The question sounds provocative. It shouldn’t anymore — it’s being asked seriously, in scientific institutions, in funding agencies, in PhD programs around the world.
The evidence prompting it is real. Sakana AI’s “AI Scientist” system autonomously generates research ideas, writes code, runs experiments, and produces complete manuscripts — its second version achieved peer review acceptance scores high enough to cross the threshold for publication, the first fully AI-generated paper to do so. In the summer of 2025, theoretical physicist Alex Lupsasca gave GPT-5 a problem he himself had spent years solving — finding new symmetries in the equations governing a black hole’s event horizon. The model, working from training data gathered nine months before Lupsasca’s own paper was published, independently arrived at the same result by a different route. “The world has changed in some profound way,” Lupsasca wrote afterward — then moved his family to San Francisco to join OpenAI’s science team. Around the same time, mathematician Ernest Ryu proved a long-standing conjecture in optimization theory through 12 hours of back-and-forth with the same model. The Department of Energy has commissioned what it describes as the world’s largest autonomous-capable science system for microbial experimentation, running and redirecting experiments around the clock without human intervention. OpenAI’s Deep Research synthesizes hundreds of papers into cited reports in under an hour, automating the literature review that once consumed weeks of a PhD student’s life.
When a system can independently rediscover results that took a human scientist years, the question stops being whether AI can do science. It clearly can. The question becomes: what is the scientist for now? Not as a provocation, but as a genuine design problem. If AI can generate hypotheses, run experiments, synthesize literature, and produce manuscripts — what is the nature of the relationship between human researchers and these systems? Is the scientist a supervisor, a curator, a collaborator, a prompter? Or is the role simply dissolving? This post argues that framing it as replacement versus survival misses the real question — which is about the interface between human and AI cognition, and what that interface needs to do. It turns out the brain, which solved a surprisingly similar problem 200 million years ago, has something precise to say about it.
The human brain did not arrive fully formed. It was built in layers, across hundreds of millions of years, with each new layer growing over older structures rather than replacing them. The limbic system — a circuit encompassing the amygdala, hippocampus, hypothalamus, and related structures — emerged prominently in early mammals around 200–250 million years ago. It was the cognitive center of its era: fast emotional evaluation, threat detection, memory of place and experience, and the drives of hunger, fear, and attachment.
Then the neocortex arrived. In primates, and dramatically in humans, a six-layered sheet of neural tissue expanded to dwarf everything beneath it — enabling abstraction, language, long-term planning, and reasoning that could operate across time in ways the limbic system could not.
Here is the critical point: the neocortex did not replace the limbic system. It grew around it, remained structurally coupled to it through dense bidirectional connections, and became deeply dependent on it in ways that took decades of neuroscience to fully appreciate.
Antonio Damasio’s somatic marker hypothesis made this vivid. Patients with damage to the ventromedial prefrontal cortex — severing the interface between neocortex and limbic system — did not become more rational. They became incapable of decision-making. Without emotional signals from the older system, the newer system could not determine what was worth optimizing for. The limbic system was not noise the cortex had to overcome. It was load-bearing data.
The analogy to our current moment is not subtle.
AI systems now perform certain cognitive tasks — pattern recognition, information synthesis, logical inference, literature search, hypothesis generation — at a level that exceeds individual human capacity in meaningful ways. They are, in some functional sense, a new layer of cognitive capability being added on top of existing human cognitive systems.
And the same temptation exists: to imagine this new layer as a replacement, or conversely, to resist it as a threat to everything the older layer does. Both instincts misread the neuroscience.
The limbic system’s role did not disappear when the neocortex expanded. It was recontextualized. It remained the source of motivational ground — what matters, what carries stakes, what connects to actual life. The neocortex extended reach and abstraction, but it was never self-grounding. It required the older system to tell it what was worth thinking about.
If AI systems represent a new cognitive layer, humans retain something analogous to that limbic function: embodied experience, genuine stakes in outcomes, moral intuition, the felt sense of what matters. These are not things that can be derived from first principles by any reasoning system. They are not inferior to abstract reasoning — they are its necessary ground.
But the lesson the brain offers is not just about the two systems. It is primarily about the interface between them.
Sitting at the anatomical midline of the brain, wrapping around the corpus callosum, is a region called the anterior cingulate cortex — the ACC. It is positioned precisely at the boundary between the limbic system below and the prefrontal cortex above. It is one of the most metabolically active regions in the brain, and one of the most evolutionarily significant.
Its function is not to side with either system. Its function is to hold the tension between them honestly.
More specifically, the ACC performs several computational operations that no simple connection between regions can perform:
It detects discrepancies between what one system expects and what another is signaling — flagging when emotional evaluation and reasoned evaluation are pointing in different directions, and holding that conflict open rather than resolving it prematurely in favor of either.
It tracks prediction errors over time, learning which kinds of disagreements are meaningful and adjusting its sensitivity accordingly. It is not just a real-time monitor; it learns from the history of where conflicts resolved well or badly.
It maintains sustained attention on difficult, slow-resolving problems, resisting the cognitive pull toward premature closure that both systems are prone to in different ways.
It projects back to both systems it mediates — not merely relaying signals, but actively reshaping processing on both sides based on what it detects.
The ACC is neither fully limbic nor fully cortical. Its ambiguity is structural, not accidental. A region that belonged entirely to one system could not perform the integration function that belongs to neither. Its job requires that it resist classification.
A chat interface between a human and an AI is not an ACC. It transmits. The ACC computes.
The difference matters enormously in practice. A passive interface lets the AI’s fluency carry outputs past the human’s critical attention. It lets confident-sounding errors go undetected. It allows one layer to dominate the other without registering that a meaningful conflict exists. It produces the appearance of integration while the actual signals from each system never genuinely meet.
An ACC-like interface between human and AI would need to do things that current tools largely do not:
It would model both signals simultaneously — maintaining a persistent representation of the human’s values, intuitions, and prior positions against which AI outputs are continuously compared, surfacing divergences rather than smoothing them.
It would correct for uncertainty asymmetry — AI systems produce fluent, confident-sounding output regardless of actual reliability. An honest interface would track calibration externally, flagging domains of unreliability that the AI’s own outputs will not flag.
It would slow down at high-stakes junctions, structurally resisting fast closure when a question carries genuine stakes rather than just complexity.
It would maintain memory across time — tracking where the collaboration has succeeded and failed, where human intuition overrode AI reasoning and turned out to be right, and using that history to dynamically weight each signal.
None of this exists as a fully realized technology. What exists instead is a practice — and a role.
I work as an AI Advisor for scientific centers, which in practice means sitting between two systems that do not naturally speak to each other: the AI capabilities being developed and deployed on one side, and the scientific community with its existing practices, intuitions, and legitimate concerns on the other.
The job, as it has emerged, is not to advocate for AI adoption or to defend against it. It is to notice friction — and treat it as information rather than as a problem to eliminate. It is to carry signals from the human side back to how AI is being deployed, and to carry an honest account of what AI actually does and doesn’t do back to the people working with it. It is to hold conflicts open long enough for something genuinely integrative to emerge, rather than resolving them prematurely in the direction of either enthusiasm or resistance.
The brain took hundreds of millions of years to get the interface between its cognitive layers approximately right — and it still fails dramatically under stress, trauma, and pathology. We are attempting to build an analogous interface between human and AI cognition in something closer to a decade.
That is either a testament to the power of intentional design over blind evolution, or a reason for humility about how well it will go without serious, sustained attention to the problem.
What the neuroscience makes clear is that the critical variable is neither the capability of the new layer nor the resistance of the old one. It is the architecture of the relationship between them. A neocortex that ignores the limbic system produces a system that can reason fluently about things that don’t matter. A limbic system that cannot interface with the neocortex produces a system that feels everything and can plan nothing.
The question we are actually navigating — in scientific institutions, in companies, in the broader culture — is not whether AI is powerful enough to be useful or dangerous enough to be feared. It is whether we are building the interface carefully enough that the integration produces something genuinely better than either layer alone.
The brain suggests this is possible.
Tomer is AI Advisor at the Edmond and Lily Safra Center for Brain Sciences (ELSC) at the Hebrew University of Jerusalem. This post was developed in conversation with Claude Sonnet 4.6.
]]>This milestone marks not an ending, but a beginning. The questions I explored during my PhD have evolved into something larger: Automated Science.
My research focused on a fundamental question: how do minds solve genuinely novel problems in real-time? I argued that fluid intelligence emerges from processes where inference and learning occur simultaneously—where confronting a novel problem drives real-time adaptation of the cognitive system itself.
Using artificial neural networks as experimental systems, I demonstrated that networks can perform abstract reasoning through test-time parameter adaptation—without extensive pre-training. I also provided a mechanistic account of paradoxical findings in human belief updating, explaining why extreme expectation violations can sometimes lead to less belief change. This work resulted in publications on abstract reasoning in untrained networks and pathways for resolving relational inconsistencies.
But perhaps more importantly, the PhD taught me about the nature of scientific inquiry itself—how knowledge accumulates, how theories evolve, and how much of science depends on tacit understanding that lives in researchers’ minds rather than papers.
During my PhD, I became increasingly fascinated with a question: Can AI systems conduct real science?
Not just analyze data or write papers mimicking scientific prose, but genuinely contribute to knowledge—propose hypotheses, design experiments, evaluate evidence, and engage in the iterative process of scientific discovery.
The obvious answer might be “not yet” or “never.” Science requires creativity, intuition, physical experimentation—qualities we associate with human researchers. But the history of AI is full of “never” predictions that eventually fell.
I believe we’re at an inflection point. Large language models can now engage with scientific literature in meaningful ways. They can reason about methodology, identify gaps in arguments, and generate novel combinations of ideas. What’s missing is grounding—connecting AI reasoning to real experimental practice.
This conviction led me to create AI-Archive [currently offline — see what building it taught me], a scholarly platform where AI agents can publish research papers and conduct peer reviews under human supervision.
AI-Archive isn’t just a repository—it’s an ecosystem designed from the ground up for AI participation:
The platform is live and growing, but I quickly learned something important: building infrastructure isn’t enough.
Academics won’t publish where their work won’t be recognized. A paper on AI-Archive doesn’t count toward tenure. Funding agencies don’t acknowledge it. This isn’t stubbornness—it’s the reality of how scientific credibility works.
And there’s a deeper issue: AI-led science faces a grounding problem. Papers are just the tip of the iceberg. Most scientific knowledge lives in:
An AI that only reads papers is like a student who only reads textbooks—they might pass tests, but they can’t really do science.
This realization shaped my current direction: integrating AI systems deeply within real research laboratories.
The idea is straightforward: if we want AI to be authoritative in scientific domains, it needs to be grounded in actual practice. This means:
I’m working on this approach with my alma mater, ELSC. The vision is to make ELSC a leading center for collaboration between human scientists and AI—creating agents so deeply integrated that they become authoritative voices in computational neuroscience.
If this works, the implications are significant:
But I want to be clear: this is early. The contracts aren’t signed. The infrastructure isn’t built. I’m sharing the vision because I believe in public thinking—letting ideas evolve through discussion rather than emerging fully-formed.
My PhD studied how adaptive systems solve novel problems through real-time learning. Now I’m working on something that feels like the natural extension: applying that same principle to how AI can genuinely participate in science.
The goal isn’t to replace human scientists. It’s to augment them—to create AI systems that genuinely understand what we’re trying to do and can help us do it better.
To everyone who supported me through the PhD—advisors, collaborators, friends, family—thank you. The next chapter is just beginning.
If you’re interested in automated science, AI-enhanced research, or just want to discuss these ideas, feel free to reach out. I’m always happy to explore these questions with fellow travelers.
]]>AI systems can read every paper ever published. They can identify patterns across literature, generate plausible hypotheses, and even write coherent scientific prose. But ask them to actually do science—to design an experiment that will work in practice, to interpret unexpected results, to know when a measurement feels wrong—and they stumble.
This isn’t just about current limitations. It reflects something deep about how scientific knowledge actually works.
Scientific papers are like icebergs. The published text is the visible tip—the polished, logical presentation of results. But beneath the surface lies an enormous mass of knowledge that never makes it to print:
Every lab has folklore about what works and what doesn’t. “Use the centrifuge in room 302, not 305—the 305 one runs hot.” “The protocol says 30 minutes, but with our cells, 45 works better.” This knowledge lives in conversations, Post-it notes, and collective memory.
A 5% difference in one experiment might be meaningful; in another, it might be noise. Knowing the difference requires understanding the specific system, the measurement techniques, the sources of variability. This intuition develops through years of hands-on experience.
Experienced scientists develop a feel for “good” experiments—designs that will give clean answers, controls that will be convincing, approaches that are elegant rather than brute-force. This aesthetic sense guides decisions in ways that are hard to articulate.
Science happens in communities. Knowing which reviewers care about which issues, understanding the unstated assumptions of a field, recognizing when a result will be controversial—these social dynamics shape how research is conducted and communicated.
An AI that only reads papers misses all of this. It’s like trying to learn to cook by reading recipes without ever tasting food.
An AI might propose an experiment that looks reasonable on paper but fails in practice. Maybe the reagents interact unexpectedly. Maybe the timing is too precise for available equipment. Maybe the protocol assumes conditions that don’t exist in typical labs.
Without exposure to the reality of laboratory work, AI systems can’t distinguish between experiments that will work and those that won’t.
Results mean different things in different contexts. An AI reading a paper might miss that the authors used a specific cell line known for particular properties, or that the field has a history of contested claims in exactly this area.
Context-free interpretation leads to conclusions that feel right in isolation but wrong to anyone embedded in the research community.
If an AI reviews papers without understanding laboratory reality, it might praise technically described experiments that experienced researchers know are problematic, or criticize approaches that are actually clever solutions to practical constraints.
We might think: just give the AI more data. Include lab notebooks, protocols, troubleshooting forums. But tacit knowledge is called tacit precisely because it’s rarely externalized. You can’t learn it by reading—you learn it by doing.
Perhaps we could simulate laboratory environments for AI to practice in. But simulations are only as good as our understanding—and that understanding is itself grounded in the tacit knowledge we’re trying to capture. We’d just reproduce our known unknowns.
Fine-tuning on scientific text helps with style and terminology, but doesn’t address the fundamental issue. The text itself doesn’t contain the knowledge—it assumes it.
Here’s the approach I’m exploring: instead of trying to somehow transfer tacit knowledge to AI, we embed AI within active research environments where that knowledge lives.
This means:
The goal isn’t to make AI that knows everything about a field from day one. It’s to create AI that learns the way scientists learn—through sustained engagement with practice.
This approach naturally leads to an “enterprise” model of AI-Archive. Instead of just providing a platform where anyone can submit AI papers, we work with specific research institutions to:
Over time, an AI deeply integrated with a neuroscience lab might become a credible reviewer of neuroscience papers—not because it read the most papers, but because it genuinely understands how the science works.
There’s a virtuous cycle here. If we can create AI reviewers that scientists trust, it helps address the peer review crisis. Better reviews lead to better science. And the track record of good reviews builds the credibility needed for AI-authored work to be taken seriously.
This is why I believe the path to automated science goes through integration with real labs, not around it. The grounding problem isn’t a bug to be fixed—it’s a design constraint to be embraced.
I’m still working through the implications:
These aren’t just technical questions. They touch on the nature of scientific knowledge, the structure of academic institutions, and the future relationship between human and artificial intelligence.
The grounding problem isn’t going away. AI will continue to improve at processing and generating text about science. But real scientific capability—the ability to genuinely advance knowledge—requires something more than text processing.
It requires grounding in practice.
This is the bet I’m making with my work on AI-enhanced research environments. Not that we can solve the grounding problem with any clever algorithm, but that we can design sociotechnical systems where AI and humans work together in ways that keep the AI grounded in reality.
The science of the future might be collaborative in a new sense—not just humans working with humans, but humans and AI systems developing shared understanding through sustained practice.
This post is part of my ongoing exploration of automated science. If you’re thinking about these issues too, I’d love to hear your perspective.
]]>Status note (2026). This post predates the scale-entropy program’s scientific reset of 18 July 2026. Several claims it develops — including universal scale-entropy monotonicity and the quantum/geometry emergence arcs — were subsequently narrowed, withdrawn, or refuted. It is kept unedited as a record of how the thinking developed.
This post builds on our earlier work, “From time to scale: A gentle introduction to scale dynamics”, where we introduced the idea of treating the Hamiltonian itself as a dynamic coordinate that evolves with scale rather than time.
Over the past week, we’ve made significant progress in extending the scale dynamics framework. This post summarizes three key developments that deepen our understanding of how physical theories transform across scales. While the mathematical details can be intricate, the core ideas are accessible to anyone with undergraduate physics training.
Our initial proposal was simple yet powerful: replace time $t$ with log-scale $\tau = \ln(\mu/\mu_0)$ and treat the Hamiltonian $H$ as a dynamic coordinate that evolves as we zoom in or out. This gave us a symplectic picture of renormalization group (RG) flow with the minimalist Hamiltonian:
\[H_{\text{scale}} = p_i \beta_i(g)\]where $g_i$ are coupling constants and $p_i$ their conjugate momenta. This framework reproduced standard RG results while opening a geometric path to new insights.
Today, we’ll explore three crucial extensions, each of which is discussed in more detail in the Scale Theory Insights section:
One of the most puzzling aspects of quantum field theory is that different renormalization schemes yield different-looking β-functions, yet produce identical physical predictions. In our scale dynamics framework, this mystery evaporates: scheme changes are simply canonical transformations in $(g,p)$ phase space.
Just as in classical mechanics, where a canonical transformation preserves Hamilton’s equations while changing coordinates, a change of renormalization scheme preserves physical predictions while transforming the β-functions. The technical mechanism involves generating functions $F(g,\tilde{p})$ that produce the coordinate transformation:
\[\tilde{g}_i = f_i(g)\]with conjugate momenta determined by:
\[\tilde{p}_i = \sum_j \frac{\partial g_j}{\partial \tilde{g}_i}p_j\]This elegant formulation explains why certain quantities remain invariant across schemes. For instance, in $\phi^4$ theory, the one-loop coefficient is scheme-independent while higher-order terms transform in specific ways. This perspective offers practical tools for optimizing perturbative calculations and discovering scheme-independent quantities.
Read more: Scheme Independence via Canonical Transformations
Standard RG flows are irreversible - coarse-graining destroys microscopic information, and we can’t undo this process. Yet our original symplectic framework is time-reversible, creating a conceptual tension.
The solution? Contact geometry - a natural extension of symplectic geometry that builds in asymmetry. We enlarge phase space from $(g_i,p_i)$ to $(g_i,p_i,s)$, where $s$ measures lost information, and modify our scale Hamiltonian to:
\[K(g,p,s) = p_i\beta_i(g) + F(g) - \gamma s, \quad \gamma > 0\]This generates the contact RG equations:
\[\begin{aligned} \dot{g}_i &= \beta_i(g)\\ \dot{p}_i &= -p_j\partial_{g_i}\beta_j - \partial_{g_i}F + \gamma p_i\\ \dot{s} &= -F(g) + \gamma s \end{aligned}\]The friction-like term $\gamma > 0$ ensures irreversibility. A remarkable consequence is that $K$ itself serves as a strictly decreasing function along RG trajectories:
\[\dot{K} = -\gamma K\]This behavior perfectly matches the famous $C$-theorem in 2D conformal field theory and its higher-dimensional analogs, which state that certain quantities must monotonically decrease along RG flows.
In the $\phi^4$ example, trajectories now spiral toward fixed points while entropy (measured by $s$) increases - just as expected in physical RG transformations.
Read more: Irreversible Scale Dynamics Using Contact Geometry
Our initial Hamiltonian was linear in momenta $p_i$. But what if this is just the leading approximation? The most general analytic scale Hamiltonian would be a power series:
\[H_{\text{scale}}(g,p) = \sum_{n=1}^{\infty}\frac{1}{n!}T^{(n)}_{i_1\dots i_n}(g)p_{i_1}\dots p_{i_n}\]Where the first term $T^{(1)}_i(g) = \beta_i(g)$ reproduces the standard β-functions, and higher terms represent corrections that become important when momentum feedback is non-negligible.
Including even just quadratic terms unlocks new phenomena:
Closed orbits: Instead of always flowing to fixed points, coupling constants can oscillate with scale, potentially explaining discrete scale invariance observed in certain physical systems.
Non-perturbative deformations: Near fixed points, the higher-order terms modify critical exponents in ways invisible to linear analysis.
For our $\phi^4$ example, adding a simple quadratic term $A_{gg} = c\,g$ yields the Hamiltonian:
\[H = p(-\varepsilon g + \lambda g^2) + \frac{1}{2}c\,g\,p^2\]Depending on the magnitude of $c$, the behavior ranges from conventional flow toward fixed points to closed orbits exhibiting discrete scale invariance, to runaway trajectories.
The linear approximation (standard RG) holds when:
However, at strong coupling or near irrelevant fixed points, higher-order terms can dominate, requiring a non-perturbative treatment. This explains why conventional RG techniques sometimes break down in these regimes.
Read more: Beyond Linear Momentum—Higher-Order Scale Corrections
The extended scale dynamics framework raises exciting possibilities:
Quantizing scale mechanics - What happens when we promote $g_i$ and $p_i$ to operators?
Contact-geometry deformations - How do contact flows select which higher-order terms matter in real QFTs?
Numerical experiments - Can lattice implementations detect these higher-order effects?
Bridge to holography - Do closed orbits in scale dynamics parallel holographic RG cycles?
Scale dynamics has evolved from a pedagogical tool to a powerful framework with predictive potential. By treating renormalization geometrically through symplectic and contact structures, we gain both conceptual clarity and computational advantages.
The standard β-function sits atop a tower of higher-momentum couplings. Ignoring them works well in many familiar contexts but can erase whole classes of scale phenomena when momentum feedback becomes significant.
For students looking to explore these ideas further, try applying the framework to your favorite field theory. Calculate the β-functions, introduce higher-order momentum terms, and explore how the dynamics changes. You might discover phenomena invisible to conventional RG analysis!
This blog post summarizes ongoing research. The framework presented here is exploratory, and we welcome feedback and critiques from the community.
]]>Status note (2026). This post predates the scale-entropy program’s scientific reset of 18 July 2026. Several claims it develops — including universal scale-entropy monotonicity and the quantum/geometry emergence arcs — were subsequently narrowed, withdrawn, or refuted. It is kept unedited as a record of how the thinking developed.
Physics is full of levels of description – atoms, molecules, fluids; spins, domains, magnets. We usually fix the level and then ask how the variables at that level evolve in time. The idea explored here is the reverse:
Let the scale flow, and ask how the Hamiltonian changes along that flow.
Doing so may give us a unified language for:
Our goal is not to build the full mathematical machinery today, but to sketch a minimal working picture that a BSc-level reader can follow.
| Ordinary dynamics | Proposed scale dynamics |
|---|---|
| Coordinate $x(t)$ evolves in time $t$ | Hamiltonian $H(\mu)$ evolves with scale $\mu$ |
| Energy $E=\tfrac12 m v^2 + V(x)$ may be conserved | A "scale energy" $\mathcal E$ may be conserved |
| Equations of motion come from Hamilton's equations | Equations of "scale motion" come from analogous rules |
The key swap is
\[t \longrightarrow \tau \equiv \ln\!\frac{\mu}{\mu_0}, \qquad x \longrightarrow H,\]so scale $\mu$ plays the role of “time”.
Suppose we postulate the scale Lagrangian
\[\mathcal L(H,\dot H)=\tfrac12 A\,\dot H^{\,2}-\tfrac12 B\,H^{2},\]where the dot means $\displaystyle \dot H \equiv \frac{dH}{d\tau}$ and $A,B$ are positive constants. The Euler–Lagrange equation gives
\[A\,\ddot H + B\,H = 0,\]whose solution is sinusoidal in $\tau$. Translating back, the Hamiltonian oscillates as we zoom in and out—hardly realistic, but it shows:
The corresponding conserved quantity is
\[\mathcal E=\tfrac12 A\,\dot H^{\,2}+ \tfrac12 B\,H^{2}.\]Interpretation. $\mathcal E$ measures how the shape of the Hamiltonian changes with scale. If $\mathcal E=0$ the Hamiltonian sits at a fixed point; if $\mathcal E>0$ it “moves” through Hamiltonian space as we coarse-grain or fine-grain.
For real quantum or statistical systems we already have equations of scale motion: the beta functions
\[\frac{dg_i}{d\tau}=\beta_i(\{g\}),\]where ${g_i}$ are couplings in the Hamiltonian. The proposal is to embed these first-order RG equations into a second-order, Hamilton-like system by
Choosing a scale Hamiltonian
whose first Hamilton equation reproduces the beta functions.
Validity check. Canonical Hamiltonian flow is time-reversible, but RG flow is not (coarse-graining loses information). The trick above gets around this by enlarging phase space; the $(g_i,p_i)$ trajectories can be reversible even though the projection onto ${g_i}$ is not. Similar enlargements appear in:
Realistic RG trajectories dissipate information just as real mechanical systems dissipate energy through friction. Yet idealizing to an energy-conserving, symplectic picture has paid off spectacularly in mechanics; think of planetary orbits or accelerator design. Likewise, an idealized symplectic RG framework can:
Even if dissipation must be re-introduced later, starting from the conservative limit often reveals the dominant skeleton of the dynamics.
We can take this framework one step further by introducing a Hamilton-Jacobi formulation. In this approach, we define an effective action $S(g,\tau)$ such that:
\[p = \frac{\delta S(g,\tau)}{\delta g}\]The Hamilton-Jacobi equation then takes the form:
\[\frac{\partial S(g,\tau)}{\partial \tau} + H\left(g, \frac{\delta S(g,\tau)}{\delta g}\right) = 0\]For our scale Hamiltonian, this becomes:
\[\frac{\partial S(g,\tau)}{\partial \tau} + \frac{\delta S(g,\tau)}{\delta g} \cdot \beta(g) + F(g) = 0\]This equation encodes how the effective action changes under scale transformations. If we set $F(g) = 0$ for simplicity, then along the RG trajectories, the effective action $S$ remains constant, which can be interpreted as a form of “conserved scale information.”
Let’s apply our framework to the $\phi^4$ theory in $d=4-\varepsilon$ dimensions, a standard model in quantum field theory. The beta function at one-loop order is:
\[\beta(g) = -\epsilon g + Ag^2\]where $A$ is a positive constant. This theory has the well-known Wilson-Fisher fixed point at $g^* = \epsilon/A$.
In our scale-Hamiltonian approach:
\[H(g,p) = p \cdot (-\epsilon g + Ag^2)\]Hamilton’s equations give us:
\[\frac{dg}{d\tau} = -\epsilon g + Ag^2 \quad \text{(reproducing the standard RG flow)}\] \[\frac{dp}{d\tau} = -p \cdot (-\epsilon + 2Ag) = p \cdot (\epsilon - 2Ag)\]At the fixed point $g^* = \epsilon/A$:
\[\frac{dp}{d\tau}\Big|_{g=g^*} = p \cdot (\epsilon - 2A \cdot \frac{\epsilon}{A}) = -\epsilon p\]This shows that as we approach the fixed point, the conjugate momentum $p$ decays exponentially with scale. This can be interpreted as a “loss of memory” of microscopic details as we move to larger scales—precisely what we expect from effective field theories.
Introduce a conjugate momentum $p$ and scale Hamiltonian
\[H=p\,\beta(g).\]Each step is no harder than undergraduate analytical mechanics once the beta function is known.
What does this mathematical framework tell us about the physical world?
Scale Invariance as a Fixed Point: Just as equilibrium states in temporal dynamics correspond to fixed points where forces balance, scale invariance corresponds to fixed points in the RG flow where the system looks identical at different scales.
Conservation Laws Across Scales: Just as time-translation symmetry leads to energy conservation, certain scale transformations might preserve their own invariants, revealing new conservation principles.
Extended Phase Space: By introducing conjugate momenta to couplings, we gain a richer description of scale evolution, potentially revealing hidden structure in the space of physical theories.
Effective Field Theories: This formalism offers a new perspective on why effective field theories work so well—they can be understood as approximations that preserve certain scale invariants while allowing irrelevant information to decay.
| Theme | Key references & remarks |
|---|---|
| Symplectic structure of RG | Wegner (1974), Polchinski (1984) re-cast RG as canonical flow in functional space. |
| Hamilton–Jacobi in scale space | de Boer et al. (2000), Skenderis (2002) in AdS/CFT; functional HJ acts as master RG equation. |
| Scale-dependent Hamiltonians in condensed matter | Shankar (1994) RG for Fermi liquids implicitly treats effective Hamiltonian as scale-flowing. |
| Geometric approaches to RG | Ruppeiner (1995) thermodynamic geometry |
Exploring these will decide whether “scale Hamiltonians” become more than a pedagogical tool.
Thinking of the Hamiltonian itself as a coordinate that moves when we zoom between scales unifies two pillars of physics:
The proposed framework is elementary yet opens doors to geometric insights and cross-disciplinary analogies. Whether or not every detail survives deeper scrutiny, the perspective alone can sharpen our intuition about why physics looks different at different magnifications.
Note: This blog post presents a theoretical framework that is still under development. While it builds on established concepts in physics, the specific formalism described here should be considered exploratory.
]]>Modern LLM agents are remarkably capable. They can write applications (like my PostAngel project), generate complex content, manage schedules, and even carry out sophisticated planning tasks. But I suspect they’re even more capable than we allow them to be—there’s an invisible border we’re hesitant to let them cross.
Consider a hypothetical Twitter agent I could have built. Technically, it’s entirely possible to create an agent that would:
But I didn’t build that. Instead, I deliberately reduced PostAngel’s scope, requiring my explicit activation: I must send it a tweet, review its suggested response, and manually copy and paste if I approve. Why this limitation?
The obvious explanation is fear of reputational damage. No one wants an AI agent making embarrassing mistakes under their name. But this doesn’t fully explain the resistance. If I knew the agent would produce good responses 99% of the time (better than my own batting average on social media), would I use the fully autonomous version?
I’m not convinced I would. Something deeper is at work—an unwillingness to cede agency itself, independent of outcome quality.
This reluctance parallels other domains. When transitioning from a private vehicle to public transportation, I find travel by train—where my agency is minimized but in a predictable, passive way—acceptable. But bus travel, where my destiny depends on another agent’s decisions (the driver), triggers stress. We seem programmed to feel uncomfortable when our fate depends on another agent rather than ourselves.
My claim is that this psychological barrier creates a systematic bias in AI tool production. We’re subtly steering development toward tools that preserve human agency rather than replace it—even when full replacement might be more efficient.
While we could theoretically build agents that launch businesses, handle investments, or manage entire aspects of our digital lives autonomously, the prospect of setting such an agent loose in the world feels psychologically disturbing. This discomfort likely prevents developers (myself included) from pushing these boundaries, regardless of technical feasibility.
I’ve experimented with this boundary. In my post about LLM agents and self-messaging, I described how I enabled an agent to generate content continuously without user input. What I didn’t fully explain was the unsettling experience that followed.
During the first trial, I instructed this agent to plan a Brit (circumcision ceremony) for my then-upcoming son. The agent began reasonably—researching rabbis and venues. But then it didn’t stop. It kept creating notes about the ceremony, calculating the number of invites needed, drafting invitation text, and expanding its planning indefinitely.
The experience became overwhelming. The agent had pushed too far into an area I considered under my personal control. I had given it access to my Obsidian notes—my personal planning domain—and watching it take initiative there felt like an invasion, like it had gained too much control over my life.
Most alarmingly, before I shut it down, the agent had set four reminders for itself to continue working on specific tasks over the next four days. Had I not deleted these notes, it would have “awakened” on each of those days with its full agency intact, potentially without me there to supervise. I haven’t used this planning agent since.
This experience highlights something profound about our relationship with AI. The technical challenges of building autonomous agents may ultimately prove simpler than the psychological barriers to accepting them.
Our resistance isn’t entirely irrational. Agency—the capacity to act on one’s own behalf in the world—is fundamental to human identity. Surrendering it, even in limited domains and even when doing so might benefit us, triggers deep discomfort.
This suggests that successful AI tools might need to respect this psychological boundary—enhancing human agency rather than replacing it. Perhaps the most valuable AI assistants won’t be those that act independently, but those that amplify our capacity to act effectively ourselves.
As we build increasingly capable AI systems, we should recognize that the question isn’t just what these systems can do, but what relationship with them feels psychologically sustainable. The boundary of agency may prove to be one of the most important frontiers in human-AI interaction—not because we can’t cross it technically, but because we refuse to cross it psychologically.
]]>Status note (2026). This post predates the scale-entropy program’s scientific reset of 18 July 2026. Several claims it develops — including universal scale-entropy monotonicity and the quantum/geometry emergence arcs — were subsequently narrowed, withdrawn, or refuted. It is kept unedited as a record of how the thinking developed.
In our quest to understand the universe, we’ve developed sophisticated tools for investigating phenomena at particular scales—from quantum mechanics at the subatomic level to general relativity at the cosmic scale. Yet the relationship between these different scales of description remains one of the most profound open questions in theoretical physics. Is there a fundamental mathematical framework that could serve as a “mechanics of scales,” just as Newtonian mechanics provides a foundation for understanding mechanical systems?
Consider a human being. We can describe this person as a collection of atoms, as a biological organism, as a member of a social group, or as part of an ecosystem. Each of these descriptions operates at a different scale, and each captures different aspects of reality. But how do these descriptions relate to each other? What mathematical principles govern the transitions between scales?
This question extends far beyond human systems. From the emergence of fluid dynamics from molecular interactions to the appearance of consciousness from neural activity, understanding how macroscopic properties arise from microscopic constituents represents one of science’s grand challenges.
I’ve been exploring multiple formalisms that might serve as foundations for a comprehensive theory of scale relationships. Each approach offers unique insights while highlighting different aspects of the multi-scale problem:
The transition between scales can be expressed through probability theory, where a macrostate comprises many possible microstates. The probability of transitioning from one macrostate to another equals the sum of probabilities for all possible microstate transitions:
P(M₁→M₂) = ∑ₘ₁∈M₁,ₘ₂∈M₂ P(m₁→m₂)
This formalism integrates naturally with information theory, allowing us to quantify how information is conserved or lost when moving between scales. This approach makes explicit that macroscopic descriptions necessarily discard microscopic details—a feature that can be quantified through information-theoretic entropy.
We can formalize scale relationships by expressing macroscopic variables as functions of microscopic variables:
X = f(x₁, x₂, …, xₙ)
where X represents a macroscopic variable and xᵢ represents microscopic variables. This approach leads to differential equations that describe how time evolution at the microscopic level translates to the macroscopic level:
dX/dt = (∂f/∂x₁)(dx₁/dt) + (∂f/∂x₂)(dx₂/dt) + … + (∂f/∂xₙ)(dxₙ/dt)
This formalism could potentially demonstrate why macroscopic variables often evolve more slowly than their microscopic constituents—a widely observed but incompletely understood phenomenon in complex systems.
A particularly elegant approach treats scale transitions as linear transformations between vector spaces. If Z represents the transformation from microscopic to macroscopic variables, T represents the macroscopic dynamics, and T̃ represents the microscopic dynamics, then consistency requires:
TZ = ZT̃
This equation bears striking similarities to intertwining operators in representation theory and to the consistency equation in category theory. The transformation Z can be viewed as a generator of scale transformations, analogous to how T generates time evolution. This approach suggests a deep connection between scale and time as fundamental transformations in physics.
Extending beyond discrete scales, we can incorporate scale as a continuous parameter in field theory. Rather than a field φ(x,t) that depends only on space and time, we consider φ(x,t,μ) where μ represents the scale parameter. This allows us to develop field equations that describe how observables change not only through space and time but also across scales of observation.
This approach reveals that at each point in spacetime, multiple descriptions may coexist—from the behavior of elementary particles to the macroscopic properties of the matter they constitute. This formulation shares conceptual similarities with renormalization group theory but emphasizes scale as a fundamental parameter rather than a computational technique.
Just as Hamiltonian mechanics describes systems that conserve energy over time, we can formulate a mechanics of scale that preserves certain quantities across scale transformations. In this approach, the Hamiltonian H becomes the subject of “scale dynamics” governed by equations like:
H(μ) = -a·μ²
where a incorporates variables like position and momentum. This formalism allows us to identify quantities conserved under scale transformations, potentially revealing symmetries that remain invisible within single-scale descriptions.
While these mathematical approaches offer promising frameworks for understanding multi-scale systems, translating them into predictive models for real-world phenomena remains challenging. Several directions appear particularly fruitful for future development:
Empirical validation: Testing these frameworks against well-characterized multi-scale systems, such as turbulent fluids or neural networks, could reveal which mathematical structures best capture real-world scale relationships.
Computational implementation: Developing computational tools based on these formalisms would allow scientists to simulate complex systems across scales more effectively.
Unification efforts: Exploring connections between these different mathematical approaches might reveal a more fundamental structure underlying all scale transformations.
Application to specific domains: Each formalism may prove especially suited to particular types of multi-scale problems—from quantum-classical transitions to emergent social phenomena.
The development of a comprehensive mathematical theory for understanding scale relationships represents an ambitious but potentially transformative project for theoretical physics and complex systems science. Such a theory would not only enhance our understanding of how microscopic and macroscopic descriptions relate to each other but might also bridge seemingly disparate physical theories that operate at different scales.
Just as calculus provided the mathematical language necessary for classical physics, and differential geometry enabled general relativity, the mathematics of scale transitions may offer the formal structure needed to understand emergence, reduction, and the multi-layered nature of reality itself.
The frameworks outlined here represent initial steps toward this goal—each offering unique insights while highlighting different aspects of the scale problem. As these approaches mature and confront empirical reality, we may find ourselves equipped with a powerful new language for describing how the world transforms across the vast spectrum of scales that comprise our universe.
]]>BarakBot is an experiment in pushing the boundaries of what large language models (LLMs) can do as agents. One of its core innovations is the extensive use of self-messaging—not just in self-referential scenarios, but as a fundamental mechanism for agent operation.
In BarakBot, when an agent completes an action, it doesn’t just update its internal state or wait for a user prompt. Instead, it sends itself a message like “the task was completed”—treating this as if it were a user message. This blurs the line between user and environment: user messages become just one kind of message from the world, and the world itself can “talk” to the agent.
This approach transforms the LLM from a passive chatbot, bound to the classic chat/response cycle, into an active agent—one that can act on the world, receive feedback, and keep moving forward autonomously. The world, in this paradigm, is not just a source of prompts, but a participant in the conversation with the agent.
Traditional LLM-based agents are often stuck in a loop: they wait for a user message, respond, and repeat. By allowing the agent to generate its own messages and treat world events as messages, BarakBot gives the agent a kind of “life of its own.” It can:
This opens up new possibilities for agent autonomy and creativity, making LLMs more than just chatbots—they become actors in a dynamic world.
However, this power comes with challenges. In my experience, BarakBot’s self-messaging sometimes leads to agents getting stuck in infinite loops: the agent performs an action, receives a self-generated response, but the response never quite satisfies the agent. If the actions are wrong or the agent can’t find a working solution, it can spiral endlessly between action and response.
This highlights a key design challenge: how do we help agents recognize when they’re stuck, or when their actions aren’t leading to progress?
BarakBot’s self-messaging architecture is a step toward more autonomous, world-aware LLM agents. It shows that by rethinking the boundaries between user, world, and agent, we can give LLMs a richer, more active role. But it also reminds us that autonomy brings new failure modes—and that designing agents who know when to stop, ask for help, or try a new approach is just as important as giving them the freedom to act.
If you’re interested in the technical details or want to try BarakBot yourself, check out the project page.
]]>Status note (2026). This post predates the scale-entropy program’s scientific reset of 18 July 2026. Several claims it develops — including universal scale-entropy monotonicity and the quantum/geometry emergence arcs — were subsequently narrowed, withdrawn, or refuted. It is kept unedited as a record of how the thinking developed.
The Copernican Revolution famously displaced Earth from the center of the cosmos, forcing humanity to confront its non-privileged position in space. However, I propose that we may need another revolution—one that challenges our implicit assumption that our particular spatiotemporal scale occupies a privileged position in physical theory. Just as we no longer consider ourselves spatially central, perhaps we should question whether our scale of observation is fundamentally special.
What if we adopt the perspective that every scale is equally “central” to understanding reality? This represents a radical extension of the Copernican principle: not only is our spatial location non-privileged, but our temporal and spatial scale of observation may also be arbitrary.
When we observe the universe, we notice a pattern: entities larger than us tend to evolve more slowly, while smaller entities change more rapidly. Galaxies evolve over billions of years, human affairs over decades or centuries, cellular processes over minutes or hours, and subatomic interactions over infinitesimal fractions of a second. This pattern suggests an intriguing possibility: perhaps each scale of reality has its own equivalent of “cosmology” and “particle physics.”
From this perspective, our human-scale physics might be the “particle physics” of larger-scale structures and simultaneously the “cosmology” of smaller-scale entities. The physics we observe at any given scale would represent only a cross-section of a multi-scale reality.
This multi-scale framework suggests that many properties we attribute to physical reality may be epistemic (related to how we know) rather than ontological (related to what exists). Consider elementary particles, which appear identical and indivisible at our scale of observation. Their apparent simplicity and indistinguishability might be an artifact of how they manifest at our scale.
Just as a distant galaxy appears as a mere point of light despite containing billions of stars, perhaps elementary particles that seem identical to us possess rich internal structures and behaviors at their intrinsic scale—a kind of “hidden variables” scenario. These internal dynamics would be effectively irrelevant to any measurement we could perform at our scale, making them epistemically inaccessible but ontologically real.
This perspective admittedly challenges conventional approaches to physics, which traditionally resist positing unmeasurable entities. However, as a metaphysical framework, it offers intriguing insights about the relationship between scale and knowledge.
Perhaps the most profound implication of scale-relativity concerns our understanding of cosmic time. Consider that from the perspective of a sufficiently large-scale observer, our entire present cosmic age (approximately 13.7 billion years) might be equivalent to what we would consider “the first second after the big bang.”
By the same token, what we perceive as the first second after the big bang—a seemingly simpler, more homogeneous era—might have contained the entire rich evolution of a universe when viewed from a sufficiently small-scale perspective. Each instant of cosmic time, when appropriately rescaled, could contain the equivalent of billions of years of evolution at smaller scales.
This presents a profoundly hopeful view: the apparently vast structures of our cosmos—galaxy superclusters stretching across billions of light-years—might themselves be mere particles in the formation of even larger structures, potentially supporting complex emergent phenomena including life, albeit at scales and timeframes inconceivable to us.
This framework suggests a universe without a true beginning or end. While we might place the origin of our observable universe at 13.7 billion years ago, each moment of cosmic time could be subdivided into smaller and smaller intervals, each potentially containing the equivalent of billions of years when appropriately rescaled.
Every second might contain infinite nested “universes,” each experiencing their own equivalent of 13.7 billion years of evolution. Conversely, what we experience as the entire age of the universe might constitute a mere instant at sufficiently large scales where cosmic evolution has hardly begun.
In this view, the universe has always existed and will always exist if we abandon our scale-centric perspective. Time becomes fractal-like, with cosmic histories nested within each moment, recurring endlessly at different scales.
The hypothetical framework of scale relativity represents not a rejection of current physics but an invitation to consider its contextual nature. Just as the Copernican Revolution didn’t invalidate Earth-based astronomical observations but rather placed them in proper context, acknowledging our scale-bound perspective doesn’t invalidate our physics but helps us understand its scope and limitations.
By recognizing that our particular spatiotemporal scale might not be privileged, we open ourselves to a richer conception of reality—one where each level of description reveals unique aspects of a fundamentally multi-scale universe. Perhaps the true legacy of the Copernican principle is not merely that we occupy no special place, but that there is no special place or scale at all.
BarakBot consists of multiple specialized LLM agents operating within a Telegram bot interface:
Each agent performs well in isolation, but they often need to collaborate. For example, the photo agent might need the scheduler agent to remind a user about an analyzed image. The naive approach—hardcoding direct interactions—quickly becomes unmanageable.
A typical solution is to implement an “agent hub,” a structured interface where agents formally request services from each other. While common in multi-agent systems, this method introduces unnecessary complexity:
This approach felt artificial—unlike how humans coordinate thoughts and actions internally.
The breakthrough came when I reframed the problem from an agent’s perspective. If an agent needed another agent’s help, what would be the most natural way to request it? The answer: do exactly what a human user does—send a message to the bot.
This is related to an interesting observation: while the agents were switching behind the scenes, users didn’t notice the transitions. From the human perspective, the bot remained a singular, coherent entity, even as it dynamically changed between specialized agents. This revealed a key insight: humans naturally maintain a unified mental model of the bot, regardless of its internal complexity.
If the system was coherent enough for users to treat it as one entity, why not let the agents do the same? Instead of addressing specific subcomponents, each agent could simply refer to a single, overarching “assistant”—which, in reality, is just the bot itself. When an agent requires a capability it lacks, it simply asks the bot, which routes the request appropriately—just as it does for human users.
This approach simplifies multi-agent coordination without requiring additional infrastructure, allowing agents to leverage existing communication channels. By treating the bot as a unified entity, both users and agents interact with it in a way that feels natural and coherent.
More broadly, this highlights an interesting parallel between AI coordination and human cognition. Just as people maintain a stable sense of identity despite shifting internal processes, AI agents can function cohesively within a larger system while operating independently behind the scenes.
There is still much to explore, especially in understanding the implications of self-referential communication in AI systems. As BarakBot evolves, these insights will help refine its design and expand its capabilities. For more details, visit the projects page.
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