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Entry 0004

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2025.05.14

Of Galton Boards and Brahman

Living in the Light of the Brāhman
Sanātana Dharma teaches that the entire cosmos is woven into
Brāhman — the boundless, self-luminous reality within and beyond all forms. To move in tune with this vastness, sages distil four practical directives: do your part with wholehearted care, release attachment to outcomes, cultivate unceasing kindness in your community so that goodness scales globally, and persevere through changing fortunes.

These principles honor both freedom and mystery. They invite us to shape what is ours to shape, to trust the wider weave of causes we cannot see, and to recognize that persistent local goodness accumulates into collective uplift. In the embrace of Brahman, every small act becomes a seed of cosmic harmony.

Here is a discussion on these principles and how a number of statistical models support them, and how a Galton board can illustrate their impacts on every facet of our lives.

Principle Directives

Put in the effort

Do Your Part & Do It Well

Shape the pegs you can reach —choices, words, duties — giving them craftsmanship and care.

Accept the rest

Accept the Rest

Beyond each chosen effort stretch countless causes you do not command. Hand the outcome back to Brahman.

Spread goodness

Local ↔ Global

Continual acts of goodwill—family to neighborhood to workplace—pool together, lifting society at large. Local kindness becomes global uplift.

Persevere

Persevere

Small, repeated nudges accumulate. Staying the course steadily shifts the moral landscape.

Galton Board • See the Curve Lean

The Galton board animates the teachings of Brahman: each peg mirrors a moral choice or the result of your effort towards an outcome - a good (from your perspective) outcome to the right, and a poor outcome to the left, each ball a life-event. You can nudge a handful of red pegs (do your part) which signifies choices that you can influence. The black ones represent choices that cannot be controlled by you - you must trust the countless bounces you can’t steer (accept the rest); by doing good things in society in general, and others doing the same, the black pegs will also favor the right-side outcome more than the left - so keep tilting locally so that goodness scales globally (local → global); and repeat (persevere).

Universal Wisdom in Every Tradition

The four principles—whole‑hearted action, trustful release, communal kindness that scales globally, and perseverance—echo through the world’s scriptures.

Tradition / TextRef.Verse (native • transliteration • meaning)
Sanātana – Bhagavad Gītā2 : 47
कर्मण्येवाधिकारस्ते मा फलेषु कदाचन ।
मा कर्मफलहेतुर्भूर् मा ते सङ्गोऽस्त्वकर्मणि ॥
karmaṇy evādhikāras te mā phaleṣu kadācana;
mā karma‑phala‑hetur bhūr mā te saṅgo ’stvakarmaṇi.
You have the right to act, never to the fruits (accept the rest). Do not imagine yourself the sole cause, nor cling to inaction.
Sanātana – Bhagavad Gītā18 : 9
नियतं सङ्गरहितम् अरागद्वेषतः कृतम् ।
अफलप्रेप्सुना कर्म यत्तत् सात्त्विकम् उच्यते ॥
niyataṁ saṅga‑rahitam arāga‑dveṣataḥ kṛtam; aphala‑prepsunā karma yat tat sāttvikam ucyate.
Duty done without attachment, seeking no fruit, benefits the whole order and is called sāttvika renunciation.
Buddhism – Dhammapada1 : 1‑2
मनोपुब्बङ्गमा धम्मा मनोसेट्ठा मनोमया;
मनसा च पदुट्ठेन भासति वा करोति वा, ततो नं दुःखमन्वेति चक्कं व वहतो पदं।

मनोपुब्बङ्गमा धम्मा मनोसेट्ठा मनोमया;
मनसा च पसन्नेन भासति वा करोति वा, ततो नं सुखमन्वेति छायाव अनपायिनी।
Manopubbaṅgamā dhammā, manoseṭṭhā manomayā …
Mind leads action; with impure intent suffering follows, with pure intent wholesome deeds bloom and happiness attends; one must cultivate purity and accept the ripening of karmic seeds.
Buddhism – Aṅguttara NikāyaIII .415
“चेतना हं, भिक्खवे, कम्मं वदामि; चेतयित्वा कम्मं कर॒ोति. अप्पमादेन sampādetha.”
“Cetanā haṃ bhikkhave kammaṃ vadāmi; having intended one acts; strive on with diligence.”
Intention is the action; fruit ripens via many causes. Persevere and accept the timing.
Christianity – Matthew (KJV)6 : 33‑34 Seek ye first the kingdom of God, and his righteousness; all these things shall be added. Take no thought for the morrow: tomorrow will take thought for the things of itself.
Christianity – James (KJV)2 : 26 As the body without the spirit is dead, so faith without works is dead; living faith serves others and endures testing.
Islam – Qurʼān3 : 159
فَبِمَا رَحْمَةٍ مِّنَ ٱللَّهِ لِنتَ لَهُمْ … فَإِذَا عَزَمْتَ فَتَوَكَّلْ عَلَى ٱللَّهِ ۚ إِنَّ ٱللَّهَ يُحِبُّ ٱلْمُتَوَكِّلِينَ
fa‑bi‑mā raḥmatin mina llāhi linta lahum … fa‑idhā ʿazamta fa‑tawakkal ʿalā llāh …
Decide firmly (act) then trust in God; God loves those who persevere in reliance and spread gentleness.
Islam – Qurʼān2 : 110
وَأَقِيمُوا ٱلصَّلَوٰةَ وَآتُوا ٱلزَّكَوٰةَ ۚ وَمَا تُقَدِّمُوا لِأَنفُسِكُم مِّنْ خَيْرٍ تَجِدُوهُ عِندَ ٱللَّهِ
wa‑aqīmū ṣ‑ṣalāta wa‑ātū z‑zakāta …
Establish prayer and charity; whatever good you send forth you will find with Allah; He rewards steadfast practice.
Judaism – Pirkei Avot2 : 16
לֹא עָלֶיךָ הַמְּלָאכָה לִגְמוֹר, וְלֹא אַתָּה בֶן־חוֹרִין לִבָּטֵל מִמֶּנָּה
Lo ʿalecha ha‑melākhā ligmor, ve‑loʾ atta ben‑ḥorīn liveṭḗl mimenna.
It is not upon you to finish the work, yet you are not free to desist; each effort adds to the whole, accepting human limits.
Judaism – Proverbs16 : 3
גֹּל אֶל־יְהוָה מַעֲשֶׂיךָ, וְיִכֹּנוּ מַחְשְׁבֹתֶיךָ
Gol el Adonai maʿasecha, ve‑yikkōnū maḥshəvōtecha.
Commit your works to the Lord and your plans will be established, shaping wider order through steady trust.
Sikhism – Guru Granth Sāhibp 286
ਸਤਿਗੁਰ ਕੀ ਸੇਵਾ ਸਫਲ ਹੈ, ਜੇ ਕੋ ਕਰੇ ਚਿਤੁ ਲਾਇ;
ਸਰਬ ਸੁਖ ਤਿਨ ਮਿਤ੍ਰਾਂ ਕੈ ਘਰਿ ਵਸਹਿ, ਜਿਸੁ ਪ੍ਰਭ ਕਿਰਪਾ ਧਾਰਿ.
ਸੇਵਾ ਕਰਤ ਹੋਇ ਨਿਹਕਾਮੀ, ਸੋ ਹੋਵੈ ਪਰਉਪਕਾਰੀ।
Satgur kī sevā safal hai, je ko kare chit lā‑e …
Service of the True Guru is fruitful; with focussed mind, one finds peace beyond ask; selfless service makes one a benefactor of all, sustained by divine grace.
Taoism – Tao Te Ching48
為學日益，為道日損。損之又損，以至於無為；
無為 而無不為。
Wéi xué rì yì, wéi dào rì sǔn; sǔn zhī yòu sǔn, yǐ zhì yú wú‑wéi; wú‑wéi ér wú bù wéi.
Study adds daily; practicing the Way subtracts daily, until effortless non‑action, yet nothing is left undone; release control and the Tao acts through you.
Confucianism – Analects2 : 4
子曰：「吾十有五而志於學，三十而立，四十而不惑，
五十而知天命，六十而耳順，七十而從心所欲，不踰矩。」
Zǐ yuē: “Wú shí‑yǒu‑wǔ ér zhì yú xué, sān‑shí ér lì … qī‑shí ér cóng xīn suǒ yù, bù yú jǔ.”
*At fifteen I set my heart on learning; … at seventy I could follow my heart’s desire without overstepping.* Lifelong self‑cultivation benefits the social order while accepting each stage.
Stoicism – Epictetus, Enchiridion§ 1
Τῶν ὄντων τὰ μὲν ἐφ᾽ ἡμῖν, τὰ δὲ οὐκ ἐφ᾽ ἡμῖν. τῶν ἐφ᾽ ἡμῖν ἐστὶν γνώμη, ὁρμή, ἐπιμονή, κ.τ.λ.
Tōn ontōn tà mén eph’ hēmín, tà dè ouk eph’ hēmín …
Some things are up to us, others not; freedom is found in the first, peace in > accepting > the second (release), requiring daily perseverance.
Red = Do your part |  Blue = Accept the rest |  Green = Local ↔ Global |  Orange = Persevere

The Probability Engine Behind the Board

Our simulator is a heterogeneous Bernoulli process governed by personal δ, societal γ, and now entropy – the raw uncertainty of Brahman’s play.

Model Summary

  • n layers, k personally controlled pegs.
  • Base probability p0 = ½; global bias γ; local bias δ.

\[ p_i = \begin{cases} p_0 + \gamma + \delta & \text{(controlled)} \\[6pt] p_0 + \gamma & \text{(other)} \end{cases} \quad;\quad S_n = \sum_{i=1}^{n} X_i \] \[ \mathbb{E}[S_n] = n p_0 + n \gamma + k \delta, \qquad \operatorname{Var}(S_n) = \sum_{i=1}^{n} p_i(1 - p_i). \]

Entropy Layer

Shannon entropy for one path: \[ H_n = -\sum_{i=1}^{n} \bigl[p_i \log_2 p_i + (1-p_i)\log_2 (1-p_i)\bigr]. \]

  • Neutral board (γ = δ = 0) → maximal Hn = n.
  • Bias lowers entropy:
    \(\displaystyle \Delta H \approx -\dfrac{(n\gamma + k\delta)^2}{\ln 4}\).
  • Energy/discipline input = negentropy injected → curve shifts but variance survives.

Brahman’s dance keeps randomness alive; Dharma lets us shape its average by spending moral energy.

Selected References

  • Galton F. (1894) Natural Inheritance.
  • Feller W. (1968) Probability Theory, vol. 1.
  • Ross S. (2021) Introduction to Probability Models, 12 ed.
  • Schelling T. (1978) Micromotives and Macrobehavior.
  • Granovetter M. (1978) “Threshold Models…”, AJS 83 (6).
  • Putnam R. (2000) Bowling Alone.
  • Shannon C. E. (1948) “A Mathematical Theory of Communication”.
  • Jaynes E. T. (1957) “Information Theory and Statistical Mechanics”.
  • Schrödinger E. (1944) What Is Life?

Corollaries of Cosmic Play

These corollaries flow from the four principles—and each can be recreated on the simulator to make the lesson tangible.

1. Good People Sometimes Suffer

Variance never drops to zero, so a few balls land left even with a positive bias. Compassion, not cynicism, is the wise response.

Model it: Set global = 0.55, effort = 0.75, run 400 balls; note a handful still fall in left-tail bins.

2. Pockets of Evil Persist

A small cluster of badly-tilted pegs can skew outcomes far beyond their number, mirroring harmful agents in society.

Model it: Reduce “pegs we control” to 5, set effort = –0.30 (left bias) while global stays 0.55. Watch a visible dent appear on the poor side.

3. Hidden Forces Reveal Themselves

If real outcomes skew worse than expected, unseen negative bias is at work—corruption, trauma, injustice.

Model it: Keep sliders at neutral (0.50/0.50) but edit code to add –0.10 to all pegs behind the scenes; compare the unexpected left skew to your baseline.

4. Utopia Would Cancel Freedom

Perfectly right-biased pegs erase randomness—which also erases choice and creativity.

Model it: Set global = 1.0, effort = 1.0. Bars collapse into the far-right bin—no curve, no variance.

5. Small Good Acts Still Matter

Each positive δ shifts the mean a bit. Over many lives the peak drifts rightward—virtue is never wasted.

Model it: Run 400 balls at effort = 0.60 vs effort = 0.50; compare black outcome line shift.

6. Perseverance Multiplies Impact

Large samples stabilise the mean. Sustained practice anchors communities in sattva.

Model it: Run 50 balls, then 400 balls with the same biases; see how tails shrink and the line smooths out.

7. Free Will vs. Constants

Humans can adjust δ peg-by-peg; a tree deity keeps a fixed bias. Freedom is risky yet powerful.

Model it: Toggle controlled peg count between 0 and 20 while global stays 0.50; watch the curve respond only when free choices exist.

8. Diagnosing Systemic Injustice

Persistent shortfalls beyond noise reveal structural bias. Dharma demands we level the pegs.

Model it: Run baseline (0.50/0.50), then secretly set left-half pegs to –0.10; outcome line diverges from dashed normal, signalling systemic skew.

Converging Paths, One Cosmic Rhythm

We began with Brahman—the boundless ground of being—and traced four practical currents: whole-hearted action, trustful release, unceasing communal kindness, and steady perseverance. Scriptures from the Gītā to the Enchiridion echo the same quartet.

Entropy—the universe’s tendency toward uncertainty—served as the background beat. A neutral board reaches maximum entropy: the wide, even bell. Every intentional bias we add is a pulse of negentropy: information, care, energy that shifts the curve rightward. In Brahman’s play, variance never dies, but free will lets us trade effort for a kinder mean.

The Galton board made it tangible. By tuning personal \( \delta \) and global \( \gamma \) we saw how small local acts, replicated, bend the collective arc. Corollaries followed: unlucky tails demand compassion; pockets of negative bias distort whole systems; total control would cancel freedom; sustained goodness slowly lowers the entropy of community life.

Thus the journey circles back: act well, lift those nearby, trust the mystery, and keep going. Every mindful nudge you offer is a spark of order in the cosmic flux—one more peg tilted toward the good in the vast, joyful field of Brahman.

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