Science had always believed that only humans understand geometry. Until we noticed the crows again

The perception of geometric regularity in shapes, a variant of elementary geometry, has long been considered an ability that only human beings had. And it is no wonder, since from quite early stages of development and across multiple cultures, our species has demonstrated a natural understanding of spatial rules. But this has changed in a species similar to crows. A radical change. Although this innate quality of humans was quite well established, science has now shown that the crows too They have geometric understanding. A cognitive milestone that rethinks what we thought we knew about animal intelligence and the evolution of pure mathematics. A myth. The scientific bases showed a notable gap between human abilities and those of the rest of the animal kingdom with regard to euclidean geometry. Previous research had already seen that primates lacked the ability to recognize geometric regularity in tests of visual perception of shapes, something fundamental, since they may be the first that come to mind when thinking about this property. And this was crucial to determining that humans have an innate ability to process geometric regularity, since the recurring inability to species like baboons After intensive training he laid these foundations. However, the researchers decided to explore these abilities in birds known for their impressive cognitive and arithmetic skills. Touch screens. To test birds’ spatial intuition, scientists from the University of Tübingen They designed an experiment based on the detection of visual anomalies. In this case, two 10- and 11-year-old male crows were trained using touch screens located inside conditioning chambers. Here the birds could observe an array that displayed six simultaneous shapes on the screen and the task was to detect an “intruder”, that is, to peck at the shape that differed in its visual parameters with respect to the other five base stimuli. The tests. For the final test, five reference quadrilaterals were used, ordered by their level of regularity: the square, the isosceles trapezoid, the rhombus, the right hinge, and a completely irregular shape. From here on, the “intrusive” figures were artificially generated moving the lower right vertex of the original figure at a fixed distance equivalent to 75% of the average distance between the vertices. Results. The most impressive thing seen was the immediacy of understanding the problem, as the crows were able to apply the concept of detecting the intruder immediately upon being exposed to the new sets of quadrilaterals. Both subjects dramatically exceeded the 16.7% chance level during their first trials, demonstrating that they understood the task without hesitating or mindlessly pecking. Furthermore, during the first 60 trials, the first crow achieved 48.3% success and the second crow 56.7%. The most impressive thing. The most revealing data from these tests was precisely that the birds showed significantly better performance with shapes that presented properties of pure Euclidean geometry, such as right angles, parallel lines or symmetry. It is crucial here to highlight that this performance advantage did not require extensive prior training, but rather the regularity effect was present from the very beginning of the testing phase. Because? Faced with the logical question of why crows achieved what other primates failed, the authors of the study recognize certain important methodological differences compared to classic experiments with baboons. In this case, they point out that the crows were subjected to a strict progress criterion during training, needing to maintain 75% correctness over five consecutive sessions. In contrast, baboons only needed to reach a criterion of 80% correct responses only once, without the need for consecutive sessions. And although this difference may make a direct and exact comparison between the species difficult, the main finding is incontestable: crows recognize geometric regularity. Images | Tyler Quiring In Xataka | Punch, the monkey clinging to a stuffed animal and a victim of bullying, has achieved the impossible: uniting the Internet under the same cause

In 1643, Descartes created one of the most important theorems of geometry. We knew he was right, but we didn’t know why. Until now

In 1643, René Descartes wrote a letter to Princess Isabel del Palatinado in which she simplified a classic problem of Western geometry and offered a solution: the so -called ‘Descartes theorem’; that, according to the famous problem that Frederick Soddy published in 1936 in Natureit can be summarized as “the sum of the squares of the four curvatures is half the square of its sum in figures.” Basically, he found a relationship between the radios of four mutually tangent circles. The problem is that the French philosopher did not explain the reasoning behind that relationship and, in fact, he never managed to find a general formula for more than four circles. His intuition is that this solution existed, but was not able to find it. That has brought mathematicians since then. A couple of years ago Daniel Mathews and Orion Zymaris, from the Australian University of Monash, They decided to try With a radically new approach. What if we use tools of theoretical physics? That was the question that was asked: As Héctor Farrés explainedinstead of pulling the tools of conventional geometry, they began to play with ‘thorn’ (a type of objects of theoretical physics that need a 720 degree turn to return to their natural position). “We use a version of thorn developed by Roger Penrose and Wolfgang Rindler, which applied to the theory of relativity,” The authors said. In this way they achieved ‘re-conceptualize’ circles as algebraic entities that can suffer from geometric transformations. That was the key to obtaining a general formula to be able to describe increasingly complex groups of mutually tangent circles. Why is it interesting? To start because it solves a historical problem of geometry. But, above all, because it does it again and with many ramifications. When Andrew Wiles He managed to demonstrate Fermat’s last theoremthere was some disappointment for the use of modern mathematical tools. In that case it was understandable: part of the grace of the problem was to find the demonstration that Fermat himself said he had discovered (but never wrote). With Descartes’s theorem is different. There was nothing to look for, just a solution to develop. And doing so shows all the potential of mathematics to destroy the limitations that lead us to grip for centuries. In the end, As Arthur C. Clarke said“When a distinguished but elderly scientist says that something is possible, it is almost certain that he is right. When he states that something is impossible, it is almost certain that he is wrong. Image | Frans Hals | Jacob Rus In Xataka | The “Matrix” fillet was always real: philosophical and metaphysical reflections on metovers

MIT has measured for the first time the geometry of electrons in the quantum world

The paths of quantum physics are inscrutable. In my opinion this appointment of Richard FeynmanNobel Prize in Physics for their contributions to quantum electrodynamics and one of the most admired scientists of the twentieth century, condenses very well The complexity of this discipline: “If you think you understand quantum physics, you don’t really understand quantum physics.” Quantum mechanics study the laws that govern The world of the very smallof the particles, as well as the interactions to which the atomic and subatomic structures are exposed. Most of these rules are radically different from the laws we have become familiar with in the world in which we live. In the macroscopic world. Many physicists have spent the last century trying to understand how known quantum phenomena work, and also striving to identify unknown quantum rules. The problem is that working with the extremely small, with the particles, is very difficult. However, this does not mean that they are not successful. He Mit (Massachusetts Technological Institute) has just been a bit very important. Physicists now better understand the quantum properties of the materials A group of MIT researchers has managed to measure accurately at the quantum level the geometry of electrons in solid materials. Expressed in this way it does not seem much, but it is a very relevant discovery. Until now, physicists had managed to measure the energy and speed acquired by these elementary particles in crystalline materials, but not their geometry at the quantum level. According to Riccardo CominProfessor of Physics at the MIT and leader of this research, “this discovery allows us to understand and manipulate the quantum properties of the materials.” Quantum geometry allows physicists to determine the geometric characteristics of the wave function Before moving forward we are interested in briefly investigating the concept of ‘quantum geometry’ to be able to understand with some precision what we are talking about. Its purpose is to describe the structure of a quantum system such as the forming, for example, by The interaction of electrons In a solid material. In practice this knowledge serves to elaborate a map that describes the probability of finding an electron in a given position. Rigorously this “map” is known as wave function. However, this is not all. Quantum geometry also allows physicists to determine the geometric characteristics of the wave function. This simply means that with this information you can know how precisely the electrons behave in a material and to what extent their properties condition. Quantum geometry helps scientists, in short, to predict the behavior of materials and design new elements or combinations of elements that can be used in aeronautics, Quantum computing or robotics, among many other disciplines. Riccardo Comin assures that “in essence we have done is to develop a plan to obtain completely new information (about the materials) that until now could not be collected.” And Mingu Kang, another of the physicists who have signed the article published in Nature Physics, duck That “this knowledge It can be applied to any type of quantum material“. The technique that these scientists have used to develop their strategy is known as photo emission spectroscopy resolved at an angle. In broad strokes it is an experimental procedure that serves to study the electronic structure of materials in a thorough way and know their fundamental properties. Image | Generated by Xataka with Ia More information | Nature Physics In Xataka | The CERN has an ambitious plan: it wants to demolish the special theory of Einstein’s relativity

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