Jupyterjones - Productivity Please !!!

Hey guys, I’m observing a high school class and was looking at a textbook, and learned that irrationals are closed under addition! Super cool, who knew!

Weirdly anti-millennial articles have scraped the bottom of the barrel so hard that they are now two feet down into the topsoil

gotta catch em all

Planetary Frequencies.

Geometry at work: Maxwell, Escher and Einstein

Maxwell’s diagram

from the 1821 “A Philosophical Magazine”, showing the rotative vortexes of electromagnetic forces, represented by hexagons and the inactive spaces between them

The impossible cube

invented in 1958, as an inspiration for his Belvedere litography.

Geometry of space-time

The three dimensions of space and the dimension of time give shape to the fourth, that of space-time.

How is geometry entangled in the fabric of the Universe?

Geometry can be seen in action in all scales of the Universe, be it astronomical – in the orbital resonance of the planets for example, be it at molecular levels, in how crystals take their perfect structures. But going deeper and deeper into the fabric of the material world, we find that at quantum scale, geometry is a catalyst for many of the laws of quantum-physics and even definitions of reality.

Take for example the research made by Duncan Haldane, John Michael Kosterlitz and David Thouless, the winners of the 2016 Nobel prize in physics. By using geometry and topology they understood how exotic forms of matter take shape based on the effects of the quantum mechanics. Using techniques borrowed from geometry and topology, they studied the changes between states of matter (from plasma to gas, from gas to liquid and from liquid to solid) being able to generate a set of rules that explain different types of properties and behaviors of matter. Furthermore, by coming across a new type of symmetry patterns in quantum states that can influence those behaviors or even create new exotic types of matter, they provided new meaning and chance in using geometry as a study of “the real”.

If the Nobel Prize winners used abstract features of geometry to define physical aspects of matter, more tangible properties of geometry can be used to define other less tangible aspects of reality, like time or causality. In relativity, 3d space and 1d time become a single 4d entity called “space-time”, a dimension perceived through the eye of a space-time traveler. When an infinite number of travelers are brought into the equation, the numbers are adding up fast and, to see how for example, a space-time of a traveler looks for another traveler,  we can use geometric diagrams of these equations. By tracing what a traveler “sees” in the space-time dimension  and assuming that we all see the same speed of light, the intersection points of view between a stationary traveler and a moving one give a hyperbola that represents specific locations of space-time events seen by both travelers, no matter of their reference frame. These intersections represent a single value for the space-time interval, proving that the space-time dimension is dependent of the geometry given by the causality hyperbola.

If the abstract influence of geometry on the dimensions of reality isn’t enough,  take for example one of the most interesting experiments of quantum-physics, the double-split experiment, were wave and particle functions are simultaneously proven to be active in light or matter. When a stream of photons is sent through a slit against a wall, the main expectation is that each photon will strike the wall in a straight line. Instead, the photons are rearranged by a specific type of patterns, called diffraction patterns, a behavior mostly visible for small particles like electrons, neutrons, atoms and small molecules, because of their short wavelength.

Two slits diffraction pattern by a plane wave. Animation by Fu-Kwun Hwang 

The wave-particle duality is a handful, since it is a theory that has worked well in physics but with its meaning or representation never been satisfactorily resolved. Perhaps future experiments that will involve more abstract roles of geometry in quantum fields, like in the case of the Nobel prize winners, will develop new answers to how everything functions at these small scales of matter.

In this direction, Garret Lissi tries to explain how everything works, especially at quantum levels, by uniting all the forces of the Universe, its fibers and particles, into a 8 dimensions geometric structure. He suggests that each dot, or reference, in space-time has a shape, called fibre, attributed to each type of particle. Thus, a separate layer of space is created, parallel to the one we can perceive, given by these shapes and their interactions. Although the theory received also good reviews but also a widespread skepticism, its attempt to describe all known fundamental aspects of physics into one possible theory of everything is laudable. And proving that with laws and theories of geometry is one step closer to a Universal Geometry theory.

What’s encrypting your internet surfing? An algorithm created by a supercomputer? Well, if the site you’re visiting is encrypted by the cyber security firm Cloudflare, your activity may be protected by a wall of lava lamps.

Cloudflare covers websites for Uber, OKCupid, & FitBit, for instance. The wall of  lamps in the San Francisco headquarters generates a random code. Over 100  lamps, in a variety of colors, and their patterns deter hackers from accessing data.  

As the lava lamps bubble and swirl, a video camera on the ceiling monitors their unpredictable changes and connects the footage to a computer, which converts the randomness into a virtually unhackable code.

Codes created by machines have relatively predictable patterns, so it’s possible for hackers to guess their algorithms, posing a security risk. Lava lamps, add to the equation the sheer randomness of the physical world, making it nearly impossible for hackers to break through.

You might think that this would be kept secret, but it’s not. Simply go in and ask to see the lava lamp display. By allowing people to affect the video footage, human movement, static, and changes in lighting from the windows work together to make the random code even harder to predict.

So, by standing in front of the display, you add an additional variable to the code, making it even harder to hack. Isn’t that interesting? 

via atlasobscura.com