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Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that…
Select two boxes or cans of food that weigh 8 ounces and 16 ounces, respectively. Have students hold each as you tell them (or they read) the weights of the containers. Give students a box or can with the weight covered and have them compare the weight of the new package to the weight of the 8- and 16-ounce samples…
The values of science and tha values of democracy are concordant, in many cases indistinguishable. Science confers power on anyone who takes the trouble to learn it. Science thrives on the free exchange of ideas; its values are antithetical to secrecy. Science holds to no special vantage points or privileged…
When we spend time in the wilderness, it can be tempting to focus our awareness on "doing" something: taking pictures; getting a certain amount of physical exercise; traveling from point A to point B; naming all the species of birds we encounter. While nature photography is a lovely craft, and we need to exercise for…
Whereas the man of action binds his life to reason and its concepts so that he will not be swept away and lost, the scientific investigator builds his hut right next to the tower of science so that he will be able to work on it and to find shelter for himself beneath those bulwarks which presently exist.
What the founders of modern science, among them Galileo, had to do, was not to criticize and to combat certain faulty theories, and to correct or to replace them by better ones. They had to do something quite different. They had to destroy one world and to replace it by another. They had to reshape the framework of…
The tendency of modern physics is to resolve the whole material universe into waves, and nothing but waves. These waves are of two kinds: bottled-up waves, which we call matter, and unbottled waves, which we call radiation or light. If annihilation of matter occurs, the process is merely that of unbottling imprisoned…
Perhaps the problem is the seeming need that people have of making black-and-white cutoffs when it comes to certain mysterious phenomena, such as life and consciousness. People seem to want there to be an absolute threshold between the living and the nonliving, and between the thinking and the “merely mechanical,”…
However, all scientific statements and laws have one characteristic in common: they are “true or false” (adequate or inadequate). Roughly speaking, our reaction to them is “yes” or “no.” The scientific way of thinking has a further characteristic. The concepts which it uses to build up its coherent systems are not…
[The chemical bond] First, it is related to the disposition of two electrons (remember, no one has ever seen an electron!): next, these electrons have their spins pointing in opposite directions (remember, no one can ever measure the spin of a particular electron!): then, the spatial distribution of these electrons is…
The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience…
I do not think that truth becomes more primitive if we pursue it to simpler facts. For no fact in the world is instant, infinitesimal and ultimate, a single mark. There are, I hold, no atomic facts. In the language of science, every fact is a field—a crisscross of implications, those that lead to it and those that…
There have always been two ways of looking for truth. One is to find concepts which are beyond challenge, because they are held by faith or by authority or the conviction that they are self-evident. This is the mystic submission to truth which the East has chosen, and which dominated the axiomatic thought of the…
Another key factor in assessing the trustworthiness of a document is the reliability or otherwise of the claims expressed within it; metadata about provenance will no doubt help in such judgements but need not necessarily resolve them. Representing confidence in reliability has always been difficult in epistemic…