Mathematical Models Quotes

The magic of the mechanisms inside each genetic structure saying exactly where that nerve cell should go - the complexity of these mathematical models is beyond human comprehension. ~ Alexander Tsiaras

What if one were to want to hunt for these hidden presences? You can't just rummage around like you're at a yard sale. You have to listen. You have to pay attention. There are certain things you can't look at directly. You need to trick them into revealing themselves. That's what we're doing with Walter, Jaz. We're juxtaposing things, listening for echoes. It's not some silly cybernetic dream of command and control, modeling the whole world so you can predict the outcome. It's certainly not a theory of everything. I don't have a theory of any kind. What I have is far more profound.'

'What's that?'

'A sense of humor.'

Jaz looked at him, trying to find a clue in his gaunt face, in the clear gray eyes watching him with such - what? Amusement? Condescension? There was something about the man which brought on a sort of hermeneutic despair. He was a forest of signs.

'We're hunting for jokes.' Bachman spoke slowly, as if to a child. 'Parapraxes. Cosmic slips of the tongue. They're the key to the locked door. They'll help us discover it.'

'Discover what?'

'The face of God. What else would we be looking for? ~ Hari Kunzru

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 - that is correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple. ~ John Von Neumann

I advise you to look for a chance to break away, to find a subject you can make your own. That is where the quickest advances are likely to occur, as measured by discoveries per investigator per year. Therein you have the best chance to become a leader and, as time passes, to gain growing freedom to set your own course.
If a subject is already receiving a great deal of attention, if it has a glamorous aura, if its practitioners are prizewinners who receive large grants, stay away from that subject. Listen to the news coming from the hubbub, learn how and why the subject became prominent, but in making your own long-term plans be aware it is already crowded with talented people. You would be a newcomer, a private amid bemedaled first sergeants and generals. Take a subject instead that interests you and looks promising, and where established experts are not yet conspicuously competing with one another, where few if any prizes and academy memberships have been given, and where the annals of research are not yet layered with superfluous data and mathematical models. ~ Edward O. Wilson

As a graduate student, I wrote a long paper connecting the dots between mathematical models of learning and language development in children. It was published in a major journal. ~ Steven Pinker

If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming. ~ George Dantzig

The difference is that we have the hardest and most painful evidence that there was a Holocaust. But, for the global warming scenario that is causing such hysteria, we have only a movie made by a politician and mathematical models whose results change drastically when you change a few of the arbitrarily selected variables. ~ Thomas Sowell

This is a point I'll be returning to in future chapters: we've seen time and again that mathematical models can sift through data to locate people who are likely to face great challenges, whether from crime, poverty, or education. It's up to society whether to use that intelligence to reject and punish them - or to reach out to them with the resources they need. ~ Cathy O'Neil

Markets aren't real. They are mathematical models, created by imagining a self-contained world where everyone has exactly the same motivation and the same knowledge and is engaged in the same self-interested calculating exchange. Economists are aware that reality is always more complicated; but they are also aware that to come up with a mathematical model, one always has to make the world into a bit of a cartoon. ~ David Graeber

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds? ~ Stephen Hawking

these models are constructed not just from data but from the choices we make about which data to pay attention to - and which to leave out. Those choices are not just about logistics, profits, and efficiency. They are fundamentally moral. If we back away from them and treat mathematical models as a neutral and inevitable force, like the weather or the tides, we abdicate our responsibility. And the result, as we've seen, is WMDs that treat us like machine parts in the workplace, that blackball employees and feast on inequities. We must come together to police these WMDs, to tame and disarm them. My hope is that they'll be remembered, like the deadly coal mines of a century ago, as relics of the early days of this new revolution, before we learned how to bring fairness and accountability to the age of data. Math deserves much better than WMDs, and democracy does too. ~ Cathy O'Neil

Nevertheless, many of these models encoded human prejudice, misunderstanding, and bias into the software systems that increasingly managed our lives. Like gods, these mathematical models were opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists. Their verdicts, even when wrong or harmful, were beyond dispute or appeal. And ~ Cathy O'Neil

Every culture has its own creation myth, its own cosmology. And in some respects every cosmology is true, even if I might flatter myself in assuming mine is somehow truer because it is scientific. But it seems to me that no culture, including scientific culture, has cornered the market on definitive answers when it comes to the ultimate questions. Science may couch its models in the language of mathematics and observational astronomy, while other cultures use poetry and sacrificial propitiations to defend theirs. But in the end, no one knows, at least not yet. The current flux in the state of scientific cosmology attests to this, as we watch physicists and astronomers argue over string theory and multiverses and the cosmic inflation hypothesis. Many of the postulates of modern cosmology lie beyond, or at least at the outer fringes, of what can be verified through observation. As a result, aesthetics - as reflected by the "elegance" of the mathematical models - has become as important as observation in assessing the validity of a cosmological theory. There is the assumption, sometimes explicit and sometimes not, that the universe is rationally constructed, that it has an inherent quality of beauty, and that any mathematical model that does not exemplify an underlying, unifying simplicity is to be considered dubious if not invalid on such criteria alone. This is really nothing more than an article of faith; and it is one of the few instances where science is faith-based, at lea ~ Dennis J. McKenna

The credit crunch was based on a climate (the post-Cold War victory party of free-market capitalism), a problem (the sub-prime mortgages), a mistake (the mathematical models of risk) and a failure, that of the regulators. ~ John Lanchester

if you take a positivist position, as I do, questions about reality don't have any meaning. All one can ask is whether imaginary time is useful in formulating mathematical models that describe what we observe. ~ Stephen Hawking

There is a history of mathematical models of oligopolistic competition dating from Cournot to the theory of games. There is also a literature generated by institutional economists, lawyers, and administrators interested in formulating and implementing public policy. It has been the tendency of these groups to work almost as though the other did not exist. ~ Martin Shubik

In other words, the idea is the there's a fourth level of parallel universes that's vastly larger than the three we've encountered so far, corresponding to different mathematical structures. The first three levels correspond to noncommunicating parallel universes within the same mathematical structure: Level I simply means distant regions from which light hasn't yet had time to reach us, Level II covers regions that are forever unreachable because of the cosmological inflation of intervening space, and Level III, Everett's "Many Worlds," involves noncommunicating parts of the Hilbert space of quantum mechanics. Whereas all the parallel universes at Levels I, II and III obey the same fundamental mathematical equations (describing quantum mechanics, inflation, etc.), Level IV parallel universes dance to the tunes of different equations, corresponding to different mathematical structures. Figure 12.2 illustrates this four-level multiverse hierarchy, one of the core ideas of this book. ~ Max Tegmark

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree. ~ Aristotle.

I don't believe in natural science. ~ Kurt Godel

He is like the fox, who effaces his tracks in the sand with his tail.

{Describing the writing style of famous mathematician Carl Friedrich Gauss} ~ Niels Henrik Abel

We boast our emancipation from many superstitions; but if we have broken any idols, it is through a transfer of idolatry. ~ Ralph Waldo Emerson

The water trading mechanism where there are transparent trades of water allocations is one that is good for us to learn from because it does allow for the marketplace to procure water for the highest and most efficient uses with the highest value in agriculture. And that might be a good model for us. ~ Marc Levine

He means that even though there is a mathematical possibility that dinosaurs and humans coexist, that possible reality would collapse because the likelihood is so astronomically small. ~ Liana Brooks

Eyebeam: What do you mean, I have "male answer syndrome"?

Sally: It's the compulsion to provide an answer to any question, even if it means resorting to pure speculation.

Eyebeam: I knew that…

Sally: It's a very widespread phenomenon.

Beth: I wonder what causes it?

Eyebeam: Cause? Well, society has chosen male role models who always exhibit total control… If a male says "I don't know", he's admitting to conversational helplessness and failing to live up to that societal standard…

Sally: Pretty pitiful, huh?

Eyebeam: Damn!

Beth: …And I always thought they learned it all in "shop". ~ Sam Hurt

I venture to give an alternative method of regarding the processes occurring in the electric field, which I have often found useful and which is, from a mathematical point of view, equivalent to Maxwell's Theory. ~ Joseph John Thomson

I was too much of a victim of the model I created. I tried Change to Win and helping Obama, and then I just ran out of Andy Stern ideas. ~ Andy Stern

If you feel dirty, insignificant or unloved, then rats are a good role model. They exist without permission, they have no respect for the hierarchy of society, and they have sex 50 times a day. ~ Banksy

A man is fortunate if he encounters living examples of vice, as well as of virtue, to inspire him. ~ Brendan Behan

The model I like to sort of simplify the notion of what goes on in a market for common stocks is the pari-mutuel system at the racetrack. If you stop to think about it, a pari-mutuel system is a market. Everybody goes there and bets and the odds change based on what's bet. That's what happens in the stock market. ~ Charlie Munger

A single model enables me to focus on one thing at a time, separating design and form and color into three successive stages. ~ Thomas S. Buechner

Someone said to me that we have to encourage more young women to want top-level editing jobs. I think that will happen naturally as we have more role models, more examples of boss ladies who aren't sad and cruel and overworked and undersexed like in DevilWearsPrada, but who are straight-up owning it and notable not for their gender but for their editorial savvy. ~ Ann Friedman

Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can't be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what's also amazing is that we own all of them. No one can patent a mathematical formula, it's ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It's too precious to be given away to the "initiated few." It belongs to all of us. ~ Edward Frenkel

The trailblazers are my role models in this industry: Sidney Poitier, Harry Belafonte, James Earl Jones, and Billy Dee Williams. I keep their pictures in my trailer and try to measure to their standards every time I act. ~ Brian J. White

testing out models, and then refining everything further, I developed a set of ideas that was transforming people's ability ~ David Rock

I can't stand when girls come to me and say they want to be a model, but they can't tell me who the top three photographers are in the world. They can't tell me who the top five biggest models are or name three cosmetics companies. They can't even name the top fashion magazines! You have to get it together and know your stuff. ~ Kimora Lee Simmons

And so to read is, in truth, to be in the constant act of creation. The old lady on the bus with her Orwell, the businessman on the Tube with Patricia Cornwell, the teenager roaring through Capote -- they are not engaged in idle pleasure. Their heads are on fire. Their hearts are flooding. With a book, you are the landscape, the sets, the snow, the hero, the kiss -- you are the mathematical calculation the plots the trajectory of the blazing, crashing zeppelin. You -- pale, punchable reader -- are terraforming whole worlds in your head, which will remain with you until the day you die. These books are as much a part of you as your guts and your bone. And when your guts fail and your bones break, Narnia, or Jamaica Inn, or Gormenghast will still be there; as pin-sharp and bright as the day you first imagined them -- hiding under the bedclothes, sitting on the bus. Exhausted, on a rainy day, weeping over the death of someone you never met, and who was nothing more than words until you transformed them with your time, and your love, and the imagination you constantly dismiss as "just being a bit of a bookworm. ~ Caitlin Moran

The difference between the girls today and models of the past is that we are not only interested in fashion: we are going in so many different directions at once. We work harder
at night and on weekends. On the modeling profession ~ Claudia Schiffer

Gauss replied, when asked how soon he expected to reach certain mathematical conclusions, that he had them long ago, all he was worrying about was how to reach them! ~ Rene Dubos

I've heard a number of our alumni - people who are running schools and school systems - think a lot about different models for the teaching profession. ~ Wendy Kopp

I don't want to be a supermodel; I want to be a role model. ~ Queen Latifah

The only thing white people have that black people need, or should want, is power - and no one holds power forever. White people cannot, in the generality, be taken as models of how to live. ~ James Baldwin

Christopher Savage have calculated that in reasonable models, we expect about ten dark-matter particles to interact with the atoms in a typical human body every year. The effects of every individual interaction are pretty negligible, so don't worry about getting a dark matter stomachache. ~ Sean Carroll

I've had over a dozen models come in and pose fro me live for these new Cirque pieces. Cirque is a world-wide phenomenon and they are just incredible athletes. I've been to all the performances and am really fascinated by all of their productions. ~ Richard MacDonald

A lot of photographers like models to be blank canvases - but bland girls don't influence me. I don't like playing with dolls; I like playing with people. ~ Mario Testino

It seems to me there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally suprise me. I do not think of mathemaatics as invented but rather discovered. ~ George Andrews

The modern world is also fascinated by innovation but scornful to tradition. Like the Athenians in Paul's day, many people do nothing but get involved in the latest fads (Acts 17:21). People stand in line to purchase the latest gimmicks, and no sooner do they learn how to use them than the manufacturers declare the models obsolete. Innovation! Progress! ~ Warren W. Wiersbe

Businesses need to proactively create models that make a difference in society and let everyone else use them, talk about them, emulate them - and build on them. ~ Muhtar Kent

Drink,Drugs and shagging models.
The rest I just wasted.'
George Best on where his millions went. ~ George Best

Every new body of discovery is mathematical in form, because there is no other guidance we can have. ~ Charles Darwin

[The works of Archimedes] are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader. ~ Thomas Little Heath

The women who intrigued me [as models] had the most beautiful necks and the most responsive hand movements. At one point, I found El Greco, and that elongated look became my way of seeing. ~ Lillian Bassman

I talked with people starting up in the middle of the recession and employees, and supplies and office space were cheap. As far as companies that are already in existence, many became more creative with how they spent their money. A lot of them stopped wasting money that they didn't know they were wasting after they looked hard at their businesses. Some had to change business models because of the economy. Their market didn't exist or wasn't as big anymore. ~ JJ Ramberg

The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation. ~ Kenneth E. Iverson

Justice to others and to ourselves is the same; that we cannot define our duties by mathematical lines ruled by the square, but must fill with them the great circle traced by the compasses ~ Albert Pike

Human myopia cannot be overcome simply by well-meaning attempts to build [climate] models that purport to peer decades and centuries ahead. Action taken now, in anticipation of supposed long run trends, may concentrate on the wrong issues and make matters worse rather than better. ~ Colin Robinson

The fact that you are even here, alive, on this planet is a mathematical miracle, and you should not spend the time that you have being busy being miserable. ~ Philip DeFranco

The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones. ~ Georg Simmel

Vacuum stands and remains a mathematical space. A cube placed in a vacuum would not displace anything, as it would displace air or water in a space already containing those fluids. ~ Roger Bacon

You really want my honest opinion?" I ask.
Anton gestures for me to go on. "Please, this is why I hired you, devochka."
I detect a little hint of sarcasm, but I go ahead and say, "I hate restaurants like this."
"Why?" He seems genuinely curious to know why.
"Because - because they're expensive."
"What is the problem? I'm paying for everything."
I shake my head. "It's not that - you see," I lower my voice, " this is where famous people eat."
"Famous?" Anton pretends to look around. "Where?"
"I think that's the guy from that prank show. And there's that guy from those vampire movies. And Maya Findlay."
"Yeah? I don't know who they are."
"Really?" I ask dubiously.
"I'm not into the famous people thing too."
"Really."
"Yes."
"Which is why you only date models who want to become actresses." I notice him giving me a look. "Sorry," I say sheepishly. ~ Maria Malonzo

Talent finds its models, methods, and ends in society, exists for exhibition, and goes to the soul only for power to work. Genius is its own end, and draws its means and the style of its architecture from within. ~ Ralph Waldo Emerson

I'm very shy. I know it's weird for a person who models lingerie and swimsuits, but I don't like to be the center of attention! ~ Marisa Miller