Visualising is a great tool when we are solving problems. We can create an image of a situation to make sense of it. Sometime we visualise to explore “what will happen if. . .?”
Visualising helps us:
- to explore a model
- to plan ahead
- to dive into a problem
Visualising to explore a model is particularly useful in situations when the situation is physically unattainable. The situation may not be possible to see for a purpose, such as a maths task in school, where the purpose it to test pupils skills in solving problems related to 3D object. Computers have made it possible to animate and visualise these types of problems.
We had interlocking cubes (all the same size) in 10 different colours, up to 1000 of each colour. We started with one yellow cube. This was covered all over with a single layer of red cubes:
This was then covered with a layer of blue cubes. Then came a layer of green, followed by black, brown, white, orange, pink and purple for as long as there were enough cubes of that colour to cover the layer that came before.
The unused cubes were put away. The many-layered cube was then broken up and each colour made into cubes. These were just of the one colour and the largest cubes possible made. For example, the red layer made three 2×2×2 cubes with two 1×1×1 cubes left over, whereas the larger layers made much larger cubes as well as smaller ones.
What colour was the largest cube that was made?
Which colour made into cubes had no 1×1×1 cubes?
Which colour was made into the most cubes including the 1×1×1 cubes?
In this problem, it is not possible to see inside a large cube. It is not possible to see the centre of the cube and the surrounding layer at the same time. You need to think in stages and then you visualising strategies to solve the problem.
But here are also other situations where it is useful to visualise to model a situation. The concept of the Big Bang – the explosion from a focused point. Projects like Beginning, an animation by Grzegorz Nowiński from Novina Studio, provide valuable insights. We can use logic to reason about what would have happened and why. But seeing the amino acids and complex life form on the surface on Earth makes it possible to gain greater insight into the model. It may help to spot strong point and weaknesses with the model.
The video below covers billions of years in a couple of minutes. Most of us have an idea of what the theory of Big Bang is about, yet this somewhat imagined view presented in the video makes it come the model of the beginning of universe come alive. Explosion and the journey onwards through the early cosmos. Asteroids and whizzing volcanoes help us to catch a glimpse of what might have happened. This project took approximately 2 weeks to finish – from scripting to animating to post production. That in itself is amazing!
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Photo: “Universe” by Salvatore Vuono