Science topics: Mathematics
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Mathematics, Pure and Applied Math
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I'm reading an article titled "Scientists Seek Life Across the Multiverse" and it says,
"If the multiverse hypothesis is correct, physicists would no longer have to find explanations for the absurdly improbable fine-tuning of the laws of nature that has made our existence possible. We are just lucky to live in a good universe among many different ones. One universe fine-tuned for life is an unlikely fluke. But one habitable universe among many is to be expected."
Another way of phrasing this is - Scientists are so eager to avoid any notion of Intelligent Design of the cosmos that they're willing to deny Earth's own scientific potential ... and their own intelligence.
Evolution can be observed in the form of adaptation of structure and function to the environment but there’s no reason to extrapolate this theory in order for it to account for life’s origin. In future centuries, human technology will develop terraforming and incredibly advanced bioengineering of cells - amino acids, proteins, water, nucleic acids, etc which were gathered in space or on planets and combined (science already knows these molecules exist out there). This could account for life’s origin since it agrees with 19th-century chemist Louis Pasteur’s proving that life can only originate from life. The origin-of-life hypothesis presented here obviously needs time travel back to a time when there was no life. This is feasible using General Relativity's concept of curved time (which is made circular via Wick rotation and future warping of space-time).
It's convenient to say Wick rotation is a form of mathematical trickery but explanation of the photoelectric effect seems to have sprung directly from Max Planck's idea of quanta - now called photons - which was also regarded for years as a mathematical convenience. Could an extension of evolution spring directly from the supposed math trickery of Wick rotation? We only need to be open to our current interpretations of science and maths not being set in stone. History has shown that presently accepted theories always change. And we are not the endpoint of history - we're simply one more step passing through it.
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The main aspect of this problem is the frequency and intensity of interaction between the elements of the Multiverse. If these parameters are large enough, then natural selection can produce results that would seem unprofitable and very strange in our Universe, but quite rational in one or more parallel ones.
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"Paper 4: Mathematical Framework for the Alcubierre Drive Using New Quarks: Unifying Dark Energy and Dark Matter"
The Dodecahedron Linear String Field Hypothesis (DLSFH) provides a viable theoretical foundation for the Alcubierre drive. By defining new quarks with the necessary properties to generate negative energy density and manipulate spacetime, this framework supports the feasibility of faster-than-light travel.
I invite the community to discuss this grand idea and our understanding of the need to explore new physics to fill the gap that Quantum Mechanics currently is missing!
A Theoretical Physicist, above all things, must have imagination and be a philosopher before he can part any knowledge of the Universe!
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I want to research on the affectivity of blended learning in Mathematics
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The general objective of the study is to explore the coping mechanisms used by mathematics teachers to improve teaching and learning in overcrowded classrooms at ...................
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There are many possibilities. Here are two major options:
1. Self-efficacy. See Bandura and social learning theory or social cognitive theory.
2. Resiliency theory. Many different models exist.
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If we have the iterative functions X= X2+Y, where X is complex number and Y constant complex number. Can one find the Y and initial value of X in iterative function from generated sequences mathematically in order to generate next values?
I look forward your comments.
Best wishes.
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Dear Qasim Mohammed Hussein, I suppose you are referring to the difference equation zn+1=zn2+c, with c being a complex constant. But, what do you mean by "generated sequences"? Do you have some terms of some solution of the difference equation and you want to calculate the constant c and the inintial condition z1? If this is the case, then the constant c is the difference of any term from the square of the previous terms; i.e.,
c=zn+1-zn2. Then, to calculate the initial condition z1, you may solve the difference equation for zn; thus, obtaining zn in terms of zn+1 and the constant c that you have calculated, and going backwards to find
zn,zn-1,...,z1.
It may be useful to note that the difference equation zn+1=zn2+c provides the famous Mandelbrot set; see, https://mathworld.wolfram.com/MandelbrotSet.html.
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FOR ME incredible! Discovering a proof for Goldbach's Conjecture is a monumental achievement in the realm of number theory. I perseverance and insight have unlocked a solution to one of mathematics' most intriguing mysteries.
MY discovery not only sheds light on a centuries-old problem but also enriches OUR understanding of prime numbers and their intricate relationships.I WILL PUBLISHE THIS AFTER TWO DAYS INSHALLHA IN WORLD.
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I would be delighted to read your proof.
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Hello ResearchGate Community,
I am an accomplished Assistant Professor and Research Associate with a diverse background spanning over 13 years in both industry and academia. Currently completing my PhD in Mathematics, with an anticipated date of July 2024, I am eager to leverage my expertise in technology adoption, statistical and mathematical modeling, and structural equation modeling (SEM) to contribute to cutting-edge research initiatives.
Skills:
Proficient in technology adoption strategies, statistical and mathematical modeling techniques, including Structural Equation Modeling(SEM) and Artificial Neural Networks(ANN). Extensive experience utilizing tools such as SPSS and AMOS to analyze data and derive meaningful insights.
Interests:
Passionate about leveraging mathematics and statistics to drive technological advancement, particularly in the realms of e-learning and online education.
Interested in exploring the dynamics of technology adoption, usage, and acceptance within higher education institutions, with a focus on post-adoption behavior, continuous intention usage, and actual usage patterns.
I am seeking a postdoctoral opportunity where I can collaborate with like-minded researchers to address complex challenges at the intersection of mathematics, statistics, and technology adoption. My goal is to contribute to the development of innovative solutions that enhance the effectiveness of educational technologies and inform strategies for organizational change.
If you are aware of any leads/opportunities or research projects aligned with my expertise and interests, I would welcome the opportunity to connect and explore potential collaborations. Please feel free to reach out to me here on ResearchGate or via email at [rockinshard@gmail.com]
Thank you for your consideration.
Warmly,
Shard
Assistant Professor | Research Associate |
PhD Candidate in Mathematics
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My paper has been published in European Journal of Mathematics and Statistics, vide Volume 4. No.6 ( 2023)
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I have today submitted my new paper on Fermat's Last Theorem to some editor.
P.N.Seetharaman
May 19, 2024.
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I would like to support students to demonstrate their understanding of the mathematical contents, any ideas or strategies about this?
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For small classes where the class size is less than 20 students:
Each week, each student may be asked to present one of their weekly homework solutions in front of the whole class on the board for 5 minutes (per student).
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Does developing reading, written, and audio mathematical language and developing students’ understanding of this language lead to the possibility of improving mathematical communication and solving verbal problems?
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I added questions on the assessment section (tasks like learning project or Investigation)
1. what have you done during the project?
2. what have you learned? what math knowledge/methods/content did you use when solving the problem?
3. describing and analyses the solutions( like graph, value table, does your solutions are reasonable? etc)
4. any challenges? what do you want to improve ?
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The circle touches AB and AC the lateral sides of the isosceles triangle ABC at the vertices B and C (Fig. 1).
On the arc of this circle, which lies inside this triangle, there is a point K so that the distances from it to the sides AB and AC are equal to 24 cm and 6 cm appropriately (Fig. 2).
Find the distance from point K to side BC.
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Liudmyla Hetmanenko , Steftcho P. Dokov Not necessarly to consider two pairs of similar triangles, because:
quadrilaterals CFKE_1 and BFKE_2 are inscriptible, so
1. angle FKE_1=angle FKE_2 (= 180-C=180-B)
2. angle FE_1K=angle FCK=1/2 arc KB=angle KBE_2=angle KFE_2,
then triangles E_1KF and FKE_2 are similar, and from here KE_1/KF=KF/KE_2 which implies KF = 12
NOTE: Trying to understand Yosef M. Yoely's answer I have some doubts! First, I thought Yosef quickly saw the similarity of triangles E_1KF and FKE_2! If not, maybe Yosef told himself that quadrilaterals CFKE_1 and BFKE_2 are similar because they have equal angles......=>conclusion.....which is not correct, two quadrilaterals with all equal angles are not necessarily similar (for example a square and a rectangle that is not a square !!).
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One doesn't need to be a philosopher, but understanding philosophical concepts relevant to their field, like epistemology or ethics, can enhance critical thinking and methodology in science, promoting more robust and ethical research practices.
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Need assistance 5 topics for my research project. But prefer them to be more related to Mathematics and Natural sciences and Health Education for senior primary learners!
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you can work on impact of AI of primary education
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The question seems to be whether mathematics is necessary or not, but the question mark is that if mathematics is essential for physics, chemistry and almost all other subjects, then they should change their methods and language to something understandable for teachers of these subjects.
Which makes sense.
Classical mathematical language and formations are redundant, in many cases illogical and contradictory, and they furthermore have the structural appearance of a heroglipic language.
Personally, I and too many of my mathematician and physicist friends find ourselves paralyzed when faced with the simplest mathematical situation.
So what !?
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Normally we do not comment on the answers of our fellow contributors but when the answer ("nature can only be described in a unitary four-dimensional x-t space"
There is no basis for this claim.)
comes from our friend Professor John Francis Miller, this should be different.
You can't ask Mother Nature if she lives and performs her functions in 3D+t space or in 4D unitary space?
But when you model nature in a 4D unit space and the numerical results in solving problems in all areas of mathematics and physics are precise and breathtaking, we consider that a respectable baseline.
We remind you that the real proof of the Schrödinger equation only comes from its exact and diverse applications.
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I have gathered 5 expert's opinion. However, as I checked for the consistency index and consistency ratio it is > 0.10 which is considered inconsistent. What are some methods u may suggest to make it acceptable? I have read some papers but I am not a mathematics major so I don't have enough knowledge to understand them.
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Please elaborate your problem in detail.
What is your topic to assess?
5 experts don't seem sufficient
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We invite discussions, suggestions, and collaborations on the following: Mathematics is the mother of all the sciences, engineering and technology, and a normed division algebra of all dimensions is the holy grail of mathematics. Singh along with Prof. SD Joshi (IIT Delhi) and Prof. Anubha Gupta (IIIT Delhi) developed normed division algebra of all dimensions which is available in preprint at: https://doi.org/10.13140/RG.2.2.18553.65120/3
A summary of "On the hypercomplex numbers and normed division algebra of all dimensions: A unified multiplication":
Key Points:
  • Expanding Number Systems: The paper proposes a way to create hypercomplex numbers (numbers with more than two dimensions) that extend the traditional complex numbers.
  • Overcoming Dimension Limitations: It challenges the previous belief that only four real division algebras exist (with dimensions 1, 2, 4, and 8).
  • Unified Multiplication: It introduces a new multiplication method, called "scaling and rotative multiplication," that enables the formation of normed division algebras in any finite dimension.
  • Key Properties:These hypercomplex number systems are non-distributive, meaning that the usual distributive property of multiplication over addition doesn't hold. They are compatible with existing multiplication for dimensions 1 and 2, meaning they smoothly extend complex numbers.
Potential Implications:
  • Broader Mathematical Applications: This work could lead to new developments in various mathematical fields, such as abstract algebra, geometry, and analysis.
  • New Frontiers in Physics and Engineering: Hypercomplex numbers have a history of applications in physics and engineering, so this expansion could open up new possibilities in those areas.
Next Steps:
  • Further Exploration: Further research is needed to explore the properties and potential applications of these generalized hypercomplex numbers and their associated algebras.
  • Rigorous Evaluation: The mathematical community will need to carefully evaluate the proposed multiplication method and its implications.
  • Interdisciplinary Collaboration: Collaborations between mathematicians, physicists, and engineers could help uncover new applications for these generalized number systems.
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Dear colleagues
In many articles I read that AHP has a strong mathematical foundation. I wonder if somebody can explain mathematically each of the steps in the AHP and ANP. Specifically, I am asking for somebody to explain rationally the following aspects:
1- It makes sense using pair-wise comparisons between two different criteria, but which is the mathematical justification of using intuition values to indicate the preferences of the DM, other than in personal problems?
2- The results from the Eigen Values (EV) or geometric mean analysis are trade-off values. Could somebody explain why they are considered equivalent to weights, when they are two different things?
3- Why in AHP AV is preferred to geometric mean?
4- Is it valid to assume that criteria preferences are constant?
5- Is it natural that the selection of criteria does not take into account the alternatives they have to evaluate? It appears that in so doing the preferences are constant, no matter to what alternatives or problem they refer. For instance, a preference of say quality is twice preferred to price, is applicable to everything, meaning that the DM cannot change his/her preferences in aspects so different as selecting a restaurant, buying a car or selecting a long-distance transportation mean.
6- Is there any axiom or theorem that says that the DM estimates must comply with transitivity?
7- Is there any axiom or theorem that says that these values and transitivity can be applied to the real world?
8- Is there any axiom or theorem that supports the idea that subjective weights can evaluate alternatives, or is it intuitive?
9- Is it real and valid that increasing or decreasing the importance of a criterion can be compensated by proportional changes in others? In case it is true, why should it be proportional? Simply because its sum is one?
10- Have users realized that decreasing, say one level, in the Saaty Fundamental Scale, is not as little as it appears to be?
11- AHP was in 1983 charged with Rank Reversal, which is true, albeit further it was found that RR happens in all MCDM methods. Does anybody know why or at least the cause that produces it, irrelevant the method?
12- Why is it assumed that a ranking is invariant when adding alternatives?
13- In sensitivity analysis, most methods work with increasing or decreasing the importance of only one criterion, while keeping the others constant. Is that realistic?
14- On what grounds AHP considers that the criterion with the highest weight is the most important. Is than correct or it is intuitive?
Thank you for your answers
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Dear Mr. Sing
Thank you for your answer
If I don't remember wrong, I mentioned that EV and Geometric mean are the only mathematical tools used by AHP.
Could you please tell me where is the mathematics in pair-wise comparisons? I fail to see any, other than comparison of criteria and assigning an intuitive preference to it.
Is this mathematical for you?
It is true that it is widely used, by respected? By who?
Not precisely for more that 100 scientists. I have also published a list of them with their opinions, could you please do the same with people supporting AHP?
You are right that proof may be elusive not only for AHP but also for all MCDM methods, since there is not a yardstick linked with reality that we can use as a reference.
However, don't you think that MCDM methods, that reach results based on reasoning, discussions, research, experience, must perform AHP's results based on intuitions and feelings?
You responded your own question when saying "subjective judgements involved".
"Numerous studies validating"? Could you mention at least one, based of course, on mathematics?
You speak of consistency, and of course, you realize that said consistency is applied to the DM estimates, nothing wrong with that.
Now I ask you two things
1- Why there should be consistency?
Do you think that an estimate done in good faith by a human being must be corrected by a formula? Too bad that there are not a formula for MCDM problms
2- Why the estimates from a person, must apply to the real-world?
Which is the mathematical axiom or theorem that supports that assumption? What happens if another DM has different estimates? Does it mean that there are two or more realities?
Not even the Quantum Theory or the Theory of Relativity propose that.
Well perhaps, if we adhere to the hypothesis of the parallel worlds
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We developed a mathematical model from mathematical point of view and we need tumor growth data that reflect number of tumor cells respect to time for our validation. We are not expert in this field and we need help from experts.
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Hello dear Abolfazl Ghoodjani. Thanks for your response. Yes ,this picture is what we need. I tried the way you said, but I didn't get the desired result. I will try this way again.
I was also very happy to communicate with you.
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We assume the answer is yes.
Furthermore, this is to be expected to occur in the heat diffusion equation and Schrödinger's PDE from a physical and mathematical point of view.
The question arises: does their combination simplify or complicate the solution?
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This is just a brief response to shed some light on the question and its answer and to thank our fellow contributors for their helpful answers.
We agree with the revealing response of our fellow professor from Bask-Spain.
The linear combination of these two conditions at a boundary exists but little mentioned (Robin boundary condition) and is expressed mathematically as:
a f + b df/dx=c, where f is the function of interest and a,b,c are 3 constants
It's clear that,
i-if a/b tends towards 0, we recover Neumann
ii-if b/a tends towards 0, we recover Dirichlet
iii-when c = 0, in the context of the diffusion equation, this can be interpreted as a partially absorbing/partially reflecting boundary where particles are both reflected and absorbed onto the assigned contact boundaries with some probability.
For diffusion, in certain geometries, the analytical expression in the form of an infinite series can be obtained by spectral decomposition of the Laplace operator, and the results are, in a way, more "complicated" than the solution of Dirichlet or of Neumann. This more “complicated” solution describes a more general phenomenon which also contains solutions for the Dirichlet and Neumann boundary conditions as limiting cases.
However, we assume that Bmatrix chain techniques can find solutions for the combined Dirichlet and Neumann boundary conditions, which is as simple as a solution for Dirichlet or Neumann alone.
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I am interested to calculate the peierls barrier for the movement of screw dislocation in BCC iron between two peierls vally. For this I am using nudged elastic band (NEB) method in LAMMPS.
We developed initial and final replicas using ATOMSK. However we have to create intermediate replicas having Kinks (between initial and final position) using linear interpolation.
Is there any mathematical relation for generating such replicas or any software that can be used for the same purpose.
Please leave your comments.
Thanks
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LAMMPS will be able to give you the intermediate configurations from the NEB calculations.
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We assume that this is true nowadays, because two mathematicians from two different mathematical fields can hardly find a common language to communicate.
The question arises: is it possible to reorganize at least the mathematical language?
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If we say yes, so, Human brain matrics are narrawer than mathematics ones and this is a mistaken claim!
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The mathematical derivation of the two-dimensional trapezoidal rule formula sounds like academic hum and numerical calculations using this formula deceive or mislead you.
So what?
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Newton-Cotes formulas and Gaussian quadratures are numerical approximation frameworks for integration that encompass trapezoidal rule while expanding numerical integration beyond...
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In general relativity, singularities, like those theorized to exist at the centres of black holes or at the origin of the Big Bang, present unique challenges to both mathematical and physical understanding. These singularities are characterized by conditions where physical laws as currently understood cease to be predictable or observable. This raises a fundamental question: Are singularities purely mathematical constructs that exist beyond the Planck scale, and thus beyond the scope of empirical validation?
General relativity predicts the existence of singularities, regions of infinite density where the gravitational field becomes infinite. Notably, the mathematical representation of these singularities involves values that approach division by zero, which is undefined and non-physical. For example, the Friedman-Robertson-Walker (FRW) solution to Einstein's field equations, which underpins the standard Big Bang model, indicates a singularity at the time of the universe's inception.
These singularities occur at scales smaller than the Planck scale, where the effects of quantum gravity are hypothesized to become significant, yet remain unquantified by existing theories. As such, singularities are not observable with current technology or provable by existing physical laws, which are based on empirical evidence. This limitation leads to the interpretation of singularities as mathematical abstractions rather than physical entities.
Given these considerations, should singularities be viewed solely as theoretical constructs within the mathematical frameworks of cosmology and black hole physics? How might advances in theoretical physics, particularly in quantum gravity, change our understanding of these enigmatic features? Whether and how singularities might bridge the gap between current mathematical theory and physical reality.
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To my understanding of our universe...there is no singularity exist in the universe, because everything is duality, general relativity is about one sun, three planets and one moon, not the universe with billions of galaxies, and our physic does not describe nature with pressure, temperature, colors, taste, smells...., where it is changing constantly. Thus the quest is invalid.
Please read my articles for more understanding.
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Imagine an enormous cylinder in a flat landscape. You are standing along the inner edge. How big would the cylinder need to be for you to not see the curvature? I.e., Instead think you are standing along a completely flat wall. Consider an average person with average eyesight. Would happily accept both the motivation, answer and calculation.
Bonus question: If you had any particular practical tools to your disposal to improve your estimate of the curvature in this scenario, what would they be and how would they help?
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Thank you for you answer Belyazid Abdellatif , if I understand it correctly, are you talking about the curvature of the earth, or the curvature of the cylinder? As I am wondering how big the cylinder need to be for you to not notice the curvature of the cylinder, not the curvature of the earth being obscured by the cylinder. Or are you meaning that the curvature of the cylinder can only be obscured by the inherent curvature of the earth? I thought that the curvature of the cylinder would be unnoticable at a smaller distance than caused by the curvature of the earth?
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1)Maybe I'm slightly less intuitive. I
consider myself kind of a skeptical empiricist/critical rationalist.
2)I don't believe concepts are eternal because they need to be adjusted to avoid contradictions.
3)Without some transcendence beyond materialism, we would NOT be able to reason.
4)Maybe reason is the ONLY absolute CONCEPT. And reason derives from God.
5)Concepts also aid execution thus, maybe I'm a more skeptical Aristotelian.
Sources:
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There is nothing wrong with being reasonable or rational in how your base your fundamental views and perception of the universe. However we live in a society where there are thousands of beliefs and variations of beliefs exist. In order to live together, we must use our intelligence for tolerance, to live with each other. It is not important to define our perceptions, but to understand them how they are.
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I believe that it is common knowledge that mathematics and its applications cannot directly prove Causality. What are the bases of the problem of incompatibility of physical causality with mathematics and its applications in the sciences and in philosophy?
The main but very general explanation could be that mathematics and mathematical explanations are not directly about the world, but are applicable to the world to a great extent.
Hence, mathematical explanations can at the most only show the general ways of movement of the processes and not demonstrate whether the ways of the cosmos are by causation, what the internal constitution of every part of it is, etc. Even when some very minute physical process is mathematized, the results are general, and not specific of the details of the internal constitution of that process.
No science and philosophy can start without admitting that the cosmos exists. If it exists, it is not nothing, not vacuum. Non-vacuous existence means that the existents are non-vacuously extended. This means that they have parts. Every part has parts too, ad libitum, because each part is extended and non-infinitesimal. Hence, each part is relatively discrete, not mathematically discrete.
None of the parts of any physical existent is an infinitesimal. They can be near-infinitesimal. This character of existents is Extension, a Category directly implied by the To Be of Reality-in-total.
Similarly, any extended being’s parts -- however near-infinitesimal -- are active, moving. This implies that every part has so (finite) impact on some others, not on infinite others. This character of existents is Change.
No other implication of To Be is so primary as these two (Extension-Change) and directly derivable from To Be. Hence, they are exhaustive of To Be.
Existence in Extension-Change is what we call Causality. If anything is existent, it is causal – hence Universal Causality is the trans-scientific and physical-ontological Law of all existents.
By the very concept of finite Extension-Change-wise existence, it becomes clear that no finite space-time is absolutely dense with existents. Hence, existents cannot be mathematically continuous. Since there is continuous (but finite and not discrete) change (transfer of impact), no existent can be mathematically absolutely continuous or discrete in its parts or in connection with others.
Can logic show the necessity of all existents as being causal? We have already discussed how, ontologically, the very concept of To Be implies Extension-Change and thus also Universal Causality.
WHAT ABOUT THE ABILITY OR NOT OF LOGIC TO CONCLUDE TO UNIVERSAL CAUSALITY?
In my argument above and elsewhere showing Extension-Change as the very exhaustive meaning of To Be, I have used mostly only the first principles of ordinary logic, namely, Identity, Non-contradiction, and Excluded Middle, and then argued that Extension-Change-wise existence is nothing but Universal Causality, if everything existing is non-vacuous in existence.
For example, does everything exist or not? If yes, let us call it non-vacuous existence. Hence, Extension as the first major implication of To Be. Non-vacuous means extended, because if not extended, the existent is vacuous. If extended, everything has parts.
The point of addition now has been Change, which makes the description physical. It is, so to say, from experience. Thereafter I move to the meaning of Change basically as motion or impact.
Naturally, everything in Extension must effect impacts. Everything has further parts. Hence, by implication from Change, everything causes changes by impacts. Thus, we conclude that Extension-Change-wise existence is Universal Causality. It is thus natural to claim that this is a pre-scientific Law of Existence.
In such foundational questions like To Be and its implications, we need to use the first principles of logic, because these are the foundational notions of all science and no other derivative logical procedure comes in as handy. In short, logic with its fundamental principles can help derive Universal Causality. Thus, Causality is more primary to experience than the primitive notions of mathematics.
Extension-Change, Universal Causality derived by their amalgamation, are the most fundamental Metaphysical, Physical-ontological, Categories. Since these are the direction exhaustive implications of To Be, all philosophy and science are based on these.
Bibliography
(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.
(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.
(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.
(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.
(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.
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Why are numbers and shapes so exact? ‘One’, ‘two’, ‘point’, ‘line’, etc. are all exact. But irrational numbers are not so. The operations on these notions are also intended to be exact. If notions like ‘one’, ‘two’, ‘point’, ‘line’, etc. are defined to be so exact, then it is not by virtue of the exactness of these substantive notions, but instead, due to their being defined so, that they are exact, and mathematics is exact.
But on the other side, due to their being adjectival: ‘being a unity’, ‘being two unities’, ‘being a non-extended shape’, etc., their application-objects are all processes that can obtain these adjectives only in groups. These are pure adjectives, not properties which are composed of many adjectives.
A quality cannot be exact, but may be defined to be exact. It is in terms of the exactness attributed to these notions by definition that the adjectives ‘one’, ‘two’, ‘point’, ‘line’, etc. are exact. This is why the impossibility of fixing these (and other) substantive notions as exact misses our attention.
If in fact these quantitative qualities are inexact due to their pertaining to groups of processual things, then there is justification for the inexactness of irrational numbers, transcendental numbers, etc. too. If numbers and shapes are in fact inexact, then not only irrational and other inexact numbers but all mathematical structures should remain inexact except for their having been defined as exact.
Thus, mathematical structures, in all their detail, are a species of qualities, namely, quantitative qualities. Mathematics is exact only because its fundamental bricks are defined to be so. Hence, mathematics is an as-if exact science, as-if real science. Caution is advised while using it in the sciences as if mathematics were absolutely applicable, as if it were exact.
Bibliography
(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.
(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.
(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.
(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.
(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.
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Mathematical Generalities: ‘Number’ may be termed as a general term, but real numbers, a sub-set of numbers, is sub-general. Clearly, it is a quality: “having one member, having two members, etc.”; and here one, two, etc., when taken as nominatives, lose their significance, and are based primarily only on the adjectival use. Hence the justification for the adjectival (qualitative) primacy of numbers as universals. While defining one kind of ‘general’ another sort of ‘general’ may naturally be involved in the definition, insofar as they pertain to an existent process and not when otherwise.
Why are numbers and shapes so exact? ‘One’, ‘two’, ‘point’, ‘line’, etc. are all exact. The operations on these notions are also intended to be exact. But irrational numbers are not so exact in measurement. If notions like ‘one’, ‘two’, ‘point’, ‘line’, etc. are defined to be so exact, then it is not by virtue of the exactness of these substantive notions, but instead, due to their being defined as exact. Their adjectival natures: ‘being a unity’, ‘being two unities’, ‘being a non-extended shape’, etc., are not so exact.
A quality cannot be exact, but may be defined to be exact. It is in terms of the exactness attributed to these notions by definition that the adjectives ‘one’, ‘two’, ‘point’, ‘line’, etc. are exact. This is why the impossibility of fixing these (and other) substantive notions as exact miss our attention. If in fact these are inexact, then there is justification for the inexactness of irrational, transcendental, and other numbers too.
If numbers and shapes are in fact inexact, then not only irrational numbers, transcendental numbers, etc., but all exact numbers and the mathematical structures should remain inexact if they have not been defined as exact. And if behind the exact definitions of exact numbers there are no exact universals, i.e., quantitative qualities? If the formation of numbers is by reference to experience (i.e., not from the absolute vacuum of non-experience), their formation is with respect to the quantitatively qualitative and thus inexact ontological universals of oneness, two-ness, point, line, etc.
Thus, mathematical structures, in all their detail, are a species of qualities, namely, quantitative qualities, defined to be exact and not naturally exact. Quantitative qualities are ontological universals, with their own connotative and denotative versions.
Natural numbers, therefore, are the origin of primitive mathematical experience, although complex numbers may be more general than all others in a purely mathematical manner of definition.
Bibliography
(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.
(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.
(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.
(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.
(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.
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THE FATE OF “SOURCE-INDEPENDENCE” IN ELECTROMAGNETISM, GRAVITATION, AND MONOPOLES
Raphael Neelamkavil, Ph.D., Dr. phil.
With the introductory claim that I make here suggestions that seem rationally acceptable in physics and the philosophy of physics, I attempt here to connect reasons beyond the concepts of magnetic monopoles, electromagnetic propagation, and gravitation.
A magnetic or other monopole is conceptually built to be such only insofar as the basic consideration with respect to it is that of the high speed and the direction of movement of propagation of the so-called monopole. Let me attempt to substantiate this claim accommodating also the theories in which the so-called magnetic monopole’s velocity could be sub-luminal.
If its velocity is sub-luminal, its source-dependence may be demonstrated, without difficulty, directly from the fact that the velocity of the gross source affects the velocity of the sub-luminal material propagations from it. This is clear from the fact that some causal change in the gross source is what has initiated the emission of the sub-luminal matter propagation, and hence the emission is affected by the velocity of the source’s part which has initiated the emission.
But the same is the case also with energy emissions and the subsequent propagation of luminal-velocity wavicles, because (1) some change in exactly one physical sub-state of the gross source (i.e., exactly the sub-state part of the gross source in which the emission takes place) has initiated the emission of the energy wavicle, (2) the change within the sub-state part in the gross source must surely have been affected also by the velocity of the gross source and the specific velocity of the sub-state part, and (3) there will surely be involved in the sub-state part at least some external agitations, however minute, which are not taken into consideration, not possible to consider, and are pragmatically not necessary to be taken into consideration.
Some might claim (1) that even electromagnetic and gravitational propagations are just mathematical waves without corporeality (because they are mathematically considered as absolute, infinitesimally thin waves and/or infinitesimal particles) or (2) that they are mere existent monopole objects conducted in luminal velocity but without an opposite pole and with nothing specifically existent between the two poles. How can an object have only a single part, which they term mathematically as the only pole?
The mathematical necessity to name it a monopole shows that the level of velocity of the wavicle is such that (1) its conventionally accepted criterial nature to measure all other motions makes it only conceptually insuperable and hence comparable in theoretical effects to the infinity-/zero-limit of the amount of matter, energy, etc. in the universe, and that (2) this should help terming the wavicle (a) as infinitesimally elongated or concentrated and hence as a physically non-existent wave-shaped or particle-shaped carrier of energy or (b) as an existent monopole with nothing except the one mathematically described pole in existence.
If a wavicle or a monopole is existent, it should have parts in all the three spatial directions, however great and seemingly insuperable its velocity may be when mathematically tested in terms of its own velocity as initiated by STR and GTR and later accepted by all physical sciences. If anyone prefers to call the above arguments as a nonsensical commonsense, I should accept it with a smile. In any case, I would continue to insist that physicists want to describe only existent objects / processes, and not non-existent stuff.
The part A at the initial moment of issue of the wavicle represents the phase of emission of the energy wavicle, and it surely has an effect on the source, because at least a quantum of energy is lost from the source and hence, as a result of the emission of the quantum, (1) certain changes have taken place in the source and (2) certain changes have taken place also in the emitted quantum. This fact is also the foundation of the Uncertainty Principle of Heisenberg. How then can the energy propagation be source-independent?
Source-independence with respect to the sub-luminal level of velocity of the source is defined with respect to the speed of energy propagation merely in a conventional manner. And then how can we demand that, since our definition of sub-luminal motions is with respect to our observation with respect to the luminal speed, all material objects should move sub-luminally?
This is the conventionally chosen effect that allegedly frees the wavicle from the effect of the velocity of the source. If physics must not respect this convention as a necessary postulate in STR and GTR and hence also in QM, energy emission must necessarily be source-dependent, because at least a quantum of energy is lost from the source and hence (1) certain changes have taken place in the source, and (2) certain changes have taken place also in the emitted quantum.
(I invite critical evaluations from earnest scientists and thinkers.)
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Every common source avoids the derivation, saying it to be too difficult. Where can i fiend volterra's original derivation? Knowing which mathematics would be necessary?
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You can find the derivation of the stress field of an edge dislocation at my lab website: https://sites.google.com/view/nmml-iisc/blog
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Dear colleagues
I am pleased to inform you that the International Conference on Nonlinear Analysis and Applications (ICNAA 2024) & Symposium on Ancient Indian Mathematics (in the memory of Late Professor S. L. Singh) is being organized by the Department of Mathematics, Pt. L. M. S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, Uttarakhand, India from May 10 to May 12, 2024 (https://icnaaa2024.wordpress.com).
Your active participation in the conference will undoubtedly contribute to the success of the event.Kindly submit the abstract of your talk at your earliest convenience.
Looking forward to your valuable contribution.
Best Regards
Anita Tomar
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Excellent news! Thanks
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Eh, I'd rather be mysteriously confusing than rigorously understandable any day. Keeps people on their toes, you know? :P
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Hello
I'm learning camsol. I studied the mathematical particle tracking method used for modeling in turbomolecular pumps, and I can model a single-stage rotor, but I can not model a single-stage rotor and stator.
Can you guide me, please?
thanks
maryam
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Now I can simulate a row of rotor and stator
My next problem is to run DSMC with Comsol software. Can I implement this method with this software?
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Hello everyone,
I am currently undertaking a research project that aims to assess the effectiveness of an intervention program. However, I am encountering difficulties in locating suitable resources for my study.
Specifically, I am in search of papers and tutorials on multivariate multigroup latent change modelling. My research involves evaluating the impact of the intervention program in the absence of a control group, while also investigating the influence of pre-test scores on subsequent changes. Additionally, I am keen to explore how the scores differ across various demographic groups, such as age, gender, and knowledge level (all measured as categorical variables).
Although I have come across several resources on univariate/bivariate latent change modelling with more than three time points, I have been unable to find papers that specifically address my requirements—namely, studies focusing on two time points, multiple latent variables (n >= 3), and multiple indicators for each latent variable (n >= 2).
I would greatly appreciate your assistance and guidance in recommending any relevant papers, tutorials, or alternative resources that pertain to my research objectives.
Best,
V. P.
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IYH Dear Vivian Parker
Ch. 19 Muthén, B. Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In D. Kaplan (ed.), Handbook of quantitative methodology for the social sciences. Newbury Park, CA: Sage.
Although this ref do not exclusively concentrate on two-time-point cases, it does contain discussions revolving around multiple latent variables and multiple indicators for those latent constructs. https://users.ugent.be/~wbeyers/workshop/lit/Muthen%202004%20LGMM.pdf
It contains rich content concerning latent growth curve models and elaborates on multivariate implementations.
While conceptually broader, it present crucial components necessary for building and applying two-time-point, multivariate latent change models.
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Greetings and courtesy to the professors and students of mathematics. I wanted to know if there is a relationship between the curves and the orthogonal paths of the differential equation with the characteristics of its solution? If the answer is yes, please state the type of relation and relational formula. Thanks
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The relationship between the categories of curves described by differential equations and the orthogonal paths, often referred to as the characteristics of its solutions, is a fascinating aspect of mathematical analysis and differential equations. This relationship has profound implications in various branches of mathematics and physics, especially in understanding the behavior of systems modeled by differential equations. Here's an overview of how these concepts are related:
  1. Differential Equations and Their Solutions: A differential equation is an equation that relates a function with its derivatives. The solutions to these equations can often be visualized as curves or surfaces in a coordinate space, where each solution represents a possible behavior of the system described by the differential equation.
  2. Categories of Curves as Solutions: The solutions to differential equations can often be categorized into families of curves or surfaces that share certain characteristics. For instance, in a two-dimensional space, solutions might form a family of parallel lines, concentric circles, or exponential curves, depending on the nature of the differential equation.
  3. Orthogonal Trajectories: The concept of orthogonal trajectories involves finding a family of curves that intersect another family of curves at right angles (orthogonally). In the context of differential equations, given a family of curves that are solutions to a particular differential equation, the orthogonal trajectories are the solutions to a related differential equation that intersects the original family of solutions orthogonally.
  4. Relationship with Characteristics of Solutions: The characteristics of solutions to a differential equation, such as stability, periodicity, or direction of flow, can often be analyzed using the concept of orthogonal trajectories. For instance, in fluid dynamics, the streamlines (paths along which fluid flows) and the equipotential lines (lines along which the potential remains constant) are orthogonal to each other. This orthogonality can provide insights into the behavior of the fluid flow, such as identifying regions of turbulence or stability.
  5. Mathematical Formalism: Mathematically, if a family of curves is described by a differential equation, the orthogonal trajectories can be found by transforming the original differential equation. This often involves a process of finding a new differential equation whose solutions are orthogonal to the solutions of the original equation. The relationship between the original differential equation and the equation for the orthogonal trajectories can reveal much about the structure and properties of the solutions.
In summary, the relationship between the categories of curves (solutions to a differential equation) and the orthogonal paths (characteristics of these solutions) is crucial for understanding the deeper properties of the solutions to differential equations. This relationship is used in various fields such as physics, engineering, and mathematics to analyze and predict the behavior of complex systems.
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I will check the complete information if some one knows. Then mention me. thanks
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I can
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Why is it necessary to study the History of Mathematics?
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A Black mathematical history
"In Journeys of Black Mathematicians, film maker George Csicsery reveals how Black scholars shaped today’s US mathematics community and provides hope for the future. “It is wonderful to learn about successes in academia and industry,” writes Black mathematician Noelle Sawyer in her review. “The question that needs to be asked now is which spaces are worth entering.” Furthering representation should not mean doing morally questionable work, such as creating weapons, argues Sawyer. “Pushing back against the inequities of the past and present should not include contributing to the oppression of others.”..."
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I am looking to estimate the diameter (nm) of a variety of double stranded plasmids (pUC19, pMAL pIII, pKLAC2, etc.) when they are natively supercoiled and when they are relaxed.
If someone could point me towards a formula it would be much appreciated! Thanks. 
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Calculating the diameter of plasmids typically involves determining the length of the plasmid DNA molecule. Plasmids are circular, double-stranded DNA molecules, and their size is commonly expressed in terms of base pairs (bp). Each base pair corresponds to approximately 0.34 nanometers (nm) of linear distance along the DNA molecule's length.
Here's how you can calculate the diameter of a plasmid:
  1. Determine the size of the plasmid: The size of the plasmid is usually provided in terms of base pairs (bp). For example, if a plasmid is 5,000 base pairs long, its length would be 5,000 bp.
  2. Convert base pairs to linear length: Multiply the number of base pairs by the length of each base pair, which is approximately 0.34 nm. This gives you the linear length of the plasmid DNA in nanometers.Linear length (nm) = Number of base pairs × 0.34 nm/bp
  3. Calculate the diameter: Since the plasmid is circular, its diameter can be calculated using the formula for the circumference of a circle.Diameter (nm) = Linear length (nm) / π
Here's a step-by-step example: Let's say you have a plasmid with 3,000 base pairs.
  1. Determine the linear length: Linear length = 3,000 bp × 0.34 nm/bp = 1,020 nm
  2. Calculate the diameter: Diameter = 1,020 nm / π ≈ 325.05 nm
So, the estimated diameter of the plasmid is approximately 325.05 nanometers.
It's important to note that this calculation provides an approximation of the plasmid's diameter based on its linear length. In reality, the plasmid molecule is not a perfect circle, and its shape and size can be influenced by factors such as supercoiling and protein binding. Additionally, experimental techniques like electron microscopy can provide more accurate measurements of plasmid size and shape.
l Take a look at this protocol list; it could assist in understanding and solving the problem.
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Category theory, with its focus on abstraction and relationships between mathematical structures, presents a promising framework for formally expressing mythologisation. This mathematical branch could potentially model the complex, symbolic narratives of myths, translating them into a system of objects and morphisms that reflect the underlying patterns and connections inherent in mythological themes. A key question arises: Can category theory effectively capture the depth and nuance of mythological narratives, preserving their rich symbolic content while providing a formal representation? Additionally, how might such a formalisation impact our understanding of myths and their role in conveying universal truths and cultural values?
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The question you address seems interesting to me : which is the relationship between "logical" structures and wisdom expressed in form of myths. Stated as this the topic is very old and it would be useful to have a look at the dialogues of Plato to be reminded of how this relationship was understood at early times. It would not expect a logical formalism like category theory to be able of rendering what myths express, for the reason that formalization has a very limited set of principles whereas human wisdom makes use of a far broader panel of dialectical methods. To take a fairly central example which is biblical wisdom (since the encyclical letter Divino afflante Spiritu) biblical exegesis has recognized the existence of different literary genres.
Other cultural environments, by the fact that they do not use our western rationality have a fairly different approach (think of Yin an Yang duality which is quite foreign in my opinion to a formalization by categorical means).
Even if the question has not been stated in terms of category theory it very likely that in modern philosophical literature (Edmund Husserl ?) you will find references to this interaction between logic and human perception. A categorical analysis could enrich or sharpen, I don't expect to be plausible that myths fit well in a categorical environment.
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- Interested in working on ethnomathematics and indigenous learning systems in mathematics.
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Hello Marc Helton Cheng Sua, consider the following:
  1. speak honestly about how mathematics has been used by colonizers towards the oppression of the colonized
  2. demonstrate how mathematical thinking is a universal trait
  3. teach mathematics in a way that leads towards the sustaining and growing of cultures that have been adversely affected by the colonial enterprise
  4. teach mathematics in a way that allows individuals to be present as their full and complete selves
  5. widen the definition of what it means to be successful in mathematics
  6. amplify the voices of those who are successful in mathematics while simultaneously maintaining and growing their connection to their culture
  7. invite students to use mathematics to solve practical problems that are important to their surrounding communities
Feel free to reach out if you need more suggestions or need anything clarified.
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Is the Fine-Structure Constant the Most Fundamental Physical Constant?
The fine-structure constant is obtained when the classical Bohr atomic model is relativisticized [1][2]. α=e2/ℏc, a number whose value lies very close to 1/137. α did not correspond to any elementary physical unit, since α is dimensionless. It may also be variable [6][7]*.
Sommerfeld introduced this number as the relation of the “relativistic boundary moment” p0=e2/c of the electron in the hydrogen atom to the first of n “quantum moments” pn=nh/2π. Sommerfeld had argued that α=p0/p1 would “play an important role in all succeeding formulas,” he had argued [5].
There are several usual interpretations of the significance of fine structure constants [3].
a)In 1916, Sommerfeld had gone no further than to suggest that more fundamental physical questions might be tied to this “relational quantity.” In Atomic Structure and Spectral Lines, α was given a somewhat clearer interpretation as the relation of the orbital speed of an electron “in the first Bohr orbit” of the hydrogen atom, to the speed of light [5].
b) α plays an important role in the details of atomic emission, giving the spectrum a "fine structure".
c) The electrodynamic interaction was thought to be a process in which light quanta were exchanged between electrically charged particles, where the fine-structure constant was recognized as a measure of the force of this interaction. [5]
d) α is a combination of the elementary charge e, Planck's constant h, and the speed of light c. These constants represent electromagnetic interaction, quantum mechanics, and relativity, respectively. So does that mean that if G is ignored (or canceled out) it represents the complete physical phenomenon.
Questions implicated here :
1) What does the dimensionless nature of α imply? The absence of dimension means that there is no conversion relation. Since it is a coupling relation between photons and electrons, is it a characterization of the consistency between photons and charges?
2) The various interpretations of α are not in conflict with each other, therefore should they be unified?
3) Is our current interpretation of α the ultimate? Is it sufficient?
4) Is α the most fundamental physical constant**? This is similar to Planck Scales in that they are combinations of other fundamental physical constants.
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Notes
* Spatial Variation and time variability.
‡ Sommerfeld considered α "important constants of nature, characteristic of the constitution of all the elements."[4]
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References
[3] 张天蓉. (2022). 精细结构常数. https://blog.sciencenet.cn/blog-677221-1346617.html
[1] Sommerfeld, A. (1916). The fine structure of Hydrogen and Hydrogen-like lines: Presented at the meeting on 8 January 1916. The European Physical Journal H (2014), 39(2), 179-204.
[2] Sommerfeld, A. (1916). Zur quantentheorie der spektrallinien. Annalen der Physik, 356(17), 1-94.
[4] Heilbron, J. L. (1967). The Kossel-Sommerfeld theory and the ring atom. Isis, 58(4), 450-485.
[5] Eckert, M., & Märker, K. (2004). Arnold Sommerfeld. Wissenschaftlicher Briefwechsel, 2, 1919-1951.
[6] Wilczynska, M. R., Webb, J. K., Bainbridge, M., Barrow, J. D., Bosman, S. E. I., Carswell, R. F., Dąbrowski, M. P., Dumont, V., Lee, C.-C., Leite, A. C., Leszczyńska, K., Liske, J., Marosek, K., Martins, C. J. A. P., Milaković, D., Molaro, P., & Pasquini, L. (2020). Four direct measurements of the fine-structure constant 13 billion years ago. Science Advances, 6(17), eaay9672. https://doi.org/doi:10.1126/sciadv.aay9672
[7] Webb, J. K., King, J. A., Murphy, M. T., Flambaum, V. V., Carswell, R. F., & Bainbridge, M. B. (2011). Indications of a Spatial Variation of the Fine Structure Constant. Physical Review Letters, 107(19), 191101. https://doi.org/10.1103/PhysRevLett.107.191101
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Dear Vladimir A. Lebedev,
Could you provide me the value of this dimensionless ratio and also the two speeds separately.
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I need to calculate the overland flow of a catchment area. I have HEC HMS software but I don't want to use it. I need a mathematical equation.
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Area of Cross-Section and Velocity as Observed at Bridge Site:
The area of cross-section is measured by taking a series of levels of the river at H.F.L. at certain intervals. The velocity in this case is determined at site by direct measurement of the velocity in place of theoretical calculation from bed slope etc.
To measure the velocity directly, the river is divided into few sections width wise and then the velocity for each section is determined by surface float placed at the centre of each section.
The time taken by the float to cover a fixed distance is noted by a stop watch and the distance travelled by the float divided by the time taken is the surface velocity of the stream. Such surface velocity is to be determined for each section and weightage average value is obtained for the purpose of flood discharge estimation.
📷
The velocity is least in the vicinity of the bed and banks and mean at the centre line of the stream at a point 0.3 d below the surface where, d, is the depth of water (see Fig. 3.6). If V, is the velocity at surface, Vb is the velocity at bottom and Vm is the mean velocity then their relationship may be established in the following equation,
Vm = 0.7 Vs= 1.3 Vb (3.15)
After the determination of the mean velocity of the stream, the flood discharge is obtained by;
Q = AVm (3.16)
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we discovered new mathematics branch for Riemann hypothesis i think do you agree with me for this proof if you agree with me please comment this. Mathematical research is a collaborative and iterative process that benefits from scrutiny and discussion within the community.
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Where is that discovered Branch? Any reference please.
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Dear researcher, what is a the most powerful computer technology support mathematics learning
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Computer technology plays a significant role in supporting mathematics learning by providing interactive tools, resources, and platforms that enhance the understanding and engagement of students. Here are some ways in which computer technology supports mathematics learning:
  1. Interactive Learning Tools: Computer software and applications offer interactive simulations, games, and activities that make learning mathematics more engaging and enjoyable for students. These tools provide immediate feedback, personalized learning experiences, and opportunities for hands-on practice.
  2. Visualization and Graphing: Computer technology enables students to visualize mathematical concepts through graphs, charts, and 3D models. Visualization tools help students understand abstract mathematical concepts, such as functions, equations, and geometric shapes, by representing them visually.
  3. Problem-solving and Critical Thinking: Computer technology supports students in developing problem-solving skills and critical thinking abilities by presenting real-world scenarios, puzzles, and challenges that require mathematical reasoning and analysis. Students can explore different approaches, test hypotheses, and evaluate solutions using digital tools.
  4. Adaptive Learning Platforms: Adaptive learning platforms use algorithms to personalize the learning experience for each student based on their strengths, weaknesses, and learning pace. These platforms adjust the difficulty level of tasks, provide targeted practice exercises, and offer remedial support to help students master mathematical concepts effectively.
  5. Online Resources and Tutorials: Computer technology provides access to a wide range of online resources, tutorials, videos, and interactive lessons that supplement traditional classroom instruction. Students can explore additional learning materials, practice exercises, and explanations to reinforce their understanding of mathematical topics.
  6. Collaboration and Communication: Computer technology facilitates collaboration among students, teachers, and peers through online discussion forums, virtual classrooms, and collaborative projects. Students can work together on math problems, share ideas, and communicate effectively using digital platforms.
  7. Assessment and Feedback: Computer technology supports formative assessment practices by providing instant feedback on students' performance, tracking their progress, and identifying areas for improvement. Teachers can use digital assessment tools to monitor student learning outcomes and adjust their instruction accordingly.
  8. Accessibility and Inclusivity: Computer technology enhances accessibility and inclusivity in mathematics learning by providing accommodations for students with diverse learning styles, abilities, and needs. Digital tools offer options for audio, visual, and tactile feedback, as well as customizable settings to support individualized learning experiences.
Overall, computer technology plays a vital role in supporting mathematics learning by offering interactive, visual, adaptive, and collaborative tools that engage students, enhance their understanding, and foster a deeper appreciation for the beauty and relevance of mathematics in the digital age.
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Many years ago I witnessed a mathematics class in Japan, in which the teacher displayed, to a class of 10 year old students, a narrow strip of paper which she identified as being one meter in length. She then proceeded to distribute one strips of paper to each child in the class, asking them to give her back "a one-half meter length of paper." Most of the students simply folded cut their strip lengthwise in half and returned one of the halves to the teacher. The teacher then placed each child's response (the actual strip of paper) on the blackboard and initiated a discussion about who had given a correct answer. I would like to find a report that refers to this research so I can share it with teachers and mathematics educators. Do you have any suggestions?
By the way, this same sort of confusion between half of the whole and half of the unit frequently appears in discussions regarding the number line. For instance, a child (or teacher) may be unsure where to locate 1/2 on a number line from 1 to 7. So I think it's a very important issue to keep track of.
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The teacher showed one strip of paper and said it was one meter long. I think you could argue that it was being treated as the whole but also as the unit. This would seem analogous to showing the students a number line from 0 to 1 and asking the student to located a certain common fraction on the line (say 1/2 or 3/4). Most young students will place the fraction at the "correct" place under this condition. But when the question is asked using a number line from 0 to 5, many students will simply find the endpoint where one half or three fourths of the number line will fall.
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Three of my articles published in Ratio Mathematics in December 2023 not yet added in research gate.
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You may add it yourself by clicking at "Add new" or "Add research" ...
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Dear Researchers,
I am reaching out to seek insights and opinions on the potential connections between chaotic dynamics, arithmetic functions, and open conjectures in analytic number theory. My interest lies in exploring the derivation of chaotic operators from mathematical constructs such as L-Dirichlet functions and conjectures like those presented by Yitang Zhang in 2022 on Landau-Siegel zeros, as well as the Montgomery conjecture on the distribution of zeros.
Specifically, I am intrigued by the possibility of deriving chaotic dynamics from these mathematical frameworks and understanding their implications for questions related to the Riemann Hypothesis.
  1. L-Dirichlet Functions and Chaotic Dynamics:Are there indications or prior research suggesting a link between L-Dirichlet functions and the derivation of chaotic operators? Has anyone explored the connection between arithmetic functions and the emergence of chaotic behavior in dynamic systems?
  2. Analytic Number Theory Conjectures:What insights can be gained from recent works, such as Yitang Zhang's 2022 theorem on Landau-Siegel zeros, regarding the potential implications for chaotic dynamics? How might the Montgomery conjecture on the distribution of zeros contribute to our understanding of chaotic systems?
  3. Riemann Hypothesis:Based on these findings, do researchers believe there is any increased validity or support for the Riemann Hypothesis? Are there specific aspects of the conjectures or arithmetic functions that may shed light on the truth or falsity of the Riemann Hypothesis?
I also want to inform you that I have recently derived a chaotic operator from Yitang Zhang's latest theorem on Landau-Siegel zeros. The work has been accepted for publication in the European Physical Journal.
My ultimate goal is to further investigate the derivation of chaotic operators from these mathematical foundations and to understand the conditions under which ζ(0.5+iH)=0. welcome any insights, suggestions, or collaboration opportunities that may arise from your expertise in these areas.
Thank you for your time and consideration. I look forward to engaging in fruitful discussions with the research community.
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There's considerable activity on all these topics, so it would be a good idea to learn to focus on the technical content rather than the sociology.
Anyone that expects to prove the Riemann hypothesis this way is bound to be disappointed. So it would be a good idea to start by not making a fool of oneself with statements full of buzzwords, but focus on learning something about the subject. Also: Technical topics don't deal with opinions.
might be useful.
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If anybody done this type of work,please answer me.
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The content of one substance in the composition of another is a mathematical term.
In particular, to determine the percentage of iodine in urine, it is necessary to divide the amount of iodine (A) by the amount of urine (B) and multiply the result by 100%.
That is: A/B*100%
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I need the above book if any one have please share with me. I will be thankful for this.
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As a lecturer you should make your university's library buy the books you need.
It is simply illegal to share copyrighted Material.
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Consciousness and mathematics
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Dear Michael,
If we go by the dictionary meaning of consciousness ("state of being aware of and responsive to one's surroundings"), in a way in each mathematical function, the dependent variable is conscious of its independent variables. For instance, in case of z=f(x,y), z is aware and is responsive to x, and y.
If we consider the psychology definition of consciousness capturing "extent of information integrated among the different parts of the brain", then the time dimension also comes into play and becomes prominent. The time dimension adds the dynamic perspective. Let me explain.
Revisiting z = f(x,y,..)
It will take the form z = f(x(t), y(t),..)
which can be approximated as
Integration of f(x(0), y(0),..),...f(x(m), y(m) ..)..
Thus, z at any point of time also contains the integrated information (not summation) of past z values. Extrapolating this analogy further, the differentiated information memorized/existing in various part of brain reflect the lived life experience of the individual/biological entity. In a way consciousness can be seen as emergent phenomenon of the mathematical dynamics which takes place as the different part of brain interacts based on triggers coming from sensory signals.
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Why the best way to learn math is to do math ?
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Doing math is like exercising a muscle; it's the most effective way to strengthen your mathematical skills. Math isn't just about memorizing formulas or theories. It's about understanding and applying concepts to solve problems. By actively engaging with math problems, you're reinforcing your understanding of mathematical principles and developing critical thinking, problem-solving, and analytical skills. Additionally, through trial and error, you gain insight into different problem-solving strategies and build resilience in the face of challenges. So, while studying theory and concepts is essential, nothing beats the hands-on experience and learning that comes from actually doing math.
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Are you a talented young mathematician and would like to continue your mathematics studies at the PhD program under my supervision at University of Ljubljana, Faculty of Mathematics and Physics? Are you simultaneously interested in the young researcher position at the Institute of Mathematics, Physics and Mechanics in Ljubljana?
If the answers to the above question are affirmative, you may contact me at aljosa.peperko(at)fs.uni-lj.si
More information about my reseach interests:
Kind regards, Aljoša Peperko
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Often PhDs dissertations are original maybe like this:
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Dear Wolfram Mathematica users, What do you consider to be the most reliable and stable version of Wolfram Mathematica that you have tried so far? For my part, the most stable version that I have tried so far is V 12.1.1, although I recognize that V 13.3.3 is superior in many aspects, especially in some graphical elements, in addition to achieving a better integration with certain repositories of the Wolfram Foundation. I have not yet tested the latest version (V 14.0).
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Hey, Hi Mohd Siddique Akbar Alam Khan . First of all thanks for the feedback. In fact, my firsts steps on Mathematica were with the v 11.2 and it seems to me a very smooth v, but I have seen that the analysis times for sequences involving prime numbers has been reduced quite a bit between 11.2 and at least v 12 onwards.
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My all proposal are rejected. I don't where it was problem. If any one have mathematical proposal ( mostly in mathematical fluid dynamics) which work was already done, please share with me and help me. I really need help.
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Please let your colleagues and native English speaker take a look over your proposal before submission. Your brief question already contains a number of grammar mistakes. You may be more successful with a polished proposal.
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How a mathematical fluid dynamics model (in most cases we solved and analysis through Navier Stokes equations and graphs) directly connect to physical models (experimental work) like mechanical ones are doing?
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Both experimental and numerical procedures are constrained by several htpotheses. Those constitute a model, you need to prescribe the math that fulfills the experinental model to have a congruent result.
if you have a more specific flow problem, the discussione could be more focused.
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benefit that a teacher get from teaching mathematics
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Teaching can have benefits whatever subject you teach. Probably when we teach a subject, it's because we love it.
So, people who teach mathematics, they disseminate something they like.
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Dear All,
Do you have any idea about any mathematics conferences that will be held in May 2024?
Regards
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The first conference in 2023 was a great success with over 800 registrations. The 2024 conference builds on this success. Participation in the conference is free of charge.
To keep the conference varied, there will be 21 presentations from different areas of statistics in clinical research. All speakers at the conference have been selected to ensure an excellent experience for the audience.
Each presentation will last 20 minutes and will also have a question and answer session. The presentations will take place on February 13, 14, and 15 between 3 and 6 pm CET.
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Fermat's last theorem was finally solved by Wiles using mathematical tools that were wholly unavailable to Fermat.
Do you believe
A) That we have actually not solved Fermat's theorem the way it was supposed to be solved, and that we must still look for Fermat's original solution, still undiscovered,
or
B) That Fermat actually made a mistake, and that his 'wonderful' proof -which he did not have the necessary space to fully set forth - was in fact mistaken or flawed, and that we were obsessed for centuries with his last "theorem" when in fact he himself had not really proved it at all?
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My two published papers in European Journal of Mathematics and Statistics on Fermat's last theorem are enclosed herewith. These are only my correct proof of mine. Please ignore the rest. I request you to kindly arrange to check my papers and offer your valuable feedback and comments please
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To improve quality instruction in secondary mathematics subject, give some strategies on how a supervisor collaborate with mathematics teachers in identifying areas needs to be improved and in implementing targeted interventions to enhance teaching and learning outcomes in mathematics.
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Rule governed behavior can be a key area of opportunity. Also, EO to enhance feedback effectiveness.
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As an author, I believe that you can share me your expertise in this matter. Thank you.
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porsupuesto. La evaluación auténtica tiene la ventaja de prestar estos múltiples servicios
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Specifically, how does subject-level random intercept and random slope influence the goodness-of-fit (R-squared) of the model?
And, if subject A contributes 10 data-points and subject B contributes 5 to the whole dataset, wouldn't A account for more of the total residual error than B? How do multilevel models control for this?
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As Rainer Duesing noted there is no such thing as R^2 for a multilevel model - at least in the sense that there is no single statistic that has all the properties of R^2. Various alternatives exist that have some of the same properties, but need to be used carefully. Also note that R^2 isn't necessarily the best goodness of fit measure in a linear model and tends to be overemphasised.
Your second question is probably more interesting because it gets at a fundamental property of multilevel models - which is they incorporate shrinkage. If we have two units A and B with 5 and 10 observations respectively we traditionally think of there being two options: (mean_A+mean_B)/2 to estimate the mean or (sum of all observations)/15. What a multilevel model does is use a kind of compromise estimate between these - effectively closer to the mean of the less noisy (often larger) unit than the (mean_A+mean_B)/2. This shrunken estimator has nice statistical properties for some purposes - arguably it is more efficient and generalises better.
There are lots of shrinkage estimators (I think) but in multilevel modeling the frequentist models use Empirical Bayes estimates.
This behaves a bit like a Bayesian prior but is estimated from the data. True Bayes also incorporates shrinkage through the prior and lots of multilevel modeling these days is Bayesian.
(The above is an attempt at a very simple non-technical explanation - there is of course more to it than this, but you really need to get a good text book for this)
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Schauder Fixed Point conjecture deals with the existence of fixed points for certain types of operators on Banach spaces. It suggests that every non-expansive mapping of a non-empty convex, weakly compact subset of a Banach space into itself has a fixed point. The status of this conjecture may depend on the specific assumptions and settings.
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A search with keywords "weak fixed point property" (which is the official name of the property you are interested in) and with "weak normal structure" (which is a widely used sufficient condition for this property) may give you a lot of information on the subject.
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I see a lot of mathematics but few interpretations in time (how it evolves, step by step with its maths).
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Thank you, I don't find by now exactly what I wanted, but it is a much better way to do the search.
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Is maths made up or real? This is the message I wrote on the website of mathematician Eugenia Cheng.
Hi! I read about you in "Nautilus" magazine. I think your statement "Some of the power of math lies in the very fact that it's made up" is a fascinating place from which to start speculating. The second step is to recall statements by Eugene Wigner and Max Tegmark. Eugene Wigner, a physicist, wrote an article in 1960 titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. He argued that mathematical concepts have applicability far beyond the context in which they were originally developed. In a recent interview, physicist and mathematician Dr. Max Tegmark, stated that “math is the true driver of the universe and the universe itself is a model of the mathematical principles”.
Something made up by humans could be unreasonably effective in the universe if humans used that maths to create the universe. That sounds impossible - pure fantasy, too unrealistic even for science fiction. But bear with me. In an article written for the magazine Nautilus, it’s stated that the journals of American physicist John Wheeler, which he always kept at hand, reveal a stunning portrait of an obsessed thinker. The article says, “He knew that quantum measurement allowed observers in the present to create the past ...” and his journal contains thoughts agreeing with “The universe has created an observer and now, in an act of quantum measurement, the observer looks back and creates the universe.” Could the origin of life be related to the movie “Interstellar”? In the movie, it’s stated that humans will oneday be able to build things they can’t make now. If we take this idea to an extreme, and take “oneday” to mean an indefinite point in the far future, will we do what is obviously regarded as impossible and create life – and conceivably, the universe itself? Someday there will be a human civilization that can build their mathematics into the creation, structure, and functioning of life and the cosmos. Emotion may well declare this an absurdity and we might retreat to things like quantum fluctuation or spontaneous creation from nothing. Logically – using Einstein’s nonlinear and interactive curved time added to limitless advance of human potential through the eons – the absurdity is plausible. Just for now, cast off any thoughts about the fragility or shortness of human existence. Believe that people will oneday be able to build things they can’t make now – and that someday there will be a human civilization that can build their mathematics into the creation, structure, and functioning of life and the cosmos.
The most fundamental ingredient in creation of the universe might be base 2 maths aka the BITS or binary digits of 1 and 0. These could be used to construct everything (even the quantum units of gravitation and electromagnetic energy), and could build in the 4 dimensions of space-time. Maybe "made up" maths is actually used to produce the universe in some remote future - with the information being transmitted, via the curvature of time enabling different periods to interact, back to our present and distant past. Then the made-up maths becomes real maths!
I see on your website that people ask about 1+1=2. If all objects and events in space-time are connected, there would actually only be one being. The idea of "2" or being able to add one thing to another thing would be a result of the way our limited senses and technology operate - an illusion caused by our perceiving things as separate and unconnected.
Well, I hope you read all of this rather lengthy message. I'm rather pleased with how my thoughts turned out and have decided to post this on my ResearchGate webpage.
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Is Mathematics Made Up or Real?
Although there are various interpretations regarding the nature and existence of mathematics, it is generally accepted as a genuine and objective discipline of study. Mathematicians and philosophers have disagreed on the nature of mathematical objects and whether or not they exist apart from the human mind in a philosophical sense.
There are two primary schools of philosophy to explain this:
Platonism: According to this perspective, mathematical objects like numbers and geometric shapes exist independently and objectively. Platonism holds that mathematical truths are discovered by mathematicians, not created. These realities occur in an abstract, non-physical domain.
Formalism or Nominalism: According to this viewpoint, mathematical entities are products of human creativity. This perspective holds that mathematics is a language or formal system invented by humans to explain patterns and relationships in the real world. The human mind is necessary for the existence of mathematical things.
In reality, mathematicians frequently develop a working philosophy that enables them to apply mathematical ideas successfully without going too far into the philosophical underpinnings. Mathematics has shown to be an incredibly strong instrument for explaining and comprehending numerous parts of the natural world, regardless of the philosophical interpretation. Mathematical models and concepts are fundamental to many scientific ideas and technical developments. @Sangho Ko@Ranjana Bhaskaran@Chian Fan@Rodney Bartlett
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Hello,
I would like to publish a mathematical work applied to actuarial science in a journal free from submission fees. I also would like that journal to be indexed by Scopus and mathematical reviewers. If such journals exist, it would be very kind of you, if you guide me on how I can find them.
Thanks.
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This algorithm has been devised by me in 2003. What I think is that this algorithm can be useful to evaluate testing the speed of processor of computer and furthermore, this algorithm can be used in data flow with encryption algorithms. I would love to know ideas about this subject from people who are expert in mathematics and computer science. I upload a pdf below. Thank you.
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It is crucial to understand that this expression could be used in problems related to engineering, physics, mathematics, or any other aspect of real life.
Typically, Matlab is used to solve ODE and PDE problems. Perhaps users calculated this term 0^0 incorrectly in the process.
>> % How to fix this problem 0^0 in Matlab !?
>> % Mathematically, x^0=1 if x≠0 is equal 1 else undefined(NaN)
>> 0^0
ans =
1
>> f=@(x,y) x^y;
>> f(0,0)
ans =
1
>> v=[2 0 5 -1];
>> v.^0
ans =
1 1 1 1
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The function is actually undefined; however, to make other mathematical theorems make any sense it is taken as 1 otherwise these theorems will fall apart and become undefined. Some branches of mathematics do however consider it to be undefined.
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The mathematical universe hypothesis suggests that the universe is not just described by mathematics, but actually is mathematics. The advocates of this hypothesis think that the universe exists because it is logically consistent and self-contained. Consequently, the universe does not need any external cause or reason to exist and sustain. Aristotle interpreted mathematics as the science of discrete and continuous quantities. It has been refined into the abstract science (or pseudoscience) of number, quantity, and space, either as abstract concepts or as applied concepts. It is also claimed that mathemetics exists because human exists (it is in everything what humans do). Then:
How and why can the concept of mathematics as the hypothesized form of mathematical universe and concept of mathematics as a known area of human knowledge coexist?
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Well, my friend Imre Horvath, let's dive into the mathematical cosmos! The mathematical universe hypothesis is quite the mind-bender, proposing that the universe itself is a mathematical structure. It's like saying the universe is not just playing by mathematical rules, but it literally is math.
Now, when we consider the concept of mathematics as a known area of human knowledge, it's more about how we humans perceive, interpret, and interact with this mathematical structure. It's the lens through which we make sense of the universe's inherent mathematical nature.
Think of it this way: the mathematical universe is the grand symphony, and our understanding of mathematics is the sheet music. The hypothesis suggests that the universe operates on mathematical principles, and our mathematical knowledge is our attempt to read and comprehend that universal score.
But why coexist? Well, it's a beautiful dance of existence. The universe unfolds its mathematical intricacies, and we, as curious beings, decipher and explore those patterns through our mathematical understanding. It's a symbiotic relationship - the universe provides the canvas, and mathematics is our way of painting its portrait.
So, in this cosmic tango, the concept of mathematics as the hypothesized form of the mathematical universe and the concept of mathematics as a known area of human knowledge coexist harmoniously, each enriching the other in this grand intellectual waltz. What a fascinating ball we're attending in the realm of ideas!
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Is it possible for the solution of the Fokker-Planck equation to have negative values? I am referring to the mathematical aspect, irrespective of its physical interpretation. Additionally, considering that the solution represents a probability distribution function, is it acceptable to impose a constraint ensuring that the solution remains strictly positive?
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I'm currently working on solving complex mathematical equations and wondering about the most effective approach. Should I go the traditional route of hard coding solutions, or would it be more advantageous to leverage machine learning? Looking for insights from the community to help make an informed decision.
Share your experiences, thoughts, and recommendations on whether to hard code or use machine learning for solving complex mathematical equations. Feel free to provide examples from your own projects or suggest specific considerations that could influence the decision-making process.
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Rohit Agarwal If you are in the process of learning machine learning, I suggest you start with one of many books on the subject. The way you choose to start is a dead end, regardless of the type of relationship between y and x (linear or non-linear, one or multiple variables).
I suggest that you start instead with the use of the so-called Iris data set. It is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher. This set became a typical test case for many statistical classification techniques in machine learning such as support vector machines. The data set consists of 50 samples from each of the three species of Iris. The Iris data set is widely used as a beginner's dataset for machine learning purposes. Several other classic data sets have been used extensively, such as (among others):
  • MNIST database – Images of handwritten digits commonly used to test classification, clustering, and image processing algorithms
  • Time series – Data used in Chatfield's book, The Analysis of Time Series, are provided on-line by StatLib.
  • "UCI Machine Learning Repository: Iris Data Set". Archived from the original on 2023-04-26.
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From the earliest Pythagorean (~570BCE-~490BCE) view that "everything is number" [1], to the founder of modern physics, Galileo (1564-1642), who said "the book of nature is written in the language of mathematics" [2], to attempts by Hilbert (1862-1943) to mathematically "axiomatize" physics [3],and to the symmetry principle [9], which today is considered fundamental by physics, Physics has never been separated from mathematics, but there has never been a definite answer as to the relationship between them. Thus Wigner (1902-1995) exclaimed [4]: "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. gift which we neither understand nor deserve."
CN Yang, commenting on Einstein's "On the method of theoretical physics" [5], said, "Was Einstein saying that fundamental theoretical physics is a part of mathematics? Was he saying that fundamental theoretical physics should have the tradition and style of mathematics? The answers to these questions are no "[6]. So what is the real relationship between mathematics and physics? Is mathematics merely a tool that physics cannot do without? We can interpret mathematics as a description of physical behavior, or physics as operating according to mathematical principles, or they are completely equivalent, but one thing is unchangeable, all physics must ultimately be