The Physics–Biology–AI Connection Lab

Every comparison in this module gets a grade:

• Level 1 · Analogy. The two things resemble each other. Useful for generating questions; not evidence.
• Level 2 · Shared mathematical structure. The same equations or formal objects describe both. Substantive: tools transfer. But identical mathematics can describe unrelated causes.
• Level 3a · Shared mechanism. The same causal process operates in both.
• Level 3b · Predictive transfer. Knowledge from one field yields a specific prediction in the other that survives testing. It is possible to have 3b without 3a: a formula can transfer and work for different underlying reasons.

You will grade each comparison yourself before reading the verdict. Keep the Connection Analyzer open in another tab if you want to write your reasoning down.

Biology. Across many species, metabolic rate $B$ scales with body mass $M$ roughly as $B \propto M^{3/4}$ (Kleiber’s law). West, Brown and Enquist (1997) proposed a mechanism: space-filling, fractal-like distribution networks (blood vessels) that minimise transport costs predict the 3/4 exponent.

AI. Kaplan et al. (2020) found that language-model test loss falls as a power law in parameters $N$, data $D$ and compute $C$ over several orders of magnitude.

Both are power laws relating a size variable to a performance or cost variable, with exponents that matter. Grade it before reading on.

Shannon noticed the formal identity in 1948. Later, E. T. Jaynes argued that statistical mechanics can be derived as inference: the Boltzmann distribution is the maximum-entropy distribution consistent with a known average energy. On that reading the connection is deeper than notation. The same principle (maximise uncertainty subject to what you know) produces both.

The physical link is also concrete in one place: Landauer’s principle says erasing a bit of information in a physical device dissipates at least $k_B T \ln 2$ of heat. That has been tested in laboratory experiments.

Biologists talk about fitness landscapes; ML researchers talk about loss landscapes. Both picture a population or a parameter vector moving through a high-dimensional space toward "better" regions. Evolutionary algorithms explicitly borrow mutation, selection and recombination.

But natural selection and gradient descent work very differently:

Networks. Gene regulatory networks, neural circuits and artificial neural networks are all graphs. Network science gives shared tools: degree distributions, motifs, modularity. Alon’s work on gene networks found recurring "network motifs" (small wiring patterns such as feed-forward loops) and studied their dynamics. Whether similar motifs in an artificial network compute the same thing is an open empirical question in each case.

Feedback and agents. An agentic AI loop (observe → plan → act → observe) is a feedback controller. Control theory’s lessons about gain, delay and stability apply directly to the loop’s structure, which is Level 2. They do not tell you whether the LLM inside the loop reasons well.

Emergence. Hopfield (1982) explicitly titled his paper around "emergent collective computational abilities": memories stored as low-energy states of an Ising-like network. That is a Level 2 bridge built on purpose: physics mathematics repurposed as a computational model. Hopfield and Hinton received the 2024 Nobel Prize in Physics for foundational work connecting physics and machine learning.

Jared Kaplan’s documented path makes a good case study in which habits travel between fields. The facts below come from his Johns Hopkins faculty page, arXiv records and the site’s Founder File on Kaplan.

• B.S. in physics and mathematics, Stanford.
• Ph.D. in physics, Harvard (2009), thesis Aspects of Holography, advised by Nima Arkani-Hamed.
• Postdoctoral fellow at SLAC and Stanford; then faculty in Physics and Astronomy at Johns Hopkins.
• His JHU page lists research in quantum gravity, conformal field theory and machine learning, including using CFT to learn about quantum gravity through AdS/CFT, and collaboration on scaling laws for neural models and on GPT-3. It notes he is a co-founder of Anthropic.
• First author of Scaling Laws for Neural Language Models (2020); co-author of the data-manifold scaling paper with Utkarsh Sharma (2020) and Explaining Neural Scaling Laws (2021).

His faculty page also carries a methodological credo, paraphrased: genuinely new ideas should lead to new equations, and without precise results it is very hard to avoid fooling yourself.

Practise reading the result itself in the Kaplan 2020 paper guide.

AdS/CFT. In 1997 Juan Maldacena conjectured that certain theories of quantum gravity in anti-de Sitter space (the "bulk") are exactly equivalent to certain conformal field theories without gravity living on its boundary. Two complete descriptions of one physical system: every bulk quantity has a boundary counterpart. It is a precisely stated duality in specific settings, supported by an enormous body of calculations, but not proven in general.

Constitutional AI. Bai et al. (2022) trained a harmless assistant using a written list of principles. In a supervised phase the model critiques and revises its own outputs against the principles. In an RL phase an AI model judges which of two responses better follows them, those preferences train a preference model, and that preference model serves as the reward (RLAIF).

The analogy. A short boundary document shapes the behaviour of a vast interior (the network’s weights), just as boundary data in AdS/CFT encode the bulk. It is evocative. Here is where it holds and where it breaks.

Three more bridges are often built through the holography metaphor:

• Holography ↔ model representations. "A model compresses the world onto a lower-dimensional surface, like holography." Low-dimensional structure in learned representations is real and measurable (see the flagship exercise). Calling it holographic adds no prediction unless a precise bulk/boundary dictionary is proposed. Level 1.
• Holography ↔ AI governance. "Rules at the boundary of an organisation govern its interior." This is a management metaphor. It carries no physics.
• Mathematical abstraction ↔ physical implementation. The same abstract object (a graph, a probability distribution, an optimisation problem) can be implemented by neurons, transistors or ecosystems. Shared abstraction licenses shared tools, not shared nature. A thermostat and a hormone loop are both negative-feedback controllers; one is not secretly the other.