Topology Quotes

Strange, how a moment of existence can cut so deeply into our being that while ages pass unnoticed, a brief love can structure and define the very topology of our consciousness ever after.

We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately - the object seemed incidental to this will to give ourselves away, utterly. To games or needles, to some other person. Something pathetic about it. A flight-from in the form of a plunging-into. Flight from exactly what? These rooms, blandly filled with excrement and heat? To what purpose?

To my wife Marganit and my children Ella Rose and Daniel Adam without whom this book would have been completed two years earlier.

Topology is destiny,' he said, and put the drawers on. One leg at a time.

Quantum machine learning promises to discover the optimal network topologies and hyperparameters automatically without human intervention.

Time and space were, from Death's point of view, merely things that he'd heard described. When it came to Death, they ticked the box marked Not Applicable. It might help to think of the universe as a rubber sheet, or perhaps not.

Um, right, okay. Have you taken any courses in interspatial manipulation? Probably not, huh?” “Can’t say that I have.” “Space-time topology?” “Nope.” “Transdimensional theory?” Rosemary made an apologetic face. “Aww!” said Kizzy, clasping her hands over her heart. “You’re a physics virgin!

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately (...) To games or needles, to some other person.

There are lots of things I don't understand - say, the latest debates over whether neutrinos have mass or the way that Fermat's last theorem was (apparently) proven recently. But from 50 years in this game, I have learned two things: (1) I can ask friends who work in these areas to explain it to me at a level that I can understand, and they can do so, without particular difficulty; (2) if I'm interested, I can proceed to learn more so that I will come to understand it. Now Derrida, Lacan, Lyotard, Kristeva, etc. -- even Foucault, whom I knew and liked, and who was somewhat different from the rest -- write things that I also don't understand, but (1) and (2) don't hold: no one who says they do understand can explain it to me and I haven't a clue as to how to proceed to overcome my failures. That leaves one of two possibilities: (a) some new advance in intellectual life has been made, perhaps some sudden genetic mutation, which has created a form of "theory" that is beyond quantum theory, topology, etc., in depth and profundity; or (b) ... I won't spell it out.

Christ Bleeding,” Makin said, staring into the valley below us. “How…” “Topology,” I said. “It’s a kind of magic.

People simply can’t accept that patterns carry their own intelligence, quite apart from the semantic content that clings to their surfaces; if you manipulate the topology correctly, that content just comes along for the ride.

We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately—the object seemed incidental to this will to give oneself away, utterly. To games or needles, to some other person.

It is as if one hemisphere of your brain is perceiving the world as reflected in a mirror. Through a mirror. See? So left becomes right, and all that that implies. And we don’t know yet what that does imply, to see the world reversed like that. Topologically speaking, a left-hand glove is a right-hand glove pulled through infinity.

The neural basis for the self, as I see it, resides with the continuous reactivation of at least two sets of representations. One set concerns representations of key events in an individual's autobiography, on the basis of which a notion of identity can be reconstructed repeatedly, by partial activation in topologically organized sensory maps. ... In brief, the endless reactivation of updated images about our identity (a combination of memories of the past and of the planned future) constitutes a sizable part of the state of self as I understand it. The second set of representations underlying the neural self consists of the primordial representations of an individual's body ... Of necessity, this encompasses background body states and emotional states. The collective representation of the body constitute the basis for a "concept" of self, much as a collection of representations of shape, size, color, texture, and taste can constitute the basis for the concept of orange.

The Gang of Four may have run multiple systems on a single motherboard, but each had its own distinct topology and they only surfaced one at a time.

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..." Klapaucius thought, and thought some more. Finally he nodded and said: "Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit." "Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming: Come, let us hasten to a higher plane, Where dyads tread the fairy fields of Venn, Their indices bedecked from one to n, Commingled in an endless Markov chain! Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers of a more ergodic zone. In Reimann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our asymptotes no longer out of phase, We shall encounter, counting, face to face. I'll grant thee random access to my heart, Thou'lt tell me all the constants of thy love; And so we two shall all love's lemmas prove, And in bound partition never part. For what did Cauchy know, or Christoffel, Or Fourier, or any Boole or Euler, Wielding their compasses, their pens and rulers, Of thy supernal sinusoidal spell? Cancel me not--for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain. Ellipse of bliss, converge, O lips divine! The product of our scalars is defined! Cyberiad draws nigh, and the skew mind Cuts capers like a happy haversine. I see the eigenvalue in thine eye, I hear the tender tensor in thy sigh. Bernoulli would have been content to die, Had he but known such a^2 cos 2 phi!

The ship had always been vast and intricate, its topology as unfathomable as the abandoned subway system of a deserted metropolis. It had been a ship haunted by many ghosts, not all of which were necessarily cybernetic or imaginary. Winds had sighed up and down its kilometres of empty corridors. It was infested with rats, stalked by machines and madmen. It had moods and fevers, like an old house.

Team Topologies provides four fundamental team types—stream-aligned, platform, enabling, and complicated-subsystem—and three core team interaction modes—collaboration, X-as-a-Service, and facilitating.

I know this may sound like an excuse," he said. "But tensor functions in higher differential topology, as exemplified by application of the Gauss-Bonnett Theorem to Todd Polynomials, indicate that cohometric axial rotation in nonadiabatic thermal upwelling can, by random inference derived from translational equilibrium aggregates, array in obverse transitional order the thermodynamic characteristics of a transactional plasma undergoing negative entropy conversions." "Why don't you just shut up," said Hardesty.

Topological anomaly? Topological anomaly? Don’t you mean witchcraft? Don’t you mean the end of civilisation? Don’t you mean some kind of spooky thing that we know nothing, absolutely fucking nothing about, to go with everything else we don’t know?

There is no pre-mapped intellectual topology path leading to truth. Truth is a process of conducting a searching investigatory dialogue with oneself in an attempt to examine and discern the contents of a person’s own mind. Every person must ask himself or herself what is essential in life.

When cognitive load isn’t considered, teams are spread thin trying to cover an excessive amount of responsibilities and domains. Such a team lacks bandwidth to pursue mastery of their trade and struggles with the costs of switching contexts.

Intersections of lines, for example, remain intersections, and the hole in a torus (doughnut) cannot be transformed away. Thus a doughnut may be transformed topologically into a coffee cup (the hole turning into a handle) but never into a pancake. Topology, then, is really a mathematics of relationships, of unchangeable, or “invariant,” patterns.

Half the time I thought I was awake but then realized reality wasn’t Hausdorff, and what kind of topology was I in anyway if Twinkies were allowed?

Then the applied mathematician comes along and ruins everything by making topology useful.

Fraa Jad took the garment from me and discovered how the fly worked. “Topology is destiny,” he said, and put the drawers on.

We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately - the object seemed incidental to this will to give oneself away, utterly. To games or needles, to some other person. Something pathetic about it. A flight-from in the form of a plunging-into. Flight from exactly what? These rooms blandly filled with excrement and meat? To what purpose?

The society of authenticity is a performance society. All members perform themselves. All produce themselves.Everyone pays homage to the cult of the self, the worship of self in which everyone is his or her own priest

To avoid the too-common trap of building a platform disconnected from the needs of teams, it is essential to ensure that the platform teams have a focus on user experience (UX) and particularly developer experience (DevEx).

With their cell phone, they have access to all people; with GPS, to all places; with the Internet, to all knowledge. They inhabit a topological space of neighborhoods, whereas we lived in a metric space, coordinated by distances.

My earliest memories are of CP4 — that's a Kähler manifold that looks locally like a vector space with four complex directions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible. I only used to spend time in anything remotely like this" — he motioned at the surrounding more-or-less-Euclidean space — for certain special kinds of physics problems. And even most Newtonian mechanics is easier to grasp in a symplectic manifold; having a separate visible coordinate for the position and momentum of every degree of freedom makes things much clearer than when you cram everything together in a single three-dimensional space.

The science of Chaos teaches us that everything is interconnected, but the contemporary developments in neuroscience, getting started with the brain neurons and their multiple connections, reveal the topology of the brain, a miniature of the universal geometry of everything.

Freud does at this point shift ground. He moves from an energetic to a topological model of the psyche. So that there be no contradiction, Freud assigns the pleasure principle to its own agency of the personality. “We know,” Freud reminds us, “that the pleasure principle is proper to a primary method of working on the part of the mental apparatus, but that, from the point of view of the self-preservation of the organism among the difficulties of the external world, it is from the very outset inefficient and even highly dangerous.” That is, the PP is blind. In itself, it is not a tendency but pure automaticity which, with respect to another topos undergoes a mutation by which is “is replaced by the reality principle.” A change in place obviates the contradiction but sets the places into relation by which the PP becomes the reality principle (RP.)

It now lately sometimes seemed like a kind of black miracle to me that people could actually care deeply about a subject or pursuit, and could go on caring this way for years on end. Could dedicate their entire lives to it. It seemed admirable and at the same time pathetic. We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately—the object seemed incidental to this will to give oneself away, utterly. To games or needles, to some other person. Something pathetic about it. A flight-from in the form of a plunging-into. Flight from exactly what? These rooms blandly filled with excrement and meat? To what purpose?

In South Texas I saw three interesting things. The first was a tiny girl, maybe ten years old, driving in a 1965 Cadillac. She wasn't going very fast, because I passed her, but still she was cruising right along, with her head tilted back and her mouth open and her little hands gripping the wheel. Then I saw an old man walking up the median strip pulling a wooden cross behind him. It was mounted on something like a golf cart with two spoked wheels. I slowed down to read the hand-lettered sign on his chest. JACKSONVILLE FLA OR BUST I had never been to Jacksonville but I knew it was the home of the Gator Bowl and I had heard it was a boom town, taking in an entire county or some such thing. It seemed an odd destination for a religious pilgrim. Penance maybe for some terrible sin, or some bargain he had worked out with God, or maybe just a crazed hiker. I waved and called out to him, wishing him luck, but he was intent on his marching and had no time for idle greetings. His step was brisk and I was convinced he wouldn't bust. The third interesting thing was a convoy of stake-bed trucks all piled high with loose watermelons and cantaloupes. I was amazed. I couldn't believe that the bottom ones weren't crushed under all that weight, exploding and spraying hazardous melon juice onto the highway. One of nature's tricks with curved surfaces. Topology! I had never made it that far in mathematics and engineering studies, and I knew now that I never would, just as I knew that I would never be a navy pilot or a Treasury agent. I made a B in Statics but I was failing in Dynamics when I withdrew from the field. The course I liked best was one called Strength of Materials. Everybody else hated it because of all the tables we had to memorize but I loved it, the sheared beam. I had once tried to explain to Dupree how things fell apart from being pulled and compressed and twisted and bent and sheared but he wouldn't listen. Whenever that kind of thing came up, he would always say - boast, the way those people do - that he had no head for figures and couldn't do things with his hands, slyly suggesting the presence of finer qualities.

The most important part of the platform is that it is built for developers.”21

thinking of software architecture as a standalone concept that can be designed in isolation and then implemented by any group of teams is fundamentally wrong.

As Allan Kelly says, “software developers love building platforms and, without strong product management input, will create a bigger platform than needed.

The purpose of a platform team is to enable stream-aligned teams to deliver work with substantial autonomy. The stream-aligned team maintains full ownership of building, running, and fixing their application in production. The platform team provides internal services to reduce the cognitive load that would be required from stream-aligned teams to develop these underlying services.

to, and some like the engineer never do get comfortable with them and use the less garish auditory side-doors; and the abundant sulcus-fissures and gyrus-bulges of the slick latex roof make rain-drainage complex and footing chancy at best, so there’s not a whole lot of recreational strolling up here, although a kind of safety-balcony of skull-colored polybutylene resin, which curves around the midbrain from the inferior frontal sulcus to the parietooccipital sulcus—a halo-ish ring at the level of like eaves, demanded by the Cambridge Fire Dept. over the heated pro-mimetic protests of topological Rickeyites over in the Architecture Dept. (which the M.I.T. administration, trying to placate Rickeyites and C.F.D. Fire Marshal both, had had the pre-molded resin injected with dyes to render it the distinctively icky brown-shot off-white of living skull, so that the balcony resembles at once corporeal bone and numinous aura)—which balcony means that

wheelchair-accessible front ramp, take a bit of getting used to, and some like the engineer never do get comfortable with them and use the less garish auditory side-doors; and the abundant sulcus-fissures and gyrus-bulges of the slick latex roof make rain-drainage complex and footing chancy at best, so there’s not a whole lot of recreational strolling up here, although a kind of safety-balcony of skull-colored polybutylene resin, which curves around the midbrain from the inferior frontal sulcus to the parietooccipital sulcus—a halo-ish ring at the level of like eaves, demanded by the Cambridge Fire Dept. over the heated pro-mimetic protests of topological Rickeyites over in the Architecture Dept. (which the M.I.T. administration, trying to placate Rickeyites and C.F.D. Fire Marshal both, had had the pre-molded resin injected with dyes to render it the distinctively icky brown-shot off-white of living skull, so that the balcony resembles at once corporeal bone and

Fast flow requires restricting communication between teams. Team collaboration is important for gray areas of development, where discovery and expertise is needed to make progress. But in areas where execution prevails—not discovery—communication becomes an unnecessary overhead.

In his life of seventy-six years, Euler created enough mathematics to fill seventy-four substantial volumes, the most total pages of any mathematician. By the time all of his work had been published (and new material continued to appear for seventy-nine years after his death) it amounted to a staggering 866 items, including articles and books on the most cutting-edge topics, elementary textbooks, books for the nonscientist, and technical manuals. These figures do not account for the projected fifteen volumes of correspondence and notebooks that are still being compiled.

It now lately sometimes seemed like a kind of black miracle to me that people could actually care deeply about a subject or pursuit, and could go on caring this way for years on end. Could dedicate their entire lives to it. It seemed admirable and at the same time pathetic. We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately- the object seemed incidental to this will to give oneself away, utterly. To games or needles, to some other person. Something pathetic about it. A flight-from in the form of a plunging-into. Flight from exactly what? These rooms blandly filled with excrement and meat? To what purpose?

Search engines and social networks are analog computers of unprecedented scale. Information is being encoded (and operated upon) as continuous (and noise-tolerant) variables such as frequencies (of connection or occurrence) and the topology of what connects where, with location being increasingly defined by a fault-tolerant template rather than by an unforgiving numerical address. Pulse-frequency coding for the Internet is one way to describe the working architecture of a search engine, and PageRank for neurons is one way to describe the working architecture of the brain. These computational structures use digital components, but the analog computing being performed by the system as a whole exceeds the complexity of the digital code on which it runs. The model (of the social graph, or of human knowledge) constructs and updates itself.

A.N. Kolmogorov and Yasha Sinai had worked out some illuminating mathematics for the way a system's "entropy per unit time" applies to the geometric pictures of surfaces stretching and folding in phase space. The conceptual core of the technique was a matter of drawing some arbitrarily small box around some set of initial conditions, as one might draw a small square on the side of a balloon, then calculating the effect of various expressions or twists on the box. It might stretch in one direction, for example, while remaining narrow in the other. The change in area corresponded to an introduction of uncertainty about the system's past, a gain or loss of information.

Perhaps the best way to approach the question of what mathematics is, is to start at the beginning. In the far distant prehistoric past, where we must look for the beginnings of mathematics, there were already four major faces of mathematics. First, there was the ability to carry on the long chains of close reasoning that to this day characterize much of mathematics. Second, there was geometry, leading through the concept of continuity to topology and beyond. Third, there was number, leading to arithmetic, algebra, and beyond. Finally there was artistic taste, which plays so large a role in modern mathematics. There are, of course, many different kinds of beauty in mathematics. In number theory it seems to be mainly the beauty of the almost infinite detail; in abstract algebra the beauty is mainly in the generality. Various areas of mathematics thus have various standards of aesthetics.

If the organization has an expectation that “everyone should see every message in the chat” or “everyone needs to attend the massive standup meetings” or “everyone needs to be present in meetings” to approve decisions, then we have an organization design problem. Conway’s law suggests that this kind of many-to-many communication will tend to produce monolithic, tangled, highly coupled, interdependent systems that do not support fast flow. More communication is not necessarily a good thing.

thing. They were just the least terrible thing I had. Technology debt is when you cheat a barely functional solution to an important problem early in the development cycle, telling yourself that you’ll revisit your fugly hack later and put something real in its place. But you don’t. So you’re forever walking around with this lurking knowledge that you’ve built a fifty-story skyscraper full of people on top of foundations made out of whatever garbage you had lying around at the time. Technology debt eats away at you, keeps you up at night. The longer you carry the debt, the more interest you have to pay, as you write more code that depends on the eldritch topologies of your hacky module, all of which will break as soon as you fix the original problem.

[...]One positions an Axis of Evil where there is none. Good is directive, directional; it has a finality in principle and therefore constitutes an axis. Evil is more of a parallax. It is never directional, and is not even opposed to Good. There is always some kind of diversion, a deviation, a curve. As Good goes straight ahead, Evil deviates. It is a deviance, a perversion. You never know where Evil is going, or how. It cannot be mastered. In almost topological terms, it is merely a deviation. Only Good could lay claim to being an axis. But this axis is projected on Evil; an imaginary Axis of Evil is created to justify the Axis of Good. This is a strategic mistake. When you try to target Evil in its unfindable axis, when you fight it militarily, with a frontal attack, you can only miss it.

The problem with taking the org chart at face value is that we end up trying to architect people as if they were software, neatly keeping their communication within the accepted lines.

Given our skills, constraints, cultural and engineering maturity, desired software architecture, and business goals, which team topology will help us deliver results faster and safer?

there needs to be a split between the responsibility of designing the cloud infrastructure process (by the cloud team) and the actual provisioning and updates to application resources (by the product teams).

To stay alive in ever more competitive markets, organizations need teams and people who are able to sense when context changes and evolve accordingly.

However, in a highly collaborative context filled with uncertainty over outcomes, relying on the org chart as a principal mechanism of splitting the work to be done leads to unrealistic expectations.

Many organizations assume that more communication is always better, but this is not really the case. What we need is focused communication between specific teams.

Keep in mind that there will never be a single “perfect” team topology for your organization.

To improve total delivery time, we would need to make big changes to our supply chain. Our current fulfillment network had been built to optimize for nearby access to our third-party shippers so we could reliably and cheaply ship products to customers in three to five days. This logistics topology had been convenient for Amazon, but not for the customers who wanted products delivered fast and free.

treating teams as collections of interchangeable individuals that will succeed as long as they follow the “right” process and use the “right” tools,

Systems thinking focuses on optimizing for the whole, looking at the overall flow of work, identifying what the largest bottleneck is today, and eliminating it.

the imbalance between formal organization structures and the way work actually gets done.

Does the structure minimize the number of communication paths between teams? . . . Does the structure encourage teams to communicate who wouldn’t otherwise do so?

anyone who makes decisions about the shape and placement of engineering teams is strongly influencing the software systems architecture.

Organization design and software design are, in practice, two sides of the same coin,

organizing team structures to match the architecture they want the system to exhibit rather than expecting teams to follow a mandated architecture design.

Dan Pink’s three elements of intrinsic motivation: autonomy (quashed by constant juggling of requests and priorities from multiple teams), mastery (“jack of all trades, master of none”), and purpose (too many domains of responsibility).

We might thus expect a re-enchantment of the world to create a healing power that could counteract collective narcissism.

Organizations should be viewed as complex and adaptive organisms rather than mechanistic and linear systems. —Naomi Stanford, Guide to Organisation Design

saddles. Furthermore, by Eq. 2 their two-dimensional stable or unstable manifolds lie completely on the boundary. The eigenvalue belonging to the remaining eigenvector is real-valued. Its

Seidel [21], and Garth et al. [4]. Feature tracking in scale-space representations of vector fields has been investigated by Bauer and Peikert [1] for tracking the evolution of vortices in scale or time. For the approach discussed

It now lately sometimes seemed like a kind of black miracle to me that people could actually care deeply about a subject or pursuit, and could go on caring this way for years on end. Could dedicate their entire lives to it. Ir seemed admirable and at the same time pathetic. We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately - the object seemed incidental to this will to give oneself away, utterly. To games or needles, to some other person. Something pathetic about it. A flight-from in the form of a plunging-into.

If the architecture of the system and the architecture of the organization are at odds, the architecture of the organization wins.

The team API should explicitly consider usability by other teams: Will other teams find it easy and straightforward to interact with us, or will it be difficult and confusing? How easy will it be for a new team to get on board with our code and working practices? How do we respond to pull requests and other suggestions from other teams? Is our team backlog and product roadmap easily visible and understandable by other teams?

Instead of choosing between a monolithic architecture or a microservices architecture, design the software to fit the maximum team cognitive load. Only then can we hope to achieve sustainable, safe, rapid software delivery. This team-first approach to software boundaries leads to favoring certain styles of software architecture, such as small, decoupled services.

​•​Stream-aligned team ​•​Enabling team ​•​Complicated-subsystem team ​•​Platform team

An enabling team is composed of specialists in a given technical (or product) domain, and they help bridge this capability gap. Such teams cross-cut to the stream-aligned teams and have the required bandwidth to research, try out options, and make informed suggestions on adequate tooling, practices, frameworks, and any of the ecosystem choices around the application stack.

Enabling teams have a strongly collaborative nature; they thrive to understand the problems and shortcomings of stream-aligned teams in order to provide effective guidance.

. After the new skills and understanding have been embedded in the stream-aligned team, the enabling team will stop daily interaction with the stream-aligned team, switching their focus to a different team.

organization size (or software scale) and engineering maturity should influence which topologies are chosen in a DevOps context,

All the examples we mentioned so far highlight the importance of thinking about teams’ capabilities (or lack thereof) and how that causes dependencies between teams.

In their 2012 paper, “A Taxonomy of Dependencies in Agile Software Development,” Diane Strode and Sid Huff propose three different categories of dependency: knowledge, task, and resource dependencies.14 Such a taxonomy can help pinpoint dependencies between teams and the potential constraints to the flow of work ahead of time.

Enabling teams and CoP can co-exist because they have slightly different purposes and dynamics: an enabling team is a small, long-lived group of specialists focused on building awareness and capability for a single team (or a small number of teams) at any one point in time, whereas a CoP usually seeks to have more widespread effects, diffusing knowledge across many teams. Of course, several enabling teams can also have their own “enabling-teams community of practice!

A complicated-subsystem team is responsible for building and maintaining a part of the system that depends heavily on specialist knowledge, to the extent that most team members must be specialists in that area of knowledge in order to understand and make changes to the subsystem. The goal of this team is to reduce the cognitive load of stream-aligned teams working on systems that include or use the complicated subsystem. The team handles the subsystem complexity via specific capabilities and expertise that are typically hard to find or grow.

Managing cognitive load through teams with clear responsibilities and boundaries is a distinguishing focus of team design in the Team Topologies approach.

Change the team working environment to help teams succeed.

In conceptual integration theory, we create new emergent structure from fusing or blending shared topology from different domains, whether they are abstract or concrete.

Therefore all the things that appear in CLS—network analysis, digital mapping, linear and nonlinear regressions, topic modeling, topology, entropy—are just fancier ways of talking about word frequency changes.

Quantum computing is not only faster than conventional computing, but its workload obeys a different scaling law—rendering Moore’s Law little more than a quaint memory. Formulated by Intel founder Gordon Moore, Moore’s Law observes that the number of transistors in a device’s integrated circuit doubles approximately every two years. Some early supercomputers ran on around 13,000 transistors; the Xbox One in your living room contains 5 billion. But Intel in recent years has reported that the pace of advancement has slowed, creating tremendous demand for alternative ways to provide faster and faster processing to fuel the growth of AI. The short-term results are innovative accelerators like graphics-processing unit (GPU) farms, tensor-processing unit (TPU) chips, and field-programmable gate arrays (FPGAs) in the cloud. But the dream is a quantum computer. Today we have an urgent need to solve problems that would tie up classical computers for centuries, but that could be solved by a quantum computer in a few minutes or hours. For example, the speed and accuracy with which quantum computing could break today’s highest levels of encryption is mind-boggling. It would take a classical computer 1 billion years to break today’s RSA-2048 encryption, but a quantum computer could crack it in about a hundred seconds, or less than two minutes. Fortunately, quantum computing will also revolutionize classical computing encryption, leading to ever more secure computing. To get there we need three scientific and engineering breakthroughs. The math breakthrough we’re working on is a topological qubit. The superconducting breakthrough we need is a fabrication process to yield thousands of topological qubits that are both highly reliable and stable. The computer science breakthrough we need is new computational methods for programming the quantum computer.

Hilbert tried to predict the future development of mathematics and to influence it by his Problems. The development of mathematics in the 20th century has followed a different path. The most important achievements — the flourishing of homotopy theory and of differential topology, the geometrisation of all branches of mathematics, its fusion with theoretical physics, the discovery of algorithmically undecidable problems and the appearance of computers — all this went in a different (if not opposite) direction.

Hilbert tried to predict the future development of mathematics and to influence it by his Problems. The development of mathematics in the 20th century has followed a different path. The most important achievements — the flourishing of homotopy theory and of differential topology, the geometrisation of all branches of mathematics, its fusion with theoretical physics, the discovery of algorithmically undecidable problems and the appearance of computers — all this went in a different (if not opposite) direction. [...] The mathematics of the 20th century mostly followed the road shown by Poincaré.

The whole beauty of constructive mathematics lies in the fact that it is just mathematics, free of any self-conscious recognition that we are writing programs when proving theorems constructively. We never have to reason about machine indices or any such nonsense, we just do mathematics under the discipline of not assuming that every proposition is decidable. One benefit is that the same mathematics admits interpretation not only in terms of computability, but also in terms of continuity in topological spaces, establishing a deep connection between two seemingly disparate topics.

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Organizations should be viewed as complex and adaptive organisms rather than mechanistic and linear systems. —Naomi Stanford,

Explicitly thinking about cognitive load can be a powerful tool for deciding on team size, assigning responsibilities, and establishing boundaries with other teams.

The Agile, Lean IT, and DevOps movements helped demonstrate the enormous value of smaller, more autonomous teams that were aligned to the flow of business, developing and releasing in small, iterative cycles, and course correcting based on feedback from users.

it recognizes that building and running software systems is a sociotechnical activity, not an assembly line in a factory.