In order to develop normally, a child requires progressively more complex joint activity with one or more adults who have an irrational emotional relationship with the child. Somebody's got to be crazy about that kid. That's number one. First, last and always.
— Urie Bronfenbrenner
Terrific Complex Numbers quotations
The shortest path between two truths in the real domain passes through the complex domain.
The northern ocean is beautiful, ... and beautiful the delicate intricacy of the snowflake before it melts and perishes, but such beauties are as nothing to him who delights in numbers, spurning alike the wild irrationality of life and baffling complexity of nature's laws.
[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.
When the number of factors coming into play in a phenomenological complex is too large scientific method in most cases fails. One need only think of the weather, in which case the prediction even for a few days ahead is impossible.
Considering the inconceivable complexity of processes even in a simple cell, it is little short of a miracle that the simplest possible model - namely, a linear equation between two variables - actually applies in quite a general number of cases.
I don't let people use me. That's why I like a small number of people in my life. The more people in my life, the more complex it becomes, so I just try to keep it at a minimum.
The intellectual evolution of the race consists in an increase in the number, delicacy, complexity, permanence and speed of formation of such associations.
... 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.
Any single historical event is too complex to be adequately known by anyone.
It transcends all the intellectual capacities of men. Our practice is to wait until a sufficient number of details have been forgotten. Of course things seem simpler then! Our memories work that way; we retain the facts which are easiest to think about.
Indeed, nowadays no electrical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics.
This growth in the number, speed of formation, permanence, delicacy and complexity of associations possible for an animal reaches its acme in the case of man.
The English language is more complex than calculus because numbers don't have nuances.
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.
You cannot communicate complicated information to large groups of people.
As you increase the number of people, you have to decrease the complexity of the information.
The only reason that we like complex numbers is that we don't like real numbers.
The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.
You could not have evolved a complex system like a city or an organism - with an enormous number of components - without the emergence of laws that constrain their behavior in order for them to be resilient.
There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another.
What differentiates human from lower-animal consciousness is time.
You can't explain the concept of "tomorrow" to your dog. Our consciousness is dominated by time - We're constantly running simulations of the future. Our brain is a prediction machine. The hallmark of intelligence, indeed of genius, is the number and complexity of the feedback loops we use in predicting the future.
I tell you, with complex numbers you can do anything.
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.
The songwriting of Hall & Oates is deceptively complex. There are a number of key changes that pass you by as you're listening to the song because they're so seamless and clever.
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.
War to me is very much like sex. You can develop a theory that says sex is primarily for the exchange of genetic material, or that it's a celebration of life, or you can make up 50,000 theories about why human beings have sex, all of which are in some sense true, all of which by themselves miss the point. Because the answer is extraordinarily complex. It may be for fun, it may be for reproduction, for financial reasons, any number of things.
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.
That doesn't mean that the top fifteen institutions in the ranking somehow don't belong there at all. But what is the difference between number two and number eight in any meaningful sense? As an administrator who worked to build a complex university, I find the assumption slightly offensive. We need to be committed to excellence, not to lists.
The social sciences, like much of biology but unlike most fields of the physical sciences, have to deal with structures of essential complexity, i.e. with structures whose characteristic properties can be exhibited only by models made up of relatively large numbers of variables.
Where you have complexity, by nature you can have fraud and mistakes.
You'll have more of that than in a company that shovels sand from a river and sells it. This will always be true of financial companies, including ones run by governments. If you want accurate numbers from financial companies, you're in the wrong world.
Pakistan always seems to have a lot of political complexities and political challenges. But Pakistan is important for a number of reasons. Primarily, it is a nuclear power. And if, in fact, al Qaeda and Taliban, which are in Pakistan and causing a lot of tragedies and deaths in Pakistan - if they would ever somehow have real influence and control of that government, then we [world] really have a problem.
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.
I've done a number of films. I've been around this. I think the biggest challenge is just getting the script right, the way that you want the script to be. It's really about capturing the complexity of emotions and creating the kind of characters that people will want to watch every week.
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.
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.
What makes something simple or complex? It's not the number of dials or controls or how many features it has: It is whether the person using the device has a good conceptual model of how it operates.