Mathematical Models Quotes

A theory is just a mathematical model to describe the observations.

What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors.

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.

The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful.

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.

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?

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.

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.

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.

Why does the universe go to all the bother of existing?

The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

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.

Is war an inevitable outcome of competing interests in a complex society? In other words, would war be the same even if human nature were very different? There are mathematical models of large groups working together that lead to conflict on a reliable basis. So there's a whole other view of war that is not psychological at all.

All models are wrong, but some are useful.

The good news is that, at least in economics, I've seen movement away from its overemphasis on mathematical models of purely rational behavior to a more eclectic and commonsense approach: research that is, among other things, more respectful of insights from psychology.

The space that we're looking through is nine-dimensional. If you build a mathematical model, the amount of searching that we've done in 50 years is equivalent to scooping one 8-ounce glass out of the Earth's ocean, looking and seeing if you caught a fish. No, no fish in that glass? Well, I don't think you're going to conclude that there are no fish in the ocean. You just haven't searched very well yet. That's where we are.

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.

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.