"One of the most fundamental notions in mathematics is that of number. Although the idea of number is basic, the numbers themselves possess both nuance and complexity that spark the imagination." (Edward B Burger, "Exploring the Number Jungle", 2000)
"To say that a thing is imaginary is not to dispose of it in the realm of mind, for the imagination, or the image making faculty, is a very important part of our mental functioning. An image formed by the imagination is a reality from the point of view of psychology; it is quite true that it has no physical existence, but are we going to limit reality to that which is material? We shall be far out of our reckoning if we do, for mental images are potent things, and although they do not actually exist on the physical plane, they influence it far more than most people suspect." (Dion Fortune," Spiritualism and Occultism", 2000)
"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 2002)
"[…] because observations are all we have, we take them seriously. We choose hard data and the framework of mathematics as our guides, not unrestrained imagination or unrelenting skepticism, and seek the simplest yet most wide-reaching theories capable of explaining and predicting the outcome of today’s and future experiments." (Brian Greene, "The Fabric of the Cosmos", 2004)
"There is a strong parallel between mountain climbing and mathematics research. When first attempts on a summit are made, the struggle is to find any route. Once on the top, other possible routes up may be discerned and sometimes a safer or shorter route can be chosen for the descent or for subsequent ascents. In mathematics the challenge is finding a proof in the first place. Once found, almost any competent mathematician can usually find an alternative often much better and shorter proof. At least in mountaineering we know that the mountain is there and that, if we can find a way up and reach the summit, we shall triumph. In mathematics we do not always know that there is a result, or if the proposition is only a figment of the imagination, let alone whether a proof can be found." (Kathleen Ollerenshaw, "To talk of many things: An autobiography", 2004)
"Imagination has the creative task of making symbols, joining things together in such a way that they throw new light on each other and on everything around them. The imagination is a discovering faculty, a faculty for seeing relationships, for seeing meanings that are special and even quite new." (Thomas Merton, "Angelic Mistakes: The Art of Thomas Merton", 2006)
"To have the courage to think outside the square, we need to be intrigued by a problem. This intrigue will encourage us to use our imaginations to find solutions which are beyond our current view of the world. This was the challenge that faced mathematicians as they searched for a solution to the problem of finding meaning for the square root of a negative number, in particular v-1." (Les Evans, "Complex Numbers and Vectors", 2006)
"Unfortunately, if we were to use geometry to explore the concept of the square root of a negative number, we would be setting a boundary to our imagination that would be difficult to cross. To represent -1 using geometry would require us to draw a square with each side length being less than zero. To be asked to draw a square with side length less than zero sounds similar to the Zen Buddhists asking ‘What is the sound of one hand clapping?’" (Les Evans, "Complex Numbers and Vectors", 2006)
"Language use is a curious behavior, but once the transition to language is made, literature is a likely consequence, since it is linked to the dynamic of the linguistic symbol through the functioning of the imagination." (Russell Berman, "Fiction Sets You Free: Literature, Liberty and Western Culture", 2007)
"If worldviews or metanarratives can be compared to lenses, which of them brings things into the sharpest focus? This is not an irrational retreat from reason. Rather, it is about grasping a deeper order of things which is more easily accessed by the imagination than by reason." (Alister McGrath, "If I Had Lunch with C. S. Lewis: Exploring the Ideas of C. S. Lewis on the Meaning of Life", 2014)
"Mathematics is a fascinating discipline that calls for creativity, imagination, and the mastery of rigorous standards of proof." (John Meier & Derek Smith, "Exploring Mathematics: An Engaging Introduction to Proof", 2017)
"The mental model is the arena where imagination takes place. It enables us to experiment with different scenarios by making local alterations to the model. […] To speak of causality, we must have a mental model of the real world. […] Our shared mental models bind us together into communities." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)
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