The Other Mathematics: ...

2009-12-04T10:26:54-05:00

The Other Mathematics: Language, Logic, and Probability in the Footsteps of Boole and Venn

Leo Depuydt (Leo_Depuydt@brown.edu)

Description as of January 25, 2009

The unity of the forms of thought in all the applications of reason, however remotely separated, will one day be matter of notoriety and common wonder; and Boole’s name will be remembered in connection with one of the most important steps towards the attainment of that knowledge.
Augustus De Morgan

This independent project is human-oriented and not machine-oriented. It is also a test pilot for a possible class. It takes as its point of departure the undeniable fact that the brain produces language and thought and that we at this time have little or no clue as to how this happens. Finding out will be one of the great assignments of the twenty-first century. But that should not discourage anyone from exploring possibilities. And it goes without saying that the matter is of no small interest.

To do this, the hard evidence to which we are limited at this time is what comes out of mouths of speakers and the pens of writers. Brain scans are not detailed enough to discern the structure of thought and language and the turning on and off of microvoltages that make it happen. However, because people understand one another when they speak, there is every reason to believe that the basic structure of the brain waves that produce language and thought is reflected in the sound waves of speech, which can also be conveyed in other mediums like writing.

The basic starting hypothesis of the present project is that most everything that relates to how the brain produces language and rational thought is digital, that is, On (1) or Off (0). Emotions are something else. The flow of “juices” such as adrenaline, dopamine, and serotonin is presumably continuous and not digital. All this cannot be proven positively at this time because knowledge of the brain is still very incomplete. In any event, the mathematics needed to handle digital structure is that of Boolean algebra. It is in a sense the “other” mathematics.

At the outset of his Elements of Algebra, Euler describes the normal and well-known mathematics as the study of anything that is “capable of increase or diminution.” In the “other” mathematics, nothing ever gets bigger or smaller. For example, adding the set of teachers to the set of teachers still only gives you the set of teachers (t + t = t, not 2t). Anyone working on the hypothesis that the brain produces language and thought digitally therefore has but little choice to study the “other” mathematics and seek ways to apply it to language. Only one thing seems sure: There’s got to be a way! And in fact, it can be demonstrated that already a sizeable number of phenomena lend themselves so easily to such an analysis that there is hope for more.

Much of the present effort will be devoted to the study of two foundational works of the digital age, namely George Boole’s Investigation of the Laws of Thought (1854) and John Venn’s Symbolic Logic (1894). In 1937, Claude E. Shannon converted Boole’s ideas for electronic circuits and the digital age began. Putting these two works at the center should give focus to the project. By means of additional discussion of case studies, it would be further investigated how the other mathematics can be applied to the structure of language and thought.

The project otherwise has a certain provisional quality. It constitutes a beginning with hopes of more to come. The proposer has written on the subject and has incipient ideas (see, e.g., Name at www.gorgiaspress.com). But it lies in the nature of the subject matter that it is exploratory. It is not clear where it will lead. It is being developed as we go along. It is of course clear where efforts like this should ultimately lead, namely to turning the camera 180 degrees on to ourselves and see us function materially 100 percent as it happens with the help of genetics and Boolean algebra.

The focus will be on the structure of language and human thought and a sufficient level of Boolean algebra. But in the long run, there is more than one field to which projects like these can be of interest, just about all of which fall outside the competence of the proposer: linguistics, biochemistry, brain science, electrical engineering, and mathematics.

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Geopolitical Implicatio...

2010-01-18T08:34:58-05:00

During one of my Master’s degree program courses at the University of Phoenix several students, our professor, and I got into a discussion about the difference in meaning between the words Hispanic and Latino. My Spanish-speaking ability is extremely limited but I told them that I thought that the word Latino has a much warmer and friendlier ring to it than does the word Hispanic which sounds rather stiff and overly formal.

Hispanic may be a term that is used primarily in demographic studies and other scholarly research. And, the word Hispanic, I believe, has a nuance of having come from the Iberian Peninsula rather than from Latin America.

Like English and French, and other languages, Castilian Spanish (Iberian- Peninsula Spanish) is considered to be the "King's" or "Queen's" language whereas Latin-American Spanish is deemed to be "inferior" just as Parisian French is considered to be the "pure standard" and the "Queen's English" is regarded as "superior" to American English. Moreover, languages and dialects are often charged with political and geopolitical ramifications.

Mandarin Chinese is deemed to be the “standard” of China, Taiwan, and Singapore with all other forms of Chinese categorized as dialects or “substandard” even though from a linguistic standpoint Cantonese, Szechuanese, and Fujianese, among many other “dialects,” are truly distinctive languages within the Han-Chinese family of languages. Those who do not speak and write a high standard of Mandarin are considered to be “uneducated” or “undereducated.” There are positive implications to standard national languages, however.

In spite of Mao Zedong’s and his cadre’s cruelty in imposing communism on China from 1949, in imposing Mandarin as the national language of the country, Mao was able to unify the many people groups of the country under one banner which enabled a much more rapid modernization of the nation than if it had remained linguistically divided. China’s economic advances would have been far slower had the imposition of a national language not occurred. Assignment of a “higher reputation” to “standard” or “national” languages does have negative consequences, though.

One of the chief consequences is that a heavy emphasis on a national language tends to simplify the linguistic culture and heritage of a nation in that lingual and cultural diversity is reduced with a number of the old “dialects” dying out. In northern Japan, for example, the Ainu language is, very unfortunately, dying out a steady rate as the number of young people who can speak the language is decreasing in that they are not able to study it in school.

The Ainu were the first people to settle the Japanese archipelago thousands of years ago and until the Meiji Period (1867-1912) were able to maintain their unique culture, language, and heritage. But with the increasing encroachment of the Japanese linguistically and culturally, over the past 140 years, or so, the Ainu have declined in numbers and cultural uniqueness, which is sad indeed. Worldwide this phenomenon has been quite common over the past 100 years, or so. Over espousal of national languages can also lead to ridiculous extremes at times.

One example of this is the French government’s attempts to maintain the “purity” of Parisian French which is France’s national language. As the University of Oregon cultural geographer and polyglot Dr. Ronald Wixman has pointed out, Parisian French is the only form of French that retains a guttural “huh” sound which entered the language from German many years ago. The French government has stubbornly attempted to resist changes to Parisian French by denouncing such borrowings as “le weekend” which French young people use very commonly.

Language changes constantly and efforts to retain its “purity” are ludicrous. Everyone should be trained to speak and write clearly in their respective national languages and beyond, but linguistically all languages, dialects, and idiolects (an individual’s unique manner of speaking) are equal with none being “inferior.”

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