I claim that mankind gets increasingly responsible for itself, mainly due to accelerating predominantly quantitative growth in science and technology. Accordingly, some very foundations of science deserve an unbiased courageous scrutiny. The very basics of mathematics cannot be correct and wrong at a time: TND! Cantor’s transfinity proveduseless. Will the process of science including necessary corrections come close to a standstill when our basic quarrels are finished? No. I intend to show why consequent dealing with not yet sufficiently resolved fundamental questions in science and society is more than just an option. It is a must. Let me critically discuss recent efforts of mine and my proposals to abandon futile illusions.
No Standstill in Fundamental Science
6 days later
Eckard Blumschein
You write:
<<Last but not least, one should already ask: Why have so many students to learn Cantor’s obviously useless set theory? It claims to be counterintuitive, while itactually arose itself from naïve intuition.>>
Do you agree with the conclusions of Alexander Zenkin, Doctor of Physical and Mathematical Sciences, in the article "SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS":
"the truth should be drawn..."
[http://www.ccas.ru/alexzen/papers/ng-02/contr_rev.htm]
Do you agree with the conclusions of the doctor of philosophical sciences, mathematician D. Bukin in the article "CRISIS OF THE FOUNDATIONS OF MATHEMATICS AS A CRISIS OF ONTOLOGY":
"The crisis of the foundations of mathematics is, first of all, the crisis of ontology, the essence of which is the inability to describe objects, the fact of being or becoming of which goes beyond the usual ideas about the world. Way out such a crisis state should be sought not so much in the improvement of the methods of mathematics itself, but in the renewal of the cognitive means of ontology, which do not deny the classical paradigm, but can go beyond its framework. is a historically proven method of comprehending the existence of a mathematical object in its development and relationship with objective reality."
[http://www.unn.ru/pages/e-library/vestnik_soc/99990201_West_soc_2011_4(24)/15.pdf]
Have you personally dealt with the "problem of the millennium No. 1" - the ontological justification/ substantiation of mathematics (ontological basification), and hence knowledge in general?
Do you agree with the philosophical testament of the Fields Prize winner mathematician V. Voevodsky((1966-2017):
<< What we now call the crisis of Russian science is not only a crisis of Russian science. There is a crisis of world science. Real progress will consist in a very serious fight between science and religion, which will end in their association."
[http://baaltii1.livejournal.com/198675.html]
6 days later
Although I had just five days for writing my essay "No standstill ... ", I included
Dear Vladimir Rogozhin,
Although I had just five days for writing my essay "No standstill ... " I included in it
- rejection of Weierstrass-based set theory which is not even worth a revolution but it obviously proved useless
- recommendation of Dedekind cut instead, as the only option to perform a symmetrical cut e.g. "at" zero.
- the late Einstein's cluelessness who already when he had agreed to disagree with Ritz 1907 denied the strict border between past and future
- my agreement with Alan Kadin on that Einstein was certainly correct when he criticized Copenhagen interpretation.
"We have to condemn without exception all celebrations of heroic military victories"
Agree 100%
Math is a tool. The tool may become useless.
Purple Yak asked for a better reference to Ritz:
Ritz criticized Einstein in Phys. Zeitschrift 9 (1908). In Phys. Z. 10(1909) he and Einstein agreed to disagree. Those who cannot read the original “Agreement to Disagree” in German might read a translation to be found a paper in English:
Robert S. Fritzius: The Ritz-Einstein Agreement to Disagree. In: Physics Essays. Band 3, Nr. 4, 1. Dezember 1990, ISSN 0836-1398, S. 371–374, doi:10.4006/1.3033451
Ritz claimed that …by mathematically reversing the direction of time, i.e., by switching to the
advanced potential, you actually invoke a different kind of physical process and
do not simply arrive at the equivalent of the retarded potential acting in reverse
time sequence. The same argument, in quantum mechanical notation, has been
recently revoiced …
Incidentally, I will defend my clear distinction between past ans future against Purple Yak (and Einstein) elsewhere.
8 days later
Dear GambogeSheep
I found what you said about time interesting. If I have it right, the standard way of thinking about time comes from the theory of Special Relativity. Einstein's explanation of the equations of Special Relativity requires different observers to have different experiences of which events are simultaneous, and the logical outcome is that events cannot then be labelled as being in the past or in the future, i.e., an event cannot, in itself, be in the past or in the future, and that label can only be given to it by a particular observer. Practically this works perfectly, which is why it has been generally accepted, even though it is a rather weird idea. However, as I discuss in my essay, if Nature actually were to consist of fundamental parts that all travel at the same speed, then the equations of special relativity would result (you will need to take my word for this as the explanation is far too long to write down here!). This approach then allows all observers to have the same experience of simultaneous events, and so agrees with our own personal experience that there is a definite past and a definite future. It also doesn't have the weirdness of Einstein's explanation. So, by invoking Occam's razor (that the simpler of the two explanations is probably the correct one), I have to agree with you that, most likely, there is a definite past and a definite future, and that Einstein, although he was definitely right about the equations, was probably wrong about the physics underlying those equations.
Dear Azure Flyingfish,
interesting points you make here! In another discussion with PurpleYak, similar things came up on the role of time. Yet, I still wonder why so many people only focus on the role of time in Special Relativity when it is actually General Relativity and the fact that not only kinematics but also mass densities have an impact on our perception and description of what we call "time" that makes things much more complicated. Does your theory also make a statement about the role of time in GR? Another question that just comes to my mind: even if different observers have different impressions about what happens when, each one of them still has their own definite past and definite future and it is possible to synchronise their perceptions in terms of a transformation into each other's frame of reference (taking into account the motions & masses). So do we really need a global past and future or can we settle for individual (local) ones?
Bests,
Beige Bandicoot.
I would agree that popular science, like too much in our media world, too often goes for spectacle and attention-grabbing to get notice or views. Going for fundamentals not transfinite numbers, ready for basic issues. In my "global externalities" essay, I note that agendas of powerful corporate forces are using science to pursue their own profit rather than the pursuit of scientific substance, pure science. Then too, scientists get tracked in old ideas, many influenced by the commercial world's concept of the new, like new particles to explain expansion of the universe or excess mass. The competitive, the power-seeking sets scientists on their own discoveries rather than community science for human discovery, as you point out. As you mention, models are closed constructs, not to be abandoned for new ideas. Too often, funding goes to the established over the new. Time grows short in our competition so on to rating. The new anonymous system is showing sparseness in rating.
a month later
I have to apologize to Vladimir Rogozin for not explaining in what I disagree with Alexander Zenkin. He argues that set theory is too abstract. I see it the other way round: Almost everybody is tempted to not just count items but also ignore that already those aristocratic ancient mathematicians who dealt with plane geometry used abstract notions like the point that has no parts, the continuous line every part of which has parts, and the somehow commensurable with the unity one unique and exact number.
Well, Leibniz's relative definition of infinity proved successful as a pragmatic discretization. However, it misled Weierstrass, Cantor and Hilbert to "intuitively" identify any number with a concrete measure. This was a loss of Euclid's abstraction.
By the way, I vote also for the distinction between the bound to reality in principle measurable but not at all changeable concrete elapsed time and the shiftable abstract notion time that includes future too.
Don't get me wrong. Having not forgotten valuable words of the old Kaganov (vnedritje!) in MEI, I highly estimate Russian science. Thank you for the other hints too.
5 days later
- Edited
interesting, Eckard Blumschein
if you can explain all the content to a deaf person, i subscribe to your ideas
if you complain that there is to much being taught why not improve your teaching method such that the the information content transmitted is increased (for various qualities)
Lazy tools for visual and acoustic communication, advertizing videos and AI will
worsen the situation for students and their teacher.
yes i agree that the tools, might promote unidirectional passive listening monologues
the key is dialogue , however, how ? because this is getting in to hybridization of language, chimerisation/ (cyborgification)
with (tech) tools ,
maybe what is lacking is clear schemes (with) clear goals)for developing of the new languages
goals can span various time length- short term or medium medium a little more, and extremely far in to the future goals
i believe humans should evolve in to new species that communicate high volume of information via various modes
in societies that look completely different from today's world
No Standstill in Fundamental Science
this is in an aggravating, negative, tone , this might help teach good balance
i think there is a lot of room to find new interesting things in what you called fundamental science with a couple of examples (cantor, bourbaki) ,personally if have the right conditions i would research, explore this field
for example
This fundamental dilemma in mathematics can only be avoided when any ideal
point in the line IR is no longer understood as it usually was. i.e., like a pixel that
has shrunk to infinitely small size.
defining a point to be something
that is +zoomed it five time -enlarged three times+ zoomed again two times (a little to the left)- enlarged four times (slightly above right) and than finally + zoomed it one more time time might lead to interesting geometries with new applicable properties .
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presumably people in the last decades have been thought more or less the same ( same defining terminology, exercises etc) trying to raise consistency educational constructions with less intuitive principles it is now desired in my opinion, this things/ axiom seems absurd , does not make sense - but lets try harder to see where does it leads if it can be made in to something.to set up the goal of playing with structures for the sake of it
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My voting against standstill in FUNDAMENTAL SCIENCE intends to make aware that the community is obliged to orient itself on reality and partially ignored compelling reasoning.
Let’s at least question lazy fruitless hypes as was for example Cantor’s Transfinitum.
Responsibility lets little room for more and more languages, merely improved methods of passive learning, promotion of putatively interesting intuitive visions, idolizations, and philosophical blur
The way to unify quantum mechanics with calssical physics is Bohr principle of correspondance. There is a problem in qunatum mechanics in itself: in a side according to Palnck theory an oscillator exhange energy as a multiple integer of a fundamental energy and in its fundamental state the oscillator have zero energy but in the other side according to Schrodinger theory the energy of the oscillator in its fundamental state is not equal to zero so the problem to resolve. This problem can be only resolved by Bohr principle of correspondance which is considered as a quantum principle applicable in low levels and high levels which also conduct us to predict vacuum energy according to quantum theory.
- Edited
Khaki Leon,
Asking myself why did you mention to me desperate efforts related to dark matter, I admit, I too was desperately looking for the solution of a contradiction. The late Einstein confessed that the now worries him seriously (from the pre-mathematical Parmesidean point of view).
In particular, Galileo, Dedekind, Terhardt, Popper, and Shannon uttered ignored arguments with which I agree: The future is open. Hilbert was persuading to me when he confirmed the TND. To me it did not matter much that Cantor got insane and the lives of Minkowski, Hausdorff, Goedel and Depenbrook were sadly also affected. I understood from Fraenkel’s 1923 book Cantor’s mistake. Mathematics is obviously in so far an empirical science as Cantor’s transfinite notion of numbers is responsible for not really deniable paradoxes and more importantly it eventually proved useless up to now.
This is not an aggravating negative tone but a definitely painful insight, a step of correction in most fundamental science.