Think you can solve it? One mathematician has already offered about $1,000 and a bottle of champagne to whoever cracks it first.
- The puzzle involves a particularly complicated type of magic square.
- Magic squares are square arrays containing distinct numbers, and the sums of the numbers in the columns, rows and diagonals must be equal.
- In 1996, the recreational mathematics writer Martin Gardner offered $100 to whoever could solve a 3x3 magic square — but using squared numbers.
docdroid.net<p>Given that you need each column, row and diagonal to add up to 15, you'd need to fill in the empty squares with a 9, 7 and 8. </p>
docdroid.net<p>That may be easy enough. But magic squares become far more difficult when they use squared numbers, a concept <a href="https://www.scientificamerican.com/article/can-you-solve-a-puzzle-unsolved-since-1996/" target="_blank">first exemplified</a> by the 18th-century mathematician Leonhard Euler. </p><p>Since, mathematicians have generated various configurations of 4x4 magic squares of squares, including 5x5, 6x6 and 7x7 versions. But nobody has yet proven that a 3x3 magic square of squares is possible — or impossible, for that matter.</p><p>To date, there have been at least two prizes offered to whoever can solve this longstanding puzzle. Martin Gardner, a science and mathematics writer who was perhaps best known for devising recreational mathematics games that appeared for 25 years in a column published by <em>Scientific American,</em> offered a prize of $100 in 1996 to whoever could crack the code first. </p><ul> <p>"So far no one has come forward with a "square of squares"—but no one has proved its impossibility either," Gardner wrote in 1998 in <em><a href="https://blogs.scientificamerican.com/observations/a-quarter-century-of-recreational-m-2010-05-26/" target="_blank">Scientific American</a></em>. "If it exists, its numbers would be huge, perhaps beyond the reach of today's fastest supercomputers."</p></ul>
Melancholia I. (A 4x4 magic square is depicted in the top right of the painting.)
Dürer's<p>In 2005, the mathematician Christian Boyer raised the stakes by offering €1,000 plus a bottle of champagne to anyone who could complete a 3x3 magic square of squares — using seven, eight or nine distinct squared integers. (Boyer also offered a prize for anyone who can show the puzzle is impossible, and he lists smaller prizes for other unsolved puzzles on his <a href="http://multimagie.com/indexengl.htm" target="_blank">website</a>.)</p><p>While both prizes remain unclaimed, some people have come close to solving the 3x3 magic square of squares, like this configuration listed on Christian Boyer's website.</p>
Researchers explore the "complex web of connections" in your brain that allows you to make split second decisions.
- Researchers at the University of Colorado discovered the cerebellum's role in split-second decision making.
- While it was previously thought that the cerebellum was in charge of these decisions, it's been uncovered that it is more like a "complex web of connections" through the brain that goes into how you make choices.
- If the decision is made within 100 milliseconds (of being presented with the choice), the change of mind will succeed in altering the original course of action.
Photo: StunningArt / Shutterstock<p>This understanding of the cerebellum's role in decision-making is new. Because the mice became less confident in their choices after the release of those agents, it appears the cerebellum is partly responsible for quick decision-making responses.</p><p>Restrepo notes that the cerebellum is responsible for a lot of learning—perhaps unsurprisingly, given its proximity to the spinal cord and its influence on motor patterns. Split-second decisions are an old evolutionary necessity and would have started evolving quite early on. As he <a href="https://news.cuanschutz.edu/news-stories/cu-anschutz-researchers-shed-light-on-split-second-decision-making" target="_blank">says</a>,</p><p>"We found an entire subset of brain cells that change after learning. It sheds further light on how the cerebellum functions and the complex web of connections that go into quick decision making."</p><p><strong>How long does it take to make a split decision and have good results?</strong></p><p>The researchers in Susan Courtney's study highlighted that timing is everything when it comes to these quick decisions. If the decision to change is made within 100 milliseconds (of being presented with the choice), the change of mind will succeed in altering the original course of action. However, if it takes at least (or more than) 200 milliseconds, the chances of the change succeeding are significantly less.</p>
Creating a better understanding by clearing up common misconceptions about the neurodiversity movement.
- The neurodiversity movement began in the late 1990s with sociologist Judy Singer.
- Previously (and in many places, currently), these neurological differences were considered medical deficits.
- Neurodiversity is the concept that there are many different variations of human functionality and that each and every variation needs to be better understood and respected.
What is the difference between neurodiversity and the medical model approach?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ2Nzc5OC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY2MTAxMDc1OH0.D1H5Ehtj11_Wa8POEKdrk8qjIQH_tALiuE1Y_kJLO8A/img.jpg?width=1245&coordinates=0%2C71%2C0%2C72&height=700" id="27068" class="rm-shortcode" data-rm-shortcode-id="bc5ae22763822d8647b1f7a2576a4f7d" data-rm-shortcode-name="rebelmouse-image" alt="concept of neurodiversity autism adhd dyslexia autism awareness" />
Credit: Hatsaniuk on Shutterstock<p><strong>What is neurodiversity?</strong></p><p>Neurodiversity is the concept that there are many different variations of human functionality and that each and every variation needs to be better understood and respected.</p><p>Previously (and in many places, currently), neurological differences such as autism or ADHD were considered medical deficits. They are still considered things that need to be treated and cured. Neurodiversity is an alternative approach to learning and disability that shifts the focus from treatment and cures to acceptance and accommodation. </p><p>The neurodiversity movement began in the late 1990s, when <a href="https://www.disabled-world.com/disability/awareness/neurodiversity/" target="_blank" rel="noopener noreferrer">sociologist Judy Singer</a> (who is on the autism spectrum), came up with the word to describe conditions such as ADHD, autism, and dyslexia. This ideology recognizes that neurological differences (such as autism or ADHD) are the result of natural variations to the human genome. </p><p><strong>What is the medical model approach? </strong></p><p>The "medical model" approach to neurological differences such as autism and ADHD focuses on treatment and suggests that there are cures and preventable causes for these neurological differences.</p><p><a href="https://blogs.scientificamerican.com/observations/the-concept-of-neurodiversity-is-dividing-the-autism-community/" target="_blank" rel="noopener noreferrer">According to Scientific American</a>, many of the people who adopt this medical model approach to autism call for prevention and the cure of serious impairments that can be associated with autism. In contrast, those who support neurodiversity see such language as threatening and offensive to individuals with neurological differences.</p>
Common misconceptions<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="6ecafde1e887dea3e2e87397aa34f922"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/0uNnTe7G_nQ?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p><strong>Myth: Neurodiversity is not a valid opinion/construct.</strong></p><p>Neurodiversity is the diversity of brains and minds. That is the basis of this movement. In this way, neurodiversity isn't just an opinion or construct, but a biological fact. <a href="https://autistinquisitor.wordpress.com/2019/04/18/myths-about-neurodiversity/" target="_blank">According to Autist Inquisitor</a>, it's parent term, biodiversity (meaning the diversity of life), is as much a fact as neurodiversity.</p><p><strong>Myth: neurodiversity only refers to autism. </strong></p><p>While the term was originally coined by an Autistic sociologist, as time passed, the neurodiversity movement expanded. Neurodiversity in itself is the diversity of all brains and all minds. Neurodivergence can therefore be associated with things like ADHD, epilepsy, etc. </p><p><strong>Myth: the neurodiversity movement does not recognize disabilities among neurodivergent people.</strong></p><p>The social model of disability says that a person is "disabled" when the (societal) environment doesn't accommodate their needs.</p><p>Hypothetically, in this social model, if there were ramps and elevators everywhere to accommodate wheelchair users, they would not be considered "disabled," as they would have access to all the same things as a person who walks (schools, jobs, restaurants, etc). Of course, providing equal opportunity wouldn't mean ignoring the difficulties wheelchair users face. </p><p><a href="https://blogs.scientificamerican.com/observations/clearing-up-some-misconceptions-about-neurodiversity/" target="_blank" rel="noopener noreferrer">According to Scientific American</a>, culture and history can have an impact on what we view as a "disability". </p><p>"Depending on time and place in history, epilepsy could make a person a respected shaman or suspected of demonic possession. Gluten allergies are much easier to accommodate now than they were 20 years ago before food companies started offering gluten-free options. If wheat and rye went extinct, gluten allergy would never be a disability again!"</p><p>The model of neurodiversity doesn't aim to pretend that autistic people don't have impairments, but this model also doesn't assume that every impairment an autistic person has is a problem or disability.</p><p>"Not wanting to socialize is different from wanting to participate and being unable to. Both are possibilities for autistic people. One requires acceptance, the other requires assistance."</p><p><strong>Myth: the neurodiversity movement opposes medical interventions and therapies. </strong></p><p>While the main goal of neurodiversity is to understand, accept, and help accommodate people with neurological differences or difficulties, there are medical interventions and therapies that have been proven to be beneficial in certain circumstances. A common misconception about people who adopt the neurodiversity movement is that they are calling for an end to medical interventions and therapies. </p><p>While therapies such as ABA (applied behavior analysis) are quite controversial due to their focus on "curing" autism instead of assisting the neurodivergent individual, there are many people who believe in both neurodiversity and the assistance of medicine and therapy. For example, a neurodiversity advocate may feel that ADHD doesn't need to be "treated" and "cured", but that the difficult symptoms of ADHD that prevent the individual from excelling in certain areas of their life could be alleviated with medication and/or therapies. </p><p>For more information on neurodiversity, click <a href="https://blogs.scientificamerican.com/observations/clearing-up-some-misconceptions-about-neurodiversity/" target="_blank" rel="noopener noreferrer">here</a>. </p>
Crows have their own version of the human cerebral cortex.
Action-packed pallia<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ0NzkyMS9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTYxNzk1NzM1OH0.Tjb3zulFW2gwhteR124F9HGbmdnCqNqQFOBQouieTJ8/img.png?width=980" id="2bbc9" class="rm-shortcode" data-rm-shortcode-id="2907e4035e553565f4446e968ee73d92" data-rm-shortcode-name="rebelmouse-image" />
Fun with Ozzie and Glenn<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ0Njk2MS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxMzY4Njc2MX0.ZgpsPMCK6qOj2o0kErvVPjdua1EnMCIwCuHHGrb3LiY/img.jpg?width=980" id="acbeb" class="rm-shortcode" data-rm-shortcode-id="2e286fecbb228a5ca8aa26fcd19f95a2" data-rm-shortcode-name="rebelmouse-image" alt="two crows in a tree" />
Ozzie and Glenn not pictured
Credit: narubono/Unsplash<p>The kind of higher intelligence crows exhibited in the new research is similar to the way we solve problems. We catalog relevant knowledge and then explore different combinations of what we know to arrive at an action or solution.</p><p>The researchers, led by neurobiologist <a href="https://homepages.uni-tuebingen.de/andreas.nieder/" target="_blank">Andreas Nieder</a> of the University of Tübingen in Germany, trained two carrion crows (<em>Corvus corone</em>), Ozzie and Glenn.</p><p>The crows were trained to watch for a flash — which didn't always appear — and then peck at a red or blue target to register whether or not a flash of light was seen. Ozzie and Glenn were also taught to understand a changing "rule key" that specified whether red or blue signified the presence of a flash with the other color signifying that no flash occurred.</p><p>In each round of a test, after a flash did or didn't appear, the crows were presented a rule key describing the current meaning of the red and blue targets, after which they pecked their response.</p><p>This sequence prevented the crows from simply rehearsing their response on auto-pilot, so to speak. In each test, they had to take the entire process from the top, seeing a flash or no flash, and then figuring out which target to peck.</p><p>As all this occurred, the researchers monitored their neuronal activity. When Ozzie or Glenn saw a flash, sensory neurons fired and then stopped as the bird worked out which target to peck. When there was no flash, no firing of the sensory neurons was observed before the crow paused to figure out the correct target.</p><p>Nieder's interpretation of this sequence is that Ozzie or Glenn had to see or not see a flash, deliberately note that there had or hadn't been a flash — exhibiting self-awareness of what had just been experienced — and then, in a few moments, connect that recollection to their knowledge of the current rule key before pecking the correct target.</p><p>During those few moments after the sensory neuron activity had died down, Nieder reported activity among a large population of neurons as the crows put the pieces together preparing to report what they'd seen. Among the busy areas in the crows' brains during this phase of the sequence was, not surprisingly, the pallium.</p><p>Overall, the study may eliminate the layered cerebral cortex as a requirement for higher intelligence. As we learn more about the intelligence of crows, we can at least say with some certainty that it would be wise to avoid <a href="https://www.nytimes.com/2008/08/26/science/26crow.html" target="_blank" rel="noopener noreferrer">angering one</a>.</p>
How Nobel Prize winner physicist Lev Landau ranked the best physics minds of his generation.
- Nobel-Prize-winning Soviet physicist Lev Landau used a scale to rank the best physicists of the 20th century.
- The physicist based it on their level of contribution to science.
- The scale was logarithmic, with each level being 10 times more valuable.
Rank 0.5 – Albert Einstein<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ0NDY3NS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYzNjI2NTU4OH0.FtBYC7oJz-ZOiiGC9y0Z50_JvQChmp-ONa3jhR3SuLA/img.jpg?width=980" id="d6f66" class="rm-shortcode" data-rm-shortcode-id="61288810a4f035ec2af8957fad4e9015" data-rm-shortcode-name="rebelmouse-image" />
Albert Einstein With Displaced Children From Concentration Camps. 1949.
Photo by Keystone-France/Gamma-Keystone via Getty Images
Rank 1<p>The group in this class of the smartest physicists included the top minds that developed the theories of quantum mechanics.</p><p><a href="http://en.wikipedia.org/wiki/Werner_Heisenberg" target="_blank">Werner Heisenberg</a> (1901 - 1976) - a German theoretical physicist, who's achieved pop-culture fame by being the name of Walter White's alter ego in <em>Breaking Bad</em>. He is known for the Heiseinberg Uncertainty Principle and his 1932 Nobel Prize award flatly states it was for nothing less than "the creation of quantum mechanics".</p><p><a href="http://en.wikipedia.org/wiki/Erwin_Schr%C3%B6dinger" target="_blank">Erwin Schrödinger</a> (1887 - 1961) - an Austrian-Irish physicist who gave us the infamous "Schroedinger's Cat" thought experiment and other mind-benders from quantum mechanics. The Nobel-prize-winner's <a href="https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" target="_blank" rel="noopener noreferrer">Schrödinger equation</a> calculates the <a href="https://en.wikipedia.org/wiki/Wave_function" target="_blank">wave function</a> of a system and how it changes over time. </p>
Erwin Schrödinger. 1933.
Satyendra Nath Bose. 1930s.
Enrico Fermi. 1950s.
Rank 2.5<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ0NDcwNy9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY0NDE1MDIxM30.Eg6tca61EredHxjqNH29HY3UeJbgBVa1nA13EhXTooU/img.jpg?width=980" id="90f86" class="rm-shortcode" data-rm-shortcode-id="0f1e6c5e13263a77b2061e1191fd8baf" data-rm-shortcode-name="rebelmouse-image" />
Lev Landau. 1962.<p><strong>Rank 2.5</strong> is where Landau initially ranked himself, rather modestly, thinking he didn't produce any foundational accomplishments. He later moved his prominence, as his achievement mounted, to the higher <strong>1.5.</strong></p>