math intuition vs artistic intuition

This is a very confusing post.

Math vs art. The inclination towards the study of reality of inanimate nature (by evidence) vs human nature/emotions (by social experience)[2].

Math vs art. The degree of one’s willingness to accept assumptions? ie. the degree of depth? of assumptions you like to based your critical thinking on. Math sinks deep into fundamental assumptions aka axioms, critique what they are being told because they are unable to move on from baseless assumptions. Art perhaps are easy going with broad (subjective but reasonable) assumptions because they are more emotion-filled and prefer expressions above the assumptions.

Math – deep critical thinking, related to the study of inanimate nature.
Art – broad? critical thinking, related to the study of human nature/emotions.
Critical(deep) thinking as a (broad)spectrum of interests: ~math-science-philosophy/morals-humanities-music-art~

Is (math/art) imagination/interpretation innate or based on prior knowledge and past experiences? We imagine and interpret based on what is meaningful to us. Are you innately deep or broad with emotions? Past experiences are involved too as people say that one needs wisdom to understand wisdom.

For example, I can only appreciate music to which the lyrics describe a scenario where I had some past experience about. But when it comes to other forms of music, I find that without past experience to relate and connect with the art piece, I would probably just fall asleep. (fall asleep actually implies that I find sleeping more valuable then trying to appreciate the song. this means that I cannot see the value of trying to understand the song. I don’t find it useful/relevant to me.) I am unable to accept/imagine in the artist’s shoe. I cannot take perspective because I cannot relate/accept the background of the artist? Why does it feel that I am losing my identity when I try to put myself into the shoe of others that I cannot relate to?

Another example is when I saw the following test paper. The teacher is supposed to prepare questions for a discussion with a class of above average English proficiency secondary students. When I read the literature excerpt, I was pretty lost. What was I suppose to make out of that text? At least now at my current age, I have some experience and knowledge about social conversations, love and engagement? I dunno. But I cannot imagine myself scrutinizing that excerpt if I am only a secondary kid. Am I suppose to be imaginative in the author’s shoe?
Actually, after going through the text with my friend, I found out that my problem lies in my willingness to accept the theme/context/background of the piece of literature. And that it was okay and perhaps necessary to research for the background of the author and context that was being portrayed. Imagination should flow naturally if I am able to accept and ground myself with the assumptions of the excerpt.

Perhaps my lack of artistic imagination (or excessive mathematical intuition) explains why I can only relate to movies that I find realistic. Actually, what do I mean by ‘realistic’? Is realistic subjective? If people can accept/imagine the content that I cannot, does the content become realistic to them but not to me. I do end up being very cynical when scenes cut abruptly or when I am unable to imagine or interpret scenes that I find unconvincing, meaningless or have no clue about. I mean how can you discern if the movie is just smoking its way through to illustrate the story? (my friend told me not to worry too much about the sense of the story, what is more important is the moral and learning principles behind the story. but I think realistic-ness is still important in the movie’s authenticity to illustrate the morals.) Some introductions can be really abstract and all over the place. I need more background and premise of the plot to help me understand what is going on. I would always prefer to prepare myself with a rough background of what the movie is to come but does this somehow kill or spoil one’s imagination to the interpretation of the story flow?

I want to believe that everyone have both mathematical and artistic intuition. Leonardo da Vinci is a living testimony that both intuition do not contradict each other. OR do they? should I inquire to ask why or should I not ask why? should I fix with logic or express with feelings[1]? While students do not seem to exhibit both prowess, it is because these intuition are still lying dormant. I see my role as a math teacher by making math relatable/meaningful to students in order to awaken/unlock their mathematical intuition. Mathematical intuition is to feel in the flow and sense of logic and the exploration of explanations to make logic flow and fit in the neatest possible sense. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Is logic emotionless? Well..there is emotion and satisfaction when you can fit the puzzle nicely. But there is probably more variety of emotions involved in artistic expression than piecing logic.

I believe it is possible to offer/scaffold prior knowledge and experiences that will instigate students’ imagination/intuition in the realm of logic/math. But can artistic intuition be scaffolded and awakened? Maybe my mathematical intuition hinders my intuition for artistic expression. What is artistic intuition anyway? Could there be a tradeoff between mathematical and artistic intuition? While I doubt that I have any artistic talent, yet I want to believe that I do have. Because I want to believe that everyone has mathematical intuition. Those who are good in math happen to be able to feel and tap on it; those who are not are just unable to feel and tap on it by their own means.

Looking at Akiane Kramarik’s artpieces, can artistic intuition really be taught to those who are inert about art? eg. me? Then perhaps not everyone will have math intuition[1]. Should I teach in the belief that I can awake every students’ mathematical intuition or admit that some are just unable to and allow them to move in their own other intuition? Is there a difference between both intuition? Is there a tradeoff between both intuition?

Maybe I should add that being able to move in your math or artistic intuition does not make you a genius in that area. The genius is measured by how deep and fluent you are able to move in the intuition. While I seem to advocate that nurture can help to kick start the basics of math or artistic intuition, the depth and fluency of one’s creativity and imagination in that intuition is likely to be a gifting or talent that is based on one’s unique innate wiring and the various experiences that follows and compounds with it.

The ponder between nature and nurture ensues. Is imagination/interpretation innate or based on prior knowledge and past experiences? It’s clearly both! We fall back to Piaget’s theory of constructivism. His theory states that we construct knowledge based on our prior knowledge via assimilation and accommodation. But Piaget didn’t explain HOW we assimilate new ideas. The process of assimilation could then be dependent on one’s innate intuition/style of relating and establishing links with the new idea into their prior knowledge. Different people would have assimilate/interpret new ideas differently based on their own intuition and innate wiring. It is intuition that helps us to assimilate new ideas.

I may not be able to appreciate an artistic concept given the gap from my prior knowledge and my inability to use artistic intuition for assimilation. But perhaps Vygotsky’s scaffolding might do the trick.

The links/lines between 1 to 10 is seen as intuition. The dotted lines is the part where I am unable to use artistic intuition to create #9&10, which might be necessary to appreciate the new idea #7&8. Vygotsky argues that external help can scaffold our internalisation of new ideas. By some external help of #9&10 that is relatable to my prior knowledge, I may be able to assimilate new idea #7&8. If assimilation is done independently without the help of others, the scaffolding portion could be seen as assimilation with imagination/creation.

Within the individual’s own mind, the individual is able to imagine and create #9&10 that is consistent with his prior knowledge and this helps him to assimilate the new idea #7&8. The creation of #9&10 is solely done by one’s own mathematical/artistic intuition to interpret the new idea. We also see that the new idea actually inspired/instigated the creation and imagination of #9&10. I coin this process as assimilation with imagination/creation. From one’s prior knowledge, the individual is able to imagine and create new information based on his intuition to help him assimilate new ideas and concepts.

So is logic emotionless? Perhaps not. The process of assimilation via mathematical/artistic or even revelatory intuition always involves and carries a gush/flood of emotions to come with it. Any form of assimilation must have involved feelings and emotions in the construction and development of understanding and knowledge. Assimilation by definition is a process of RELATING and establishing links with the new ideas into one’s prior knowledge. Assimilation also involves the instinct to orientate one’s prior knowledge in a way that can best fit with new concepts and ideas. Below is perhaps how I would visualise intuition.

Firstly, it is intuition that holds prior knowledge together. Intuition is able to grow outwards from one’s prior knowledge to assimilate new ideas/experiences.  Intuition can involve the imagination and creation of new ideas based on one’s prior knowledge. The construct from intuition is dependent on both prior knowledge and the new knowledge to be assimilated. Intuition also involves rotation of the prior knowledge in its personal way to relate with the new knowledge. Intuition can be seen as the bridge between prior knowledge and new knowledge.

Are there other factors that could affect intuition?

feelings? food? mood? personality? friends? Actually, all these factors fall as either internal prior knowledge or external ideas and influences. As mentioned, the construct from intuition is dependent on both prior knowledge and the new knowledge to be assimilated.

The three factors that permeates diversity of creative and critical thinking in the construction of knowledge.
1. different prior knowledge and past experiences.
2. different innate wiring and intuition. (and integrity).
3. the nexus of life forces and vast existing external knowledge that influences and triggers/inspire intuition to function, defend, construct, assimilate and create.

It is interesting to note that any one component is affected by the other two. Prior knowledge is dependent on how intuition holds it and the new ideas that influences it; Intuition operates based on prior knowledge and the external knowledge to be assimilated; New knowledge is formed by prior knowledge and intuition.

Can I extend the model to infer that one’s behavior and choice of exposure to new influences is dependent on prior knowledge/experiences and personal intuition? ie. we make choices based on our prior knowledge/experiences + personal intuition = current identity.

Footnotes:

[1] But perhaps artistic intuition is a gift, while scientific/mathematical intuition can still be nurtured? Perhaps I am just making up reasons to pacify myself…
but cf. one can train to be melancholic ie. deep thinking. but can one train to be sanguine? sanguineness is a gift but melancholicness can be nurtured. Evidence1: you believe because you see/experience but happy are those who believe though they do not see/experience. – John 20:29 => it is possible to learn to believe and create meaning/experience through thoughts and analysis. Evidence2: Math is compulsory subject but art/music is not.

Is it possible to train someone to become bubbling with emotions? but it seems possible to train someone to use their mind to control their emotions. (does emotions cloud rationality/focusedness or rationality controls emotions?). Emotional vs rational. Being rational not to hinder good emotions eg. humour, social skills, music, but to destroy bad emotions eg. impulsiveness, addiction, inconsideration (9th fruit: self-control). I advocate that being emotional is a natural/gift but rationality can be nurtured/trained.
Still, being aware that one’s rationality can suppress one’s emotions, he can train/learn to relax his rationality if he wants to express and bubble in emotions.

[2] anthropology? more anthology than anthropology.

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