How Many Different Worlds Can One Map Contain?

When someone completes a test in JakToMám, what do they actually get?

When a person completes a test in JakToMám, they receive a result: a personal map of concepts.

Some concepts are close to each other, others are far apart.
An image of relationships within their inner world emerges.

At first glance, it may seem as if this map is a direct imprint of a single specific answer — one particular matrix of symbol assignments.

But mathematics tells a much more interesting story.

A single map can correspond to an unimaginably large number of different possible answer matrices.

And that is one of the reasons why the map is such a powerful tool.

How the test is actually constructed

In the test, you might have for example:

• 20 concepts (e.g. Self, Mother, Love, Good…)
• 16 symbols
• for each concept, you select 8 symbols

Each response therefore creates a table (matrix):

• rows = concepts
• columns = symbols
• a cell contains 1 if the symbol is assigned
• 0 if not

Mathematically, it looks simple.
But the number of all possible ways to fill this table is enormous.

The number of combinations for choosing 8 symbols out of 16 is:

12,870

And since we do this for 20 concepts, we get:

12,870²⁰ ≈ 1.5 × 10⁸²

That is a number with 82 zeros.

For comparison:

• the number of atoms in the observable universe is estimated at around 10⁸⁰
• the space of all possible test responses is therefore larger than the number of atoms in the universe

Of course, most of these matrices would look completely random.
Human responses occupy only a small, structured fraction of this space.

But even so, the space is vast.

From matrix to map

From this table, distances between concepts are then calculated.

• if two concepts share many symbols → they are close
• if they share few → they are farther apart

From these distances, a map is created in a plane using a mathematical method (MDS – multidimensional scaling).

The map is therefore not a direct picture of the answers.
It is a geometric representation of relationships between concepts.

A surprising fact: one map ≠ one matrix

And here comes the interesting part.

Many different matrices can produce the same relationships between concepts.

For example:

• it does not matter whether two concepts share the symbol “circle” or “star”
• what matters is mainly how many symbols they share

That is why different specific tables can lead to the same distances between concepts.

And therefore to the same map.

Just by permuting symbols

Even a simple trick shows how quickly the number grows.

If we only permute the symbols across columns, the relationships between concepts remain the same.

The number of ways to permute 16 symbols is:

16! (factorial) = 20,922,789,888,000

which is about 21 trillion.

And that is just a very small fraction of all matrices that can produce the same map.

In reality, there can be many more.

What this implies

The map you see as a test result is not a single specific “imprint of answers.”

It is rather a stable image of relationships.

Mathematically speaking:

The map represents an entire family of different possible matrices
that share a similar structure of relationships between concepts.

And that is actually good news.

Because it means the map is not overly sensitive to small random variations or minor changes in answers.
It captures a deeper structure, not just individual details.

Like a map of a landscape

It is somewhat like a map of a landscape.

Different paths, trails, or details may change.
But the shape of mountains, valleys, and rivers remains.

The JakToMám map tries to capture exactly this shape —
the landscape of relationships within your inner world.

And that is why it can be surprisingly accurate.