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

--
You received this message because you are subscribed to the Google Groups "Dual N-Back, Brain Training & Intelligence" group.
To unsubscribe from this group and stop receiving emails from it, send an email to brain-trainin...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/brain-training/19451f6b-3ee2-46eb-a88a-c6839ffaa2f2n%40googlegroups.com.

[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. 

[Conner Lambden]

Interesting conversations here! This is more of a linguistic approach, looking at meta-distinctions instead of logic/syllogisms/attention, etc. https://intelligencemax.ai/science

[Michael]

Hi Connor,

I think meta-distinctions are an excellent idea!

That said, I think there is a cross-stimulus inconsistency in the latent meta-rule being rewarded so far by the generator.

For example, let's take one I took from:
 “oOo is playing a real-time strategy game where she must choose which of two enemy bases to scout. Base Alpha is defended but predictable. She's raided it twice before and knows the guard rotation cold. Base Beta is lightly guarded but shrouded in fog of war; her scouts have never reached it. Scouting one base costs her a full turn; she can only pick one. Which base gives her the sharper strategic edge, and why?”

The preferred answer is:

> “Beta. An unknown base is worth scouting because new intel compounds her advantage.”


This rewards marginal information gain under uncertainty.

But the canyon item (let me know if you want me to copy and paste this as well) marks:

> “Listen for echoes to judge canyon depth, then decide.”


incorrect, while preferring:

> “Turn back; one sensory signal (wind) is not a reliable canyon-exit indicator.”


That seems inconsistent. If wind is non-diagnostic, an independent second cue should ordinarily become more valuable, not less.

The authentication item (again, let me know if you want me to copy and paste it) reinforces the contradiction by rewarding:

> “Study the photocopy thoroughly first to form a hypothesis, then open the original only if you must verify something critical.”

Across these stimuli, the intended meta-distinction appears to be information gain versus sampling cost, irreversibility and asymmetric danger. Yet only the canyon item penalises further low-cost evidence gathering without stating any additional time, exposure or commitment cost. The generator should make that hidden variable explicit or treat the exploratory answer as conditionally defensible.

I totally get it though, AI models are rough sometimes when it comes to this more nuanced work, which meta-distinction requires the specialisation for, especially earlier AI models. I am not sure if the later models would handle it better.

One recommendation is to add either or both of: (1) weighted, non-binary scoring; and (2) evidence-grounded caveats identifying the assumptions on which each answer depends. An AI model may also score more consistently across trials if it tracks and reuses its prior assumptions, rather than evaluating each scenario in isolation and silently changing its decision criterion. 

Or if you're going to run cheaper models on the free tier and that's the only reason for the errors, it would lend much more confidence from a user testing out the product if the AI generator being used only ran meta-distinction scenarios it could run consistently accurately across many trials. 

Again, excellent ideas!

Best regards

[Michael]

I am really looking forward to seeing how your work evolves overtime as well Alberto, excellent stuff! Very interesting!