“ Humans value the similarities they can see among all of that chaos they see out there.”
People make sense of confusing situations by thinking about similar concepts / situations.
We look for sameness to help us understand
We appreciate symmetry in nature and science, and reproduce it in art.
Sometimes we express ideas in set ways so as to identify trends to understand better (e.g. graphs are used to explain and express many varied theories and concepts, ranging from economics, to thermodynamics, to grade distribution!)
Can you think of an example?
Some general examples
When you meet someone new for the first time, you’d tend to talk about what you have in common.
If a car mechanic is talking to someone who doesn’t drive, but who cycles, about acceleration / deceleration / braking / cornering, the cyclist would understand these concepts through identifying the symmetries in the ways of motion
The common theme of “2 cows” is used to describe a number of very different political systems (capitalism, socialism, etc). / nationality quirks (what a Swiss corporation would do, what an Indian corporation would do) – a humorous (and rather stereotypical!) take on their distinguishing characteristics.
Why use symmetry to understand concepts?
We naturally identify symmetry as a means to understand
If an object has symmetry, it has fewer features to describe. We need to describe only the theme and the number of ways in which it is repeated, like one house in a row of identical houses 1
An Eye for Uniformity
Human beings appreciate continuity and uniformity - a car without dents, a newly painted room, a flawless diamond, a landscaped garden, evenly pruned bushes. Much time and effort goes into producing continuity, smoothness, evenness, sameness. We are lovers of pattern - we tile, we weave, search for and create symmetry, and in general make patterns of all kinds.
We like our ideas, situations and objects have something in common, to replicate elements: silverware to have the same design, shapes to be repeated in an oriental rug, themes to be replayed in our music.
The love of symmetry…
A number of studies have shown that humans and animals alike find members of the opposite sex that have symmetrical features more physically attractive.
When looking for a life partner, some people value physical attractiveness (facial symmetry), others may look for someone who has the same principles, interests, goals (symmetry that’s not restricted to physical appearance).
Identifying the differences
Since we were children, we were given problems to solve based on identifying differences. On Sesame Street , "Which of these things is not like the others? Which of these things doesn't belong?" appears in every episode!
Uniqueness is the appreciation of “which one of these is not like the others”. We are naturally capable and constantly taught to recognize differences. Difference means that the concept/object stands out in our minds; that it is separate from all other concepts/objects; that it is distinct.
Symmetry in language
Language is man-made, and in more pictorial languages, words often mirror their literal meaning
The Chinese word that connotes evenness, balance , harmony, peace:
Symmetrical and reflective of its meaning.
In Chemistry, much of our understanding of the behaviour and properties of elements is derived from the balancing of equations.
Conservation Laws and Noether’s theorem are based on notions of continuous symmetry.
Space is isotropic – the same in all directions
As much as art can be created from symmetry, art can also be borne of the breaking of symmetry
Escher’s symmetry paintings
Symmetry and the Cosmos
Some theorise that nature evolves through the unpredictable breaking of some of its symmetries
Natural State (symmetrical) Outcome (any number of possibilities) External Process
“ Breaking of the Sameness”
Why? - fresh ideas, different perspective
E.g. The basic spongecake is made of eggs, flour and butter. And all spongecakes consist of these ingredients. But the sameness is broken when chocolate, fruit, flavouring is added.
We sometimes understand things by looking at why they are not similar, by differentiating them.
An analogy: a blank sheet of paper has more symmetry than one filled with words – in order for it to evolve into something with more structure and more information, symmetry has to be broken.
Links to other problems
G102 Problem 1: Elements of Truth (Atomism / Holism)
Sameness extends down to the concept of atoms – all matter is comprised of atoms – the idea that “universal laws presuppose a certain unity in the material world and unchangeable laws cannot be established without the presupposition that something unchangeable must be hidden behind all changes” (Encarta)”.
G101 Problem 12: Too Much Information (Classification)
Symmetry exists within domains
G101 Problem 8: What do you Mean? (Concepts)
Symmetry exists within concepts (this problem builds on this idea, where students are shown that symmetry between potentially disparate concepts can help us understand them).
Ideas we’ve discussed today…
Constructing knowledge is not just the pursuit of truth and purpose, but also beauty!
Identifying symmetry can help in reconciling apparently disconnected observations.
In understanding how we acquire/obtain knowledge, we are able to relate how similarities, symmetries, and patterns can help us learn more effectively
We can also understand concepts better through breaking them down, looking at WHY they exist outside of the ‘sameness’.
Knowledge is deeply humanistic – the same essential ideas and concepts span the sciences as well as the arts.