Science topics: Mathematics
Science topic
Mathematics - Science topic
Mathematics, Pure and Applied Math
Questions related to Mathematics
Is the core idea of the article "On the Relativity of the Speed of Light" really difficult to understand?
When writing this paper, I followed the unspoken rule that they should tactfully question the wrong theories of celebrities, so the real point of view is relatively hidden. After so many years, some scientists still do not correctly understand the core idea of this article:
"The Lorentz transformation is not wrong, but it was completely misinterpreted by Einstein, who lacked basic mathematical knowledge and basic logical knowledge. See the paper: https://www.researchgate.net/publication/356285369_On_the_Relativity_of_the_Speed_of_Light. If Einstein's explanation is valid, then there must be a complete space-time transformation that Einstein should have thought of but ignored. Such a deduction of complete space-time transformation in the sense of relativity denies the invariance of the relative speed of light, which is the focus of relativity. Some people angrily say that Einstein is actually very ignorant, which may be true. The root cause of the world's carnival in the theory of relativity lies in the simple charm of ignorant imagination. The so-called exact solution of the Dirac equation that the textbook promotes the success of the important application of relativity in quantum mechanics is also completely wrong! The correct exact solution has been given in part, see Mathematics & Nature 3 (https://mathnature.github.io/, 2022). It is absurd, then, that a false conclusion should be claimed to have been extensively tested experimentally.”
I recently published a paper proposing a rigorous proof of the Riemann Hypothesis by integrating noncommutative spectral geometry and topological field theory.(doi.org/10.13140/RG.2.2.29395.90405) The idea revolves around constructing a noncommutative spectral manifold, where the zeros of the Riemann zeta function are encoded in the spectrum of a Dirac-like operator. By analyzing the stability of gauge field configurations using Yang-Mills action and studying quantum adiabatic dynamics, I demonstrate that the Berry phase is quantized only when the zeros lie on the critical line.
This method not only offers a potential resolution to the Riemann Hypothesis, but it also bridges the fields of analytic number theory, quantum mechanics, and noncommutative geometry. I would love to hear thoughts and insights from fellow researchers regarding the use of topological field theory in this context and whether this approach could offer a new perspective on other major open problems in mathematics and physics.
Synergy has to do with obtaining a total greater than the sum of its parts, but this seems not to be a logical thing if we think just in terms a real numbers in which 1+1 = 2.
In fact in my book
Physics and the Principle of Synergy
today available in researchGate:
and published in Amazon in 1999, there is a proposal how the Principle of Synergy can be applied not only to the physical, but to other areas of human thought, and how based on the most beautiful equation of mathematics, I mean Euler’s relation, it is possible to obtain a sum greater that the sum of its part, so that mathematically Synergy can be represented.
A whole greater than the sum of its parts is a concept that has been considered metaphysical, but that most prolific mathematician of all times, in his work with infinite series in 1745, found that relationship that was described as the most beautiful relationship in mathematics in a 1998 competition held by Intelligencer, called Euler's relation. This relationship in fact includes all numbers: one, zero, the equals sign, but also the square root of minus one, as well as infinity, of course, since it is an infinite series. It is this concept the one then that permits to describe mathematical the concept of Synergy and that has permitted to deduce all fundamental equation of physics in a unified framework of reference:
* that of the pendulum a real harmonic oscillator
* that of the gravitational field including that of the planet mercury obtained by Einstein, but in this case obtained with a mathematical tool not so much complicated as was done with Tensor Analysis
* those of SR in another approach, in which linear moving is just a special case of the more general solution obtained with the BSU concept in which covariance is included as it is a consequence of the isomorphic property of Euler’s relation mentioned above and finally the
* Schrödinger’s wave equation
and most probably it will serve even for that new field of physics called Quantum Field Theory, as in fact it is a real harmonic oscillator, that vector in the complex plane, that remains invariant in spite of change, as Euler’s relation remains the same with those mathematical operations that represent change: integration and derivation.
Edgar Paternina
retired electrical engineer
I published an presentation "Three-Body Problem", where new equations for the interaction of celestial bodies and a solution method are proposed.
If you look on the Internet, it seems that everyone is enthusiastically looking for a solution to the three-body problem. And then someone exclaimed: "I found it!". "And around the silence, taken as a basis," - as Vaenga sings by russian. It turns out that those who are passionately searching, the process of searching is important. It cannot be stopped. You must constantly experience the drama of chaos in the Universe and be proud of your belonging to those physicists who tirelessly prove that there is no other World, because it follows from mathematical solution.
Yes, the World is mathematically substantiated, mathematics is a project, a tool and material for creating the World. But mathematics can be just a game for the mind. You need to find the mathematics that describes the project of the Universe. Mathematics that proves that there is no Building cannot be a project of the Universe.
It turns out that many seekers like mathematical games. I appeal to seekers of truth.
Solomon Khmelnik
February 15, 2025
Consider the question: What if this philosophical construct (presented within an image, attached below) were plotted on a three-dimensional mathematical graph? Only then would the scientific facts behind it be fully justified.
Take, for example, the Penrose Triangle—an "impossible" figure first conceptualized 62by Swedish artist Oscar Reutersvärd in 1934 and later rediscovered in the 1950s by physicist Roger Penrose. Described as "impossibility in its purest form," this figure was popularized by Penrose and further explored in the works of M.C. Escher. It appears to be a solid structure composed of three straight sections of square beams, seamlessly joined at right angles.
However, its paradoxical nature cannot be conclusively analyzed through mere physical observation and philosophical interpretation. Instead, by mathematically plotting the enclosed three-dimensional image onto a precise three-dimensional graph, its inherent absurdity becomes evident. The deceptive illusion, which seems structurally feasible in a two-dimensional representation, is mathematically exposed as an impossible configuration in three-dimensional space.
Image
Abstraction vs. Reality
Addressing the statement: "Abstract mathematics is based on logical principles rather than empirical validity. It does not rely solely on physical evidence."
When we add one apple to another, we perceive two apples. However, the concept of "two" itself is an abstract mathematical construct rather than a directly observable physical entity. The sum exists as a logical principle within mathematics, not as a tangible proof in itself.
All real numbers—1, 2, 3, and beyond—are fundamentally conceptual, created within the framework of mathematical reasoning rather than derived from physical evidence. While mathematical concepts often align with physical reality, their foundation is purely abstract, shaped by human perception and logical consistency rather than empirical observation.
Mathematics is not confined to the physical universe; its abstract principles hold universally, independent of space, time, or physical existence. It is the fundamental language of the cosmos—objective, unique, and uninfluenced by human divisions such as culture, religion, or race.
Physicists seek mathematical formulations to explain the origins, structure, and dynamics of the universe. In doing so, they attempt to decipher the underlying mathematical order that governs both the observable universe and any potential realities beyond it. Understanding the universe is, in essence, understanding its mathematical nature.
For philosophy to be scientifically meaningful, it must be grounded in abstract mathematical logic. Without mathematical rigor, philosophical reasoning remains speculative and cannot be accepted as a scientific discipline.
Conclusion
This distinction underscores a fundamental contrast between philosophy and science: while philosophy interprets illusions conceptually, science—through mathematical rigor—reveals their underlying reality.
Attachment: the image as stated in the above mentioned text.
Chaos Theory, Chaotic dynamics
Recent HSC mathematics results in Mauritius indicate a concerning trend: a 5.52% decline in student performance within a year. The overall pass rate dropped from 91.8% in 2022 to 82.9% in 2024, with fewer students achieving top grades. This trend raises critical questions about the effectiveness of teaching methodologies, student engagement, and systemic issues in mathematics education.
This discussion seeks to explore key challenges contributing to this decline, including:
- Mathematics Anxiety – How do fear and stress impact learning?
- Lack of Individualized Support – Are students receiving the guidance they need?
- Peer Pressure & Learning Culture – Is excelling in mathematics socially discouraged?
- Overemphasis on Memorization – Are students understanding concepts or simply learning formulas for exams?
- The Role of Technology – Could AI, digital tools, and interactive platforms bridge the learning gap?
Given the increasing importance of STEM careers, AI, and data-driven industries, how should mathematics education evolve?
Key Discussion Points:
🔹 What strategies have been most effective in improving mathematics achievement at different educational levels?
🔹 How can technology be integrated to make learning more engaging and effective?
🔹 Should curricula prioritize real-world applications of mathematics rather than abstract problem-solving?
🔹 What pedagogical innovations (e.g., flipped classrooms, gamification, inquiry-based learning) have worked in other contexts?
I welcome insights from educators, researchers, and policymakers on addressing these issues and improving student outcomes in mathematics.
It is the theory of probability, where probability and mathematical statistics are used to analyze data and draw conclusions. Mathematical tools in statistics include statistical analysis, hypothesis testing, probability distributions, etc. These tools are used to analyze samples and predict the likely behavior of societies and statistical events in general.
Does Every Mathematical Framework Correspond to a Physical Reality? The Limits of Mathematical Pluralism in Physics
Introduction
Physics has long been intertwined with mathematics as its primary tool for modeling nature. However, a fundamental question arises:
- Does every possible mathematical framework correspond to a physical reality, or is our universe governed by only a limited set of mathematical structures?
This question challenges the assumption that any mathematical construct must necessarily describe a real physical system. If we take a purely mathematical perspective, an infinite number of logically consistent mathematical structures can be conceived. Yet, why does our physical reality seem to adhere to only a few specific mathematical frameworks, such as differential geometry, group theory, and linear algebra?
Important Questions for Discussion
v Mathematical Pluralism vs. Physical Reality:
- Are all mathematically consistent systems realizable in some physical sense, or is there a deeper reason why certain mathematical structures dominate physical theories?
- Could there exist universes governed by entirely different mathematical rules that we cannot even conceive of within our current formalism?
v Physics as a Computationally Limited System:
- Is our universe constrained by a specific subset of mathematical frameworks due to inherent physical principles, or is this a reflection of our cognitive limitations in developing theories?
- Why do our fundamental laws of physics rely so heavily on certain mathematical structures while neglecting others?
v The Relationship Between Mathematics and Nature:
- Is mathematics an inherent property of nature, or is it merely a tool that we impose on the physical world?
- If every mathematical structure has an equivalent physical reality, should we expect an infinite multiverse where every possible mathematical law is realized somewhere?
v Beyond Mathematical Formalism:
- Could there be fundamental aspects of physics that are not fully describable within any mathematical framework?
- Does the reliance on mathematical models lead us to mistakenly attribute physical existence to purely abstract mathematical entities?
Philosophical Implications
This discussion also touches on a deeper philosophical question:
Are we merely discovering the mathematical laws of an objectively real universe, or are we creating a mathematical framework that fits within the constraints of our own perception and cognition?
If mathematics is merely a tool, then our physical theories may be contingent on human cognition and not necessarily reflective of a deeper objective reality. Conversely, if mathematics is truly the "language of nature," then understanding its full structure might reveal hidden aspects of the universe yet to be discovered.
Werner Heisenberg once suggested that physics will never lead us to an objective physical reality, but rather to models that describe relationships between observable quantities. Should we accept that physics is not about describing a fundamental "truth," but rather about constructing the most effective predictive models?
Introduction: Conceptual Remnants and the Challenge of Physical Objectivity
Physics has long been regarded as the science dedicated to uncovering the fundamental laws governing nature. However, in contemporary theoretical physics, there is an increasing reliance on mathematical models as the primary tool for understanding reality. This raises fundamental questions:
- Is physics still unknowingly entangled in issues arising from emergent effects?
- Could these emergent effects create a gap between physical reality and the virtual constructs generated through mathematical modeling?
Throughout the history of science, there have been instances where physicists, without fully grasping fundamental principles, formulated models that later turned out to be mere consequences of emergent effects rather than reflections of objective reality. For instance, in classical thermodynamics, macroscopic quantities such as temperature and pressure emerged as statistical descriptions of microscopic particle behavior rather than fundamental properties of nature.
The crucial question today is: Are we still facing similar emergent illusions in modern theoretical physics? Could it be that many of the sophisticated mathematical models we use are not pointing to an underlying physical reality but are merely the byproducts of our perception and modeling techniques?
Mathematical Models and Conceptual Remnants: Are We Chasing a Mirage?
Mathematics has always been an essential tool in physics, but over time, it has also shaped the way we think about physical reality. In many areas of theoretical physics, mathematical methods have advanced to a point where we may no longer be discovering physical truths but instead fine-tuning mathematical structures to fit our theoretical frameworks.
- Has theoretical physics become a vast computational engine, focusing on adjusting relationships between mathematical variables rather than seeking an independent physical reality?
- Could it be that many of the concepts emerging from our models are mere reflections of mathematical structures rather than objective entities in nature?
Examples of such concerns can be found in theories like string theory, where extra spatial dimensions and complex symmetry groups are introduced as necessary mathematical elements, despite lacking direct experimental verification. This raises the possibility that some of these theoretical constructs exist only because they are mathematically required to make the model internally consistent, rather than because they correspond to something physically real.
Fundamental Critique: Should We Even Be Searching for Physical Objectivity?
One of the most profound implications of this discussion is that the very question of whether physics describes "physical reality" might be fundamentally misguided.
Werner Heisenberg once argued that physics will never lead us to an understanding of an objective physical reality. Instead, what we develop are models that describe relationships between observable phenomena—without necessarily revealing the true nature of reality itself.
- Perhaps physics should not aim to discover a reality independent of our models since every model is ultimately a mathematical structure shaped by human perception.
- If the goal of physics is not to describe "absolute truth" but rather to create predictive models, should we then accept that we will never fully grasp "what actually exists"?
Finally: Between Computational Accuracy and Physical Reality
The final question in this discussion is: Are we still trapped in emergent effects that arise purely from our mathematical approaches rather than reflecting an objective physical reality?
- Should physicists strive to distinguish between mathematical models and physical objectivity, or is such a distinction inherently meaningless?
- Is the search for an independent physical reality a conceptual mistake, as Heisenberg and others have suggested?
Ultimately, this discussion seeks to examine whether physics is merely a computational framework for describing phenomena, or if we are still subconsciously searching for a physical reality that might forever remain out of reach.
I would need a detailed mathematical derivation of mimetic finite difference operators in cartesian as well as curviliniear, in particular spherical coordinates. I also need to know how the pole problem in spherical coordinates can be tackled when using mimetic operators. Does anybody have a hint for me?
ORCiD: 0000-0003-1871-7803
February 10, 2025
Absolute Collapse Condition
Mass Acquisition at Planck Frequency:
In Extended Classical Mechanics (ECM), any massless entity reaching the Planck frequency (fp) must acquire an effective mass (Mᵉᶠᶠ = hf/c² = 21.77 μg). This acquisition of mass is a direct consequence of ECM's mass induction principle, where increasing energy (via f) leads to mass acquisition.
Gravitational Collapse:
At the Planck scale, the induced gravitational interaction is extreme, forcing the entity into gravitational collapse. This is a direct consequence of the mass acquisition at the Planck frequency, where the gravitational effects become significant.
ECM's Mass-Induction Perspective
Apparent Mass and Effective Mass:
The apparent mass (−Mᵃᵖᵖ) of a massless entity contributes negatively to its effective mass. However, at the Planck threshold, the magnitude of the induced effective mass (|Mᵉᶠᶠ|) surpasses |−Mᵃᵖᵖ|, ensuring that the total mass is positive:
|Mᵉᶠᶠ| > |−Mᵃᵖᵖ|
This irreversible transition confirms that any entity at fp must collapse due to self-gravitation.
Implications for Massless-to-Massive Transition
Behaviour Below Planck Frequency:
Below the Planck frequency, a photon behaves as a massless entity with effective mass determined by its energy-frequency relation. However, at fp, the gravitating mass (Mɢ) and effective mass (Mᵉᶠᶠ) undergo a shift where induced mass dominates over negative apparent mass effects.
Planck-Scale Energy:
Planck-scale energy is not just a massive state—it is a self-gravitating mass that collapses under its own gravitational influence. This suggests that at Planck conditions, the gravitationally induced mass dominates over any negative mass contributions, maintaining a positive mass regime.
Threshold Dominance at the Planck Scale
Gravitational Mass Dominance:
At the Planck scale, gravitational mass (Mɢ) is immense due to the fundamental gravitational interaction. Since |+Mɢ| ≫|−Mᵃᵖᵖ|, the net effective mass remains positive:
Mᵉᶠᶠ = Mɢ = (−Mᵃᵖᵖ) ≈ +Mᵉᶠᶠ
This suggests that at Planck conditions, the gravitationally induced mass dominates over any negative mass contributions.
Transition Scenarios for Negative Effective Mass
Conditions for Negative Effective Mass:
The condition −Mᵃᵖᵖ > Mɢ could, in principle, lead to a transition where the effective mass becomes negative. This might occur under strong antigravitational influences, possibly linked to:
• Dark energy effects in cosmic expansion.
• Exotic negative energy states in high-energy physics.
• Unstable quantum fluctuations near high-energy limits.
Linking Effective Mass to Matter Mass at Planck Scale
Matter Mass Emergence:
Since Mᵉᶠᶠ ≈ Mᴍ, under these extreme conditions, it implies that matter mass emerges predominantly as a consequence of gravitational effects. This aligns with ECM’s perspective that mass is not an intrinsic property but rather a dynamic response to gravitational interactions.
Conclusion
This work on ECM provides a detailed and nuanced understanding of how gravitational interactions can induce mass in initially massless particles, leading to gravitational collapse at the Planck scale. This perspective not only aligns with fundamental principles but also offers potential explanations for cosmic-scale phenomena involving dark matter, dark energy, and exotic gravitational effects. The detailed mathematical foundations and the implications of apparent mass and effective mass in ECM further clarify how mass can dynamically shift between positive, zero, and negative values based on gravitational and antigravitational influences.
The concept of infinity is well known in Mathematics and I have no disagreement with this. But, in real world, something like number of species or number of water molecules or even number of stars, are anything exist that beyond finite?
It is well known that Medal Fields Prize is intended for excellent research of mathematicians under forty years old because many mathematicians think that the main contributions in the life of the researchers are obtained when they are younger than forty. I do not believe so. It is true, by common experience, that the students of Mathematics, which are constantly in interaction at the same time, with several (and sometimes, very different) subjects, develop a high degree of good ideas which inspire them and lead them to obtain new and interesting results. This interaction between different branches is expected to remain (more or less consciently) up to forty years old. By the same reason, if necessary, whoever researcher, independently of his/her age, may return to study the different mathematical matters and create new important contributions, even in his/her very definite area of research. Furthemore, it may help to overcome a blockade. It is incredible the fact that when one studies again different matters it inspires you, and combined with your experience and knowledge, you see the contents of these different subjects with new perspective, often helping in your area of research creating new knowledge and solving problems. This is the motive why I believe that the career of each mathematician is always worthly and continuous independently of his/her age as demonstrated by most senior mathematicians in all the areas of research who are living examples for us.
What is your opinion on the relationship between the age of a researcher and the quality of his/her contributions?
Thank you very much beforehand.
Hi all
I'm an final semester ug btech student. I want to do research in mathematics and publish a paper for the same. Can anyone help me finding out problem statements for the same?
# 163
Dear Sarbast Moslem , Baris Tekin Tezel, Ayse Ovgu Kinay, Francesco Pilla
I read your paper:
A hybrid approach based on magnitude-based fuzzy analytic hierarchy process for estimating sustainable urban transport solutions
My comments:
1- In the abstract you say “The study employs the newly developed Magnitude Based Fuzzy Analytic Hierarchy Process, chosen for its accuracy and computational efficiency compared to existing methods”
Are you aware that Saaty explained that it is incorrect to apply fuzzy in AHP because it is already fuzzy?
Since when using intuition ensures accuracy? Do you have any proof of what you say?
Sensitivity analysis does not ensure quality, what it does us to find how strong is a solution
2- In page 2 you talk about linear regression for evaluation. Linear regression is used to predict the value of a dependent variable on the value of one or more independent variables.
3- In page 3 “AHP offers mechanisms for ensuring consistency in decision-making through pairwise comparisons and sensitivity analyses”
True, AHP ensures consistency by FORCING to adhere to transitivity, by imposing the DM to change his/her estimates.What it ensures, is transitivity without any mathematical foundation,just for the sake of the method. Therefore, this ‘consistency’ is fabricated.
Even if there is a real consistency, it reflects the coherence of the DM, but it does not necessarily mean that consistency and weights can be applied to the real-world. There is no mathematical support for this assumption, neither to assume that the world is consistent, let alone common sense; it is convenient indeed, for the method, but useless for evaluation
4- Page 3 “On the other hand, expressing the data in the form of fuzzy numbers to better express the uncertainty in individual judgments has led to the suggestion and widespread use of fuzzy AHP (FAHP) methods, which include calculations based on fuzzy arithmetic”
5- In several parts of the paper it mentions validation of results. That is only a wish, because no MCDM method has any real yardstick to compare to. It is another and very common fallacy.
6- Pag 8, Fig 4. I understand of that waiting time does not depend on speed but on frequency buses arrival (Number of buses of the same route per hour). The more the frequency the lesser the waiting tine. What role do have the buses speed here? It appears that this concept does not come from transportation experts.
“Reaching to the destination without shifting buses”
I guess that interchanging buses or routes is more adequate
“Need of transfer” normally refers to paying a single ticket, that allows a pax to change bus routes, that is, you he can board another bus with the same ticket
Your definition on “Time availability” does not seen too coherent, because what “Number of times that UBT is deployed??? over a route” mean?
“Limited time of use” (C4.2)????. I understand that you want to say ‘Operating hours’, that is start running and finish running, or simply ‘Scheduling’. I am afraid that your expression does not belong to the urban transportation industry.
Please do not be offended with my observations, it is not my intention. Only that is you want readers understanding what you write, you must use the appropriate words. If not, your work risks to be misunderstood and downgraded
Why “providing new buses” is related to “comfort” in stops?
7- Page 9 “In other words, it models the state of uncertainty in the mind of the decision-maker.”
Very true, but why those uncertainties of a MIND can be translated to real-life? In other words, what theorem or axiomsupports that what the DM estimates can be used in real-world? It is a simple assumption that even defies common sense. In my opinion, it does not make any sense to apply fuzzy to invented values. Yes, one will get a crisp value, and what is it good for? For nothing
These are some of my comments. Hope that they can help you
Nolberto Munier
Mathematics and statistics have been used to develop encryption techniques used to protect against cyber threats and ensure the security of information and data. Mathematics is also used to generate complex passwords and develop machine learning models to detect cyber attacks and threats in networks. In addition, various mathematical concepts such as algebra, geometry, statistics, and numerical analysis are used in specific areas such as security software development, software bug checking, databases, and complex networks.
A control volume is a mathematical construct used in the process of creating mathematical models of physical processes.
We assume that the control volume in R^4 space (3D+t external control) is incomplete and almost useless for dealing with complex physical and mathematical problems.
On the other hand, the 4D x-t unitary control volume called Cairo techniques and B matrix space is the complete universal space adequate for the description of classical and quantum physics situations as well as mathematical events.
In a way, this is the correct approach to the unified field theory (energy density).
My answer is negative and thoroughly substantiated via 2 points.
1) The easiest part (lesser limiting factor) he has to comprehend the approach used in physics thinking and epistemology (i.e. working with hypotheses instead of etiological thinking, refraining from teleological inquiries etc), the importance of relying on maths, relevancy of equations etc. Not easy but can be accomplished to large degree by serious commitment and authentic interest
2) ease with representations (geometrical, model-wise etc) of physical systems and working cognitively on that level, abstract aplicational mathematical thinking (this may not be easy even for mathematicians) etc. This is something that required in my opinion an in-born trait
Need CBSE India 10th board examination data on the mathematics subject.
In the attached paper titled, "Approximate expressions for BER performance in downlink mmWave MU-MIMO hybrid systems with different data detection approaches", mathematical operator ℝ{.} is used with minus sign in Equation (14). Can anybody help explain the meaning of this operator? Why minus sign is used?
Hi dear professors. I want to share with you a little formula of arithmetics in order to know the usefulness of this formula and its meaning according to you. This is the formula like in the attached picture: 1+8*E^2≠3*F^2 where E and F can be any integers.
The proof is easy in the article of this link:
Under the theme “Mathematics for All, Mathematics as a Path to Development,” one of the best examples of math's impact on daily life is its application in medical imaging, such as CT and CBCT scanners.
How do these devices work?
Mathematics is at the heart of it! When X-rays are emitted from a source, they pass through tissues and are captured by detectors. Along their path, these rays undergo absorption or attenuation, which depends on the properties of the tissue they traverse. Each ray's path represents a unique equation, where the unknowns are the attenuation values of the points it passes through.
As the source rotates around the object, it generates multiple paths, creating a system of n equations with n unknowns. Sophisticated software solves this complex system using advanced algorithms, such as the Radon Transform or iterative methods, to reconstruct the internal structure of the object as a detailed 3D image.
How does this contribute to development?
Mathematics is the backbone of such groundbreaking technologies, enabling precise diagnostics and effective treatment planning. This practical application of equations demonstrates how math can transform our world.
Now it’s your turn:
What other applications of mathematics in medicine and engineering do you think are underexplored? How can we further harness the power of math as a tool for development?
Let’s explore the incredible role of mathematics in everyday life together in this discussion!
I want a qualitative scale that contains questions that reveal the mathematics teacher's perception of beauty and simplicity in mathematics?
Conventional fragility is defined as probability of failure. Based on concise mathematics, it is found that if fragility is probability of collapse then the design curve is probability of survive. The sum of these two is equal to 1. Consequently, if a member (structure) is designed based on a give curve, then its fragility of collapse is also known!.
Scale the horizontal axes of a fragility curve (s) of a structure, between 0 and 1. Then:
what is the probability of collapse at s=0.5 ?
what is the probability of survive at s=0.5
Don you agree with the above findings? Why ?
Can the physical reality be represented mathematically?
Well actual physics, can be represented mathematically with the Basic Systemic Unit, based on Euler’s relation with its most remarkable property of remaining the same in spite of change, that permits to deduce the fundamental equations of physics such as :
* that of the pendulum a real harmonic oscillator
* that of the gravitational field including that of the planet mercury obtained by Einstein, but in this case obtained with a mathematical tool no so much complicated as was done with Tensor Analysis
* those of SR in another approach, in which linear moving is just a special case of the more general solution obtained with the BSU concept in which covariance is included as it is a consequence of the isomorphic property of Euler’s relation mentioned above and finally the
* Schrödinger’s wave equation
For those interested in the way all this is obtained you can see my papers:
QUANTUM PHYSICS
https://www.researchgate.net/publication/384190006_Quantum_Physics (https://www.researchgate.net/publication/384190006_Quantum_Physics)
A QUANTUM THEORY OF GRAVITATION
https://www.researchgate.net/publication/385592651_A_Quantum_Theory_of_GravitationNewpdf (https://www.researchgate.net/publication/385592651_A_Quantum_Theory_of_GravitationNewpdf)
SPECIAL RELATIVITY WITH ANOTHER APPROACH
https://www.researchgate.net/publication/382357270_Special_Relativity_Another_Approach (https://www.researchgate.net/publication/382357270_Special_Relativity_Another_Approach)
that I really hope will contribute to overcome the great crisis of physics, because the great incompatibility between QM and GR.
So yes, actual physics, can be represented mathematically in a real coherent way, but for it is necessary to make a real paradigm shift.
Edgar Paternina
retired electrical engineer
Einstein overcomplicated the theory of special and general relativity simply because he did not define time correctly.
A complete universal or physical space is a space where the Cartesian coordinates x, y, z are mutually orthogonal (independent) and time t is orthogonal to x, y, z.
Once found, this space would be able to solve almost all problems of classical and quantum physics as well as most of mathematics without discontinuities [A*].
Note that R^4 mathematical spaces such as Minkowski, Hilbert, Rieman. . . etc are all incomplete.
Schrödinger space may or may not be complete.
Heisenberg matrix space is neither statistical nor complete.
All the above mathematical constructions are not complete spaces in the sense that they do not satisfy the A* condition.
In conclusion, although Einstein pioneered the 4-dimensional unitary x-t space, he missed the correct definition of time.
Universal time t* must be redefined as an inseparable dimensionless integer woven into a 3D geometric space.
Here, universal time t* = Ndt* where N is the dimensionless integer of iterations or the number of steps/jumps dt*.
Finally, it should be clarified that the purpose of this article is not to underestimate Einstein's great achievements in theoretical physics such as the photoelectric effect equation, the Einstein Bose equation, the laser equation, etc. but only to discuss and explain the main aspects and flaws of his theory of relativity, if any.
Computational topology of solitons
The well-established research area of algebraic topology currently goes interdisciplinary with computer science in many directions. The Topological Data Analysis gives new opportunities in visualization for modeling and special mapping. A study on metrics used or simplicial complexes are reliable for future results in the area of mathematics.
Today, the machine learning from one side is a tool for the analysis in topology optimization, topological persistence and optimal homology problems, from other side the topological features in machine learning are new area of research, topological layers in neural networks, topological autoencoders, and topological analysis for the evaluation of generative adversarial networks are in general aspects of topology machine learning.
On practical point of view, the results in this area are important for solitary-like waves research, biomedical Image analysis, neuroscience, physics and many others.
That gives us opportunity to establish and scale up an interdisciplinary team of researchers to apply for funding for fundamental science research in interdisciplinary field.
More Info: https://euraxess.ec.europa.eu/jobs/249043
Updated information of my thoughts and activities.
This is meant to be a one-way blog, albeit you can contribute with your recommendations and comments.
In a project with analysis of log-linear outcomes I have not found the solution to this problem. (log is the natural logaritm)
I assume it is simple, but I am out of clue, and I hope someone more mathematical proficient can help.
Nominations are expected to open in the early part of the year for the Breakthrough Prize in Fundamental Physics. Historically nominations are accepted from early/mid-January to the end of March, for the following year's award.
Historically, the foundation has also had a partnership with ResearchGate:
The foundation also awards major prizes for Life Sciences and for Mathematics, and has further prizes specific to younger researchers.
So who would you nominate?
Differential Propositional Calculus • Overview
❝The most fundamental concept in cybernetics is that of “difference”, either that two things are recognisably different or that one thing has changed with time.❞
— W. Ross Ashby • An Introduction to Cybernetics
Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.
In accord with the strategy of approaching logical systems in stages, first gaining a foothold in propositional logic and advancing on those grounds, we may set our first stepping stones toward differential logic in “differential propositional calculi” — propositional calculi extended by sets of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target universe.
What follows is the outline of a sketch on differential propositional calculus intended as an intuitive introduction to the larger subject of differential logic, which amounts in turn to my best effort so far at dealing with the ancient and persistent problems of treating diversity and mutability in logical terms.
Note. I'll give just the links to the main topic heads below. Please follow the link at the top of the page for the full outline.
Part 1 —
Casual Introduction
Cactus Calculus
Part 2 —
Formal_Development
Elementary Notions
Special Classes of Propositions
Differential Extensions
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2#Differential_Extensions
Appendices —
References —
It is provable that quantum mechanics, quantum field theory, and general relativity violate the the axioms of the mathematics used to create them. This means that neither of these theories has a mechanism for processes that they describe to be feasible in a way that is consistent wth rules used to develop the math on which that are based . Thus, these theories and mathematics cannot both be true. This is proven with a $500 reward for disproving (details in the link). So I can prove that the above mentioned theories are mathematical nonsense, and I produce a theory that makes the same predictions without the logical mistakes. https://theframeworkofeverything.com/
Within a specific problem, without the whole picture?
I am currently working on optimizing our inventory management system and need to calculate the monthly safety stock for various SKUs. I have already generated weekly safety stock values based on historical data and lead times. However, I need to adjust these values for a monthly period considering several factors:
1. SKU Contribution Ratio: This ratio indicates the importance of each SKU. A higher ratio means the SKU is more critical and should have a higher safety stock.
2. CCF Factor: This factor reflects our past ability to fulfill orders based on historical order and invoice data.
3. Monthly Stock Reduction Percentage: This percentage shows how much stock is typically left at the end of each month. If this value is 100% for four consecutive months, it indicates no need to keep that much inventory for the respective SKU. Conversely, if the values are decreasing, it suggests that the safety stock has been used and needs to be adjusted.
Given these factors, I need to determine a safety factor for the month, which will be used to adjust the weekly safety stock values to monthly values.
Could you suggest scientific methodologies or models that can effectively integrate these factors to calculate the monthly safety stock?
please help me to find a theory that supports my study about storytelling in teaching mathematics
Famous mathematicians are failing each day to prove the Riemann's Hypothesis even if Clay Mathematics Institute proposes a prize of One Million Dollars for the proof.
The proof of Riemann's Hypothesis would allow us to understand better the distribution of prime numbers between all numbers and would also allow its official application in Quantics. However, many famous scientists still refuse the use of Riemann's Hypothesis in Quantics as I read in an article of Quanta Magazine.
Why is this Hypothesis so difficult to prove? And is the Zeta extension really useful for Physics and especially for Quantics ? Are Quantics scientists using the wrong mathematical tools when applying Riemann's Hypothesis ? Is Riemann's Hypothesis announcing "the schism" between abstract mathematics and Physics ? Can anyone propose a disproof of Riemann's Hypothesis based on Physics facts?
Here is the link to the article of Natalie Wolchover:
The zeros of the Riemann zeta function can also be caused by the use of rearrangements when trying to find an image by the extension since the Lévy–Steinitz theorem can happen when fixing a and b.
Suppositions or axioms should be made before trying to use the extension depending on the scientific field where it is demanded, and we should be sure if all the possible methods (rearrangements of series terms) can give the same image for a known s=a+ib.
You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.
Differential Logic • 1
Introduction —
Differential logic is the component of logic whose object is the description of variation — focusing on the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition that broad naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component governs the use of a “differential logical calculus”, that is, a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.
Simple examples of differential logical calculi are furnished by “differential propositional calculi”. A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target universe. Such a calculus augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.
Resources —
Logic Syllabus
Survey of Differential Logic
Differential Logic • 18
Tangent and Remainder Maps —
If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition f = pq : X → B in the following way.
The next venn diagram shows the differential proposition df = d(pq) : EX → B we get by extracting the linear approximation to the difference map Df = D(pq) : EX → B at each cell or point of the universe X. What results is the logical analogue of what would ordinarily be called “the differential” of pq but since the adjective “differential” is being attached to just about everything in sight the alternative name “tangent map” is commonly used for df whenever it's necessary to single it out.
Tangent Map d(pq) : EX → B
To be clear about what's being indicated here, it's a visual way of summarizing the following data.
d(pq)
= p ∙ q ∙ (dp , dq)
+ p ∙ (q) ∙ dq
+ (p) ∙ q ∙ dp
+ (p) ∙ (q) ∙ 0
To understand the extended interpretations, that is, the conjunctions of basic and differential features which are being indicated here, it may help to note the following equivalences.
• (dp , dq) = dp ∙ (dq) + (dp) ∙ dq
• dp = dp ∙ dq + dp ∙ (dq)
• dq = dp ∙ dq + (dp) ∙ dq
Capping the analysis of the proposition pq in terms of succeeding orders of linear propositions, the final venn diagram of the series shows the “remainder map” r(pq) : EX → B, which happens to be linear in pairs of variables.
Remainder r(pq) : EX → B
Reading the arrows off the map produces the following data.
r(pq)
= p ∙ q ∙ dp ∙ dq
+ p ∙ (q) ∙ dp ∙ dq
+ (p) ∙ q ∙ dp ∙ dq
+ (p) ∙ (q) ∙ dp ∙ dq
In short, r(pq) is a constant field, having the value dp ∙ dq at each cell.
Resources —
Logic Syllabus
Survey of Differential Logic
Program Description:
A program that converts mathematical equations from PDF files into editable equations within Word documents. The program relies on Optical Character Recognition (OCR) technology for mathematical equations, ensuring accuracy in retrieving symbols and mathematical formulas. It allows users to easily edit the equations directly in Word and provides support for various mathematical writing formats, such as LaTeX or MathType.
Program Features:
Accurate Conversion: Can read complex mathematical equations from PDF files.
Word Integration: Offers direct import options into Word documents.
Mathematical Format Support: Supports multiple formats such as MathML and LaTeX.
User-Friendly Interface: A simple design suitable for researchers and students.
Multi-Platform Compatibility: Works on operating systems like Windows and macOS.
Examples of programs that may meet this description include:
Mathpix Snip
InftyReader
You can try one of them to find the best solution for your need
I have started an investigation about the utilization of AI for teaching mathematics and physics.
In this framework, I would like any insights and previous findings.
Please send me similar studies.
Thanks you in advance
what about generate 3D shape using different ways: GAN or mathematics with python or LLMs or LSTMs and the related works about this !
Dear Esteemed Colleagues,
I hope this message finds you well. I am writing to invite your review and insights on what I believe to be a significant development in our understanding of the Riemann Hypothesis. After extensive work, I have arrived at a novel proof for the hypothesis, using a generalization of the integral test applicable to non-monotone series, as outlined in the attached document.
As a lead AI specialist at Microsoft, specializing in math-based AI, I have employed both traditional mathematical techniques and AI-based verification algorithms to rigorously validate the logical steps and conclusions drawn in this proof. The AI models have thoroughly checked the derivations, ensuring consistency in the logic and approach.
The essence of my proof hinges on an approximation for the zeta function that results in an error-free evaluation of its imaginary part at $x = \frac{1}{2}$, confirming this as the minimal point for both the real and imaginary components. I am confident that this new method is a significant step forward and stands up to scrutiny, but as always, peer review is a cornerstone of mathematical progress.
I warmly invite your feedback, comments, and any questions you may have regarding the methods or conclusions. I fully stand by this work and look forward to a robust, respectful discussion of the implications it carries. My goal is not to offend or overstate the findings but to contribute meaningfully to this ongoing conversation in the mathematical community.
Thank you for your time and consideration. I look forward to your responses and the productive discussions that follow.
Sincerely,
Rajah Iyer
Lead AI Specialist, Microsoft
I was briefly reviewing your proof and noticed something unusual in this part.
I am interested in the study of visual subcompetence in education, specifically how visual tools and technologies can be integrated into the educational process to enhance the development of professional competencies in future teachers, particularly in mathematics education.
I am looking for research and definitions that highlight and specify the concept of visual subcompetence in education. Specifically, I am interested in how visual subcompetence is distinguished as part of the broader professional competence, particularly in the context of mathematics teacher education.
Can you suggest any study that uses Ethnographic Research design?
I apologize to you all! The question was asked incorrectly—my mistake. Now everything is correct:
In a circle with center O, chords AB and CD are drawn, intersecting at point P.
In each segment of the circle, other circles are inscribed with corresponding centers O_1; O_2; O_3; O_4.
Find the measure of angle ∠O_1 PO_2.
Can you explain the mathematical principles behind the Proof of Stake (PoS) algorithm, including how validator selection probabilities, stake adjustments, and reward calculations are determined
توضيح كيفية التعليم الأخضر في مادة الرياضيات للأطفال
Bonjour,
Je suis actuellement en train de travailler sur un projet de recherche portant sur l'utilisation de l'optimisation mathématique pour déterminer le taux directeur optimal en politique monétaire. J'aimerais savoir s'il existe des travaux de recherche récents ou des modèles spécifiques qui ont abordé ce sujet. De plus, je suis à la recherche de conseils sur la manière de structurer mon modèle et de choisir des variables pertinentes pour ce type d'analyse. Toute suggestion de lecture ou d'expertise serait grandement appréciée.
Merci d'avance pour votre aide
As an academic working and pursuing a PhD degree in Egypt, both in private and public universities respectively, I wanted to put forward a simple question:
What is the role of universities, and other academic institutions, today? Was there ever a time where universities were agents of revolutionary action and change, or was it only a subject of the overall consumerist system?
We can take many steps back till the Ancient Egyptian times, where scribes and priests were taught writing, mathematics, and documentation of daily exchanges. All the way till today's era of digital globalization and mass education, where knowledge production process has become more of a virtual canvas rather than actual knowledge. Has knowledge ever served its purpose? Have academic institutions, and of course academic scholars, ever delivered the true purpose of education?
Was, and still, education's main sole purpose is economic prosperity of certain classes, hence socio-economic segregation?
Scientists believe theories must be proven by experiments. Does their faith in the existence of objective reality mean they are classical scientists who reject quantum mechanics' statements that observers and the observed are permanently and inextricably united? In this case, scientists would unavoidably and unconsciously influence every experiment and form of mathematics. In the end, they may be unavoidably and unconsciously influencing the universe which is the home of all experiments and all mathematics.
There exists a neural network model designed to predict a specific output, detailed in a published article. The model comprises 14 inputs, each normalized with minimum and maximum parameters specified for normalization. It incorporates six hidden layers, with the article providing the neural network's weight parameters from the input to the hidden layers, along with biases. Similarly, the parameters from the output layer to the hidden layers, including biases, are also documented.
The primary inquiry revolves around extracting the mathematical equation suitable for implementation in Excel or Python to facilitate output prediction.
It seems it is common to combine basic observations to create new observable, which are then used for PPP and other applications. Basic observations such as pseudorange and carrier-phase observations are real measurement from GNSS. These real observations are combined to create entirely new observable which is not direct, physical, and real. Amazingly, these new observable solves the real problem such as PPP (e.g. Ionosphere -free combination).
- What is the theory behind this?
- Any similar approach like this in other scientific field or any simple analogous explanation?
- You could direct me to resources such as videos, or literature.
In triangle ∆ABC (with ∠C = 90°), the angle CBA is equal to 2α.
A line AD is drawn to the leg BC at an angle α (∠BAD = α).
The length of the hypotenuse is 6, and the segment CD is equal to 3.
Find the measure of the angle α.
This problem can be solved using three methods: trigonometric, algebraic, and geometric. I suggest you find the geometric method of solution!
A minion is a low-level official protecting a bureaucracy form challengers.
A Kuhnian minion (after Thomas Kuhn's Structure of Scientific Revolutions) is a low-power scientist who dismisses any challenge to existing paradigm.
A paradigm is a truth structure that partitions scientific statement as true to the paradigm or false.
Recently, I posted a question on Physics Stack Exchange that serves as a summary of the elastic string paradigm. My question was: “Is it possible there can be a non-Fourier model of string vibration? Is there an exact solution?”
To explain, I asked if they knew the Hamiltonian equation for the string vibration. They did not agree it must exist. I pointed out there are problems with the elastic model of vibration with its two degrees of freedom and unsolvable equations of motion can only be approximated by numerical methods. I said elasticity makes superposition the 4th Newtonian law. How can a string vibrate in an infinite number of modes without violating energy conservation?
Here are some comments I got in response:
“What does string is not Fourier mean? – Qmechanic
“ ‘String modes cannot superimpose!’ Yet, empirically, they do.” – John Doty
“ A string has an infinite number of degrees of freedom, since it can be modeled as a continuous medium. If you manage to force only the first harmonic, the dynamics of the system only involve the first harmonic and it’s a standing wave: this solution does depend on time, being (time dependence in the amplitude of the sine). No 4th Newton’s law. I didn’t get the question about Hamilton equation.
“What do you mean with ‘archaic model’? Can I ask you what’s your background that makes you do this sentence? Physics, Math, Engineering? You postulate nothing here. You have continuum mechanics here. You have PDEs under the assumption of continuum only. You have exact solutions in simple problems, you have numerical methods approximating and solving exact equations. And trust me: this is how the branch of physics used in many engineering fields, from mechanical, to civil, to aerospace engineering.” – basics
I want to show the rigid versus elastic dichotomy goes back to the calculus wars. Quoting here from Euler and Modern Science, published by the Mathematical Association of America:
"We now turn to the most famous disagreement between Euler and d’Alembert … over the particular problem of the theory of elasticity concerning a string whose transverse vibrations are expressed through second-order partial differential equations of a hyperbolic type later called the wave equation. The problem had long been of interest to mathematicians. The first approach worthy of note was proposed by B. Taylor, … A decisive step forward was made by d’Alembert in … the differential equation for the vibrations, its general solution in the form of two “arbitrary functions” arrived at by means original with d’Alembert, and a method of determining these functions from any prescribed initial and boundary conditions.”
[Editorial Note: The boundary conditions were taken to be the string endpoints. The use of the word hyperbolic is, I believe, a clear reference to Taylor’s string. A string with constant curvature can only have one mathematic form, which is the cycloid, which is defined by the hyperbolic cosh x function. The cosh x function is the only class of solutions that are allowed if the string cannot elongate. The Taylor/Euler-d’Alembert dispute whether the string is trigonometric or hyperbolic.
Continuing the quote from Euler and Modern Science:
"The most crucial issue dividing d’Alembert and Euler in connection with the vibrating string problem was the compass of the class of functions admissible as solutions of the wave equation, and the boundary problems of mathematical physics generally, D’Alembert regarded it as essential that the admissible initial conditions obey stringent restrictions or, more explicitly, that the functions giving the initial shape and speed of the string should over the whole length of the string be representable by a single analytical expression … and furthermore be twice continuously differentiable (in our terminology). He considered the method invalid otherwise.
"However, Euler was of a different opinion … maintaining that for the purposes of physics it is essential to relax these restrictions: the class of admissible functions or, equivalently, curves should include any curve that one might imagine traced out by a “free motion of the hand”…Although in such cases the analytic method is inapplicable, Euler proposed a geometric construction for obtain the shape of the string at any instant. …
Bernoulli proposed finding a solution by the method of superimposition of simple trigonometric functions, i.e. using trigonometric series, or, as we would now say, Fourier series. Although Daniel Bernoulli’s idea was extremely fruitful—in other hands--, he proved unable to develop it further.
Another example is Euler's manifold of the musical key and pitch values as a torus. To be fair, Euler did not assert the torus but only drew a network show the Key and Pitch can move independently. This was before Mobius's classification theorem.
My point is it should be clear the musical key and pitch do not have different centers of harmonic motion. But in my experience, the minions will not allow Euler to be challenged by someone like me. Never mind Euler's theory of music was crackpot!
The need of a paradigm shift in physics
Is it possible in a world as fragmented as ours to present a new concept of Unity in which Science, Philosophy and Spirituality or Ontology can be conceived working in Complete Harmony?
In this respect the late Thomas S. Kuhn wrote in his
The Structure of Scientific Revolutions
"Today research in parts of philosophy, psychology, linguistic, and even art history, all converge to suggest that the traditional paradigm is somehow askew. That failure to fit is also increasingly apparent by the historical study of science to which most of our attention is necessarily directed here."
And even the father of Quantum Physics complained strongly in his 1952 colloquia, when he wrote:
"Let me say at the outset, that in this speech, I am opposing not a few special statements claims of quantum mechanics held today, I am opposing its basic views that has been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody. It has been worked out in great detail to form a scheme of admirable logical consistency which has since been inculcated in all young students of theoretical physics."
Where is the source of this "crisis of physics" as has been called?
Certainly the great incompatibility between General Relativity and Quantum Mechanics is in a certain sense, one of the reasons, of that great crisis, and that shows clearly the real need of a paradigm shift.
As one that comes from the Judeo-Christian tradition, that need of a real paradigm shift was of course a real need too. Philosophers such as Teilhard de Chardin, Henry Bergson, Charles Pierce and Ken Wilber, all of them worked for it!.
Ken Wilber said that goal of postmodernity should be the Integration of the Big Three, Science, Philosophy and Spirituality, and a scientist as Eric J. Lerner in his The Big Bang Never Happened, show clearly in it, how a paradigm shift was in cosmology is a real need too.
My work about that need started in 1968, when I found for the first time, an equation that was declared the most beautiful equation of mathematics, I mean Euler's relation found by him in 1745, when working with infinite series. It was this equation that took me in 1991, to define what I now call a Basic Systemic Unit, that has the most remarkable property to remain the same in spite of change, exactly the same definition of a Quantum as defined by professor Art Hobson in his book The Tales of Quantum, and that the University of Ottawa found when working with that strange concept that frightened Einstein, the entanglement concept, that seemed to violate Special Relativity.
Where is the real cause of the incompatibility between GR and QM?
For GR Tensor Analysis was used, a mathematical tool based on real numbers, and with it there was the need to solve ten functions representing the gravitational field:
"Thus, according to the general theory of relativity, gravitation occupies an exceptional position with regards to other forces, particularly the electromagnetic forces, since the ten functions representing the gravitational field at the same time define the metrical properties of the space measured."
THE FOUNDATION OF THE GENERAL THEORY OF RELATIVITY
By A. Einstein
Well the point is that, in that metrics that define the GR, time is just another variable, just as space, and as so with the same symmetrical properties, at the point that is can take both signs positive and negative, so time travel could be conceived just as a space travel, and any direction, in fact Stephen Hawking in his A BRIEFER HISTORY OF TIME, writes:
"It is possible to travel to the future. That is, relativity shows that it is possible to create a time machine that will jump you forward in time." Page 105
This is exactly the point that has made physics some sort of metaphysics, and as so created the great crisis of physics. While QM is based on the complex Schrödinger's wave equation or on complex numbers, in which the symbol sqr(-1), is a symbol to separate two different orders of reality, such as Time and Space, GR is based just on real numbers.
The Basic Systemic Unit concept, based on Euler's relation is in fact the definition of a Quantum, and as so it can be used to deduce all fundamental equations of physics as can be seen in my paper... resolving in this way that great crisis of physics
Quantum Physics
Edgar Paternina
retired electrical engineer
I have been seeing and following a lot of work on these topics, it even seems that there are more results on them than on the corresponding classical topics, particularly on general topology.
What could be the cause of such results?
Has our mathematical knowledge progressed as much as contemporary science?
1- Assume a rectangle in the second dimension; this rectangle's components are lines. Its geometric characteristics are perimeter and area.
2- Assume a cube in the third dimension. Its components are the plane. Its geometric characteristics are area and volume.
3- What are the names of its components by transferring this figure to the 4th dimension? And what is the name of its geometric characteristics? And with the transfer to the 5th and higher dimensions, our mathematics has nothing to say.rectangle is just a simple shape how about complex geometric shapes?
According to new physical theories such as strings theory, we need to study different dimensions.
Modifying the original Feistel structure will it be feasible to design a lightweight and robust encryption algorithm. Somehow changing the structure's original flow and adding some mathematical functions there. I welcome everyone's view.
Homomorphic encryption is a type of encryption that lets you perform mathematical operations on encrypted data without decrypting it first. This means that the raw data remains encrypted while it's being processed, analyzed, and run through algorithms
Given:
In an isosceles triangle, the lengths of the two equal sides are each 1, and the base of the triangle is m.
A circle is circumscribed around the triangle.
Find the chord of the circle that intersects the two equal sides of the triangle and is divided into three equal segments by the points of intersection.
What is the mathematic difference between AI and AC?
Standardization of AI and AC based on the DIKWP model(初学者版)
I am interested in the existence of intelligent tutoring systems for teaching physics and mathematics in secondary schools or artificial intelligence tools that can be used in the classroom for student-teacher collaboration in these subjects, preferably with free access.
I am also interested in any relevant studies/research or information on the above topic.
National Achievement Test are given to learners like in Grade 10 on the following subjects like Science, Mathematics and English, to assess how much students learned in a specific disciplines
Let me share a quote from my own essay:
"Dynamic flows on a seven-dimensional sphere that do not coincide with the globally minimal vector field, but remain locally minimal vector fields of matter velocities, we interpret as physical fields and particles. At the same time, if in the space of the evolving 3-sphere $\mathbb{R}^{4}$ the vector field forms singularities (compact inertial manifolds in which flows are closed), then they are associated with fermions, and if flows are closed only in the dual space $\mathbb{R}^{4}$ with an inverse metric, then the singularities are associated with bosons. For example, a photon is a limit cycle (circle) of a dual space, which in Minkowski space translationally moves along an isotropic straight line lying in an arbitrary plane $(z,t)$, and rotates in the planes $(x,t)$, $(y,t)$." (p. 12 MATHEMATICAL NOTES ON THE NATURE OF THINGS)
Hi all
i was wondering if anyone knew of a valid and reliable assessment of task-based engagement that could be used to compare student engagement across different types of tasks in mathematics?
thanks
James
In triangle ABC, the median BM_2 intersects the bisector AL_1 at point P.
The side BC is divided by the base of the bisector AL_1 into segments CL_1=m and BL_1=n.
Determine the ratio of the segments AP to PL_1.
Dear research community members I would like to post a preprint of my article in Mathematics but need an endorsement If anyone can do this for me I will greatly appreciate for once Secondly I will send you my new paper with explanations
Endorsement Code: SP84WZ
Thanks a lot
P.S I don't know the procedure The moderator sent me a link
Ruslan Pozinkevych should forward this email to someone who's registered as an endorser for the cs.IT (Information Theory) subject class of arXiv
or alt visit
and enter SP84WZ
Once again thank you and apologize for bothering
How do we improve the inflation prediction using mathematics?
Ate there any Research Project and Grants for individuals without involvement of employer in Mathematics?
We assume that the difference is huge and that it is not possible to compare the two spaces.
The R^4 mathematical space considers time as an external controller and the space itself is immobile in its description or definition in the face of curl and divergence operators.
On the other hand, the unit space 4 D x-t time t is woven into the 3D geometric space as a dimensionless integer.
Here, the curl and divergence operators are just extensions of their original definitions in 3D geometric space.
Is there a galactic rotation anomaly? Is it possible to find out the speed and time of the galactic rotation anomaly?
Is there a galactic rotation anomaly? Is it possible to find out the speed and time of the galactic rotation anomaly?
Abstract: Orbital speeds of stars, far from centre of a galaxy, are found roughly constant, instead of reductions predicted by current gravitational theories (applied on galactic and cosmological scales). This is called the anomalous rotation of galaxies. This article intends to show that constant angular speeds of all macro bodies in a galaxy are natural phenomenon and there is no mystery about it.
Keywords: Galaxy, Stable galaxy, rotational anomaly.
A planetary system is a group of macro bodies, moving at certain linear speed in circular path around galactic centre. Central body of planetary system is by far the largest and controls mean linear speeds of all other members. Gravitational attractions between macro bodies of planetary system cause perturbations in their directions of motion, resulting in additional curvatures of their paths. When perturbed paths of smaller macro bodies are related to central body in assumed static state, we get apparent orbital paths of planetary bodies. They appear to revolve around static central body in elliptical/circular paths. Apparent orbital paths are unreal constructs about imaginary static state of central body. They are convenient to find relative positions of macro bodies in the system and to predict cyclic phenomena occurring annually. In reality, planetary bodies do not orbit around central body but they move in wavy paths about the central body. Central and planetary bodies move at a mean linear speed along their curved path around galactic centre.
Perturbations of orbital paths of macro bodies in planetary system are related directly to their matter-content and inverse square of distance from central body. Distance from central body has greater effect of magnitudes of perturbations. Hence, normally, paths of planetary bodies at greater distance from central body are perturbed by lesser magnitudes. Curvatures and thus angular speeds of their apparent orbits reduce as distance from central body increases. Since planetary system has no real spin motion, this is an imaginary phenomenon. However, many learned cosmologists seem to take spin motion of planetary system as real phenomenon and consider that members of all spinning group pf macro bodies should behave in similar manner, i.e. angular (spin) speed of members should reduce as their distance from centre of system increases.
Stable galaxy consists of many macro bodies revolving around its centre. This group can be considered as a spinning fluid macro body, rotating at a constant angular speed. Gravitational collapse initiates spin motion of galactic cloud and maintains constant spin speed of outer parts of stable galaxy. Centre part of galaxy, which is usually hidden, may or may not be spinning. We can observe only visible stars and their angular speeds about galactic centre. Linear motions of macro bodies, caused by gravitational attractions towards other macro bodies in the system, have two components each. One component, due to additional linear work invested in association with it, produces macro body’s linear motion, in a direction slightly deflected away from centre of circular path. Other component, towards centre of its circular path, is caused by additional angular work invested in association with it. This component produces angular motion of macro body.
All matter-particles in a fluid macro body, spinning at constant speed, have constant angular speeds. Consider a matter-particle at O, in figure 1, moving in circular path AOB. XX is tangent to circular path at O. Instantaneous linear speed of matter-particle is represented by arrow OC, in magnitude and direction. It has two components; OD, along tangent XX and DC, perpendicular to tangent XX and away from centre of circular path. This component, DC, represents centrifugal action on matter- C particle due to its motion in circular path. In
order to maintain constant curvature of path, X D O X matter-particle has to have instantaneous A linear (centripetal) motion equal to CE E
toward centre of circular path. If magnitudes B Figure 1 and directions of instantaneous motions are as shown in figure 1, matter-particle maintains its motion along circular path AOB at constant angular speed.
Should the matter-particle increase its instantaneous linear speed for any reason, both components OD and DC would increase. Component OD tends to move matter-particle at greater linear speed along tangent XX. Outward component DC tends to move matter-particle away from centre of its circular path. The matter particle tends to increase radius of curvature of its path. This action is usually assigned to imaginary ‘centrifugal force’. In reality expansion of radius of curvature of path is caused by centrifugal component of linear motion. Reduction in centripetal action also produces similar results.
Should the matter-particle decrease its instantaneous linear speed for any reason, both components OD and DC would reduce. Component OD tends to move matter-particle at lesser linear speed along tangent XX. Reduction in outward component DC tends to move matter-particle towards centre of its circular path. The matter particle tends to reduce radius of curvature of its path. Reduction of radius of curvature of path is caused by reduction in centrifugal component of linear motion. Increase in centripetal action also produces similar results.
In other words, matter-particle regulates its distance from centre of its circular path so that its angular speed remains constant. This is the reason for action of centrifuges. As linear speeds of matterparticles increase, they move outwards, in an effort to maintain their angular speed constant.
Additional work, done for linear motion of a matter-particle and additional work, done for its angular motion are entirely separate and distinct. Additional work for linear motion of a matter-particle can produce only linear motion and additional work for angular motion can produce only angular motion. In the case, explained above, increased in linear speed of matter-particle is considered. That is, additional work invested in association with matter-particle is of linear nature. It can only increase its linear motion. As no additional work for angular motion is invested matter-particle cannot change its angular speed. Instead, matter-particle is compelled to move away from centre of its rotation, so that it can increase magnitude of linear motion while keeping magnitude of angular motion constant.
Similarly, increase in centripetal effort invests additional work required for angular motion of matterparticle. Matter-particle tends to increase magnitude of its angular motion. Curvature of its path
increases by reducing its distance from centre of circular path. Matter-particle tends to move towards centre of circular path, so that it can increase its angular speed while keeping its linear speed constant.
Every macro body in a stable galaxy behaves in a manner similar to matter-particle, represented in figure 1. They tend to position themselves in the system, so that their linear and angular speeds match corresponding works associated with them. Macro bodies strive to maintain their angular speeds constant by keeping appropriate distance from centre of rotation. Macro bodies towards the central region may experience additional centripetal effort. They might increase their angular motion and move towards central point to merge with black hole present there. In due course of time, macro bodies on outer fringes move away from galaxy and destroy its stability.
In a galaxy, various macro bodies arrive at their relative position gradually by error and trial, during which their relative positions and linear and angular speeds are stabilized. Galaxy, as a whole, stabilizes only when constituent macro bodies have reached their steady relative positions and motions. In order to maintain stability, it is essential to maintain relative positions of all constituent macro bodies by having constant and equal angular speeds and linear speeds corresponding to their distances from galactic centre. Change in relative position or linear or angular speed of even one macro body is liable to destabilize the galaxy.
As and when superior 3D matter-particles at the fringe of galaxies attain linear speeds approaching speed of light, they break-down into primary 3D matter-particles and produce halo around equatorial region. Halos of neighbouring stable galaxies interact to prevent their translational movements and maintain steady state of universe.
Therefore constant angular speeds of constituent macro bodies of stable galaxies are their natural states. There are no mysteries or anomalies about them. This phenomenon is mystified by those who consider imaginary spin motions of planetary systems are real. Therefore, assumptions of dark matter, time dilation, modification of gravitational laws, etc and complicated mathematical exercises are irrational and unnecessary to prove non-existing rotation anomaly of galaxies.
Conclusion:
Galactic rotation anomaly is a non-existing phenomenon derived from imaginary spin motions of planetary systems about their central bodies in assumed static states. Constant angular speeds of stars in a galaxy confirm static state of galactic center (in space), rather than produce an anomaly.
Reference:
[1] Nainan K. Varghese, MATTER (Re-examined), http://www.matterdoc.info
Reply to this discussion
Chuck A Arize added a reply
5 hours ago
Yes, there is a galactic rotation anomaly observed as the discrepancy between the predicted and actual rotation speeds of galaxies. This anomaly, often attributed to dark matter, shows that the outer regions of galaxies rotate faster than expected. Measuring the speed and time of this rotation anomaly involves detailed observations of galactic rotation curves and modeling, which reveal the velocity profile and suggest the presence of unseen mass influencing the rotation.
Abdul Malek added a reply
3 hours ago
Abbas Kashani > "Is there a galactic rotation anomaly?"
There is a galactic rotation anomaly, but only according to officially accepted theories of gravity and the (Big Bang) theory of the formation of the galaxies inferred for a finite, closed and a created (in the finite past) universe.
But all these theories based on causality and theology are wrong! The dialectical and scientific view is that the universe is Infinite, Eternal and Ever-changing, mediated by dialectical chance and necessity. Gravity is a dialectical contradiction of the unity of the opposites of attraction and repulsion (due to inherent free motion of matter particles, vis viva). In short (human) time scale, new galaxies are seen to be formed through the dissipation and/or ejection of matter in the form of stars, star clusters or even a large part of the galaxy as quasars from the existing galaxies.
So, the observed high orbital velocities of the starts, star clusters etc. at the periphery of the galaxies and of the planets at the periphery of the planetary systems within the galaxies is just a natural phenomena and there is no anomaly!
"Ambartsumian, Arp and the Breeding Galaxies" : http://redshift.vif.com/JournalFiles/V12NO2PDF/V12N2MAL.pdf
KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Legacies in Theoretical Physics, Cosmology and in Ruling https://www.rajpub.com/index.php/jap/article/view/9106
"THE CONCEPTUAL DEFECT OF THE LAW OF UNIVERSAL GRAVITATION OR ‘FREE FALL’: A DIALECTICAL REASSESSMENT OF KEPLER’S LAWS":
Article THE CONCEPTUAL DEFECT OF THE LAW OF UNIVERSAL GRAVITATION OR...
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Preston Guynn added a reply
4 days ago
Your discussion question statement is:
- "Is there a galactic rotation anomaly? Is it possible to find out the speed and time of the galactic rotation anomaly? Orbital speeds of stars, far from centre of a galaxy, are found roughly constant, instead of reductions predicted by current gravitational theories (applied on galactic and cosmological scales). This is called the anomalous rotation of galaxies."
The limit of galactic rotation velocity is expected because rotation minus precession has a maximum velocity. Our solar system's relative rotation velocity with respect to the Milky Way galaxy is at this maximum, and as a fraction of speed of light the observed velocity can be designated vg/c, and is determined in the single page proof of the quantum of resistance:
Article The Physical Basis of the Quantum of Resistance is Relativis...
The detailed proofs are in:
Article Thomas Precession is the Basis for the Structure of Matter and Space
Note that the observed velocity is the difference between rotation and precession.
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Dale Fulton added a reply
3 days ago
The galactic rotation "anomaly" (flat rotation curve) is actually a misinterpretation of the measurements of the galactic rotations, when performed with spectrographic (redshift) measurements. This has misled astronomers since the inception of the spectrographic velocity measurements, as being totally doppler shift, whereas they contain many non-linear components of redshift due to gases and other effects from each galaxy. Recent measurements of the Milky Way galaxy rotation curve prove that this is the case, i.e, that spectrographic velocities are misleading, and that proper motion or parallax is the only way to accurately measure those velocities.
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André Michaud added a reply
20 hours ago
There is no galactic rotation anomaly. Such a concept emerges from the lack of careful study of past historical discoveries about orbital structures in the universe established since Ticho Brahe first collected his data about the planetary orbits in the solar system, from which Johannes Kepler abstracted his 3 laws, that were then mathematically confirmed by Newton.
The galactic rotation parameters are well known by those who studied the true foundation of astrophysics. Put in perspective in this article:
Article Inside Planets and Stars Masses
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Abbas Kashani added a reply
44 seconds ago
Preston Guynn
Dale Fulton
André Michaud
Greetings and politeness and respect to the great and respected professors and astronomers, I am very grateful for your efforts, dear ones. Thank you and thank you
Abbas Kashani
Mohaghegh Ardabili University
It will be better if there will be any mathematical relation or suggest some research articles?
During Kurt Gödel's lecture on the occasion of Albert Einstein's birthday in 1945, this question was already raised by John Wheeler. Gödel did not comment on it. Both Einstein and Gödel did not believe in quantum theory. Is there currently any reference or article that relates to this question? From today's scientific perspective, is there a relationship between Heisenberg's Uncertainty Principle and Gödel's Incompleteness Theorem? Even so, when both the principles arise from different theoretical frameworks and serve different purposes within their respective domains. Please provide references.
Can we apply the theoretical computer science for proofs of theorems in Math?
Comment les enseignants de mathémattiques du cycle primaire conçoivent-ils leurs évaluations? Quelles conceptions ont-ils pour le concept d'évaluation?
Would someone be kind enough to answer the question why there is a Pareto Principle related to Grades in Primary Education in Mathematics, but please without counter-questions such as who says or where it is written that it is so. If Primary Education in Mathematics lasts, for example, 8 years (the number varies between countries), then in the first three grades 80% have excellent and very good grades in Mathematics, and 20% good and bad. In the fourth grade, this ratio is approximately 50%:50%. However, from the fifth to the eighth grade, the relationship is reversed and only 20% have excellent and very good grades, and 80% good and bad. Sometimes, for some reason, the ratio is 70:30 instead of 80:20, but the relationship and regularity exists. I thank you in advance for your reply, as well as for your kindness and time.
With the term “gravity”, we refer to the phenomenon of the gravitational interaction between material bodies.
How that phenomenon manifests itself in the case of the interaction of two mass particles at rest relative to an inertial reference frame (IRF) has, in the framework of classical physics, mathematically been described by Isaac Newton. And Oliver Heaviside, Oleg Jefimenko and others did the same in the case of bodies moving relative to an IRF. They described the effects of the kinematics of the gravitating objects assuming that the interaction between massive objects in space is possible through the mediation of “the gravitational field”.
In that context, the gravitational field is defined as a vector field having a field- and an induction-component (Eg and Bg) simultaneously created by their common sources: time-variable masses and mass flows. This vector-field (a mathematical construction) is an essential element of the mathematical description of the gravitational phenomena, and as such an element of our thinking about nature.
One cannot avoid the question of whether or not a physical entity is being described by the vector field (Eg, Bg) and what, if any, is the nature of that entity.
In the framework of “the theory of informatons”[1],[2],[3], the substance of the gravitational field – that in that context is considered as a substantial element of nature - is identified as “gravitational information” or g-information” i.e. information carried by informatons. The term “informaton” refers to the constituent element of g-information. It is a mass and energy less granular entity rushing through space at the speed of light and carrying information about the position and the velocity of its source, a mass-element of a material body.
References
[1] Acke, A. (2024) Newtons Law of Universal Gravitation Explained by the Theory of Informatons. https://doi.org/10.4236/jhepgc.2024.103056
[2] Acke, A. (2024) The Gravitational Interaction between Moving Mass Particles Explained by the Theory of Informatons. https://doi.org/10.4236/jhepgc.2024.103060
[3] Acke, A. (2024) The Maxwell-Heaviside Equations Explained by the Theory of Informatons. https://doi.org/10.4236/jhepgc.2024.103061
In his article "More is different", Anderson said that new laws of physics "emerge" at each physical level and new properties appear [1]; Wheeler, when claiming that "law without law" and "order comes out of disorder", argued that chaotic phenomena " generate" different laws of physics [2][3]. What they mean is that the laws, parameters, and constants of the upper level of physics appear to be independent of the laws of physics of the lower level. Is this really the case? Are we ignoring the conditions that form the physical hierarchy, thus leading to this illusion?
Let's suppose a model. The conditions for the formation of new levels are at least two: i. Existence of low-level things A,B ...... , the existence of interaction modes a, b,...... ; two, the existence of a sufficient number of low-level things, NxA, MxB....... Then when they are brought together, there are many possible combinations, e.g., (AA), (AAA), (AAA)', ...... , (AB), (BA), (AAB)', (BAB), ........ Then it escalates to [(AA)(AA)], [(AB)(ABA)], ....... What this actually leads to is a change in the structure of things and a corresponding change in the way they interact. The result of the "change" is the appearance of new physical phenomena, new forces, and so on.
Physics is an exact match for math, so let's use math as an example of this phenomenon. Suppose we have a number of strings (threads) that can be regarded as underlying things, then, when a string is curled into a circle, L=2πR, the law of the relationship between the length of the string and its radius, and the irrational constant π appear; when two strings are in cascade, L=l1+l2, the law that the total length of the string is equal to the sum of the individual string lengths (Principle of superposition) appears; and, when three strings form a right triangle, the law of Pythagoras, c2=a2+b2, the law of sums of interior angles of triangles ∠A + ∠B + ∠C = 180° , and the irrational constant √2 appear ...... ; and the transcendental number e appears when the string length L grows in a fixed proportion (continuous compound interest)[4]‡ ...... ; when the string vibrates, sine waves (sinωt) appear; when two strings are orthogonal, i appears ...... ; and when more kinds of vibrating strings are superimposed under specific conditions, more phenomena appear *.......
All these "qualitative changes" do not seem to be caused by "quantitative changes", but more by the need to change the structure. As mathematical theorems emerge, so must the laws of physics, and it is impossible for physics to transcend mathematics. Therefore, as long as there is a change of structure in physics, i.e. the possibility of symmetry breaking [5]**, new "symmetries", new "laws", new "forces", new "constants", new "parameters" are almost inevitable.
Can we try to attribute all physical phenomena to emergence under hierarchical structural conditions? For example, the fine structure constant‡‡and the Pauli exclusion principle emerge because of the formation of atomic structure; the "nuclear force" emerges because of the combination of protons and neutrons; The "strong interaction force" and "weak interaction force" appeared because of the structure of protons and neutrons. We should pay attention to the causal relationship here. Without structure, there would be no new phenomena; it is the more fundamental interactions that form structure, not these new "phenomena".
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Notes
* e.g. Blackbody radiation law, Bose statistics, Fermi statistics, etc.
** Should there be "spontaneous symmetry breaking"? Any change in symmetry should have a cause and a condition.
‡ What does it mean in physics if e will appear everywhere and the individual mathematical constants appear so simply? They must likewise appear at the most fundamental level of physics.
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2024-07-27 补充
In addition to the structure and statistics generated by the interactions that result in new laws of physics, the expression of the different orders of differentials and integrals of such generating processes is another important way of making the laws of physics emerge.
Typical examples of such expressions can be seen @ Ingo D. Mane: “On the Origin and Unification of Electromagnetism, Gravitation, and Quantum Mechanics“：
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Referencs
[1] Anderson, P. W. (1972). More Is Different: broken symmetry and the nature of the hierarchical structure of science.
. Science, 177(4047), 393-396. https://doi.org/doi:10.1126/science.177.4047.393
[2] Wheeler, J. A. (1983). ‘‘On recognizing ‘law without law,’’’Oersted Medal Response at the joint APS–AAPT Meeting, New York, 25 January 1983. American Journal of Physics, 51(5), 398-404.
[3] Wheeler, J. A. (2018). Information, physics, quantum: The search for links. Feynman and computation, 309-336.
[4] Reichert, S. (2019). e is everywhere. Nature Physics, 15(9), 982-982. https://doi.org/10.1038/s41567-019-0655-9;
[5] Nambu, Y. (2009). Nobel Lecture: Spontaneous symmetry breaking in particle physics: A case of cross fertilization. Reviews of Modern Physics, 81(3), 1015.
Please suggest me, I want to present my research work.
how i can calculate mathematically COD concentration if i add 1gr from glucose to 1 L distilled water
I am need someone to collaborate with me to make article. Especially in international journal.
The video "The Biggest Question Physicists Aren't Asking" (https://www.youtube.com/watch?v=iVyl8pGd44I) says the Michelson-Morley experiment of 1887 didn't disprove the existence of the aether. It reminds us that Hendrik Lorentz explained the experiment's negative results with his Lorentz ether theory (LET), which he initially developed in 1892 and 1895. The theory was improved in 1905 and 1906 by Henri Poincaré - and it was based on the aether theory of Augustin-Jean Fresnel, Maxwell's equations, and the electron theory of Rudolf Clausius. The video says Albert Einstein's alternative to the aether in Special Relativity is preferred by physicists because it makes fewer assumptions. Interestingly, Einstein wondered in later years about the possibility of the aether actually existing.
Just as the building blocks in chemistry are atoms and molecules, the building blocks physics could use to determine what the aether is might be binary digits and topology. There are two clues to this conclusion. First - in his book "A Brief History of Time", Stephen Hawking states that quantum spin tells us what particles actually look like. A particle of matter has spin 1/2 and must be completely rotated twice (720 degrees) to look the same. Added to this is - a Mobius strip must be travelled around twice in order to reach the starting point. The second clue was supplied by a paper Einstein published in 1919. That paper asks if gravitation and electromagnetism play a role in forming elementary particles.
The clues can produce the following hypothesis. The BITS or binary digits of one and zero code for a Mobius strip (similar to the way that topological figure can be viewed on the Internet). Then two Mobius figures are joined to create a Klein bottle: possibly, the doughnut-shaped figure-8 version of the Klein. The Klein bottle is immersed in the 3rd dimension, with binary digits filling in any holes or gaps to produce a technically flat and simply-connected result. This procedure is similar to computer art's Sky Replacement, where the 1s and 0s can make a smooth blue sky stretching from horizon to horizon. The 1s and 0s naturally exist on quantum scales, and imaginary numbers are essential in quantum mechanics. So the complex (real+imaginary) numbers of Wick rotation could be given a practical use by being a subroutine of the Mobius strips and becoming the 4th dimension of time which can't be separated from the dimensions of space. Trillions of Mobius strips could form a photon while trillions of more complicated figure-8 Klein bottles might form the more complicated graviton. Interaction of photons and gravitons (in a process called Vector-Tensor-Scalar [VTS] Geometry) creates the Mobius-based matter particles. In this scenario, the aether - the medium waves travel through - wouldn't be an abstract thing called space filled with alleged Virtual Particles which can't be detected and may not even exist. The medium would be a sea filled with photons and gravitons.
Another possibility is that there is no medium for the gravitational and electromagnetic waves, and that there truly is no aether. In that case, waves would not merely be described by mathematics but would literally be the result of maths. A 3D (three dimensional) cube can be regarded as a reality coded on a 2D surface - in other words, the cube is a projection from a square. The 2D square would be a nonlinear (angular) math object resulting from adding four lines, each one being separated from those adjoining it by 90 degrees. The cubic shape would result from adding, in one direction, multiple layers of the information in the square. Instead of programming a set of points to follow a straight line, they can be represented curvilinearly as a waveform and described by Fourier analysis, v=f(lambda), etc. Interacting particles can produce waves just as masses can curve spacetime to produce gravity and gravitational waves. VTS Geometry plausibly explains the inverse - it doesn't solely regard mass as the producer of gravity but also regards gravity, partnering with electromagnetism, as producer of mass. Inverting quantum mechanics, gravitational and electromagnetic waves create particles with mass (protons, neutrons, quarks, electrons, etc - even the Higgs boson). As Stephen Hawking and Leonard Mlodinow point out in their book "The Grand Design", ultimate reality does not have to be described with quarks though it certainly can be. In this paragraph, the idea of curved space is replaced by gravitational and electromagnetic waveforms travelling on curved trajectories.
what is difference between green production and regular production in inventory control with theoretical expression and mathematical term ?
What is going with physics?
Two excellent books written by experts in the field:
- Eric J. Lerner “THE BIG BANG NEVER HAPPENED,
- and Lee Smolin and his The Trouble with Physics,
show that the Great Crisis of Physics, will not be solved if we don’t change our frame of references, abandoning once and for all, the way we are trying to solve those fundamental problems of physics. Institution such as ResearchgGate, certainly are way to make easier to obtain that goal, but then it is necessary, that people open their minds to new ways to “seeing reality”… not the one they are using in mainstream physics, such as GR and Big Bang and so on…
“THE STRANGE CAREER OF MODERN COSMOLOGY
In our century the cosmological pendulum has swung back. The universe of present-day cosmology is more like that of Ptolemy and Augustine than that of Galileo and Kepler. Like the medieval cosmos, the modern universe is finite in time-it began in the Big Bang, and will end either in a Big Crunch or in a slow decay and dissipation of all matter. Many versions, like Stephen Hawking's, are finite in space as well, a perfect self-enclosed four-dimensional sphere. There is a gap between the heavens and the earth: in space there exist strange entities, governed by the pure and ethereal mathematics of general relativity-black holes, cosmic strings, axions-which cannot, even in principle, be studied on earth.
The nineteenth-century universe evolved by laws still in action today, as did that of the Jonians, yet the universe of modern cosmology is the product of a single, unique event, qualitatively different from anything occurring today-just as the medieval cosmos was the product of the creation. While scientists of a century ago saw a universe of continuous change, evolution, and progress, today's researchers see a degenerating universe, the ashes of a primordial explosion.
To earlier scientists, and to most of today's scientists outside cosmology, mathematical laws are descriptions of nature, not the true reality that lies behind appearances. Yet today cosmologists assume, as did Plato and Ptolemy, that the universe is the embodiment of preexisting mathematical laws, that a few simple equations, a Theory of Everything, can explain the cosmos except for what "breathed fire" into these equations to make them come alive.
Big Bang cosmology does not begin with observations but with mathematical derivations from unquestionable assumptions. When further observations conflict with theory, as they have repeatedly during the past decades, new concepts are introduced to "save the phenomenon"-dark matter, WIMPs, cosmic strings-the "epicycles" of current astronomy.”
“Alfven wrote sixty years later, "The people were told that the true nature of the physical world could not be understood except by Einstein and a few other geniuses who were able to think in four dimensions. Science was something to believe in, not something which should be understood. Soon the bestsellers among the popular science books became those that presented scientific results as insults to common sense. One of the consequences was that the limit between science and pseudo-science began to be erased. To most people it was increasingly difficult to find any difference between science and science fiction."^ Worse still, the constant reiteration of science's incomprehensibility could not fail to turn many against science and encourage anti-intellectualism.”
THE BIG BANG NEVER HAPPENED
Eric J. Lerner
“THE TROUBLE WITH PHYSICS
In this illuminating book, the renowned theoretical physicist Lee Smolin argues that fundamental physics – the search for the laws of nature- is loosing its way. Ambitious ideas about extra dimensions, exotic particles, multiple universes, and strings have captured the public’s imagination- and the imagination of experts. But these ideas have not been tested experimentally, and some, like string theory, seem to offer no possibility of been tested. Yet these speculations dominate the field… As Smolin points out, the situation threatens to impede the very progress of science…” Brian Appleyard, Sunday Times(London)” "
Edgar Paternina
Retired electrical engineer
How do mathematicians recognize the article entitled "On the Nature of Some Euler's Double Equations Equivalent to Fermat's Last Theorem", published in Mathematics, Volume 10, Issue 23 (December-1 2022) by MDPI?
btw have u ever know about math bounded and reality bounded? for example it happen when student interpret the solution of problem toward mathematics. if you have experience or research about that, please let me know and lets discuss it. Thannk you!
Greetings mathematicians and physicists,
As we know, the idea of assuming a higher space dimension than the natural 3 dimension is effective in solving many physical and mathematical problems.
Here, I'll pose some philosophical questions about " time ", and I don't know where they'll lead us when we try to answer them.
- Why isn't time expressed in two or more variables, like space?
- Do we really live in one time?
- What happens to ODE and PDE when we impose temporal duality in the unknown, such as u(t,s) and u(t,s,x)?
- Now, what is the exact solution of this differential equation: u_t(t,s)+u_s(t,s)-u(t,s)=0, u(0,0)=u_0, t,s>0.
I look forward to hearing from you soon. Thank you so much.
Best from Algeria,
Khaldi Said, Phd student in mathematics.
There are several definitions of mathematical creativity. Please share your favorite definition of mathematical creativity
Recent research papers and journals on indigenous knowledge system
Is there any geometrically derived mathematical expression for the duration of the natural day at any latitude and any time of the year?
In the isosceles triangle ABC (AC=AB), the angle at the vertex is 20°.
Point D is chosen on the side AB such that AD=BC.
Find the measure of angle CDB.
another way ... construct an equilateral triangle ADE with side AD where point E is located outside the triangle ABC (on the right side of line AC) ... find 2 congruent triangles:
ABE and BAC
because AB is a common side, AE = BC, and the angle between these corresponding sides is 80 degrees, ... therefore BE=AC
next, triangle ADB is congruent to to triangle EDB
because both triangles have 3 equal sides,
thus, angle ABD = angle EBD = a half of 20 ... etc.
Please give answer. Also explain mathematical equations behind this.
