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Computational and Mathematical Metaphors

I believe that making connections between concepts is where meaning really lies so I will ask a series of questions hoping they would offer a fresh perspective and trigger some inspiring ideas in the replies.
- How is language and symbolic systems related to thinking?
- Does computer science and mathematics fit into the definition of language?
- What are some of the concepts of mathematics and computer science that are essentially mental concepts by which we think? (e.g. Variable, Abstraction, Dimension, Recursion..etc)
- What is more important, to know how to use these concepts or to know how they are related to thinking? Application vs Reflection?
- In other words, is it enough to think or is it also important to think about thinking?
- Are mathematical and computational concepts something to be seen or something to see by?

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    Jun 4 2014: Any form of language is important. The Universe has more than one way to communicate events and experiences, so it would not be wise for anyone to naively reject one language over another, when it's unifying communication. That is why nature allowed our minds to create pictures, emotions and connections when stimulated by another likened process. Not to mention that we are our creation; our creations are ourselves. Everything we created, thought of, or discovered, was already existent, just not transferred from the cosmic sea to the collective conscious sea yet.

    The Universe's design exists in all of our creation, thus it's really not our creation.
  • May 30 2014: Hi Dear Amir,I teach Information Technology subject at high school.Infact it is a lot about computer science:design works with all kinds of softwares,including computer languages programming.I am teaching visual basic computer language programming this term.It is reaslly not easy for students to learn it.Because they feel very difficult to understand a lot of computer programming conceptions:available,functions,procedure,binary...I kept thinking of it ,someday I found it out:because binary is totally a new thing for lots of people,people aren used to talking about it as much as mathematics everywhere.So what is the value of computering thinking:binary,I am thinking of it.I am not clear about it yet, I think binary computer science is very close to mathematics,but they are a lot different:I called them are two different wonderful world about thinking...I encourage my students to learn both of them,especially computer programming...I am also searching computer science and mathematic,thinking issue...i am sort of interested in it,if you too,i hope we can keep on contacting to keep on discussing of it.Thank you.
  • May 30 2014: Amir

    I would think that your questions are more to the philosophical spectrum. Before language, I would assert, there were concepts, thoughts of things, of events, perhaps outcomes, which eventually took on the form of guttural sounds. Such sounds became associated with particular things and language was born. I see mathematics or any form there of, as simply an advanced language based upon the human talent to conceptualize. That we are reasoning beings, it is then inherent within the species to define, organize and make sense of that which we perceive and we will do so on the foundation laid by others, by a language of sounds, motions, glances, expressions and symbols as in 1 and 0's, E=MC2 or dog.
    We are defined as Homo sapiens-sapiens The Wise Man. For me it is not The Wise Man, but the questioning man, the building man, the creating man, the reasoning man. The essence of Man is his capacity to reason, to ask a question and then answer himself and that is what I think you are referring to in your "In other words---" It is not enough to think, as to what tv program to watch, but to reason why this, why that. Why light, why earth, why and what if, is the thinking about thinking it is reasoning.
    As to be seen or see by, both. Eye glasses did not exist until they were conceptualized in the mind of a man now he uses them to see with.
    I don't know if any of this was to your points, but I enjoyed it. Good questions, very good exercise in abstraction. Questions to be answered, a reasoning process, thinking about thinking.
    .
    • May 30 2014: Thanks for your reply Charles.
      "Language is based upon the human talent to conceptualize" is about what I wanted to say. What I wanted to say is that language, mathematics and programming are taken for granted and admired for their outcome not their sources. We deal with language as a means of communication, mathematics as a tool for solving problems, programming as a tool for controlling a computer, and their significance is measured with respect to the end result. These disciplines are regarded as a set of ""external"" tools that we use for achieving these outcomes, and through practice our minds subconsciously adapt to these rules and reasons about them to apply them. On the other hand, there's a whole other dimension that is neglected that these tools are actually internal tools (internal to the mind) and that language, mathematics and programming are mappings of the mind. The recognition of that fact and applying it on the linguistic and mathematical concepts does not only enhance the capacity to use them, but also gives them more meaning and depth (in other words adds to their conceptual beauty). I think the metaphor of construction in software, langauge and proofs as powerful as it is in showing the idea of combining blocks for building structures, it hides the idea that in the case of those disciplines the building blocks are not external blocks that we learn and use but are internal mind constructs.

      I am not trying to state that thinking in language, mathematics and programming is important. Is is obviously important as also is thinking in biology, chemistry and physics. What I want to emphasize is that mathematics for example does not "require" thinking or, it "is" thinking as opposed to other natural sciences. I'll continue in another reply due to the character limit.
      • May 30 2014: Amir

        Having brought four sons through college level and having some experience in teaching at that level, I would agree with you, in that, American education is not geared to critical teaching or thinking. The analogy of the eye glass is precisely as you say. It is a tool by which to see, reason, with greater clarity and depth not as an end in itself.
        "--but I'm talking about concepts that are already deep and general that are stripped out of their depth" To this, I think, is the crux of your search. Without the magnification of the reading glasses the words on the the paper, the concepts, contained in the words would not exist for me therefore there is no window to their promise. They are non-existent. They did not reach the "source" of examination, the capacity to reason, to question their existence.
        I would disagree however, with language vs mathematics, communications vs problem solving. Both come from the same source, one is Arabic one is English, both are language, both solve problems, one leads to the other.
        Yes, to the "mind constructs." The eye glasses were first such a construction, a reality within the mind.
        Is this what is real or is reality the physical fabrication of that primary reality. The language of math, whether simple or quantum physics, eye glasses or a chess grand master are all a construction of the mind, the capacity to reason.
        I think we are speaking to the same thing and for me an enjoyable process, but you present such a vast array of variables. As one who is working on eight decades can we narrow the scope? Man is a reasoning being, a questioning animal who provides his own answers. Reason is multi-layered, as art and creativity. Are you saying that Man possesses an innate knowledge waiting to be tapped or that knowledge is an aspect of an evolutionary knowledge base spurred on by Man insatiable need to ask a question. the capacity to reason?
    • May 30 2014: Continuing from the previous reply. Education should give more attention to learning how to think about any topic and its importance in practicing any field. But in those purely mental fields, recognizing their distinguishing nature is also important. Following from your eye glasses analogy, education focuses on the eye glasses as an external object and may for example study the lens and the frame structure and shape but hide the aspect of that glasses are not only seen as glasses but are seen by. Language is not just a set of words and rules for communication but are the glasses by which we think. We need to think in order to use language or to solve a problem in mathematics or to write a program and also to understand history and study natural phenomena. But we need also to realize that thinking is through language, that language is not just object of thought but also the means of it.
      I have 2 examples in mind showcasing that idea. The concept of abstraction in computer science is perceived as a design principle that allows for code reuse when in a field like cognitive science and philosophy is a much, seriously much, more deeper concept than for just code reuse. I am not talking about generalizing and extrapolating small ideas into other contexts (that would be a good idea though) but I'm talking about concepts that are already deep and general that are stripped out of their depth. The other example is variables which is also related to abstraction and the significance of generalization and conceptualization in thinking, but variables in computer science is treated as placeholders for values.
      Why do these concepts seem trivial from the point of view of computer science and mathematics, and obviously deep in philosophy such as computational theory of the mind and philosophy of language and mathematics. Why are these concepts introduced as external tools that require the mind to be adapted when they could be introduced as internal, familiar and intuitive concepts!?