For our world the following sentence is valid – The more gentleness the more beauties. Quite a interesting event in nature, such incredible gentleness and beauty (see flowers, butterfly wings) is superior to such rough reality. Everywhere in nature we see, we perceive a fine balance that controls the most violent worldly forces – let us call them, for example, the four fundamental forces. Very roughly and violent processes at micro or macrolevel. Microlevel means thermal movements or quantum fluctuations. Macro level mean processes in the universe. See two images below – the left illustrate quantum field and the right illustrate metagalaxies.

In contrast to the immense gentleness about in the middle – see organic compounds, structures and bonds of organisms, especially artworks, musis, craftworks and inventions of human beings. See next image below

The appearence of beauty and functionality in the world –  we get a curve of the distribution of beauty in the universe as a function of magnification with a maximum in the middle. And with two minima on each side of the curve. See an image below.

See also artworks. A work of art such as a painting or a sculpture must be viewed at a certain distance. It is difficult to judge details with a microscope or magnifying lens. Or, on the contrary, too be distant. A certain distance is needed, which depends on the size of the artwork. Certainly under a magnifying lens one can see interesting and beautiful details, but under a microscope the interesting and beautiful details will decrease. And when we submit the artwork to structural analysis, that’s the end of the beauty. Conversely, if we move too far away from the artwork, we can perceive the whole, but without the details that give the work its beauty and freshness. And when we move away from the work for tens if not hundreds of metres, we no longer see anything, the beauty has disappeared, our eye can no longer distinguish it. And so it is with the nature around us.
The machine is not only functional but also beautiful. Beauty is the expression of well-balanced functionality. Functionality not only to the machine, but also to its immediate surroundings. See following image

a photo of a steam locomotive
From observed experience we know that beauty, functionality, and mutual harmony occur in transitional states, areas of transition between pure order and pure chaos. Most beauty is contained in the transition between laminar and turbulent flow. See the beautiful curves when the flow of the medium changes from laminar to turbulent. See an image below

The most beautiful shapes and structures between laminar and turbulent state. This beauty disappears in the chaos of turbulence or in the tightness of orderliness. See the ugly disorder of chaos versus the cold and boring beauty of ideally spaced crystals.

Certainly the chaos, the chaotic appearances are different every time, unexpected and always ugly, disorderly. Certainly orderliness is expected, predictable, but boring and cold, its “beauty” as cold as ice. But transition state – always new, unexpected and beautiful or functional. But when is that moment of creation of transient state? Better expressed, when in space-time appears that impression of beauty, of functionality?

The artwork can only be viewed after it has been made. It is hard to judge the right moment of creation, painting, formation what it will be and how beautiful and stimulating it will be. 

True Functionality is connected with Beauty. All the beauties of the world together with the possibilities to form matter are given by atomic physics – more precisely by the intolerance of bound electrons to occupy the same shells in the atomic orbits – see Pauli’s exclusion principle. 

The base of matter – atoms. Very stable grouped sets of different excitations of omnipresent quantum field.

  • The base of the atom is the nucleus. There must be protons with neutrons together, not only protons. The strong nuclear force Fs makes (attracts) protons and neutrons hold together. It is not really possible to make two protons hold together. There is a repulsion force Fr, then Fr>Fs . See below – protons red, neutrons blue

    Only one neutron between two protons is not enough. 2*Fs ≅Fr – after decay of neutron, see stability! There must be neutrons, then the strong nuclear forces can balance out the electric repulsion. Then 4*Fs>Fr for two protons with two neutrons (helium) or particle alpha. This fact allows the nuclear fission reaction, especially for the heavier element nuclei. And for the nuclei of the heaviest elements like uranium and plutonium, chain fission reaction is possible. In the other hand to make nuclear fusion is possible for the lightest elements, but not for hydrogen. It is very difficult to give adequate comparisons. Of course, the strong nuclear force is about 100 times stronger than the electromagnetic force. But it has a very short radius with a peculiar trajectory. Moreover, a proton or a neutron are not spheres, but very hard to define appearances of quarks with interchangeable gluons. Just like the electron is not a ball rapidly orbiting an atomic nucleus but a cloud of probabilistic appearance. A wave-particle at the quantum level. 
    Notice –  There is the question of the origin of elements heavier than protons (hydrogen nuclei) at the beginning of the universe. Without a neutron, two protons can’t get close to each other. The neutron is absolutely necessary for nuclear reactions, whether fusion or fission. After all, alpha particles (helium nuclei) are the basis of nuclear physics. The reaction of two protons (hydrogens) fusing together can take place in stars like the Sun. And it’s extremely slow, because neutrons are needed together with a weak nuclear interaction. On Earth, for thermonuclear reactions, we have to use nuclei of heavier elements such as deuterium (an isotope of hydrogen), lithium, etc. Because neutrons are present in these nuclei. When we are on the gentleness and beauty which is expressed on such rough and violent processes (see the stability of atomic nuclei and atoms). It is very interesting how the weak nuclear force by neutron decay controls the strong attractive nuclear force against the strong repulsive electromagnetic force. The weak nuclear force is something like a trigger in a weapon or technological process – a small impulse causes a strong reaction – here the decay of the atomic nucleus.

Let’s go back from nuclear physics to atomic physics. The envelopes (shells or orbitals) of atomic nuclei of the periodic table appear incomplete, except for the noble gases. The origin of the incompleteness is the electron intolerance formulated by W. Pauli as the exclusion principle.  See below part of the periodic table

Incomplete atoms have a terrific tendency to fill their orbitals to full electron count. This is the origin of the chemical bonding of atoms into myriads of different molecules. Especially carbohydrates. E.g. HF, H2O, H3N (NH3), H4C (CH4), … , (C6H12O8)n, …
CaF2, … , etc.
The same incompleteness of atoms we can observe in flowers – stamens and pistils, which must be joined by external forces in order to preserve the biological species.
Along with the possible combinations of atoms into molecules, discretization decreases and continuity increases. Such fragile and gentle structures like artworks, like music songs, like flowers, etc, in short such gently structures are modulated at the chemical bonds thanks to the delicacy of the valence electrons placed around such a rough and brutal base as the atomic nucleus is. Comparison – it is the same as with sculpture clay. Such clay has been prepared from rocks by crushing, pulverising and floating it – the result is plasticised fine clay for sculptors and ceramists.
By the way – see quantum mechanics in prehistoric ages. Especially metal treatment by thermal process. The ancients found it very strange when they heated a metal it would first not shine, then appear dark red, then red, then orange to yellow colour and finally almost white. However, the colour of the radiation should have been the same! Only changing in intensity from the slightest shining to a blinding shining.

What’s the point of all this? All the “incomplete” atomic orbitals, all the samples whatever there are in nature. What is the purpose of knowledge whose current state is the quantum field theory – field properties of matter and radiation. The “peak” is the wave equation starting with Erwin Schrödinger. There is a new base unit – Planck constant as a speed of light. How to prove, how to verify that Planck’s constant is always the same throughout the history of the universe? After all, in physics we measure only and only ratios – the ratio of the measured quantity to the base unit. How do you detect a change in the base unit?   Yes, in terms of the basis of knowledge, there have been no new discoveries, no new fundamental insights. It’s still just a reworking of the procedures for solving the wave equation and applying it to other systems and problems – certainly quantum computers, certainly the discovery of gravitons, quantum chemistry and many many more. But basically it is just a confirmation of physics ideas that are 70 years old and more – gravitons, antimatter, quantum fields with zero vacuum fluctuations – with excited particle-waves that repeatedly disappear and appear again. It is still just a reworking of the wave equation solution procedures and its application to other systems and problems, still just a calculation of quantum states, e.g., standing wave states associated with particle-waves. What is remaining? A unified field theory? Reducing quantum mechanics to the simple statistical appearance of particles, impulses and energies is hardly possible anymore. What then? To find a universally valid formula for ever-changing conditions? Reality still surprises us, it is impossible to write a universal formula. A universal formula for chaotic events or a universal classification of biological species. However, the difference between the biology of the Palaeozoic and the current Quaternary is fatal. The answer is probably for each person to decide for himself in what situation he finds himself.

A short note on the origin of waves, particles, atoms, chemical bonds and thus molecules. Let’s have an ice crystal. When we heat this crystal, we get water or water vapor. And when we cool the water, we get the original ice crystal again. That sounds logical. We even know why it happens – chemical bonds dependent on internal energy. But let’s think differently – at the beginning of the universe, according to known hypotheses, there were no ice-snowflake crystals. Where have the laws of physics been hidden? Where have the chemical bonds been hidden, where has the diversity of chemical compounds and the diversity of biological species been hidden? Let’s go back to our ice crystal. Sometimes in the primordial forms of our universe the “condensation” of particle-waves must have started, then the fusion of atoms, but according to what laws? Where have all the laws been hidden? However, laws, rules and processes are frameworks – each species is an unrepeatable original – no two snowflakes in the world are exactly alike. Every physical process is slightly different at the quantum level. What have been the degrees of freedom in the beginning of the universe? In other words, what was randomly realized in a given framework, what “condensed” in the course of the cooling of the universe, already has a uniquely given path with all the reciprocal properties. That leads to the framework repeatability of physical and chemical processes as we know them today. If we accept this hypothesis then there may be other groupings, other chemical bonds and other biological species in different universes. The temporary conclusion is – random processes take place in a given frame and these are then repeated, again randomly, but in a sequence of given frames, which frames then gradually change. Randomness vs. necessity. But there is a contradiction. If the particles are roughly the same (or so we think), why do biological species change rapidly over geological epochs?
If we plant a pine seed it won’t grow into a maple tree and vice versa. This is the way the world works. Although pine trees were not in Devon and in the future… ?

Go back to the Beauty and Functionality in the world. Where was an artwork (in the same way every product) before it was created? In the beginning there was a movement of Wisdom (mind) inside the creative man, after that there was the artwork. What’s going to happen to the artwork through its entire existence? What happens to the artwork when it ceases out of existence? There will be new artwork better then last one. But creation ability is not possible to destroy.

Some people are so sensitive to feel hidden intention which will then be seen visibly in the world. The purpose of our life is to grow in this experience to perceive the invisible hidden intentions by verifying this perception in its visible results in the world. More about it in section Theology.

See abstract images and real images. Not only artworks but also pieces of engineering endeavours such as machinery, engines, clocks, turbines, etc. We are familiar with real images or real engines. Abstract ones are new to us. But like real images then abstract images could be beautifull. Their common attribute is a beauty. In the first case – the beauty in the real world, in the second case – the hidden beauty gradually becomes visible. It’s the same in engineering. The common attribute is a functionality. Real images for us could be abstract for others and vice versa. Consider the prehistoric fauna and flora of devon could be abstract for us. It´s the same in engineering – consider the first engines in the 19th century.
Current nature in the world with real images is only one expression of Beauty. One expression from many possible expressions, from infinity possible expressions.  The common denominator of all images („real“ and „abstract“) is Beauty at any kind – shapes vs. colours. See also multiverse universes.

Engineering – interesting development of human beings called engineers. In the beginning, in prehistoric times, there was only ore, coal, limestone and fire. Throughout ancient times, engineers made metal tools, weapons and simple mechanisms (water wheels, screw pumps). In the Middle Ages, engineers built he first mechanisms such as mechanical clocks, weaving looms and so on. Not that mechanisms built or replicated themselves. And in modern times, we already have mechanical computing devices, typewriters, precise pendulum clocks, right down to high-precision atomic clocks.

All tools, devices, devices over the ages (from swords and knives to various mechanisms and processes to high-precision atomic clocks) did not happen randomly. They didn’t just happen by the way. But they were created by a big effort, a painful experience of a few people called engineers. The painful experience was replaced by the immense joy of a working invention or of putting an idea into practice. It doesn’t matter what you are, if you’re an engineer, scientist, artist, craftsman, carrier, economist, hairdresser, pilot, doctor, teacher or something else. One should be something – to reach the fullness of humanity. Live out the painful experience with following immense joy of the obtained abilities. And so still. In engineering, there is no absolute best solution to a given problem. There is a good solution and an even better solution. But no one can guarantee that the even better solution is the best.

The devices were built not by themselves, but by experienced and capable people. Watchmaking is a beautiful example. The accuracy of clocks increased through the ages to the current level of atomic clocks. These instruments did not self-construct, they were built by engineers. In fact, the machine with given accuracy produces another machine (even itself) with a given original accuracy – no more! A machine production with a given accuracy cannot produce, for example, more accuracy gears than the given accuracy of the machine.

At first glance, a mystery of increasing accuracy of products. How to achieve with a given accuracy of the production machines a much higher accuracy of next products?

   to be continued …

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Technical drawings