Essay Abstract
We present a paradigm where our scientific vocabulary is exclusively mathematical and therefore the limits of mathematics are the limits of our scientific vocabulary.
Author Bio
Syed Raiyan Nuri Reza is an undergraduate student at New York University, Shanghai. Syed Rastin Nuri Reza is a college applicant
Dear Reza
I envy the extremely well written essay.
I also think:
physicists regularly come up with unexpected conjectures, most often using completely illegal tools.
For me it is also:
The absence of mathematics is the absence of clarity.
There may be an absence of semantic clarity in my essay, but I firmly believe in the benefits of mathematical clarity that you can see at the end of my essay.
Regards,
Branko
Dear Branko,
Thank you for your kind words. I'm glad we are in broad agreement.
I look forward to reading your essay at the earliest and will leave a comment accordingly.
Kindest regards,
Reza
Dear Branko,
Thank you for your kind words. I'm glad we are in broad agreement!
We also apologize for the delay in our response; we made the mistake of adding a comment instead of replying to your response.
Kindest regards,
Raiyan and Rastin Reza
Dear Syed Raiyan Nuri Reza,
I enjoyed reading your essay with very deep metaphors. Congratulations! but why didn't you dig into ontology, into the most distant meaning-distinguishable depths, to "grasp" the ontological structure of the "language of Nature", give your own approach to solving the age-old problem of substantiation (justification, "foundations of mathematics"), and therefore knowledge in general? I called this problem the ontological basification of mathematics.... Plato and Galileo gave a good mathematical-ontological hint. Look also critically at my ideas.
kind regards,
Vladimir
Dear Vladmir,
Thank you for your kind comment, and I am delighted you found my metaphors meaningful!
I tried to minimize commentary on the ontology of mathematics in part because a lot of scientists (wrongly in my opinion) find such discourse irrelevant to their day to day practice of science, and to what they view as scientific progress. Their argument hinges on the notion that empirical boundary demarcating the boundary of science and mathematics renders results of formal proofs and theorems of limited relevance.
I wanted to demonstrate even if a scientists chose to remain silent on the ontology of mathematics, mathematical theorems and ideas will still exert profound impact on the natural sciences simply because without mathematics we cannot say anything sophisticated and worthwhile on what we observe, measure, and experiment on.
I look forward to reading your essay, rating it, and leaving a meaningful critique!
Dear Vladimir,
In my comment I dropped an "i" in your name. I am really sorry! It was a typo.
Kind Regards,
Raiyan Reza
Dear Prof Syed Raiyan Nuri Reza,
Very nice thought provoking essay. You nicely said mathematics is developed by humans for a better understanding of Nature. I want to pose a little question the mathematics developed by observation of universe, if some thing is wrong while formulating the problem, will the nature show all the predictions done by mathematics?
Best Regards
=snp
Dear Raiyan Reza and Rastin Reza,
Thank you very much for reading my essay , kind comment and evaluation of my ideas. .. As Hegel said "the owl of Minerva begins its flight only at dusk'. It is obvious that the dusk in the foundations of knowledge has not yet come... Or mathematicians and physicists believe that everything is clear in "fundamental science". But I agree with Carlo Rovelli: Physics Needs Philosophy / Philosophy Needs Physics . And Math, the "language of Nature" as well. Undoubtedly, we must all continue, regardless of why, to "dig" further into ontology. Perhaps you will have a completely different vision of the ontological basis of "fundamental knowledge" and the Universe.
I wish you success in the contest, new research, and all the best!
With kind regards,
Vladimir
Dear Satyavarapu Naga Parameswara Gupta,
Thank you for finding my essay to your liking and for finding time to leave a thoughtful message!
For avoiding any misunderstanding, I want to inform you as I am a lowly undergrad as of now, therefore I am not entitled to the honorific: Prof.
Moving forward, a little clarification on our thesis (produced with my co-author, Rastin Reza). My submission does not delve on the motivation behind the development of mathematics. There are many branches of mathematics that had been developed in the post and are currently undergoing development in the present without any consideration of the physical reality.
Therefore, our essay does not claim mathematics is developed for observation of nature, which is what I understood from you comment:
"You nicely said mathematics is developed by humans for a better understanding of Nature."
However, we entertained the idea that perhaps no observation we make can ascend to the status of science without finding mathematical expression.
Accordingly, if indeed there is an error at the level of formulation of our equations, then further observation of Nature will show divergence between what we formulated and what we predicted.
I, along with my co-author, look forward to reading your essay!
Kind Regards,
Raiyan Reza
Dear Vladimir Rogozhin,
Thanks for your well wishes, and we too wish you well both in this context and with your research work!
As Hegel said "the owl of Minerva begins its flight only at dusk'. It is obvious that the dusk in the foundations of knowledge has not yet come.
Beautifully said, it is true, we do not have answers to foundational questions confronting mathematics and natural sciences, and doing so will usher a dawn to our quest for knowledge.
Best Wishes,
Raiyan Reza and Rastin Reza
Dear Raiyan Reza,
what a beautiful written essay. I sadly must agree with you, that it seems, that the limits of our mathematical language are the limits of our understanding of the universe.
The mystery then of course is why mathematics is so incredibly effective in describing the universe.
Other questions arise on what mathematics actually is and what mathematical concepts actually acquire meaning. Mathematics finally is a tautological web of concepts with no connections to the physical world. (Is that true?) So why should math give any understanding of nature.
Sometime I contemplate the spaces between things. We do not have word for these. Why?
In my essay I imagine the universe as realization of different mathematical structures, that might change in time and in different environments and giving raise to changing laws. Let me know of what you think of these proposals, if you find the time.
Luca
Dear Luca Valeri,
Thanks for your kind feedback and good evaluation of my essay!
Entertaining the paradigm of mathematics as the exclusive language of human advanced cognition (hence language of science), the answer to mathematics' unreasonable effectiveness ( borrowing Wigner's remark) is we only can model what is mathematical, and nothing beyond it.
So any aspect of reality beyond mathematics is beyond our grasp of cognition and conceptualization.
I by no mean propose this as final answer, merely following the conclusion of the tentative and speculative ideas I ( & my co-author) presented in the essay and I suppose this is how our paradigm will address the mystery of mathematics' profound connection to reality.
I intentionally avoided discussion on the ontological status of mathematics in my essay because I wanted to show even if we chose to ignore the problem ( and it is an important problem) of what precisely is the ontic status of mathematical object, the 3 uns of undecidability, uncomputability, and Unpredictability would matter to the scientists.
Finally, I eagerly look forward to reading your work and its contribution to this interesting conversation, and will leave behind a feedback.
Kind Regards,
Raiyan Reza
Dear Syed Raiyan Nuri Reza
Thanks, I appreciate your comment.
Regards,
Branko
Dear Reza. Fantastic work there.rated you accordingly. How does human nature write physics leading to the 3uns?kindly Review my opinion here. https://fqxi.org/community/forum/topic/3525 thanks All the best.
Dear Professor Michael Muteru,
Thanks!
I am looking forward to reading your essay!
Kind Regards,
Raiyan Reza
Dear Syed Raiyan Nuri Reza
Ok I did not call you Prof now, But your essay shows that you are very intelligent, worth to be called a Prof.....
Have a look at my essay please and leave a comment and rate it. Then I want to rate your essay well...
Best wishes
=snp
Hello Syed and Syed!
This was a great essay! I really enjoy your perspective and digging deep into the questions about whether or not math is an artifact of our thinking mind or something that is inherent to nature itself. It's extremely interesting, especially since it could be both! Our minds have evolved from nature, so it's strange to think that, from one point of view, mathematics also evolved from nature.
Strange to think about, right!? You make very good points about how this is a strange phenomenon. I do tend to lean in the direction that math is structured in a way that reflects our perspective, understanding, and view of the world, which is a result of our physiology. But then again, if we were to meet an alien species someday, I think their math would be very similar to ours. Things such as physical symmetries are universal, even if a base-ten counting system (developed to accommodate counting our very own ten digits) is not.
Thank you for the insightful read!
Alyssa
Dear Dr. Alyssa Adams,
Thank you for your kind feedback!
I am in agreements. While in the essay I did not reflect on the ontological status of mathematics, merely that we cannot reason scientifically without the usage of mathematics, I believe that math while deeply linked to our psychology is at the same time independent of it.
Alien species aside, we can also readily use computers to do mathematics, and I think that is a good argument that mathematics indeed is independent of the human mind.
An interesting experiment is to ask complete novices in computer science and mathematics to code some basic arithmetic. For instance, raising a number by an exponent. Many people don't know that any number raised to zero is one, and indeed would be surprised that their correct code automatically gives the right response. If mathematics was purely psychological, then there was no way they could have given a code that produced a counter-intuitive but correct ans. Or at least this is how I would interpret this situation.
Again, thanks for your feedback here!
Best Wishes,
Raiyan Reza
Dear Syed Raiyan Nuri Reza,
Thank you for rating my essay, I am giving my reply to your post there.
I rated you well today, it is the 8 th rating, not to be confused...
Best wishes
=snp
