Does Human Knowledge Double Every 5 Years?

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.

Oncology

Entrez is the integrated, text-based search and retrieval system used at NCBI for the major databases, including PubMed, Nucleotide and Protein Sequences, Protein Structures, Complete Genomes, Taxonomy, and others. It is a service of the National Library of Medicine and the National Institutes of Health. However, it is included within Scirus, so the results will be taken from Scirus.

Searching with the term 'oncology' returns 148,053 results. 57,936 were published between 2002 and 2006 (inclusive). That's only 39% of the total, so it doesn't look like human knowledge of cancer has doubled in the past five years on that basis. In the preceding five years (1997-2001), only 38,153 results were published. That means that the most recent five year period did not even double the preceding five year period.

The CAGR for academic publications for oncology is 9.23% (since 1920), which would double every 7.85 years. Patent growth since the first filing in 1973 is 28.62%, which would double every 2.75 years. Using the same base date of 1920 would yield a CAGR of 10.02%, doubling every 7.26 years. I don't know which date distorts the picture less.

And the fact is, we don't know how many times we will have to double our knowledge of cancer before we will be able to make a big difference in the lives of those who have it. I have to say, I think I'd rather see the growth rate we note in nanotechnology here--and yes, I think I am saying I would make the trade off. I'm not advocating central planning of scientific research--I'm just wondering if research incentives are correctly allocated.

Now champions of nanotechnology wll say that nanotechnology in general has many direct applications to medicine in general, and further that some nanotechnology research is specifically concerned with oncology. And it's true. My reservation comes from my suspicion (for which I have zero evidence) that this is engineering led (hey--come here and see what my new toy can do!) rather than medicine-led (can you build something that will do x, y, and z in the following sequence and make sure it does not do a, b or c?) If my suspicion is correct, this wil prolong the search for solutions rather than shorten it.

Is there a truce in the war on cancer? Best put out that cigarette. Because we see that, although oncology did see a doubling of knowledge every five years up to 1991, that hyper-growth tailed off afterwards. Note that hypergrowth started before Nixon's war on cancer. Note that growth since hypergrowth stopped has been perfectly respectable--14,000 papers published in 2006 (more in 2006 than in the entire decade of the 80's), and 4,000 patents filed. And note especially that growth in patents has continued to double every five years. Make of it what you will.

The figures are below. Click to see the numbers.

Relevant Research from 1988

It would have been very strange if I were the only one asking this question and doing some research. I'm glad to find some prior work on this, not least because it means I'm not the only one who cares.

A report on the International Conference on Fifth Generation Computer Systems in 1988, written by Jakob Nielson, refers to research by Jorg Siekmann of the University of Kaiserslauten in the then West Germany.

Nielson writes, "Siekmann reported that the number of scientific journals doubles every 15 years, the number of books in university libraries doubles every 10 years, and the number of scientific publications doubles every 5 years. The knowledge explosion has already reached a level where in chemistry it is often cheaper to conduct a possible duplication of an experiment than to search the literature to find whether the result of a previous experiment can be used." That last bit is scary--I wonder if it's still true. Let's see if we can find more about Siekmann and his research.

Google likes him--a little too much. There are 108,000 search returns on his name.

The University has some material about him: Jörg H. Siekmann is the head of several research groups working in artificial intelligence at the "Universität des Saarlandes" and at the German Research Centre for Artificial Intelligence (DFKI) in Saarbrücken. He is a professor in the department of computer science and a director at the DFKI. The five research groups are:

Automated Reasoning for Mathematics: OMEGA 
Competence Center e-Learning
Formal Methods: VSE
Multi-Agent Systems
The IT-Security Evaluation Centre

Currently he is the chairman of the collaborative research centre "Resource-adaptive cognitive Processes" (SFB 378) funded by the German Science Foundation (DFG). He is chairman of the network of excellence on computational logic (CoLogNet), and vice president of the International Federation on Computational Logic (IFCoLog) . His main research interests are Artificial Intelligence, Automated Reasoning, Multiagent Systems and e-Learning in Mathematics.

But I can't find any more information about his statement at the conference. However, I did stumble across something quite interesting that might lead to the origin of the statement  Human Knowledge Doubles Every Five Years. See next post (above).

Epidemiology

Well, Scirus, the database of Scientific knowledge I've been using frequently on this weblog, has a lot of material relating to epidemiology. I feel a bit vulnerable relying on this source so heavily--if anybody has suggestions for freely available information, I will happily (well, grumblingly and slowly and swearing occasionally) replicate these searches on it.

Searching for epidemiology on Scirus returns 1,500,983 results. 315,678 of these are journal articles. 8,530 are patent results and the other million plus are 'other' web results. So, focusing on journal articles and patent results since 1920, let's see if the numbers double every 5 years.

Human knowledge (as expressed by journal articles published) about epidemiology has not doubled in the past five years. Only 106,722 of the 315,678 journal articles were published between 2001 and 2006. It's truly a triumph of the human mind, but it is not doubling. It is a compound annual growth rate (CAGR) of 8.85%, which would result in a doubling every 9 years. Looking at the time series, we see dips and lulls and a steadily progressive trend line, with a couple of jumps. When I get the graphs prepared, it will be easier to see.

Overall, CAGR for epidemiology is 6.22%, which doubles every 11.49 years. Overall growth in patents is 17.37%, which doubles every 4.33 years.

However, backing out the 2007 patents (198) leaves a total of 8,332. Of that number, 5,444 (65%) were filed between 2001 and 2006. So while academic investigation did not double in the past five years, commercial research and development more than did so. Indeed, epidemiology patents appear to have more than doubled in every five year period since 1987, when 19 patents were filed, a CAGR of 22.76%.

I suppose, if we treated one journal article and one patent as exactly equal, we could add them up and compare the totals. But, as I certainly don't have any reason to think that might be the case, I'm not going to. The figures are below if you want to do it, though.

Click below to see the data.

How Would We Define Victory?

Well, time to define a few things here. We are trying to discover if human knowledge doubles every 5 years. To do this, we are testing three hypotheses:

1. We learn so much new information that the actual stock of knowledge is double what it was 5 years ago. We are testing this by seeing if scientific publications and patents are doubling every 5 years. We also look and see if there are twice as many scientists and researchers as 5 years ago.
2. That new and old human knowledge is accessible and usable to twice as many people as it was 5 years ago. We're looking at things like the size and reach of websites like Wikipedia, and also referring to our search for more creators and users of information.
3. We are disproving incorrect hypotheses at such a rate that we are doubling human knowledge by unlearning untruths, which corrects mistakes and frees up time for productive learning.

But this is a bit simplistic.  If I know one thing and learn another, have I doubled human knowledge or just what I have learned? Is a learned fact human knowledge before it is published?

If I know one thing and, without learning another, communicate that one thing to another human being, does that double human knowledge because two of us now know it? Or is that just repetition?

If I discover an hypothesis is not correct, does it make any difference if others continue to hold the old and incorrect belief?

And then we must make things difficult by defining knowledge. Many of you will have seen the pyramid that has data at the bottom, information on top of it, then knowledge and then wisdom. The implication is that data is a fact revealed, information is the fact in context, knowledge is is the fact absorbed and assimilated, and wisdom is right action based on knowledge as experienced. But is that an accurate or adequate definition of knowledge? Is it sufficient?

Wikipedia has a definition--it's a bit long, but the start is promising. Of course the start is a quote from Oxford's English Dictionary. "Knowledge is defined (Oxford English Dictionary) variously as (i) facts, information, and skills acquired by a person through experience or education; the theoretical or practical understanding of a subject, (ii) what is known in a particular field or in total; facts and information or (iii) awareness or familiarity gained by experience of a fact or situation." Yeah, that's it.

So does learning that the Earth is more than 6,000 years old mean anything if millions don't believe it? If creationists make learned scientists spend time in court patiently explaining evolution instead of working in the laboratory--their true 'field of the Lord,' have we learned anything? Does knowledge have to be unanimously held, or unanimously available?

Boy, where's a philosopher when you need one?

Back to Global Warming

And back to Scirus, the compendium of scientific publication. Okay, it's a search engine returning titles of journals, patents, etc.

What are we to make of the fact that searching for global warming on Scirus returns 100,000 more results than a similar search for nanotechnology? It's been studied for 20 years longer than nanotechnology, so global warming should reflect that... But there are 8,000 fewer academic articles in the database (28,000 for nanotech vs. 20,584 for global warming). What does that mean?

We found 5,184 patents on the Scirus database for nanotechnology. For global warming... 9,419. Scientists and technologists have been studying global warming for more than twice as long, so that may mean nothing. But, let's look at the statistics and see what they tell us.

As shown below, playing by the same rules as we did for nanotechnology and the study of Mars, we hereby proclaim a base year of 1975, as it saw 18 journal articles published and one patent filed. That gives us 31 years to measure growth. This indeed gives us a CAGR (Compound Annual Growth Rate) of 16.85%, which in fact does show doubling every five years! Hooray, we have another winner!

The CAGR for patents is higher yet--26.08%. (But again, it seems to have leveled off in 2002.) We saw below that growth was disappointing in the subsector of climate modelling, but it's being more than made up for elsewhere.

But, given the potential gravity of the consequences of global warming, am I the only one to look at the growth rates of human knowledge in this field, compare them to the growth rates for nanotechnology, and feel slightly disappointed?

The data is below. Click if you want to see the numbers.

Nanotechnology and Human Knowledge

There's a search engine called Scirus for scientific information. A search performed on Sunday, 22 April 2007 with the search term 'nanotechnology' returned 637,500 results. Fortunately, we can winnow that down to 28,846 journal results and sort them by date. (We also found reference to 5,148 patents) So, here we go again... 23,489 of those journal articles were published after 2002 ended. That's 81% of the total. Similarly, 4,494 patents were filed since the end of 2002, 87% of the total.

Using 1987 as a base year, we find CAGR in journal publications of 42.03%, which would double in 1.98 years. For patents, we see a CAGR of 44.91%, which would double every 1.87 years.

And this is why Ray Kurzweil and the rest of the Singularity gang get excited. Remember we need annual growth of 14.87% to double in five years. Nanotechnology has got it in spades.

Last year's growth was 37.87%. Maybe they will take over the world... but I will explain later why I think growth in nanotechnology is a necessary, but not sufficent pre-requisite for the Singularity.

Note that the advanced search by year  yielded 28,863 journal results (but it found all 5,148 patents )(one reason these types of databases drive academic researchers crazy--I hear Google Scholar is worse, and I'm afraid I'm going to find out soon...)

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...

Human Knowledge and Mars

(This part is repeated from the previous post): NASA and the Smithsonian Institute maintain a database called the Astrophysics Data System. Harvard University is kind enough to host it here. Available to you and I is an abstracting service which will return brief descriptions of articles found by keyword searches. You see where I'm going here?

For a description of coverage and limitations of the database, click here. Then, let's have some fun.

A search for the word Mars in titles and abstracts performed on April 21 2007 returned 20,978 results.

(This is where the new stuff starts): Here we report on 5-year periods going back to 1900. We show annual percentage growth on the previous 5-year total. It isn't pretty--much more like real life than any smooth logarithmic curve. In 22 five-year periods, we show an annual percentage growth above 14% (shown in bold) in only 3 five-year periods(you need a 14.87% annual growth to double every five years). In 7 of the five-year periods, there is a decline in publications (inefficient post, wars, depressions, Mars being further away... lots of logical reasons why this might have occurred).

The serious question is, if our studies of Mars, which have benefited from major government funding from several large governments, and have also benefited from being topical, exciting, and having large sources of data available recently, do not show exponential growth, where would we expect to actually find a doubling of human knowledge every five years? If not here, where?

What I think it shows me is that when there is a lot of funding, real news, a research goal, and the availability of new and important data, we focus on the subject, do the research and improve knowledge. But for extended periods, things just sort of tick along, improving respectably in many years, but showing declines in others. What do you make of the following?

Click if you want to see the numbers.