Quotes & Sayings About Complex Numbers

In the work of Ramanujan, the number 24 appears repeatedly. This is an example of what mathematicians call magic numbers, which continually appear, where we least expect them, for reasons that no one understands. Miraculously, Ramanujan's function also appears in string theory. The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. In string theory, each of the 24 modes in the Ramanujan function corresponds to a physical vibration of the string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. (Since physicists add two more dimensions when they count the total number of vibrations appearing in a relativistic theory, this means that space-time must have 24 + 2 = 26 space-time dimensions.) — Michio Kaku

The simplest single-celled organism oscillates to a number of different frequencies, at the atomic, molecular, sub-cellular, and cellular levels. Microscopic movies of these organisms are striking for the ceaseless, rhythmic pulsation that is revealed. In an organism as complex as a human being, the frequencies of oscillation and the interactions between those frequencies are multitudinous. — George Leonard

Mathematical analysis and computer modelling are revealing to us that the shapes and processes we encounter in nature -the way that plants grow, the way that mountains erode or rivers flow, the way that snowflakes or islands achieve their shapes, the way that light plays on a surface, the way the milk folds and spins into your coffee as you stir it, the way that laughter sweeps through a crowd of people - all these things in their seemingly magical complexity can be described by the interaction of mathematical processes that are, if anything, even more magical in their simplicity. Shapes that we think of as random are in fact the products of complex shifting webs of numbers obeying simple rules. The very word "natural" that we have often taken to mean "unstructured" in fact describes shapes and processes that appear so unfathomably complex that we cannot consciously perceive the simple natural laws at work.They can all be described by numbers. — Douglas Adams

As the number of unexplained, irreducibly complex biological systems increases, our confidence that Darwin's criterion of failure has been met skyrockets toward the maximum that science allows. — Michael Behe

I suggest that this is a good time to think soberly about our responsibilities to our descendents - those who will ring out the Fossil Fuel Age. Our greatest responsibility, as parents and as citizens, is to give America's youngsters the best possible education. We need the best teachers and enough of them to prepare our young people for a future immeasurably more complex than the present, and calling for ever larger numbers of competent and highly trained men and women. — Hyman Rickover

He loved numbers, their patterns and secrets, the way something complex could be reduced to something simple. In mathematics, unlike life, there was always a solution, a definite answer. — Lisa Kleypas

We are accustomed to live in hopes of good weather, a good harvest, a nice love-affair, hopes of becoming rich or getting the office of chief of police, but I've never noticed anyone hoping to get wiser. We say to ourselves: it'll be better under a new tsar, and in two hundred years it'll still be better, and nobody tries to make this good time come tomorrow. On the whole, life gets more and more complex every day and moves on its own sweet will, and people get more and more stupid, and get isolated from life in ever-increasing numbers. — Anton Chekhov

A romantic understanding sees it primarily in terms of immediate appearance. If you were to show an engine or a mechanical drawing or electronic schematic to a romantic it is unlikely he would see much of interest in it. It has no appeal because the reality he sees is its surface. Dull, complex lists of names, lines and numbers. Nothing interesting. But if you were to show the same blueprint or schematic or give the same description to a classical person he might look at it and then become fascinated by it because he sees that within the lines and shapes and symbols is a tremendous richness of underlying form. — Anonymous

The pages and pages of complex, impenetrable calculations might have contained the secrets of the universe, copied out of God's notebook.
In my imagination, I saw the creator of the universe sitting in some distant corner of the sky, weaving a pattern of delicate lace so fine that that even the faintest light would shine through it. The lace stretches out infinitely in every direction, billowing gently in the cosmic breeze. You want desperately to touch it, hold it up to the light, rub it against your cheek. And all we ask is to be able to re-create the pattern, weave it again with numbers, somehow, in our own language; to make the tiniest fragment our own, to bring it back to eart. — Yoko Ogawa

Indeed, nowadays no electrical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics. — Keith Devlin

Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers. — Carl Friedrich Gauss

The things by which our emotions can be moved - the shape of a flower or a Grecian urn, the way a baby grows, the way the wind brushes across your face, the way clouds move, their shapes, the way light dances on the water, or daffodils flutter in the breeze, the way in which the person you love moves their head, the way their hair follows that movement, the curve described by the dying fall of the last chord of a piece of music - all these things can be described by the complex flow of numbers.

That's not a reduction of it, that's the beauty of it. — Douglas Adams

Now our world is at the present time firmly in the grip of a mechanical monster, whose head - if you want to call it that - is the World Engineer's Complex. That monster is opposed to us and can keep all too good a tab on us through every purchase we make with our credit numbers, every time we use the public transportation or eat a meal or rent a place to live. — Gordon R. Dickson

We live in a society right now which is the last phase of the ecosystem in terms of the old entertainment value, or the old entertainment construction, which is we've gone down to this instant gratification, instant numbers, instant understanding, instant. But it's like the exact - it has perfected itself to the instant click, when, in a way, creativity originates as a much more complex beast. So we now have to reinvent a new canvas where we can indulge in it. And that's where the digital revolution creates a whole new ecosystem of entertainment. — Nicolas Winding Refn

Each of the 24 modes in the Ramanujan function corresponds to a physical vibration of a string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. — Michio Kaku

Man! The most complex of creatures, and for this reason the most dependant of creatures. On everything that has formed you, you may depend. Do not balk at this apparent slavery ... a debtor to many, you pay for your advantages by the same number of dependencies. Understand that independence is a form of poverty; that many things claim you, that many also claim kinship with you. — Andre Gide

I recited Pi to 22,514 decimal points in five hours and nine minutes. I was able to do this because of weeks of study, aided by the unusual synaesthesic way my mind perceives numbers as complex multidimensional coloured and textured shapes. — Daniel Tammet

I tell you, with complex numbers you can do anything. — John Derbyshire

Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.

Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...

To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples. — Jonathan Black

The discovery of the fractals had proven that in a world of chaos, there is a way to understand the natural world by using something as definite and precise as values and numbers. Things and events that were beyond our understanding slowly emerge as distinctively clear as figures and images, leaving no room for mysteries and ambiguities, making the universe more understandable in the eyes of people. With this, it presents a definite point of view in the way complex things are to be observed, which would represent irregularities and open up new paths for discovery. — Tim Clearbrook

In however complex a manner this feeling may have originated, as it is one of high importance to all those animals which aid and defend one another, it will have been increased through natural selection; for those communities, which included the greatest number of the most sympathetic members, would flourish best, and rear the greatest number of offspring. — Charles Darwin

China's economy became more complex. By now there is a large number of small- and medium-sized companies that work quite differently from big, state-owned enterprises. They don't follow any long-term business plan and don't rent office space for years to come. They start out and need an office right away, for a week, a month or half a year, and they want to be among other entrepreneurs like themselves. — Zhang Xin

The only reason that we like complex numbers is that we don't like real numbers. — Bernd Sturmfels

Certain supplementary restrictions imposed on the text compel us to perceive it as poetry. As soon as one assigns a given text to the category of poetry, the number of meaningful elements in it acquires the capacity to grow and the system of their combinations also becomes more complex. — Yuri Lotman

The English language is more complex than calculus because numbers don't have nuances. — Andy Rooney

The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers. — Keith Devlin

As experimentation becomes more complex, the need for the co-operation in it of technical elements from outside becomes greater and the modern laboratory tends increasingly to resemble the factory and to employ in its service increasing numbers of purely routine workers. — John Desmond Bernal

It's called being in love. It's more frightening than confronting your deepest fear and opens you to being hurt beyond the physical plane." He placed a hand over his heart. "It might seem as though it's a weakness to you but it is proof that we are more than numbers, experiments, or whatever else Mercile intended us to be. It takes bravery and strength to feel such strong emotions for one person when we were denied from birth the chance to ever care about anything or anyone. I'm not saying it's easy or painless. It is probably one of the most complex things I've experienced. Jessie is my life. My heart beats for her and I will admit to all that I wouldn't want to go on if I lost her. The unmated ones don't understand and are currently looking confused or horrified. I'm hopeful they'll know the ups and downs of falling in love one day. It's a gift and a curse at times but everyone should experience it. It's a part of life and we are survivors. — Laurann Dohner

We live in a culture that's been hijacked by the management consultant ethos. We want everything boiled down to a Power Point slide. We want metrics and 'show me the numbers.' That runs counter to the immensely complex nature of so many social, economic and political problems. You cannot devise an algorithm to fix them. — Carl Honore

the exploiter asks of a piece of land only how much and how quickly it can be made to produce, the nurturer asks a question that is much more complex and difficult: What is its carrying capacity? (That is: How much can be taken from it without diminishing it? What can it produce dependably for an indefinite time?) The exploiter wishes to earn as much as possible by as little work as possible; the nurturer expects, certainly, to have a decent living from his work, but his characteristic wish is to work as well as possible. The competence of the exploiter is in organization; that of the nurturer is in order - a human order, that is, that accommodates itself both to other order and to mystery. The exploiter typically serves an institution or organization; the nurturer serves land, household, community, place. The exploiter thinks in terms of numbers, quantities, "hard facts"; the nurturer in terms of character, condition, quality, kind. — Gregory Pence

The strange word nymphomation, used to denote a complex mathematical procedure where numbers, rather than being added together or multiplied or whatever, were actually allowed to breed with each other to produce new numbers. — Jeff Noon

Actually, the world is not complex. It is the task of trying to figure it out with words or numbers that is complex. — Alan W. Watts

There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another. — Keith Devlin

I wish that one would be persuaded that psychological experiments, especially those on the complex functions, are not improved [by large studies]; the statistical method gives only mediocre results; some recent examples demonstrate that. The American authors, who love to do things big, often publish experiments that have been conducted on hundreds and thousands of people; they instinctively obey the prejudice that the persuasiveness of a work is proportional to the number of observations. This is only an illusion. — Alfred Binet

Real life issues are not mathematical equations. We're not calculators crunching numbers. We're humans sorting through complex, multi-layered issues, and we're doing so while enduring the (sometimes profound) personal effects of our conclusions. While we want to be reasonable, we are inexorably pulled in the direction of our oldest mental habits and by our deepest life-impacting needs. We're repelled by those ideas which can jeopardize our comfort, safety, and happiness. We can try to be fair, but all the while we are fighting against our needs and fears. There are things we don't want to be true (or false). Our lives are built on certain beliefs which, if disproved, could wreck us. These are the truths that we 'can't handle'. — Daniel Ionson