# Ed GerckPlanalto Research · Mathematics and Physics

Ed Gerck

Ph.D. (Physics, LMU, München)

Digital computers are exact using B={0,1}, enabling set Q, and for arbitrary-length numbers. Thanks to Moore 🙏🙏

## About

221

Publications

274,182

Reads

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628

Citations

Citations since 2017

Introduction

https://www.mdpi.com/2227-7390/11/1/68 . Quantum computing is not done by a cryogenic behemoth, but is ubiquitous; the mind and the atoms do it. Thus, math and physics can do it. I am not defining nature nor evolution. I am just pointing out "not this way!".
✍️ https://www.researchgate.net/post/Introduction_blog_using_RG_and_AI

Additional affiliations

June 2014 - December 2022

**Planalto Research**

Position

- Researcher

Description

- A scientific cooperative, and successor of Gerck Research. Page at https://www.linkedin.com/company/planalto-research/

May 2001 - March 2022

**NMA, Inc.**

Position

- Principal Investigator

Description

- Developed and widely published blockchain in 2001, thus protected and prohibited any patent. Protected by trade-secrets. End-to-end encryption and authentication that is secure and easy to use, and works in any platform without change.

January 2000 - April 2022

**Safevote, Inc.**

Position

- Principal Investigator

Description

- Chief scientist and lead developer of provably secure and private online voting technology, first positively qualified by the California Secretary of State in 2000 and by the Swedish Government's Ministry of Justice Statskontoret in 2001. Pre-empted any patent on Witness-Voting systems by publishing widely on many venues, including Springer-Verlag.

Education

January 2021 - December 2022

**Planalto**

Field of study

- Discrete Mathematics, Quantum Computing

September 1980 - January 1983

September 1979 - March 1983

## Publications

Publications (221)

A new method of calculus, makes integral calculus follow differential calculus, that follows absolutely exact modular arithmetic in a finite set of integers. The result is the same formulas of conventional calculus but faster to learn, to use, and leading to new applications. Discontinuous functions can now be differentiated, GR can meet QM, factor...

We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report --- contrary to conventional assumptions --- that differentiation of discontinuous functions (DDF) exists in the set Q, which is central to algorithms for quantum computation. DDF have been thought to exist not in...

When making binary decisions, one is helped by the LEM: Law of the Excluded Middle. This is fast, however, recognized as an internal measure of success, much like a Procrustean Bed. This leads to the well-known Gödel uncertainty, exemplified by the liar's paradox,
where known true statements cannot be logically verified in the system under conside...

This work shows that biology, as a natural science, can soon be "exactly as measured", as physics, and promote the development and application of love and 5 types of faith in a clinical treatment. This promises to be an outstanding help for medicine, and a reduction on the irreducibility that currently plagues it. The current diagnosis and treatmen...

Quantum computing began in 2022, yet it became possible in 1978. This work introduces the quantum set, called Q*, and deprecates mathematical complex numbers (MCN), with the use of an impossible operation, the square-root(-1). The new set uses, on purpose, the same name as the letter as the set Q of rationals, but with an added rotation and arithme...

This work shows that non-boolean logic can be used in medicine to help application of love and 5 types of faith in a clinical treatment. The current diagnosis and treatment methods of medicine can profit from being reformed and use modern methods of quantum computing and non-boolean logic in order to aspire to reach better performance. Non-statisti...

According to given references, the mathematical real-numbers (MRN) are immeasurable with probability 1. The only difference between FT (Fourier Transform) and the FFT (Fast Fourier Transform) is that FT considers a mythical “continuous” signal, while the FFT takes a discrete signal as input. Thus, FT = FFT. The FFT, with efficient implementations t...

We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report --- contrary to conventional assumptions --- that differentiation of discontinuous functions (DDF) exists in the set Q, which is central to algorithms for quantum computation. DDF have been thought to exist not in...

ABSTRACT:
Irrational numbers, with unbounded length, can be used algebraically as a "name'', such as e. Albeit, they cannot be used in arithmetic, as a value. Computer calculations, need to be able to use arithmetic to compute numerical results. E.g., although the Euler number e is defined as the finite unitary area under a unit hyperbole from 1 t...

As well-known, waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. Although these equ...

Classical information theory follows the discovery by Shannon, of a 1:1 mapping between digital circuits and Boolean (binary) logic. But, at the turn of this century, it was discovered that besides the passing/blocking (on/off) functions of a relay, a digital circuit could also process information coherently. This was called "network coding" and fo...

Introducing what we call Digital Constructivism (DC), this work does not use or change Conventional Mathematics (CM). This presents a "click-mathematics", that works as Lego, where one can take apart derivatives to create and assemble differential forms, solving differential equations qua algebra. Integrals are solved by observation, without effort...

This work uses the algebraic approach to show how we communicate when applying the quantum mechanics (QM) concept of coherence, proposing tri-state+ in quantum computing (QC). In analogy to Einstein's stimulated emission, when explaining the thermal radiation of quantum bodies in communication, this work shows that one can use the classical Informa...

The Schrödinger equation for bound states depends on a second derivative, that only exists iff the solution is continuous, which is -- by itself -- contradictory, and cannot be digitally calculated. Photons can be created in-phase by stimulated emission or annihilated by spontaneous absorption, and break the LEM, more likely at lower frequencies, a...

The development of nanoelectronics devices needs to involve quantum computing in allowing prediction of the desired structure of matter. Whether we want to use binary logic, ternary logic, or other is still open. This work uses the algebraic approach to show how one can communicate when applying the quantum mechanics (QM) concept of coherence, prop...

With our quantum computer (QC) now working to easily factor large numbers, this work describes various tests, that anyone can perform, using the well-known RSA cryptosystem. We are providing this as a public Zero-Knowledge Proof (ZKP) that anyone can verify online as soon as the paper describes the address, which is public, without compromising the...

We are bringing a large chunk of theoretical physics to bear on important mathematical problems. Conversely, one hopes to learn from a century of analytic number theory and Galois numbers to better understand several issues of modern physics. But it is in prime number calculations and making the first quantum computer (QC) that is presented here. T...

The double-slit experiment is seen as a "coherent multiplier", by following ASE (amplification by stimulated emission), as in a LASER. The photon is a particle in this model, but can be harmonized with the wave picture by considering finite integer fields, as Galois fields. This is considered in universality.

We present a new vision on the double-slit experiment (DSE), that does not use any waves or the so-called wave-particle duality. It is based on particles, viewed as localized vibrations. The DSE is explained physically as a LASER. LASER means Light Amplification by Stimulated Emission of Radiation. Mathematically, this work uses the algebraic appro...

This work uses the algebraic approach to show how we communicate when applying the quantum mechanics (QM) concept of coherence, proposing tri-state+ in quantum computing (QC). In analogy to Einstein's stimulated emission, when explaining the thermal radiation of quantum bodies in communication, this work shows that one can use the classical Informa...

Our goal is to allow quantum computing to have a quantum computation test, without using hardware. The implementation problem is how can it handle in code what needs to satisfy the Bohr quantum hypothesis. The chosen method is to calculate in code what is 0/0, an undefined operation in mathematics, although the inverse operation is valid -- any num...

This work uses the algebraic approach to show how we communicate when applying the quantum mechanics (QM) concept of coherence, proposing tri-state+ in quantum computing (QC). In analogy to Einstein's stimulated emission, when explaining the thermal radiation of quantum bodies in communication, this work shows that one can use the classical Informa...

The Schrödinger equation for bound states depends on a second derivative, that only exists iff the solution is continuous, which is -- by itself -- contradictory, and cannot be digitally calculated. Photons can be created in-phase by stimulated emission or annihilated by spontaneous absorption, and break the LEM, more likely at lower frequencies, a...

An algebraic approach, with Galois fields (GF), directly or extended, is proposed in terms of practical classical and quantum applications. Information is shown to be tri-state+ in communications and in information transfer with or without bodies, where GF(3^n) offer a better match than two-state solutions using Boolean logic.The work is based on m...

Although quantum mechanics (QM) unquestionably requires discrete values, it has been presumably accurate when using continuity with derivatives to calculate them. We calculate the second derivative as a first-order difference equation, depending on the curvature (1D). This is variationally solved for natural numbers, representing the quantum levels...

The Schrödinger equation for bound states (SEBS) depends on a second derivative, that only exists iff the solution is continuous, which is -- by itself -- contradictory, and cannot be digitally calculated. Physical representations of quantum systems, cannot, thus, follow some computational aspects of quantum mechanics. This is solved by considering...

Classically, information processing and communication are described by a tri-state system. This has replaced the Boolean algebra of a two-state system, also in gate construction with physical systems. The most fundamental entity in today`s quantum theory of information is, however, still a two-state system, the qubit. This work corrects this stance...

A QFT replaces the old SM -- where there are no "particles" in Nature, only localized vibrations of a field. Therefore, there is no "wave-particle" situation -- there are no classical waves and no particles in Nature, nor any "mixture" thereof. The "wave-particle" duality is observer-dependent, not a "fact" of Nature. Only quantum waves exist in Na...

The solutions to the relativistic Euler-Lagrange equation for the Lagrangian of a system are given here, and describe the evolution of that physical system, correctly and exclusively in terms of momentum -- mass is not used. We do not live in 4D, but in 3D+1D world, which is physically realizable within 4D, while 4D is unseen. This takes the same f...

There are more real numbers than there are natural numbers, which opens the door to the investigation of the different sizes of infinity, and is reflected in the Lebesgue measure in mathematics. All that we can physically measure, though, are finite rational numbers. In that background, we propose first that infinity should mean an unknown number i...

The conclusion that the measurement of extremely small distances is physically impossible, which preempts continuity, was already considered by Leon Brillouin ca. 1956, and now is proved in this work, as well as reporting on new results including the scalability of quantum computing, quantum chaos theory, and the unification of general relativity w...

The conclusion that the measurement of extremely small distances is physically impossible, which conflicts with continuity, was already considered by Leon Brillouin ca. 1956, and now is revisited in this work, advancing Galois fields. Consequently, we report new results including the scalability of quantum computing and the unification of general r...

We formulate a QM variational principle in all coordinates of relativistic spacetime in equal footing as fractal dimensions, with entanglement, and consider an abstract, discrete field f(x) with a topology given by the finite rational numbers, all that one can measure physically, which permeates spacetime. Next, we consider vibrations of this discr...

This work introduces the quantum theory of gravitation (QTG) in general relativity (GR). The QTG includes: (1) quantum mechanics (QM), with a discrete topology for spacetime; (2) energy, with a quantum spacing; (3) geometry, with real numbers in a physical dual space; (4) quantum entanglement, with the self-similar (fractal dimension) equivalence S...

The prevailing custom in medical and psychological communications has been to send a fax. Faxes are currently fundamental to the entire health system, certainly in the USA, where the great majority of practitioners use faxes. Similarly, in 2018, two-thirds of Canadian doctors reported that they primarily used fax machines to communicate with other...

There are no particles in Nature, no electrons either. This changes EM. The Maxwell equations are no longer valid, and as they did not foresee the laser, they do not foresee the next "laser". We show that quantum mechanics (QM) has completely removed the scientific support for Maxwell equations in electromagnetism (EM), which turn into a hollow str...

We investigate secure communications in an inhomogeneous medium, e.g. the Internet, where a semiotic model is used to represent the entire data being transmitted. The semiotic model calls for four different channels: signs (names), references, referents, and trust. Trust follows the definition by Gerck in 1997 (“trust is that which is essential to...

This book deals with the physics of solving the Schrödinger equation for bound states. One can read many books similar to this, but the premise and consequences are different for this work. Our premise here is a novel mathematical correspondence between the Schrödinger equation for bound states, the Sturm-Liouville problem, and finite differences o...

How trustworthy is the information in Wikipedia (WP)? This question is important for all WP users. Since March 13, 2007, this experiment conducts a long-range test to help answer this question, focusing on physics and mathematics topics. The answer is also applied to improve or deny the trustworthiness of online data sharing, WP, and online use in...

A set of macro-world processes that "always win'' in the limit, would not be possible at first sight in thermodynamics, but are shown here, using Shannon's Information Theory. We also discuss Shannon's unicity in Appendix A, using concepts of thermodynamics, as the amount of entropy, as disorder, that can be added to a text by enciphering it. The m...

By requiring variations in all directions to equal zero (the variational principle), one can obtain the Euler-Lagrange equation both in SR and in the Schroedinger equation regime (non-SR QM) -- as well-known -- leading to RQM (SR + QM), and QFT as well-known. This extends, not contradicts, F = ma, Newton's law, and also obeys the Euler-Lagrange equ...

This book shows that the Euler-Lagrange (E-L) equation points to new physics, such as special relativity, quantum mechanics, electromagnetism, general relativity, and thermodynamics theories, and is likely to point to whatever we may find in Nature, such as dark matter and dark energy, as a general formalism. This work also reviews the E-L equation...

The topological genus in the precession of Mercury is shown to be 0, not 1. It has a different topology than currently assumed. This breaks Kepler's first and third laws, while supporting Kepler's second law. We also suggest that quantum mechanics (QM) is already harmonized with special and general relativity (SR/GR), under digital constructivism -...

Different formulations of special relativity (SR) exist today, of what is, more and more, seen in all sciences, fitting the original name of a "theory of invariants". We present here a number of misconceptions still persistently affecting the Minkowski formulation of SR, which is the formulation tested and preferred in physics. Other formulations o...

The problem described here include basing beliefs on misinformation and pseudoscience, albeit it also includes the human tendency to be on the intersubjective or even subjective “right” -- even though not objectively right. Consensus (i.e., "Byzantine agreement") is one of the fundamental problems in fault-tolerant distributed systems, and in Theor...

The extension of special relativity (SR) to arbitrary motion, including accelerated, and general relativity (GR) constitutes the basics of this joint study of SR and GR, in terms of the same spacetime formulation, presenting a consistent theory. The GR principle of equivalence, however, is shown to have problems, when not formulated as originally s...

One can not really visualize √2, but one can visualize √-1, and apply it in physics and engineering. This work is an exploration of complex analysis as a tool for physics and engineering, and offers new topics. Although nothing in reality is a “complex number,” it includes an overview of the topics in four investigations, included as appendices. Re...

Continuity is well-defined in calculus. This does not mean that continuity exists in Nature, as in physics, engineering, chemistry, biology, geology, computer code, or in constructive mathematics. It does not. It is not seen nor able to be made. Continuity just means an academic condition affecting pure mathematics. That is academically acceptable,...

Comments by the authors, held to a minimum. If additional help seems needed, please contact by PM.

Different formulations of special relativity (SR) exist today, of what is, more and more, seen in all sciences, fitting the original name of a "theory of invariants". We present here a number of misconceptions still persistently affecting the Minkowski formulation of SR, which is the formulation tested and preferred in physics. Other formulations o...

A set of macro-world processes that "always win" in the limit, would not be possible at first sight in thermodynamics, but are shown here, using Shannon's Information Theory. This is also of importance to the issue of the arrow of time. It shows that the second law of thermodynamics can be circumvented, while the first law cannot. We suggest that N...

This work shows that the Euler-Lagrange (E-L) equation points to new physics, as in special relativity, quantum mechanics, thermodynamics, and quantum field theory, and is likely to point to whatever we may find in Nature, such as electromagnetism, general relativity, dark matter and dark energy, as a general formalism. This work also reviews the E...

This work reports on different efforts to causally prevent "microscopic" folding of past, present, and future from "macroscopically" affecting reality, and is represented in reverse by a large number of birds doing a macroscopic pattern in the sky, albeit microscopically avoiding it. For a metaphor in CS, a finger may type D on a keyboard, but G wa...

This work calls out the entire set of Clifford Algebra results (including multivectors) physically, due to its lack of covariance with special relativity (SR), which cannot be solved, and the lack of mathematical isomorphism with tensors. The mathematical correctness of the Clifford Algebra is not affected. As a result, proved here, Cl(3,1), Hesten...

In addition to the traditional division of observers, into inertial or not, we verify that observers can -- more significantly and independently -- also be divided into comoving (i.e., same position and speed) or not, introducing collective effects. This expands, without conflict, Minkowski spacetime and the SR/GR notion of independent reality to a...

Consensus (i.e., "Byzantine agreement") is one of the fundamental problems in fault-tolerant distributed systems, here tested in an open, online, large discussion in ResearchGate. As we show here, the disruption or noise can be used in feedback, to help separate noise from signal, turning the problem into that of filtering-out the noise, not blocki...

Students usually overreact when facing an error, by others or even their own. This paper deals with this issue, as well as how to best present an item for routine academic evaluation (such as a list of exercises), where errors may come up. How to handle an error? Errors are treated according to information theory, but do not follow Boolean logic. I...

Without using Maxwell's equations, this work introduces the Electron Magnetism Model (EMM) of electromagnetism. The EMM is an invariant, gauge model, overcoming special relativity limitations, without necessary collective effects (can be a single particle). The EMM generates a correct electromagnetic field, as well as experimentally-correct E and B...

Physical possibility must come from Nature (the physics-defined independent channel), as an empirically-defined world, which can be at odds with a mathematically-defined world. We show that only an underlying 4D+ spacetime, with a "fusion" of space and time, that one cannot uniquely divide, can explain all the experimental facts. The results are ob...

This work is an exploration of complex analysis as a tool for physics and engineering, offering new topics. Although nothing in reality is a “complex number,” it includes an overview of the topics in four investigations. Results begin and end in real number theory, but have a path through the complex plane, which influences the result, but remains...

The topological genus in the precession of Mercury is shown to be 0, not 1. It has a different topology than currently assumed. This breaks Kepler's first and third laws, while supporting Kepler's second law. We also suggest that quantum mechanics (QM) is already harmonized with special and general relativity (SR/GR), under digital constructivism -...

We introduce probability, exploring both the Frequency and Bayes definitions. We also examined an aspect of the evolution of the teen brain, the development of the frontal lobe cortex, until age of 45 years-old. Teens can access “Superpowers” by following this method. A decision is right if it obeys two conditions. We also review the Dempster Shafe...

It is known that finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when the eigenvalues correspond to highly oscillatory eigenvectors. Numerically, integration has to take increasingly smaller steps. This occurs also for high-index eigenvalues. We present an analytical solution, without this...

This work introduces a new form of the second derivative in an orthonormal, complete, infinite set of functions {e -× , x.e -× , x 2 .e -× , …}. The form can be calculated, piecewise and exactly, on only two points, and is called the "Exponential Difference". The linear piecewise combinations obey the boundary conditions y(0) = y(oo) = 0, usual in...

We consider the Sturm-Liouville Eigenvalue (SLE) problem, and also the inverse SLE (iSLE) problem. This work presents a mathematical model for the Matrix-Variational Method (MVM), to solve both SLE problems, in physics, due to Gerck et. al., from 1979. We show an intuitive model, with fitting suggestions that can be used for teaching physics, inclu...

The extension of special relativity (SR) to arbitrary motion, including accelerated, and general relativity (GR) constitutes the basics of this joint study of SR and GR, in terms of the same spacetime formulation, presenting a consistent theory. The GR principle of equivalence, however, is shown to have problems, when not formulated as originally s...

Things do not shut-off because of acceleration, and quantum mechanics must agree. The way physicists have viewed the Einstein theory of special relativity (SR) has changed throughout the years, including by Einstein. We discuss the existence of relativistic neutral particle accelerators (RNPA), providing four natural examples. Their not existence,...

This work is, first, a literature review on interpreting length contraction and time dilation, in special and general relativity, with a view to Cosmology, based on the definitions of comoving. It is shown here that the usage is different but coherent. Second, comoving and non-comoving, as well as length contraction and time dilation, are shown to...

The idea that consciousness is not biological but ubiquitous is based on Newtonian physics, used in the Third Law, and extended to quantum
mechanics in stimulated emission. This work proposes how to measure what we seem to understand by consciousness, and do so even online. The idea may seem uncanny, and even cognitively dissonant, and it certainly...

NOTE: Global warming is NOT a global issue from the viewpoint of known Physics. Because of the Earth's rotation (Coriolis effect), it must differ in North and South hemispheres, that have different, non-comunicating, pollution rates. The Amazon is not the "lungs of the world." If we see a global effect, as we may have seen in Australia and Brazil,...

This work revisits the view of G. Ellis and P. Silk, that intends to define the demarcation of physics, by presenting a tested alternative. Emerging in the past 150+ years in physics, but seems unnoticed in its effects, however promising to all sciences. Our task is to find in all the relative data from phenomena (which is all physics is limited to...

This work introduces a relativistic, Electron Magnetism Model (EMM) of electromagnetism. The presence of an electric field proves there is an electric charge, while the presence of a magnetic field proves there is an electric charge in motion, according to the EMM. In the quantum regime, we go even more microscopically, introducing the quantum EMM,...

he Scientific Method is a fundamental tool in exploring the limits of knowledge and life. However, its understanding is often beset by misconceptions, leading to errors in advanced research and even day-to-day decisions.

We show that a focus on the absolute, the invariant, has helped scientists and egineers solve the problems they are investigating. Over the past 150 years physics has gone from a science of testable, relative relationships between variables to a science of invariable, universally valid absolutes. This presentation discusses how this Big Idea in phy...

The Scientific Method is a fundamental tool in exploring the limits of knowledge and life. However, its understanding is often beset by misconceptions, leading to errors in advanced research and even day-to-day decisions. For example, it is a common mistake to think of a hypothesis as a guess or a prediction, or to assume that a hypothesis must inc...

[The full slide deck will be added here as a dataset, after the presentation at the La Jolla Riford Library, Calif., 6:30 PM, 2 August, 2016] It is assumed that any process in the brain can be investigated in natural science terms, such as using physics, chemistry, neurosciences and biology. The mind is often described as a result of brain activiti...

[This presentation is planned as a hands-on workshop in the BioLab program at the La Jolla Riford Library, Calif., at 6 PM, 5 July, 2016] A fundamental merit of natural science, including physics and biology, is being a science of testable relationships. But this is also exactly its fault. Yes, we have multiplied the power of our means of observati...

How trustworthy is the information in Wikipedia (WP)? This question is important for all WP users. Since March 13, 2007, this experiment conducts a long-range test to help answer this question, focusing on physics and mathematics topics. The answer is also applied to improve or deny the trustworthiness of online data sharing, WP, and online use in...

This workshop includes the Scientific Method and the Brownian Motion experiment, directly applying and contrasting scientific principles in exploring the limits of life and physics. People may find this shocking, but science is not about finding truth. In science, a YES means ”not yet false”. A NO means ”may be true”. Science is about exploring, an...

This paper discusses some limitations and failure modes of the conventional approach to information security, including aspects that are frequently treated in isolation but have a strong coupling to each other, such as physical, technical, administrative, and external control elements. We analyze a common failure mode that we call "The Fort Knox Sy...

We view the scientific method as a game, where everyone can play, everyone wins, but it matters how well you play. We also review what does it mean to be alive and the Brownian Motion experiment, as a key experiment in many areas, from Botany to Biology, Physics, Chemistry, Mathematics, Engineering, Finances, and Wall Street. We use the Brownian Mo...

PREAMBLE: This is an early example (12 years ago) of using Ukraine's "scorched earth" approach, where we try to cope with the mounting hazards of Internet security, as we apply war terms and methods.
ABSTRACT: We show that one can create an arms-race scenario where defenders (users) are always one step behind. We motivate the need to find ways an...

We present a new, comprehensive framework to qualitatively improve election outcome trustworthiness, where voting is modeled as an information transfer process. Although voting is deterministic (all ballots are counted), information is treated stochastically using Information Theory. Error considerations, including faults, attacks, and threats by a...

Comparing truth and trust lead to a better understanding of both, and more secure designs. (READ AS AN APPENDIX AT https://www.amazon.com/dp/B07ZPLYCMD )

For two parties in a dialogue, this paper classifies all possible certification procedures in two models: extrinsic and intrinsic, with a combined mode. All known security designs correspond to the extrinsic model -- which depends on references that are extrinsic to the current dialogue, with certification relative to a third-party or past events....

This work applies to all online applications and services that require user login or access control, possibly the top security problem facing Internet users today. We appraise the affordability, security and usability of Internet user access control systems by using five frequently asked questions. We evaluate username/password and the cryptographi...

Online secure delivery of documents, health records, legal signatures, credit authorizations, and goods such as music and movies are increasingly supported by regulation worldwide. However, email security has been lagging in providing suitable delivery means. This work extends a previous usability and security comparison of the secure email technol...

This is a public discussion paper on email security. The paper is published in sections, each section presented after sufficient time for feedback. Join the discussion in the Blog and help shape this paper and its conclusions.

## Questions

Questions (156)

## Projects

Projects (14)

INTRODUCTION
QM stands for quantum mechanics, CS for computer science, CC for cellphones/computers, and Mathematics seems to have somehow missed all three.
Now is the time to catch up. We have come to a stand off. Students are ending up neurologically sick -- feeling math-averse (neurophobia and math trauma).
It is not a matter of selection. Only group/rote work [1] seems to infuse Mathematics, as taught today, even in highly-qualified students. Paradoxically, one finds that the more intellectually qualified, the more averse!
And yet current Mathematics still tries to "instruct" it to the students, and other disciplines, in the US and the world.
This failure has been denied [1], and the “fault” has been put on the victims -- the students. Paradigm shifts are needed: first, QM.
According to QM, only integer numbers should be necessary to build all one can see in nature. Otherwise, all of Physics would be contradicted. This would also contradict all of CS and all of CC. Computers, for example, only work with integers, and are error-free.
Since this contradiction is not even imaginable, QM is ontologically correct. Therefore, all sciences must reflect it, according to a "holographic principle" (HP) in nature, including Mathematics.
The HP is often referred to as "the micro as in the macro" or vice-versa.
These two words macro and micro are commonly viewed as antonyms, meaning that they are the opposite of each other. Macro means on a large scale. Micro means on a very small scale. Both are important, though often complementary, views of nature. The view from the macro, while taking into account the micro, is called "universality" in Physics.
The QM main principle was given by Niels Bohr as, "all states at once". This needs to be understood as different from the following possibilities:
"Copenhagen interpretation", or
a "collapse" of the quantum function upon measurement, or
waves, as a picture of QM, or
wave-particle duality, or
the Heisenberg principle, or
a probabilistic view of QM.
In opening the "black box" of QM as viewed by Bohr, QM does not represent Natur (defined by the philosopher Kant), but Wirklichkeit (ditto). It is not how nature is, but seems to work. A story.
A known analogy is the Plato's Cave". The shadows one can see on the wall are Wirklichkeit, and the open reality outside is Natur. After watching Wirklichkeit for some time, people can make an idea what Natur looks like, even though imprisoned in the Cave.
QM is, ontologically, how one can describe Wirklichkeit -- which is the subject of Physics. Natur may not have QM behavior, and continuity may exist in Natur.
Mathematics is not concerned with Wirklichkeit only, but can include Natur. Although, as no one can see Natur, one is led to treat any "pure" Mathematics as a speculation.
Albeit, Mathematics must agree with Physics in the realm of Wirklichkeit.
This does not happen today, and creates a clash. The inconsistency is seen as an opening. What IS mathematics?
Today's calculus teaching can be seen as relying on outdated ideas, going back before QM, computer science (CS), and cellphones/computers (CC) were discovered. Three major paradigm shifts seem to have been missed.
But these three paradigm shifts represent how science is done, in our seemingly endless task in going from Wirklichkeit to Natur.
One recognizes then, that science does not behave continuously, but by jumps -- that break from the past, and open a new future -- in going from Wirklichkeit to Natur, and back -- does the envisioned Wirklichkeit reproduce the actual Wirklichkeit?
This has been called a "paradigm shift" (PS) by T. S. Kuhn in Structure of Scientific Revolutions [2].
David Hilbert [3], at the turn of the XX century, proposed twenty-three problems intended to guide research in the dawning century, claims otherwise, that “History teaches the continuity of the development of science.”
Michael Harris [4], a mathematician, writes that he, "would still be glad to lift the veil, but we no longer believe in continuity. And we may no longer be sure that it’s enough to lift a veil to make our goals clear to ourselves, much less to outsiders."
The outdated ideas currently in Mathematics date back to the time of Newton, Leibnitz, and Cauchy, before the 3 PSs mentioned. They include (aka Fictions, or incorrect models): microscopic continuity, infinitesimals, hyper-reals, Cauchy epsilon-deltas, and Cauchy accumulation points.
Even in 4-year universities one finds classes, such as at Caltech, MIT, CSU, and abroad, teaching Fictions today [1].
This failure can be denied [1], and the “fault” can be put on the victims -- the students. But, there is no feeling of inferiority. PS [2] combats this, American style -- by innovation.
A technical innovation can reduce this gap by a PS [2] -- already heralded and error-free, as one can see in the history of sciences (contradicting David Hilbert [3]).
This reduces risk by following an experimental model that works, even though no one has explained it mathematically, without Fictions.
By jump-starting to QM one has a solution, which we mark as a first paradigm shift.
Where Fictions interfere with known Physics, they must be mercilessly deprecated -- although, and yet, current Mathematics still tries to "instruct" it to the students, in the US and the world.
The other paradigm shifts, stand for computer science (CS), and cellphones/computers (CC).
We now introduce a coherent, holographic principle (HP), a universe, and understanding yet to be discovered, as two new paradigm shifts -- and gain a cosmic perspective: who is the Creator of all this marvelous scheme?
This final PS leads to a comment. One does not need to learn anything, confirms https://www.researchgate.net/profile/Robert-Fuchs
One just has to observe.
Mathematics seems, thus, to be discovered — as a hologram and coherent with other sciences, and not, somehow, invented by mere humans.
ACTION PLAN
This new RG project will follow this -- in QM, and reforming mathematics by a PS [2].
It is future-proof, as special relativity is, and promises to be as revolutionary to several disciplines.
The main innovation is to obtain the same traditional formulas, with added results. But only using integers, which the Mayans did in astronomy, Per Martin-Löf in CS, and CC use -- avoiding Fictions, and any difficulty to teach them [1].
AG embraced this method successfully at top public high-schools in La Jolla and San Diego, Calif., avoiding group/rote work, using its futility [1] to the students' advantage.
To counter-exemplify, if one calculates a derivative using Fictions, one would soon pass the matter limits in molecular size, atoms and even quarks. This makes results unphysical and untrustworthy -- as students know today.
To exemplify, CC can calculate this text as it is stored in magnetic domains, and subject to many read/write errors. Coprocessors do not calculate in “reals”. Encryption defends e-commerce. All these methods use only integers, and are error-free.
To further reduce business risk, facing expected skeptical opposition, we plan to add more technical personnel, attracted by the timely opportunity, combating fear, uncertainty, and doubt (FUD), and the Dunning-Kruger effect, through several PSs [2].
We envision a series of books, talks, and online material, emulating today the goals of the School Mathematics Study Group of 1958, when Sputnik stunned America, and learning from opposing FUD. The books include some introductory self-teaching books and others, more advanced.
REFERENCES
[1] https://edsource.org/2022/high-calculus-failure-rates-thwart-students-across-csu/664771
[2] T. S. Kuhn, Structure of Scientific Revolutions, 1962.
[3] David Hilbert, Paris International Congress of Mathematicians (ICM), 1900.
[4 I] Michael Harris, “Mathematics Without Apologies”, Princeton University Press, ISBN 978-0-691-1-17583-6, 2017.

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We are revisiting the Scientific Method. It can be better understood using TCS (theoretical computer science) and univalent mathematics theory. It is not a guess. It is not testing many probable hypothesis.