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So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality.
To a person who is studying algebra, it is often more useful to solve the same problem with three or four different methods, than to solve three or four different problems. By solving problems by different methods, one can by the comparison clarify which of them is shorter and more effective.
The subject of probability is over two hundred years old and for the whole period of its existence there has been dispute about its meaning.
A thousand probabilities do not make one truth.
Probability does not exist.
I see and approve better things, but follow worse.
In a traditional probabilistic analysis, the statistical parameters of uncertain quantities initial geometric imperfections or elastic moduli are presumed to be known, which must be inferred from on-site measurements. Because the available data of such measurements are often limited to permit the probabilistic analysis, a new discipline, called convex modeling of uncertainty, is applied to obtain estimates of the upper and lower bounds of the buckling loads. From a structural safety point of view, the least favorable lower buckling load should be used in design. Critical comparison of the probabilistic and convex analyses is performed.
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