Cryptocurrencies and quantum technology.

Encrypting information increases security. And security is trust. Did you think what could happen if somebody breaks the code that the central bank uses to ensure the currency? That allows the hacker to start to make lots of currency. In normal trade, people use digital currency. The big difference between digital currency and cryptocurrency is that the last one is not controlled by the state. Cryptocurrency is like stock. Investors can buy those things and then sell them to other people. Or they can exchange their cryptocurrency for state money or real money. The problem is that nobody controls Bitcoin or other cryptocurrencies. 

There is a lot of money in the cryptocurrency companies' accounts. And if that money will be released to the markets that causes hyperinflation. The main problem with U.S. economics is connected to its role as the dominating actor in global marketing. There are lots of dollars stored in the other state’s banks. And if those dollars are released to markets that collapses the dollar’s value. Bitcoin can cause a similar effect. But the main difference is that the central banks don’t even know or control the money that those cryptocurrency companies handle. 

The bitcoin countdown has begun. Quantum computers can crack the Bitcoin security algorithm in less than a week. But there is a possibility that some actors have already cracked that code. The AI-driven learning neural network can do many of the same things as quantum computers. And in those systems, the AI-driven network architecture drives autonomous workstations to run the code-breaking algorithms. In those kinds of systems, the AI can share the number line that the defending system creates using the Riemann Zeta function between those workstations. Then those systems can try to crack the security key. 

If the system can use the botnet with thousands of computers that thing can make the de-encryption very fast. And that can endanger Bitcoin. The main problem with Bitcoin, and other cryptocurrencies is that they offer a place where actors can dump their money. There is no bottom in cryptocurrencies. The thing that makes cryptocurrencies dangerous is that a considerable part of the state currency can be dumbed into cryptocurrency. There is a lot of currency out of marketing. When the state sees that there is not enough money, it can deliver more currency.  

The contract that the cryptocurrency can be bought from investors means that if the cryptocurrency company delivers very much state currency to the market it collapses the value of the currency. The inflation mechanism is so simple. Only a lot of money is needed. And when the number of currency compared to state ownerships and state merchandise rises that drops the value of currency. There is lots of money invested and locked in cryptocurrencies. There is a possibility that somebody starts to create their own cryptocurrency using stolen or cracked security code. Suppose this is not noticed in cryptocurrency companies. It can cause a dramatic collapse in marketing. 

https://www.rudebaguette.com/en/2025/06/bitcoins-countdown-has-begun-experts-reveal-when-quantum-computers-will-finally-shatter-its-legendary-encryption/

What if we put computers to think mathematically?

When we think about programming and the computer's memories every single memory unit in the computer hardware has a certain address. The artificial intelligence connects and disconnects those memory points into the new orders. And that can make a computing process that mimics thinking. Every single memory address is like a piece of the puzzle. If every single memory unit has a certain number that makes it possible to point certain points from the computer memory. 

When we think about things like thinking we could easily connect those memory units with orders that the large language model, LLM gets by using the numeric values of the memory units and then calculate them with the ASCII marks. In the ASCII system, every single mark on the keyboard has a numeric value. 

For example, the letter A has a numeric value 61 in decimal and 41 in hex. A little a (a) has values 97 in decimal and 61 in hex. That's why it's not the same as the letter big or small in passwords. The numeric system is also important. The hexadecimal ("Base-16" system where the 10 comes after 16) and regular decimals are different. 

In that system 10 is marked in the numeric line like this. 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10. In binary system 10 comes after 9 like this. 0,1,2,3,4,5,6,7,8,9,10.

Same way every single color has a numeric form in the computer memory. The system is known as RGB.  The system can use CCD cameras to make observations. 

Another thing is to use the values that fit to computer or programmer better. The color red can have a numeric value "200" and then the depth of that color can have 99 states. The system can turn every color into its own numeric value. 

The deepest red can be the 299. The data that CCD camera pixels give can be numeric. The system can see what numeric value every pixel gives and then it can make the model about things that it sees. So all data that travels into the system can turn into numeric. 

Token ring. If we think of this model as the computing cycle of the AI.  The system connects data into that data cycle. Every point in the cycle. There is the computer's image.

This can be the new way to handle large language models, LLMs are not to turn their mathematical models for words. The system can translate data that users input there into the mathematical model. Then the LLM starts to operate and process data in the mathematical form. That kind of thing can be lighter for computers than the words that we use. Mathematics is easier for computers, and when we think about the ability to turn words into mathematical form, we must remember that ASCII codes are basically numbers. Those numbers can sum, division, and multiplicate easier than words. 

That means the LLM can turn every single word that it has into numbers. Then that system can make calculations using the numbers. The ability to handle data in numeric form makes those systems more effective. The system can use the "token ring" type data handling, or computing model. The token ring model is known from data networks. However, the same model can introduce how the system surrounds data in it. Every time, when the system makes the data cycle it connects information into that data cycle. 

The system makes a certain number of calculations in every round. In those calculations, the system connects data from the sensors and memories in the data flow. The system doesn't need to show that information to the users before it drives it through the cycle as many times as ordered.

https://www.geeksforgeeks.org/ascii-table/

https://www.quantamagazine.org/to-make-language-models-work-better-researchers-sidestep-language-20250414/

https://www.rapidtables.com/web/color/RGB_Color.html

https://en.wikipedia.org/wiki/Hexadecimal

https://en.wikipedia.org/wiki/RGB_color_model

Solving Glaubert's optimum rotor disk can make new aerodynamics possible.

"By refining a long-standing aerodynamic problem, Divya Tyagi unlocked new potential for wind turbine design. Her mathematical breakthrough could enhance energy efficiency and inspire future innovations. Credit: SciTechDaily.com" (ScitechDaily, Student Refines a Century-Old Math Problem That Could Transform Wind Energy)

Glaubert's optimum rotor disk can help to make more effective wind generators. But, it can also help to make more effective turbines and turboprops. In the last case. 

The researcher must determine the speed of the wind that travels (or should travel) through Glaubert's optimum rotor disk. And then. 

Developers can make the formula to create a customized optimal Glaubert disk for that windspeed.

The aircraft cannot travel faster than its exhaust gases. And the jet engine. Just accelerates air that travels in the engine tube. The exhaust gas cannot travel faster than the burning speed in the fuel-air mixture. The problem with the fast low-hypersonic jet engines like ramjets has no moving parts. 

The engine cannot start when the aircraft stays on the runway. The airspeed in the ramjet must be about Mach 1. The problem is that the blower will face the air that travels through it with a speed that is over Mach 5 if the aircraft travels with hypersonic speed. If somebody can make a blower that can inject air into the ramjet engine with a speed that is Mach 6+ that thing will revolutionize aviation. 

Solving Glaubert's optimal rotor disk problem is the thing. That can improve the efficiency of the wind turbine. 

Developers can use the same formula to solve the turboprop engines' development problems. And the other thing is this. Solving this problem can also give new energy-effective solutions for turbojet engines. 

Glaubert's optimum disk makes it possible to calculate the ideal size and speed for certain disks. 

That formula can make it possible to calculate the ideal size for wind turbine propellers. 

The system must only know the average wind speed. Or the most usual wind speed. That helps to make more effective wind turbines than before. 

The prediction in Glaubert's optimum disk is that the disk gets its energy from free-flowing air. But there is the possibility to make. The changes there the force goes opposite through the disk. We can think that Glaubert's optimum disk opens the road to the more effective turbines and turbojets. 

In that case, the airflow that the turboprop makes. Is, handled as the free flow. The thing that the researcher must do is to create value for the free airflow.

That thing happens when the researcher determines the goal speed. And then. The other things like the wing, or disk size must be put to fit with that airflow. That is one of the things that can make aircraft more effective than before. 

https://scitechdaily.com/student-refines-a-century-old-math-problem-that-could-transform-wind-energy/

https://wes.copernicus.org/articles/10/451/2025/

https://en.wikipedia.org/wiki/Asymptote

Researchers think that Einstein's theories don't stand on the edge of the Universe.

"Gravitational lensing of distant galaxies by the galaxy cluster Abell 2390, observed by the Euclid satellite. © ESA/Euclid/Euclid Consortium/NASA, image processing by J.-C. Cuillandre (CEA Paris-Saclay), G. Anselmi" (Unige, Einstein’s equations collide with the mysteries of the Universe)

There is not very much research where the Theory of General Relativity is tested in extremely low gravity and energy levels. Those theories are well-tested around black holes. But there is not very much data about things like how gravity waves or some other waves or particles interact in conditions. Where energy travels out from them very fast. 

The edge of the Universe is a mysterious place. There the energy and material face lower than exists our Universe. Or otherwise saying the energy in our Universe faces a cosmic void. Energy travels from space filled with quantum fields and wave movement to the cosmic void or into cosmic nothing. That space is not possible in the Universe. There are no absolute vacuums in the Universe. That we know. That means energy can travel only out from the Universe. 

When we think about energy fields there is a thin string. Those strings are so-called time arrows (or arrows of time). The time arrow means the particle or energy beam that travels in the Universe. When that time arrow releases its kinetic energy. It transfers it to other particles. So when a time arrow travels forward, it pushes energy to particles around it. And then that thing pushes those particles back in time. 

Then we can think of the time arrows as energy fields that travel out from the point where the Big Bang happened. When the distance between the time arrow and the Big Bang turns longer. There is space between those energy strings. That space means that more energy will travel between those time arrows. And that space makes it possible for particles like photons to start to make curves between those time arrows, like energy beams and particles.  The energy level between those beams or time arrows turns lower. 

That means at the edge of the universe could be very extraordinary gravity waves. Those gravity waves can have a structure where they have two wavelengths. The normal gravity waves and other waves or strings connect them into one bigger entity. Or maybe there are so-called spiral gravity waves that travel forward like serpentines. But that is only theory. 

And that means the particles start to deliver energy or wave movement faster than previously. That means time travels faster in particles at the edge of the Universe. The edge of the universe is a mysterious place, as I wrote before. There the particle travels out from the universe to the place, where there is no energy at all. 

When we think about the shape of the Universe, we must realize that the Universe is a so-called false vacuum. The thing that limits the speed of light is for example quantum fields. Or scattering effect. When a particle travels from a false vacuum to a real vacuum there is nothing that can limit its speed. But the other thing is that energy travels out from the particle faster than in the Universe. Those things are not researched very much. 

https://www.unige.ch/medias/en/2024/les-equations-deinstein-se-heurtent-aux-mysteres-de-lunivers

https://en.wikipedia.org/wiki/Arrow_of_time

https://en.wikipedia.org/wiki/General_relativity

The mysterious genius Srinivasa Ramanujan.

Srinivasa Ramanujan (1887-1920). (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

The number theory is thankful to Srinivasa Ramanujan (1887-1920). The thing that makes this person, who was born into a poor Indian family in colonial India was a self-educated person, who made a lot of things in mathematics. Those theories are still handy tools for many types of advanced calculations. There are many interesting details in the life of that young person, who passed away in 1920. Many people say that Srinivasa Ramanujan died too early. If that person could live a longer life, he might stand in the place of Albert Einstein. 

There were many interesting things in Ramanujan's early life. The thing is that Ramanujan failed twice in college. Because of his passion for mathematics. And that's why he flees from home. Maybe he was afraid that his parents were angry. Finally, he went to Trinity College Cambridge where he started to work with Hardy and Littlewood in 1914. 

Pages from Ramanujan’s lost notebook. (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

"Ramanujan’s first letter to G.H. Hardy included formulas (5), (6) and (7), strange nested fractions that Hardy said “defeated me completely; I had never seen anything in the least like them before.” (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

(Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

There are lots of theories that this man created. At a young age, this man was very poor and also he had very big health problems. In 1912 he sent letters to famous mathematicians and one of them, G.H Hardy the expert in number theory and analysis at the University of Cambridge. When Hardy got the letter from Srinivasa Ramanujan. That man said, that his greatest work for mathematics was that he found Ramanujan. Then Hardy called Ramanujan to England. There Ramanujan made some works for Cambridge. He lived in England from 1914 to 1919. Then he returned to India where he died in 1920. 

"Hardy and Ramanujan collaborated closely for years. They exchanged letters about mathematics until Ramanujan’s death." (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

And then he went sick. After returning to India Ramanujan died. An interesting thing is that Ramanujan died almost similar way as his colleague Nils Henrik Abel (1802-1829), a Norwegian mathematician. He came to his university, did impressive work, and then got some illness and then that ultimate genius died at a young age, 32. 

Images: (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

Ramanujan work. 

Still today Ramanujan's work is very highly respected. 

The main thing that Ramanujan did is this: he introduce a way to calculate fractional numbers. There are five ways to introduce number 4.  The number four can be shared in pieces like this (2+2), or, (2+1+1), or, (1+1+1+1), or, (1+1+2). And then it is easier to make things like division calculations. 4/8 can be introduced like this: (1+1+2)/(2+2+2+2). And we all know that 4/8=1/2. 

The interesting thing is that. Those numbers can also be decimal numbers, which means that we can introduce as an example number 1 in this mode. (0,25+0,25+0,25+0,25). Or we can introduce number four in this mode. (0,5+0,5+0,5+0,5+0,5+0,5+0,5+0,5). Or we can share 0,5 to two 0,25. That is one of the most interesting things in mathematics. There are many ways to benefit from that model. 

The Ramanujan theorems play a key role in singularity calculations. There the curves and lines connect a series of points. The introduction for that is in the Quanta magazine article. 

The thing is that Ramanujan's work could help Grigory Prelman in his work with the Poincaré theorem. 

https://www.quantamagazine.org/srinivasa-ramanujan-was-a-genius-math-is-still-catching-up-20241021/

https://en.wikipedia.org/wiki/G._H._Hardy

https://en.wikipedia.org/wiki/John_Edensor_Littlewood

https://en.wikipedia.org/wiki/Niels_Henrik_Abel

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

List of Ramanujan work. 

• Ramanujan's sum
• Landau–Ramanujan constant
• Mock theta functions
• Ramanujan conjecture
• Ramanujan prime
• Ramanujan–Soldner constant
• Ramanujan theta function
• Rogers–Ramanujan identities
• Ramanujan's master theorem
• Hardy–Ramanujan asymptotic formula
• Ramanujan–Sato series

Wikipedia, Srinivasa Ramanujan

All images: (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

How nano- and quantum technology, mathematics, and geometry are working together?

 How nano- and quantum technology, mathematics, and geometry are working together? 

Hofstadter's butterfly 

Researchers found Hoftadter's butterfly from the graphene. Hoftadter's butterfly is a butterfly-looking geometrical structure. Researchers can use that kind of structure to calculate the positions of the qubits. Or, sharper saying Hoftater's butterfly can be an effective tool for modeling the point where binary data transforms into the qubit. 

The area of Hofadter's butterfly can tell what is the right distance between the transmitter that transmits information into qubit. In that model, the qubit is multiple Hofstadter's butterflies that can transport information into the sensors. 

When energy hits to layer it can make Hofstadter's butterfly. The outside force can form that butterfly simultaneously if some force at corners pulls an energy field in that form where a circular energy field forms. That can used in a system that turns binary data into qubits. 

"Rendering of the butterfly by Hofstadter" Wikipedia/Hofstadter's butterfly

"Example of non-integer dimensions. The first four iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses the scale factor (S = 3) and the number of self-similar objects (N = 4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26." (Wikipedia,Hausdorff dimension)

What would somebody do with the information about overlap points and lines? 

Or, What is the minimum mass of dust that can cover the entire paper? 

Do you know what is the Hausdorff's dimension? That commons the term dimension, which means Hausdorff's dimension can calculated and determine how much some group or pattern fills in dimensions. Hausdorff's dimension is the same thing, without depending on space or dimension 2 or 3D. 

"Imagine an endless piece of blank paper covered with a smattering of lines pointing every which way. A gust of wind comes and sprinkles dust on top of the paper — in effect covering the lines with points. Say a helpful mathematician tells you how much dust covers any one line. Based on that one piece of information, can you figure out how much dust is there in total?" (BigThink.com/Mathematicians Cross the Line to Get to the Point)

Another way to ask that thing is, what is the minimum number of sand bites that can cover the entire area? And what is the minimum number of lines that can connect them? 

What would somebody do about information about the distances of the lines and points? Or sharper what would somebody do about information about the minimum number of lines that are connecting a certain number of points that are randomly at level? 

And in that case, those points don't form stable geometrical structures. That information is one of the mathematical problems, and it is important when particles that form a system communicate with each other using coherent communication tools like lasers. This is one of the things that the modern technology turns interesting. 

When researchers create smaller and smaller quantum-scale structures they must have something that moves objects. The line can symbolize a laser- or other energy beam, and the point could be a particle that the system moves. 

When we think about the material and its smallest particles, we face the situation that every single particle is in its ball. The truth is that the quantum field around the particle is not the ball. It is a structure that form changes when electrons are changing their place around the atoms. 

That is the thing that makes it hard to make precise calculations about quantum gravity and extremely small-scale interactions. And those interactions are the most important things in quantum-scale technology. 

https://www.quantamagazine.org/a-mathematicians-guided-tour-through-high-dimensions-20210913/

https://www.quantamagazine.org/mathematicians-cross-the-line-to-get-to-the-point-20230925/

https://scitechdaily.com/ancient-graphite-reveals-a-quantum-surprise-scientists-discover-hofstadters-butterfly/?expand_article=1

https://en.wikipedia.org/wiki/Hausdorff_dimension

https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly