Unreasonable Effectiveness Research Articles

The unreasonable effectiveness of equilibrium gene regulation through the cell cycle

Systems like the prototypical lac operon can reliably hold repression of transcription upon DNA replication across cell cycles with just 10 repressor molecules per cell and behave as if they were at equilibrium. The origin of this phenomenology is still an unresolved question. Here, we develop a general theory to analyze strong perturbations in quasi-equilibrium systems and use it to quantify the effects of DNA replication in gene regulation. We find a scaling law linking actual with predicted equilibrium transcription via a single kinetic parameter. We show that even the lac operon functions beyond the physical limits of naive regulation through compensatory mechanisms that suppress non-equilibrium effects. Synthetic systems without adjuvant activators, such as the cAMP receptor protein (CRP), lack this reliability. Our results provide a rationale for the function of CRP, beyond just being a tunable activator, as a mitigator of cell cycle perturbations.

The unreasonable effectiveness of early discarding after one epoch in neural network hyperparameter optimization

To reach high performance with deep learning, hyperparameter optimization (HPO) is essential. This process is usually time-consuming due to costly evaluations of neural networks. Early discarding techniques limit the resources granted to unpromising candidates by observing the empirical learning curves and canceling neural network training as soon as the lack of competitiveness of a candidate becomes evident. Despite two decades of research, little is understood about the trade-off between the aggressiveness of discarding and the loss of predictive performance. Our paper studies this trade-off for several commonly used discarding techniques such as successive halving and learning curve extrapolation. Our surprising finding is that these commonly used techniques offer minimal to no added value compared to the simple strategy of discarding after a constant number of epochs of training. The chosen number of epochs mostly depends on the available compute budget. We call this approach i-Epoch (i being the constant number of epochs with which neural networks are trained) and suggest to assess the quality of early discarding techniques by comparing how their Pareto-Front (in consumed training epochs and predictive performance) complement the Pareto-Front of i-Epoch.

The Unreasonable Effectiveness of Algorithms

We calculate the social return on algorithmic interventions (specifically, their marginal value of public funds (MVPF)) across multiple domains of interest to economists—regulation, criminal justice, medicine, and education. Though these algorithms are different, the results are similar and striking. Each one has an MVPF of infinity: not only does it produce large benefits, it provides a “free lunch.” We do not take these numbers to mean these interventions ought to be necessarily scaled but rather that much more research and development should be devoted to developing and carefully evaluating algorithmic solutions to policy problems.

The unreasonable effectiveness of the total quasi-steady state approximation, and its limitations

In this note, we discuss the range of parameters for which the total quasi-steady-state approximation of the Michaelis–Menten reaction mechanism holds validity. We challenge the prevalent notion that total quasi-steady-state approximation is “roughly valid” across all parameters, showing that its validity cannot be assumed, even roughly, across the entire parameter space — when the initial substrate concentration is high. On the positive side, we show that the linearized one-dimensional equation for total substrate is a valid approximation when the initial reduced substrate concentration s0/KM is small. Moreover, we obtain a precise picture of the long-term time course of both substrate and complex

Does the Differential Structure of Space-Time Follow from Physical Principles?

This article examines Wigner's view on the unreasonable effectiveness of mathematics in the natural sciences, which was based on Cantor's claim that 'mathematics is a free creation of the human mind'. It is contended that Cantor's claim is not relevant to physics because it was based on his power set construction, which does not preserve neighborhoods of geometrical points. It is pointed out that the physical notion of Einstein causality can be defined on a countably infinite point set M with no predefined mathematical structure on it, and this definition endows M with a Tychonoff topology. Under Shirota's theorem, M can therefore be embedded as a closed subspace of RJ for some J. While this suggests that the differentiable structure of RJ may follow from the principle of causality, the argument is constrained by the fact that the completion processes (analyzed here in some detail) required for the passage from QJ to RJ remain empirically untestable.

Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems

The fully nonlinear notion of resonance−geometrical resonance−in the general context of dissipative systems subjected to spatially periodic phase-modulated potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system’s energy when the potential is stationary. The geometrical resonance solutions represent a local symmetry whose critical breaking leads to a new analytical criterion for the onset of chaotic instabilities. This physical criterion is deduced in the co-moving frame from the local energy conservation over the shortest significant timescale. Remarkably, the new physical criterion for the onset of chaotic instabilities is shown to be valid over large regions of parameter space, thus being useful beyond the scope of current mathematical techniques. More importantly, the present theory helps to understand the unreasonable effectiveness of the Melnikov’s method beyond the perturbative regime.

The Unreasonable Effectiveness of Algorithms

The Unreasonable Effectiveness of Algorithms

The Unreasonable Effectiveness of Algorithms

The Unreasonable Effectiveness of Algorithms

The applicability of the concept of the field of rationality in the explanation of the fundamental role of symmetries in physics

The introduction of the concept of the field of rationality and its correlates (the field of potentiality and the formal field) by Józef Życiński and Michał (Michael) Heller opened up space for the philosophical explanation of the unreasonable effectiveness of mathematics in capturing regularities built into the physical reality. The presented study is a response to the clear incentive of these authors towards the development of the understanding and applicability of these concepts. It is argued that identifying symmetries within the field of rationality not only helps to articulate the fundamental role of symmetries in physics but also provides a better grasp on the issue of potentialities for the emergence of complexity in the Universe. Additionally, some global properties of this field can be more deeply comprehended. By indicating the drawbacks and limitations of this approach, perspectives for further inquiry into the meaning and usefulness are suggested.

The Unreasonable Effectiveness of Physics in Mathematics

The Unreasonable Effectiveness of Physics in Mathematics

The unreasonable effectiveness of large language models in zero-shot semantic annotation of legal texts.

The emergence of ChatGPT has sensitized the general public, including the legal profession, to large language models' (LLMs) potential uses (e.g., document drafting, question answering, and summarization). Although recent studies have shown how well the technology performs in diverse semantic annotation tasks focused on legal texts, an influx of newer, more capable (GPT-4) or cost-effective (GPT-3.5-turbo) models requires another analysis. This paper addresses recent developments in the ability of LLMs to semantically annotate legal texts in zero-shot learning settings. Given the transition to mature generative AI systems, we examine the performance of GPT-4 and GPT-3.5-turbo(-16k), comparing it to the previous generation of GPT models, on three legal text annotation tasks involving diverse documents such as adjudicatory opinions, contractual clauses, or statutory provisions. We also compare the models' performance and cost to better understand the trade-offs. We found that the GPT-4 model clearly outperforms the GPT-3.5 models on two of the three tasks. The cost-effective GPT-3.5-turbo matches the performance of the 20× more expensive text-davinci-003 model. While one can annotate multiple data points within a single prompt, the performance degrades as the size of the batch increases. This work provides valuable information relevant for many practical applications (e.g., in contract review) and research projects (e.g., in empirical legal studies). Legal scholars and practicing lawyers alike can leverage these findings to guide their decisions in integrating LLMs in a wide range of workflows involving semantic annotation of legal texts.

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning.

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

The Unreasonable Effectiveness of Deep Evidential Regression

There is a significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware regression-based neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, notably with the capabilities to disentangle aleatoric and epistemic uncertainties. Despite some empirical success of Deep Evidential Regression (DER), there are important gaps in the mathematical foundation that raise the question of why the proposed technique seemingly works. We detail the theoretical shortcomings and analyze the performance on synthetic and real-world data sets, showing that Deep Evidential Regression is a heuristic rather than an exact uncertainty quantification. We go on to discuss corrections and redefinitions of how aleatoric and epistemic uncertainties should be extracted from NNs.

Fractals: The Secret Code of Creation

Fractals: The Secret Code of Creation

What’s the Use? The Unreasonable Effectiveness of Mathematics by Ian Stewart

What’s the Use? The Unreasonable Effectiveness of Mathematics by Ian Stewart

Борьба сомнения с созерцанием: к ситуации в современной философии математики

The article deals with the concept of intuition (ϑεωρία, intuitio, Anschauung, Wesensschau) and the method of doubt in the philosophy of mathematics from Antiquity to the present day. In the classical philosophy of mathematics, there was no doubt about the attainability of reliable mathematical knowledge. Doubt was always present, but did not claim to deconstruct contemplation. The objects of contemplation are either the higher world of “ideas” (Plato, Neoplatonists), or innate ideas (René Descartes, Gottfried Leibniz), or a priori forms (Immanuel Kant), or something mysterious, perhaps the subconscious (Henri Poincaré). Edmund Husserl was the last classical philosopher to require intuition, and Kurt Gödel was the last mathematician. Modern mathematics is characterized by a departure from intuition, and therefore the philosophy of mathematics has fundamentally changed: now intuition is being questioned. The article provides a brief overview of the history of doubt, from Plato to the triumph of doubt in the second half of the 19th and early 20th centuries. The overthrow of intuition occurs in the works of Hans Hahn, Ludwig Wittgenstein, David Bloor and modern nominalists (Hartry Field). Often, intuition is replaced by a formal conclusion, logic, as was the case with Poincaré and David Hilbert. However, the deconstruction of intuition has deeper implications for the philosophy of mathematics than replacing it with logic. Logic, in turn, also needs to be justified. Why are modus ponens and the substitution rule considered reliable formal operations? Here logical evidence comes into play: Husserl showed that it is also a kind of intuition. However nothing should be obvious, including the simplest formal operations should be considered as purely conventional. What philosophy of mathematics awaits us in the future? The article makes the assumption that mathematics will be considered as a kind of game according to arbitrary rules. This is the current trend of its development. However, this trend is contradicted by the problem of applications of mathematics and Eugene Wigner’s riddle of “the unreasonable effectiveness of mathematics in the natural sciences.”

The Vacuum as Imaginary Space. The Unreasonable Effectiveness of Complex Numbers

The background to the article is the classic and quantum understandings of the vacuum and the use of imaginary numbers in quantum models. The purpose of the article is to outline the possible understanding of the vacuum as imaginary space always coupled with the real space in the complex space of complex numbers. This understanding relates to the duality real-potential, collapsed–collapsible, and superimpositions of waves-phenomena as in quantum mechanics. The incomputability of the imaginary parts may represent the physical meaning of the permanent potential pending nature of the vacuum. The presence of imaginary numbers in models may be intended as warranty that it is not possible to compute definitive results, but it is possible to have pending multiple equivalences and superimpositions as in quantum physics and emergent collective processes in complexity. We consider how much the complexity (i.e., the study of emergence and chaos) may be considered related to and represented by complex numbers (i.e., properties of their dual variables and their collapsibility in real numbers). The usage of imaginary numbers may also be intended as the expression or manifestation of something we do not understand yet, as it was for the indemonstrability of the fifth Euclidian postulate and the unavailability of a distribution law for prime numbers. We conclude that a new global understanding is necessary and capable of explaining what we understand as the unreasonable effectiveness of complex numbers.

The Unreasonable Effectiveness of the Chaotic Tent Map in Engineering Applications

From decimal expansion of real numbers to complex behaviour in physical, biological and human-made systems, deterministic chaos is ubiquitous. One of the simplest examples of a nonlinear dynamical system that exhibits chaos is the well known 1-dimensional piecewise linear Tent map. The Tent map (and their skewed cousins) are instances of a larger family of maps namely Generalized Luröth Series (GLS) which are studied for their rich number theoretic and ergodic properties. In this work, we discuss the unreasonable effectiveness of the Tent map and their generalizations (GLS maps) in a number of applications in electronics, communication and computer engineering. To list a few of these applications: (a) GLS-coding: a lossless data compression algorithm for i.i.d sources is Shannon optimal and is in fact a generalization of the popular Arithmetic Coding algorithm used in the image compression standard JPEG2000; (b) GLS maps are used as neurons in the recently proposed Neurochaos Learning architecture which delivers state-of-the-art performance in classification tasks; (c) GLS maps are ideal candidates for chaos-based computing since they can simulate XOR, NAND and other gates and for dense storage of information for efficient search and retrieval; (d) Noise-resistant versions of GLS maps are useful for signal multiplexing in the presence of noise and error detection; (e) GLS maps are shown to be useful in a number of cryptographic protocols - for joint compression and encryption and also for generating pseudo-random numbers. The unique properties and rich features of the Tent Map (GLS maps) that enable these wide variety of engineering applications will be investigated. A list of open problems are indicated as well.

Vedic Hridaya Chakshu : Why is mathematics so effective in Exploring Nature

Mathematics rightly viewed, wrote Russell in his 'Study of Mathematics', 'possesses not only truth, but supreme beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." The physicist Eugene Wigner once remarked that [t]he miracle of the appropriateness of the language of mathematics for the formulation of the laws of (Nature) physics is a wonderful gift which we neither understand nor deserve.' Steven Weinberg is another physicist puzzled with it, put, "It is very strange that mathematicians are led by their sense of mathematical beauty to develop formal structures that physicists only later find useful, even where the mathematician had no such goal in mind." The question is , how does the mathematician, who is more like an artist than an explorer, while working in abstract, away from nature, arrive at the most appropriate descriptions of nature? Nearly 82 years ago, Eugene Wigner set the puzzle up in his famous paper to call it "the unreasonable effectiveness of mathematics". It is a puzzle well known to the scientists and philosophers, but caught very little attention in the philosophical literature, which may be due to the presuppositions in the paradigm shift from a formalist philosophy of mathematics, and the rise of anti-realist paradigm in the philosophy of Mathematics. Whatever it may be, but when we look at the issue from our Vedic perspective, we find that the Vedas and Brahmanas provide irrefutable foundations where there can be no place for this so-called puzzle. In this paper we present some of the key ideas from the Vedas and Shatpath Brahmana, which provide the very foundation, a misunderstanding, of which leads to such a puzzle.

Swap Rate fallback: unreasonable effectiveness of approximations and alternatives

Observes that cash-settled swaptions with collateral discounting are impacted by the Swap Rate fallback mechanisms decided by working groups/ISDA. The legacy vanilla swaptions are becoming exotic products, as the mechanism is based on a non-linear transformation of the OIS swap rate, and generate convexity adjustments. It turns out that those two effects almost cancel each other and lead to almost vanilla products. Henrard analyses those cancelling effects and the risk management impacts. Based on those insights, Henrard proposes an adjusted fallback mechanism that reduces further the exotic features and simplifies further the risk management of the legacy book.