Happy 70th Mick! (7/26/43) Time is still on your side!
An original German film herald for Fritz Lang’s METROPOLIS (1927). A serious rarity, and a lovely piece of original ephemera from the film. (SOLD).
I’ve got that too - not that rare though :p
What is 1 - 2 + 3 - 4…? Before you read on, guess!
In mathematics, 1 - 2 + 3 - 4 +… is the infinite series whose terms are the successive positive integers, given alternating signs. The infinite series diverges, meaning that its sequence of partial sums, (1, −1, 2, −2, …), does not tend towards any finite limit. Nonetheless, in the mid-18th century, Leonhard Euler figured out the sum of this infinite series, though a rigorous explanation wouldn’t arrive until much, much later. Leonhard Euler wrote what he admitted to be a paradoxical equation: 1 - 2 + 3 - 4… = 1/4.
The image above is a visualization of the terms and partial sums of 1 - 2 + 3 - 4 +… going out to the horizon.
- The terms are indicated as black lines executing displacements to the camera’s right, plus a constant displacement away from the camera.
- The partial sums are where the terms end; they are indicated as black circles.
- The action takes place on an infinite horizontal plane. The integers are located on the gray lines. The horizon is picked out by a bluish sky.
So basically, it’s a horizontal graph of 1 - 2 + 3 - 4… with the first point being at zero. When you add one, it zig-zags up to positive one. Subtract two, and it zig-zags down to negative one. Add three, and it zig-zags up to positive two, and so on.
Now, look at the visualization and squint your eyes. See the graph as somewhat of a triangle. Imagine a straight line going down the center of that triangle…where is that line? If you thought, “about a quarter of the way between 0 and 1”, then you just figured out the sum of the infinite series 1 -2 +3 - 4…! Learn more about this method.
David Bowie - Aladdin Sane (1973)
The name of the album is a pun on “A Lad Insane”. Although technically a new Bowie ‘character’, Aladdin Sane was essentially a development of Ziggy Stardust in his appearance and persona, as evidenced on the cover by Brian Duffy and in Bowie’s live performances throughout 1973 that culminated in Ziggy’s ‘retirement’ at the Hammersmith Odeon in July of that year. Moreover there was not the thematic flow on this album that was present on its predecessor. Bowie himself described Aladdin Sane as simply "Ziggy goes to America", most of the tracks being observations he composed on the road during his 1972 US tour.
The Formal Generators Of Structure
Axonometric visual experiments by architects Stanley Tigerman & G. T. Crabtree - via Data Is Nature:
Architect Stanley Tigerman’s‘The Formal Generators of Structure’ (Architecture & Urbanism Journal, 1975) explored the combinatorial use of rectilinear shapes to generate volumetric, optical and architectonic compositions. Spatial configurations of the square and cruciform are extruded to create axonometric projections reminiscent of the ‘ideal’ geometricism of the De Stijl school. They are also reminiscent of the works of Op-artists such as Albers and Vasarely who toyed with the square to infinity through structural multiplicity and chromatic modulation.
A collection of images can be found at RBDRD here
More at Data Is Nature can be found here
Planet Travel Posters Sets Mars & Venus by Ron Guyatt
Space tourism is still a long ways off, but it’s not hard to imagine that someday, tourists will visit the natural geological landmarks of other worlds much like they tour the Grand Canyon, Mount Everest or Ayers Rock. Each of these great tourist destinations needs a classic retro travel poster to entice visitors. Until the day people settle off world and make their own destinations many of these may be the places that people will want to travel too. I hope that these posters can inspire people to think beyond our world to the limitless possibilities of the Universe.
Posters Available at My Store
Apollonian Gasket Variations by Fdecomite
In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from triples of circles, where each circle is tangent to the other two. It is named after Greek mathematician Apollonius of Perga.
An example of a simple Apollonian Gasket:
By viewing the example, it may be simple to deduce the construction of an Apollonian Gasket, however, instructions can be found here in this wonderful Vihart video. Have fun creating your own Apollonian Gaskets!
There’s another fractal hiding in one of these gaskets. Can you spot it?
Sunday’s Scorcher by Alan Friedman
Supersymmetric glue: the search for gluinos
One of the biggest unanswered questions of particle physics is why the mass of the Higgs boson is relatively small when the Standard Model suggests a more natural value would be many thousands of trillions of times higher. We don’t know the answer to that question, but a popular proposed explanation invokes the idea of supersymmetry. Theories that include supersymmetry can very easily explain the Higgs boson’s low mass.
A theory that includes supersymmetry comes with a price. These theories predict that for every known particle, a cousin supersymmetric particle exists. These cousins have the same properties as the familiar ones, except they have a different subatomic spin. There’s only one problem. None of these cousins has been observed. The simplest form of supersymmetry has been definitively ruled out.
More Martin Gardner Puzzle Love
So simple, but SO annoying!
Cut each of the four shapes into two identical pieces. The pieces can be mirror images of each other.
Someone?? Meep [CJH]
P.S. It took me forever, but if you get stuck — solutions!