Petr Krylov Methods of Analogies

Prologue

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— Parallel lines do not intersect!

— That depends on what kind of monitor you're using.

If it's flat, then no—they really don't intersect.

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We live in a world obsessed with straight lines.

Look around. The interfaces on our phones are grids of pixels lined up in neat rows. Our cities are built from glass-and-concrete boxes.

Charts, reports, presentations—everything obeys a strict geometry. Even art—from Malevich’s Suprematism to digital minimalism—looks for beauty in right angles and clean lines.

“Parallel and perpendicular” has become another word for “beautiful.” “Logical” has become another word for “true.”

And there is a reason for that.

Mathematics, logic, and computers have given humanity unprecedented power over the world. We have learned to count with a precision our ancestors could scarcely have dreamed of.

We have digitized everything that can be digitized, and now we have answers to every question—provided the question is properly framed and already entered in our databases.

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But there is a paradox.

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The more precisely we count, the less we understand.

The more data we have, the harder it becomes to see the whole picture.

The more logical our reasoning, the more often it drives us into a dead end with no exit—because the exit lies beyond logic.

We get figures precise to the nanodecimal—yet still no answer.

Straight lines are beautiful, but nature draws none.

Logic is elegant, but the human mind works differently. We can admire the computer all we like, but it does not think the way we do.

Thank God for that.

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There is another way of thinking.

A way older than logic, older than mathematics, older than writing itself. A way people have always used—but one they stopped noticing because it became as invisible, as natural, as air.

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This is analogical thinking.

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Not 'either-or,' but 'both are alike.' Not 'therefore,' but 'as if.' Not a straight line of cause and effect, but a web of similarities and correspondences in which everything is connected to everything else.

This way of thinking does not replace logic. It makes logic meaningful.

Because before you can prove anything, you have to understand exactly what it is you are proving. And understanding comes only by relating the unknown to the known.

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This book is not a textbook on logic or a manual of mathematics.

It is about what was left behind when the digital ship set sail. About the methods of analogy humanity has been gathering for thousands of years.

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We will trace the history of thought—from drawings on cave walls to the Antikythera mechanism, from alchemical retorts to neural networks.

We will see how geniuses used analogy where logic fell silent. And at the end, an unexpected surprise awaits. But no spoilers.

If you are firmly convinced that the world is made of straight lines, and that truth can be born only of logical reasoning—this book is for you.

If you feel that something important got lost behind the numbers, but you can’t quite say what it is—this book is for you.

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We are not going to argue that logic is bad.

We will show something else: that it had a mother, and her name was Analogy.

And as everyone knows, you don’t choose your mother. You simply love her.

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Chapter 1. Magical likeness—cave paintings, ritual magic.

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When we were children, my sister and I fought a lot. I had a whole arsenal of toy weapons; she had only a tiny rag doll and a little needle.

– So what?

– What do you mean, what...

Have you ever heard of a voodoo doll?

He came crawling on his knees, meek as anything, begging for mercy and surrender!

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1.1 The World Before Logic

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To understand how analogies work, you have to imagine a mind in which they have not yet been set apart from reality.

Modern human beings draw a sharp boundary: between “I” and “the world,” “thought” and “thing,” “symbol” and “image,” “object” and “subject,” and a host of other categories.

For Paleolithic humans, that boundary—that opposition, really—did not yet exist. More precisely, it was so permeable that we would call it “intuition.” They called it life.

There was no writing, and so no rigid way of pinning concepts down. There was no logic as a formal system, and so thought was shaped not by terms but by whole images.

A neurophysiologist would say the right hemisphere was dominant: the world was perceived as a single, connected, breathing whole. Castaneda would say that the “logician” was still too much of a child to hold any power.

Human beings did not see themselves as separate from nature. They were part of it. And their relationship with the world was built not on “why” but on “as if.”

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1.2 The Fundamental Task: Survival

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Maslow’s hierarchy of needs in the Paleolithic was starkly simple: food, safety, health, reproduction. Everything else was a luxury—one that arrived much later in history. And even then, not for everyone.

Hunting: get meat. Medicine: don’t die of disease. Defense — to fend off predators or a hostile tribe. Reproduction — so the family line would continue.

Every one of these tasks came down to a single problem: the world is unpredictable. The animal may get away, the illness may not recede, the enemy may prove stronger. What was needed was a way to exert influence over the unpredictable.

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1.3 The Law of Conservation of Energy in the Primitive Mind

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We know the law of conservation of energy as a principle of physics. In the primitive mind, it existed as a felt reality, grounded in experience: energy does not vanish; it passes from one form to another. From one place to another. From one form to another. From a living animal to its painted image. From the sick person to their image. From the dying to the newborn.

This was not abstract knowledge. It was perception and personal experience—something lived through. The world is a closed system: nothing vanishes; it only changes shape.

And as we now know, the brain of a sentient being possesses a key feature: the so-called mirror neurons. It is precisely their presence that enables an intelligent being to “mirror” one kind of information or another. In essence, that means becoming analogous to another object or process.

From there, it is only a short step to the central discovery.

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1.4 The Law of Similarity

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If energy flows and the world is one, then like can act upon like.

This is not a logical deduction. It is intuition made method.

If you draw a bison on a cave wall and then pierce it with a spear, even in a virtual, phantom game, you can acquire certain skills and behavioral patterns.

And those skills may prove genuinely useful when the time comes to hunt a real bison. But this game has to be played well — and with inspiration.

Because here, Stanislavsky is life itself. And its verdict — “I don’t believe it” — means failure, with all the consequences that follow, often bleak and even fatal for the “actor.”

Make a figurine of the sick person and perform acts of healing over it, and the illness will recede.

Put on an animal’s hide and dance its dance, and you will take on its strength and agility.

To the modern mind, this looks like foolish, theatrical paganism and superstition. Pointless and futile.

For Paleolithic man, it was a technology. Often the only one he had. And those who failed to use every chance open to them sometimes simply died out, like mammoths.

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1.5 Shaman as a system operator

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In any society, individual people vary in their abilities. In any complex undertaking, there are specialists. And the more complex the matter, the fewer the specialists. There were masters of the craft when it came to the technology of total, conscious ‘mirroring’ as well.

A Shaman is not a ‘sorcerer’ in the way we use the word.

Perhaps it is someone whose ‘mirror’ neurons fire a little more often, and a little more effectively. Perhaps more than just a little.

But above all, it is someone who can work with—and truly understands—likenesses, analogies, visualizations, identification, disidentification, and a great many other things besides. Not in theory, but in practice. At the level of conscious skill and unconscious reflex.

He knows which image fits which task. He remembers which rituals worked for his ancestors. He sees connections where others see only scattered events.

The shaman was the first master of analogy. His drum is not a musical instrument, but a way of tuning the mind to the right rhythm.

His dance is not entertainment, nor is it foolish clowning for the benefit of his naive, trusting tribesmen. It is a time-tested method, proven across generations, for entering a state in which resemblance becomes reality.

And above all: the shaman works for the tribe. His magic is a collective tool for survival. If the tribe survives, so does he. If he dies, that whole chain of profane imitation is broken once and for all.

The ritual brings people together, synchronizes their intentions, and creates a shared field of meaning. Hunters who have passed through the ritual act with greater coordination and confidence. It is precisely this cohesion—the ability to act as a single living organism rather than a scatter of separate individuals—that both sports coaches and special-forces sergeants try to forge through countless training sessions and field exercises.

And in the hunt, cohesion and confidence matter no less than the sharpness of the spear. Often, they are what decide the outcome.

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1.6 Applying the Method

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Hunting.

In the caves of France and Spain, archaeologists have found images of bison pierced by spears. This is not art in our sense of the word. It is a ritual of preparation. A band of hunters spent the night in a cave, painting the walls, dancing, slipping into trance, rehearsing the patterns of behavior, the division of roles, and the details of the hunt. They were creating that very plan and sequence of action not in words, but through muscle memory and newly formed conditioned reflexes.

By morning, the bison on the wall had been “killed.” The hunters went out on the real hunt in the kind of state that today’s coaches would call “programmed for success.”

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Medicine.

Many cultures have preserved rituals involving the making of a figurine representing the sick person. The figurine was then subjected to actions meant to heal the person it represented. In one form or another, this practice was found almost everywhere. Few people realize it, but even the ancient statues of gods and heroes belong to the same cultic tradition, only in a somewhat altered form.

From a modern point of view: a placebo. But a placebo—without wandering into esoteric or metaphysical thickets—works, if people believe in it. And faith was, more often than not, if not absolute, then at least widely shared.

“… and by your faith shall you be healed …”.

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Fertility.

Ritual dances that imitate the growth of plants or the mating of animals are a way of “setting the process in motion” through resemblance. What is at work here is the—often ritual—synchronization of social consciousness with the consciousness of individual members, enabling a transition to a new stage of the cycle. A kind of symbolic ritual “throwing of the switch” onto a different trajectory of life.

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1.7 What Was Really Going On Here

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A skeptic will say, “But that doesn’t work. A spear thrust into a drawing doesn’t kill a bison.”

And he would be right, if by “working” we mean a direct physical effect. But the method of ritual analogy works differently.

It works through the mind of the hunter, the shaman, and the tribe’s collective consciousness.

It primes the psyche for success.

It brings the group into sync.

It creates a sense of control in an unpredictable world.

It passes on knowledge through vivid forms—stories, dances, drawings.

A person who has gone through the ritual acts differently from one who has not. Which means the method works.

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What’s more, a ritual of resemblance creates what might be called a 'ski-track' effect.

When someone repeats a ritual that someone else has already practiced over and over, they enter the required state more easily.

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1.8 Why This Is a Method of Analogy

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There is no 'if–then' logical inference here. There is an act of likening.

The drawing becomes a bison.

The figurine becomes the sick person.

A collective sending becomes the growth of grain.

Here, analogy does not explain the world; it creates the necessary reality in the mind, so that it can later be brought into being in the world.

This is the first and most ancient method of analogy. It was born not out of idle curiosity, but out of the need to survive. And it still works today—in visualization, in ritual, in any sphere where the mind must first be aligned with the right image before action begins.

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1.9 Transition to the next chapter

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Magical analogy operated through whole, undivided images. But people quickly discovered that analogy could be drawn not only between “everything and everything else,” but also between particular properties and functions. That gave rise to the next method—functional transfer. We’ll turn to it in Chapter Two.

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Chapter 2. Functional Transfer: The First Tools.

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Men, marry petite, slender women—fur coats are cheaper for them.

And buy one you will, sooner or later.

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2.1 From Analogy to Action

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Magical analogy operated through whole, undivided images. Humans likened the bison to a drawing, and themselves to the bison in a ritual dance. But in tackling practical problems, they discovered something else—something simpler and more tangible.

Nature had already solved many of humanity’s problems.

All that remained was to adapt those ready-made solutions to human use.

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2.2 What Humans Learned from Nature

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Paleolithic humans lived within nature, not apart from it. Day after day, hour after hour, they watched:

How a sharp fang tears flesh.

Like a claw sinking into hide.

Like a horn piercing a defense.

Like a strong bone bearing weight.

Like a cup-shaped leaf or shell holding water.

Like an animal hide retaining heat.

He did not think, ‘I need to invent a knife.’ He thought: ‘I need something that does what a fang does.’ And he took a fang.

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2.3 The First Functional Transposition

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The simplest and most ancient transposition is to use ready-made natural forms for their original purpose, only in human hands.

Fang and claw became the first cutting tools.

Horns were the first thrusting weapons.

Hides became the first clothing and the first shelter.

Shells, gourds, and horns became the first containers.

Bones became the first handles and levers.

Human beings invented nothing. They merely borrowed ready-made solutions from Mother Nature.

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2.4 From Borrowing to Modification

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And then the most interesting part began. People noticed: if a fang cuts well, and stone can be shaped, then stone can be given the shape of a fang.

That is how the first knife came into being. Not a fang, but a stone sharpened into the shape of a fang.

The function migrated from one bearer to another. This is no longer borrowing, but a transfer of function.

The bowl imitates cupped hands, then a shell, then a clay vessel modeled on the shell.

The hammer imitates the fist, then a stone clenched in the fist, then a stone tied to a stick.

The needle imitates a fish bone or a plant thorn.

Every object we hold in our hands today has a natural prototype, first glimpsed—often thousands of years ago.

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2.5 Why This Is a Method of Analogy

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Here analogy operates not at the level of image (this drawing is a bison), but at the level of function (this object works like a fang).

What humans recognized was a similarity not in appearance, but in action. They carried over not the form, but the principle.

This was a huge step in the evolution of thought. From concrete resemblance (“a bison as a drawing”) to abstraction (“sharp as a claw”). Abstraction is born from analogies between functions.

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2.6 Examples That Have Survived to the Present Day

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Many solutions borrowed from nature are still in use today almost unchanged.

The medical syringe and needle echo the snake’s venom gland and fang.

The saw mirrors the serrated edge of a leaf or an insect’s jaw.

Velcro was invented in the twentieth century, but its model came from the burdock burr (a direct continuation of the method).

The lever works on the principle of a joint—or of a root prying up a stone.

For insulation, wool, down, and feathers are still the best—and often the most desirable—materials.

Even modern design—bionics—is really the same method of functional borrowing, only now made conscious and technological.

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2.7 What This Method Has Given Us

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Time savings. There’s no need to reinvent the wheel—nature has already drawn up the plans.

Reliability. Nature’s solutions have been tested by millions of years of evolution.

A foundation for further development. From fang to knife, from knife to sword, from sword to the machine.

Understanding Function. Human beings learned to see not only objects, but what they do.

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2.8 Moving on to the Next Chapter

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By borrowing ready-made solutions, human beings quickly realized that what could be carried over was not just form and function, but social role as well. That is how totems and kin-based identity emerged. How human beings came to be wolves, eagles, or bears is the subject of the third chapter.

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Chapter 3. Totemic identity: “we are like wolves,” “we are like ravens” (clan totems).

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“Now this is the Law of the Jungle—as old and as true as the sky;

And the Wolf endures only while he keeps it,

But break this Law, and death is sure to follow.

Like a web of lianas, the Law winds on, growing both ways:

For the strength of the Pack is the Wolf,

And the strength of the Wolf is the Pack.”

Rudyard Kipling, “The Law of the Jungle” (adapted from V. Toporov’s translation).

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3.1 From Borrowing Form to Borrowing Essence

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Humankind learned to take ready-made forms from nature: a fang became a knife, a hide became clothing, a shell became a cup. Then it learned to transfer functions: a stone shaped like a claw could cut no worse than the real thing.

But sooner or later, the question had to arise: could one transfer not only form and function, but the beast’s very nature—its essence itself? Its strength, agility, cunning, its ability to survive?

The answer was yes. Thus was born the method of totemic identification.

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3.2 Totemism as Systematic Plagiarism

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A totem is not just a “guardian beast.” It is humanity’s attempt to appropriate an entire package of natural solutions evolution had worked out long before human beings ever appeared.

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The wolf is strong, resilient, lives in a pack, obeys the pack leader, and never abandons its own. A person who identifies with the wolf is trying to become like it. What he copies is not the form itself (putting on a wolf skin is easy enough), but its behavior, hierarchy, psychology, and vital force.

This is no longer just borrowing a tool. It is the borrowing of a way of life, a mode of thought, sometimes even a kind of behavioral “code.” What today is called the archetype and an egregoric connection.

The totem school was history’s first attempt to take from nature a ready-made model of survival and apply it to a human group.

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3.3 From the totem to philosophical and military schools

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The more complex society became, the subtler these borrowings grew.

Animal-based martial arts styles (wushu, kung fu) are a direct outgrowth of the method of analogy. A person does not merely don a tiger’s skin; he moves like a tiger, strikes like a tiger, waits like a tiger, breathes like a tiger. By imitating its outward form, he learns the animal’s inner mechanics.

The tiger is supple strength and sudden ferocity.

The monkey is cunning and agility.

The crane is balance and distance.