Pythagorean Square in OurNumerology: an uncertain lineage and its closest known parallels

Not every numerology method arrives with a book, an identified author and a clean history of origin. The Pythagorean Square used in OurNumerology is a good example. I added it mainly because users asked for it. Some people knew it from numerology courses and it appeared in the working practice of Polish numerologists, but when I tried to trace the exact source of this particular version, I could not find a definitive answer. The people teaching it did not provide a publication that documented where this exact construction came from either.

I could therefore do what sometimes happens in numerology: attach the name of Pythagoras, mention ancient Greece, add a few thousand years of tradition and call the matter settled. I am not going to do that. We do not have evidence that this exact algorithm, this construction of the square and this set of lines were used by Pythagoras. The label Pythagorean Square is not proof of provenance. In fact, when we compare the method with better documented systems, different parts of it resemble different traditions. That is far more interesting than inventing a neat origin story.

What do we mean by Pythagorean Square in OurNumerology?

In Numerology Portrait, Pythagorean Square remains a separate OurNumerology legacy method. It is not the Lo Shu Grid, it is not our Numerology Grid, and it is not the Psychomatrix. This separation is deliberate: a similar-looking 3×3 diagram or the common use of digits 1–9 is not enough to make two methods identical.

The Square uses the layout:

3 | 6 | 9 2 | 5 | 8 1 | 4 | 7

and eight straight relationships:

1–4–7, 2–5–8, 3–6–9, 1–2–3, 4–5–6, 7–8–9, 1–5–9 and 3–5–7.

Those eight relations are preserved in the legacy implementation as separate line values. That geometry is more useful for provenance research than the word “Pythagorean” itself, because it gives us something concrete to compare with known sources.

The closest documented relative: Hettie Templeton and David A. Phillips

The closest well-documented parallel I found is not Henryk Rekus but the Western Birth Chart and Arrows of Individuality tradition associated especially with Hettie Templeton and David A. Phillips. In The Complete Book of Numerology, Phillips uses exactly the arrangement 3–6–9 / 2–5–8 / 1–4–7. He calls the upper row the Mind Plane, the middle row the Soul Plane, and the lower row the Physical or Practical Plane. He then interprets eight straight lines crossing the chart, with names such as the Arrows of Intellect, Emotional Balance, Practicality, the Planner, the Will, Activity, Determination and Spirituality.

The history of those arrows is particularly revealing. Phillips explicitly says that he learned them from his teacher Hettie Templeton. He also states that it is uncertain whether Pythagoras used this part of the system at all. In the material he regarded as surviving fragments of the older tradition, he did not find a reference to the Arrows. Templeton, on the other hand, had encountered them in early twentieth-century practice and spent years experimenting with, modifying and developing them.

That is an important clue for us. We have a documented tradition using exactly the same geometry, yet even one of its main modern authors does not claim that every part of it can be directly proven to come from Pythagoras. Numerology Portrait should be at least as careful.

The problem: OurNumerology Square is not calculated like Phillips's Birth Chart

If the OurNumerology Pythagorean Square were simply a copy of Phillips's Birth Chart, the question would be much easier. It is not. Phillips places the digits that actually occur in the birth date into the Birth Chart. Repetitions remain visible, while zero does not occupy one of the nine cells. He does not first generate four working numbers in the manner familiar from Psychomatrix systems.

The preserved OurNumerology variant, however, produces the following trace for 19 August 1991:

19 8 1991 → 38 → 2 / 36 / 9

and then displays:

33 | 6 | 9999 2 | — | 88 111 | — | —

This cannot be produced from the raw birth-date digits alone. The geometry and much of the interpretive language can therefore be close to a Western Birth Chart while the source-digit construction follows a different logic.

How is the OurNumerology Square constructed?

Using 19 August 1991, we begin by summing all digits of the date:

1 + 9 + 0 + 8 + 1 + 9 + 9 + 1 = 38

The first derived value is therefore 38. In the project-preserved variant, that value is recursively reduced:

3 + 8 = 11 → 1 + 1 = 2

so the next value is 2. The third value is obtained by subtracting twice the first non-zero digit of the birth day from the first sum. For day 19, that digit is 1:

38 − 2 × 1 = 36

Finally:

3 + 6 = 9

The derived set is therefore:

38 / 2 / 36 / 9

We add the digits of those values to the birth-date digits, exclude zero from the nine cells, and count occurrences of 1–9. In this example there are three 1s, one 2, two 3s, one 6, two 8s and four 9s. That is exactly how the displayed Square arises.

This construction is very close to one modern Psychomatrix variant. That does not mean the Square should inherit Psychomatrix interpretations.

Psychomatrix-like calculation, Birth-Chart-like interpretation

This is probably the most useful conclusion from the comparison. The digit-generation layer resembles the Russian/post-Soviet Psychomatrix family, while the geometry, planes and eight lines are much closer to the Western Templeton–Phillips Birth Chart. I have not been able to confirm who combined those two layers, or whether a single identifiable author did so at all.

It may be a later course-based hybrid that developed by combining existing techniques. It may also derive from a specific publication we have not yet located. At present there is no evidence strong enough to name an author, so Numerology Portrait should not invent one.

This distinction matters in practice. Alexandrov's Psychomatrix interprets 1 as character and will, 2 as energy, 4 as health, 5 as logic, 8 as duty and so on. Phillips's Birth Chart uses a different vocabulary: 1 is ego-expression and communication, 2 intuition and sensitivity, 3 the conscious mind and memory, 4 practicality and order, 5 the emotional centre and freedom of expression, 6 creativity, 7 learning through experience, 8 intuitive wisdom and independence, and 9 ambition, responsibility and idealism. Two grids may look almost identical while answering different interpretive questions.

Reading the cells 1–9

For the interpretive layer, the Western Birth Chart is the strongest documented comparison because its geometry and lines match the Square closely. This does not mean we declare Phillips the source of the OurNumerology method. It means we use his system as the nearest documented interpretive analogue.

1 is associated with self-expression, communication, personal presence and initiative. Repetition may strengthen independence and directness, while an extreme concentration can turn the same quality into stubbornness or excessive focus on one's own way of acting.

2 belongs to the emotional plane and relates to sensitivity, intuition and receptivity to the surrounding atmosphere. Repeated 2s can intensify subtle perception, but a very heavy concentration may also correspond, within this symbolic framework, to easier emotional overload.

3 opens the mental plane. Phillips connects it with the conscious mind, rational understanding and memory. Numerology Portrait should not turn that symbolism into a neurological or IQ claim. It is better used as a reflective language for how information is processed and consciously organised.

4 sits at the centre of the practical plane and represents order, practicality, organisation and the ability to create stable structures. An excess may show the shadow side of the same quality: rigidity, impatience or a desire to control every detail.

5 occupies the centre of the entire chart and the middle of the Soul Plane. Phillips associates it with love, feeling and freedom of expression. In modern language we can read it as contact with one's emotional centre and the capacity to respond flexibly without losing oneself.

6 occupies the centre of the Mind Plane and is primarily associated with creativity and the integration of ideas. Its shadow can appear as worry, mental tension or the attempt to control reality by constantly thinking through every possibility.

7 completes the practical plane and represents learning through personal experience. It is less about theoretical knowledge than about lessons that become real because we have lived through something, tested it and had to understand it practically.

8 sits at the active end of the emotional plane. Phillips connects it with intuitive wisdom, independence and the capacity to turn inner perception into action. In shadow, independence can become distance or reluctance to receive help.

9 occupies the active end of the mental plane and combines ambition, responsibility and idealism. Multiple 9s may strongly emphasise vision and mental direction. If the concentration becomes extreme, thought, plans and ideals may begin to dominate the more practical or emotional layers of the chart.

More is not automatically better

Because the Square counts repetitions, it is tempting to treat more digits as a higher score. That would be a poor interpretation. Three 1s do not mean “three times better personality”, and four 9s do not prove four times greater intelligence. What matters is the balance of the whole structure.

A concentrated number can be an easily accessible resource, but it can also become overused. Organisation can become control, expression can become dominance, sensitivity can become overload, ambition can become pressure, and independence can become isolation. Repetitions therefore need to be read as both potential and possible shadow.

A missing number is not a diagnosis either. It only means that a quality is not strongly represented in this particular numerological construction. Real people develop abilities through environment, education, relationships, experience and conscious practice. An empty box is much more useful as a reflective prompt than as a verdict.

The 1–4–7 plane: practical expression

The lower row 1–4–7 is the Physical Plane in Phillips's system, and when all three numbers are present it forms the Arrow of Practicality. It connects the initiative of 1, the organisation of 4 and the experiential learning of 7. In practical terms, it asks how easily we move from intention to concrete action and how strongly we need tangible results.

A strongly occupied practical layer may support organisation, hands-on involvement and effectiveness. Its shadow may emerge when practicality crowds out reflection or emotional nuance. Phillips called the fully empty 1–4–7 line an Arrow of Disorder. Numerology Portrait can preserve the structural idea while using calmer language: building order, routines and practical execution may require more conscious effort.

The 2–5–8 plane: feeling and inner balance

The middle row 2–5–8 corresponds to the Soul Plane. A complete line is the Arrow of Emotional Balance. It combines the receptivity of 2, the emotional centre of 5 and the independent wisdom of 8. It does not mean that someone “always controls their emotions”. It is better understood as a symbolic capacity to connect feeling, expression and a stable inner centre.

Older language calls the completely empty 2–5–8 line the Arrow of Hypersensitivity. We do not use that as a psychological diagnosis. It can instead become a question about emotional regulation, boundaries and the degree to which the atmosphere around us affects our internal state.

The 3–6–9 plane: mind

The upper row 3–6–9 is the Mind Plane. It connects the conscious mind and memory of 3, the creativity of 6 and the ambition and idealism of 9. When complete, Phillips calls it the Arrow of the Intellect. It is not an IQ test. A more responsible interpretation is symbolic ease in linking information, generating ideas, organising thought and maintaining mental direction.

Phillips called the completely empty 3–6–9 row the Arrow of Poor Memory. Numerology Portrait should not reproduce that wording as a diagnosis. A safer modern reading is that certain forms of organising information, sustaining concentration or deliberately developing mental technique may require more conscious work.

The 1–2–3 line: planning

The first vertical line, 1–2–3, connects self-expression, sensitivity and thought. Phillips calls it the Arrow of the Planner. It can be read as an ease in moving from a first response, through perception of a situation, toward a mental plan. A plan, however, is not the same thing as execution; other parts of the chart still determine how easily ideas become action.

The 4–5–6 line: will

The middle column 4–5–6 passes through the centres of all three planes and forms Phillips's Arrow of the Will. It combines the structure of 4, the emotional centre of 5 and the creative problem-solving of 6. It can be viewed as a symbolic backbone for maintaining direction when action requires organisation, engagement and the ability to find a workable solution.

Its complete absence was called the Arrow of Frustration. In our language, this can be reframed as a pattern in which translating internal intention into organised execution may require greater patience and consciously built structures.

The 7–8–9 line: activity

The right-hand column 7–8–9 forms the Arrow of Activity. It combines experience, independence and ambition. A strong configuration may support movement, involvement and the need to do something tangible in the world. The shadow is not necessarily lack of energy but difficulty stopping long enough to ask whether every action is actually necessary.

Phillips called the completely empty line the Arrow of Passivity. We can describe it more cautiously: initiating and sustaining visible action may be less automatic and may benefit from deliberate activation and structure.

The 1–5–9 diagonal: determination

The diagonal 1–5–9 is the Arrow of Determination. It links the personal self, the emotional centre and mental direction. In constructive expression it represents persistence and the ability to stay with a goal. The same quality taken too far becomes stubbornness or an inability to revise a plan when circumstances change.

The fully empty counterpart was traditionally called the Arrow of Procrastination. Numerology Portrait does not need to label a user a procrastinator. It can simply suggest that the path from intention to consistent completion may benefit from consciously designed structure and progress checks.

The 3–5–7 diagonal: meaning and learning through experience

The other diagonal 3–5–7 is the Arrow of Spirituality. It links understanding, the emotional centre and lived experience. In Numerology Portrait, “spirituality” does not have to mean religion or metaphysics. The line can be read more broadly as a need to search for meaning, learn through personal experience and integrate intellectual understanding with what has actually been lived.

Phillips ultimately called its completely empty counterpart the Arrow of the Enquirer. This is a useful example of how numerology systems themselves evolve. He had earlier encountered the name Arrow of Scepticism but changed the language because his observations led him to see the pattern more as a need to investigate and reach one's own conclusions. Traditions change through practice and interpretation; they are not necessarily delivered once as a complete immutable package.

Complete, empty and partial lines

Classic Arrows are straightforward at the extremes. If all three cells contain their number, a complete line is present. If all three are empty, the corresponding empty pattern exists. Most real charts, however, sit somewhere between these two situations. A person may have 1 and 5 without 9, or several repetitions in one cell while another remains empty.

Numerology Portrait should not pretend that a partial line is a complete Arrow. It can display the line as complete, partial or empty while preserving the real digit distribution. At the same time, I do not want to invent an arbitrary “73% active” score unless a clearly identified school actually defines such a scale.

Example: 19 August 1991

For our example the Square is:

33 | 6 | 9999 2 | — | 88 111 | — | —

The first thing we see is the strong concentration in the upper, mental part of the chart: two 3s, one 6 and four 9s. The 3–6–9 line is complete and heavily populated. In Phillips's language this would be a clear Arrow of the Intellect, but rather than writing “this person is extremely intelligent”, a more useful statement is that the structure strongly emphasises information processing, ideas, creativity, ambition and mental direction.

The 2–5–8 row contains a 2 and two 8s but lacks the central 5, so the emotional line is not complete. The lower 1–4–7 row contains three 1s but no 4 or 7, so the practical plane is not complete either. The contrast is more interesting than any isolated label. It lets us ask what happens when a heavily occupied mental layer meets a much less complete practical and emotional structure.

Why not simply call this Phillips's Birth Chart?

Because that would be methodologically inaccurate. The layout and line interpretations are very close, but the inputs are different. Phillips uses raw birth-date digits. The preserved OurNumerology variant adds digits generated by additional calculations. As a result, a line that would be incomplete in Phillips's original Birth Chart may become complete after derived digits are added in OurNumerology.

We can therefore call Phillips's system a very close interpretive analogue, not an identical method.

Why not call it Psychomatrix?

For the same reason. Psychomatrix may use a very similar working-number construction, but it has its own cell and line semantics. A missing 4 in Alexandrov's Psychomatrix is interpreted in the context of the health cell, while 4 in the Templeton–Phillips Birth Chart belongs to practical order and organisation. The same digit is being asked a different question.

That is why Psychomatrix and Pythagorean Square remain separate methods in Numerology Portrait, even when a particular calculation variant produces a similar-looking grid.

What about Henryk Rekus?

Rekus was an obvious candidate to investigate because he documented many systems and strongly influenced Polish numerology. After comparing the confirmed methods, however, I do not see enough evidence to attribute the OurNumerology Square to him. His documented Vedic Square is a 9×9 table in which cell values are produced by multiplying row and column values and reducing the product to 1–9. That is a completely different mechanism.

His Chi-sue work, meanwhile, uses the classical Lo Shu arrangement 4–9–2 / 3–5–7 / 8–1–6, which is again a different geometry. A later course tradition could certainly have borrowed or mixed material associated with Rekus, but we currently have no source linking the exact OurNumerology Square to him.

Rekus therefore remains a historical possibility worth remembering, not a proven attribution.

What do we actually know about the origin?

We know that the method was used in practice and was familiar enough for users to request it in OurNumerology. We know that people teaching it did not provide a clear original source. We know how the preserved algorithm works and which eight lines it uses. We also know that its geometry and line interpretation have a very close documented parallel in the Templeton–Phillips tradition.

What we do not know is who combined that interpretive model with the derived-number construction preserved in OurNumerology. We do not know whether this came from one author, one course, a Polish adaptation of foreign material or a gradual hybridisation of several schools.

That boundary should remain visible.

How should Numerology Portrait present the Square?

First, with a full calculation trace. A user should not see only the final 3×3 grid. They should be able to open the result and see that the process began with 19 August 1991, produced 38, then 2, 36 and 9, and then inspect which digit occurrences came directly from the birth date and which came from derived values.

That transparency matters especially when provenance is uncertain. The less confidently we can describe a method's genealogy, the more precisely we should show what the calculator actually does.

Next come the nine cells, three planes and eight lines. A complete line may receive its associated interpretation. An empty line may be presented as a developmental theme. A partial line should show exactly which elements are present rather than pretending to be a full Arrow. In Professional, it also makes sense to expose the method variant and offer comparison with Psychomatrix and other grids.

Then the old question “Why does this calculator give me a different result?” stops being a problem. The answer becomes: because it uses a different method — let's look at which one.

Unknown provenance does not mean we must discard the method

Lack of a source becomes a serious problem when we pretend it does not exist. If we clearly document the algorithm, interpretation, implementation history and closest known parallels, we can still use a method without inventing a false origin story.

The OurNumerology Pythagorean Square is exactly such a case. I cannot responsibly write, “X created this method in year Y.” I can say that this version circulated in parts of the Polish numerology community, entered OurNumerology because users asked for it, its exact author has not been established, and its structure shows a striking interpretive resemblance to the Western Birth Chart while its calculation resembles the Psychomatrix family.

That answer is much more useful than adding Pythagoras simply because his name looks good in the title. Numerology Portrait should show how a method is actually calculated, how it has been interpreted, which known traditions it resembles, and where evidence ends and hypothesis begins.

Sources and comparison points

The main comparison for geometry and interpretation is David A. Phillips, The Complete Book of Numerology, especially the chapters on the Birth Chart and the Arrows of Individuality. Phillips identifies Hettie Templeton as his teacher of the Arrow technique and explicitly notes the uncertainty over whether Pythagoras used the Arrows at all.

For comparison with Polish systems, the documented methods of Henryk Rekus are also useful precisely because his Vedic Square and Chi-sue demonstrate that sharing the word “square” does not imply the same algorithm. For the OurNumerology variant itself, the primary technical reference remains the preserved legacy Square calculation trace and project documentation.