In an earlier post (Elliptic trapdoors) I did my best to explain addition and multiplication along an elliptic curve. The diagram showed a point P doubled to produce 2P, then added to itself to produce 3P, and added again to produce 4P. The dotted lines indicated the mirror reflection operation to arrive at the final…More
Elliptic fields
One property of algebraic equations is that you can perform the same simple arithmetical operation on both sides of the equation and the equivalence still holds for the same x and y values, e.g. y = 2x has the same values if both sides are multiplied by the same number e.g. 6y = 12x. The…More
Sharing a secret number
Here’s a naive method for two people to agree a secret number. The number to be shared is simply an integer, which is a key for some other encrypted communication channel. It could even be a PIN to a bank account, an access code for a door or the combination code to a shared locker…More
Elliptic trapdoors
Elliptic curves are amongst a family of curves that make up the alluring surfaces of much contemporary organically-inspired architecture. They are also the basis of encryption methods that secure digital communications. A trapdoor is a one-way portal. You can go through it easily in one direction, but it’s difficult to come out again in the…More
RSA public key encryption
I’m continuing this dive into public-private key encryption. As outlined in a helpful blog post by Nick Sullivan, the kind of encryption I described in the last two posts relies on a simple property of numbers. It’s easy to multiply two numbers, even if very large, but more difficult to factor a number, i.e. find…More
Asymmetric key encryption
An encryption key is a string of characters that you feed into an encryption algorithm to either encrypt or decrypt a message. An asymmetric key system has two keys. There’s a public key to encrypt a message. It’s public because anyone can see it and use that key. But once the message is encrypted using…More
Primes
Some secure encryption methods make use of prime numbers. I’ll examine the method in the next post, but here’s some properties of primes relevant to encryption, presented via simple grid geometry. Hopefully that connects this esoteric field with spatial shapes such as rectangular rooms on a gridded plan. Composites A composite number is a positive…More
Failure for sale
Things that don’t function properly are valuable commodities if their failure offers advantage for someone. In fact, it’s information about that failure that’s the commodity. Consider an urban example. You see that your neighbours have left one of their windows unlatched as they are about to move out for the weekend. So, you’ve detected a…More
Shibboleth
A Shibboleth is a kind of pronunciation test. You can tell where someone is from, or not from, by asking them to say a particular word. It can also indicate where someone has been. I can tell with a degree of certainty if someone has been to Australia by the way they say “Melbourne.” If…More
Wittgenstein’s secret place
The philosopher Ludwig Wittgenstein (1889-1951) wrote diary entries in code. I’ve been reading Dinda Gorleé’s book Wittgenstein’s Secret Diaries: Semiotic Writing in Cryptography. There are several touch points with architecture and place. Wittgenstein had trained as a mechanical engineer, and undertook a serious foray into architecture when he designed his sister’s house, which followed the…More
Cryptography for space aliens
“Anticryptography” is a loose term to designate a type of cryptographic message that is legible to someone who has no knowledge of the plain text language from which the message derives. Nor do they have access to the method of encryption, or anything like an encryption or decryption key. Nor is the message meant to…More
Quantum entanglement for designers
The idea of the quantum Internet (QI) adds a new dimension to city infrastructures. Quantum physics is even more difficult to grasp than the blockchain. But I’ll give it a shot, starting with lasers. Lasers A laser beam is a concentrated beam of coherent light within a narrow colour band (i.e., frequency range). You can…More
Quantum Internet
Quantum computers can potentially remove the need to iterate through the huge numbers of combinations required to crack a code, reconstruct an original source document from a hash string or derive the key used to encrypt a file.More
How architecture keeps its secrets
Here’s a basic application of the containment principle. If you put something into a cardboard box and close the lid then it’s concealed from view. Buildings also conceal things. I discussed the house-museum of the architect John Soane in a previous post. Soane was a practitioner within a secret society (Freemasonry), which in turn traded in…More
Seven secrets
Architecture has even more in common with the theory and practice of secret-keeping than do secret societies. I would add the offer of crypts, basements, darkened rooms and cupboards to the reasons secret societies gravitate towards architecture: its histories and theories, functions, types and symbols. I’ve started reading (listening to) Dan Brown’s novel The Lost…More
Secret architecture
The prominent Regency architect John Soane (1753-1837) was a member of a secret society. In an account provided by architectural historian David Watkin, Soane “took Freemasonry very seriously” (402). Though he wasn’t initiated as a member until the age of 60 his work adopted the mood of Freemasonry. “He reflected its deistic philosophy in his…More
Secret society
There exists a secret society, custodian of the theory and practice of secrets. Its adherents embrace the systematic invention, application and promotion of codes and ciphers. As it includes architects and mathematicians amongst its adherents, this society preserves and embeds arts of semiotics, geometry, combinatorics, indices, logics, riddles, paradoxes, and mechanisms to examine the arts…More
Secrets of the lodge
A lodge is a shelter, probably with only simple functional articulation of parts (i.e. rooms), as in the case of a shed, pavilion, cabin, booth or bothy (in Scotland). Related to lodge, we have loggia, an annexe to a building that is open on some of its sides, like a porch or verandah. The lodge…More
Camouflaged incitement
Everyone fights, or are prepared to say they do. As I noted in my last post, Fighting words, a major charge against Trump was that he exhorted his followers to “fight like hell.” His defence lawyers countered with a lengthy sound montage instancing peace-loving politicians (I think all Democrats) invoking the word “fight” in their…More
Fighting words
“Surveying the tense crowd before him, President Trump whipped it into a frenzy, exhorting followers to ‘fight like hell [or] you’re not going to have a country anymore.’ Then he aimed them straight at the Capitol, declaring: ‘You’ll never take back our country with weakness. You have to show strength, and you have to be…More
Crypto-conspiracy
CryptoArt is a term applied to artworks that are bought, sold and authenticated on a blockchain. In this sense, CryptoArt is no more a genre, sub-genre, style or movement in art than auction art, gallery art or collectible art. “Art” is not a protected or regulated noun and invites appendage to many other nouns. A…More
CryptoArt 101
Now that the worth of my Bitcoin wallet has risen to double figures (in £s) I’m ready to invest in some digital art. Digital artworks are static or moving digital pictures, such as animated GIFs, though the category could include any digital asset: video, sound file, music score, computer code, 3D computer model, etc. In…More
Decryptopolis
Newly elected US Members of Congress and their staff were disoriented and nervous as they hid in the basement of the Capitol. Included in their concern was the fear of contracting COVID-19 while close to one another, and in the company of people who wouldn’t wear masks (Washington Post). Elsewhere I’ve identified cases where the…More
Deplatformed
Facebook and Twitter have “deplatformed” Trump. In any grievance it’s shrewd practice to focus on just one offence rather than confuse the case with a barrage consisting of all the complaints you could advance. Following that restrained practice, Twitter Inc. drew attention to Trump’s 2 most recent tweets. In their Twitter blog the company declared:…More
Filter variables
When did you decide to grow a beard? Not every event over which a person assumes agency has a singular moment or an origin. Nor does it, of necessity, involve a decision. A slightly less gendered scenario is that of strolling through the neighbourhood — perhaps as exercise during pandemic restrictions. Sometimes we just wander…More
What’s the use of variables?
Trumpian-style relativism and denialism assumes the right to make up some numbers and refuse others: votes, profits, employment rates, infections and crowd sizes. That’s to mistake variable for uncertain, unreliable and arbitrary as if “up for grabs.” Variables 101 In maths and logic a variable is a symbol standing for something unspecified, though you might…More
Unclear thinking
It came upon a midnight clear. Clarity and its converse unclarity are in the air this season: as people seek clarity on what they can and cannot do during this phase of the pandemic. Clarity is about optics. Something is clear if the perception of it is unobstructed by darkness, fog, blur, glare, distortion or…More
Secret norms
“Normal” is an architectural term, according to the OED derived from the Latin noun norma which was a square of wood used by carpenters and masons for creating right angles. As known to any student of geometry, a line (or wall) is normal to another if it meets it at right angles. The term has…More
Place is the code
In cryptographic communication, a sender has a message in mind then converts that into a coded signal. The sender dispatches the signal through a communication channel and it is picked up by a recipient who decodes the message. The coding and decoding algorithms at either end of the channel select from an array of alternative…More
Permeable portals
The satirical fantasy The Good Place is ostensibly about the afterlife, and features different mechanisms for moving between the Good Place, the Bad Place, the Medium Place and Earth via magical doors, a hot air balloon, a train, a snap of the fingers, pneumatic chutes and giant round doors that clamp shut like the iris…More
Parallel worlds
He’s making few public appearances but “the pixels of his Twitter feed continued to live in a world of alternative reality,” echoed the Washington Post this week about Trump. Meanwhile, His Dark Materials that also taps into a multiverse of realities is back on the BBC. A helpful entry in Wikipedia under multiverse lists several…More
Hidden dimensions
Cryptography hides messages from the senses, observation and interpretation. It belongs within an array of practices that fit comfortably within the field of semiotics. I’m content to think that cryptographic practices extend C.S. Peirce’s semiological pragmatism. After all, messages hidden in code are signs. On the subject of messaging, I’m also interested in hiddenness as…More
How to fail at populism
Twitter replaced some of Trump’s recent tweets about the US election with the message: “Some or all of the content shared in this Tweet is disputed and might be misleading about an election or other civic process” — followed by a link to Twitter’s Civic Integrity Policy. As votes for Joe Biden (D) secured the…More
High energy superstition
My online searches into the mathematical techniques of Hidden Markov Models (HMM) led me to this diagram, known as a numogram. I have redrawn it here from the numerous instances on websites and books connected with the short-lived CCRU (Cybernetic Culture Research Uni) at the University of Warwick, and its legacies. At face, it’s a…More
Counting letters
A substitution cipher is one of the simplest methods for encrypting a message. A unique symbol stands in place of every letter in the hidden message. The symbol set can be just about anything, as long as each symbol maps uniquely to the letters of whatever alphabet you are using for the message you wish…More
Speech to text
A city that’s legible is easy to understand and to navigate, i.e. to read. You can read a city’s people, moods, signs, and what it denotes and connotes. In a previous post I explored the prospect that you might write a city, as well as read it. According to this theory, a city participates in…More
II V I and all that Jazz
With more time spent teaching in front of a computer I’ve learnt more about developments in automated speech recognition. Software that turns speech into text (as transcriptions and closed captions) is a major accomplishment. Practically it’s “artificial intelligence” (AI). Researchers attempt the same with music: turning an audio music track into musical notation: notes on…More
What’s popular?
What’s it like to be liked? The WordPress blogging platform delivers analytics for each blog post providing the author with stats on visits, likes and comments. You would expect older posts to have more visits than recent visits. So it’s hard to compare the popularity of posts. But you can compare these stats if you…More
What comes next?
It’s a banal truism: events follow one another in sequence, inexorably. You brush teeth, you wash face, you pour cereal, you eat cereal, you rinse bowl, you attend online meeting, you get dressed … Such sequences often follow patterns. In some cases, a researcher might want to detect those patterns: to predict what comes next,…More
Hidden beats
The online book City Rhythm published in 2018 explores rhythm to explain cities and their internal diversity, as well as differences between cities. As I have explored elsewhere, mundane and ordinary events are also everyday events i.e. events that occur every day, repeatedly, and relate to people’s habits, their habitual activities. So a rhythmanalysis can focus…More
Is blogging obsolete?
Text-based blogging, or weblogging, developed in the 1990s as a medium for recording and presenting date-stamped content, accessed through a single web address, presenting the most recent post at the top of the home page. I’ve been doing this for 10 years now. So it’s time to reflect. Video blogs (vlogs) and audio podcasts have…More
Visitor rhythms
August 25, 2020 marked the tenth anniversary of this blog site. To mark the occasion I thought I would experiment with visitor statistics and their rhythms. WordPress provides helpful visitor statistics that indicate topics that have most attracted readers — or that people are most likely to stumble across. My most viewed post by far…More
Tremble and drift
For philosopher Henri Lefebvre, rhythms are influenced by their context. They also vary. The waves on the sea provide an obvious example. Perturbations across water involve counter movements, complex overlays of movement, and the patterns rely on the shape and materials of the shore, the tides, weather conditions, and water traffic. He contrasts rhythm with…More
Visualising 2D Discrete Cosine Transforms
I’m interested in the Discrete Cosine Transform (DCT) method as a means of hiding one image inside another. It’s also a key technique in image compression. I’ve implemented the DCT method on an Excel spreadsheet. The image below is an 8×8 grid of pixel values, in grey ranging from 0 = black to 255 =…More
COVID-19 Rhythmanalysis
Rhythms permeate the city, and these rhythms overlap, combine, aggregate and interfere with one another. That’s the gist of Henri Lefebvre’s book entitled Rhythmanalysis. By my reading the concept fits within the genre of research concerned with everydayness, the quotidian, which implies a concern with ordinary things and everyday phenomena that repeat. (See post: Time…More
Beyond averages: DCT graphics
The visual field is full of smooth curves. Shadows don’t have sharp edges but fade out. Colours blend, sometimes imperceptibly. At some level of detail, most things transition smoothly, but to varying degrees. The variation across such transitions is noticeable in a high quality digital photograph, i.e. a pixel image. Here is a random row…More
The culture of the GIF
GIF image files have 8 bit colour for red (R), green (G) and blue (B), i.e. 256 shades each for RGB. Most smartphone cameras currently provide 10 bit colour. So if you convert your photographs to GIF format they will be of lower quality. Apart from that the GIF format provides lossless compression. So GIF…More
Subliminal messaging
There’s no real evidence that subliminal messaging works. By most accounts, the experiments of the marketing psychologist James M. Vicary in the 1950s were a hoax. The theory was that we pick up words and images presented to us in ways that defy conscious awareness. Audiences in a cinema could be induced to buy a…More
Hiding one surface inside another
What’s it like to get inside a surface? I’ve been reading Avron Stroll’s seminal philosophy book Surfaces. He exhausts most of the ways people use the word “surface” in everyday speech. E.g. you can be on a surface or under it, but it’s not usual to speak of a surface inside a surface. And some…More
Ornament and crime
The Austrian architect Adolf Loos (1870-1933) wrote Ornament and Crime. It is a celebrated polemic against the superfluity of ornament in the modern industrial age: “not only is ornament produced by criminals but also a crime is committed through the fact that ornament inflicts serious injury on people’s health, on the national budget and hence…More
