In order to understand and to appreciate the importance of the mathematics of uncertainty, we must understand the meaning of the uncertainty first. This note serves to add just a bit of information in this direction.

Wikipedia has included the the following areas of studies, with different ways of investigation methodologies; physics, philosophy, statistics, economics, finances, insurance, psychology, sociology, engineering and information science.

As you can see, statistics is just one of the many fields which are concerned with the uncertainty. Statistics basically deals the estimated amount or percentage by which an observed or calculated value may differ from the true value.Uncertainty is a condition of being uncertain and doubt. The word doubt implicated the humane brain information and thought processes,it becomes clear the concept of uncertainty must include other fields of studies.

Further exploration of the meaning for uncertainty, in our opinion,is to look at the antonyms such as Merriam-Webster Dictionary, An Encyclopedia of Britannica Company, or the like, these words include assurance, belief, certainty, certitude, confidence, conviction, sureness, surety, trust, chance and luck.

Uncertainty itself may range from a falling short of certainty to an almost complete lack of conviction or knowledge especially about an outcome or result. Doubt is a good illustration of appreciation for other areas of study beyond statistics.Doubt suggests both uncertainty and the lack of ability to make decision.

The most popular example concerning uncertainty is the quotes from Hamlet,it signifies literature beauty.

Although Alan Turing saw that computers might become intelligent, the Turing theory, in itself, does not tell us how! The SP theory of intelligence aims to plug the gap.

From Zhaohao Sun,

I agree to the idea of Gerry on “Although Alan Turing saw that computers might become intelligent, the Turing theory, in itself, does not tell us how! “, I studied the paper of Turing in 1950, and my motivation is that Turing told us in 1950 that computer might use deception method  or trick method in order to pass the Turing test and show its intelligence to human being, therefore, I published a few articles on deception and intelligence since then. I still have an unpublished article on my table and I will submit it for possible publication in your journal.

Separation of oral and writing forms in Chinese language(s), superiority and disadvantages of this, future of Chinese language – are fascinating subjects. I do not know Chinese and can only ask questions based on those languages I know, mostly English and Russian.

From theoretical considerations, we know that sounds of a language affects us emotionally. This is a direct affect perceived by ancient emotional brain areas (unlike other emotions that might perceive after understanding conceptual contents of various situations). Thus we might conclude that in Chinese language connections between emotional and conceptual contents is less strong than in some other languages (like Russian).

The cognitive functions of these emotions specific to language sounds are not well understood. In animals emotional and conceptual content of vocalization is fused, not separated. Animals cannot separately think and vocalize. Emergence of human language and ability for deliberate thinking required separation of emotions and concepts. In this regard separation of writing and sound forms helps evolution of conceptual thinking in Chinese language.

From this point on, there are more questions than answers:

1) An important function of a language is to use sounds (of words) for pointing to objects and events in the world. Emotionality of language sounds unfies conceptual contents of words with objects in the world. But emotionality of languages could be an ambivalent quality. “Too low” emotionality may lead to disconnect between language and the world. “Too high” emotionality may lead to “strong” connections and to a loss of adaptivity of language, loss of ability to perceive new contents. What is the “optimal” emotionality of a language? What is the optimal “strength” of connection between language and the world?

2) This could be studied by psycholinguistics and cultural anthropology. By looking at the world languages we can see different evolutionary paths of cultures with “too emotional” and “unemotional” languages. We should keep in mind that connections between the mind and the world are dynamic evolving processes.

3) This direction of research could also be studied by simulating language and cultural evolution.

4) What is a cognitive function of “tonality” of Chinese language? Whereas in English and Russian pitch variations are only used for expressing emotions, in Chinese it is used for both, emotional and conceptual contents. Currently there is no scientific answer to the question of cognition and tonality

5) Of course, connections between language sounds and the world are not the only factors directing cultural evolution. What are the other factors? How do they interact with language?

I am looking forward to hearing answers from people who know Chinese and its cultural history.

From Lin Hong

This is a good lesson for me to know more about psycho-linguistics. I knew emotion is an indispensable part of intelligence. Now I know more elaborations on this. I have long perceived that language affects culture. Leonid’s words attests that this is true. This also explains why contemplation on a culture often end in criticizing the language. I do believe studies on emotional and conceptual functions in languages are very important. Could they even tough the roots of religions? I would like to find out whether models can be built to measure the emotional and conceptual components in a language.

The tones in Chinese play a central role in Chinese classic poetry. I don’t know anything other than the rhythmic functions they play in the tonal patterns of poems.

As a layman to linguistics, I would like to see more studies on the questions issued here.

From Leonid Perlovsky

Thank you for telling me about the role of tones in Chinese classic poetry. There are beautiful translations of Chinese classic poetry to Russian made by the best Russian poets. But it is impossible for me to say how well the rhythmic functions of tones are translated into Russian.

From Lin Hong

I am not sure how poems can be translated well, especially poems that rely on tonal patterns like Chinese poems. Once I tried to translate some Chinese poems. I found some good Chinese poems no long sound good (by meaning) in English. I had a colleague who was a good poet. He told me there are two types of poems: poems that convey a thought and poems that express a mood. He said English doesn’t convey feelings (which means English poems more convey thoughts) but French conveys feelings. According to him, in terms of poetry writing, languages may not be exchangeable. At this point, a thought is emerging in my mind: Are languages barriers to human’s cognitive functions?

To kick-off the discourse on the philosophy of the mathematics of uncertainty, we simply draw parallel to the statement from Wikipedia’s definition of the mathematical philosophy. ”The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implication of mathematics”  —-Bertrand Russell, Introduction to mathematical philosophy.

Stanford Encyclopedia of Philosophy has an interesting observation; If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science. The reason for such distinction is mathematics as a science can be very different from other sciences. Philosophy of Mathematics and the real world can be and should be studied via;

(1)human nature

(2)religion

(3)truth

What kind of message should we send to all Chinese language speakers? Language is changing and  is evolving constantly, even we don’t feel it!

WATSON has proved that AI, if you do it right, can even beat human for limited usage. Therefore, there appears to have an urgency in reforming Chinese language, unless you just want it dead!? For a different reason as compared with Hu Shihzhi and other historical reforms, this time the overwhelming urge would be the digital computer and information revolution, which, by the way, is way much larger and its impact huge!

What do you think? We need a cohesive united front to win this battle.

From Hong Lin,

While I am not fully aware of exactly what problems Chinese language is facing in the modern age, I did hear some sayings from linguists that Chinese language has separate oral and writing forms and thus it is an obsolete language. I also heard counter arguments from scholars who advocate Chinese language that it does have superior features other languages don’t have. While I cannot present my opinions in theory, I do have bilateral feelings about Chinese language: on one hand, I cannot appreciate the writing efficiency of Chinese characters on computers (partially because I am not a good typist). On the other hand, as a lover of Chinese language, I am always ready to argue for Chinese, especially classical Chinese language’s succintness, flexibility, and expressiveness, and that most importantly, I don’t think China’s modernization has to come with abusing its own language. Therefore, in an altitude of a novice in linguistics, I do want to learn what problems Chinese language is facing and what possible solutions can be developed.

Although Alan Turing saw that computers might become intelligent, the Turing theory, in itself, does not tell us how! The SP theory of intelligence aims to plug the gap.

There is an overview of the theory in Computing as compression: the SP theory of intelligence, with a focus on how ‘computing’ may be understood as information compression via the matching and unification patterns, and with a concept of multiple alignment at centre stage.

Comments will be welcome.

On 13th Feb.1913, Bertrand Russell wrote to his friend Goldie “….I expect you will find China much more interesting—much more civilized and more aware of the subtler values –at least if you could get in touch with the educated people…..”

Bertrand Russell had lived in China for years because he had genuine deep feelings and strong desire to understand Chinese civilization. From the tone of his writing, it is quite clear most British folks did not know too much about Chinese and their culture. I feel today the situation has not improved that much.

Bertrand was so genuine that he wrote a whole book about his impression, even some suggestions. He cared so much about his book on China that he has documented in detail how hard he has tried to get the feedback to his book on China. His friend Conrad wrote to him about the feedback.”The Heathen Chinese, is all I know about the Chinese. But after reading your extremely interesting view of the Chinese Problem I take a gloomy view of the future of their country. He went on to say that my views
[Bertrand Russell] of the future of China “strike a chill into one’s soul” the more so, he said, as I pinned my hopes on international socialism.

One of the very first observation by Bertrand Russel on Chinese is that Chinese are callous. With Bertrand’s genuine feeling toward Chinese, I do recommend strongly for Chinese people to study carefully not only the strong characteristics, but the negative as well. Very often, most people would not tell you the truth and simply to be silent. This actually is quite harmful at long run. No criticism, no progress! Very simple!

Reference: The Autobiography of Bertrand Russell {1872-1914}, An Atlantic Monthly Press Book,Little,Brown and Company, Boston, London, 1967

Dear Paul,

Thank you for your information and thought on Mathematical Uncertainty The following is my thought on “Mathematical Uncertainty and Beyond”

1. Uncertainty is ubiquitous. Uncertainty is the essence for any decision making. Uncertainty is motive for any research and development. Without uncertainty there would  be not any research and development.  Then “I have uncertainty therefore I am”, just as “*I think*, *therefore I am”*. Mathematics of uncertainty is the motive for research and development of mathematicians.

2. Professor Guo Jun Wang said “There are two worlds:the real world and the mathematical world”. In fact, there are many intermediate worlds between the real world and the mathematical world, both of the latter can be considered extreme world: real world as world 1, mathematical world as world n +2. Then the number of the intermediate worlds is n, (n is a large integer in the finite world, n is infinite in the infinite world, we consider n is an integer).  Then from a mathematician viewpoint, the whole system consists of n + 2 worlds. All these worlds are useful for mathematicians.

3. Any mapping from one world to another world has uncertainty, e.g.

mapping from world j to world j + 1 has uncertainty,  (j = 1, 2, …., n + 2), this mapping can be considered as abstraction or generalization. we have then n +1 mappings for abstraction or generalization, from a shortest path viewpoint.

3. Similarly,  any mapping from one world to another world has uncertainty, e.g. mapping from world j+1 to world j  has uncertainty,  (j = 1, 2, n + 2), this mapping can be considered as specification or application. We also have n +1 mappings for specification or application  from a shortest path viewpoint. We have at least 2(n +1) mappings between the real world (1) and the mathematical world (n+2). This implies we have at least  2(n +1) uncertainties between the real world (1) and the mathematical world (n+2).

4.   Beauty lies in uncertainty, then we have at least 2(n +1) kinds of

beauties for mathematicians. If we use network or graph theory  to reveal the uncertainties and beauties, we will find much more uncertainties and beauties between the real world (1) and the mathematical world (n+2). In fact, every mentioned worlds have also infinite or finite uncertainties. Then we are facing infinite uncertainties around us in the continuum between the real world and the mathematical world.

5. There are two main important tools to look at these (mathematical) uncertainties or beauties. These tools are telescope and microscope (you should use them as tool x and tool y). Different researchers prefer to use different tools because of different personalities. Using telescope one can provide a holistic and strategic perspective to the world j.  In the battle only the commander can use   telescope to know the situation of enemy…

Few can use telescope to look into a few worlds (e.g. j-1, j, j+1) or many uncertainty in a world j. Using telescope  one can investigate a mentioned uncertainty in-depth. The modern history of science and technology proves that using telescope to look at any uncertainty is invaluable. The majority of researchers are trying to use telescope to investigate a few mentioned uncertainties in world j in particular in mathematical world (n+2) for his/her whole life.

6. It is significant to use the above approach to look at fuzzy logic, fuzzy mathematics, etc.

The above idea is motivated by scientific paradigm of Kuhn (1962).

There are three things in evaluating the good mathematics: (1) useful, (2) beautiful, and (3) simple

If only (1) useful but not (2) and (3), those type of math are only good for temporary use. It can not stay very long. Hilbert and Poincare said that only the math can stay that are beautiful and simple.

It is very important to young mathematicians to choose how to do math personally. For me, I like to do useful math, meanwhile, I also look for
a simple solution. (Simple is beautiful in most of cases)

I do not agree with Halmos’s “applied math is bad math.” In Gauss and Newton time, math are applied always. It is beautiful too. Nowadays, people use
computer tech to make math useful in any aspect. It is less beautiful now.

I would like to say SMU should looking for the math that have these three properties. I can say this: Unless, we reach a beautiful math in our study, we may not converge to a big discovery. Einstein said that the nature has its simple rules.

Terry Tao has listed 23 or 26 reasons for the good math work. I do not believe his statements. I just trust what Hilbert said. For a short period of time, “useful” is a
good measure. Actually, no matter what area we work with, simple and beautiful are the only measure (in any philosophy eastern or western). The modern math
society make so many 200/300/400/500 pages proofs for some famous conjectures. I do not like that. I do not even believe them in terms of proofs.

Fuzzy logic needs to work on these “beautiful” and “simple” issues as well as SMU. I knew I might hurt some of your feelings, but I must express the thing I felt is true.