Updated information of my thoughts and activities.
This is meant to be a one-way blog, albeit you can contribute with your recommendations and comments.
Announcement of quantum computing breaking RSA for numbers larger than 10^1000 (the maximum number reported by IBM in arxiv was 35). This is to be compared (as possible) with our Announcement.
See https://www.linkedin.com/posts/edgerck_rsa-cybersecurity-has-been-broken-by-quantum-activity-7112926622009229312-Xey7
NO. It is impossible to doubt, the race was over before it begun.
Quantum computing started in 1982 at the Max Planck Institute for Quantum Optics (MPQ) [1-3].
[1] DOI /2227-7390/11/1/68
[2] DOI 10.1016/0771-050X(80)90020-0
[3] June 1982, Physical review A, Atomic, molecular, and optical physics 26:1(1).
ZSentry was the only cybersecurity that let you do what you want, not what silos want, and it was certified to be HIPAA compliant, albeit it was killed by Google when it stopped to offer free customized domain names to clients of Google Gmail.
This was a natural evolution for Google but killed many business models, many companies.
ZSentry pioneered blockchain in 2001. ZSentry was all-In-one, with App, Client and API. Relieved privacy, security, mobility and compliance concerns, with no changes -- while working transparently with silos, like Apple. It was already optimized for mobile use, Android and Apple, in 2004 to 2018.
Now, ZSentry has a revival coming soon, not dependent on Google, still end-to-end HIPAA compliant, and certified by the U.S. government to be HIPAA compliant, albeit also post-quantum secure.
This will be proposed and verified publicly, subjected to NIST and the IETF, and by public scrutiny. Investors will be rewarded by a donation model plus a paid service, and the company NMA is seeking just 2 million US dollars in consolidation investment. Development team payroll is guaranteed, by other activities.
The company had initially just 1 million US dollars in angel investment, to finance product launch; which it accomplished successfully. It is a comparatively riskeless investment, vis-a-vis what was developed and tested publicly already.
It is also the only tested and viable post-quantum algorithm, necessary for all and to be offered publicly -- with the demise of RSA (see publication in ResearchGate for large primes).
The ZSentry algorithm will be published, avoiding export restrictions and patents. Also, it will be free to use, but supporting a paying model for updates.
ZSentry is a good replacement for PGP, and X.509 or a PKI, solving lingering questions on certificate revocation and change, including non-repudiation.
Coming soon ...
Quantum computing reveals quantum properties in numbers?
This question reached a YES conclusion" in ResearchGate. It is in my profile at ResearchGate, at:
https://www.researchgate.net/profile/Ed-Gerck
It serves the purpose of explanation to those interested, as an open group, from a core of 10 participants.
This deprecates the Peano axioms, and provides a new source for 4+ quantum properties of numbers, that affects N, Z, and Q -- deprecating R and C, eliminating irrational numbers, infinitesimals, and p-adic numbers while changing Newton calculus to confirm Mādhava's formulation in India -- 250 years before Newton in the UK.
People who want to read my 2 PH.D. thesis can request a copy at each library.
The last one (in Mathematics and Computer Science, awarded with A+ by Planato Research in the U.S.) is easier. It was published in totum, without cost, on Christmas Day 2022, by MDPI at their journal Mathematica and is free online. It invalidates not only irrationals, but infinitesimals, imaginary numbers, p-adic numbers, and Newton calculus. A very clear thesis!
My PHD in physics was not only done at 2 prestigious places in Munich, the MPQ and the LMU, and received the maximum grade (sehr gut), but developed the basis for quantum computing -- which has been pursued since 1997.
Quantum computing started in 1982 at the Max Planck Institute for Quantum Optics (MPQ) [1-3].
[1] DOI /2227-7390/11/1/68
[2] DOI 10.1016/0771-050X(80)90020-0
[3] June 1982, Physical review A, Atomic, molecular, and optical physics 26:1(1).
Attending private messages, the only course required by LMU for my doctorate, was a quantum physics lab course taught by myself with school supervision.
I also supervised my own PHD thesis with work at the MPQ and evaluated by LMU, under orientation by 2 Professors at MPQ/LMU (Prof. Herbert Walther and Prof. Karl Kompa). Several Dr.s from our MPQ high-power laser group participated, with special efforts by Drs. Witkowski and Ernst Fil -- who I shared a room with, and was a co-author in several publications. I am grateful to all.
Quantum computing owes a large credit to https://www.researchgate.net/profile/Jason-Gallas who applied the new method to a difficult problem, including magnetic fields and Rydberg states, generating a scaling law -- which we co-published. See "Scaling Laws for Rydberg Atoms in Magnetic Fields". Jan 1983. Physical Review Letters 50(5):324-327. DOI: 10.1103/PhysRevLett.50.324. By Jason A C Gallas, Ed Gerck, and Robert F O'connell.
He was a doctoral student at the sane time, at MPQ/LMU.
The development of quantum computing faced the criticisms of mathematics colleagues, because it postulated (1) the differentiation of discontinuous functions; and (2) the non-existence of imaginary numbers -- both impossible considerations at the time.
This motivated us to approach the problem from the mathematics side, as a more fruitful approach, ĺeading to consider irrational numbers as an empty set and R=C=Q -- which uncluttered the number field.
In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of the set of rational numbers Q such that the field extension K/Q has finite degree (and hence is an algebraic field extension). Thus K is a field that contains Q and has finite dimension when considered as a vector space over Q.
The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory. This study reveals hidden structures behind usual rational numbers, by using algebraic methods.
What is controversial at first, is that the Gaussian rationals, denoted Q( i ) (often read as " Q adjoined i) or set G, are NOT considered. The first (historically) non-trivial example of a number field is considered an illusion, plaguing mathematics for 500 years. Its elements would be of the form a + bi; where both a and b are rational numbers and i is the imaginary unit (not considered existent, as it can NOT be numerically calculated in the set Q). A strange fact is that the imaginary unit would equal its own negative, i=-i.
I’m happy to share these online profile projects. I just had COVID by transmission from school. I am negative now, the prior vaccination and boosters helped -- I just needed time.
I worked while at the Hospital, check them out here. Meanwhile, Ann and Edgardo found W2 employment in Tuolumne County School District. and are finding their voice.
https://lnkd.in/gAjeMjwz
https://lnkd.in/gF3eDF-C
https://lnkd.in/g9pqYnJQ
linkedin.com/in/edgerck
As an engaged and militant intellectual, I stand at the end of a German tradition which looks forward to Jean-Paul Sartre, and in modern republican France my position stands as a symbol of rationalism and in the defense of tolerance.
I recognize I am a man of apparent paradoxes (I use three-states logic, not binary): the bourgeois who could turn into aristocratic pretensions on the heights of recognized natural science, with 2 Ph.D.s, but who as plain man later became a voice of what was once the old French Revolution; the conservative in aesthetic matters who appeared as a radical in religious issues.
I am a scientist who learned to trust God absolutely.
I am, above all, the master ironist, a provocateur, who, perhaps more than any other person, gave to the Enlightenment that is bound to come to Quantum Mechanics (QM).
QM is not random. QM will come to mathematics and physics; its characteristic and defining tone of voice of tolerance and Quantum Mechanics (QM).
It is OK for others to display prejudice. It will die off.
QM is the most rigorous model one can use in everything. QM is not random. Who lives, will see it in time. That is the proof each one will have and accept in self-sufficiency.
I can wait 40 or more years for my oppositors to die; similar to Yuri Knorosov, the Russian who lived in Ukraine and decoded the Mayan language, time only makes the right to be the obvious, and denies falsity. He was opposed not only by pretensions but also by dialectics, the false conviction.
A smaller weight can lift a larger weight In a double-pendulum experiment, easily calculated by the Euler-Lagrange Equation, as reviewed in one of our books at Amazon.
One observes a curious fact: a smaller weight can lift a larger weight when oscillating. The effect is larger if the length of the chord is about the same for both pendula. It's called "sympathetic resonance ".
What happens is that the reaction force created by the centrifugal force, transmitted along the chord, acts on the other pendulum -- raising its larger weight.
This shows that we too, in comparison, though presenting a "small weight" in life, can move the inertia of a larger body, by help from God.
We feel we are doing that.
The set Q has undefined numbers. They can be seen as "holes" to use a physics terminology that is helpful in semiconductors.
No one can use a number inside a hole, because such number is undefined and undefinable.
This means, independently of humans, that topology has changed, as irrational numbers are an empty set.
No more fake continuity, of humans. No more limits. No more convergence. Respect the quantum properties.
The continuum never existed in nature (it's QM) and cannot be simply postulated in mathematics.
Mathematics is always discrete and the Schrödinger equation demands it. Mādhava was right, 250 years before Newton.
The derivative of the second differential must be discontinuous. It can yet model curvature.
All opinions in contrary stand revoked.
There are phenomena in the physical realm which simply don't have classical explanations -- try as one may, and that is why QM has to be used in nature.
One example is stimulated emission. Another example is provided by the double-slit experiment. One cannot just "pick and choose" controversially understood experiments.
On the other hand, there are phenomena in the classical realm in physics which are controversial, until one finds a QM explanation. One example is called the "ultraviolet catastrophe".
There are also examples in mathematics which simply don't have classical explanations -- try as one may, and that is why QM has to be used in mathematics.
One example is the 4 quantum properties of numbers. This dismisses Peano axioms, that have 0 quantum properties for numbers.
A special request: how come my MDPI paper was published quickly, without cost, and on Christmas. Do I talk to God?
This is not a first.
Ramanujan frequently said, "An equation for me has no meaning, unless it represents a thought of God."-and he wasn't kidding.
Like ancient Hindu and Mayan mathematicians, Ramanujan only noted the results and summaries of his works; no proof was worked out for the formulae he came up with. His formula for partitions looks like a QM equation.
I follow the same tradition, and I pray before, during and after finding mathematical solutions. In that, I hear a higher voice, indicating the way to the solution or... the solution itself.
Any mathematician can profit from this method.
Pray before, during, and after the work -- and God or his higher helpers surely will help you. You will never work on your life. There is a place for God in mathematics, logic, physics, chemustry, science, and in any art. Right in it.
Every work becomes a prayer, and no act is committed by myself. I am just a messenger and its first beneficiary.. Any of my brothers and sisters can do the same, and I am not special. God has no gender and everyone receives what they need. We all have what we need. Life is beautiful and useful, forget the apparent contradictions -they are just "counter".
Watch the lilies in the field. God gives what we need., and forgets nothing.
God does not forgive, we should neither. Instead, forget any offense. They do not exist, aren't real. Only the good is real. Also in mathematics, any science, skill, or art. Everything says of perfection; expresses the perfect Creator. The noise just highlights the signal. Everything helps. Life shines from splendor to splendor. Everything is already solved -- and you are that solution, there is a path already prepared for anyone. We never die, but live in higher planes of existence -- even now. This is not the first nor the last time we meet. Refresh your memory.
Once one intellectually accepts that Irrational numbers are an empty set, one concludes that R=C=Q.
The calculus by Newton is wrong and by Mādhava is right. There is a much faster FFT. RSA is broken.
Then the post-quantum encryption begins.
Mathematics has changed, and "the cat can't go back to the same bag".
MDPI has been targeted by competitors, who are themselves predatory. Do not believe all you read online, particularly at WeakPedia.
By myself, I can testimony that MDPI has been very fair, approved one of my publications by merit without any cost, and has a free preprint service that allows cutting edge research to better attract attention.
It comes close to this platform in fairness.
Tolerance is required to be fair.
How many REAL roots MUST one write for a n-polynomial? From 0 up to n.
Of course, one can write 7 real roots for a 7-th degree polynomial, only find 3, or find no real root (0).
There is no insolvability of a quintic (or higher) equation.
That was a mistake, using an illusion (imaginary numbers).
Quantum mechanics is not random! There is, in nature, nothing random, nothing without a cause. Everything is stimulated.
This agrees with a currently proposed model, that views qantum mechanics (QM) through the lens of decision theory (by way of game theory), not through probability theory.
While parameters are modeled as random variables on Ω (which are merely functions from Ω to a target set), the authors note that this does not imply that their values are selected at random.
This "model allows an interpretation of the parameters as being selected at random with some probability measure on Ω, which is the common interpretation of QM physics, but it also allows an interpretation in which the values of the parameters are selected through a decision model, i.e., in which the parameters are nodes in a game and the probability measure can be interpreted subjectively, but with a different assumption of free choice."
The result is that there is no free choice.
The paper, by @Michael Baczyk and @Ghislain Fourny , can be downloaded for free at
https://link.springer.com/article/10.1007/s40509-023-00309-0#ref-CR28 or Article Nashian game theory is incompatible with quantum physics
We learn through problems, that dialectic "logic" does not work.
Also, voting is not science. Soviet methods are ineffective.
Clearly, there are no opponents here.
We are all mining the gold of truth using discussions. Life is eternal in spirit.
The noise just highlights the signal. Some people lose time by discussing researchers; not research. The bodies flow dow by the river of time.
I do not argue against binary logic, just that it cannot be applied consistently in the real world.
Binary logic can be used, with limitations, in digital circuits. Better to use three-states with Verilog. Intel pioneered this.
Digital circuits, contrary to Shannon, are not isomorphic to relays. This deprecates bits and qubits.
The number π is undefined according to the Hurwitz theorem.
The number π is a rational number with arbitrary-length. If that sounds like a new form of rational number, it's not so in computer science (CS).
In CS, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision.
Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.
Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required.
More at WP.
Responding to a message in another forum, to https://www.linkedin.com/in/petermaustin @peter austin
Quantum mechanics (QM) does not violate classical rules. This is a common misconception.
The equivalence principle rules QM and is a good help here. It states that all physical systems are connected by a coordinate transformation to the free one with vanishing energy.
Alternatively, this can be understood as that, for any given point, it is possible to find a quantum coordinate system with respect to which we have definite causal structure in the vicinity of that point. In QM, everything is stimulated. There is no effect without a cause.
Therefore, the equivalence principle can be restated to the meaning that whatever has inertia must also participate in gravitational interactions. Therefore, light waves must have weight, and must lose energy when they rise through a gravitational field -- even though a photon has no mass (but has energy).
If you are isolated from the outer world, QM and GR say thst under these circumstances, if you take an object and drop it, it does NOT fall necessarily and reach the floor/base.
One of the most basic assumptions of fundamental physics is that the different properties of mass -- weight, inertia and gravitation -- always remain the same in relation to each other. No experiment performed inside a closed room can tell you whether you are at rest in the presence of gravity or accelerating in the absence of gravity, pointwise.
Although all measurements to date confirm the equivalence principle, quantum theory postulates that there should be a violation, near the point. This is not an inconsistency.
However, this is the reason why ever more precise tests of the equivalence principle are particularly important.
So, although all measurements to date confirm the equivalence principle. we expect QM to violate the equivalence principle by allowing the stability of unstable states, or by the reverse.
For example, we denonstrated experimentally that, in 1982 at the Max Planck Institute of Quantum Optics (MPQ), with an excimer effect changing by many orders of magnitude a metastable state in an excited iodine atom. What was stable, became UNSTABLE, extreme amounts of light resulting -- from few atoms!
We also calculated that the planet Mercury has an open orbit around the Sun, and can escape -- using QM. The preprint is at my profile in ResearchGate.
Albeit, there is nothing random in QM. Probability is not in QM. Probability is a model-- we could also use decision theory; as has been recently announced by Michal Baczyk and Ghislain Fourny. See
Article Nashian game theory is incompatible with quantum physics
Therefore, if we multiply two numbers whose last digit is equal to 1, we must obtain a number whose last digit is 1 -- also in QM.
There is no cause otherwise, there is no carry value possible at that least significant position.
But, if we multiply two numbers whose second-to-last digit is equal to 1, we may use a carry value.
So, 1×1 can be 2, that way. Not random, but causal. This may explain how QM works. There is nothing random in QM. Everything is exact.
Responding to private message, probability remains as a measure of uncertainty, there is no probability 0 nor 1, it is always 0 < p < 1.
The solution to avoid probability is equivalent to look for zeroes or ones.
That is what I mean by getting probabilities out of quatum mechanics.
Quantum mechanics is our most rigorous model of nature.
By getting probabilities out of quantum mechanics, we enable quantum computing.
We pass rational numbers and use natural numbers.
Then, 0^n=0 and 1^n=1, immediately, for any n in the set N.
A faster FFT becomes possible, avoiding both complex numbers and rational numbers. We face less complexity, and can multiply numbers faster, using a faster FFT.
We are showing this in code, and will share here soon. We already shared about pathological RSA.
See posting. So, the first results are encouraging.
The flowers, that cannot see, use prime numbers to communicate. See image.
Discontinuous functions (not just distributions) can be differentiated as I showed in [1], op. cit. (see on my ResearchGate Introduction) at every point of set Q.
This contradicts Courant, Apostol, etc. Students are learning prejudice, wrong intuition ... and are revolting by dropping out of ... mathematics. The best leave first.
No experiment performed inside a closed room can tell you whether you are at rest in the presence of gravity or accelerating in the absence of gravity, albeit just pointwise.
Although all measurements to date confirm this equivalence principle, quantum theory postulates that there should be a violation, near the point. This is not an inconsistency, it is not at the point itself. QM can violate the equivalence principle by allowing the stability of unstable states, or by the reverse.
As an example, we denonstrated experimentally that, in 1982 at the Max Planck Institute of Quantum Optics (MPQ).
We discovered an infrared excimer effect changing by many orders of magnitude a metastable state in an excited iodine atom. What was stable, became UNSTABLE, extreme amounts of light resulting -- from few atoms! The result was published and created a limitation for high-power operation of the iodine laser.
See, fot example, "XeI((2)pi(1/2)-(2)sigma(1/2)) excimer emission at 1.3 micron" in Feb 1982. Optics Letters, 7(1):25-7.
Albeit, there is nothing random in QM. Probability is not intrinsic to QM. Probability is just a model -- we could also use decision theory; as has been recently announced. See
https://lnkd.in/gXAx4XQp
Therefore, if we multiply two numbers whose last digits are equal to 1, we must obtain a number whose last digit is 1 -- not a random result. There is no cause otherwise, there is no carry value possible at that least significant position.
But, if we multiply two numbers whose second-to-last digit are equal to 1, we may use a carry value. The resul is that 1×1 may be equal to 1 or even 2, which can look random. But this is not wrong and not a random result.
Regarding QM, the laws remain the same, they are just interpreted individually.
Each atom can behave differently, as changed by fields. See my publications in case of doubt.
Even the mass of two bodies can change, as they get closer to each other. Mass can change with fields, in interchange. Not with speed, or acceleration -- which are common misconceptions.
Dear E.D.Gerck,
I am unable to understand the introduction of acceleration in Special relativity without affecting the inertial nature of inertial frame?
Regards
RC: Try using the Minkowski formulation of SR. There is no "inertial frame" as the "bedrock" of SR.
Einstein's Theory of Special Relativity remains based on the two principles discovered by him. One is that the laws of physics don't change, even when objects move at constant speeds to each other. The other is that the speed of light is the same for everyone, no matter how they move in relation to the light source. Details are given in the preprint noted.
What is to "exist" in mathematics?
It cannot be one's own imagination, or anyone's own imagination. It does not communicate to others.
It must be at least intersubjective, similar to a medical diagnosis. It must be based on accepted facts, by others. It must communicate.
In mathematics, some have defined to "exist" to mean that "it can be constructed".
That has intersubjectivity, and does not require physical occurrence or properties.
Then, it can aspire to become objective, similar to the odd numbers, or prime numbers. Friend or foe, everyone knows what is meant -- it became now objective.
To "exist", then, is not abstract. It has a relation to other things, and which do not need physical occurrence. It is not arbitrary, however.
Continuing, to "exist"could mean to "aspire to become objective".
In that sense, it would be similar to the odd numbers, or prime numbers. Friend or foe, everyone knows what is meant -- it became now objective.
To "exist", then, is not abstract -- again. It has a relation to other things, and which do not need physical occurrence. It is not arbitrary, however.
When one says that irrational numbers do no "exist" numerically, what Is meant?
That no one can store them (it would require infinite memory), no one can write them (it would require infinite time), no one or anything can produce them (it would require infinite frequencies), no one can read them (it would require infinite time), and no one or anything can communicate them numerically (it would require infinite power).
We can add, mathematicallyto some, "that no one can numerically construct them".
These statements now, can be both intersubjectively and objectively evaluated.
They can be understood by others, not just by self.
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 and less refutability [1].
Non-statistical decision- making can be made using multiple (> 2) states, followed by quantum or classical computing.
Variance is admitted not to accommodate for any error, but needs to conform to the facts of specificity, which may vary individually and in time.
[1] https://www.researchgate.net/publication/369560023/
AGC (mentioned above) is with the Max Planck Institute for Nuclear Physics; in Heidelberg, Germany.
I was in 1982 with the Max Planck Institute for Quantum Optics, near Munich, Germany.
There is a very good academic record in those places.
AGC just made a remarkable deduction in physics. Nature experimentally shows to have QM as a rigorous model.
QM is our most rigorous model of nature. QM is not willy-nilly.
He did that by proving a negative: there are no irrational numbers in nature.
Can Mathematics do the same?
Pay attention: More than a revolution in physics happened in 1926. In a letter to physicist Hendrik Lorentz on June 6, 1926, Schrödinger wrote,
“What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Ψ [the wave function] is surely fundamentally a real function.”
So, no one is really being innovative in opposition.
There is no continuity in nature, concluded AGC in RG.
Advances in all sciences will have to result. Nature is solving problems only numerically (i.e., using finite difference schemes, as we calculated in 1982).
Typical of the current RG researchers, one should however NOT ignore the momentous conclusion by AGC. Let us focus on the consequences forward. QM has been confirmed in nature.
We lived under the illusion that what we once imagined is true. In psychology, it is called schizophrenia, a mental pathology, and it is apparent.
There is no continuity in nature. End of story.
Dear Ed Gerck - it is well known that one mans irrationality is an other mans discreteness - and vice verse, as it all depends on the point of view. The most famous instance is that rational angles yield irrational shadows - while irrational angles can yield rational shadows, such as in the natural Poisson Degeneracy with cos ϴ = 1/3, indeed possessing a totally irrational angle, while wielding a perfectly rational extent.
So the question is:
"Is it possible to avoid irrationality altogether with a proper coordinate system that evades all incommensurables ?"
In my book the answer is yes, as Nature indeed works like that - by transforming itself to a local coordinate system where everything is both rational and linear.
So one should not really worry about that cos (π/5) and cos (π/4) are both irrational while cos(π/3) and cos(π/2) are rational - as it all depends on the point of view.
All the best, and sincerely yours,
gko
REF: Preprint Our Natural Space
GKO: your comment is well received, to the effect "Is it possible to avoid irrationality altogether with a proper coordinate system that evades all incommensurables ?"
The set Q has no irrational numbers and is the proper coordinate system to be used.
What we thought were irrational numbers are undefined and cannot be measured (Hurwitz theorem).
All numbers formerly known as "irrational numbers" are rational numbers with arbitrary-length.
ED: Thanks - while still - it is indeed strange, that the most irrational number of all, the Golden Ratio (ϕ), is still the most 'natural' number - ruling everything from the most stable quantum orbits - to the most economical distribution of leaf for a certain plant to maximise their exposure to the Sun !
So perhaps, life is a sucker for nonlinearity, by working in mysterious ways - as those mysterious irrational ways seem to be the most rational strategy for survival?
All the best,
gko
We can do quantum computing in a commercial cellphone, up to 10^1000 decimal digits. That is (1 googol)^10. This opens the market ... to watches.
No other machine comes even close, or is smaller.
The US, through Planalto Research, just won the implementation of quantum computing, with less than $1,000 in equipment cost!
And it forms the mathematical geometric brigde between exact quantum and what many (unfortunately) still many perceive as "continuum".
There are two types of quantum computing (QC) techniques: with complex numbers, and without.
The former include: Shor's algorithm, adiabatic QC, quantum annealing principles, and others. Capital cost is about $10M.
The latter is the simultaneous, multifactor logic, with 'all states at once' technique of QC, proposed by Planalto Research and us. We factored more than 10^1000 decimal digits, and the capital cost was less than $1,000.
Physicists routinely use scattering of physical waves and interference measurements to determine periodicity of physical objects such as crystal lattices.
In an important well-known work, Bennett (the physicist Charles Bennett, 1973) showed that any classical computation can be transformed into a reversible form, which allows quantum mechanics (QM) to be used in computation creating quantum computation QC!
This answers the question: (1) what role can QM have in QC? The answer is: QM can be used in QC. We go from physics to mathematics, as in a “wormhole”!
Today, we could announce it. Quantum computing (QC) has become a reality.
The QC version used here has simultaneous multiple-states logic (following ‘all states at once’), with more than a googol of possible states.
We show that the equivalence of different QC techniques (with IBM, Google and others compared with our version of QC) has been hidden for about 2,500 years – since Pythagoras.
All our QC computations were done in a commercial cellphone, or a commercial Linux desktop, as our QC devices -- opening the user market to many industries. No cryogenics or special materials were used.
A post-quantum, HIPAA compliant, end-to-end, patent-free, export-free, secure online solution, is being created, based on ZSentry as used from 2004 to 2014, to replace RSA. One needs a quantum-resistant algorithm, because all existing public-key encryption can be broken.
In order to try to censor this work, someone (see LinkedIn archives) spread the unfounded rumor that the preprint file was a way to spread virus.
I hope that LinkedIn deletes that account and that the person is fired.
The file is safe and scanned for virus. Cybersecurity needs protection!
Mathematics did not accept the fix. Physics is right -- irrational numbers do not exist, not even in our finite imagination.
On all that, the irony is that what physics says is irrelevant -- relevant, only, is nature.
One can consult Tarski on what logic stands for. The language of nature. Snow is white because "snow is white". Mathematics needs to evolve.
Attending to a private message, the correct attribution to that older article of mine is:
Mathematics 2023, 11, 68 -- DOI /2227-7390/11/1/68 -- and it was published cost-free due to interest.
The article single-handedly changes mathematics irrevocably and immediately outdated all textbooks on analysis.
Comparing to elusive truth, how much is an irrational falsity worth?
A sound, archetypical, immemorial, cross-species, well-known, and logical rule is that it is better to reject 100 truths than to accept one falsity. A rejected truth can be accepted tomorrow, but an accepted falsity contaminates the thought immediately.
Truth is worth 1:100 a falsity, maybe more. This applies to all discussions at RG.
A circle can be perfect when all points in it are in the set Q. Everything is perfect when all points are in the set Q.
Nature is perfect, all points are in the set Q, and nature is modeled by quantum mechanics naturally.
Mathematics is not exempt, otherwise unavoidable contradictions happen.
There are no irrational, infinite, imaginary, p-adic, or real numbers.
People are also barking up the wrong tree when they imagine that nature or even God are guided by the folly of humans.
A belief is a probability that supports the claim (cf. DS).
True beliefs reach 100%, as empirically verifiable (by experiments only) trust.
When not empirically verifiable, trust becomes a story.
Stories must be cautiously told. They can be subject - to use a Russian term - to prelest. But when spoken after one's self-absorbing ego has been set aside, truth does manifest and is empirically defined. Nature is not Boolean nor deductive. Nature cannot be axiomatic.
Thus is reality well definable, not using Gödel's uncertainties-- without prelest, and somethings are wrong when their belief is 0%, when the limits of neurosis are reached as we see often.
BTW, the term prelest is a Russian word which has come into English usage for lack of a precise equivalent, although it is often translated as "spiritual delusion ," "spiritual deception," or "illusion," accepting a delusion for reality in contrast to spiritual sobriety.
For example, the prelest that infinitesimal, irrational, imaginary, and p-adic numbers exist in nature and mathematics.
That prelest has derailed QC, so far.
Nature, that we consider existing for time immemorial-- not just for the last 13.8 billion years, is always right.
Any incorrect process has followed an evanescence path -- like the monstrous dinosaurs-- and helped nature evolution to higher forms.
Any process imagined by frail humans are condemned before starting, therefore.
This gives us a sense of humidity-- and motivates us to observe and be thankful.
Physics is a story about nature. It must reject prelest -- illusions -- and bring mathematics to the physical phenomenon. This explains the reason and the existence of numbers, and everything else.
As a first example of a stopgap measure, to counter a vulnerabily in RSA (announced by us), consider requiring 4 prime numbers; and their product is the RSA key.
The first 2 you know, and the last two are two unknowns. The product does not have to be long. How difficult it is to break the public key?
Attending a private question, pi is an arbitrary-length rational number of the form m/n always, with m, n integer numbers of arbitrary-length and n!= 0. See paper in ResearchGate, this follows QC.
Any numerical expression of pi that one can find, read, measure, or calculate is of that form.
There are no irrational numbers in physics and in mathematics. All is rigorous. So is QC.
Attending another private question the basis of QC is QM.
And the basis of QM can be, for most purposes, the Schrödinger equation for bound states -- which can be cast as an eigenvalue problem.
Current mathematics (e.g., Courant, Apostol, etc.) does not allow the Schrödinger equation to exist, although it does. There is no differentiation of discontinuous functions, only for distributions.
However; we published about a year ago how to use the set Q to differentiate any discontinuous function. Anyone can test, it's publicly accessible, at https://www.mdpi.com/2227-7390/11/1/68
This deprecates the human-made sets R and C. There are no irrational, and p-adic; numbers either. They are a prelest.
The sets to consider are B, N, Z, and Q. All physical phenomena can be built from the set B = {0,1}, so is QC -- tested up to about 10 Googols numerically. Logic only depends on 0 and 1, even their non-existence (3 state logic, breaking the LEM and the Gödel uncertainties). Nature is not definable by Boolean logic, axioms, and is not deductible.
That is why QM is our most rigorous model of nature, and QC is able to express it numerically -- in exact form, using arbitrary-length rational numbers, that use arbitrary-length integers.
The previous comment can be applied as a provable basis for a new cybersecurity approach, where all calculations are in integers, with modular arithmetic.
The security of an algorithm becomes that the only possible attack is exhaustive search -- which becomes prohibitive for large enough arbitrary-length integers.
How did computing evolve in 60 years? How does a modern cellphone compare?
It is probably common knowledge that a person using a smartphone today has more computing power at their disposal than the U.S. Space Programme did during the 1960s.
The National Aeronautics and Space Administration (NASA) used five IBM System 360 model 75J computers, each of which cost US$ 3.5 million (about US$ 25 million today), for the Apollo series of Moon missions.
The System 360 series, which came out in 1965, is credited with creating a broad market for information technology (IT) products.
A System 360 computer took up a substantial amount of space, a largish office room being required to house its multiple discrete elements, and needed constant cooling. Each model 75 had 8 megabytes (MB) of memory and a data processing speed of 2.54 million instructions per second (MIPS).
By way of contrast, the hand-held iPhone 5s smartphone, which came out in 2013, has 1,024 MB of memory and a processing speed of 18,200 MIPS.
We can heartly laugh at people who laugh at cell phones computing power.
The latest Galaxy cell phone is an unkown powerhouse in computing. With QC, it soars.
Ignorance is, indeed, bliss. Without QC and refrigeration, the old Apple iPhone 12, for example, could perform approximately 11 teraflops, or 11 trillion operations per second — more than 5,000 times faster than the CRAY-2 -- a supercomputer, in a large refrigerated room. In a pocket!
Attending to a private message, thank you, once one goes onto the prelest that imaginary numbers, irrational numbers, or other illusions exist, one is going to find them in QM.
But, in an alternative path, where they do not exist, one does not find them.
The same happens in a computer program. Once one declares a variable to be in set C, values in the set C are going to be found. But the hardware only knows of 1 and 0.
I published in [1] real solutions of the Schrödinger equation for bound states, with their real eigenvalues and real eigenvectors, in 1982, for many potentials, and applied that to Rydberg states [2], deriving scaling laws. That used the set Q, with no set C.
Those op.cit. references are provided for further information. They are in my ResearchGate profile.
As well-known, a person using a smartphone today has more computing power at their disposal than the U.S. Space Program did during the 1960s.
So, HIPER Cal Pro (contact at HiPER Labs Android Support ) can become a powerhouse of computing.
I can collaborate (freely, in time) and add quantum computing at room temperature!
We report the first numerical realization of the exact solution in the field of integers of arbitrary but finite-length, of the prime number quantum potential V(M,x), defined as the potential used in the single-particle Schrödinger equation of bound-states with eigenvalues given by the first M prime numbers.
We obtain a confining quantum potential with a natural shape given by the eigenvalues as E_m = 3 + 2m, m a natural number /3^n, and higher-order corrections, reproducing exactly all prime numbers with arbitrary-length, confirming the existence of a closed-form expression for any prime number [1].
Our results also confirm previous publications [1-2], using for the first time digital circuits at room temperature to show factorization of large numbers with cryptographic interest, such as the well-known RSA-2048.
This shows the numerical realization of quantum potentials with certain sequences of integers as energy levels and not of others.
In perspective of [1,2], we demonstrate the effective reality of using only physical quantum systems for fast mathematical tests, exploring a bridge between isolated Number Theory in pure Mathematics and natural Quantum Physics.
[1] E. Gerck, “Algorithms for Quantum Computation: The Derivatives of Discontinuous Functions”, published at Mathematics 2023, 11, 68.
[2] E. Gerck, A. Gerck, “QC Algorithms: Faster Calculation of Prime Numbers”, published at https://lnkd.in/dk3iaKWY
Ed Gerck Congratulations, imho only very few really understand what you achieved here - let alone what the options are from such!
If you have the time to do do, I‘d really be interested how your (exact) closed form expression for the primary iSpace prime constant 6961 would look like, as such has been in recent year identified to be nothing else than the (integer!) Quantum of time in form of 1/6961 iSpaceSecond expressible in new novel fully human artefact free iSpace-IQ unit system (yet lossless convertible to iSpace-SI and with this fully lab compatible MKS/A-SI units) - which changes everything physically to a model imho fully compatible to your core ideas of an integer (geometry) only based number representation.
Have a short 1/2 walk thru my 65+ lines of exact arbitrary precision Mathematica code, to proove beyond reasonably doubt on electron charge, Planck constant and electron mass in both eV/c^2 and Kg representations (in both very different unit systems iSpace-IQ and iSpace-SI) to show the identified SI human artefact integer (!) time factor is all one needs to remove from physical result equations of any kind to suddenly be able to literally „see“ the (integer geometric) ultimate lowest level physics behind (h/(2*e) to become 3 (!) etc.):
Method iSpace - Quick check of α and Φ0 from Markoulakis & Antonidakis
Preprint iSpace - Quantization of Time in iSpace-IQ Unit-System by 1/...
Thanks, kind regards and please stay well (as it’s not fully unproblematic to be able to break RSA-2048 in our world, unfortunately … as is my understanding of leap-frog style progress made)!
Christian
CGW: Thank you. Following your request, I read your manuscript with interest.
As I see in my own case for QC, the mathematics was preceded by the recent discoveries following Campos, that irrational numbers and infinitesimals do not exist in nature, and by the Hindu mathematician Mādhava of calculus, 250 years before Newton.
What is the prelest? Since Newton and Leibniz, and countless others, including the most common names we learned to admire, such as Courant and Apostol, they all fell to the illusion that infinitesimals and irrationals exist in Mathematics. And "proved" them.
There is one thing in your exposition that I find difficult to coherently accept. That basic constants in Physics are due to any Mathematics.
My internal voice told me, at the beginning of this "trip" , in 1976, that I should bring the Schrödinger equation for bound states to Mathematics-- not the reverse. Mathematics was in contradiction! Mathematics could not be trusted. Today, that is clear, and how to correct it with Mādhava calculus, is the solution we need in order to advance in QC.
Likewise, between Mathematics -- that can support any number and type of constants -- and Physics -- that has additional information from "wormholes" we are beginning to discover (but were always there), there is a prelest that "smoothly" covers the ... gap. Eliminate the (unnecessary) illusions! There is no "smoothing" needed!
Electron charge, Planck constant, time, and electron mass are mathematically unrelated. No matter the mathematical "proof" one fancies one "finds", a main point is missing. God wanted.
The Almighty is what can break any security algorithm. We ignore what we ... ignore.
This also means that I can unreservedly accept your arguments. I am powerless.
Ancient chinese "saw" organs that do not exist in the human body, and yet some of their medical treatments were ... more effective than a random process. The unseen exists, and can be used effectively. The placebo effect happens in nature, as the "pharmacy of the mind" and can be used within its rules, positive, and negative directions. Just like a phone. It "speaks" although it is a medium, not the message.
Thus, although the identified human artefact integer (!) time factor seems to be all one needs to remove from physical result equations of any kind to suddenly be able to literally "see“ the (integer geometric) ultimate lowest level physics. It might also be a wormhole or ... prelest. The scientific method may help disambiguate.
Now that we showed that there is a "wormhole" connecting (1) Applications of the Schrödinger equation for bound-states and (2) QC at room temperature, allowing one to, e.g., break cryptography in RSA-2048 -- we can reverse the course and envision OTHER methods for QC (possibly) allowing yet new realizations.
For example, we can use the new "wormhole" to connect the Schrödinger equation for bound-states with continued fractions, using large real tridiagonal matrices.
And, we can use it to understand that complex numbers do not appear in QM -- as Erwin Schrödinger explained in 1926.
And, we can use large real tridiagonal matrices to understand how we can connect the FFT, and improve upon it -- making it faster.
And, his has the potential to improve the multiplication of two large numbers.
And, more later ...
Ed Gerck “Electron charge, Planck constant, time, and electron mass are mathematically unrelated.“ And here you‚re wrong - in good company of mainstream - you want to reform. But there is no such thing as half pragnant. Your welcome to follow your own model, but let me allow to state the (mathematical) fact no one ever on earth for eternal future will ever be able to find a equal exact, yet simpler solution. And you have - philosophically very interesting - but physical (practical) useless answer given (that such should not be that simple mathematically - yet it is. Nature does not care what we believe or not. Such is science.
Ed Gerck Ed, could you please do me the favor to answer my request to give me the results of your core representation of prime 6961 equation (with respect to your initial post claimed above to be able to)? Only if such are few simple calculations for you, not if it would take more than a few minutes at most. Thank you!
CGW: Out of respect for your divine nature, what can one say of the number 6961?
6961 belongs to the set N, it is odd, it is a prime number, its predecessor in the predefined eigenvalue sequence V(M,x) is the number 6959, which is a prime number, although its numerical successor by the same derivative (6963) is not a prime number.
However, its next successor by the same derivative (6967) is a prime number, continuing the sequence V(M,x) as:
V(M,x) = 6967 + 2m, m a natural number except higher-order corrections, in the same way that V(M,x) = 3 + 2m, m a natural number except higher-order corrections.
Thus, one expects that 6969 is not a prime number, but 6971 to be, while 6973 is not ... but 6975 is a prime number.
This sequence of prime numbers goes algorithmically on, revealing what has been intuitively called "wheels within wheels", a regularity of sorts.
This atemporal classification, is a partition of elements according to their resemblance as defined first by C.H. Jung in terms of archetypes, cross-species, cross-elements, thus universal. Time is not included.
This is larger than the Ruliad, and contains what cannot be described by Boolean logic. Thus, binary logic is not enough.
This excludes mass or any measure of inertia, of amount of matter. Which excludes gravitation, and space curvature. The number 6961 stands by itself.
To the confused: in this age of "fake news", what is right?
We reported here that exact and unique prime numbers p and q are rigorously factored by the +220 year-old, tried and found to be always true, Prime Factorization Theorem (PFT).
So, every integer greater than 1 can be uniquely represented as a product of integer prime numbers, with indistinguishability of factor order. Gauss confirmed, cell phones using Android can calculate it, it is a well-known fact.
One can calculate the product p×q = K using arbitrary-length integers, and with ONE-SHOT their supposed trap-door inverse -- which is stunningly absent.
This immediate invalidity then breaks the well-known #RSA public cryptography algorithm, which our QC reveals, single-handedly changing #cybersecurity.
We are bringing a large chunk of theoretical physics to bear on important mathematical problems, using nature to confirm the way forward.
Conversely, one hopes to learn from a century of analytic number theory and Galois numbers (both, when it is measurable and as an imaginary prelest) to better understand several issues of modern physics (ditto).
But it is in numerical prime number calculations and making the first quantum computer (QC) that have been our focus in several preprints presented here.
A new version of the manuscript on QC is downloaded, which may be ready for publication and benefitted from community feedback. Thank you all.
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