A Quote by Richard P. Feynman
If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.
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Our minds are specifically adapted to developing certain theories, and we have a science if the theories that are available to our minds happen to be close to true. Well, there is no particular reason to suppose that the intersection of true theories and theories that are accessible to the mind is very large. It may not be very large.
Rigor is always appropriate when investing in markets, whatever the ultimate conclusions may be.
In living literature no person is a competent judge but of works written in his own language. I have expressed my opinion concerning a number of English writers; it is very possible that I may be mistaken, that my admiration and my censure may be equally misplaced, and that my conclusions may appear impertinent and ridiculous on the other side of the Channel.
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.
We think we know what we are doing. We have always thought so. We never seem to acknowledge that we have been wrong in the past, and so might be wrong in the future. Instead, each generation writes off earlier errors as the result of bad thinking by less able minds - and then confidently embarks on fresh errors of its own.
I think we are all slightly down in the dumps after another loss. We may be in the wrong sign... Venus may be in the wrong juxtaposition with somewhere else.
The method of science depends on our attempts to describe the world with simple theories: theories that are complex may become untestable, even if they happen to be true. Science may be described as the art of systematic over-simplification-the art of discerning what we may with advantage omit.
But some of these theories are so bold that they can clash with reality: they are the testable theories of science. And when they clash, then we know that there is a reality; something that can inform us that our ideas are mistaken.
Science progresses not by convincing the adherents of old theories that they are wrong, but by allowing enough time to pass so that a new generation can arise unencumbered by the old errors.
I shall often go wrong through defect of judgment. When right, I shall often be thought wrong by those whose positions will not command a view of the whole ground. I ask your indulgence for my own errors, which will never be intentional, and your support against the errors of others, who may condemn what they would not if seen in all its parts.
There is no rigorous definition of rigor.
In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.
Of course, if 40% of women need oxytocin to progress normally, then something is wrong with the definition of normal.
The circumstances of human society are too complicated to be submitted to the rigor of mathematical calculation.
You can convert the teachers, and you can convert the kids, but if they go home saying they want to be a physicist, and the parents question why they would want to do that, then it makes it very difficult.
What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.
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