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Our Mission

Our primary mission is to increase awareness of serious... oversights in science and mathematics, not only among the scientific and mathematical communities, but also the general public.

These are not the usual moral, social-sociological, political, ecological, philosophical or many other such failings, that science is perennially condemned for, that e.g. the current, ever recurring “science wars” are all about. These... oversights are science — and mathematics — failing scientifically and mathematically.

Still overlooked by scientists and laypeople alike is a fundamental fact: science has a long history of failing at science per se, i.e. failing on its own “turf”, and on its own terms, not just e.g. “epistemologically”. (Epistemological failings are dismissed by most scientists as “that’s just philosophy, not real science”.) And mathematics does not escape this situation, either.

We are all coming to depend more and more on science to provide guidance in an ever more complex world, and we need to know and understand its flaws and failings as well as its strengths and successes. Science and mathematics, despite their reputations, are quite fallible.

Some... oversights seem — at first — to be more historically fascinating (and even more psychologically... alarming) than fundamental to scientific theory per se, such as the fact that Newton’s Laws actually predict that lighter and heavier bodies, a la Galileo, will fall at different rates due to their asymmetric gravitational interactions — except, fascinatingly, at Lagrangian points L4-5. (Even if released separately, they each cause e.g. the Earth to accelerate toward themselves at a different rate — straight from Newton’s Laws — thus yielding a different overall “falling” rate relative to the Earth, unfortunately not practically measurable.)

This theoretical falling rate difference — see Newton’s Great... Oversight for equations, history, commentary — is also observable-verifiable astronomically as the Trojan asteroids, first predicted by Lagrange and later observed by the astronomer, Max Wolf, in 1906. Starting with the non-zero falling rate difference, it takes only algebra and trig — instead of the usual differential equations, and perhaps even perturbation theory — to generate the above contour plot showing the tadpole and horseshoe orbits associated with Trojan points. (Well, Mathcad 2000 helped quite a bit when this and other plots were generated a couple of years ago.)

At first, it is obviously a fascinating question for historians and psychologists:

• How and why did Newton himself miss it?!

but, on second thought:

• How and why did Einstein — and Eddington — miss it, too?!

(The falling rate difference for lighter and heavier bodies has implications for relativity that have never been analyzed and discussed, or even acknowledged, publicly.  It is relevant to relativity which holds — i.e. the theory requires — that lighter and heavier test particles “accelerate” at precisely the same rate.)

And there is another set of fascinating questions for historians and psychologists, based on alarming (bordering on terrifying) facts:

• How and why has every scientist and teacher of physics
  since Newton also missed it, as well?!

• And why do leading scientists get overtly angry if one
  questions Galileo just as Galileo questioned Aristotle
  and Ptolemy?!

Perhaps this falling rate... oversight, and others, when finally appreciated, will begin to knock the foundations out from under relativity. (E.g. there are also oversights in Einstein’s “equivalence principle”, which also underpins relativity.) Will people one day speak of Einstein’s Great... Oversights?!

Some oversights, like the inconsistencies (more than one source) in the currently accepted standard variants of Set Theory (ZF, ZFC, von Neumann, etc.), will cast profound doubt on perhaps 2/3 of modern (early 21st Century) mathematics, much of which will need significantly revised foundations. There exist truly Fundamental... Oversights in Mathematics. For example...

  The Good Shepherd’s Paradox, A New Paradox of Infinity in Set Theory. The reader is invited to try to “reorder” or otherwise get the lone ball and all of the infinity of other balls and “wee small glasses” to pair up strictly 1-ball-to-1-glass... without cheating. NOTE that, for our purposes here, each ball-glass pair is abstractly equivalent to every other pair. There is a transfinite variant of automata theory’s halting problem involved here.

Our mission is to first gain community and public recognition that these... oversights have actually occurred, and that they are very serious, especially for science’s theories, methodologies and especially its psychologies, and then to help give initial impetus and direction to collaboratively studying the various hows, whys, and what to do next(s).

As we submit more and more to science and its use to control our daily lives, it is good to remember that even “modern” science is not only fundamentally fallible, but that it can fail in its foundations for hundreds of years without notice.