Is it possible to examine the extent of human knowledge? How big is the universe of knowledge, and what do we know about it?

Using the Internet has given me a sense of what total access to knowledge might be like. Having been a researcher all my life and having delved wholeheartedly into many realms of knowledge, the potential I see on the horizon is exciting.

My question about knowledge is based on my long experience as a researcher. My work has ranged widely, and has been sufficiently diverse, to place me, I believe, among the top 100 serious intellectual explorers in this country. That is why I feel compelled to examine this issue.

The explication of knowledge that follows is based on my own goal of showing that the borders of knowledge in our society are comprehensible, that their extent is within our conceptual grasp, and that an understanding of this vision will drive our society, in its search for new knowledge, in a direction that I feel is important and fruitful for the common good.

When Denis Diderot compiled the first encyclopedia in the Western world, in 1680, using contributions from the most respected minds of his countrymen, his goal was to display the brilliance and power of Enlightenment learning in stark contrast to the Church's foundations of faith and orthodoxy.

The contents of our daily newspapers, movies, and radio and TV shows are not knowledge, for in most instances it consists of standard stories being repeated millions of times. About 1 percent of this dialogue may provide data that could be used for the development of knowledge, which results from the application of intelligence to relevant categories of data.

I have used the term relevant data in lieu of the more common term information, because information has been used in too many irrelevant contexts that are familiar to the reader ("we need this information by 2 P.M.") but misleading in the current context. An alternative term&emdash;structured data&emdash;has been suggested and is somewhat appealing because it embodies a notion that transforming data into a higher order of use involves structure. An example would be data about rocks on the bottom of the Thames River, which over time were converted into a series of lighted buoys that still later were printed on ship captains' charts. This is an example of data being structured into a new form.

The reason I have chosen relevant data over structured data may be evident from this example. London shipping based on navigational buoys is of minor significance in our current world, and this masterful organization of data is of little relevance today. Having structure does not necessarily bring data into the larger body of relevant knowledge.

Knowledge is the application of intelligence and experience to relevant data.

Some thinkers on this subject have suggested that this definition of knowledge does not exclude music, dance, and all the details of daily life. I disagree. All of these things can be potential data, if there is a way for the application of intelligence to turn it into relevant knowledge.

Let's examine dance, for example. Much dance is now recorded on video, so that it is possible to create data categories that are quantifiable. The more cogent question concerns the knowledge of dance. Let's assume that that knowledge is most likely to be possessed by a dancer, a person with a history of decades of performances. What would that person's knowledge be like?

I would argue that an excellent dancer can study a videotape (potential data) of a dance performance in a genre in which he or she has had experience and could then reproduce that dance fairly well. (Experience here is a synonym for the selection of relevant data and the application of dance intelligence.) The ability of this experienced dancer to reproduce the video of a dance represents knowledge, the ability to bring to life recorded data.

Such a reproduced dance might be below average in comparison to the quality of the original dance and might not be be a faithful reproduction of the original. And that is my point. The knowledge, or structured experience, that uses the video data to recreate the original is there, even when the genius, passion, and vitality that created the original dance is missing. The knowledge of dance allows for the transmission of a dance performance to the dancer, who can thereby reproduce it successfully. That is sufficient to be quantifiable. The same applies to music and to the details of everyday life.

The issue of the arts being separate from knowledge arises specifically in the case of the British philosopher, Gilbert Ryle, who pointed out that "thinking" is based on words, while the arts are not based on words. Knowledge and thinking are not synonymous, nor is knowledge conditional on thinking.

In summary, the arts are not separate from the rest of knowledge.

When I wade into a subject matter to examine the knowledge available in it, I often start with the Encyclopedia Britannica. While a large portion of the EB is not knowledge, merely names of people, places, and objects (data and some relevant data categories), the overall total of 330 megabytes is a rough estimate of the sum of knowledge in the EB. If the EB were to include visual components that are relevant to the knowledge it already includes, we would choose 2-to-1 bytes for the ratio of knowledge-relevant visuals to words conveying knowledge. ( "One picture is worth a thousand words is way off base when it comes to data storage.")

That would make an EB with compressed visuals equal to 1.0 gigabyte of knowledge.

When I use the EB as the basis for my estimate, I am taking the most recent edition. Knowledge is contextual, and the context changes over time, so knowledge needs to be available in a current form. This is most obvious in the case of science, but it is also true in every other domain. Reading an old EB is fascinating, but it is also frustrating because the context of knowledge has changed so much since it was written.

When I jump into a subject and do thorough research, I find that the amount of knowledge inside and outside of the EB varies considerably. On subjects the EB writes about in depth, it can include more than 10 percent of the knowledge of that subject. On other subjects, such as money, the coverage is in the .1 percent range. On average, I feel the amount of knowledge covered in the EB is approximately 2 to 5 percent of the total knowledge of each subject.

Projecting this number, we get the total for "knowledge" of 20 to 50 gigabytes. Just to be safe, if safety is possible in such an outrageous and presumptuous endeavor, let me suggest an upper limit of 100 gigabytes. That is not much in terms of today's data-storage technology.

This estimate is based only on the store of knowledge in our own Anglo-American society. All other cultures, with their comparable encyclopedias, are known to us only through their channels of contact with us: experts on other societies and the skilled translations that have been made of published material. The issue of knowledge outside our social universe is further discussed below.

My focus on knowledge in our society is intended to reify my view that most of the world's cultures are separated by Worfian boundaries. Benjamin Worf was an anthropologist who wrote, early in the 20th century, about the Hopi and argued persuasively that non-Hopi could not reasonably comprehend the world view of the Hopi, because the boundaries between societies are significant and formidable.

For me, the separation exists because each society, as a whole, carries on its own dialogue. This dialogue is pervasive, including nearly everyone within the society. It is a dialogue readily sensed when you leave your country for a month and then return (newspapers read while overseas do not convey the deeper sense of the dialogue). It is blatant when you are gone for a few years, as in the case of the Peace Corps workers who were out of the country anytime between 1968 and 1975, when the dialogue was changing abruptly and extensively. When these people returned, they were completely out of touch, and they knew it. I believe the same Worfian-dialogue isolation of societies applies, with even more vengeance, to the boundaries separating the knowledge of societies.

I am readily aware of the distinct bodies of knowledge of such ancient cultures as the Chinese, Indian, and Japanese. Ancient cultures seem to be especially inaccessible to outsiders, non Chinese, non Indian and non Japanese in this case. My personal experience as a Jew vivifies this difference. My own encounters with my ancient culture has been with Talmudic knowledge. I must state, personally that most Talmudic knowledge is inaccessible to outsiders. This knowledge is written, but its vitality is carried on in oral teachings. Being able to perceive the world through the Talmudic perspective is a feat not available to outsiders, regardless of desire, persistence, or temperament. Since the 16th century, Jesuits and other scholarly groups have focused much effort on bringing this body of knowledge into the Christian domain. Yet, in my opinion they have failed.

From this I can extrapolate to our access to the knowledge of other societies. I don't think much is possible.

What can be said about the magnitude of knowledge outside our society? Nothing. There is one primary reason that an estimate of knowledge beyond ours cannot be made: We don't know how many separate human societies there are. I've listed three ancient ones: India, China, and Japan. They are obvious because of their size and age. Four others are the world of Islam, the Latin-language nations, the Jews, and Tibet.

Having named seven, I run into some genuine difficulties. Are some of the sub-groups of these major societies autonomous? For example, is Persia divisible from Islam? Are the Aztecs and other tribes distinct from Latins? Do the Germans and French form groups that are significantly distinct from the English? Are some of the large groups that don't fall into the major categories significantly different, such as the Filipinos, the Cambodians, the Slavs, and the West Africans? How about the coherent smaller groups, such as the Inuit, the Pacific Islanders, the Eritreans, and the Berbers? I don't propose to define these boundaries. I can't even figure out how to approach that special problem.

Many of the societies I have listed are very old. Most possess a large body of written and recorded material, have their own language and they clearly evince historic endurance. Survival alone suggests a sizable body of knowledge for coping with the world that in turn suggests that the society has carved out a unique place in the world.

In some instances, such as the Rom people (the Gypsies), a small segment of one society (Indian) migrated and survived in dozens of far-off nations for nearly a millennia, yet they remained cohesive. The Rom people, however, do not have a body of independent written work. This suggests clearly to me that the knowledge in Indian society, from which they left, is large and significant: If a small part of knowledge breaks away from a larger body and it remains viable in many diverse complex worlds, this suggests that the larger original body of knowledge is highly potent.

A Chinese encyclopedia, Yung Lo Ta Tien, was completed in 1408. It contained 11,095 books. I looked at a sample of five volumes in the Library of Congress in May 1996 and counted an average of 68 pages per book, of which 14 pages were illustrations. I counted 40,000 characters per book. Using the same ratio of illustrations to bytes as used above in the EB case, and using a ratio of four Chinese characters for seven English words (an estimate from a friend who is translator), that totals 6.5 gigabytes using the same methodology as was used for estimating the EB. It also makes the contents of the Chinese encyclopedia 6.5 times greater than that the EB.

Knowledge has two observable properties: First, it has meaning only in context. Second, knowledge (within any society) has arithmetic properties. It can be additive or subtractive.

Knowledge is inherently contextual. Knowledge of Planck's constant and its function in physics is of little relevance to most issues in biology, music, or marine engineering. Nearly all knowledge is of this form.

An extreme statement about knowledge was made by Berkeley Prof. Paul Feyerabend: knowledge is always a list, like an auto mechanic's. Check the battery connection, then check the gas line, then check the spark plugs, etc. There is no universal mechanic's knowledge that is transferable, say, to gas turbines.

I wouldn't go that far. I would suggest that some of the central metaphors that govern the work of a mechanic can be applied to a variety of engineering tasks, but that all of the knowledge about the auto mechanism is contextual. An experienced mechanic may learn a new field faster because he or she has workable metaphors about how materials and tools work (strength, flexibility, etc.). But I wouldn't let an auto mechanic work on my airplane engine without any additional training.

Knowledge (within any one society) also has arithmetic properties; that is, It can be additive or subtractive. An example of additive knowledge is the knowledge, discussed earlier, that is related to transportation on the Thames River. From the early knowledge of shoals, rocks, and reefs, we moved to beacons and then maps. This process was an additive path. Recently, we have added more knowledge: a sonar map of the entire river bottom. The earlier knowledge was appropriate to early boats, and what we have now is appropriate to a variety of today's vessels. Not much of the earlier knowledge is lost; instead, it has more added to it and it is condensed.

A subtractive path has been the religious-based knowledge, widely accepted from the Middle Ages until the 20th century, that nearly all health was related to state of mind (as per Mary Baker Eddy). As a consequence, English seamen in the 1700s and 1800s continued to develop scurvy for more than 150 years after a citrus cure was known. This occurred because solid empirical tests were rejected in the face of a well-entrenched belief that a good ship captain wouldn't allow his crew to develop scurvy. That knowledge was subtractive. That type of knowledge still is.

Knowing that knowledge is additive and subtractive doesn't add to our discussion except to suggest that if we made an effort to survey knowledge (in the sense that an encyclopedia is a survey of knowledge), we might learn more about which subtractive parts of our knowledge mislead us.

Encyclopedias are compiled to include knowledge that is considered valid and either ignore knowledge that the publishers know to be erroneous, or to qualify it as erroneous knowledge (this is the way the EB treats astrology: It is described at length because of its long history and then summarized as "void of intellectual value").

I am not convinced that contemporary Americans have a more complete grasp of the knowledge available to us than our prehistoric predecessors did. The first ordinary person's writings, in my Anglo-American society, that I know of, is the saga of Eric the Red. This candid monologue of a strong individual (the unknown author) doesn't suggest a less complete grasp of the knowledge available to his society than we have access to today.

I know that my progressive peers would point to contemporary medicine and technology as proof of our growing knowledge. I think that argument is weak. We might spend less time being sick, and live longer but that does not necessarily mean our individual fund of knowledge is greater than that of a comparable person several centuries ago.

There is another way to look at the question of growing or declining knowledge.

I've met several people from developing countries who were educated in Euro-American universities but who enthusiastically returned to their tribal villages. They tell me that they preferred to live where more of the relevant elements of their life were comprehensible to them; among these were East Indians and West Africans.

Their implicit definition of knowledge is understanding the variables in one's life. They wanted to live where their knowledge gave them the greatest access to the variables in their life. In this light, the growth of knowledge takes on a different perspective.

This suggests a measurement of knowledge based on how the body of knowledge generates personal comfort within the larger society. These people went back to live in villages where a relatively greater proportion of their own knowledge resulted in personal comfort.

A society in which people have proportionately less knowledge of the relevant variables in their lives might be the one in which the most individuals have stressful lives. Comfort and stress in a society are not easily determined. But they could be determined.

What we interpret as a growing body of knowledge may, I think, be only the result of a rapidly growing corpus of relevant data. We are a post-agricultural society that has more time to produce such data, and the recent technology gives us more capability to do so. Measured in terms of whether our corpus of knowledge helps us to lead more comfortable lives, is not obvious to me.

One of the reasons for writing this article is to push a modest agenda:

What I think would be helpful to our society would be to identify subtractive knowledge. The benefit would be to increase the total additive knowledge.

By analogy, I once used an Israeli map that used subtractive knowledge (the methodology for this subtractive knowledge came from Russians-Israeli immigrants ). I followed three roads that led nowhere, wasting several hours. The map showed roads and towns that were not there. That subtractive knowledge could be replaced with additive knowledge and my net welfare (and disposition) could have been improved that day.