Stanislas Dehaene gave a presentation about his quest to understand what makes humans so special during a workshop at the Vatican.
In 1996, Dr. Dehaene wrote The Number Sense: How the Mind creates Mathematics, a book about the evolutionary roots of our mathematical instinct. Dr. Dehaene thinks that part of the answer might be our intuitions about geometry.
The subject of symbols, myths and religious sense in humans since the first humans emerged a couple of million years ago was addressed by the Vatican. Dr. Dehaene began his slide show with a bunch of pictures of symbols engraved in rock. Some of the photos he took were taken in southern France. The Bronze Age is thought to have started around 3,300 B.C. to 1,200 B.C. He showed a photo of a stone implement that was spherical at one end and triangular at the other.
The idea of a triangle, the laws of physics, and the square root of negative 1 capture the essence of being human.
He acknowledged that it was no small leap from imagining a triangle to creating religion. Before becoming a neuroscientist, he had a degree in mathematics and a master's in computer science. He said, "This is what we have to explain: Suddenly there was an explosion of new ideas with the human species."
A study comparing the ability of humans and baboons to perceive geometric shapes was published last spring. The team wondered what the simplest task in the geometric domain was, independent of natural language, culture, education and so on. The challenge was to measure a deeper cognitive process.
The line of investigation has a long history and is fascinating according to a cognitive scientist at New York University who has collaborated with Dr. Dehaene on other research. Plato believed that humans were innately aware of geometry, while Noam Chomsky believes that language is innately human. Dr. Dehaene wants to do the same thing as Dr. Chomsky did for language.
In the experiment, subjects were shown six quadrilaterals and asked to identify the one that was different from the others. The task was easier for all the humans when the baseline shape or outlier shape were present.
The researchers called this the geometric regularity effect, and they admit that it is a fragile hypothesis.
The team found no difference with the baboons. The study was run by a cognitive psychologist at Aix-Marseille University.
The testing booths and 19-inch touch-screen devices are popular with the baboons, who live at a research facility in the South of France. The baboons were free to enter the testing booth of their choice, there were 14 of them, and they were maintained in their social group during testing. Their performance collapsed when they were presented with regular polygons.
The symbols were used to see if the baboons could pick out a non matching symbol.
Frans de Waal, a primatologist at Emory University, said in an email that the results are striking and that there seems to be a difference between the perception of shapes by humans and baboons.
The researchers tried to duplicate the performance of humans and baboons with artificial intelligence, using neural-network models that are inspired by basic mathematical ideas of what a neuron does. The models failed to reproduce the regularity effect because they failed to match the performance of the baboons. The model was given a list of properties of geometric regularity, such as right angles, parallel lines, and it closely replicated the human performance.
The results set a challenge for artificial intelligence. The ability to manipulate symbols and abstract concepts is what the human brain does. This is the subject of his newest book, How We Learn: Why Brains Learn Better Than Any Machine.
Yoshua Bengio is a computer scientist at the University of Montreal. He said that Dr. Dehaene's work shows that human brains are using abilities that we don't yet find in machine learning.
He said that when we combine symbols and recomposing pieces of knowledge helps us to generalize. This gap could explain the limitations of A.I. and the system's inflexibility when faced with different environments. It is an indication of where A.I. research needs to go.
Dr. Bengio noted that from the 1950s to the 1980s symbolic-processing strategies dominated, but these approaches were motivated less by the desire to replicate the abilities of human brains than by logic. The neural-network revolution began in the 1990s and gained traction in the 2010s. Dr. Bengio was a pioneer of this method, which was inspired by the human brain.
Neural-networks can be trained to generate, or imagine, symbols and other representations.
It's not impossible to do abstract reasoning with neural networks, but we don't know how to do it.
If we had not had the idea of the geometric triangle elsewhere, we wouldn't know it through the one we see on paper.
They propose a language of thought to explain how geometric shapes are thought to be. They find inspiration in computers.
Dr. Dehaene said that when you look at a geometric shape, you immediately have a mental program for it. The drawing of the shape is the output.
Josh Tenenbaum, a computational cognitive scientist at the Massachusetts Institute of Technology and an author of the new paper under review, likes to ask how humans manage to extract so much from so little. He wants to solve the puzzle of the leaps.
He said that the distinction is one of hardware versus software, essentially. It is an approach motivated by the British mathematician and computer scientist Alan Turing and the idea that thinking is a kind of programming.
The programmers proposed a programming language for drawing shapes. There must be thousands of them by now, Mr. Sabl said.
The language is made up of geometric primitives, including basic building blocks of shapes, as well as rules that dictate how these can be combined to produce symmetries and patterns. Mr. SablE9;-Meyer said that the ultimate goal is to develop a good candidate theory for cognitive functioning.
The DreamCoder was developed a few years ago by Kevin Ellis, who is now a computer scientist at Cornell University. DreamCoder modeled how the mind might use the programming language to find the shortest possible program for any given shape or pattern. The mind operates in the same way according to the theory.
A programming language was developed to generate shapes. The brain is similar to programs in a language.
Shapes found in many cultures include lines, circles, spirals, zigzags, squares and squares of circles.
The programming language drew increasingly complex shapes.
Geometric shapes found in many cultures include lines, circles, spirals, zigzags, squares and squares of circles.
The programming language drew increasingly complex shapes.
Humans were added back into the equation by testing the ability of subjects to process shapes of varying complexity that the programming language had generated. They measured how long it took people to memorize a shape such as a curve, compared with how long it took them to find it in a group of similar shapes. The longer the program, the more difficult a shape is to remember or discriminate from others.
The baboons are trying a test. At Dr. Dehaene's NeuroSpin neuroimaging lab, functional M.R.I.s are used to measure neural activity while subjects entertain geometric confections. The data shows that the brain regions involved in the prefrontal and parietal lobes overlap with those associated with the human number sense.
The brain areas that light up for geometry are what Dr. Dehaene and his former student, Marie, called the math-responsive network.
Dr. Dehaene believes that there is something more basic, more fundamental that is thought to be the quality of language.
We propose that there are multiple languages and that language may not have started as a communication device but as a representation of facts about the outside world.
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