Eucalculia v5.2 – Advanced Number Sense Training

[Alberto Flaño Lombardo]

Eucalculia is an evidence-based cognitive training tool designed to strengthen number sense and relational thinking through three complementary mechanisms:

What It Trains

• Subitizing – Instant quantity recognition (seeing "5" without counting)
• Relational Evaluation – Comparing numerical properties (parity, magnitude, sums)
• Relational Integration – Computing and comparing derived relationships across hierarchical levels

The Science Behind It

Eucalculia operationalizes Halford's relational complexity hierarchy in the numerical domain:

• Level 0: Binary relations (e.g., "Are both numbers even?")
• Level 1: Computation on retained values (e.g., "Sum of all four quantities?")
• Level 2: Comparing computations – ternary relations (predicts fluid intelligence)
• Level 3: Comparing comparisons – quaternary relations (theoretical ceiling of human relational processing)

Key Features

• Multiple representations: Dots, dice, dominoes, tally marks, fingers, abacus, Roman numerals, clocks, and more
• Adaptive difficulty: Exposure times and category weights adjust based on your performance
• Evidence-based: Built on Relational Frame Theory, Posner paradigm, and numerical cognition research
• Structured progression: Nested trial cycles ensure integration (not just memorization) is the cognitive bottleneck

Why It Matters

The same relational integration demand trained in Levels 2-3 is what predicts fluid intelligence performance. It's training the cognitive architecture underlying abstract reasoning.

Developed by: Alberto Flaño Lombardo

https://edefakiel.github.io/Eucalculia/eucalculia_5_2.html

[newbie]

  Hello. By any chance, what are your current thoughts on “cognitive flexibility,” which you mentioned before? Do you still consider it to be central to intelligence?

2026년 4월 25일 토요일 오후 11시 4분 48초 UTC+9에 Alberto Flaño Lombardo님이 작성:

[Alberto Flaño Lombardo]

I created this thread long ago using the pseudonym Leonardo: https://groups.google.com/g/brain-training/c/bn3S4CqUQH4

[Alberto Flaño Lombardo]

I think that it is easy to see how everything I believed then made Eucalculia what it is. The next update will be massive, btw.

[Abc]

Stop talking you're sending me emails Alberto the resident of Morio

Also my discord username is braintraining and I'm the *unique* expert of brain training

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[Alberto Flaño Lombardo]

I don't understand a word of what you're saying.

[Abc]

天上天下 唯我独尊

To view this discussion visit https://groups.google.com/d/msgid/brain-training/d52fe1dd-b847-482c-912b-b18e5db2deb5n%40googlegroups.com.

[Alberto Flaño Lombardo]

The telegraphy is anonymous, if you send your files to me, I will use them to finesse the software: https://edefakiel.github.io/Eucalculia/eucalculia_v6_5_22an.html

[Alberto Flaño Lombardo]

Minor fixes: https://edefakiel.github.io/Eucalculia/eucalculia_v6_5_22az.html

[Person Guy]

Two claims of yours interested me, Alberto, which were years ago: “Relations + Syllogisms → Analogies → Boolean Gates = IQ, to the best of our knowledge”
+
“¬A ⇐ B; B ≡ C; ¬C → D; ¬C ≡ ⊤; E → (B > A); .
What of the following are true? C ≡ A; D → ¬C; (A < B) ← E; ¬C ≡ A.
Of course, letters can be substituted by geometrical forms, colors or whatever.
Training like this would make you a genius, but I don't think this is exactly what you want.”

Given it’s 2026 now, I’m wondering if your view on these two takes have changed.

[Alberto Flaño Lombardo]

It's probably "easier" than that: https://www.sciencedirect.com/science/article/pii/S0160289620300672

Relation processing + mental representations = intelligence. 

Relation processing is the important mechanism, but you need to be able to form mental representations to process the relationships without continuous external stimuli, which is how intelligence is really applied in the real world outside the laboratory. 

[Person Guy]

I really wonder how we can improve the abilities you mentioned. Given that you are in the top 1%, training that will benefit you is scarce. 

[Alberto Flaño Lombardo]

Are you sure about that?

https://animusiocandiblog.wordpress.com/2026/05/18/analisis-estilometrico-longitudinal-de-quince-anos-de-produccion-textual-convergencia-entre-metodos-independientes-y-validacion-psicometrica/

[Person Guy]

My apologies for the assumption. The article you sent is insightful. What exactly did the methodology of your relational training consist of?

[Alberto Flaño Lombardo]

No need to apologize. Sorry, but I can't elaborate any longer right now, I wish I could, nothing would make me happier. My training looked pretty much like this: 

https://youtu.be/h_gdkr5Bu5M?feature=shared

Take care.

[Jack]

Very interesting; I was going to try it out, but I get a '404 File not found' page when I click the link. Is that just a problem on my end, or is Eucalculia down at the moment? 

[Fredo Corleone]

The game is incredibly good, the old link here is broken.

This is a working link: I added a lot of stuff: https://edefakiel.github.io/Eucalculia/Eucalculia

[Alberto Flaño Lombardo]

I think this is the most interesting version of the game currently: https://edefakiel.github.io/Eucalculia/Eucalculia_experimental

A little bit unstable, but with a lot of added things.