Our answer is certainly YES.
Albeit, in spite of experiments, some supposedly highly-qualified people think that even quantum computing (QC) makes nothing unlimited.
They also say that due to (magical, no one defines it coherently) superposition, exponentially (and more) speed up algorithms can exist but … nobody has shown that it can indefinitely speed up algorithms.
What can one say to that? Would it be helpful to have a manuscript that shows things can be calculated unlimitedly? Only using B={0,1} ?
What is your qualified opinion?
A private message asks if I could focus the manuscript on solving continued fractions to any limit of terms. Not the actual number, but that the number can be calculated.
That would include division and this seems to be a problem. For example, with division by 3, or 7.
What is your opinion?
To the private message, with continued fractions one can show that the simplicity of a very large number of rational parameters beats hands down the complexity of one parameter in mathematical real-numbers and mathematical complex numbers-- that are not computable or analogly calculable at all -- not even in quantum computing.
It is the future. Large numbers of parameters using computable rational numbers-- not unphysical mathematical real-numbers or complex numbers, like the present Standard Model in physics.
It may look "off the left field" and strange to try to mix in numbers with any material sense, which seems non-existent, self-authorizing mathematicians to invent (Dedekind, 1888).
However, we are not like Don Quixote with windmills. Quantum computing opens to us a new understanding on numbers.
This was introduced by Friedrich Ludwig Gottlob Frege, a German philosopher, logician, and mathematician.
Frege did not have the tools of quantum computing yet, and no one quite understood numbers clearly until quantum computing was demonstrated to be possible in 2022.
Discontinuous functions could not be differentiated -- but now that is calculated exactly, they are just digital. The Schrödinger equation does not describe a continuous or imaginary function (cf. Schrödinger's own declaration to this effect, in 1926), but such functions are everywhere discontinuous -- they are just digital.
This allows us to see that mathematics is by nature exact, digital (we did not invent the Digital Age) -- for quantum reasons (+4) not developed by any human on Earth (proof of yet unknown extraterrestrials or even ultraterrestrials?).
A physical fact now, that confirms the late Frege and the current Peter Shor algorithm in "pure" mathematics. Albeit not qubits, p-adic numbers and other arbitrary inventions-- and it confirms the new set Q* (that conforms with the sets B, N, Z, and Q). Isomorphism is an unseen link, but is being revealed as well as the +4 quantum properties of numbers.
A prime number is the same on Earth as in the star Betelgeuse. Prime numbers are not arbitrary, and are objective. We can use them for communication even with non-humans -- see the film Contact.
Plants show prime numbers in nature, communicating with insects and humans. See figure.
Again and again hidden private messages from the other world to Senior Professor Donn Ed Gerck , to which he continues giving recondite gibberish replies !!
Ed Gerck
you speak of the Advent of
Quote :
" Large numbers of parameters using computable rational numbers-- not unphysical mathematical real-numbers or complex numbers, like the present Standard Model in physics. "
Explain and be our Teacher Master . .. . I wanna learn , Plzz ; ; ; ; ; ; ;
To remember Closure.
Closure describes the case when the results of a mathematical operation are always defined. For example, in arithmetic, addition on rational numbers has closure: whenever one adds two rational numbers, the answer is a rational number.
By adding two, that extends by the PFI to an unlimited number n in N. One can also experiment. There is no "oscillation in addition" in the cases under discussion, using the sets B, N, Z and Q. It remains addition, indefinitely.
There is no oscillation in mathematical operations ONLY in case one applies numbers of certain types . . . , , ,, , , ,,, . . . .. .
To show "that the simplicity of a very large number of rational parameters beats hands down the complexity of one parameter in mathematical real-numbers and mathematical complex numbers-- that are not computable or analogly calculable at all -- not even in quantum computing." one just has to ... experiment. Calculate, e.g., square-root(-1), not possible.
To understand it, see (e.g.)
https://www.researchgate.net/publication/368838533/
New text was added to the prime flower posting above, clarifying questions that I received by both public and private messages. Every tool by RG finds its right use ...
Trans-human communication includes not just extraterrestrials (that naturally exist, or it would be a terrible waste of space and time).
Plants also show prime numbers in nature, communicating with insects and humans. See figure in that comment.
A physical fact now, that confirms the late Frege and the current Peter Shor algorithm in "pure" mathematics. Albeit not qubits, p-adic numbers and other arbitrary inventions-- and it confirms the new set Q* (that conforms with the sets B, N, Z, and Q).
Isomorphism is an unseen link, but is being revealed as well as the +4 quantum properties of numbers.
We are not alone. We know that without using rockets.
Mathematics is by nature exact, digital (we did not invent the Digital Age) -- for quantum reasons (+4) not developed by any human on Earth.
This is a proof of yet unknown extraterrestrials or even ultraterrestrials -- their effect becomes obvious (maybe contact is possible now).
We need to consider this fact and tell that to our brothers, to Russians, Ukrainians, and others. There is no conflict U.S. versus China. Everyone has a right to their own way, so the Father told us -- how?
We are all defined equally -- as we are all essentially divine (also those one calls "enemies"). Jesus told us that -- love your enemy, he is a brother in need, and he too will evolve.
The Earth is just one world among trillions. Let's live in peace. If you are not happy here, there is an exact reason for it -- your own past deeds. Live better today, for a better tomorrow.
Nothing happens randomly. Everything is exact. Causality exists, by natural law. Old theologies must change, as well as old sciences. The pandemic brought us a new realization.
Blessed are the afflicted. Why? Because they pray. Let us be blessed without affliction, from splendor to splendor. Our progress is our own reward.
Do you think that a number is non-material, thus an abstract concept that mathematics is free to invent?
Instead, number is a semiotic concept.
Mathematical semiotics was introduced by Friedrich Frege, a logician and mathematician.
Frege did not consider
quantum computing (QC), and no one quite understood numbers in physical terms until Peter Schor in 1994 (cf. DOI /2227-7390/11/1/68 ).
Discontinuous functions could not be differentiated -- but that can now be calculated exactly. Numbers are digital now, and FFT is common.
The Schrödinger equation never described a continuous or imaginary function (cf. Schrödinger's own declaration to this effect, in 1926), but such functions can now be seen. Numbers are digital now, and the laser exists.
These 2 views mean that mathematics is by nature exact -- for +4 quantum reasons.
These +4 quantum reasons support Frege's semiotic view of numbers and Peter Shor's algorithm in mathematics. QC becomes physical.
It all depends on the operator ...........
It is not a precondition that eigenvalues of operators in general are not real numbers with odd or even values. In fact, the theory of operators with Lorentzian signature is somewhat exotic - most mathematical texts consider only the Riemannian case, where the operator is simply self-adjoint under the canonical positive-definite inner product induced by the Riemannian metric.
Moreover, it depends on whether one means "eigenvalues" in the strict sense of real vectors on complex numbers, which cannot be properly defined as odd or even in a series: as elements of the point spectrum or in the non-strict sense of physicists, or simply as any element of the spectrum (e.g.: consider the position operator x
on L2(R3,dx)
has no eigenvalues or all R as eigenvalues?).A more specific answer concerns bases. Recall that a linear mapping is defined independently of a basis: it is simply a mapping of the vector space onto itself. We can express the linear mapping by a matrix with respect to a basis, but how do we choose the basis? Eigenvalues play an important role in situations where the matrix is a transformation from a vector space to itself. Systems of linear ordinary differential equations equations are the most important examples. The values of λ may correspond to frequencies of oscillations, critical values of stability parameters, or energy levels of atoms. Singular values play an important role,
When the matrix is a transformation from one vector space to another vector space, possibly with a different dimension. Systems of over- or underdetermined algebraic equations are the most important examples. We could always choose the canonical basis in \mathbb{R}^n, since it is easy to perform vector and matrix computations when most entries of all vectors are zero. We also have a good visual idea (at least in up to three dimensions) of what a matrix might mean in terms of this basis. If we had to divide the three-dimensional world around us into small volumes, we would describe it in terms of small cubes rather than small arbitrary parallelepipeds.
REZA
A private message asks, "How about my training on quantum circuits using non-abelian anyons?".
There is more room at the top.
Any training is useful, but that training leads to no future. So, end it and start on quantum computing as done at the Max Planck Institute of Quantum Optics in 1982, using the set Q.
Be able to easily solve the Schrödinger equation for bound states, with any potential, and collect the dust of failed attempts.
Understand continued fractions, as providing a solution to the Schrödinger equation for bound states-- with only addition and encoding in the boolean set, where 0^n=0 and 1^n=1.
For example, help improve the FFT.
A 30-qubit-quantum computer would equal the processing power of a conventional computer that could run teraflops ,,,,,,,
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