"So much of science consists of things we can never see: light ‘waves’ and charged ‘particles’; magnetic ‘fields’ and gravitational ‘forces’; quantum ‘jumps’ and electron ‘orbits’. In fact, none of these phenomena is literally what we say it is. Light waves do not undulate through empty space in the same way that water waves ripple over a still pond; a field is only a mathematical description of the strength and direction of a force; an atom does not literally jump from one quantum state to another, and electrons do not really travel around the atomic nucleus in orbits. The words we use are merely metaphors." (K C Cole, "On Imagining the Unseeable", Discover Magazine, 1982)
"How deep truths can be defined as invariants – things
that do not change no matter what; how invariants are defined by symmetries,
which in turn define which properties of nature are conserved, no matter what.
These are the selfsame symmetries that appeal to the senses in art and music
and natural forms like snowflakes and galaxies. The fundamental truths are
based on symmetry, and there’s a deep kind of beauty in that. (K C Cole,
"The Universe and the Teacup: The Mathematics of Truth and Beauty",
1997)
"Math has its own inherent logic, its own internal truth. Its beauty lies in its ability to distill the essence of truth without the messy interference of the real world. It’s clean, neat, above it all. It lives in an ideal universe built on the geometer’s perfect circles and polygons, the number theorist’s perfect sets. It matters not that these objects don’t exist in the real world. They are articles of faith." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)
"Mathematicians do not see their art as a way of simply calculating or ordering reality. They understand that math articulates, manipulates, and discovers reality. In that sense, it’s both a language and a literature; a box of tools and the edifices constructed from them." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)
"Mathematics can function as a telescope, a microscope, a sieve for sorting out the signal from the noise, a template for pattern perception, a way of seeking and validating truth. […] A knowledge of the mathematics behind our ideas can help us to fool ourselves a little less often, with less drastic consequences." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)
"Mathematics is a way of thinking that can help make muddy
relationships clear. It is a language that allows us to translate the
complexity of the world into manageable patterns. In a sense, it works like
turning off the houselights in a theater the better to see a movie. Certainly,
something is lost when the lights go down; you can no longer see the faces of
those around you or the inlaid patterns on the ceiling. But you gain a far
better view of the subject at hand."
"Mathematics seems to have astonishing power to tell us how
things work, why things are the way they are, and what the universe would tell
us if we could only learn to listen. This comes as a surprise from a branch of
human activity that is supposed to be abstract, objective, and devoid of
sentiment."
"One of the main reasons that large numbers grow so
explosively is that multiplication is a powerful engine for growth - even when
the only number you happen to be multiplying is insignificantly puny, like the
number two."
"Another limit imposed by reality is its sheer complexity, which makes it impossible to predict some ordinary things (like weather) at the same time that it’s possible to predict truly extraordinary things (like the fate of the universe)." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)
"Abstractions are a way to distill the essence from an otherwise unfathomable situation." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)
"Imagining the unseeable is hard, because imagining means having an image in your mind. And how can you have a mental image of something you have never seen? Like perception itself, the models of science are embedded inextricably in the current worldview we call culture." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)
"Science [...] involves looking mostly at things we can never
see."
"The abstractions of science are stereotypes, as two-dimensional and as potentially misleading as everyday stereotypes. And yet they are as necessary to the process of understanding as filtering is to the process of perception." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)
"The subjects of science are not only often unseeable; they are also untouchable, unmeasurable, and sometimes even unimaginable."
"If two quantum particles are entangled, they become, in
effect, two parts of a single unit. What happens to one entangled particle
happens to the other, no matter how far apart they are." (K C Cole, "Wormholes
Untangle a Black Hole Paradox", 2015) [source]
"Like many a maturing beauty, string theory has gotten rich
in relationships, complicated, hard to handle and widely influential. Its
tentacles have reached so deeply into so many areas in theoretical physics,
it’s become almost unrecognizable, even to string theorists." (K C Cole, "The
Strange Second Life of String Theory", Quanta Magazine", 2016) [source]
"String theory today looks almost fractal. The more closely people explore any one corner, the more structure they find. Some dig deep into particular crevices; others zoom out to try to make sense of grander patterns. The upshot is that string theory today includes much that no longer seems stringy. Those tiny loops of string whose harmonics were thought to breathe form into every particle and force known to nature (including elusive gravity) hardly even appear anymore on chalkboards at conferences." (K C Cole, "The Strange Second Life of String Theory", Quanta Magazine", 2016) [source]
"[…] Einstein showed, for 'stuff' like space and time,
seemingly stable, unchangeable aspects of nature; in truth, it’s the
relationship between space and time that always stays the same, even as space
contracts and time dilates. Like energy and matter, space and time are mutable
manifestations of deeper, unshakable foundations: the things that never vary no
matter what." (K C Cole, "The Simple Idea Behind Einstein’s Greatest Discoveries",
Quanta Magazine, 2019) [source]
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