Nosimpler

A general account of how diverse states of consciousness arise from brain activity requires a quantitative framework that generalises across them. The Entropic Brain Theory proposes that states of consciousness can be ordered along a single dimension defined by the entropy of spontaneous neural activity, but this prediction has not been tested across pharmacological and clinical perturbations within a common analytical pipeline. Here we quantify the temporal ir-regularity of time-resolved small-world topology using sample entropy, applying the same pipeline to pharmacological (psychedelics, modafinil, propofol anaesthesia) and clinical (schizophrenia) fMRI datasets. Propofol anaesthesia occu-pied the low-entropy end of the axis; psychedelic states and schizophrenia occupied the high end. The ordering tracks combined modulations of the level and content of consciousness, ranging from reduced awareness under anaesthesia to the heightened arousal and expanded experience of psychedelic states and the disorganised, dysregulated processing of schizophrenia. Crucially, this result was not reducible to fluctuations in mean functional connectivity, and was sup-ported by convergent reorganisation of higher-order association cortex under psychedelics and anaesthesia, alongside a distributed loss of network specificity in schizophrenia. These findings provide cross-condition empirical support for an entropic continuum of brain states and identify the temporal diversity of large-scale network reconfiguration as a primary axis of conscious dynamics.

arXiv:2606.15120v1 Announce Type: new Abstract: The slogan ``information is physical,'' introduced by Rolf Landauer and developed through quantum information theory and black-hole thermodynamics, has achieved near-axiomatic status in modern physics. Yet the ontological status of information remains surprisingly underexamined: most discussions either reduce information to a form of energy or treat it as a purely mathematical object. This paper proposes a third position. I argue that information is neither a physical substance nor a free-floating abstraction, but rather \emph{the structure of physically realizable alternatives} -- a counterfactual structure that a physical system instantiates in virtue of the possibility space available to it. Building on Shannon's combinatorial definition, the Landauer principle, the no-cloning theorem, and the black-hole information paradox, I show that the informational content of any physical event is constituted by the set of outcomes that \emph{could have occurred} but did not. This counterfactual reading dissolves several persistent confusions: it explains why erasing information dissipates heat without making information ``material,'' why quantum superposition is informationally richer than any classical mixture, and why information loss in black holes is physically significant beyond mere bookkeeping. The proposal sits within a structural-realist framework but departs from standard structural realism by locating the relevant structure in modal, not merely actual, relations. I conclude by sketching implications for the foundations of quantum mechanics, quantum gravity, and scientific ontology more broadly.

arXiv:2606.17965v1 Announce Type: cross Abstract: According to the recent Wealth Thermalization Hypothesis (WTH) the wealth inequality in the world is described by the Rayleigh-Jeans (RJ) thermal distribution of interacting agents in a society with social stratification. In this concept, the wealth layers of society are associated with energy levels from a nonlinear dynamical system conserving two integrals of motion being total energy and probability norm. This leads to RJ condensation and the formation of a huge poverty phase of low wealth and a tiny oligarchic phase that captures a main part of total society wealth. This RJ phenomenon has similarities with self cleaning in multimode optical fibers and constraint driven condensation in various physical systems. We analyze real Lorenz and Pareto curves for wealth of households in countries and the world, Gross Domestic Product of countries, market capitalization of companies at stock exchange of Hong Kong, Shanghai, London, bitcoin transactions, world trade between countries and show that the WTH theory gives a good description of these curves. On the basis of this comparison we argue that the RJ thermal distribution provides a universal description of wealth inequality in the world.

Proceedings of the National Academy of Sciences, Volume 123, Issue 24, June 2026.
SignificanceStepping into a new visual environment, we immediately start to explore that environment with our eyes. What factors shape how we selectively allocate our attention? Participants explored 360°, real-world environments while their gaze was ...

Proceedings of the National Academy of Sciences, Volume 123, Issue 24, June 2026.
SignificanceThe Whorfian hypothesis posits that basic language categories alter one’s perception of the world in a fundamental manner. Some of the most compelling evidence in favor of this hypothesis came from electrophysiological responses that indicated ...

Proceedings of the National Academy of Sciences, Volume 123, Issue 23, June 2026.
SignificanceTwo-sample testing examines whether two probability distributions on some feature space differ based on random samples. It is fundamental in statistics and machine learning, especially when feature spaces are complex. Such settings are ...

Phensy et al. show that prefrontal gamma activity is composed of multiple, cell-type-specific synchrony patterns that differentially manifest during decision-making and outcome periods and track changes in behavioral strategies. These patterns offer a new framework for understanding cognitive flexibility and its disruption in disorders such as schizophrenia.

How does the brain navigate uncertainty in a dynamic environment? In this study, Hosford, Mei, et al. show that computations implemented across a network of thalamic and cortical circuits continuously update internal representations of recent experiences to help mice make decisions based on limited or ambiguous information.

Nature, Published online: 27 May 2026; doi:10.1038/s41586-026-10496-6

Uniformly doped, ultrathin single-crystalline silicon nanomembranes can be vertically stacked at low temperature using a roll-transfer-printing process that is scalable to wafer scale and tolerant to substrate topology and surface roughness for constructing high-performance monolithic three-dimensional integrated circuits.

arXiv:2605.27159v1 Announce Type: new Abstract: In this work, we establish a direct connection between supplemented Dyck language and the signed expectation value of chains of second quantization operators relatively to the physical vacuum and relatively to a one-determinant state. Inspired by the fact that Dyck language provides an example of the emergence of the Catalan numbers in linguistic framework analysis, we show that these numbers are central when numbering the terms remaining when eliminating vanishing contributions detected by our application of Dyck language to fermionic second quantization. From the translation of creation and annihilation operator - or of pairs of operators - into a bracket alphabet, we derive simple and intuitive sufficient conditions for the nullity of expectation values that does not require an explicit application of Wick's theorem. This is done here with respect to the physical vacuum or relatively to a one-determinant state. We also extend this translation into a diagrammatic framework that allows a visual determination of the signature of fully contracted terms, reproducing the results of Wick's theorem. This approach has been extended to the case of (nested) commutators of pairs of fermionic second quantization including at least one excitation or deexcitation operator. Our results have been implemented in a software, MobiDyck, whose source code is freely available on the web. The algorithmic approach inspired by our work on Dyck language is detailed in this paper. Finally, a comparison of our diagrammatic approach with Goldstone diagrams is provided and closes the article.

Nature Neuroscience, Published online: 25 May 2026; doi:10.1038/s41593-026-02314-z

Lozano et al. show that REM sleep is gated by low-dimensional brainstem network dynamics, in which opposing neuron populations across the midbrain and pons determine when transitions into REM sleep can occur.

During wakefulness, neuromodulators operate largely independently to support behavior and cognition. By contrast, sleep reorganizes their activity into a coordinated brain rhythm. During sleep, the major neuromodulators—norepinephrine, acetylcholine, ...

Theo Baker spills Silicon Valley secrets and revisits his efforts to expose a shocking breach of research integrity

Stereoisomers of C13Cl2 exhibiting helical orbitals around a ring of carbon atoms were synthesized by atom manipulation on NaCl surfaces. We resolved the enantiomeric geometries of the singlet states by atomic force microscopy and mapped their helical ...

Speech requires precise serial ordering of words and phonemes into novel combinations. To accomplish this, the brain is believed to flexibly prepare utterances before producing them, even allowing pronunciation of never-before spoken words. To discover how neural populations achieve this, intracortical activity from premotor cortex was recorded while two speech neuroprosthesis pilot clinical trial participants attempted to speak factorially-balanced phoneme sequences. During preparation, activity encoded not only the next-phoneme, but multiple upcoming phoneme positions spanning whole words. We found that word-level plans were formed by compositionally combining phoneme representations, a mechanism that may enable efficient planning of novel sequences. When utterances contained more than one word, premotor cortex activity was largely limited to the first word, suggesting that articulatory planning is segmented by higher-order features. Together, these results reveal a compositional, hierarchically-segemented planning geometry, potentially a universal neural strategy for sequence organization across higher levels of language.

Gene syntax—the order and arrangement of genes and their regulatory elements—shapes the dynamic coordination of both natural and synthetic gene circuits. Transcription at one locus perturbs the transcription of adjacent genes, but the molecular basis of ...

Natural image representations are distributed across many dimensions of visual cortex activity, but little is known about how the multidimensional structure of these representations evolves over time following stimulus onset. Here we examined the temporal dynamics and latent dimensional structure of natural object representations in large-scale EEG and MEG data. We also compared these data with leading representational models derived from large-scale human similarity judgments and deep neural networks. Our findings reveal a rapid expansion of stimulus dimensionality in the brain, which peaks within 100 milliseconds and gradually decays over hundreds of milliseconds. The dynamics of these dimensionality changes tracked the decoding accuracy for both behavioral embeddings and neural network features, suggesting that dimensionality may be a general indicator of representational expressivity. Interestingly, the dimensionality of the neural representations could not be fully explained by leading behavior-based or neural network models. Follow-up experiments showed that the remaining neural variance carried additional perceptually relevant information not yet explained by leading models. Together, these findings reveal previously unrecognized complexity in measurements of dynamic human brain responses to natural objects.

Nature, Published online: 22 April 2026; doi:10.1038/d41586-026-01338-6

Webs of star-shaped cells called astrocytes connect distant parts of the brain, allowing long-distance exchange of molecules.

Recent studies describe Eye Movement-related Eardrum Oscillations (EMREOs), low-frequency signals recorded in the ear canal that arise from the tympanic membrane and are triggered by saccadic eye movements. Because EMREOs are thought to arise from motor elements in the peripheral auditory system, we examined how two known modulators of these elements affect the EMREO time course. First, the activity of outer hair cells (OHC) can be suppressed by the medial olivocochlear reflex (MOCR). If OHCs contribute to the generation of EMREOs, activation of this reflex should reduce EMREO amplitude. To test this, we compared EMREO amplitudes elicited by saccades performed in silence and in the presence of contralateral noise. Second, gravitational cues linked to head orientation may influence EMREOs via oculomotor control circuits that possibly modulate middle ear muscles. To test this, we recorded EMREOs while participants made saccades with their head upright (0 degrees azimuth) and with their head tilted 30 degrees in either direction. Across both experiments our data reveal no clear modulation of the EMREO time course by these experimental manipulations. Together with other recent studies these findings advocate for a stability of the EMREO time course towards multiple experimental modulations and fuel speculations that the signal may serve as a temporal reference frame when combining signals across the senses.

Proceedings of the National Academy of Sciences, Volume 123, Issue 16, April 2026.
SignificanceWe present sparse identification of nonlinear dynamics with shallow recurrent decoders (SINDy-SHRED), which jointly solves the sensing, model reduction and model identification problem with simple implementation, efficient computation, and ...

Author(s): Gabriel Sorci, Joshua Foo, Dietrich Leibfried, Christian Sanner, and Igor Pikovski

High-precision clocks based on quantum systems will work in a regime where a quantum description of proper time might be necessary.

[Phys. Rev. Lett. 136, 163602] Published Mon Apr 20, 2026

The impressive progresses in machine learning have revived the fear that humans might eventually be wiped out or enslaved by artificial superintelligences. This is hardly a new fear. For example, this fear is the basis of most of Isaac Asimov’s books, who imagined that robots are built with three laws to protect humans.

My point here is not to demonstrate that such events are impossible. On the contrary, my point is that autonomous human-made entities already exist, and cause the exact same risks that AI alarmists are talking about, except they are real. In this context, evil AI fantasies are an anthropomorphic distraction.

Let me quickly dismiss some misconceptions. Does ChatGPT understand language? Of course not. Large language models are (essentially) algorithms tuned to predict the next words. But here we don’t mean “word” in the human sense. In the human sense, a word is a symbol that means something. In the computer sense, a word is a symbol, to which we humans attribute meaning. When ChatGPT talks about bananas, it has no idea what a banana tastes like (well, it has no idea). It has never seen a banana or tasted a banana (well, it has never seen or tasted). “Banana” is just a node in a big graph of other nodes, totally disconnected from the outside world, and in particular from what “banana” might actually refer to. This is known in cognitive science as the “symbol grounding problem”, and it is a difficult problem that LLMs do not solve. So, maybe LLMs “understand” language, but only if you are willing to define “understand” in such a way that it is not required to know what words mean.

Machine learning algorithms are not biological organisms, they do not perceive, they are not conscious, they do not have intentions in the human sense. But it doesn’t matter. The broader worry about AI is simply that these algorithms are generally designed so as to optimize some predefined criterion (e.g., prediction error), and if we give them very powerful means to do so, in particular means that involve real actions in the world, then who knows whether using those means might not be harmful to us? At some point, without necessarily postulating any kind of evil mind, we humans might become means in the achievement of some optimization criterion. We built some technical goals into the machine, but it is very difficult to ensure that those are aligned with human values. This is the so-called “alignment” problem.

Why not. We are clearly not there, but maybe, in a hypothetical future, or at least as a thought experiment. But what strikes me with the misalignment narrative is that this scenario is not at all hypothetical if you are willing to look beyond anthropomorphic evil robots. Have you really never heard of any human-made entities with their own goals, which might be misaligned with human values? Entities that are powerful and hard to control by humans?

There is an obvious answer if you look at the social rather than technological domain: it is the modern financialized multinational corporation. The modern corporation is a human-made organization that is designed in such a way as to maximize profit. It does not have intentions or goals in a human sense, but exactly like in the AI alignment narrative, it is simply designed in such a way that it will use all means available in order to maximize a predefined criterion, which may or may not be perfectly aligned with human values. Let’s call these companies “profit robots”.

To what extent are profit robots autonomous from humans? Today’s modern large corporations are owned not by people but in majority by institutional stakeholders, such as mutual funds, i.e., other organizations with the same goals. As is well known, their multinational nature makes them largely immune to the legislation of states (hence the issues of fiscal optimization, social dumping, etc). As is also well known, a large part of the resources of a profit robot is devoted to marketing and advertisement, that is, in manipulating humans into buying their products.

Profit robots also engage in intense lobbying to bend human laws in their favor. But more to the point, the very notion of law is not the same for a profit robot as for humans. For humans, a law is something that sets boundaries on what could be done or should not be done, morally. But a profit robot is not a person. It has no moral principles. So, law is just one particular constraint, in fact a financial cost or risk – a company does not go to prison. A striking example of this is the “Dieselgate”: Volkswagen (also not owned by humans) intentionally programmed their engines so that their car emissions remained hidden during the pollution tests required to authorize their cars on the US market. As far as I know, shareholders were not informed, and neither were consumers. The company autonomously decided to break the law for profit. Again, the company is not evil: it is not a person. It behaves in this non-human way because it is a robot, exactly like in the AI misalignment narrative.

We often hear that ultimately, it is the consumers who have power, by deciding what to buy. This is simply false. Consumers did not know that Volkswagen cheated on pollution tests. Consumers rarely know in what exact conditions the products are made, or even to what corporation the products belong. This type of crucial information is deliberately hidden. Profit robots, on the other hand, actively manipulate consumers into buying their products. What to think of planned obsolescence? Nobody wants products that are deliberately designed to break down prematurely, yet that is what a profit robot makes. So yes, profit robots are largely autonomous from the human community.

Are profit robots an existential risk for humans? That might be a bit dramatic, but they certainly do cause very significant risks. A particular distressing fact illustrates this. As the Arctic ice melts because of global warming, oil companies get ready to drill the newly available resources. Clearly this is not in the interest of humans, but this is what a company like Shell, who is only directly owned by humans in the proportion of 6%, needs to do to pursue its goals, which as any other profit robot, is to generate profit by whatever means.

So yes, there is a risk that powerful human-made entities get out of control and that their goals are misaligned with human values. This worry is reasonable because it is already realized, except not in the technological domain. It is ironic (but not so surprising) that billionaires buy into the AI misalignment narrative but fail to see that the same narrative fully applies to the companies that their wealth depends on, except it is realized.

The reasonable worry about AI is not that AI takes control of the world: the worry is that AI provides even more powerful means for the misaligned robots that are already out of control now. In this context, evil AI fantasies are an anthropomorphic distraction from the actual problems we have already created.

Yesterday I had a great conversation with Dmitri Tymoczko about groupoids in music theory. But at this Higgs Centre Colloquium, he preferred to downplay groupoids and talk in a way physicists would enjoy more. Click here to watch his talk!

What’s great is that Tymoczkyo not faking it: he’s really found deep ways in which symmetry shows up pervasively in music.

At first he tried to describe them geometrically using orbifolds, which are spaces in which some singular points have nontrivial symmetry groups, like the tip of a cone formed by modding out the plane by the action of the group ℤ/n\mathbb{Z}/n. But then he realized that the geometry was less important than the symmetry, which you can describe using groupoids. That’s why his talk is called “Beyond the geometry of music”.

I’m helping him with his work on groupoids, and I hope he explains his work to mathematicians someday without pulling his punches. I didn’t get to interview him yesterday, but I’ll try to do that soon.

For now you can read his books A Geometry of Music and Harmony: an Owner’s Manual along with many papers. What I’ve read so far is really exciting.

The principle of explosion is that in an inconsistent system everything is provable: if you prove both and not- for any , you can then conclude for any :

$$(P \land \lnot P) \to Q.$$

This is, to put it briefly, not intuitive. But it is awfully hard to get rid of because it appears to follow immediately from two principles that are intuitive:

1. If we can prove that is true, then we can prove that at least one of or is true. (In symbols, .)

2. If we can prove that at least one of or is true, and we can prove that is false, then we may conclude that that is true. (Symbolically, .).

Then suppose that we have proved that is both true and false. Since we have proved true, we have proved that at least one of or is true. But because we have also proved that is false, we may conclude that is true. Q.E.D.

This proof is as simple as can be. If you want to get rid of this, you have a hard road ahead of you. You have to follow Graham Priest into the wilderness of paraconsistent logic.

Raymond Smullyan observes that although logic is supposed to model ordinary reasoning, it really falls down here. Nobody, on discovering the fact that they hold contradictory beliefs, or even a false one, concludes that therefore they must believe everything. In fact, says Smullyan, almost everyone does hold contradictory beliefs. His argument goes like this:

1. Consider all the things I believe individually, . I believe each of these, considered separately, is true.

2. However, I also believe that I'm not infallible, and that at least one of is false, although I don't know which ones.

3. Therefore I believe both (because I believe each of the separately) and (because I believe that not all the are true).

And therefore, by the principle of explosion, I ought to believe that I believe absolutely everything.

Well anyway, none of that was exactly what I planned to write about. I was pleased because I noticed a very simple, specific example of something I believed that was clearly inconsistent. Today I learned that K2, the second-highest mountain in the world, is in Asia, near the border of Pakistan and westernmost China. I was surprised by this, because I had thought that K2 was in Kenya somewhere.

But I also knew that the highest mountain in Africa was Kilimanjaro. So my simultaneous beliefs were flatly contradictory:

1. K2 is the second-highest mountain in the world.
2. Kilimanjaro is not the highest mountain in the world, but it is the highest mountain in Africa
3. K2 is in Africa

Well, I guess until this morning I must have believed everything!

The Law of Excluded Middle says that for any statement P, “P or not P” is true.

Is this law true? In classical logic it is. But in intuitionistic logic it’s not.

So, in intuitionistic logic we can ask what’s the probability that a randomly chosen statement obeys the Law of Excluded Middle. And the answer is “at most 2/3—or else your logic is classical”.

This is a very nice new result by Benjamin Bumpus and Zoltan Kocsis:

• Benjamin Bumpus, Degree of classicality, Merlin’s Notebook, 27 February 2024.

Of course they had to make this more precise before proving it. Just as classical logic is described by Boolean algebras, intuitionistic logic is described by something a bit more general: Heyting algebras. They proved that in a finite Heyting algebra, if more than 2/3 of the statements obey the Law of Excluded Middle, then it must be a Boolean algebra!

Interestingly, nothing like this is true for “not not P implies P”. They showed this can hold for an arbitrarily high fraction of statements in a Heyting algebra that is still not Boolean.

Here’s a piece of the free Heyting algebra on one generator, which some call the Rieger–Nishimura lattice:

I disagree with this statement, but boy, Hilbert sure could write!

We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. As a by-product, a topological classifier is defined that uses an open sub-covering of the data set. This sub-covering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.

Primates can recognize objects despite 3D geometric variations such as in-depth rotations. The computational mechanisms that give rise to such invariances are yet to be fully understood. A curious case of partial invariance occurs in the macaque face-patch AL and in fully connected layers of deep convolutional networks in which neurons respond similarly to mirror-symmetric views (e.g., left and right profiles). Why does this tuning develop? Here, we propose a simple learning-driven explanation for mirror-symmetric viewpoint tuning. We show that mirror-symmetric viewpoint tuning for faces emerges in the fully connected layers of convolutional deep neural networks trained on object recognition tasks, even when the training dataset does not include faces. First, using 3D objects rendered from multiple views as test stimuli, we demonstrate that mirror-symmetric viewpoint tuning in convolutional neural network models is not unique to faces: it emerges for multiple object categories with bilateral symmetry. Second, we show why this invariance emerges in the models. Learning to discriminate among bilaterally symmetric object categories induces reflection-equivariant intermediate representations. AL-like mirror-symmetric tuning is achieved when such equivariant responses are spatially pooled by downstream units with sufficiently large receptive fields. These results explain how mirror-symmetric viewpoint tuning can emerge in neural networks, providing a theory of how they might emerge in the primate brain. Our theory predicts that mirror-symmetric viewpoint tuning can emerge as a consequence of exposure to bilaterally symmetric objects beyond the category of faces, and that it can generalize beyond previously experienced object categories.

In a dynamical systems description of spatiotemporally chaotic PDEs including those describing turbulence, chaos is viewed as a trajectory evolving within a network of non-chaotic, dynamically unstable, time-invariant solutions embedded in the chaotic attractor of the system. While equilibria, periodic orbits and invariant tori can be constructed using existing methods, computations of heteroclinic and homoclinic connections mediating the evolution between the former invariant solutions remain challenging. We propose a robust matrix-free variational method for computing connecting orbits between equilibrium solutions of a dynamical system that can be applied to high-dimensional problems. Instead of a common shooting-based approach, we define a minimization problem in the space of smooth state space curves that connect the two equilibria with a cost function measuring the deviation of a connecting curve from an integral curve of the vector field. Minimization deforms a trial curve until, at a global minimum, a connecting orbit is obtained. The method is robust, has no limitation on the dimension of the unstable manifold at the origin equilibrium, and does not suffer from exponential error amplification associated with time-marching a chaotic system. Owing to adjoint-based minimization techniques, no Jacobian matrices need to be constructed and the memory requirement scales linearly with the size of the problem. The robustness of the method is demonstrated for the one-dimensional Kuramoto-Sivashinsky equation.

Memories initially formed in hippocampus gradually stabilize to cortex, over weeks-to-months, for long-term storage. The mechanistic details of this brain re-organization process remain poorly understood. In this study, we developed a virtual-reality based behavioral task and observed neural activity patterns associated with memory reorganization and stabilization over weeks-long timescales. Initial photometry recordings in circuits that link hippocampus and cortex revealed a unique and prominent neural correlate of memory in anterior thalamus that emerged in training and persisted for several weeks. Inhibition of the anteromedial thalamus-to-anterior cingulate cortex projections during training resulted in substantial memory consolidation deficits, and gain amplification more strikingly, was sufficient to enhance consolidation of otherwise unconsolidated memories. To provide mechanistic insights, we developed a new behavioral task where mice form two memories, of which only the more salient memory is consolidated, and also a technology for simultaneous and longitudinal cellular resolution imaging of hippocampus, thalamus, and cortex throughout the consolidation window. We found that whereas hippocampus equally encodes multiple memories, the anteromedial thalamus forms preferential tuning to salient memories, and establishes inter-regional correlations with cortex, that are critical for synchronizing and stabilizing cortical representations at remote time. Indeed, inhibition of this thalamo-cortical circuit while imaging in cortex reveals loss of contextual tuning and ensemble synchrony in anterior cingulate, together with behavioral deficits in remote memory retrieval. We thus identify a thalamo-cortical circuit that gates memory consolidation and propose a mechanism suitable for the selection and stabilization of hippocampal memories into longer term cortical storage.