It was our use of probability theory as logic that has enabled us to do so easily what was impossible for those who thought of probability as a physical phenomenon associated with "randomness". Quite the opposite; we have thought of probability distributions as carriers of information.
Interpretation
Probability theory provides a logical framework that transforms challenges into manageable concepts, contrasting with viewing it merely as randomness.
In this quote, Edwin Thompson Jaynes emphasizes the power of probability theory when approached as a logical tool rather than merely a description of randomness. This perspective allows for deeper insights and manipulation of probability distributions, which serve as vessels of information rather than just enigmatic occurrences. By viewing probability through the lens of logic, complex problems become solvable, illustrating the importance of conceptual understanding in utilizing mathematical frameworks effectively.
In practice
In a lecture on statistics, one might use this quote to illustrate the importance of understanding probability theory.
There is a great difference between discoveries and inventions. With discoveries, one can always be skeptical, and many surprises can take place. In the case of inventions, surprises can really only occur for people who have not had anything to do with it.
Men became scientific because they expected Law in Nature, and they expected Law in Nature because they believed in a Law Giver.
We carry stores of DNA in our nuclei that may have come in, at one time or another, from the fusion of ancestral cells and the linking of ancestral organisms in symbiosis. Our genomes are catalogues of instructions from all kinds of sources in nature, filed for all kinds of contingencies.
A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.
The Secretary of Hygiene or Physical Culture will be far more important in the cabinet of the President of the United States who holds office in the year 2035 than the Secretary of War.
There is much that science doesn't understand, many mysteries still to be resolved. In a Universe tens of billions of light-years across and some ten or fifteen billion years old, this may be the case forever. We are constantly stumbling on new surprises
Subscribe for the occasional hand-picked quote. No noise.