Latest news with #DouglasHofstadter
The Guardian
04-08-2025
- Entertainment
- The Guardian
Did you solve it? Ambigrams – you won't believe these flipping words!
Earlier today I wrote about ambigrams, a type of writing that is designed to be read in more than one way. Typically, an ambigram is a word or phrase that has left-right mirror symmetry, or reads the same upside down. (To read the article click here.) I set the following challenge – scroll down to see designs by ambigram author (and public intellectual) Douglas Hofstadter and by readers of this column. Flipping words Design an ambigram for the following words: 1. DAVE 2. OHIO 3. UTAH 4. RED 5. Your own name First, here are Hofstadter's designs, taken from his latest book, Ambigrammia. 1. And another Dave: 2. 3. above the headline, and here is his name: Thanks to all the readers who sent it examples. Here are my favourites: Ambigrammia by Douglas Hofstadter, with an introduction by Scott Kim, is out now on Yale University Press. I've been setting a puzzle here on alternate Mondays since 2015. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.
The Guardian
04-08-2025
- Entertainment
- The Guardian
Can you solve it? Ambigrams – you won't believe these flipping words!
Douglas Hofstadter is probably best known as the author of Gödel, Escher Bach, a classic of popular science writing published in 1979. In 1983, he coined the word 'ambigram', meaning a piece of text that can be read in more than one way, an art form pioneered in the 1970s by the typographers Scott Kim and John Langdon. Typically, an ambigram is a word or phrase that has left-right mirror symmetry, or reads the same upside down. Hofstadter, aged 80, is professor of cognitive science and comparative literature at Indiana University, and has produced thousands of ambigrams over the decades. Here's one that is pleasingly self-referential, taken from his latest book, Ambigrammia. It has a vertical line of symmetry through the 'g', which means you can read it left to right, and also in a mirror. The 'ambi' when reflected reads 'rams'. Here's another one, geographically appropriate, that has 180 degree rotational symmetry. (It reads the same upside down.) Isn't it clever? The dots underneath the 'r' and the 't' do not distract from the letters, but when upside down are clearly the dots on two 'i's. Hofstadter describes each ambigram as a 'pocket-sized creativity puzzle.' So I thought they would make a perfect challenge for this column. Flipping words Design an ambigram for the following words: 1. DAVE 2. OHIO 3. UTAH 4. RED 5. Your own name The aim in an ambigram is legibility. You want the word to be as readable as possible. Usually an ambigram has perfect symmetry (mirror or rotational) as in the the two examples above, but not always, as in 'GREEN' in the top image. You can use upper case, lower case, or a mixture of the two. You will need to experiment at first. How much you can tweak a letter without making it unrecognisable, and how much you can add without overwhelming the eye? With DAVE, the A and the V are (almost) inversions of each other. Harder is to see how to make an E into an upside down D. I'll be back at 5pm UK with Hofstadter's designs for 1 to 5. If you would like me to feature your designs of your names in that post, please either email me or tag me on Twitter or Bluesky. Ambigrammia by Douglas Hofstadter, with an introduction by Scott Kim, is out now on Yale University Press I've been setting a puzzle here on alternate Mondays since 2015. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.
Yahoo
23-03-2025
- Science
- Yahoo
The butterfly effect: A misaligned experiment accidentally unfolds quantum wings
In a remarkable scientific breakthrough, researchers at Princeton University have observed a fractal energy pattern in quantum materials that had only been predicted on paper for nearly fifty years. Known as Hofstadter's butterfly, this intricate design emerges from the behavior of electrons in certain conditions. Originally theorized in 1976 by physicist Douglas Hofstadter, the pattern had never been directly observed in an actual material — until now. The discovery came as a surprising outcome of research focused on superconductivity, where a small experimental mistake opened the door to this long-sought-after observation. The discovery was made possible by recent developments in materials science, where scientists are able to stack and twist extremely thin layers of carbon atoms — known as graphene — into specific structures. This twisting creates moiré patterns, a kind of interference design similar to overlapping fabrics. 'These moiré crystals provided an ideal setting to observe Hofstadter's spectrum when subjecting electrons moving in them to a magnetic field. These materials have been extensively studied, but up to now the self-similarity of the energy spectrum of these electrons had remained out of reach,' explained Ali Yazdani, James S. McDonnell Distinguished University Professor at Princeton. Interestingly, the discovery happened by accident. The research team, led by Yazdani, was originally studying superconductivity in twisted bilayer graphene. 'Our discovery was basically an accident,' admitted Andrew Nuckolls, one of the researchers. 'We didn't set out to find this.' Dillon Wong, postdoctoral research associate and co-lead author of the paper, elaborated, 'We were aiming to study superconductivity, but we undershot the magic angle when we were making these samples.' This misstep produced a longer moiré periodicity than planned — but exactly the right conditions for observing the fractal spectrum. capable of imaging atoms by measuring the tiny quantum currents that flow between the microscope tip and the surface. While using the STM, the team noticed unusual behavior in electron energy levels. 'The STM is a direct energy probe, which helps us relate back to Hofstadter's original calculations, which were calculations of energy levels,' said Myungchul Oh, a postdoctoral research associate and co-lead author. Electrical resistance measurements in past studies had hinted at the butterfly pattern, but the STM allowed for direct visualization. 'Sometimes nature is kind to you,' said Nuckolls. 'Sometimes nature gives you extraordinary things to look at if you stop to observe it.' The team's work also shed light on how electrons interact with each other in these complex materials. While Hofstadter's original calculations did not account for electron interactions, this experiment showed that including these effects made the models more accurate. 'The Hofstadter regime is a rich and vibrant spectrum of topological states, and I think being able to image these states could be a very powerful way to understand their quantum properties,' said Michael Scheer, a graduate student and co-lead author. Though immediate applications are unclear, this accidental discovery opens exciting new possibilities for understanding quantum materials. The study was published in the journal Nature.
