Introduction:
Blog date: Oct/22/2020
How to form a bond with others online? It can be done, using information (what one does not expect) and trust (what one knows that one knows). I am studying this, directly and online, for 17+ years, though it takes time to develop finesse. I am also learning computer programming and Brazilian Portuguese. Programming is the process of breaking a large, complex task into smaller and smaller subtasks until the subtasks are simple enough to be performed directly. Portuguese is very intersubjective.
Current entry in Blog: see last answer with Blog posting date.
Blog date: Oct/22/2020
How to form a bond with others online? It can be done, using information (what one does not expect) and trust (what one knows that one knows). I am studying this, directly and online, for 17+ years, but it takes time to develop finesse. I am also learning computer programming and Brazilian Portuguese. Programming is the process of breaking a large, complex task into smaller and smaller subtasks until the subtasks are simple enough to be performed directly. Portuguese is very intersubjective.
Blog date: Oct. 28, 2020
We humans can learn a lot from the Plantae Kingdom. Flowers give visual and olfactory gifts, a means of communication that we should simply appreciate. In return, we can value their extravagance. Also, in our search for alien origins we must acknowledge that the plants appeared on this planet long before the humans, which makes "us" the late arrivals!
What to expect of the future? This was already announced and explained by the medium Francisco Cândido Xavier and others, like Divaldo Franco, and Adriano Correa Lima, providing what Allan Kardec called the "Universal Control of Spirits" -- in dealing effectively with the question, of how to believe it?
So, until 2057, we expect ... difficulties. And the difficulties will exist just to hide their lessons, in what may seem oftentimes to be a divine miracle, and was captured already in the German linguistic experience as a famous proverb, "aus der Not, eine Tugend machen" -- or, "out of necessity, make a virtue". The difficulties are a way for us to learn farther, faster and more securely. How to develop a new vaccine fast, if there is no dire need and focus, and no resources nor laws -- a pandemic? Complaining has no hope of solving it.
Our planet is already in the process of regeneration of such crude epistemology and pedagogy, as I just realized. That which appears to be evil, punishment, and expiation, or even atonement, is to be eliminated, and productive efforts can be more fruitful by moving forward always. Let's move forward only, for the sake of evolution. We realize what the educator Pestalozzi exemplified in the 1800s.
Therefore, changes will likely occur in the physical and spiritual aspects, in the process of so-called death -- disencarnation and reincarnation -- and our planet will have a new face between 2057 and 2060, after this transition that is happening.
As we investigated op. cit. before, in our studies reported here, how to rely on received information? One can use trust (community-based and emergent, cf. Michael Polanyi), compared with confidence only (authority-based, often fallible). Mutiple channels winning over a single channel. When something is trustworthy, one usually has to see diversity and redundancy, which become itself a simple sign of trustworthiness. The truth is, therefore, fractal. We have to see it everywhere, in the macro and in the micro, and repeatedly.
"Everything will change dramatically. Needs, perispiritual and neuropsychic structures, work, time, social characteristics and the very resources of material nature will become much more subtle."
Many of us, are relieved that we survived 2020. Thinking that with a newly elected US president, and 5 vaccines, the year 2021 is looking hopeful. Indeed, that seems true, but for a different reason. Everything is always good and useful, that's why the Earth exists. Forget the apparent contradictions, they are just "contra". All channels for progress are open, because they never closed.
It is right then to be hopeful, but we should maintain constant viligance, at least until 2057. The ideas of "always a catastrophe" , "gloom and doom", "it's better to be pessimistic", "done but not good enough", this crude psychology of today, will be gone. We can always do better, because we can learn. Education is foreign to punishment. Life is a blessed school.
As the passion fruit flower shows, we could still anticipate and work for new medicines, more beauty, other climate situations, persistent economic divides, forced mass migration, and new opportunities like establishing a permanent base on the Moon -- but what matters is to be helpful to others, not a personal project. The above exerpt is a reminder to think long term in terms of an internal change for others, including after our physical exit from this planet. Let's work for a future that we are unlikely to see, and do it selflessly -- with self-denial and self-forgetfullness. Good is good when good for others, should we be able to finally practice, unimpeded by criticism. Until then, criticism is good, good for us.
Trees communicate with one another, mutatis mutandis, our cells, veins and arteries are all in collaboration. Our cells reproduce every 3 months and regenerate. We are living "borgs." Life is fractal. Humans are departing and arriving hourly. This planet is now in "red alert." For too long, the humans have imposed on the plant, animal, mineral and fungus kingdoms. Now is a good time to think of others, including the plants.
For a probabilistic model see:
https://www.amazon.com/Using-Statistics-Probability-Save-Your-ebook/dp/B07ZPMSDGY/ref=sr_1_2?dchild=1&qid=1612136803&refinements=p_27%3ATiffany+Vogel+Gerck&s=books&sr=1-2
Our interpretation of math evolves.
Kronecker, by stating, "God made the integers, all else is the work of man" has two implications.
Kronecker wrote a memoir on the algebraic solvability of equations extending the work of Évariste Galois on the theory of equations. He was particularly interested in finitism, as not accepting the existence of infinite objects such as infinite sets. While all natural numbers are accepted as existing, the set of all natural numbers is not considered to exist as a mathematical object.
Finite fields are fundamental in: computer science, number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory.
Qubits may be currently prevalent in quantum, but tri-state is already being used, classicaly, and Claude Shannon did not have the last word on Information Theory, not even the first.
Like Newton, that gave us a good start in calculus, with infinitesimals, but Leibniz and Apostol did better for the future.
If computer code cannot provide a continuous variable, just a quantized representation of it, then anything simulated by a computer code can work equally well if it is provided by a quantized variable! If one does not need continuity to represent reality -- then, reality does not depend critically on continuity.
Yes, and this follows from the Curry-Howard relationship, between computer code and structural logic. And the same applies for infinity, and infinitesimal. Nothing that cannot be calculated by computer code can exist, and vice-versa. Evidenced in the Curry-Howard relationship. Nature seems to be constructive. If one can't construct, even with non-existing materials, does not exist -- and vice-versa. No one can construct infinitesimals.
The meaning of the motif that Nature’s voice can be heard, is collaboration. This might be the overall message of the pandemic, not isolation. Collaboration in robots, collaboration in the family, which is the cradle of our life. It is in the family that we learn collaboration, with respect for one another first, and then going outside the family. Jesus gave us the example to follow.
Thank you for the last postings, but I deleted the last images. The animals and collage can be cute, mainly because we project ourselves in them. I find that their actions have other, internal, reasons.
Since the purpose of RG is science, and my purpose is mathematics, these are far beyond what animals and objects can offer and my blog can focus on a difference we can make in promoting math for fellow humans.
Let's remember that COVID is an animal virus, epidemic, but turned into a nightmare pandemic on humans when it reached us -- by our sick insistence on eating said animals!
Why are we not able to tap more often into immutable values, like math? Maybe because we spend far too much time on vestibular activities, or maybe because we spend too much time being shallow, distracted, not meditating.
For those who see the Earth as a school, such time is truancy. We need to think deeply, and act consequently. In the Star Trek Voyager series, Captain Janeway, herself, when discussing temporal mechanics (whatever that might be), we hear that "there is no time like the present ". In looking for a justification for this dictum, we see that we can't control the past, and we can't control much the future. But the present, that is easier to control.
I am writing my paper on probability, and how to recover from errors. The mathematical theory offers a simple way out -- reuse the error. That is a way to deal with indeterminacy, as a measure of uncertainty, of information itself (Shannon). The Law of Excluded Middle looses its grip, and there are states between True and False. -- the world is not Boolean!
What does the consumption of animals, aka eating meat, have to do with mathematics?
The answer is that, using a simple probability model of yes/no, we can prove mathematically that we are more than 99.99% vegetarian. Of course, there is also a chemical question, and we (occidentals) have trained our bodies to offload to animals (that we then, eat) the task of producing food.
For example, there are 20 amino acids that we share with all creation, plants and animals. Of these amino acids, 9 are essential to us, in that we do not produce them. We can only obtain these 9 amino acids from what we eat. With the advance of nutrition technology, we can get them from properly enriched yogurt. No animals need to be harmed. We can also get them from plant sources, when no animals need to be bothered. We should look for the last alternative, and this blog stands for that separation.
We need to respect the animals, our friends. The monkeys, like the japanese found, like a very warm bath. A human might not feel comfortable in that temperature. We all have different needs and different semantics, which is a mathematical way to say we obey different, but clear, rules. We are vegetarians, and it is time we act consequently.
Wolfgang F. Schwarz
,As an undergrad at UCSC, I was first introduced to dendrochronology (or tree-ring dating), the scientific method of dating tree rings to the exact year they were formed. Dating them can give data for dendroclimatology, the study of climate and atmospheric conditions during different periods in history from wood.
So I very much agree with Wohleben that, "... the amazing processes of life, death, and regeneration he has observed in the woodland and the amazing scientific mechanisms behind these wonders, of which we are blissfully unaware. Much like human families, tree parents live together with their children, communicate with them, and support them as they grow, sharing nutrients with those who are sick or struggling and creating an ecosystem that mitigates the impact of extremes of heat and cold for the whole group. As a result of such interactions, trees in a family or community are protected and can live to be very old"
Yes, trees do communicate by scents, care for one another, share resources and warn the external collective. All of this is well documented, in the recods of the forests, in the trees themselves.
This post is about my own private agony of error correction. No, I do not have OCD, and am not really indecisive, although I may have the occasional excess cup of coffee.
It is just that oftentimes, I write something, then break to eat or sleep, only to find some reaction or comment I did not expect. Then I realize, what I wrote, and what was "received" are not the same, at all!
The English language is limited, and nuance is highly individualized. For this reason, I decided late in my life, my forties, after becoming a grandmother, to attempt to proceed in mathematics. Much to my surprise, there is much confusion in the math world, as well.
Am hoping the study of Galois Fields and quantum mechanics will provide some solace. In my dreams, everything fits together in a beautiful way, much how the pyramid builders planned it.
TG; To support your statement, after "What does the consumption of animals, aka eating meat, have to do with mathematics?", I have a few words.
By not eating cadavers, even fish cadavers, we train our bodies to be more in harmony with all living beings in nature. That includes chemicals in digestion, and the mind -- understood as not only that which is supported by the physical structures of the brain. While a banana tree naturally offers its fruits, and feels no pain to drop them, a fish fights to stay alive in a way that a plant does not.
Thus, being one with nature, it becomes easier to be one in mathematics, where everything fits together in a beautiful way.
Considering the recent events in the United States, we must be consequential and consider what the reactions of others will be. Some will respond with elation and relief.
Actions have consequences. In math, as well. A mistake in the beginning causes lots of extra work. Better to focus, breathe, and wait for inspiration. Silence is an answer. A blank page is better than pages of gibberish, less errors to correct.
I am very happy with Tiffany Gerck, for my part I tell you that I love programming from a young age, and I would love to be able to collaborate on the subject you write, I also love Portuguese, in fact I listen to a lot of Portuguese music, I worked several years in Angola and Portuguese as a language is very beautiful. Those two hobbies are at least the same. Best regards
Hendrics Ramos Companioni ,
Prazer em conhecê-lo! Algumas expressões só podem ser ditas em português. Uma das minhas preferidas é fazer uma viagem na maionese. Tipo, semana passada, fiz uma viagem na maionese! Not exactly sure how to translate, but "a trip in the mayonaise" is to have a comical unexpected result, maybe a little awkward, but ending well.
As for programming, I am just a beginner, exploring python. Seems like the entire world has increased an appreciation for online communication. The value of safety, privacy and easy to use encryption are becoming more mainstream.
Da mesma forma, também é um prazer conhecê-lo, trabalho diretamente com programação há cerca de 14 anos e ainda me considero inexperiente. a cada dia esse campo se expande muito mais. Saudações e espero poder colaborar no futuro.
Differences between natural languages and programming languages:
Daniel Ross expressed exactly what I was looking for, at:
https://www.quora.com/Whats-the-difference-between-natural-languages-and-programming-languages
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Programming languages are (designed to be) easily used by machines, but not people.
Natural languages (like English and Portuguese) are easily used by humans, but not machines.
Programming languages are unambiguous, while natural languages are often multiply ambiguous and require interpretation in context to be fully understood (also why it’s so hard to get machines to understand them). Natural languages are also creative and allow poetry, metaphor and other interpretations. Programming does allow some variation in style, but the meaning is not flexible.
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Humans are fascinating, mimicry is fun, and we have been in social isolation. Still, must convince myself, programming is not a dark art!
Thanks for sharing the web, I really liked the article that appears on natural languages and programming languages. a big greeting
The pandemic has made it possible to break paradigms and overturn old ways of doing things.
Crisis = opportunity
We must keep moving forward, discover, and evolve (like children).
We have a choice: cling to old outdated values or adapt and remain curious, active participants.
We are evolving, and so is our understanding of living, exchange, medicine, math, physics, even our exercising, eating, and shopping habits! These days taking a walk outside is a simple pleasure to be grateful for.
Taking indeterminacy into account:
Our study on a third truth value, in a non-boolean algebra, is showing that logic is not always black/white, or yes/no.
See: Preprint Tri-state+ communication symmetry using the algebraic approach
We have explored this theme logically, but it is a topic that we all may grasp intuitively.
Indeterminancy is something that people accept or not.
For example, in some cultures, when asked a question, the responder will reply, "God willing" or, "If God so wants," or say oxala!, or say inshallah! This type of response demonstrates an understanding that we humans can not possibly control things like, the weather, timing, actions of others, collective effects, and so on....
Understanding that, means, an "outside intelligence" is in control, not me, and indeterminacy is a comfortable space.
If the individual believes the illusion that they are "in control," without accepting an "outside intelligence" or even the contributions of others, indeterminacy could be quite uncomfortable.
So, consider, what you think about indeterminacy, in math and physics.
Every day, everything is the same:
Wake up.
Smile
Joke
Eat.
Watch.
Write.
Joke
Write
Watch
Every day the same.
Every day it's the same. Every day, we repeat, and we repeat and there is beauty in that. Heaven is monotonous. No one complains about a beautiful monotony. The song Cotidiano / Quotidian (with English lyrics) by Chico Buarque seems simple and obvious, but in fact there is a deeper message in that.
In physics and math also.....there is monotony....and simplicity.....and beauty. The best clear and easy to understand, fitting together seemlessly.
Hi all of you, hello Tiffany Gerck, if we talk about numbers they are closer to the creator. For 40 years I have been dealing with productivity using mathematics and in particular to read beyond my theory and codes. Numbers are everywhere around us and everything moves with math. In the chaos, there are constant hidden patterns that only a few can see beyond. The theory of codes arises from the study processes on random games where it is possible to calculate the mathematical code that will come out in the future. I built intelligent computer machines which according to my theory, the best possible solution. In fact, the publication applying the principle of galenic phytotherapy to the choice of plants to harmonize and mathematics, as well as their medicating function. The work here is the true and published testimony proven on a close circle of people and everything worked, each person with the identical compound solved different health problems in all people tried the compound dropwise, only 5 sublingual . It is an extraordinary thing that many still cannot use due to the power of nature and the various possibilities of use. Here I launch the idea of involving other researchers to prove this mathematical miracle of Nature that I have designed, all demonstrable also towards Viruses and Bacteria, even Covid-19.
Article "Ten plants for well-being, united by Natural Mathematical M...
Dear Luigi Barone,
As said long ago, God created the integers and the rest was created by man. As co-creators we can extend integers to complex numbers and more.
Many balk at sqrt(-1) but seem ready to accept sqrt(2), which cannot be visualized, whereas sqrt(-1) can be seen as a rotation. We find that finite integers can build a field, so the 4 arithmetic operations are valid with finite integers, whereas infinitesimals cannot be constructed and cannot explain even 1/3.
What you found is known since ancient times, as in the Antikythera Mechanism, revealing the harmony in cosmology. Much sucess in revealing a higher law than mathematics!
The world being so serious, in order not to succumb to "the gloom and doom" going around, I am working on a reference frame shift, not only to see the positive, but humor in situations.
October 12 is children's day in Brazil, and Brazilians LOVE jokes.
Portuguese jokes require translation, not all are so politically correct or could seem offensive. Brazilians generally are MUCH more light hearted about skin color. Brazil is not for beginners, said the poet.
For example: "Samba do crioulo doido" is the dance of the crazy black man, a crioulo, a famous carnival float designer, and the organizers kept changing the design year after year, he would design the float, prepare it, make changes, prepare again, with all the changes he got all mixed up...and he went nuts.
So, when someone mixes too many topics, its called a "Samba do crioulo doido."
Which I did so many times, before I decided to study math. Not allowed to mix types in math... but when I mixed up the toothpaste and the cosmetics in the medicine chest, it upset the mathematicians in our house.
We laugh a lot because of cultural mixups, but mostly because physics, math and the humanities...will combine in unique permutations not being really allowed. For example, "relativistic mass" is a crime against movement being relative ... so that a moving quark won't make you get fat!
We laugh a lot because of cultural mixups too, but mostly because physics, math and the humanities...will combine in unique permutations. (Not to mention the obvious differences in Brazilian- US cultures.)
Personally, I am interested in the future of belief systems, whether they are recognized or not. In my view, whether recognized or not, everyone is a medium. Not only in the Brazilian tradition of the French philosopher Alan Kardec and the religion of umbanda, but atheists as well receive communication from other realms. Mostly, our thoughts are not our own! Our thoughts do not all come from our own minds, but from the contributions of others.
When something is to be communicated to this plane, it originates in the higher planes of existence. Otherwise, our existence is too primitive for the reverse to happen. We are not able to create anything of value, novel or interesting. In order to communicate there needs to be a compatible structure first. Sympathetic resonance must be established. In order to recieve more complex thoughts, we must be calm, content and receptive. But first we pass through hardship, often seen and perceived as sadness, in order to develop. Eventually we accept, like in the effort of learning a music instrument. After the notes are learned, execution becomes possible, then composition with the addition of other elements. No one produces alone, is the ultimate realization. We must, always, be grateful.
Must be patient. We see that nature has no hurry, everything comes at the right time. In Galois fields there are no errors. We can calculate things exactly, no infinitesimals and no irrationals. Only integers. Cryptography is done that way, with integer arithmetic, and is exact.
Hearing still about the events in DC on January 6, the resistance to a simple act of vaccination against a mortal disease, the victimhood behind wearing a mask, and the current "holiday" of Halloween, one can see that there is now a belief in the US of "who cries, wins". Who is a victim, true or not, wins. Therefore, all around us we see .... victims. Everyone wants to win, no matter how unhappy everyone feels, or sick, or dies.
Instead, the Brazilian life lesson is "who smiles, wins." I did not believe it, at first. One day I saw a photo of barefoot adults, smiling, walking in the rain. They had just learned that they lost their home in a flood. How could they be smiling? But that is the Brazilian way, to trust God, and whatever happens is good, because God wanted (even death and destruction). The end of the caterpillar is the beginning of the butterfly.
In Germany, one can appreciate the German system, "Who works, wins". They learned it after 2 gruesome World Wars.
I think a happy medium is, "Who smiles and works, wins". It is similar but more complete than the UK life lesson, which is, "Who dares, wins" -- which is also the motto of their special forces.
Indeed, as the Romans said long ago, "luck protects who dares" or, "luck follows initiative". In Latin, "Audaces Fortuna Sequitur".
That is all in for you, as our Halloween message in 2021. "Who smiles and works, dares. And who dares, wins. Luck protects who dares."
TG: We did not come to this world to condemn the imperfect, because everyone (including us) is imperfect, even Jesus ("perfect only the Father").
No, your message and your blog are that we came here so that others might be saved by our example of persistence. Good is good ... when good for others!
Have learned a lot from discussions on RG, especially in math. Motivated by the question, Do irrational numbers exist in nature? By Andre Gontijo Campos. With help from Ed Gerck, I got this realization:
We are back to how mathematics was, before it was corrupted by divorcing it from nature. Mathematics is quantum because only quantum values exist in nature, they are called "integers". Integers are all a computer (human, machine, or otherwise) needs to know.
A machine computer can use use spintronics, a human computer can use biological synapses, a seraphic being can use force fields, it does not matter. Operation is distinct from implementation.
It does not matter what the corrupting forces are either. They are a multitude, but one can reduce them to a single effect -- they have reduced the destruction that we (collectively) have tried to use mathematics for. Return always happens, and not just language got its Babel time.
But physics helps us break free, by referring to nature. The world exists for 13.8 billion years, and events don't happen randomly, cause and effect is always obeyed exactly -- imagine the precision, since the Big Bang. This is reflected mathematically in integer arithmethic, with x mod p. The Antikythera mechanism, in ancient Greece, is an example, in predicting many orbits, all exactly.
In that, Feynman pointed it well, and his words are here:
https://www.youtube.com/watch?v=NM-zWTU7X-k
As Ed Gerck says, bias can be seen as a consequence of trust and, thus, natural. As we learn to trust, as we learn to rely on received information, some of that is learned at an early age, before fully conscious, before we develop a brain organ known as "cerebral cortex".
This organ starts to grow around 16 years old, and usually peaks around 45 years old. Decision-making is directly impacted, but humans can get "superpowers" by learning probability, especially Bayes.
This is explored in my book, in a high-school setting, in:
https://www.researchgate.net/publication/331414312_Statistics_and_Probability_to_Save_Your_Life
Seen that way, rather than somehow shameful, bias is mostly a consequence of early education.
Early education can also bypass natural limitations.
For example, Mozart could compose and play piano at 4 years old, when it is impossible to do so normally, as even the bones in the hand are not fully developed yet.
Gauss, also when very young and about 4 years old, could correct his father's arithmetic results, in calculations. When in school, his elementary teacher planned some time off while keeping the kids busy in class, and asked them to give him the sum of all integer numbers starting from 1 to 100. He was surprised when Gauss seemed idle, and asking Gauss, got the right result. Gauss had solved it as a series sum, using the middle term, something he was not taught at that age.
Many kids learned reading by themselves, trying to read the newspapers. A very young kid, playing with a calculator, but unable by age to calculate himself, told his father that 0 was not really a number. That's because, he said, it does not divide any number, like the others do.
There are many parents stories, showing that kids tend to see things in suprisingly different, although right, ways.
My hypothesis is that young kids, yet without bias from "education", can use their minds in non-binary ways, although using binary synapses. A kid in kindergarten can fairly divide a cookie in 3, an unending decimal.
To test this hypothesis, I tried to teach probability and Bayes model to high school seniors, in decision making, to totally suprising results for them and others. They could make wise decisions that older parents, with frontal lobe developed, could not. They delivered what I called "superpowers".
Neuroscience needs to update their results. People can separate observation from implementation, so that ternary logic can be used in a binary computer, as the physical brain with its synapses. Likewise, we observe that people can learn, listen, and converse in a language they have not learned yet, arriving at new conclusions while sleeping, as many people did, so we are not isolated nor incapacitated when sleeping. We are always thinking, always in communication, always working. COVID just made it clearer.
The future will take these and other natural possibilities into account, I hope. What I have seen is my own convincing factor. You may know more, and please feel welcome to share them by PM or publicly, here.
I can't really do anything if my heart is not in it. No one likes a "dictatorial command".
EG recognized that as "La Donna é mobile."
Initially, I was offended, but then I understood, as I realized that it is not a fault, but expected, and reasonable.
As a teacher, when students would complain that I (or another) changed state of mind, I would play the canzone by Giuseppe Verdi.
After all, new information comes in, and the world is not static, so we must pivot to survive.
Our incarnations are brief. It is easy to have the mistaken impression that we are in control. But we are not.
Sometimes it is necessary to "go along" with the ideas of others, for the sake of peace. And in other occasions, we must "face the battle royal" and do what the heart feels is right.
Because, if one makes a choice that goes agains one's inner convictions, suffering will surely result. Often times in the physical body as well. Have been told, "to forget about the physical".
Which reminds me, why give up anthropology for math? Did not happen. I evolved and required more quantitative thoughts.
Always enjoyed problem solving and finding solutions. Nothing better than a good solution.
It just so happens that the only degree I ever completed was a BA in anthropology...but compared to the collective hours of math/physics/logic study and editing....its just a drop in the bucket.
And....that degree was part of the journey.
Both my parents, all siblings, All our children work in math related fields...in addition to my spouse.
It became clear, early on, that a career in finance, accounting, real estate or banking would not be a good fit...and I could always benefit from the knowledge of others.
Languages were natural, and Computer Science interesting, yet intimidating...
Mathematics immersion became necessary for survival!!!
No one cares for my long winded answers....but a solution to a long standing problem...or even a glimmer of insight....is invaluable.
"Further, and still beyond my reach, but interesting, is "collective eletrodynamics". In his book, "Collective Electrodynamics" Carver Mead makes the subject quite approachable. In his foreward, he remarks,
"Many phenomena that in the past were seen as separate are now understood to be the same: Fire is a chemical reaction, not a separate element; temperature is energy; light is electromagnetic radiation; molecules are an aggregation of atoms; mechanical forces are electromagnetic in origin;...Each of these equivalences represents a major unification and simplification of the knowledge base. Ideas formerly occupying separate conceptual spaces now occupy the same conceptual space.
I was only briefly introduced to continued fractions, but EG published on them long ago, in 1980,
Article Continued fraction calculation of the eigenvalues of tridiag...
and continued fractions are well modeled in wooden puzzles.
Little wooden puzzles? Familiar toys that held a secret message for us. Not unlike the Antykthera mechanism.
To understand the rest of the story...it is in his blog.
The quote "jigsaw of squares" mentioned by EG, is not of arbitrary shapes (NOT a standard jigsaw puzzle), but is made up of only squares and rectangles. In summary, only squares are used, of different sizes. A rectangle can be made by two equal squares.
Any number has only one value, although many names are possible. Here, a number is a 1:1 mapping between a name and a value. This one value is represented by a "jigsaw of squares", always. No need for infinitesimals, Cauchy epsilon-deltas, nor hyper-reals.
Klotski (from Polish: klocki, lit. 'wooden blocks') is a sliding block puzzle thought to have originated in the early 20th century. The name may refer to a specific layout of ten blocks, or in a more global sense to refer to a whole group of similar sliding-block puzzles where the aim is to move a specific block to some predefined location. A "jigsaw of squares" can be thought of as a Klotski, and it can have unlimited blocks. Rational numbers have Klotskis of finite blocks. Finite integers can be put in 1:1 correspondence with rrational numbers, hence Klotskis.
The famous 1/3 problem in conventional mathematics (CM), is thought to be representable to infinity as 0.333... . Therefore, it is apparently not knowable, and where in CM one takes the leap that 1/3 = 0.333..., where a knowable (1/3) would be equal to an unknowable (0.333...). However, in continued fractions, 1/3 is the inverse of 3, which is 3 square blocks, knowable.
Have all the respect in the world for those in any field of mathematics. Requires dedication, tolerance, intellectual discipline and a willingness to accept the ideas of predecessors. But has to change. Or, how long should we, intelligent beings, parrot Cauchy epsilon-deltas-- when the topology is quantum? Finite integers are a field in mathematics and the basis of the 4 operations of arithmetic. Now, calculus with finite integers! Cauchy is outdated--by facts! We must base calculus on finite integers, giving analysis a new goal: to follow nature.
And the current state has to eventually advance to reflect the knowledge of current times.
There may be others that think differently among us. Already we have communication from films, in movies like, "Stand and Deliver" , "The Man Who Knew Infinity" the story of Ramanujan, "Flatland", and sequel, "The Arrival", "Mars" "The Day the Earth Stood Still"....and others.
Am waiting for more films on the contributions of the Mayans, the Egyptians, the Persians, Omar Khayyam, the Russians, the Turks....especially what has been considered taboo in American culture.
Until then, will do my best to provide feedback on a rather ambitious project, I am collaborating on 2 new books. Perhaps by sharing my own perspective, as I did in my project on RG, others will also. My interest is in attracting others to mathematics, which I do believe is important. , and one could be more....tolerant, saving exactness over ego. Any feedback is always welcome.
Regarding my new project entry, in:
https://www.researchgate.net/project/Gifted-Education-for-STEM
This is the context. It began with frustration with the math education of our youngest son in elementary school, and tried to leave the topic for the men. But I had a newfound appreciation for math. The recognition that without mathematical study, communication would be limited. Much of the population utilizes binary logic, though ternary logic is much appreciated!
Inspired by Richard Feynman, the idea that the best way to learn something is to teach it.
The influences: "Men of Mathematics" (where are the females???), "Developing Math Talent" by two females, and "The Man Who Counted" by Malba Tahan (fictional name of Brazilian author posed as an Arab and perhaps inspired by Omar Khayyam, e.g., with impressive solution for world peace by dividing a camel inheritance)
Found myself called to teach math for gifted students at one of the best high schools in La Jolla -- and learning from their students.
Was told, that, "Our math department is cursed, but you are welcome to join us!" There was a profound sense of frustration with calculus, and yet appreciation for discrete mathematics and computer science within the student community. I began to realise that my discomfort was not unusual.
Attempted college level calculus, but recognition of falsity kept me from accepting the apparent reasonableness.
About that book I am writing with EG, on a new calculus approach. We are using, in print and in online fixed version (Kindle), a format that is both interactive and open, where students can move at their ow pace.
This format has been invented-- before even the Internet! We are using what has been called "programmed instruction". This means having many versions of a book, within the same version, all leading to the same conclusions. Savy students can forge ahead, while delayed learners can entertain their doubts.
How To Update Your Beliefs Systematically - Bayes’ Theorem
People may think that emotions "sell", that emotions are some sort of "magic cocktail". RG has opinions that try to convince one to not follow logic, and rely on emotions. But mathematics is not invented, it is discovered.
Yet, logic has mathematical, infallible laws, one can and must rely on. Emotions, however, know no logic, and are used to "justify" breaking logic. How illogical!
The solution is to avoid an emotional pitch. It only reaches illogical customers-- but we are learning how logic works.
One can use Bayes theorem on updating beliefs. Its logic may confuse you, and guess .... who is right?
For example, the first two videos below may help, but the third video is ... a flop, for logical reasons that I explain below it. Everything is impossible, until it is done!, according to the correct use of Baye's theorem.
On Baye's theorem on updating beliefs vs conspiracy theories, or fear:
https://lnkd.in/g6HciRCW
https://lnkd.in/gSfzq3pg
https://lnkd.in/gQQn7DFz
Contrary to the narrator in the third video above, Baye's theorem tells us why Pearl Harbor was attacked, which the narrator does not seem to accept. Some of the causes still exist today, and 9/11 is evidence. Do not fall into the logic trap of the third video ... it is based on emotions.
What happens is... that ignorance is bliss. This is what a friend may mean, when offering you a "magic cocktail" or ...
But take stock on Baye's theorem. And... be aware and happy! Everything happens well, also for women. Instead of crying, think.
For anyone that wants to live to be 300 years young:
See Xeno Mueller for motivation.
He did his research...on himself! As an Olymic athlete, he demonstrates interval training interspersed with personal insights.
Watch "Great rowing workout. 45 Minutes". Hard for the ones who want to suffer happily, and great for all.
https://youtu.be/Tn-_AGEMwWM
Wait for the 3rd edition of our book, "Quickest Calculus", we are working on it from feedback. Quantum computing will easily follow from it. It will be significantly expanded. We will promote it free online for about 5 days. It will be available for anyone worldwide on Amazon. We will inform when available.
Mathematical Real-Numbers (MRN) are an incompatible mixture of types, where the MRN cannot be measured with probability 1 (cf. Nicolas Gisin, and others). They are a mixed bag. Have a Merry Christmas, Nicolas!
MRN are revealed to be an unnecessary invention by Dedekind (in 1888), and make calculus incomprehensible. We get the same calculus formulas in the set Q, the rational numbers, as explained in our book, "Quickest Calculus " with free PDF, and available in print.
I am Open For Business, in tutoring for calculus, free for the first 100 hours. No one needs anymore to be math-adverse.
Irrationals are solvable in algebra, albeit not numerically.
Examples using algebra (all algebra results are exact):
√2 = 2.sin(45 degrees)
log(√(a/b)) = 1/2.(log a - log b)
log(√3) = 1/2.log 3
√x.√x = x
((√2)^√2)^√2 = 2
e = ln(1)
i^i= e^(-45 degrees)
π (+ k.2.π.n) = 2×arcsin(1) (+ k.2.π.n), where k is in the set N.
π - √2 = 1.727 379 091 216 698 189 660 954 659 069 804 805 627 497 523 998 157 747 798 264 854 317 083 927 824 101 959 777 647 291 014 475 495 ...
It's not only infinitesimals that became outdated. Today, vectors are also no longer used in more advanced physics and engineering. You won't find research papers using them.
Vectors do not work past 2D. E.g., the product of 2 vectors is not a vector. One needs scalars, multivectors, or tensors. Math should also stop using vectors, one day.
Scalars are simpler, and better. See Euler-Lagrange methods, that only use scalars and yet can do more than the Newton method with vectors.
From our book "Quickest Calculus" in free PDF at RG:
"Vectors, multivectors, and complex numbers are not used in this book. This book uses numbers as scalar quantities only. This can be easily extended to multivectors and complex numbers though, following Grassmann and Clifford. Vectors are restricted to 2D, and not considered trustworthy in physics, hence not to be trusted in mathematics in the 21st century."
Do you need the references for Grassmann and Clifford? There has been no important paper published using vectors in physics journals, for +100 years. One uses scalars in Hamilton also or Lagrange formulations.
Some references from our book "Quickest Calculus":
[1.1] Hermann Grassmann, "A New Branch of Mathematics: The Ausdehnungslehre of 1844 and Other Works", Open Court Pub Co., ISBN: 0812692764, 1995.
[1.2] John Browne, "Grassmann Algebra", Barnard Publishing, ISBN: 978-1479197637, 2012.
[1.3] William E. Baylis (Ed.), Clifford (Geometric) Algebraic, Birkhäuser, ISBN: 3-7643-3868-7, 1996.
From a previous conversation, by EG. It is worth repeating. This is not philosophy.
In the 21st century, one cannot talk any more about continuity, infinitesimals, Lie numbers, or qubits.
Many solutions and tools in mathematics, not to mention physics and biology, are hidden when one insists. For example, Boolean derivatives, and quantum solutions to Schrödinger's equation. Not only eigenvalues are discrete but there are no continuous eigenvectors. There is also no wave-particle "duality". GR meets QM. Quantum computing needs tri-state+.
A lot of opportunities will be missed by those who lag. New fields are being created as we speak.
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