``The scientist does not study nature because it is useful; he studies
it because he delights in it, and he delights in it because it is
beautiful. If nature were not beautiful, it would not be worth knowing,
and if nature were not worth knowing, life would not be worth living.
Of course I do not here speak of that beauty that strikes the
senses, the beauty of qualities and appearances; not that I undervalue
such beauty, far from it, but it has nothing to do with science; I mean
that profounder beauty which comes from the harmonious order of the parts,
and which a pure intelligence can grasp.''
``The point of philosophy is to start with something so simple as not to
seem worth stating, and to end with something so paradoxical that no
one will believe it.''
``Things should be as simple as possible, but not simpler.''
``It is strange that we know so little about the properties of numbers.
They are our handiwork, yet they baffle us; we can fathom only a few
of their intricacies. Having defined their attributes and prescribed
their behavior, we are hard pressed to perceive the implications of
---James R. Newman
``Our minds are finite, and yet even in these circumstances of finitude
we are surrounded by possibilities that are infinite, and the purpose
of human life is to grasp as much as we can out of the infinitude.''
---Alfred North Whitehead
``Computer Science is no more about computers than astronomy is about
---E. W. Dijkstra
``To use: Apply shampoo to wet hair. Massage to lather, then rinse.
---A typical hair-washing algorithm that fails to halt
``But let your communication be Yea, yea; Nay, nay: for whatsoever is
more than these cometh of evil.''
---An early proposal for binary code, Matthew 5:37
``All Cretans are liars.''
---Epimenides, who was himself a Cretan
``Trying to define yourself is like trying to bite your own teeth.''
``There is no ``royal road'' to geometry.''
---Euclid to King Ptolemy I
``So, Na'ralist observe,
A Flea Hath smaller fleas that on him prey,
And these have smaller fleas to bite 'em
And so proceed ad infinitum.''
``God used beautiful mathematics in creating the world.''
``Nature uses as little as possible of anything.''
``The development of an organism ... may be considered as the execution
of a ``developmental program'' present in the fertilized
egg. ... A central task of developmental biology is to discover the
underlying algorithm from the course of development.''
---Aristid Lindenmayer and Grzegorz Rozenberg
``Fractal geometry will make you see everything differently. There is
danger in reading further. You risk the loss of your childhood vision of
clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains,
torrents of water, carpets, bricks, and much else besides. Never again
will your interpretation of these things be quite the same.''
---Michael F. Barnsley
``Clouds are not spheres, mountains are not cones, coastlines are not
circles, and bark is not smooth, nor does lightning travel in a straight
``The universe is full of magical things patiently waiting for our wits
to grow sharper.''
``Beauty is the first test; there is no permanent place in the world for
---G. H. Hardy
``Mathematics is the science of patterns.''
---Lynn Arthur Steen
``It is indeed a surprising and fortunate fact that nature can be expressed
by relatively low-order mathematical functions.''
``Everything you've learned in school as ``obvious'' becomes less and less
obvious as you begin to study the universe. For example, there are
no solids in the universe. There's not even a suggestion of a solid.
There are no absolute continuums. There are no surfaces. There are no
---R. Buckminster Fuller
``Chaos is the score upon which reality is written.''
``... it may happen that small differences in the initial conditions
produce very great ones in the final phenomena.''
``Prediction is difficult, especially of the future.''
---Mark Twain (also attributed to Niels Bohr)
``I am strangely attracted to you.''
``There is no excellent beauty that hath not some strangeness in the
``Big whorls have little whorls,
Which feed on their velocity;
whorls have lesser whorls,
And so on to viscosity.''
---L. F. Richardson
``Chaos often breeds life when order breeds habit.''
---Henry Brooks Adams
``Nature itself, even in chaos, cannot proceed except in an orderly and
``It turns out that an eerie type of chaos can lurk just behind a facade of
order---and yet, deep inside the chaos lurks an even eerier type of order.''
``Amid the turmoil and tumult of battle, there may be seeming disorder
and yet no real disorder at all.''
``All stable processes we shall predict. All unstable processes we shall
---John von Neumann
``Order is not sufficient. What is required, is something much more
complex. It is order entering upon novelty; so that the massiveness of
order does not degenerate into mere repetition; and so that the novelty
is always reflected upon a background of system.''
---Alfred North Whitehead
``Nothing in Nature is random. ... A thing appears random only through
the incompleteness of our knowledge.''
``God has put a secret art into the forces of Nature so as to enable it
to fashion itself out of chaos into a perfect world system.''
``If patterns of ones and zeros were ``like'' patterns of human lives
and death, if everything about an individual could be represented in a
computer record by a long string of ones and zeros, then what kind of
creature would be represented by a long string of lives and deaths?''
``The chess-board is the world; the pieces are the phenomena of the
universe; the rules of the game are what we call the laws of Nature.''
---T. H. Hardy
``Some primal termite knocked on wood. And tasted it, and found it good.
And that is why your Cousin May Fell through the parlor floor today.''
``Go to the ant, thou sluggard; consider her ways, and be wise.''
``... and the thousands of fishes moved as a huge beast, piercing the water.
They appear united, inexorably bound by common fate. How comes this
``Do onto others as you would have them do onto you.''
``Eye for eye, tooth for tooth, hand for hand, foot for foot.''
``Morality is the herd-instinct in the individual.''
``A technique succeeds in mathematical physics, not by a clever trick, or a
happy accident, but because it expresses some aspect of a physical truth.''
---O. G. Sutton
``What is important is that complex systems, richly cross-connected
internally, have complex behaviours, and that these behaviours can be
goal-seeking in complex patterns.''
---W. Ross Ashby
``I see the world in very fluid, contradictory, emerging, interconnected
terms, and with that kind of circuitry I just don't feel the need to
say what is going to happen or will not happen.''
``If this seems complex, the reason is because Tao is both simple and
complex. It is complex when we try to understand it, and simple when
we allow ourselves to experience it.''
``I want to stay as close to the edge as I can without going over. Out on
the edge you see all kinds of things you can't see from the center.''
---Kurt Vonnegut, Jr.
``Life is pleasant. Death is peaceful. It's the transition that's
``A hen is only an egg's way of making another egg.''
``Natural selection is a mechanism for generating an exceedingly high
degree of improbability.''
---Sir Ronald Fisher
``The goal of science is to build better mousetraps. The goal of nature
is to build better mice.''
``Mathematicians are inexorably drawn to nature, not just describing what
is to be found there, but in creating echoes of natural laws.''
``Plasticity is a double-edged sword: the more flexible an organism is
the greater the variety of maladaptive, as well as adaptive, behaviors
it can develop; the more teachable it is the more fully it can profit
from the experiences of its ancestors and associates and the more it
risks being exploited by its ancestors and associates.''
``Repetition is the only form of permanence that Nature can achieve.''
``I bet the human brain is a kludge.''
``As a net is made up of a series of ties, so everything in this world is
connected by a series of ties. If anyone thinks that the mesh of a net
is an independent, isolated thing, he is mistaken. It is called a net
because it is made up of a series of interconnected meshes, and each
mesh has its place and responsibility in relation to other meshes.''
``If the brain were so simple we could understand it, we would be so simple
``The sciences do not try to explain, they hardly even try to interpret,
they mainly make models. By a model is meant a mathematical construct
which, with the addition of certain verbal interpretations, describes
observed phenomena. The justification of such a mathematical construct
is solely and precisely that it is expected to work.''
---John von Neumann
``Breadth-first search is the bulldozer of science.''
``The most extensive computation known has been conducted over the last
billion years on a planet-wide scale: it is the evolution of life.
The power of this computation is illustrated by the complexity and beauty
of its crowning achievement, the human brain.''
``When two texts, or two assertions, perhaps two ideas, are in
contradiction, be ready to reconcile them rather than cancel one by the
other; regard them as two different facets, or two successive stages, of
the same reality, a reality convincingly human just because it is complex.''
``To see a World in a grain of Sand,
And a Heaven in a Wild Flower,
Infinity in the palm of your hand,
And Eternity in an hour.''
``The process of preparing programs for a digital computer is especially
attractive, not only because it can be economically and scientifically
rewarding, but also because it can be an aesthetic experience much like
composing poetry or music.''
---Donald E. Knuth