A Glimpse into a Probable Marriage of Tiny Scale and Macro Grasp of Science V2

A Glimpse into a Probable Marriage of Tiny Scale and Macro Grasp of Science

🌀 A Glimpse into a Probable Marriage of Tiny Scale and Macro Grasp of Science

A personal exploration in symbolic regression, physics, and philosophical debugging

👋 Prologue

Let’s face it — most of us don't wake up thinking, “Today I will blend Planck’s constant and relativistic energy into a genetic programming experiment!” But that’s more or less what happened. With a little help from DEAP, some physics constants, and a lot of coffee, I wandered into an unusual, possibly meaningful direction.

This post describes an attempt to let symbolic regression guess at a connection between two physics equations — one from the quantum world, and one from Einstein’s playbook.

💡 The Idea

We were curious: if two major energy equations — one from quantum physics and one from relativity — both describe energy, could a symbolic regression model hint at a connection between them?

Rather than aiming for a scientifically valid or physically verified formula, this experiment was meant to explore the capability of genetic programming to evolve symbolic expressions — even in the absence of real-world data.

We treated the exercise as a thought experiment: feed the model with arbitrary placeholder values, and observe what kinds of mathematical relationships emerge from evolutionary pressure alone.

🧪 The Setup

Using DEAP, a genetic programming library in Python, we asked the computer to evolve expressions like:

x2 = f(x1)

Where:

  • x1 = wavelength (meters)
  • x2 = velocity (m/s), which we would use to compute γ and plug into the RHS

Fitness was based on how close:

hc / λ ≈ γ mc²

We added a basic constraint: skimming constant-only outputs like f(x) = 1.0.

Note: We didn’t use empirical or observed data. The inputs were synthetically generated to drive evolution, not to reflect physical truth. This means the formulas discovered are not expected to correspond to any known laws of nature — they’re simply artifacts of the chosen setup.

🔍 The Adjustment with k/k

Suppose the model evolves:

x2 = x1   # wavelength = velocity?

Clearly, the units don’t match. Wavelength is in meters, velocity is in m/s. So we sneak in a little trick: 

E = hc / λ = hc / (λ × k) × k
  • k has units of 1/s
  • λ × k = v → now the denominator has units of velocity
  • The extra factor of k in the numerator rebalances units so the final result is still in Joules

✅ Final Adjusted Formula

E = (hc × k) / v

Compare with:

E = γ m c² = mc² / √(1 - (v/c)²)

So equating both sides:

(hc × k) / v = mc² / √(1 - (v/c)²)

This formula is an output of symbolic regression guided by artificial targets — a way of testing the method, not revealing nature. Any resemblance to real physics is coincidental or structurally imposed by the mathematical forms in play. It’s a speculative exercise, not an assertion about how the universe works.

🧬 GP Program Snapshot (Pseudocode)


pset = createPrimitiveSet("MAIN", 1)  # x1 = wavelength
addPrimitives(pset, [add, sub, mul, div, log, sqrt, ...])
addEphemeralConstants(pset, [h, c, pi, e, rand101])

def eval_individual(ind):
    func = compile(ind)
    x1 = wavelength
    x2 = func(x1)
    lhs = (h * c) / x1
    rhs = γ(x2) * m * c²
    return abs(lhs - rhs)

# Skim constant functions
# Run evolution

🤔 Final Thoughts

This project was never about uncovering a grand unifying law — it was about watching how symbolic regression behaves when set loose on symbolic physics. Without real data or physical constraints, the model evolved forms that are mathematically interesting, but not grounded in experimental science.

Still, there's value in this: by building and observing the evolution process, we gain intuition about how machine learning tools "think," and how symbolic expressions can emerge even from noise.

Symbolic regression isn’t a shortcut to discovery, but it can be a useful lens for creativity, imagination, and early-stage exploration.

Attribution: Symbolic regression code and DEAP framework usage by the author. Scientific sanity checks, formatting, and rubber-duck debugging provided by ChatGPT (OpenAI). Constants courtesy of NIST.

Uses DEAP (MIT License) — © DEAP Development Team.

⚠️ Disclaimer

This blog post reflects an experimental and speculative exploration of symbolic regression applied to physical equations. No claims are made regarding the scientific accuracy or applicability of the derived expressions beyond the toy modeling context.

This work is shared in the spirit of curiosity, computational play, and creative thinking — not as a replacement for rigorous physics or engineering.

Comments

Post a Comment

Popular posts from this blog

Evolving Activation Functions: A Personal Exploration with Transformers

Image
⚠️ Disclaimer (Please Read First) This blog post presents a personal, exploratory experiment using publicly available tools and datasets (e.g., Tatoeba, DEAP, Hugging Face Transformers). It is not a lab-verified study, and results have not undergone peer review or formal statistical validation. The findings, interpretations, and conclusions shared here are based on limited-scale experiments using Google Colab and consumer-level hardware. They are intended for educational and exploratory purposes only. There is no guarantee on the accuracy, stability, or reproducibility of the experimental results. Any interpretations or applications are entirely at the reader’s discretion. Readers are encouraged to replicate, adapt, or challenge the outcomes in more rigorous or production-grade environments. We often tweak our models by adjusting the data, trying new optimizers, or changing the architecture—but how often d...
Read more

Solving Logic with Simplicity: A Scalar-Magnitude Neural Network That Cracks XOR

In this personal experiment, I explored a novel neural network design built on the idea of using a scalar magnitude-based activation — effectively replacing conventional nonlinear functions like ReLU or sigmoid with a simple identity function ( y = x ), such that  x is computed as a vector magnitude. The input projection is transformed using this formula: x = || Σ aᵢ · i · eᵢ || = sqrt(Σ (aᵢ · i)²) Where: aᵢ are learned scalar weights per feature i is the positional index of each input eᵢ is the basis vector Despite the simplicity, this architecture not only solves the linearly separable OR gate problem, but also successfully learns the non-linearly separable XOR gate — a common benchmark used to evaluate the expressiveness of neural networks. To be confirmed by future experiments, hypothetically, scaling the z-score with sqrt(1/n) per feature is effective for normalizing the sum of squared values and maintaining balanced feature contributions in ...
Read more