24th Jan, 2023
Planalto Research
Discussion
Started 16th Dec, 2022
Can irrational numbers be calculated in algebra?
Irrational numbers are uncomputable with probability one. In that sense, numerical, they do not belong to nature. Animals cannot calculate it, nor humans, nor machines.
But algebra can deal with irrational numbers. Algebra deals with unknowns and indeterminates, exactly.
This would mean that a simple bee or fish can do algebra? No, this means, given the simple expression of their brains, that a higher entity is able to command them to do algebra. The same for humans and machines. We must be able also to do quantum computing, and beyond, also that way.
Thus, no one (animals, humans, extraterrestrials in the NASA search, and machines) is limited by their expressions, and all obey a higher entity, commanding through a network from the top down -- which entity we call God, and Jesus called Father.
This means that God holds all the dice. That also means that we can learn by mimicking nature. Even a wasp can teach us the medicinal properties of a passion fruit flower to lower aggression. Animals, no surprise, can self-medicate, knowing no biology or chemistry.
There is, then, no “personal” sense of algebra. It just is a combination of arithmetic operations.There is no “algebra in my sense” -- there is only one sense, the one mathematical sense that has made sense physically, for ages. I do not feel free to change it, and did not.
But we can reveal new facets of it. In that, we have already revealed several exact algebraic expressions for irrational numbers. Of course, the task is not even enumerable, but it is worth compiling, for the weary traveler. Any suggestions are welcome.
Most recent answer
The comments above show how following the RG ToS is necessary for a scientific conversation.
But the legal responsibility of enforcing the RG ToS falls only on RG, per EU law.
Meawhile, it is suggested to read the question text, with the latest references. Also, private messaging is available.
Popular replies (1)
We need to be optimistic, because that is the lesson from nature. An animal can self-medicate, obeying natural laws in chemistry that are unknown to animals. A tree grows when pruned, so we can see this pandemic as an opportunity. Let's grow, nature is not a zero-sum game!
Irrational numbers and mathematical real-numbers are uncomputable, with probability 1.
But irrational numbers can be calculated exactly in algebra and that is how animals are able to calculate-- in a network of thoughts, which does not have to hierarchical!
It can exist as an ontology, like the Internet. We, then, have to he mindful who we connect to. We can always connect to "DNS" to get the correct directions, or to a rogue DNS, of an attacker...
4 Recommendations
All replies (5)
Intellectual work by humans is very inspiring, but Physics knows that nature is at least 13.8 billion years ahead of us, and there might be other universes still older.
There just was not a single Big-Bang -- if one can happen, more can happen ... We might be late-comers on a feeric Tohu-wa-bohu. Evolution is a very long road.
Infinity is lame to algebra, not unknown and not indeterminate. But it is not a number, so there are no arithmetic rules to multiply/divide or add/subtract it to 1 or any number. We know that 0.x = 0, where x is a number.
2 Recommendations
We need to be optimistic, because that is the lesson from nature. An animal can self-medicate, obeying natural laws in chemistry that are unknown to animals. A tree grows when pruned, so we can see this pandemic as an opportunity. Let's grow, nature is not a zero-sum game!
Irrational numbers and mathematical real-numbers are uncomputable, with probability 1.
But irrational numbers can be calculated exactly in algebra and that is how animals are able to calculate-- in a network of thoughts, which does not have to hierarchical!
It can exist as an ontology, like the Internet. We, then, have to he mindful who we connect to. We can always connect to "DNS" to get the correct directions, or to a rogue DNS, of an attacker...
4 Recommendations
Since the 17/19th centuries, “the differential and integral calculus is based upon two concepts of outstanding importance, apart from the concept of number, namely, the concept of function and the concept of limit.” according to the well-known textbook by R. Courant in Germany and worldwide.
Without including any philosophical opinions, the system of rational and irrational numbers build a continuum of numbers, such that each point on an axis corresponds to just one number, and each number corresponds to just one point on the axis, called the system of mathematical real numbers(MRN).
Therefore, all MRN in the number line can be separated into one of two sets — the rationals (expressible as the ratio of two integers), and the irrationals (all the remaining MRN, which are, thus, not rationals). Every MRN is one of either. This construction is often credited to Richard Dedekind in ETH Zurich, in 1888, writing, “Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things.”
Because uncountably infinite sets are always larger than countably infinite sets, one can conclude that there are more irrational numbers than rational ones. It is worth mentioning that the rationals and the irrationals are both dense, but unlike the rationals, the irrationals are not “sparse” and do not have zero measure mathematically.
This fact emphasizes that rationals and irrationals are really quite different -- even though one can find a rational between any two irrationals, actually an infinite number of them, and an irrational between anytwo rationals.
See more at "Algorithms for quantum computation: the derivatives of discontinuous functions", available at:
2 Recommendations
Similar questions and discussions
Is Reality quantum?
Our answer is YES. This question captures the reason of change: to help us improve. We, and mathematics, need to consider that reality is quantum [1-2], ontologically.
This affects both the microscopic (e.g., atoms) and the macroscopic (e.g., collective effects, like superconductivity, waves, and lasers).
Reality is thus not continuous, incremental, or happenstance.
That is why everything blocks, goes against, a change -- until it occurs, suddenly, taking everyone to a new and better level. This is History. It is not a surprise ... We are in a long evolution ...
As a consequence, tri-state, e.g., does not have to be used in hardware, just in design. Intel Corporation can realize this, and become more competitive. This is due to many factors, including 1^n = 1, and 0^n = 0, favoring Boolean sets in calculations.
[2]
Preprint The quantum set Q*
Scientists Support Ukraine
Like so many, I am shocked and saddened at seeing war break out in Europe. My thoughts – and those of the ResearchGate team – are with the people of Ukraine and everyone affected.
ResearchGate is an international company, whose purpose is to enable scientists across the world to work together openly and collaboratively, regardless of borders or nationality. We have people from over 40 countries on our staff of around 200, and being based in Berlin, we are profoundly aware of the human cost of conflicts, the echoes of which have shaped and scarred our home city. We join with the international community in condemning the actions of the Russian state.
We have been asking ourselves: What can we do?
From today, we will offer free advertising space worth $2.5 million on our network to humanitarian organizations working to respond to the crisis. ResearchGate benefits from over 50 million visitors every month, and we hope this initiative can help raise funds and awareness for those organizations that are having direct impact and need support.
We also want to use our platform to highlight the response from the scientific community. Personally, I have found the messages of support from scientists everywhere to be truly heartfelt, and I would like to highlight some of the community initiatives I’ve seen here:
- Science for Ukraine provides an overview of labs offering a place for researchers and students who are affected to work from, as well as offers of employment, funding, and accommodation: https://scienceforukraine.eu/
- Labs supporting Ukrainian Scientists is an expansive list of labs and PIs offering support at this time. Submissions go here: https://docs.google.com/forms/d/e/1FAIpQLSeRGe5Da_b6GGyC6VT7CLGViGs06SzeuX7wRKpC4K5tnvlhgg/viewform Find the full list here: https://docs.google.com/spreadsheets/d/1HqTKukfJGpmowQnSh4CoFn3T6HXcNS1T1pK-Xx9CknQ/edit#gid=320641758
- This open letter from European scientists expressing solidarity and promoting peace is open for signatures: https://www.ipetitions.com/petition/an-open-letter-from-european-scientists-against
Additionally, I’m posting here some of the organizations responding to the crisis and actively soliciting donations:
- Doctors Without Borders / Médecins Sans Frontières (MSF): https://www.doctorswithoutborders.org/what-we-do/countries/ukraine
- The UN Refugee Agency: https://donate.unhcr.org/int/en/ukraine-emergency
- UNICEF: https://www.unicef.org/emergencies/conflict-ukraine-pose-immediate-threat-children
To help gather more support for these initiatives, please consider sharing this post further (you don’t need a ResearchGate account to see it), and I will continue to update it with other initiatives as I find them. You can also click “Recommend” below to help others in your ResearchGate network see it. And if you know of any other community initiatives that we can share here please let us know via this form: https://forms.gle/e37EHouWXFLyhYE8A
-Ijad Madisch, CEO & Co-Founder of ResearchGate
-----
Update 03/07:
This list outlines country-level initiatives from various academic institutions and research organizations, with a focus on programs and sponsorship for Ukrainian researchers:
Irrationals solved in algebra?
Our answer is YES. Irrationals, since the ancient Greeks, have had a "murky" reputation. We cannot measure physically any irrational, as one would require infinite precision, and time. One would soon exhaust all the atoms in the universe, and still not be able to count one irrational.
The set of all irrationals does not even have a name, because there seems to be no test that could indicate if a member belongs to the set or not. All we seem to know is it is not a rational number -- but what is it?
The situation is clarified in our book Quickest Calculus, available at lowest price in paper, for class use. See https://www.amazon.com/dp/B0BHMPMMTY/
There, Instead of going into complicated values of elliptic curves, and infinite irrationals, algebra allows us to talk about "x".
No approximating rational numbers need to be used, nor Hurwitz Theorem.
Thus, one can "tame" irrationals by algebra, with 0 (zero) error. For example, we know the value of pi. It is 2×arcsin(1) exactly, and we can calculate it using Hurwitz Theorem, approximately.
GENERALIZATION: Any irrational number is some function f(x), where x belongs to the sets Z, or Q -- well-defined, isolated, and surrounded by a region of "nothingness". The set of all such numbers we call "E", for Exact. It is an infinite set.
What is your qualified opinion?
