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.

Alzheimers and Human Knowledge

Alzheimer's disease destroys human knowledge, but perhaps more importantly, it decoheres the personality that organises this knowledge. It is only human knowledge that can defeat this destroyer of human knowledge. It has been described,  treated (unsuccessfully) and researched for a century.

Let's see what Scirus tells us about the growth of human knowledge (and the commitment of research resources) on this. (BTW, I recently had another look at the sources Scirus uses, and it includes PubMed, so I won't be replicating this search there.) (And I got a quick scare by starting with the search term 'Alzheimers,' which only returned 1,428 results--if you're fact-checking me, and I hope to God someone is, use 'alzheimer.')

A search for Alzheimer on Scirus returns 1,274,572 results on Scirus, of which 112,401 are journal publications containing the term in the title, abstract or text. The search also returned 67,900 patents.

In the extended post, I will give the results by year and by five-year period. That's a Sunday morning for you--hot coffee and a database to search.

Okay--we'll assign 1920 as the base year for journals and infer 4 journal articles published that year, giving us a CAGR (Compound Annual Growth Rate) of 9.65%. This would indicate that human knowledge regarding Alzheimer's Disease doubles every 7.52 years.

However, the first patent was filed in 1976, which gives us a CAGR of 11.26%. This would double every 6.5 years. So, although work proceeds at a good rate and human knowledge is increasing, there is nothing like the growth rate seen in areas such as nanotechnology or global warming.

Again, we see that patent growth, starting at a later date, grows much more quickly than academic publishing. I am personally mystified as to why research into prions has grown twice as quickly as research into Alzheimers. Many more people suffer from Alzheimers than CJD, and the potential for both alleviating human suffering and reaping large rewards are much greater. The overall totals for Alzheimers research are greater than prions, don't get me wrong--but why is the growth trend favoring prions?

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.

Prions

It's back to Scirus to see trends in publications and patents regarding prions.

Prions are infectious agents composed only of proteins, and are implicated in BSE (bovine spongiform encephalopathy, AKA mad cow disease) and Creutzfeldt-Jakob Disease (CJD) which as far as I can tell is more or less a human equivalent.

Prions were hypothesized in the 60s and actually found in the 80s, winning a Nobel prize for the disoverer, Stanley Prusiner.

The human disease is quite rare. Mad cow disease is not. Both are fatal. There is a public good to be pursued in preventing CJD and private profit in preventing mad cow disease. The two together should stimulate research. With a short timeline to look at, it will be interesting to see if human knowledge doubles every five years.

Scirus returns 13,518 journal publications with 'prion' in the title, abstract or text, and 8,781 patents. Because there is a bird called the fairy prion (Pachyptila turtur), I will actually have to look at the results... darn.

We hereby proclaim a base year of 1981, when 5 journal articles and no patents were published. That gives us a CAGR (compound annual growth rate) of 25.57% and we have another winner! Human knowledge has doubled every 5 years regarding prions! And patents have grown even more rapidly, at 33.76%--huzzah!

However, as we have seen elsewhere, a note of caution--while patent growth has consistently exhibited hypergrowth characteristics, journal publications have leveled off, with the period 2002-2006 growing 'only' 66% over the preceding five-year period.

Click below to see the results.

Programming, Software and Computer Science

Computer programming has a lot of work and a lot of people centered around it. If the Singularitarians are correct, we're going to need them all.

After all, what good is it if computing speeds and memory keep doubling if we cannot program computers to do what we want them to do? And the Singularitarians want computers to do some pretty ambitious things. In fact, given their wish list, it seems clear that human knowledge of computer programming has to double every five years if we are going to get the magic box to do what we want it to do. We will need new programming languages, tighter coding, better algorithms, and quite possibly a new way of looking at programming. Is this happening?

We've seen elsewhere that the number of people engaged in computer sciences has grown to 180,000 new entrants per year in the U.S. alone--and considering the base date for this field, that is evidence of healthy growth. Let's use Scirus to see what this growth in professionals has produced in the way of patents and journal articles.

Preliminary results: between 2002 and 2006, 38,685 journal articles were published with the word 'programming' in the title or abstract. As the total is 145,404, only 26.6% of all journal articles were published in the last five years. Of the 367,971 patents noted on Scirus with 'programming' in the title or description, 201,548, or 54.7% were published between 2002 and 2006--so that has doubled. Not the first time we have seen differing growth rates for journals and patents.

For 'software,' the period 2002-2006 saw 224,696 journal articles published, 46% of the total of 486,262. For patents, as with 'programming,' the period was more robust--589,919 out of a total of 900,846, or 65% of the total.

The base year for 'programming' is 1940, when a UK patent was filed for improvements on a statistical calculating device. The compound annual growth rate for journal publications is 12.55%--good, but not good enough to double every five years (it is less than six years, to be fair). The compound annual growth rate for patents is 12.83%.

Remember that we need a CAGR (Compound Annual Growth Rate) of 14.87% to double every five years.

For 'software, the base year is 1965, when 5 journal articles were published and 1 patent was filed. And software is a winner, with CAGR of 22.83% for journal publications!  Hooray for coders everywhere! And a double huzzah to IBM, Microsoft, Sun and countless others, as patent growth since 1965 has a CAGR of 33.53%. Another winner!

As there are so many more patents than journal publications for both search terms, we should probably give more weight to patents, and be extremely pleased that human knowledge appears to have doubled in the past five years in this area, especially given the gloomy results reported in my previous post last week.

Click below to see results and analysis.

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.

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.