How mathematics built the modern world

"Mathematics was the cornerstone of the Industrial Revolution. A new paradigm of measurement and calculation, more than scientific discovery, built industry, modernity, and the world we inhabit today." Full article by Bo Malmberg and Hannes Malmberg @ worksinprogress

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Neural-inspired NorthPole energy-efficient computing chip

"The amount of data humans process and send around the globe on a daily basis is astonishing. However, the energy cost involved is high, and there is a strong need for designing energy-efficient devices. Modha et al. describe a chip with a neural inspired architecture, called NorthPole, that achieves substantially higher performance, energy efficiency, and area efficiency compared with other comparable architectures (see the Perspective by Iyer and Roychowdhury). A key feature of this chip is the recognition that for almost all kinds of computing, access to memory plays as important a role as logic processing. Unlike analog in-memory computing, this purely digital system has the option of tailoring the bit precision as needed, which allows for optimization of the power usage". Full Article @ Science.




Modeling systems

Pi the Movie

Fibonacci Sequence

The magic of Fibonacci numbers by Arthur Benjamin

Peter Hilton (1923-2010) discusses intriguing number tricks that can be explained by analysing the properties of Fibonacci numbers and the related Lucas numbers. The explanations themselves benefit from further explanations which, in their turn, lead to further discoveries. Recorded at Imperial College London during the 1996 London Mathematical Society Popular Lecture series.

D'Arcy Thompson

Patterns of Life – D’Arcy Thompson, Structuralism and the Shape of Life

Treasures of the Library 5. D'Arcy Thompson, On growth and form

BLOOMS: Strobe Animated Sculptures Invented by John Edmark from Charlie Nordstrom on Vimeo. "This series of 3D printed sculptures was designed in such a way that the appendages match Fibonacci's Sequence, a mathematical sequence that manifests naturally in objects like sunflowers and pinecones. When the sculptures are spun at just the right frequency under a strobe light, a rather magical effect occurs: the sculptures seem to be animated or alive!"

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Colossus, electronic analog

"Let us not imagine, however, that Colossus was a programmable, general-purpose computer in the modern sense. It could logically combine two data streams – one on tape, one generated from ring counters – and count the number of 1s encountered, and that was all. Much of the “programming” of Colossus was actually carried out on paper, with operators executing decision trees prepared by analysts." From, The Electronic Computers, Part 2: Colossus.

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Advances on cracking Antikythera Mechanism

"Freeth and colleagues at University College London (UCL) believe they have finally cracked the puzzle using 3D computer modelling. They have recreated the entire front panel, and now hope to build a full-scale replica of the Antikythera using modern materials". News article at BBC News, full article at Scientific Reports.

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From Bones to Turing Machines

The Lebombo Bone and Other Ancient Mathematical Objects
African Binary code

  The Ishango Bone

Turing Machine Simulator
Turing Machine Simulator 2
Turing Machine Simulator 3 (Java)

A Turing Machine Overview
BTW, my thoughts on the recent Turing Biopic and a related news article.

The Manchester Baby (1948)

MESM 1950 (Kyev)

Some resources about the Abacus
The Abacus in Various Number Systems
Demo (The Chinese Abacus)
Mechanical Calculators
The Pascaline

The Antikythera Mechanism

The Antikythera Mechanism Research Project
NOVA: Ancient Computer

Another video of the Antikythera Mechanism
Babbage, Lovelace and the Analytical Engine
The Difference Engine
The Analytical Engine
9 Neat Facts About the World's First Computer Programmer, Ada Lovelace 
Ada Lovelace and the Analytical Engine
Helping Ada Lovelace with her Homework: Classroom Exercises from a Victorian Calculus Course

It Started Digital Wheels Turning

Cool implementation of Babbage's Difference Engine using LEGO! Photos, description of adder and carry propagation logic, mechanical issues, etc. at: By Andy Carol

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How Claude Shannon Invented the Future

"The heart of his theory is a simple but very general model of communication: A transmitter encodes information into a signal, which is corrupted by noise and then decoded by the receiver. Despite its simplicity, Shannon’s model incorporates two key insights: isolating the information and noise sources from the communication system to be designed, and modeling both of these sources probabilistically. He imagined the information source generating one of many possible messages to communicate, each of which had a certain probability. The probabilistic noise added further randomness for the receiver to disentangle." Full article @ Quanta Magazine.

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Module 1 - From Borges to Shannon

Some pointers to the Jorge Luis Borges stories we discussed in class.

The Library of Babel
The Garden of Forking Paths
Interview with Jorge Luis Borges Borges' biography.

Information Basics
"The heart of his theory is a simple but very general model of communication: A transmitter encodes information into a signal, which is corrupted by noise and then decoded by the receiver. Despite its simplicity, Shannon’s model incorporates two key insights: isolating the information and noise sources from the communication system to be designed, and modeling both of these sources probabilistically. He imagined the information source generating one of many possible messages to communicate, each of which had a certain probability. The probabilistic noise added further randomness for the receiver to disentangle." Full article @ Quanta Magazine.

Entropy Applet
Letter frequency in English
Word and Letter Frequency in English
Entropy of English
Text Mechanic - Text Manipulation Tools
Shuffle Letters and Narakeet.
1952 – “Theseus” Maze-Solving Mouse @ cyberneticzoo.com

Claude Shannon Demonstrating Theseus

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The role of complexity for digital twins of cities

"We argue that theories and methods drawn from #complexity science are urgently needed to guide the development and use of digital twins for cities. [...]. This is the foundation for a new approach that treats cities not as large machines or logistic systems but as mutually interwoven self-organizing phenomena, which evolve, to an extent, like living systems." Full paper @ Nature Computational Science.

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A Relational Macrostate Theory Guides Artificial Intelligence to Learn Macro and Design Micro

"a general theory for how macroscopic properties emerge from conservation of symmetries in the mapping between observations, we provide a machine learning framework that allows a unified approach to identifying macrostates in systems from the simple to complex, and allows the design of new examples consistent with a given macroscopic property." Full article @ Arxiv.



Accumulation and maintenance of information in evolution

Cool work using information theory to establish upper bounds on information maintenance on organism populations. They "prove a general bound on the rate at which information can accumulate per generation, [finding] that both accumulation and maintenance of information are most efficient (require the least fitness variation per bit) when individual loci experience weak selection. This is relevant for selection on traits influenced by many small-effect loci—a common genetic architecture according to genome-wide association studies." Full paper @ PNAS.

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Complexity science and networks in 20 min

An introduction video to the history and ideas of complexity science and networks in 20 min by Petter Holme.

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What Data Can't Do

"if more data isn’t always the answer, maybe we need instead to reassess our relationship with predictions—to accept that there are inevitable limits on what numbers can offer, and to stop expecting mathematical models on their own to carry us through times of uncertainty." Full article at the New Yorker.

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A few things you should know about complex systems

"Complexity science, also called complex systems science, studies how a large collection of components – locally interacting with each other at small scales – can spontaneously self-organize to exhibit non-trivial global structures and behaviors at larger scales, often without external intervention, central authorities or leaders. The properties of the collection may not be understood or predicted from the full knowledge of its constituents alone. Such a collection is called a complex system and it requires new mathematical frameworks and scientific methodologies for its investigation." A very nice explanation of key concepts with acompanying simulations.



The Hard Lessons of Modeling the Coronavirus Pandemic

"In the fight against COVID-19, disease modelers have struggled against misunderstanding and misuse of their work. They have also come to realize how unready the state of modeling was for this pandemic." Full article @ Quanta Magazine.

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Michael Goldhaber, Simon and the attention economy

"Most of this came to him in the mid-1980s, when Mr. Goldhaber, a former theoretical physicist, had a revelation. He was obsessed at the time with what he felt was an information glut — that there was simply more access to news, opinion and forms of entertainment than one could handle. His epiphany was this: One of the most finite resources in the world is human attention. To describe its scarcity, he latched onto what was then an obscure term, coined by a psychologist, Herbert A. Simon: 'the attention economy.'" Full article @ NY times.




To Understand This Era, You Need to Think in Systems

Even though Zeynep Tufekci is a bit dismissive of the existence of complex systems science as a discipline and even departments, this is a great podcast on the Ezra Klein series.

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modelling Covid, Interdisciplinarity, and Complexity

"The pandemic has created a tragic ‘natural experiment’ - a once-in-a-century jolt that could produce unexpected insights. As well as modelling the spread of disease, researchers have had to track the dynamics of social behaviour. Because of modern digital footprints, they have been able to do this in more detail than ever, providing unique insights into how individuals and communities respond to outbreaks. These behavioural changes, whether driven by explicit government policies or local awareness of infection risk, have in turn had complex social, economic and health impacts. Untangling such effects will no doubt be the subject of research far into the future." Full news article @TheGuardian.

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molecular collectives that regulate genes

Cells use condensed ‘blobs’ to collect the molecules involved in regulating genes, sort of "network fluids with viscoelastic properties". Opens very interesting theoretical possibilities for stochastic information processing in eukaryotes. Full article @ chemistryworld.com.

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Multilevel complexity Phil Anderson’s article “More Is Different”

How a Landmark Physics Paper from the 1970s Uncannily Describes the COVID-19 Pandemic. "Phil Anderson’s article “More Is Different” describes how different levels of complexity require new ways of thinking. And as the virus multiplies and spreads, that’s just what the human race desperately needs". Together with Simon's paper on Hierarchies, and the more complex version of hierarchical (control) complexity by Howard Pattee, these three papers form a essential set in understanding multilevel complexity. Full blog post by Clifford Brangwynne at Scientific American.

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A stretch from bugs to priors and biases

Tom Standage follows a nice random walk from (transcription) bugs to prior biases in AI... Very much a big a conceptual stretch, but, hey, anything that brings back Babbage-Lovelace and programming the first Turing machine (the analytical engine before Turing) is a lot of fun---thank you Thiago for the link.

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Rapid response to change driven by cross-species gene exchanges

"Gulf killifish have made a stunning comeback in Houston with the help of genetic mutations imported from interspecies mating with Atlantic killifish Scientists have suspected that mixing genes through hybridization 'can benefit populations experiencing rapid environmental change,' Clint Muhlfeld, an aquatic ecologist with the United States Geological Survey (USGS) who was not involved in the study, tells The Scientist in an email. 'But to my knowledge this is the first comprehensive study to directly and scientifically support this prediction." The paper itself is another nice example of bioinformatics methods helping understand bioloigy and new phenomena caused by human impact: "Given the limited migration of killifish, recent adaptive introgression was likely mediated by human-assisted transport. We suggest that interspecies connectivity may be an important source of adaptive variation during extreme environmental change." Full news article @ The Scientist and Original Article in Science.

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AI Uses Images and Omics to Decode Cancer

Machine learning can analyze photographs of cancer, tumor pathology slides, and genomes. Now, scientists are poised to integrate that information into cancer uber-models. Full article @ The Scientist.

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CRISPR Computer in Human Cells

A CRISPR/Cas9-based core processor that enables different sets of user-defined guide RNA inputs to program a single transcriptional regulator (dCas9-KRAB) to perform a wide range of bitwise computations, from simple Boolean logic gates to arithmetic operations such as the half adder. [...] In principle, human cells integrating multiple orthogonal CRISPR/Cas9-based core processors could offer enormous computational capacity. Full article @ PNAS

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AI, DDI, and Chat Bots

"Adapting chatbots to medicine has the potential to help millions, if not billions, of people around the world, right when they most need it. If you have a mobile phone, you have access to a doctor. Imagine the positive effect on people's lives with this equalising force. Especially in developing countries where doctors can be few and far between, or in developed countries where health care can be expensive and not immediate. Even if we can help to reduce people's anxiety about something going wrong with their body (or the body of someone in their care) until they can get to a doctor, that can be an immense relief of global suffering. Medical chatbots can offer relevant high-quality information, reassurance, answers, and ways of thinking about the situation that might be more useful. They would not replace human doctors, but they could help to set a new, increased standard of care. [...] A retrospective review in Geriatric Oncology found that 75% of [Cancer] patients had a potential drug–drug interaction. Pharmaceutial chatbots can be a resource for physicians, preventing these unintentional drug–drug interactions. Chatbots can also be useful as diagnosticians." Full article at The Lancet.

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DNA Computer executes six-bit algorithms

"A general-purpose, reprogrammable molecular computer has been constructed from DNA by a team of researchers in the US and Ireland. The system can execute different algorithms ranging from copying and sorting processes, generating random walks and executing cellular automata. It works by the self-assembly of DNA strands or ‘tiles’ into helices that form tubular structures by complementary base pairing. The emerging patterns on the tubes encode the output from the algorithm, and can be read out mechanically using an atomic force microscope (AFM) to inspect the molecular structures." News Article @ Chemical World and Full research paper @ Nature. (Thanks to Thiago Carvalho for link)

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genetic Memory can have More symbols

"The DNA of life on Earth naturally stores its information in just four key chemicals — guanine, cytosine, adenine and thymine, commonly referred to as G, C, A and T, respectively. Now scientists have doubled this number of life’s building blocks, creating for the first time a synthetic, eight-letter genetic language that seems to store and transcribe information just like natural DNA. Synthetic DNA seems to behave like the natural variety, suggesting that chemicals beyond nature’s four familiar bases could support life on Earth." Full news article @ Nature News, scientific article @ Science.

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Manfred Eigen: Steps Towards Life (and Information)

"Manfred Eigen, who shared the 1967 Nobel Prize in Chemistry for devising a method to time chemical reactions that had been thought too swift to measure, died on Feb. 6 in at his home in Göttingen, Germany. He was 91." Obituary @ NYTimes. Anyone who has taken my courses knows how much I admire his work, and has certainly seen images from his wonderful little book "Steps Towards Life"; a must for anyone interested in understanding how the concept of information is fundamental to understand life and evolution. A giant of Science.

Great interview from a series where his thinking is explored at length.

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How Alan Turing Deciphered Shark Skin

"[Turing's] theory outlined how endless varieties of stripes, spots, and scales could emerge from the interaction of two simple, hypothetical chemical agents, or 'morphogens.' Decades passed before biologists seriously considered that this mathematical theory could in fact explain myriad biological patterns. The development of mammalian hair, the feathers of birds, and even those ridges on the roof of your mouth all stem from Turing-like mechanisms." News article @ Nautilus, full research article @ Science Advances

The arrangement of denticles on a stained shark embryo (left) closely mirrors the pattern produced by researchers’ mathematical Turing model.

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Optical Neural Nets Reborn

Lin et al "have created a 3D-printed artificial neural network that uses light photons to rapidly process information." This very cool device reminds me of  Weston and Von Foerster's Numa-Rete device from the 1960s at the BCL in Urbana (which Von Foerster told me was a favorite of John Von Neumann because it could even count doughnut-shape objects without error). News article @TheScientist and paper in Science.

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The quantified heart

"In September 2017, a screenshot of a simple conversation went viral on the Russian-speaking segment of the internet. It showed the same phrase addressed to two conversational agents: the English-speaking Google Assistant, and the Russian-speaking Alisa, developed by the popular Russian search engine Yandex. The phrase was straightforward: ‘I feel sad.’ The responses to it, however, couldn’t be more different. ‘I wish I had arms so I could give you a hug,’ said Google. ‘No one said life was about having fun,’ replied Alisa." Full article @ Aeon. Thanks Thiago for link.

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Social biases in AI

The Hippocratic oath for data scientists would be a good start, though I am sure greater regulation is needed. There needs to be government agencies (NIST?) who query commercial and government AI systems with blackbox system identification techniques. They would statistically test against non-biased response distributions; If public systems fail hypothesis testing (e.g. chi-square) against fair distributions, they should be further investigated, their algorithms subpoenaed, and prosecuted if need be---same for data scientists shown to fail any future oath. See book reviews @ The New York Review of Books. (Thank you Thiago for link)

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Genetic adaptation in Humans helps deep divers

"The indigenous Bajau people (“Sea Nomads”) of Southeast Asia live a subsistence lifestyle based on breath-hold diving and are renowned for their extraordinary breath-holding abilities. However, it is unknown whether this has a genetic basis. Using a comparative genomic study, we show that natural selection on genetic variants in the PDE10A gene have increased spleen size in the Bajau, providing them with a larger reservoir of oxygenated red blood cells. We also find evidence of strong selection specific to the Bajau on BDKRB2, a gene affecting the human diving reflex. Thus, the Bajau, and possibly other diving populations, provide a new opportunity to study human adaptation to hypoxia tolerance." Full article @ Cell.

News Article from CNN: Diving deep on one breath could be in a 'sea nomad's' DNA

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