&D' written in March 2007 by Bob Sternbridge. It touches on a number of topics I've written about below, and has some interesting numbers:

• The number of computing patents filed in China has risen from 2,000 to 20,000 in five years! Clear doubling in the right time frame. (Pity the increase was not replicated in Japan or Korea, which were also included in the study)
• The number of communications patents filed in China has also risen in the same time frame, from 8,000 to 30,000--again a doubling! Sadly, again not replicated in Japan or Korea.
• More importantly, the total number of Chinese patent applications is growing by 25% per annum. But the article then says that Japan and US patent filings have been flat or declining in recent years. And a lot of the patent filings are by multinational corporations
• R&D spending in China has risen from 89.6 billion yuan in 2000 to 245 billion yuan between 2000 and 2005
• The number of researchers in China grew 77% over the ten years from 1995 to 2004

I think it will take me a couple of hours to digest this and incorporate it into previous posts. More later.

Whew--We Find That Something Has Doubled

It would have been truly strange not to find some area where there is evidence of a doubling of activity. I actually think we'll find more as we go on. But the past two weeks have been somewhat discouraging, so I'm happy to report that we see clear evidence of a doubling in the growth rate of patent filings in China over the past 5 years, and a doubling of the total number of academic patent filings worldwide between 1995 and 2000.

An article titled 'Rapid Patenting Growth By Academic Institutes In The People's Republic Of China' by Simon Pratt, published in June 2005 shows a doubling of the growth rate (not the actual numbers) of patent filings by academic institutions in China, and a doubling of academic patent filings worldwide by universities between 1995 and 2000 (see chart below). Sadly, that growth rate has not been sustained since 2000.

It is not unalloyed good news--worldwide, academic patent filings are a response to governmental decisions to allow universities to retain, license and exploit intellectual property, so there may just be substitution here--the same patent might previously have been filed by an individual at the academic institution or someone who had access to the reseach. But I'm so happy to find something relevant that has doubled in five years that this seems like a minor quibble.

Here is the chart showing the number of academic patent filings worldwide since 1980. As with all the charts on this weblog, clicking on the chart will bring it up in a readable size.

Will Emerging Countries Double Human Knowledge For Us?

Maybe not--they may not even replace the shortfall in scientists and engineers in the OECD.

In December 2005, Vivek Wadhwa, a professor at Duke University, wrote an article that was published in Business Week. He was trying to allay fears of India and China as outsourcing monsters that would eat engineering jobs. Wadhwa said that Duke students were wondering if they should even enter the profession if the jobs would migrate to Asia. Wadhwa, Professor Gary Gereffi and some Duke students researched the topic. They published a report (large PDF) that may indeed lay some outsourcing fears to rest.

However, for those who are anticipating that a surge in Asian technical knowledge workers will step into the shoes of Western students who are abandoning technical fields of study, the report brings no comfort.

In China in 2004, 644,106 engineers graduated. However, only 351,537 were four-year degrees. Worse, due to differences in definitions, the latter figure includes motor mechanics and industrial technicians.

In India in 2004, a total of 215,000 engineering graduates were produced. However, only half (112,000) were four-year degrees--the remaining being 3 years.

In the US, a total of 70,000 engineers graduated with 4-year diplomas, a figure that rises to 222,325 if computer science graduates are included. Indeed, the number of science and engineering doctorate degrees awarded in the United States dropped by 7 percent from 1998 to 2001, according to a
separate National Science Foundation study made public this week. However, enrollment in science and engineering graduate programs rose in 1999 and 2000.

As I have not found historical data for China and India, I don't know if their output has not only doubled, but also taken over the load for the disappearing Western graduates--including the implied doubling that we are looking for. We do know that they have been pumping out engineers for quite a while, so their figures are unlikely to be doubling--just growing as fast as they can. So, this post isn't really finished. But it doesn't look as though the results will support the principal contention in Hypothesis 1, that human knowledge is doubling every five years.

More to follow.