19 papers · ranked by Valyu relevance
Marie Amalric, Liping Wang, Pierre Pica, Santiago Figueira + 3 more
'Mariano Sigman' 'Stanislas Dehaene' 'Randy Gallistel'] During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel…
S. Romano, A. Salles, M. Amalric, S. Dehaene + 2 more
Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of…
Sergio Romano, Alejo Salles, Marie Amalric, Stanislas Dehaene + 3 more
'Mariano Sigman' 'Santiago Figueira' 'Zaid Abdo'] Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share…
Stanislas Dehaene, Mathias Sablé-Meyer, Lorenzo Ciccione
Concepts of exact number are often thought to originate from counting and the successor function, or from a refinement of the approximate number system (ANS). We argue here for a third origin: a shared language-of-thought (LoT) for geometry and arithmetic that involves primitives of repetition, concatenation, and…
Trieu H. Trinh, Yuhuai Wu, Quoc V. Le, He He + 1 more
Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning1-4, owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to…
Guo, Hongyu
Tarski's first-order axiom system E 2 for Euclidean geometry is notable for its completeness and decidability. However, the Pythagorean theorem—either in its modern algebraic form a 2 + b 2 = c 2 or in Euclid's Elements—cannot be directly expressed in E2, since neither distance nor area is a primitive notion in the…
Mathias Sablé-Meyer, Lucas Benjamin, Cassandra Potier Watkins, Chenxi He + 4 more
The perception and production of regular geometric shapes, a characteristic trait of human cultures since prehistory, has unknown neural mechanisms. Behavioral studies suggest that humans are attuned to discrete regularities such as symmetries and parallelism, and rely on their combinations to encode regular geometric…
Shuang Tian, Xiaomin Mao, Dahui Wang, Xiaoying Wang + 1 more
Perception and mental imagery are widely thought to rely on overlapping neural representations, giving rise to perception-like visual experiences during imagery generation. However, such overlap, by itself, is agnostic to the nature of the underlying neural geometry for both perception and imagery. Here we addressed…
Loe Feijs
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal grammar or a mechanism which explains significant aspects of the human faculty of…
Günther Eder
The aim of this article is to contribute to a better understanding of Frege’s views on semantics and metatheory by looking at his take on several themes in nineteenth century geometry that were significant for the development of modern model-theoretic semantics. I will focus on three issues in which a central semantic…
Xinyuan Yan, Aaditya Krishna, Katie Van Arsdel, Ivy Gautam + 19 more
The human brain has the remarkable ability to understand and express similar concepts in multiple languages. To understand how it does so, we examined responses of hippocampal neurons during passive listening, directed speaking, and spontaneous conversation, in both English and Spanish, in a small group of balanced…
Eldar Straume
This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical differential geometry came to an end, and the Riemannian geometric approach started to be developed. Moreover, the discovery of…
John T. Baldwin
We distinguish the axiomatic study of proofs in geometry from study about geometry from general axioms for mathematics. We briefly report on an abuse of that distinction and its unfortunate effect on US high school education. We review a number of 20th century approaches to synthetic geometry. In doing so, we…
Henryk Fukś
In three articles [1, 2, 3] published in CNJ in 2012 and 2016 (updated author's versions available on arxiv.org), we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation (long overdue) of this cycle. It tells the story of selected important developments in the…
Semir Zeki, Zachary F Hale, Ahmad Beyh, Samuel E Rasche
There are different definitions of axioms, but the one that seems to have general approval is that axioms are statements whose truths are universally accepted but cannot be proven; they are the foundation from which further propositional truths are derived. Previous attempts, led by David Hilbert, to show that all of…
Suniyya A. Waraich, Jonathan D. Victor
Low-level features are typically continuous (e.g., the gamut between two colors), but semantic information is often categorical (there is no corresponding gradient between dog and turtle) and hierarchical (animals live in land, water, or air). To determine the impact of these differences on cognitive representations…
Authors not listed
Previously we posited that a systematic and general description of stereoisomerism could be based upon the principles of the polytopal rearrangement model. The most daunting challenge to this end is to comprehensively describe all possible geometries for arbitrary n-coordinate centres, ABn, and for this we have…
Authors not listed
The range of geometric configurations possible for an arbitrary coordination centre ABn, is a key aspect of stereoisomerism and molecular geometry in general. Despite this, much focus within Chemistry concerning ABn geometries has not taken a rigorous and holistic approach. Using a precise definition for configurations…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…