vol III Development:

Chapter 1: Epistemology

page 7: The limits to human knowledge

We may think of knowledge in two ways, as data, and as understanding. We acquire knowledge as data when we learn things by rote or 'off by heart', like a list of all the elements in the periodic table. We acquire understanding when we learn how things work and fit together. We can understand many of the properties of the elements from how they relate to one another in the periodic table. Michael Dayah

This division of knowledge leads us to two questions: how much can we remember? and how much can we understand?

This work recognizes three limits to knowledge: internal inconsistency, system infinity and limited bandwidth.

First, let us assume that an internally inconsistent system or statement is outside the bounds of knowledge. We cannot make sense of it, but it may serve as the foundation for the question: why this inconsistency? Inconsistency is a source of curiosity. How can a heavy bird fly on light air?

Second, knowledge is represented by information, and all information is physically encoded. The amount of information we can store in a physical system is measured by its entropy. We say we have reached 'system infinity' when the amount of information we wish to store exceeds the entropy of our system. One cannot store 11 megabytes of data in 10 megabytes of memory. You might say compress the data, but there is a limit to compression, so that system infinities ultimately limit the complexity of possible knowledge. Rolf Landauer

Third, there is a dynamical aspect to knowledge, since knowledge of a changing situation requires changing knowledge, which requires communication. The rate at which two sources can communicate is measured by bandwidth. Bandwidth relates to system infinity as space-time does to space; in other words, it introduces a time dimension into the communication of information upon which knowledge is based. Bandwidth (computing) - Wikipedia

Greater bandwidths can communicate information faster, but the rate of communication is always finite. All human knowledge, therefore, is based on the collection of finite amounts of data through our senses.

We face a further problem in traditional theology when it comes to knowledge of God. God is considered to be invisible, mysterious and completely beyond human ken. As Aquinas and many others have pointed out, we cannot know what God is, but only what God is not, the via negativa. This view is reinforced by the hypothesis that God is completely simple (omnino simplex) so that it has no features upon which the human senses and mind can grasp. Aquinas 20

On this site we identify God and the world and see the fixed features of the world as fixed points in the divine dynamics. From this point of view all our knowledge and experience is knowledge and experience of God. Because God's fixed points are as complex as the transfinite numbers, however, the limitations listed above apply to our knowledge. Transfinite numbers - Wikipedia

The Roman Catholic Church holds that God is immutable, and that knowledge of God may remain fixed and 'irreformable' forever. The God of natural religion is dynamic, so that continual observation is needed to keep up. This is not possible without sufficient bandwidth.

Transcending these limits

Each of these limits can be overcome to some degree, although the only entity capable of complete knowledge of the divine Universe is the Universe itself. Inconsistent statements can be modified to obtain consistency.

We can overcome our individual system infinities by working together in parallel by communication, and by finding more imaginative and powerful expressions of our knowledge.

Finally, we can increase our effective bandwidth with tools like printing presses, computers and optical fibres.

Ultimately, however, there are limits to how much we can know. There will always be further mysteries seeking solution. Barring accident or very bad management, there seems no reason why our planet and ourselves should not last until the Sun engulfs us or becomes too dim to sustain life on Earth.

Something along these lines is predicted to happen in five billion years or so. We have a lot to learn. There is plenty of time to learn, but our rate of learning may become crucial if our environment changes too quickly.

(revised 7 August 2014)

Copyright:

You may copy this material freely provided only that you quote fairly and provide a link (or reference) to your source.

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Horgan, John, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age, Little Brown and Co 1996 Amazon Editorial Review From Publishers Weekly 'Scientific American columnist Horgan here interviews an impressive array of scientists and philosophers, who seem sharply divided over the prospects and possibilities of science. Among the pessimists, molecular biologist Gunther Stent suggests that science is reaching a point of incremental, diminishing returns as it comes up against the limits of knowledge; philosopher Thomas Kuhn sees science as a nonrational process that does not converge with truth; Vienna-born thinker Paul Feyerabend objects to science's pretensions to certainty and its potential to stamp out the diversity of human thought and culture. More optimistic are particle physicist Edward Witten, pioneer of superstring theory (which posits a universe of 10 dimensions); robotics engineer Hans Moravec, who envisions superintelligent creative robots; and physicist Roger Penrose, who theorizes that quantum effects percolating through the brain underlie consciousness. Other interviewees are Francis Crick, Noam Chomsky, David Bohm, Karl Popper, Murray Gell-Mann, Sheldon Glashow, Ilya Prigogine and Clifford Geertz. Despite the dominant doomsaying tone, this colloquium leaves much room for optimism.' Copyright 1996 Reed Business Information, Inc.  Amazon   back

Meadows, Donella H, and Jorgen Randers, Dennis L Meadows, The Limits to Growth: a report for the Club of Rome's project on the predicament of mankind, Earth Island 1972 Amazon Editorial Review: From Publishers Weekly Updated for the second time since 1992, this book, by a trio of professors and systems analysts, offers a pessimistic view of the natural resources available for the world's population. Using extensive computer models based on population, food production, pollution and other data, the authors demonstrate why the world is in a potentially dangerous "overshoot" situation. Put simply, overshoot means people have been steadily using up more of the Earth's resources without replenishing its supplies. The consequences, according to the authors, may be catastrophic: "We... believe that if a profound correction is not made soon, a crash of some sort is certain. And it will occur within the lifetimes of many who are alive today." After explaining overshoot, the book discusses population and industrial growth, the limits on available resources, pollution, technology and, importantly, ways to avoid overshoot. The authors do an excellent job of summarizing their extensive research with clear writing and helpful charts illustrating trends in food consumption, population increases, grain production, etc., in a serious tome likely to appeal to environmentalists, government employees and public policy experts. Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved  Amazon   back

Popper, Karl Raimund, Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge and Kegan Paul 1972 Preface: 'The way in which knowledge progresses, and expecially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism; that is, by attempted refutations, which include severely critical tests.' [p viii]   Amazon   back

Popper 1972, Karl Raimund, Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge and Kegan Paul 1972 Preface: 'The way in which knowledge progresses, and expecially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism; that is, by attempted refutations, which include severely critical tests.' [p viii]   Amazon   back

Wiesethan, Simon L, The Sunflower: On the Possibilities anbd Limits of Forgiveness, Schocken Books 1997 Amazon Editorial Review: 'Author Simon Weisenthal recalls his demoralizing life in a concentration camp and his envy of the dead Germans who have sunflowers marking their graves. ... one day, a dying Nazi soldier asks Weisenthal for forgiveness for his crimes against the Jews. What would you do? This important book and the provocative question it poses is birthing debates, symposiums, and college courses. ... Among the contributors: Sven Alkalaj, Bosnian Ambassador to the U.S., Moshe Bejski, retired justice of the Supreme Court of Israel, Robert McAfee Brown, leading Protestant theologian, Robert Coles, Harvard professor of social ethics and author, The Dalai Lama, Eugene Fisher, National Conference of Catholic Bishops, Matthew Fox, author and leading Episcopalian theologian, Yossi Klein Halevi, Israeli journalist and son of a Holocaust survivor, Arthur Hertzberg, rabbi and author, Theodore Hesburgh, President Emeritus of the University of Notre Dame, Hans Konig, Cardinal of Vienna, Harold Kushner, rabbi and best-selling author, Primo Levi, Italian Holocaust survivor and author, Cynthia Ozick, novelist and essayist, Dennis Prager, author and conservative radio commentator, Dith Pran, photographer and subject of the film "The Killing Fields" about the Cambodian genocide, Albert Speer, German Nazi war criminal and author, Tzvetan Todorov, French literary critic, Harry Wu, Chinese human rights activist.'  Amazon   back

Links

Aquinas 20, Summa I, 3, 7: Whether God is altogether simple? , 'I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back

Aquinas 80, Summa I 14 1: Is there knowledge in God, 'I answer that, In God there exists the most perfect knowledge. To prove this, we must note that intelligent beings are distinguished from non-intelligent beings in that the latter possess only their own form; whereas the intelligent being is naturally adapted to have also the form of some other thing; for the idea of the thing known is in the knower. Hence it is manifest that the nature of a non-intelligent being is more contracted and limited; whereas the nature of intelligent beings has a greater amplitude and extension; therefore the Philosopher says (De Anima iii) that "the soul is in a sense all things." Now the contraction of the form comes from the matter. Hence, as we have said above (Question 7, Article 1) forms according as they are the more immaterial, approach more nearly to a kind of infinity. Therefore it is clear that the immateriality of a thing is the reason why it is cognitive; and according to the mode of immateriality is the mode of knowledge. Hence it is said in De Anima ii that plants do not know, because they are wholly material. But sense is cognitive because it can receive images free from matter, and the intellect is still further cognitive, because it is more separated from matter and unmixed, as said in De Anima iii. Since therefore God is in the highest degree of immateriality as stated above (Question 7, Article 1), it follows that He occupies the highest place in knowledge. back

Bandwidth (computing) - Wikipedia, Bandwidth (computing) - Wikipedia, the free encyclopedia, 'In computer networking and computer science, bandwidth, network bandwidth, data bandwidth, or digital bandwidth is a measure of available or consumed data communication resources expressed in bits/second or multiples of it (kilobits/s, megabits/s etc.). Note that in textbooks on wireless communications, modem data transmission, digital communications, electronics, etc., bandwidth refers to analog signal bandwidth measured in hertz—the original meaning of the term. Some computer networking authors prefer less ambiguous terms such as bit rate, channel capacity and throughput rather than bandwidth in bit/s, to avoid this confusion. back

Elementary particle - Wikipedia, Elementary particle - Wikipedia, the free encyclopedia, 'In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made.' back

Michael Dayah, Dynamic Periodic Table, 'Ptable has a rich history stretching back to September 1997, a year before the founding of Google. It was introduced as a piece of HTML artwork and published to the web October 1, 1997. Simple dictionary element descriptions were added later in December. A version utilizing HTML 4 and CSS was introduced March 1999 and replaced the original version September 2004. Wikipedia integration and the addition of other languages came in August 2005. Dynamic layout switching was later added in September. The first low resolution-friendly layout (no names) came in October 2006. Interactivity was radically enhanced throughout summer 2007 and continues into the present day. The color scheme was tweaked to be friendly to non-deuteranomalous individuals with interactive assistance from Kasey and Heather.' back

Quantum mechanics - Wikipedia, Quantum mechanics - Wikipedia, the free encyclopedia, 'Quantum mechanics, also known as quantum physics or quantum theory, is a theory of physics providing a mathematical description of the interaction of matter and energy.' back

Rolf Landauer, Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that, on the ultimate nature of the laws of physics are included.' back

Scholasticism - Wikipedia, Scholasticism - Wikipedia, the free encyclopedia, 'Scholasticism is a method of critical thought which dominated teaching by the academics (scholastics, or schoolmen) of medieval universities in Europe from about 1100–1500, and a program of employing that method in articulating and defending orthodoxy in an increasingly pluralistic context. It originated as an outgrowth of, and a departure from, Christian monastic schools. . . . The main figures of scholasticism historically are Anselm of Canterbury, Peter Abelard, Albertus Magnus, Duns Scotus, William of Ockham, Bonaventure and Thomas Aquinas. Thomas Aquinas's masterwork, the Summa Theologica, is often seen as the highest fruit of Scholasticism. . . . 'sun back

Sun - Wikipedia, Sun - Wikipedia, the free encyclopedia, 'The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields. . . . The Sun was formed about 4.57 billion years ago when a hydrogen molecular cloud collapsed. . . . The Sun does not have enough mass to explode as a supernova. Instead, in about 5 billion years, it will enter a red giant phase, its outer layers expanding as the hydrogen fuel in the core is consumed and the core contracts and heats up.' back

Transfinite numbers - Wikipedia, Transfinite numbers - Wikipedia, the free encyclopedia, 'Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back