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God is Power— Infinite, Irresistible, Inexorable, Indifferent. All that you touch You Change. All that you Change Changes you. The only lasting truth Is Change. God Is Change. As wind, As water, As fire, As life, God Is both creative and destructive, Demanding and yielding, Scultpor and clay. God is Infinite…
We should not retreat to a curriculum advisory committee and ask, “Now where should we fit this topic into the already overloaded curriculum?” Although we cannot discard all the fragmented subjects in our present school system and start from scratch, we can and should ask all teachers to stretch their subjects to meet…
The proof is elegant and the result profound. Still, it is typical mathematics; so, it’s a good example to reflect upon. In doing so, we will begin to see the elements of the mathematical image, the standard conception of what mathematics is. Let’s begin a list of some commonly accepted aspects. By ‘commonly accepted’…
An analysis of the paradoxes to be avoided shows that they all result from a kind of vicious circle. The vicious circles in question arise from supposing that a collection of objects may contain members which can only be defined by means of the collection as a whole. Thus, for example, the collection of propositions…
This simple equation, which states that the quantity 0.999, followed by an infinite string of nines, is equivalent to one, is the favorite of mathematician Steven Strogatz of Cornell University. "I love how simple it is — everyone understands what it says — yet how provocative it is," Strogatz said. "Many people don't…
Gradually, at various points in our childhoods, we discover different forms of conviction. There’s the rock-hard certainty of personal experience (“I put my finger in the fire and it hurt,”), which is probably the earliest kind we learn. Then there’s the logically convincing, which we probably come to first through…
On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done…
A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have…
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 surprises. Yet some New Age and religious writers assert that scientists…