Understanding the orbital dance of three celestial objects has challenged mathematicians for centuries. Now, the game has changed.
Undeterred after three decades of looking, and with some assistance from a supercomputer, mathematicians have finally discovered a new example of a special integer called a Dedekind number.
Only the ninth of its kind, or D, it is calculated to equal 286 386 577 668 298 411 128 469 151 667 598 498 812 366, if you’re updating your own records. This 42 digit monster follows the 23-digit D discovered in 1991.
Grasping the concept of a Dedekind number is difficult for non-mathematicians, let alone working it out. In fact, the calculations involved are so complex and involve such huge numbers, it wasn’t certain that D would ever be discovered.
Cavities at the sides of a water channel can cause waves to be completely absorbed, suggesting new techniques for protecting coastlines.
If waves of water, light, or sound were to impinge upon a hypothetical object called a perfect absorber, they would be neither reflected nor transmitted; they would simply vanish. Researchers have now demonstrated perfect absorption using ordinary water waves traveling down a narrow channel [1]. The waves are canceled out by their own reflections from cavities built into the side of the channel. With further development, the researchers believe that the effect could be used to reduce erosion or protect sensitive structures by using an array of elements deployed near coastlines.
“We were motivated by the need to control or absorb waves in rivers or to protect coastlines,” says mathematical physicist Agnes Maurel of ESPCI Paris. “Completely absorbing wave energy is even better than redirecting it, and you can also imagine perhaps harvesting such energy.”
Experts have searched for decades for a polygon that only makes non-repeating patterns. But no one knew it was possible until now.
An hypothesized term to fix a small mathematical inconsistency predicted electromagnetic waves, and that they had all the properties of light that were observed before and after him in the Nineteenth Century. Unwittingly, he also pointed science inexorably in the direction of the special theory of relativity
My last two articles, two slightly different takes on “recipes” for understanding Electromagnetism, show how Maxwell’s equations can be understood as arising from the highly special relationships between the electric and magnetic components within the Faraday tensor that is “enforced” by the assumption that the Gauss flux laws, equivalent to Coulomb’s inverse square force law, must be Lorentz covariant (consistent with Special Relativity).
From the standpoint of Special Relativity, there is obviously something very special going on behind these laws, which are clearly not from the outset Lorentz covariant. What i mean is that, as vector laws in three dimensional space, there is no way you can find a general vector field that fulfills them and deduce that it is Lorentz covariant — it simply won’t be so in general. There has to be something else further specializing that field’s relationship with the world to ensure such an in-general-decidedly-NOT-Lorentz covariant equation is, indeed covariant.
Sperm can “defy the laws of physics”, according to new research.
The laws of motion have helped us to comprehend the behaviours of the natural world for centuries, but sperm appears to go against one of the laws set down by Isaac Newton.
Kenta Ishimoto and his fellow mathematical scientists from Kyoto University have revealed new research which suggests that sperm actually display qualities which don’t follow Newton’s third law of motion.
Some researchers see formal specifications as a way for autonomous systems to “explain themselves” to humans. But a new study finds that we aren’t understanding.
As autonomous systems and artificial intelligence become increasingly common in daily life, new methods are emerging to help humans check that these systems are behaving as expected. One method, called formal specifications, uses mathematical formulas that can be translated into natural-language expressions. Some researchers claim that this method can be used to spell out decisions an AI will make in a way that is interpretable to humans.
Research Findings on Interpretability.
It is increasingly clear that memories are distributed across multiple brain areas. Such “engram complexes” are important features of memory formation and consolidation. Here, we test the hypothesis that engram complexes are formed in part by bioelectric fields that sculpt and guide the neural activity and tie together the areas that participate in engram complexes. Like the conductor of an orchestra, the fields influence each musician or neuron and orchestrate the output, the symphony. Our results use the theory of synergetics, machine learning, and data from a spatial delayed saccade task and provide evidence for in vivo ephaptic coupling in memory representations.
High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.
Forget politics; if you want to divide a crowd, ask if anyone enjoys mathematics. But even the most maths-averse people may still be impressed by two researchers who have solved a problem that has been stuck in the same puzzling place since 1937.
