Quotes & Sayings About Mathematical Models

The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke. — John Allen Paulos

From a mathematical point of view, however, trust is hard to quantify. That's a challenge for people building models. Sadly, it's far easier to keep counting arrests, to build models that assume we're birds of a feather and treat us as such. Innocent people surrounded by criminals get treated badly, and criminals surrounded by law-abiding public get a pass. And because of the strong correlation between poverty and reported crime, the poor continue to get caught up in the digital dragnets. The rest of us barely have to think about them. — Cathy O'Neil

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

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

It is clear that the building of models is not a purely mechanical process but requires skill of a high order - not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies. — Kenneth E. Boulding

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

For far too long economists have sought to define themselves in terms of their supposedly scientific methods. In fact, those methods rely on an immoderate use of mathematical models, which are frequently no more than an excuse for occupying the terrain and masking the vacuity of the content. — Thomas Piketty

All sorts of risk-benefit analyses and models of herd immunity tend to produce the conclusion that vaccination benefits the individual as well as the public. When Harvard researchers recently used game theory to build a mathematical model of vaccination behavior during an influenza epidemic, they found that even "a population of self-interested people can defeat an epidemic." No altruism is required. — Eula Biss

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

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

An essential pedagogic step here is to relegate the teaching of mathematical methods in economics to mathematics departments. Any mathematical training in economics, if it occurs at all, should come after students have at the very least completed course work in basic calculus, algebra and differential equations (the last being one about which most economists are woefully ignorant). This simultaneously explains why neoclassical economists obsess too much about proofs and why non-neoclassical economists, like those in the Circuit School, experience such difficulties in translating excellent verbal ideas about credit creation into coherent dynamic models of a monetary production economy. — Steve Keen

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

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

Nothing has done more to render modern economic theory a sterile and irrelevant exercise in autoeroticism than its practitioners' obsession with mathematical, general-equilibrium models. — Robert Higgs

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

Yes," I continued, "I discovered this model recently and her style never fails to be mathematically perfect. She seems to come by it naturally. As if she were born resonant. I notice Japanese models tend to do this. Like I said, they seem to have resonance somewhere deep in their culture. But Yuri Nakagawa, she's the best I've ever seen. The best model, with the most powerful resonance. I need her to probe deeper
into this profound mathematical instinct, which I call resonance. — Alexei Maxim Russell

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

The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device. — John Kenneth Galbraith

When physicists create a mathematical model of a physical process, they rely on the mathematical framework that can represent that process as closely as possible. When Newton developed a model of forces and motion, the appropriate mathematical framework was calculus. When Einstein developed a model of wave-particle motion, he relied on the mathematics of wave equations and eigenvalues. For many models in scientific computation, the computational framework that best aligns with our need is object orientation. — Anthony Scopatz

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

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

The math-powered applications powering the data economy were based on choices made by fallible human beings. Some of these choices were no doubt made with the best intentions. 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 they tended to punish the poor and the oppressed in our society, while making the rich richer. — Cathy O'Neil

The problem of the origin of the laws of physics is an acute one for physicists. Einstein's suggestion that they may turn out necessarily to possess the form that they do has little support. It is sometimes said that a truly unified theory of physics might be so tightly constrained logically that its mathematical formulation is unique. But this claim is readily refuted. It is easy to construct artificial universe models, albeit impoverished ones bearing only a superficial resemblance to the real thing, which are nevertheless mathematically and logically self-consistent. — Paul Davies

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

Modern economics is a set of formal models and equations purporting to fully determine human behaviour, at least in the economic realm. And there is no way that uncertainty can be compressed into determinate mathematical models. — Murray Rothbard

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