#four

anonymiss@despora.de

The #Number #Five Is Nothing Like the Number #Four

Our #brains #process them in completely different ways.

source: https://www.theatlantic.com/science/archive/2023/12/processing-numbers-four-five-biology/676380/?gift=bt1n2vDjnfxxzkH_t7B8m4IBC69GwvvR7NuTR_ScRwg

More than 150 years ago, the economist and philosopher William Stanley Jevons discovered something curious about the number four. While musing about how the mind conceives of numbers, he tossed a handful of black beans into a cardboard box. Then, after a fleeting glance, he guessed how many there were, before counting them to record the true value. After more than 1,000 trials, he saw a clear pattern. When there were four or fewer beans in the box, he always guessed the right number. But for five beans or more, his quick estimates were often incorrect.

Jevons’s description of his self-experiment, published in Nature in 1871, set the “foundation of how we think about numbers,” Steven Piantadosi, a professor of psychology and neuroscience at UC Berkeley, says. It sparked a long-lasting and ongoing debate about why there seems to be a limit on the number of items we can accurately judge to be present in a set.

Now a new study in Nature Human Behaviour has edged closer to an answer by taking an unprecedented look at how human brain cells fire when presented with certain quantities. Its findings suggest that the brain uses a combination of two mechanisms to judge how many objects it sees. One estimates quantities. The second sharpens the accuracy of those estimates—but only for small numbers.

It’s “very exciting” that the findings connect long-contested ideas to their neural underpinnings, Piantadosi, who was not involved in the study, says. “There’s not many things in cognition where people have been able to pinpoint very plausible biological foundations.” Although the new study does not end the debate, the findings start to untangle the biological basis for how the brain judges quantities, which could inform bigger questions about memory, attention, and even mathematics.

The ability to instantly judge the number of items in a set doesn’t have anything to do with counting. Human infants have this number sense even before they learn language. And it’s not limited to humans: Monkeys, bees, fish, crows, and other animals also have it. A monkey needs to be able to quickly judge the number of apples in a tree, and also how many other monkeys it’s competing against for those apples. A lion, when confronted by other lions, has to decide whether to fight or flee. Honeybees need to know which area has the most flowers for foraging. A guppy has better chances of escaping a predator if it joins a shoal. “The bigger the shoal, the safer that little fish is,” Brian Butterworth, a cognitive neuroscientist at University College London who was not involved in the new work, says.

This innate number sense is therefore crucial to survival, increasing an animal’s chances of finding food, avoiding predators, and ultimately reproducing. “It simply pays off for the survival of an animal to be able to differentiate numeric quantities,” says Andreas Nieder, a professor of animal physiology at the University of Tübingen, in Germany, who co-led the new study. The fact that this ability is found in diverse animals, from insects to humans, suggests that it arose a long time ago, and its neural basis has interested cognitive scientists for decades.

In 2002, when Nieder was working with the neuroscientist Earl Miller at MIT as a postdoctoral fellow, they published one of the first pieces of evidence that numbers are linked to specific neurons. In a behavioral experiment using monkeys, they found that these neurons, which are located in the prefrontal cortex, where higher-level processing takes place, have preferred numbers—favorite numbers that, when perceived, make the cells light up in brain scans.

For example, some neurons are tuned to the number three. When they’re presented with three objects, they fire more. Other neurons are tuned to the number five and fire when presented with five objects, and so on. These neurons aren’t exclusively committed to their favorites: They also fire for numbers adjacent to them. (So the neuron tuned to five also fires for four and six objects.) But they don’t do it as often, and as the presented number gets further away from the preferred number, the neurons’ firing rate decreases.

Nieder was excited by the deeper questions the work presented about the development of mathematical ability. Numbers lead to counting, and then to symbolic number representations, such as Arabic numerals that stand in for quantities. Those symbolic numbers underpin arithmetic and mathematics. “For us to know how numbers are represented [in the brain] is setting the foundation for everything that’s coming later,” Nieder says.

He went on to learn as much as he could about number neurons. In 2012, his team discovered that the neurons respond to their preferred numbers when they’re estimating the quantity of a set of sounds or visual items. Then, in 2015, they showed that crows also have number neurons. In a show of “amazing crow behavior,” Nieder says, the birds could correctly peck the number of dots or Arabic numerals displayed to them.

However, no one had identified number neurons in humans. That’s because studying the human brain is notoriously difficult: Scientists usually can’t access its activity ethically in experiments while people are alive. Brain-imaging tools don’t have the resolution needed to distinguish individual neurons, and scientific curiosity alone can’t justify implanting invasive electrodes in the brain.

To peer into a living brain, Nieder needed to find patients who already had electrode implants and who would consent to being part of his research. In 2015, he contacted Florian Mormann—the head of the cognitive and clinical neurophysiology group at the University of Bonn, who is one of the few clinicians in Germany who does single-cell recordings in human patients—to see if he and his patients would join Nieder’s search for human number neurons. Mormann said yes, and their teams got to work examining the brain activity of his epilepsy patients, who had previously had electrodes implanted to improve their medical care.

Nine patients did simple calculations in their heads while researchers recorded their brain activity. Sure enough, in the data, Nieder and Mormann saw neurons firing for their preferred numbers—the first time number neurons had been identified in the human brain. They published their findings in Neuron in 2018.

Neuroscientists are of course driven to understand the mind, Nieder says, so “finding such neurons in the human brain is extremely rewarding.” To continue their quest, Nieder and Mormann launched a new study to find out how the neurons represent odd and even numbers. The researchers recruited 17 epilepsy patients and showed them flashes of dots, ranging in number from one to nine, on computer screens. The participants indicated whether they saw an odd or even number while electrodes recorded their brain activity.

Over the next few months, as Esther Kutter, a graduate student studying with Nieder, analyzed the resulting data, she saw a clear pattern emerge—right around the number four. The data, which comprised 801 recordings of single neurons firing, showed two distinct neural signatures: one for small numbers and one for large. Above the number four, the neurons’ firing for their preferred number grew progressively less precise, and they erroneously fired for numbers close to the preferred one. But for four and below, the neurons fired precisely—with the same small amount of error whether firing for one, two, three, or four objects. The misfiring in response to other numbers was largely absent.

This surprised Nieder. He hadn’t previously seen this boundary in his animal studies: Those experiments had included numbers only up to five. He hadn’t set out to probe Jevons’s observation, nor did he expect to see a neural boundary confirm what behavioral studies had found. Up until that point, he had been convinced that the brain had just one mechanism for judging numbers—a continuum that got fuzzier the higher the numbers climbed.

The new data changed that for him. “This boundary popped out in different ways,” Nieder says. The neural patterns suggested that there is an additional mechanism that suppresses smaller-number neurons from firing for the wrong numbers. Piantadosi and Serge Dumoulin, the director of the Spinoza Centre for Neuroimaging, in Amsterdam, had both previously published papers supporting the idea that only one mechanism manages the neuronal interpretation of numbers. Yet they were struck by Nieder and Mormann’s new data showing that there are, in fact, two separate mechanisms.

It’s “real validation that large and small numbers have different neural signatures,” Piantadosi says. But he cautioned that two signatures can emerge from a single process; whether it should be described as one mechanism or two is still up for debate. “This is just beautiful,” Dumoulin says. “This type of data wasn’t available, and certainly not in humans.”

However, one more major uncertainty remains. The researchers didn’t study the prefrontal or parietal cortices, where the majority of number neurons are located in monkeys. Instead, because of where the patients’ electrodes were inserted, the study focused on the medial temporal lobe, which is involved in memory. It isn’t the first place in the human brain you’d investigate to understand numbers, Nieder says. “On the other hand, the medial temporal lobe is also not the worst place to look for such neurons.”

That’s because the medial temporal lobe is linked to number sense. It’s active when children learn calculations and multiplication tables, and it’s intimately connected to regions where number neurons are thought to lie, Nieder says. It’s not clear why number neurons are present in this region, Butterworth says. “The things that we thought were specific to the parietal lobe seem to be reflected also in parts of the medial temporal lobe.”

One possibility is that these aren’t number neurons at all. Pedro Pinheiro-Chagas, an assistant professor of neurology at UC San Francisco, thinks these could instead be concept neurons, which are located in the medial temporal lobe and are each linked to specific concepts. For example, one famous study found a concept neuron that responded directly and specifically to images of the actor Jennifer Aniston. “Maybe they are not finding the mechanisms of the number sense … Maybe they’re finding concept cells that are also applied to numbers,” Pinheiro-Chagas says. “As you have the concept of Jennifer Aniston, you could have the concept of three.”

The level of analysis is “just really outstanding,” says Marinella Cappelletti, a cognitive neuroscientist at Goldsmiths, University of London. The researchers provide “compelling evidence” for dual mechanisms in the medial temporal lobe. She thinks it would be valuable, however, to see whether these mechanisms operate in other brain regions as well, if the opportunity presents itself. “I see these findings as looking into a window,” Cappelletti says. “It would be nice to open it up a bit more and tell us more about the rest of the brain.”

The new findings have clear parallels to the limitations of working memory. People can hold only a certain number of objects in their awareness, or working memory, at one time. Experiments show that number is also four. The agreement between the boundary of number sense and that of working memory is “hard to ignore,” Cappelletti says.

The mechanisms may be related. In previous studies of number sense, when a participant stopped paying attention, they lost their ability to precisely judge the true value of numbers four and below. That suggests that the small-number system, which suppresses adjacent misfirings with small numbers, might be intimately tied to attention. Nieder now hypothesizes that the small-number system turns on only when you’re paying attention to what’s in front of you. He’s hoping to test this idea in monkeys, in addition to looking for a neural boundary at four that their experiments haven’t yet captured.

The latest research “seems to be the beginning of a new leap” in our understanding of number perception, Pinheiro-Chagas says, which could have useful applications. He hopes it will be fodder for discussions in math education and even artificial intelligence, which struggles with numerosity perception. Large language models are “pretty bad at counting,” he says. “They are pretty bad at understanding quantities.”

Better characterizing number neurons can also help us understand who we are. Next to the language system, number representation is humans’ second-biggest symbol system. People use numbers frequently and in a variety of ways, and we and our ancestors have used math to describe the world for millennia. In that sense, math is a fundamental part of being human. And, as this study starts to show, this calculation prowess might all stem from a finely tuned network of neurons in the #brain.

#science #mathematics #education #news #numbers

aljazeera@squeet.me

Why is the Putin-Kim meeting important? | Al Jazeera Newsfeed

North Korea’s president Kim Jong Un is in Russia to meet his counterpart Vladimir Putin for the first time in four years. Al Jazeera’s Defence Editor Alex Ga...#AlJazeera #AlJazeeraEnglish #AlexGatopoulos #KimJongUn #Putin-Kim #VladimirPutin #alJazeera #aljazeeraEnglish #aljazeeralive #aljazeeravideo #aljazeeraEnglish #aljazeeralatest #aljazeeralive #aljazeeralivenews #explains #four #important #latestnews #meeting #newsheadlines #president #years
Why is the Putin-Kim meeting important? | Al Jazeera Newsfeed

ramnath@nerdpol.ch

enter image description here
#triquetra #cross

The #Carolingian Cross is but one variation in the vast historical imagery of Christian symbolic representations of the Crucifixion of Jesus, going back to at least the ninth century.[1] All crosses and Christian symbols have an inherent meaning arising from a multitude of sources and distinct features that set them apart from other religions.[2] From both a design aspect and a theological perspective, the Carolingian Cross consists of a mixture of Christian and pre-Christian concepts built over a long history of cultural adaptation, religious iconography, liturgical practices and theological premises. German graphic designer Rudolf Koch in 1932 published a collection of 158 plates of drawings of Christian symbols. Under the heading of "Cross", this includes twelve drawings of Christian cross variants. One of these, the "Carolingian Cross" (Karolingisches Kreuz) shows a cross of #four #triquetras

Iron Age
The term triquetra in archaeology is used of any figure consisting of three arcs, including a pinwheel design of the type of the triskeles. Such symbols become frequent from about the 4th century BC ornamented ceramics of #Anatolia and #Persia, and it appears on early #Lycian coins.[1]

The triquetra is found on runestones in Northern Europe, such as the Funbo #Runestones, and on early Germanic coins.[citation needed] It bears a resemblance to the valknut, a design of three interlacing triangles, found in the same context.

Insular art
The triquetra is often found in insular #art, most notably metal work and in illuminated manuscripts like the #Book-of-Kells. It is a "minor though recurring theme" in the secondary phase of Anglo-Saxon sceatta production (c. 710–760).[2] It is found in similar artwork on early Christian High Crosses and slabs. An example from early medieval stonework is the Anglo-Saxon frithstool at Hexham Abbey.[3]

The #symbol has been interpreted as representing the #Holy #Trinity, especially since the #Celtic revival of the 19th century. The original intention by the early medieval artists is unknown and experts[who?] warn against over-interpretation.[2] It is, however, regularly used as a Trinitarian symbol in contemporary Catholic iconography.

Buddhist tradition
The triquetra has been a known symbol in Japan called Musubi Mitsugashiwa.[citation needed] Being one of the forms of the Iakšaku dynasty signs, it reached #Japan with the dynasty's Kāśyapīya spreading technology and Buddhism via Kingdom of Khotan, #China and #Korea.[citation needed]

Modern use
The triquetra is often used artistically as a design element when Celtic #knotwork is used, especially in association with the modern Celtic Nations. The triquetra, also known as a "trinity knot", is often found as a design element in popular Irish jewelry such as claddaghs and other wedding or engagement rings.

Celtic pagans or neopagans who are not of a Celtic cultural orientation may use the triquetra to symbolise a variety of concepts and mythological figures. Due to its presence in insular Celtic art, Celtic Reconstructionists use the triquetra either to represent one of the various triplicities in their cosmology and theology (such as the tripartite division of the world into the realms of Land, Sea and Sky),[5] or as a symbol of one of the specific Celtic triple goddesses – for example the battle goddess, The #Morrígan. The symbol is also sometimes used by #Wiccans, #White Witches, and some New Agers to symbolise the #Triple #Goddess, or as a #protective symbol.[6]
https ://en.wikipedia.org/wiki/Triquetra

nowisthetime@pod.automat.click

#Xavier-Reyes-Ayral on the Passing of Pope Benedict: Are the Chastisements Upon Us?
Are we nearing the End Times?
Many prophesies have pointed hearers back to the #Third #Secret #of #Fatima and the possibility of the martyrdom of a pope. Garabandal seer Conchita Gonzalez said that after Pope John XXIII there would be #four more #popes "until the end of the times." With Benedict XVI's death, the #fourth has #now #passed. What other #information have we heard from #mystics, #visionaries and #prophets regarding the popes, the #EndTimes and the #calamities yet to come?

In this Part Two of our conversation with Xavier Reyes-Ayral, author of "Revelations: The #Hidden Secret #Messages and Prophecies of the Blessed #Virgin #Mary," Reyes-Ayral and Dr. Christine Bacon discuss the #revelations and prophecies that have been fulfilled, those that are nearing and what we can do to prepare. You will not want to miss this engaging conversation!
Source: https://youtube.com/watch?v=arOqshTY13Q

(See Part One at https://youtu.be/DLp79K4ly0c )

legeneralmidi@diaspora.psyco.fr

https://www.franceculture.fr/economie/solar-brother-et-ses-fours-briquets-ou-chargeurs-quand-le-soleil-est-la-il-faut-sen-servir

Solar Brother et ses #fours, #briquets ou #chargeurs : quand le soleil est là, il faut s’en servir !

Par #AnnabelleGrelier #Demainléco

Briquet solaire

Trois fois lauréate du #concoursLépine, la jeune pousse veut devenir la première marque de #foursolaire grand public en Europe. Si les performances de la #thermodynamique semblent avoir été oubliées des industriels, #SolarBrother parie sur son retour en force chez les artisans et les particuliers.

#GillesGallo, le fondateur de Solar Brother, a su faire preuve de patience et de détermination pour promouvoir sa passion pour l’ #énergiesolaire. Avant d’avoir lancé sa #startup, il dirigeait une entreprise de fabrication industrielle de four solaire qu’il a maintenu pendant douze ans. Mais faute de soutien et d’intérêt pour cette technologie il a dû déposer le bilan et cesser son activité.

Dans les années 2000, l’industrie et l’ #écologie n’intéressaient pas grand monde et trouver des financements était difficile. Il n’y en avait que pour internet et les applications. Avec la pandémie, on a enfin redécouvert le besoin de fabriquer en France et retrouver la fierté d’être autonome. - Gilles Gallo

Avec le sentiment qu’il n’avait pas pu aller au bout de son idée, le chef d’entreprise et son stagiaire ingénieur de l’époque, #GatienBrault, ont remonté une structure plus petite, en visant des produits du quotidien comme un #briquet et un #four. Des produits qui plaisent au concours Lépine qu’ils gagnent par trois fois. De levée de fonds en prêt de la BPI, Solar Brother décolle enfin.

Comment l'entreprise souhaite démocratiser l'énergie #solaire à concentration

Faire confiance au solaire
A 47 ans, Gilles Gallo est d’une génération où tous les enfants se sont amusés en colonie de vacances ou chez les scouts à allumer des feux de camps à l’aide des rayons du #soleil à travers une loupe. La France a même était leader mondial du solaire à concentration avec en 1983 l'inauguration de la première centrale électrique #Thémis dans les Pyrénées et ses 200 héliostats, miroirs géants orientés vers le soleil. Mais curieusement, depuis vingt ans, ce qui ne semblait plus à prouver est devenu presque source de moquerie, bon pour les professeurs Tournesol ou les petits inventeurs. Il faut pourtant retrouver confiance en l’énergie solaire comme source de chaleur, estime le fondateur de Solar Brother pour qui le principal frein à l’utilisation plus large des fours solaires est le doute.

Les gens n’y croient pas. Quand vous dites à quelqu’un que vous avez un #briquetsolaire il vous dit que l’on va mettre trop de temps à allumer quelque chose. Quand vous leur dites qu’avec un four solaire vous pouvez cuisiner ils vous répondent qu’il ne faut pas être pressé et que le soir on mange plus. Les gens doutent de l’énergie solaire alors que c’est l’énergie la plus puissante au monde !

Du pain, des grillades, des poulets, Solar Brother multiplient les démonstrations pour démontrer que par jour de beau temps il n’est vraiment pas compliqué ni long de cuisiner grâce à l’énergie solaire. Et des jours d’ensoleillement notre pays n’en manque pas, c’est en moyenne 300 jours par an dans le sud et 150 à 200 jours dans le nord.

Sans doute trop habitué à disposer d’énergie en appuyant sur un bouton, on en oublie qu’il y a des sources gratuites d’énergie à disposition et inépuisables dont on ne se sert pas. Alors quand le soleil est là, il faut s’en servir ! C’est le credo de Solar Brother qui vient d’installer un #foursolaire collectif capable de monter à 250 degrés en 100 minutes dans un restaurant au nord de Marseille. À Château-Gombert, le patron du "Présage" cuisine au solaire et l’adresse attire de plus en plus de clients et de curieux. Également équipé d’une parabole recouverte de miroirs dite Schaeffer, il possède plusieurs types de four solaire pour des cuissons différentes et ses recettes sont indexées sur la consommation d’énergie qu’elles nécessitent.

La règle des 3 C
La start-up installée dans l’incubateur #UrbanLab, dans le 18e arrondissement de Paris, commercialise sur son site des fours de différentes puissance allant de la cuisson douce à plus de 250 degrés et de différentes tailles, du four collectif au four pour enfants car il est indispensable pensent ses fondateurs de faire de la pédagogie pour réhabiliter cette magnifique énergie. Ils ont d’ailleurs mis les plans de leurs fours en open source sur leur site pour que tout le monde puisse y accéder gratuitement et le construire par soi-même ce qui permet d’en diviser par 4 ou 5 le prix.

Un four solaire ce n’est pas un gadget c’est une habitude à prendre. Il faut économiser les énergies fossiles quand on le peut. Sans oublier qu’un four solaire ça ne fait ni feu, ni flamme, ni fumée et on peut s’en servir partout dans un jardin, à la plage ou sur un balcon.

Et surtout, il ne consomme rien. Selon les lois de la thermodynamique, le four solaire marche avec la règle des 3 C, explique Gilles Gallo qui peut se targuer d’avoir aujourd’hui vingt ans d’expérience dans ce domaine.

Le premier C comme Concentration des rayons solaires grâce à des miroirs, puis Captation avec un corps noir ou de couleur foncée pour absorber les rayons infra rouge et le dernier C pour la conservation qui permet de concentrer la chaleur autour de l’aliment pour monter en température. Car ce n’est pas le four lui-même qui chauffe mais la marmite placée à l’intérieur ; le four que l’on peut plier et déplier en 5 minutes, reste, quant à lui toujours froid et propre.

Solar System s’inscrit dans une démarche low tech. La petite entreprise crée, développe et commercialise ses produits tout en confiant la fabrication à de multiples sous-traitants français. Du made in France avec des matériaux issus de plastique recyclé pour les fours, de carton recyclé pour les emballages et de toiles de parachute up cyclées pour les sacs de transport.

Devenir la première marque européenne
Si avec sa première entreprise Gilles Gallo n’était finalement pas dans la tendance de l’époque, il pourrait bien en être autrement avec Solar Brother, assure son associé Gatien Brault.

Depuis la crise sanitaire, les attitudes changent et les consciences se sont réveillées. On assiste à un véritable désir de retrouver des modes de consommation plus simples plus écologiques mais surtout les gens sont en recherche d’autonomie

Ce qui relevait d’une véritable innovation en 1759 lorsqu’Horace Benedict de Saussure, physicien suisse auteur d’une thèse sur la chaleur qui mettra au point quelques années plus tard le premier #capteursolaire, reste aujourd’hui un sujet de recherche pour les étudiants ingénieurs de Polytech Marseille. Il reste encore de nombreuses pistes d’expérimentations et d’améliorations à trouver dans les technologies solaires.

Aux entreprises de créer et de produire les meilleures applications du fruit de ces recherches pour des utilisateurs en demande de consommation responsable. Solar Brother est aujourd’hui la première marque de #four solaire grand public en France et sans concurrent en Europe, elle mène actuellement une levée de fonds auprès de business angels et de fonds éthiques pour s’internationaliser.

Ce n’est ni inventer le fil à couper le beurre ni une virée chez les Amishs que propose cette marque qui vient de déposer ses statuts d’ #entreprise à mission, juste pouvoir utiliser facilement ce que la nature nous donne gratuitement. Une idée lumineuse.