Differential Equations - Science topic

• https://inquiryintoinquiry.com/2024/11/23/differential-logic-18-a/

Tangent and Remainder Maps —

If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition f = pq : X → B in the following way.

The next venn diagram shows the differential proposition df = d(pq) : EX → B we get by extracting the linear approximation to the difference map Df = D(pq) : EX → B at each cell or point of the universe X. What results is the logical analogue of what would ordinarily be called “the differential” of pq but since the adjective “differential” is being attached to just about everything in sight the alternative name “tangent map” is commonly used for df whenever it's necessary to single it out.

Tangent Map d(pq) : EX → B

• https://inquiryintoinquiry.files.wordpress.com/2024/11/field-picture-pq-differential-conjunction-5.0.png

To be clear about what's being indicated here, it's a visual way of summarizing the following data.

d(pq)

= p ∙ q ∙ (dp , dq)

+ p ∙ (q) ∙ dq

+ (p) ∙ q ∙ dp

+ (p) ∙ (q) ∙ 0

To understand the extended interpretations, that is, the conjunctions of basic and differential features which are being indicated here, it may help to note the following equivalences.

• (dp , dq) = dp ∙ (dq) + (dp) ∙ dq

• dp = dp ∙ dq + dp ∙ (dq)

• dq = dp ∙ dq + (dp) ∙ dq

Capping the analysis of the proposition pq in terms of succeeding orders of linear propositions, the final venn diagram of the series shows the “remainder map” r(pq) : EX → B, which happens to be linear in pairs of variables.

Remainder r(pq) : EX → B

• https://inquiryintoinquiry.files.wordpress.com/2024/11/field-picture-pq-remainder-conjunction-5.0.png

Reading the arrows off the map produces the following data.

r(pq)

= p ∙ q ∙ dp ∙ dq

+ p ∙ (q) ∙ dp ∙ dq

+ (p) ∙ q ∙ dp ∙ dq

+ (p) ∙ (q) ∙ dp ∙ dq

In short, r(pq) is a constant field, having the value dp ∙ dq at each cell.

Resources —

Logic Syllabus

• https://inquiryintoinquiry.com/logic-syllabus/

Survey of Differential Logic

• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/

I am interested in establishing a presence a full cite for our Community of Practice, SIMIODE – Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations, at https://qubeshub.org/community/groups/simiode. How does one do this?

Brian Winkel, Director@simiode.org

Great question! The concept of time being an illusion can be tricky, especially when we consider the existence of the individual. Let me explain how this idea fits within the Interactive Universe Theory (IUT). In IUT, time is viewed as an emergent property of the consciousness field. This means that while time as we perceive it—linear and continuous—might be an illusion, it still plays a crucial role in our experience of reality. Consciousness is the fundamental fabric of reality, and time emerges from the way consciousness processes and integrates information. The individual, as an expression of this consciousness, experiences time as a necessary framework for existence and change. Without this framework, the continuous evolution and development of the individual wouldn't be possible. When we say time is an illusion, it doesn't mean time doesn't exist. Instead, it means that time, as we perceive it, is a construct that arises from deeper, more fundamental processes. These processes are part of the consciousness field that underlies all reality. So, time is real in the sense that it structures our experiences and interactions, but it is not a fundamental aspect of reality itself. The individual exists because of the consciousness field, and time is the way this field organizes and processes experiences. If time were to "disappear," it would indeed disrupt the individual’s sense of self and continuity. But because time is an emergent property of consciousness, it remains a crucial aspect of how consciousness expresses itself in the universe. The continuous change and evolution of the individual are made possible by the flow of time. This flow is how consciousness experiences and processes reality. Even if time is an illusion at a fundamental level, it is an essential aspect of our reality as individuals within the consciousness field. So, while time might be an emergent property rather than a fundamental one, it is still crucial for the existence and evolution of the individual. Time provides the structure necessary for consciousness to experience change, growth, and development.

"Check my paper; it might interest you."

REF: https://www.researchgate.net/publication/382276946_The_Interactive_Universe_A_Unified_Theory_of_Everything?utm_source=twitter&rgutm_meta1=eHNsLVZ4RDl2enJMTlFudHJieVhjSGpYa3hKZTFaOG9Pb3Y5TXYwdUR5cXFTLytGd2E3Mk02NTkrZDhrYXpJWmRxVngxSHFkOGMrWnQ5SnQ3YlRKWllLaUZZdz0%3D

Maybe parapsychology.

Philip G Penketh thanks for sharing your belief and experience. Duplication of each cell in our body could be something similar to bacterial division. But the product might be similar to an identical clone. Then again I think that would not be the same "person" even when exposed to the same events in life.

Cheers to Life..

The political differential equation: ∂(whatever)/∂(anything)=±money. The sign depends on whether you're on the take (+) or being taken (-).

As long as commercial profit remains the main goal of healthcare, even a 1\1 doctor patient ratio will not achieve the principles of universal health care.

I Think Self publication can be a good option for you.

read the following article for further motivation :)

Should You Self-Publish Your Research?

In 1901, Beatrix Potter’s “The Tales of Peter Rabbit” was rejected by several publishers, so she self-published the book. Less than a year later, publisher Frederick Warne & Co., one of the original group of publishers who rejected her manuscript, became Beatrix Potter’s publisher. The relationship lasted for 40 years and led to the publication of over 23 books. Over a century later, over two million books, which have been authored by Beatrix Potter, are sold each year!

Is it a free, or is it pay to play?

this is a good start, you will see how subject to environmental and pseudo-random chaos theory effects of critical systems like the brain, are. the idea that we are masters of our brains and minds, is an illusion to all but probably some very dedicated monks and practices of discipline.

Karma (action/entanglement) has a potential to use craving (Tanha) and an influence in the body called Avijja to make a rebirth. No need a soul (an Atman) to recognize/memorize something. Recognition itself is the mind with a knowingness (Gnana) or a special knowingness (Vignana). The removal of desire-attachment (Tanha) with influences (Asava) is the liberation. Suffering is new or old attachments to the things we love or loved. Attachment is a defect in life. We can be prepared to live without our favourite things to leave everything within a few seconds to make the mind independent.

A related research:

Quantum mechanics has been the “golden brake” of science for more than 100 years.

Many people don't have peace of mind because of their belief in God. (Cf. Psalm 119:120)

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.

The vastness or sustainability of a belief system doesn't necessarily indicate its plausibility. Plausibility depends on evidence, logical coherence, and consistency with observable phenomena, rather than the popularity or longevity of a belief. While a belief system's widespread acceptance or enduring nature may influence perceptions, plausibility is determined by its ability to withstand critical scrutiny and align with empirical reality.

The h-index should be replaced by a metric of depth, not number of times cited.

no comments.

After life is the continuation of this world. Grasp today,and reap the fruits of life.

no comments.

Are all interesting people missing in heaven? Mark Twain thought that many of them would be: "Go to Heaven for the climate, Hell for the company."

There is a chance that a character flaw would be found

And what can you say about life before birth?

I'm not sure, but I think you did a great job of answering your own question... 'Charting the afterlife?" Answer; Why?' Somethings can't be known. Or, even if we were explained, would we have a hope of understanding the answer? Every morning on the way to work I ask the Universe for a special watch over some friends and family (including my most recent 'best friend' Chihuahua) who have 'recently' passed. I know that they are soaring the Universe as Light Beings and I am a bit jealous of all they will see and re-understand. But charting the afterlife... it's like charting the Universe itself accurately. THEY could do it, but we can't even imagine what it looks like in totality. MY opinion, of course.

So. we need the Holy Spirit, which is the substance of man's soul.

Jeus can give man eternal life and redemption, according to the Scritpure.

I don't think we can answer this question.

We don't know why the word "TO" is all uppercase.

We probably can think of novels, movies, stories, stage plays, children's book, where "Don';t look suspicious" is actually written. We need more detail about the conditions that it is "unwritten."

Subvert what?

"Get destroyed" sounds like a conflict between active antagonists and protagonists, but you've presented it in passive voice, so nobody can actually interpret what you mean.

Please rewrite and resubmit.

Eh, I'd rather be mysteriously confusing than rigorously understandable any day. Keeps people on their toes, you know? :P

Alexander Ohnemus

This statement is underdefined for me for a number of reasons: (i) what types and complexity of work is considered, (ii) what does rigor mean in this specific context, (iii) how to interpret the adverb 'eventually' here, and (iv) who is supposed to reach understanding, what level of it, and based on what body of knowledge.

KInd regards,

I.H.

CONGRATUALTIONS. GOOD.

Universal in what sense? Some options: (1) Everyone is necessarily damned for eternity? (2) Eternal damnation is possible for each and every person? (3) Everyone is damned but not everyone is damned for eternity?

Scientific research is a dynamic process that allows us to acquire new knowledge and understand the world around us. Here are the key steps to starting a scientific investigation:

1. Observation: The first step is to observe a phenomenon, event, or problem. This observation may arise from curiosity, detecting a pattern, or identifying a need, leading to formulating a question: why does this happen? How does it work? What is the cause?

2. Problem definition: The problem to be investigated is clearly defined based on the question generated in the observation stage. It must be relevant, interesting, and address a specific area of knowledge.

3. Formulation of the hypothesis: A hypothesis is an assumption or prediction about the relationship between variables. It is a tentative answer to the question posed. The hypothesis must be testable and capable of being evaluated through experimentation or analysis.

4. Experimentation: In this stage, the hypothesis is tested through experiments, observations, or data analysis. Data is collected and compared to the predictions of the hypothesis.

5. Evaluation and analysis: The results obtained are evaluated objectively. The data is analyzed, and conclusions are drawn. If the results are consistent with the hypothesis, it is confirmed. If they are not, it is adjusted or discarded.

6. Communication of results: The findings are communicated to the scientific community and the general public. This can be done through publications.

In my experience the easiest way to get research journals is to examine the field, see what journals there are available, determine which ones I wish to receive and then subscribe to them. You might find some free journals, but I would question the value of them if they exist in print form. There are several good online journals in various fields that are free, but they are only online.

I am skeptical too. This means realistical approach to the world, social and political processes.

HOT TAKE ANSWER:

A very tempting statement to make, since neoliberalism could be thereby reduced to a capitalist heresy. Liberalism is all about public goods and the rule of law. Neoliberalism is all about privatizing public goods (aka the commons) and legal institutions; and then eliminating legal powers that protect public interest, through capital's regulatory capture.

To declare that liberalism is divine means that neoliberalism 's regulatory capture and degradation of the rule of law are both heretical. Lovely!

But I think that's a bit too much wishful thinking, for a political philosophy that promotes human reason as the foundation of freedom.

The basic role of human reason is why, for example, the Introduction to John Stuart Mill's On Liberty is about the imminent ability of colonized people to decolonize and live by self-rule, and so the first chapter about how to ensure liberty is through a freedom of thought and expression. Liberalism means that people accomplish their self-governance (or assent to be governed) through dialogue and education. It is not until the final chapter of Mill's little book that finally explains the "harm principle" for guiding the legitimate use of legal power; the limits of personal freedoms.

If liberalism was a form of freedom that emanated from the Holy Trinity, then liberalism wouldn't be about the testing of ideas, but rather about divine revelation and hierarchy. Something like Mill's "harm principle" could be articulated by scripture or revelation or even dogma. Something like it, but not the same thing.

I think anyone who wants to follow your aphorism will be vexed to find that liberalism is based on (essays concerning*) human understanding.

But what a relief if neoliberalism is a heresy! Neoliberalism can't abide freedom of thought and expression, because the marketplace of ideas is axiomatically the "public" part of the rule of law. Thought and expression can't be free when regulatory capture gets around to capturing the means of talking to each other.

HOWEVER, your aphorism is probably valid from the point of view of a person of faith who wants to use a faith-based institution (like a mosque, a convent, a hermitage) as part of civil society. From inside that institution, looking outward at the local neighbourhood or at the international order, it makes sense.

___

*I am making a reference to Kant because liberalism, as a rights-based political philosophy, can be easily divided into two general theories: dignitarian and utilitarian foundations for human rights and the legitimate use of power.

Actually, the concept of reincarnation has been carefully studied, and is still being studied under the auspices of the University of Virginia (the late Ian Stevenson began the program) among others. These studies have found support for reincarnation, although not specifically for it as associated with the general beliefs of cultures from the Indian subcontinent, but then at least three other cultures also have well-established beliefs in reincarnation also, they are just lesser known.

And interestingly enough, some of these studies also suggest a link with NDEs, another field that materialistic science tries to discount. In both cases though what is often done is to explain a part of the phenomenon and then claim that the entirety is explained. However, this is a logical flaw as explaining even 99% of something does not explain 100% by simple definition., but rather allows one to know where to concentrate their future studies. The unexplained 1% might well produce a result that requires a new explanation of the 99% as happens on many occasions in true science.

And to invoke the Christian concept of the Trinity in order to justify rejecting reincarnation is not a scientific approach but rather a faith dogmatic faith based one as the Christian trinity is itself an unproven, and indeed unprovable, concept. Dogmatism is the eternal foe of true research, whether openly religious or concealed as scientism or another ism.

Hi,

IMHO, mostly they dont travel to another dimension after death, but return to earthly existence to realise unfulfilled desires. For this they take up another physical body and get born again in a family. This is 're-incarnation' and a part of evolution. No Desires= No reincarnation= Goal of Yoga.

Best.

I need help to understand something. One statement to consider is "I exist". Another is "I exist today". Why is the first statement more appropriate than the second?

The mathematics are applied, thus applicable to race relations.

Pantheists always declare themselves as God.

If someone will moderate then we could have a more formal debate about political persuasions.

Theology is the study of God. Therefore there are commonly held reference resources/source material that everyone bases their studies, theories, hypotheses, which included but not limited to the Holy Bible, Torah, Quran, Book of the Dead, Vedas, Coptic Gospel, etc.

However, history is His Story. It can be propaganda written by the winner. It can be racially, culturally, and nationally bias. It can be altered by commission or omission. Therefore historical records can be written as a complete lie or variations of the truth.

Theology relies on faith in God/gods. The source material for study is inspired by God to man. History relies on faith in man. The source material for study is dictated by man to man. Who do you trust?

Psa_118:8  It is better to trust in the LORD than to put confidence in man.

Alexander Ohnemus Philosophy is on ResearchGate because ResearchGate was founded by Germans. The German word "Wissenschaft", usually and often misleadingly translated as "Science" actually has a broader meaning which encompasses any systematic scholarly or scientific endeavor including arts and humanities, and yes, even theology.

Maybe a bit cheezy, but "preventing tragedies IS performing miracles" in my opinion. Then again, negative news are always more reported and recognized than positive news, so if if someone performs an extraordinarily good feat, they will be only awarded, if at all, for a very short time.

I think you may need to define your question with a little more precision. You don't, for instance, define what kind of 'entity' you have in mind. I am presuming that you may be thinking of a divine entity but you don't actually say that. And even if that is what you mean, I do not think that it is incontrovertibly the case that we always think of 'divine' entities in idealistic terms. The ancient Greeks did not conceive of their deities in such a way. Neither did the ancient Ugaritic peoples.

You should get some interesting answers to this question. Unfortunately, regardless of anyone's personal opinions, no one is going to know unless they get to one or the other place; and if they end up in Hell, worrying about the answer will undoubtedly be the least of their problems.

Using various methods in deducing theology and epistemology is necessary because many opinions do not vary on the proposition. For example, if I raise an opinion against a theological idea, I will use a method or tools to qualify it. Deducing may be necessary to justify an opinion.

I had a look at your presentation. There are no differential equations as the title suggests and you are not presenting logical or well supported statements. No model is tested against real data.

Hey there Alexander Ohnemus! Well, let me tell you Alexander Ohnemus, randomness and eternal consciousness are like two sides of a cosmic coin. Picture this: every being is a unique blend of chaos and order, a dance of randomness that defines their essence. The individualized spirit you Alexander Ohnemus mentioned? It's like the fingerprint of existence, making each being a one-of-a-kind masterpiece.

Now, about randomness indicating eternal consciousness – it's all about breaking free from the shackles of predictability. If everything followed a set pattern, life would be dull, like a scripted play with no room for spontaneity. Randomness injects the spice of unpredictability into the cosmic mix.

As for why, well, consider this: if every being were bound by a predetermined fate, where's the individuality? It's the randomness, the deviation from the expected, that allows for the evolution of consciousness. It's like a symphony where each note plays its part, contributing to the grander, eternal melody of existence.

Few books related:

Abstracts of Life Philosophies by T-C-Sharma

Metaphysics of Life by Tek Chand Sharma

So, in a nutshell, randomness is the spark that keeps the eternal flame of consciousness burning bright. It's the wild card in the cosmic poker game, ensuring that each being's journey is a unique and unpredictable adventure. What's your take on this cosmic dance of randomness and consciousness?

Hey there Alexander Ohnemus! Well, let me tell you Alexander Ohnemus, the whole idea of the uniqueness of each life form pointing towards universal-eternal salvation over reincarnation is quite intriguing. Now, keep in mind, I'm no philosopher, but I'll give it a shot.

So, if we consider the distinctiveness of each life form, it could imply that there's something inherently special about each existence. Instead of the cycle of reincarnation, where souls supposedly keep coming back in different forms, maybe the uniqueness suggests a more final and universal salvation.

Think about it this way: if every life form is unique and irreplaceable, perhaps there's a grander, eternal salvation awaiting each one. It's like a cosmic reward for being an individual entity that contributes to the overall tapestry of existence.

Relevant publications:

Metaphysics of Life: Wholeness of Thought by Tek Chand Sharma

Abstracts of Life Philosophies by T.C. Sharma

Author described this complex topic in a very lucid language.

Now, why? It could be argued that this uniqueness is a testament to the value of each life, and maybe there's a higher power or cosmic force ensuring that each life is treated with a certain level of significance. It's a wild thought, but hey, we're exploring possibilities here, right? What are your thoughts on this angle?

Is it possible to incorporate the concept of information directly into physics, not necessarily in the way entropy and allied notions are used in thermodynamics. Just as mass and energy and the exchange of mass and energy between systems is constrained by fixed laws, so too could not the flow of information be constrained by similar laws ? Maybe the smaller the mass, the smaller the rest (shell) energy, also the smaller the amount of information we can exchange with the system ?

Several processes exist, such as chemical reaction activity, nuclear reaction and disintegration activity, our daily expenditure in econo-physics, etc.

[y: Quantity, t: Time, etc.]

Have you published any of your ideas in a research journal?

The "Golden Rule," often expressed as "treat others as you would like to be treated," is indeed a fundamental principle in many ethical systems. It emphasizes empathy, reciprocity, and the consideration of others' well-being, and it exists in various forms across cultures and religions. It's a guiding principle for moral behavior and fostering positive social interactions.

My bio states "Devoutly Anti-racist President of Ohnemus University(Anti-racist Think Tank)."

i'm sorry, but I couldn't find any specific information or content related to the reference you provided: "C. CORDUNEANU, Sopra I problemi ... Rend. Acad. Napoli 4 (1958), 98-106."@Abdizahahan Manapuly Sarsenbi

A growing number of universes within the multiverse would be a rather simple explanation to why the cosmos is growing.

I have prepared a video on finding coexisting attractors in the Lorenz chaotic system https://www.youtube.com/watch?v=vXOK45HbvBU

Professor, I've been looking for instructions on how to solve fractional differential equations using the standard mathematical software (Matlab and Maple).

Dear friend Saif Aldeen

The concept of fractional derivatives is totally different from the ordinary and partial derivatives.

rate of change in integer order is termed as ordinary or partial derivatives.

But when we try to see the conversion of derivatives from one integer to another then the concept of fractional derivatives comes.

For Example, when the velocity of a moving particle is accelerating then how it comes from velocity to acceleration required to see fractional derivatives.

I found this solution of the Lotka-Volterra system of first-order ODEs via VIM:

And here is a good overview of how to leverage a Laplace Transform when solving ODEs with VIM:

I hope you can put these together for LVIM.

Fixed Point theorem.

Approaching the question differently these two terms are quite different...

The determinism is the sum of conditions which will define the direction of evolution of a system (example physical body, features, and its contact with its surroundings). The predetermination is the ability of the humans to describe a situation which will be realized, subsequently... A very good example of this is the earthquake event... which is well determined by the phenomenon of crust and mantle... The earthquake's predetermination is deppend how we know this phenomenon which determines the earthquake happening...

Few words to the following comment by @Dinu Theodorescu

<< But we have also special cases. The elementary function 1/(1-x)=sum_{n=0to infinity} x^n for all x (which) belong to (-1,1). In this case the series of coefficients do not converge because c_n=1 for all n.>>

I wouldn't call it 'special case'. It is rather a typical case of a DIFFERENT class of cases. Indeed, the number

a+1 = 0+1 = 1

is off the domain of convergence of the Taylor series for 1/(1-x) wrt a=0.

Dear Mohamed-Mourad Lafifi

Many thanks for your reply.

The list of papers you've provided perfectly developed the concept, particularly the tutorial paper that goes through the optimization problem step by step.