On 4/13/2013 5:10 AM, WM wrote: > By the > way, Oberth's ideas at his times have been considered as ridiculous as > mine few years ago.
What is ridiculous are not your ideas.
What is ridiculous is your desire to treat the issues of mathematical investigation in terms of "right" and "wrong".
Your ideas with respect to treating counting as concatenations of symbols are to be found in the Russian school of constructive mathematics.
Prattling on about how ideas you do not like should be abolished is distasteful, at best. Making claims that sound mathematical, but are not, is unprofessional. Pretending that these claims are grounded in the physical universe as described by empirical evidence is bad philosophy.
That is what is ridiculous.
The issues of transfinite arithmetic do have bearing on the mathematics used by physicists. It may well be that some confluence of empirical data and set-theoretic models actually decide a question in the future. But unless untestable theories such as string theory or loop quantum gravity are considered and unless forcing models on countable transitive models of set theory examine different modal possibilities, that confluence will never be recognized.
It is clear that certain physical investigations do not require any mathematics or physics beyond the late nineteenth century. This is the same mathematics and physics whose probabilistic models depend on a classical probability theory based on measure theory that uses the axiom of choice. Your views of what is required from mathematics fall into this pre-axiomatic era.
The problems arose as all the mathematics used to coordinate all of the empirical data became the justification for the truth of the philosophies developing in that industrial age. Everyone thought the mathematics would simply justify the beliefs of the new professionals called "scientists".
Mathematics has certainly supported empirical science, and, empirical science has contributed a great deal to mathematics. But, those philosophical debates are precisely what created the information age. You may look to Claude Shannon for the details of bits and bytes. He was employed by a commercial enterprise whose unit of measurement had been the almighty dollar. But, the theory of algorithms derives from those philosophical debates.
Undoubtedly, as the discipline of mathematics is practiced primarily in computational environments, the significance of classical mathematics with its classical logic will be less prominent. The "newspeak" of this culture is already felt with phrases like "common era" to obscure the system of calendar dates based on the influence of Christianity in Western culture. One is now hearing how it is too expensive to change the clocks on computing systems to keep synchronized with astronomical calculations. I can see a day when people speak of "nominal time" disconnected from "GPS time" or "satellite time" just because "counting with crayon marks" is the "right way".
Anyway, your narrow views are just your beliefs.
What is ridiculous is that you insist that everyone should abide by your views. What is not ridiculous is that you probably feel that the current situation in the mathematical community is imposing that exact situation on you. You are fortunate that this is probably the worst injustice "the system" commits against you.