beerbellyblunt
1. Take a circle and draw some points on the boundary. For every point you draw, you must also draw its antipode (point on the opposite side of the circle).
2. Draw some points in the interior wherever you want. 3. Label the points either +1, -1, +2, or -2 as you wish. The only stipulation is that antipodes must have opposite sign.
4. Draw triangles however you want without crossing lines.
Tucker’s Lemma says that you will ALWAYS end up with at least one line that has endpoints of either +1 and -1 or +2 and -2. Try it! More info and proof here.
Never say, “I tried it once and it did not work.”
Ernest Rutherford (via fyp-science)
“In 1972, Edward Lorenz gave a presentation titled: “Predictability: Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” The term “butterfly effect” was born. Lorenz, who was born on this day in 1917, was a pioneer of chaos theory, which analyzes how subtle changes in the initial conditions of a system can lead to widely differing outcomes. This 2013 Physics Today article examines Lorenz and the birth of chaos theory.” - Physics Today
Chaos at fifty by Adilson E. Motter and David K. Campbell is an article that lays out the discovery of chaos. I found it a very satisfying and informative read about dynamical systems, the butterfly effect, bifurcations, predictability and fractals. You should probably go check it out by clicking on the bolded title. 👍
“Chaos sets itself apart from other great revolutions in the physical sciences. In contrast to, say, relativity or quantum mechanics, chaos is not a theory of any particular physical phenomenon. Rather, it is a paradigm shift of all science, which provides a collection of concepts and methods to analyze a novel behavior that can arise in a wide range of disciplines.” - Chaos at fifty
Image above: “The Lorenz attractor, as revealed by the never-repeating trajectory of a single chaotic orbit. The spheres shown here represent iterations of the so-called Lorenz equations, calculated using the original parameters in Edward Lorenz’s seminal work. (Spheres are colored according to the iteration count.) From certain angles, the two lobes of the attractor resemble a butterfly, a coincidence that helped earn sensitive dependence on initial conditions its nickname—the butterfly effect. An animated visualization of the attractor is available here. (Image courtesy of Stefan Ganev.)”
Congratulations on adopting a scientist! Regardless of their field they will require much coffee, free food, and love. Here are some field specific tips for keeping your scientist happy and healthy!
Biology: make sure they don't get overly invested in their model organism by reminding them about the flaws inherent in their system on a regular basis, but also make sure to join in when they criticize other models in favor of their own
Chemistry: don't let them do that 'just one more reaction' at 10 pm. make sure they get out of the lab and see the sun on a regular basis. try to keep them from partying too hard when they do leave the lab
Geology: humor their rock puns but don't let the lick the rocks (they will tell you they need to lick the rocks to identify them, but don't fall for it)
Astronomy: try not to let them become completely nocturnal. point out nice stars to them and look suitably impressed by their "pictures" of planets that don't look like anything to you
Physics: take them to the park on a regular basis to remind them that things larger than subatomic particles exist. bring a frisbee or a ball to play catch with and be impressed by their ability to calculate trajectories
Math: always make sure to have free batteries for their calculators and a mathmatica user guide on hand. Humor them when they tell you why space without angles is important
Ecology: make sure they remember to wear sunscreen and keep an eye on them in the field. Remind them to come inside and analyze their data occasionally
Psychology: don't mention Freud or ever call them a soft or social science, but make sure you gently remind them that social factors can impact reproducibility and try to keep them from drawing sweeping conclusions about the inherent nature of humanity
Neuroscience: be suitably impressed by their newest experiment and then remind them that people are not mice as often as possible
Computer Science: make sure they take breaks while debugging by limiting their supply of coffee. Nod and smile when they go off on indexing and arrays. Make sure they always have a rubber duck.
Make sure to keep your scientist away from engineers unless they have been properly socialized to interact in a translational household. The most important thing is to remember to hug your scientist on a regular basis and remind them that there is life outside the lab
🤐
The possibilities for the new field of two-dimensional, one-atomic-layer-thick materials, including but not limited to graphene, appear almost limitless. In new research, Penn State material scientists report two discoveries that will provide a simple and effective way to “stencil” high-quality 2D materials in precise locations and overcome a barrier to their use in next-generation electronics.
In 2004, the discovery of a way to isolate a single atomic layer of carbon – graphene – opened a new world of 2D materials with properties not necessarily found in the familiar 3D world. Among these materials are a large group of elements – transition metals – that fall in the middle of the periodic table. When atoms of certain transition metals, for instance molybdenum, are layered between two layers of atoms from the chalcogenide elements, such as sulfur or selenium, the result is a three-layer sandwich called a transition metal dichalcogenide. TMDs have created tremendous interest among materials scientists because of their potential for new types of electronics, optoelectronics and computation.
Read more.
Fatality 💀
“We TOLD you it was hard.” “Yeah, but now that I’VE tried, we KNOW it’s hard.”
Here to Help [Explained]