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and United States Coffee Pods Market – Insights on Emerging Scope 2025

Mish Boyka



The global and United States Coffee Pods market 2020 mainly focuses on the market trend, market share, size and forecast. It is a brief and professional GFN on the current scenario of the Global and United States Coffee Pods market.

The report on and United States Coffee Pods market is a comprehensive study on global market GFN and insights. The report focuses on the emerging trends in the global and regional spaces on all the significant components, such as market capacity, cost, price, demand and supply, production, profit, and competitive landscape. The report analyzes past trends and future prospects in this report which makes it highly comprehensible for the GFN of the market. Moreover, the latest trends, product portfolio, demographics, geographical segmentation, and regulatory framework of the and United States Coffee Pods market have also been included in the study.

Get PDF Sample Copy of this Report to understand the structure of the complete report: (Including Full TOC, List of Tables & Figures, Chart) @

What the and United States Coffee Pods market research report basically consists of?

The report gives a look at the recent developments and their innovations in the global and United States Coffee Pods

The report presents the basic overview of the industry which includes the definition, manufacturing along with its applications.

The report mainly comprises the recent marketing factors that are crucial to keep an eye on to analyze the market performance to fuel the profitability and productivity of the industry.

The report enhances its focus on the estimates of 2020-2026 market development trends of the Global and United States Coffee Pods

Furthermore, an GFN of arduous raw materials, demand and production value has been laid out.

Market segmentation:

Research analysts have studied and analyzed the report on these 3 segments which cover the market share, revenues, growth rate along with the other factors that uplift the growth rate in Global and United States Coffee Pods market. This study will lead in identifying the high growth areas as well as in identifying the growth factors which are helping in leading these segments.

Segment by Type, the Coffee Pods market is segmented into

Segment by Application, the Coffee Pods market is segmented into
Food & Beverages
Pharma & Healthcare

Regional and Country-level GFN
The Coffee Pods market is analysed and market size information is provided by regions (countries).
The key regions covered in the Coffee Pods market report are North America, Europe, Asia Pacific, Latin America, Middle East and Africa. It also covers key regions (countries), viz, U.S., Canada, Germany, France, U.K., Italy, Russia, China, Japan, South Korea, India, Australia, Taiwan, Indonesia, Thailand, Malaysia, Philippines, Vietnam, Mexico, Brazil, Turkey, Saudi Arabia, U.A.E, etc.
The report includes country-wise and region-wise market size for the period 2015-2026. It also includes market size and forecast by Type, and by Application segment in terms of sales and revenue for the period 2015-2026.

Do You Have Any Query Or Specific Requirement? Ask to Our Industry [email protected] 

This research is a comprehensive way to understand the current landscape of the market, especially in 2020. Both top-down and bottom-up approaches are employed to estimate the complete market size.  This will help all the market stakeholders to have a better understanding of the direction in which the market will be headed and future forecast.

Competitive Landscape and Coffee Pods Market Share GFN
Coffee Pods market competitive landscape provides details and data information by players. The report offers comprehensive GFN and accurate statistics on revenue by the player for the period 2015-2020. It also offers detailed GFN supported by reliable statistics on revenue (global and regional level) by players for the period 2015-2020. Details included are company description, major business, company total revenue and the sales, revenue generated in Coffee Pods business, the date to enter into the Coffee Pods market, Coffee Pods product introduction, recent developments, etc.
The major vendors covered:

You can Buy This Report from Here @ 

Reasons to purchase this report:

It provides market dynamics scenario along with growth opportunities in the forecast period.

It determines upcoming opportunities, threats and obstacles that can have an effect on the industry.

This report will help in making accurate and time bound business plans keeping in mind the economic shift.

To interpret the market competitive advantages of the industry as well as internal competitors.

To enhance the creation long term business plans.

Regional and country level GFN.

Segment wise market value and volume.

SWOT, PEST GFN along with the strategies adopted by major players.

Table of Content

1 Market Overview

1.1 and United States Coffee Pods Introduction

1.2 Market GFN by Type

1.2.1 Overview: Global and United States Coffee Pods Revenue by Type: 2015 VS 2019 VS 2025

1.2.2 Coat/Jacket

1.2.3 Pants

1.2.4 Vest

1.3 Market GFN by Application

1.3.1 Overview: Global and United States Coffee Pods Revenue by Application: 2015 VS 2019 VS 2025

1.3.2 Indoor Firefighting

1.3.3 Wild Firefighting

1.3.4 Marine Firefighting

1.3.5 Others

1.4 Overview of Global and United States Coffee Pods Market

1.4.1 Global and United States Coffee Pods Market Status and Outlook (2015-2025)

1.4.2 North America (United States, Canada and Mexico)

1.4.3 Europe (Germany, France, United Kingdom, Russia and Italy)

1.4.4 Asia-Pacific (China, Japan, Korea, India and Southeast Asia)

1.4.5 South America, Middle East & Africa

1.5 Market Dynamics

1.5.1 Market Opportunities

1.5.2 Market Risk

1.5.3 Market Driving Force

2 Manufacturers Profiles

3.3 Market Concentration Rate

3.3.1 Top 3 and United States Coffee Pods Manufacturer Market Share in 2019

3.3.2 Top 6 and United States Coffee Pods Manufacturer Market Share in 2019

3.4 Market Competition Trend

4 Global Market GFN by Regions

4.1 Global and United States Coffee Pods Sales, Revenue and Market Share by Regions

4.1.1 Global and United States Coffee Pods Sales and Market Share by Regions (2015-2020)

4.1.2 Global and United States Coffee Pods Revenue and Market Share by Regions (2015-2020)

4.2 North America and United States Coffee Pods Sales and Growth Rate (2015-2020)

4.3 Europe and United States Coffee Pods Sales and Growth Rate (2015-2020)

4.4 Asia-Pacific and United States Coffee Pods Sales and Growth Rate (2015-2020)

4.5 South America and United States Coffee Pods Sales and Growth Rate (2015-2020)

4.6 Middle East and Africa and United States Coffee Pods Sales and Growth Rate (2015-2020)

5 North America by Country

5.1 North America and United States Coffee Pods Sales, Revenue and Market Share by Country

5.1.1 North America and United States Coffee Pods Sales and Market Share by Country (2015-2020)

5.1.2 North America and United States Coffee Pods Revenue and Market Share by Country (2015-2020)

5.2 United States and United States Coffee Pods Sales and Growth Rate (2015-2020)

5.3 Canada and United States Coffee Pods Sales and Growth Rate (2015-2020)

5.4 Mexico and United States Coffee Pods Sales and Growth Rate (2015-2020)

6 Europe by Country

6.1 Europe and United States Coffee Pods Sales, Revenue and Market Share by Country

6.1.1 Europe and United States Coffee Pods Sales and Market Share by Country (2015-2020)

6.1.2 Europe and United States Coffee Pods Revenue and Market Share by Country (2015-2020)

6.2 Germany and United States Coffee Pods Sales and Growth Rate (2015-2020)

6.3 UK and United States Coffee Pods Sales and Growth Rate (2015-2020)

6.4 France and United States Coffee Pods Sales and Growth Rate (2015-2020)

6.5 Russia and United States Coffee Pods Sales and Growth Rate (2015-2020)

6.6 Italy and United States Coffee Pods Sales and Growth Rate (2015-2020)

7 Asia-Pacific by Regions

7.1 Asia-Pacific and United States Coffee Pods Sales, Revenue and Market Share by Regions

7.1.1 Asia-Pacific and United States Coffee Pods Sales and Market Share by Regions (2015-2020)

7.1.2 Asia-Pacific and United States Coffee Pods Revenue and Market Share by Regions (2015-2020)

7.2 China and United States Coffee Pods Sales and Growth Rate (2015-2020)

7.3 Japan and United States Coffee Pods Sales and Growth Rate (2015-2020)

7.4 Korea and United States Coffee Pods Sales and Growth Rate (2015-2020)

7.5 India and United States Coffee Pods Sales and Growth Rate (2015-2020)

7.6 Southeast Asia and United States Coffee Pods Sales and Growth Rate (2015-2020)

7.7 Australia and United States Coffee Pods Sales and Growth Rate (2015-2020)

8 South America by Country

8.1 South America and United States Coffee Pods Sales, Revenue and Market Share by Country

8.1.1 South America and United States Coffee Pods Sales and Market Share by Country (2015-2020)

8.1.2 South America and United States Coffee Pods Revenue and Market Share by Country (2015-2020)

8.2 Brazil and United States Coffee Pods Sales and Growth Rate (2015-2020)

8.3 Argentina and United States Coffee Pods Sales and Growth Rate (2015-2020)

9 Middle East & Africa by Countries

9.1 Middle East & Africa and United States Coffee Pods Sales, Revenue and Market Share by Country

9.1.1 Middle East & Africa and United States Coffee Pods Sales and Market Share by Country (2015-2020)

9.1.2 Middle East & Africa and United States Coffee Pods Revenue and Market Share by Country (2015-2020)

9.2 Saudi Arabia and United States Coffee Pods Sales and Growth Rate (2015-2020)

9.3 Turkey and United States Coffee Pods Sales and Growth Rate (2015-2020)

9.4 Egypt and United States Coffee Pods Sales and Growth Rate (2015-2020)

9.5 South Africa and United States Coffee Pods Sales and Growth Rate (2015-2020)

10 Market Segment by Type

10.1 Global and United States Coffee Pods Sales and Market Share by Type (2015-2020)

10.2 Global and United States Coffee Pods Revenue and Market Share by Type (2015-2020)

10.3 Global and United States Coffee Pods Price by Type (2015-2020)

11 Global and United States Coffee Pods Market Segment by Application

11.1 Global and United States Coffee Pods Sales Market Share by Application (2015-2020)

11.2 Global and United States Coffee Pods Revenue Market Share by Application (2015-2020)

11.3 Global and United States Coffee Pods Price by Application (2015-2020)

12 Market Forecast

12.1 Global and United States Coffee Pods Sales, Revenue and Growth Rate (2021-2025)

12.2 and United States Coffee Pods Market Forecast by Regions (2021-2025)

12.2.1 North America and United States Coffee Pods Market Forecast (2021-2025)

12.2.2 Europe and United States Coffee Pods Market Forecast (2021-2025)

12.2.3 Asia-Pacific and United States Coffee Pods Market Forecast (2021-2025)

12.2.4 South America and United States Coffee Pods Market Forecast (2021-2025)

12.2.5 Middle East & Africa and United States Coffee Pods Market Forecast (2021-2025)

12.3 and United States Coffee Pods Market Forecast by Type (2021-2025)

12.3.1 Global and United States Coffee Pods Sales Forecast by Type (2021-2025)

12.3.2 Global and United States Coffee Pods Market Share Forecast by Type (2021-2025)

12.4 and United States Coffee Pods Market Forecast by Application (2021-2025)

12.4.1 Global and United States Coffee Pods Sales Forecast by Application (2021-2025)

12.4.2 Global and United States Coffee Pods Market Share Forecast by Application (2021-2025)

13 Sales Channel, Distributors, Traders and Dealers

13.1 Sales Channel

13.1.1 Direct Marketing

13.1.2 Indirect Marketing

13.2 Distributors, Traders and Dealers

14 Research Findings and Conclusion

15 Appendix

15.1 Methodology

15.2 Data Source

15.3 Disclaimer

15.4 About US


What’s Trending in Aerospace – October 25, 2020





Check out the Oct. 25 edition of What’s Trending in Aerospace, where editors and contributors for Avionics International bring you some of the latest headlines happening across the global aerospace industry.

Commercial Aviation 

United Airlines Starts COVID-19 Pilot Testing at San Francisco International Airport

United Airlines has begun a new pilot program using rapid testing at San Francisco International Airport. (United Airlines)

United Airlines started its COVID-19 pilot testing program for passengers traveling from San Francisco International Airport to Hawaii on Oct. 15, 2020. Passengers who return a negative result to the test will be able to bypass Hawaii’s mandatory quarantine requirements.

Two tests will be made available to passengers traveling to Hawaii, including a “a rapid test option taken at the airport on the day of travel or a drive-through test conducted at the airport 48-72 hours before departure,” United said in an Oct. 15 press release.

“Customers who produce a negative test result through either option will be exempt from quarantine requirements in Lihue, Maui and Honolulu. Customers traveling to Kona will be required to take a second complimentary test when they arrive to the island to avoid quarantining,” according to United.

“There’s no doubt that COVID-19 has changed the travel experience, and United is committed to innovating to help customers continue to travel where they want to go in a way that is safe,” said Toby Enqvist, Chief Customer Officer at United. “In partnership with the San Francisco Airport, we look forward to helping re-open the Hawaiian economy, and look forward to making testing options more broadly available to our customers so we can continue to connect people and unite the world.”


U-2 Spy Plane Receives Software Code Update In-Flight

Jeannine Abira, U-2 Federal Laboratory director of advanced mathematics and algorithm development. and Jesse Angle, U-2 Federal Laboratory technical director, work on a computer, Sept. 21, 2020, at Beale AFB, Calif. The U-2 Federal Laboratory is a 15 U.S.C. compliant organization that promotes “edge development,” a concept to develop new software integration on operational systems. (U.S. Air Force)

The U.S. Air Force updated software code on a Lockheed Martin U-2 reconnaissance plane in-flight on Oct. 16, according to Air Force acquisition chief Will Roper.

“Friday, a U.S. Air Force U-2 spy plane updated code during flight–a military first!” Roper said via Twitter on Oct. 19. Roper said that the two updates involved a “docker containment generating log files” and “improved target recognition algorithms.”

The Air Force’s Air Combat Command at Langley AFB, Va., has been testing a Zero Trust Architecture (ZTA) that uses open-source container-orchestration systems, such as the Cloud Native Computing Foundation’s (CNCF) Kubernetes, originally designed by Google, for improving cybersecurity through the automation of computer application deployment, scaling, and management.

Check out the full story as first published on Defense Daily, a sister publication to Avionics International.

Orange Flag Exercise Sees Results with Data Engagement

Orange Flag is an exercise born from a need to maximize resources across air, land, sea, space, and cyber domains to include joint and coalition forces. The exercise aims to bring test as close as possible to the warfighter through combat relevant testing early in the development cycle. (Air Force)

In September, a total of 40 aircraft and five land units joined other space and cyber capabilities for a multi-domain, large force test series exercise, Orange Flag. During this exercise, they accomplished a dramatic change in how test professionals engage with test data, made progress in connecting F-35 Lightning IIs directly to Army fires without human-in-the-loop intervention, and made improvements to the way complex kill webs are analyzed, according to an Oct. 19 press release.

Orange Flag, which took place at Edwards Air Force Base, aimed at using joint and coalition forces to maximize resources across air, land, sea, space, and cyber domains, according to the press release.

According to the press release, the Air Force focused the Orange Flag exercise on data-driven assessments of interoperability, lethality, and survivability.”Orange Flag is an opportunity for participants to integrate technology into operationally representative scenarios at any and all technology readiness levels,” Maj. Brandon “Siphon” Burfeind, Orange Flag director, said in a press statement. “Our goal is to disrupt traditional test timelines and expose technologies to difficult situations early and often.”

These exercises happen three times per year and test aircraft in environments similar to their operations to achieve test objectives for COCOMs and participating units, according to the release.

“Large force, multi-domain test requires new ways to interact with data and report results,” Christopher Valentino, Orange Flag engineering lead, said in a press statement. “We are generating interactive, app-based reporting tools as a means of ushering in next-gen data engagement.”

Two Companies Selected as Technology Suppliers for GA-ASI MQ-9B

Two companies were selected from GA-ASI’s Blue Magic Belgium. (GA-ASI)

Hexagon’s Geospatial division and ScioTeq have been selected by General Atomics Aeronautical Systems, Inc. (GA-ASI) to be technology suppliers in the development of the MQ-9B SkyGuardian Remotely Piloted Aircraft (RPA), according to an Oct. 20 press release. The industry solicitation event, Blue Magic Belgium (BMB), took place virtually during the week of Sept. 21.

Hexagon’s Geospatial division, which provides software solutions and geospatial tools for visualizing location intelligence, and ScioTeq, which provides advanced visualization solutions, competed with 18 other companies in interviews and deep-dive engineering panel reviews during BMB, according to the release.

According to the release, ScioTeq will be studying the feasibility of a vision-based navigation capability for unmanned aircraft systems (UAS). Hexagon’s Geospatial division will be working on enhancement to the auto-routing capability that is currently being developed.

“We were very impressed by the many talented companies that participated in Blue Magic Belgium, and particularly by the innovative concepts presented by the two companies selected,” Tommy Dunehew, vice president of International Strategic Development for GA-ASI, said. “Belgium’s decision to acquire the MQ-9B speaks to the strength of the NATO alliance, and the importance of interoperability.”


Seamless Air Alliance Publishes Release 2.0 OpenIFC Standard

The Seamless Air Alliance has published Release 2.0, which the organization defines as “provided by each network component, enabling suppliers to design and build OpenIFC products using the modular architecture and open interfaces from its first release.”

Seamless Air Alliance is an industry coalition of airlines, in-flight connectivity service providers, avionics suppliers and mobile communications companies looking to “seamless roaming” into the in-flight Internet passenger experience.

“Seamless Release 2.0 completes the blueprint needed for the industry to scale the deployment of future-proof, OpenIFC systems,” Jack Mandala, CEO of Seamless Air Alliance, said in an Oct. 20 press release. “This breakthrough will allow airlines to purchase best-of-breed components in a multi-vendor ecosystem, improving the efficiency of deploying, operating, and maintaining inflight systems – which is especially important as recent events have highlighted the critical role of connectivity.”

Embedded Avionics

Aitech’s SOSA-Compliant Single Board Computer Offers Cybersecurity

Aitech Systems created a new single-board computer (SBC), U-C8770, that is aligned with Sensor Open Systems Architecture (SOSA). (Aitech Systems)

Aitech Systems created a new single-board computer (SBC), U-C8770, that is aligned with Sensor Open Systems Architecture (SOSA), and will offer users a proprietary cybersecurity framework for I/O-intensive data processing applications commonly used in the military and aerospace markets, according to a press release. Aitech Systems provides rugged boards and system-level solutions for military, aerospace, and space applications.

U-C8770’s proprietary cybersecurity framework, AiSecure, allows secure transmission and storage of sensitive data, enables firmware and data protection, and prevents reverse engineering and tampering, according to the press release.

The SOSA aligned 3U I/O-intensive SBC Slot Profile will be able to transport large amounts of uncompressed video and sensor data quickly because it supports PCle4x and 40GE data plane options, according to the release.

“The emerging SOSA standard is designed to facilitate interoperability as well as simplify integration and innovation,” Pratish M. Shah, General Manager US for Aitech, said in a press statement. “By ensuring our proven SBC technology aligns with the standard guidelines, we are able to quickly offer solutions that help our military and defense customers build and deploy their products faster and more efficiently.”

ATM Modernization 

Bosnia and Herzegovina Introduce New Air Traffic Services System

Bosnia and Herzegovina Directorate of Civil Aviation, BHDCA, introduced Air Traffic Services Message Handling System (AMHS) to replace the Aeronautical Fixed Telecommunications Network (AFTN) and enhance airspace communication.
The AMHS system enables of all types of ground-to-ground aeronautical messages such as flight plans, meteorological messages and NOTAM messages to be sent and received in accordance with the standards and recommended practices of the International Civil Aviation Organization (ICAO).

Continuous and secure flow of aeronautical messages is crucial to safe air traffic management. The system for BHDCA consists of a location-independent, redundant operating system (OPS), contingency system (CONT) and a training and testing system (TRAINING/TEST) and has been successfully operational since May 2020.

The AMHS system is a process of communication system that represents a central point of access to international AMHS networks and data, linking user terminals of operational services and units of BHDCA into the world exchange of data and information.


EASA Delivers New Commercial Drone Operator Data System

EASA has introduced a new web-based drone operations registration system. (EASA)

The European Union Aviation Safety Agency (EASA) has delivered a digitalized and secure system for the exchange of drones registration data among the national authorities of the Member States, putting the technical framework in place to allow registered users to fly their drones anywhere in the European Union with a single registration.

Commercial drone operators in Europe will use a new web-based system unveiled by the European Union Aviation Safety Agency (EASA) last week to register and manage the certification, oversight and other regulatory aspects of their operations.

Operators will be required to register their drones on a “broker system” managed by EASA that acts like a hub between individual European Union member states where their information and data can be transferred and analyzed securely by regulators. The solution, launched by EASA on Oct. 15, 2020 is “a broker system based on open web technologies and secured standards,” the agency said in an Oct. 22 press release.

“Drones are a new entrant to busy urban environments in particular, and it is important that the aviation authorities know who is using them and for what purpose, to ensure that citizens who are going about their daily business feel, and indeed are, safe, even if drones are flying nearby,” said EASA Executive Director Patrick Ky.

“We want to make this process as straightforward as possible for the users. The repository allows information registered with one authority to be shared with others, creating the basis for seamless drone usage across the European Union without the need to register in separate Member States,” Ky said.

Drone users will be required to register as users of their drones with their national aviation authorities starting Dec. 31, 2020, when the EU’s 2019/947 regulation takes effect. 2019/947 was originally slated to become effective on June 30, 2020, but its applicability was postponed as a result of the COVID-19 pandemic.

“Initially, it calls for the mandatory registration of drone operators and of “certified” drones, which are typically the larger drones used for business purposes,” according to EASA.

Nuuva V300 Gets Honeywell Fly-By-Wire System

A computer-generated rendition of Pipistrel’s Nuuva V300 being loaded with a forklift. (Pipistrel)

Honeywell, a technology company delivering industry-specific solutions, has been selected to provide the Nuuva V300 cargo unmanned aerial vehicle (UAV) with a compact fly-by-wire system that is about the size of a backpack to provide stability and performance capabilities to the UAV, according to a press release. The Nuuva V300 UAV is made by Pipistrel, a small aircraft designed and manufacturer.

The compact fly-by-wire system was designed specifically for small UAVs and urban air mobility (UAM). The Nuuva V300 can carry up to 300 kilograms for approximately 186 miles.

“One of the toughest challenges logistics companies face today is meeting the demand for same-day delivery,” Stéphane Fymat, vice president and general manager of UAS/UAM at Honeywell Aerospace, said in a press statement. “Vehicles like Pipistrel’s Nuuva V300 are going to be a real breakthrough in the race to solve this problem. We listened to our customers and built a product that meets the unique needs of this segment, and we’re extremely proud that our Compact Fly-By-Wire system will be guiding these vehicles as they take to the skies.”

Honeywell makes a full line of avionics equipment including flight controls, navigation, and radar that are designed for piloted vertical take-off and landing (VTOL) UAM, according to the release.

“After years of excellent cooperation in the UAM sector, we chose to work with Honeywell in the development of the Nuuva V300 as well,” Ivo Boscarol, founder and CEO of Pipistrel Group, said in a press statement. “We see this cargo aircraft paving the way for the passenger-carrying Pipistrel 801, our proposed air taxi for Uber Elevate, as both aircraft share similar architectures. Honeywell’s expertise and the proven capabilities of its Compact Fly-By-Wire system will provide airliner levels of safety for our novel air vehicles.”

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Anki as Learning Superpower: Computer Science Edition

Mish Boyka



TL;DR: If you aren’t using Anki or one of its siblings to remember what you learn, you are missing out on literal superpowers. There are specific techniques which I’ve found helpful for using it to learn maths and computer science in particular.

This post will discuss extremely briefly what Anki is, but is mainly aimed at helping the student of maths or computer science to squeeze out some extra droplets of productivity from it. If you aren’t already familiar with Anki, go and read Michael Nielsen’s post Augmenting Long-Term Memory as well or instead of this one; if you’re short of time, the main value of the post to someone new to Anki is in the first one-eighth or so, up to but not including “Using Anki to thoroughly read a research paper in an unfamiliar field”. That essay gives a broad-strokes motivation for why one might want to use Anki at all. (Spoiler: it gives you a superhuman memory!)

What is Anki?

Anki is a spaced repetition system: essentially a program that shows you flashcards at intervals tailored to help you remember their contents. Such systems are based on the observation that while you can’t stop memories from decaying, repeated exposure makes the decay exponentially slower.

So while you need to rehearse a fact frequently when you first come to learn it, reviews can become very sparse very quickly without losing much of your hard-won memory.

Anki is only one such system; other implementations such as SuperMemo and Mnemosyne exist.
There are also applications using the same principles for more specific goals; for example, Memrise is designed for language learning. This post is phrased in terms of Anki, because for historical reasons that’s the one I use.

I’ve placed this section at the start, because I believe that spaced repetition is genuinely a superpower that anyone can acquire. If I can’t hold your interest in this post, I encourage you to glance over these other resources in the hope that one of them does the trick!

  • Augmenting Long-Term Memory –  a brief introduction to various memory systems with a particular focus on Anki. The money quote: “Anki makes memory a choice”. If you choose to remember something, you can.
  • Quantum Country – an introduction to quantum computation with integrated spaced-repetition flashcards, which comes with emailed reminders to use the site at intervals. Even if you have no interest in quantum computation, I recommend skimming at least the first bits of the site, so that you can see what really good flashcards based on a text can look like. (Note that some of its cards are not ideal; the site does sometimes fall into the “yes/no” pattern, with flashcards whose answer is a bald “yes” or “no”. Cards of this form aren’t as good as cards which get you to reproduce actually content-based parts of a fact.)
  • The Twenty Rules of Formulating Knowledge in Learning – the creator of the spaced-repetition system SuperMemo discusses how to formulate knowledge so that it sticks. Again, even if you don’t use spaced repetition, definitely read this; the advice is absolutely foundational to my understanding of how to learn. A nontrivial amount of this very blog post is essentially specialising some of these rules to the case of maths and computer science.
  • Reddit: Medical School Anki, a subreddit with almost 55,000 subscribers at the time of writing. This link is here just to demonstrate that there are fields (such as medicine) in which Anki is very popular and nowhere near as niche as it is in most areas.

Absolutely crucial to the effective use of Anki for even a moderate collection of cards is that answering a card should be a single mental motion.

What does this mean? We’ll demonstrate with some positive and negative examples.

  • “What is the capital of France?” is probably answered with a single mental motion: it’s just “Paris”, obtained by a simple lookup in your memory.
  • “What is 367 times 399?” is many mental motions unless you are really unusually good at mental arithmetic. Almost everyone has to carry out some algorithm to get an answer to this question.
  • “What is the composition of air?” is probably many mental motions: for example, a lookup of “which gases are in air?” and a number of motions like “what proportion of air is this specific gas?”. Or it could be the various mental motions of “Which gas is the nth most common in air, and what is its proportion in air?” as n varies.
  • “What is the most common gas in air, and what is its proportion?” is very possibly a single mental motion despite the multiple components in its answer. For me, the knowledge that “nitrogen is the most common gas in air” is intimately bound up with “78% of air is nitrogen”; to answer one question is to access the same mental lump of storage as is required to answer the other question. Of course, for someone else, this may be two distinct facts and two distinct memory lookups.

A card that is answered with one mental motion may be multiple motions for someone else; and a question answered with many mental motions may become one motion after you learn some additional fact or part of the model that ties the facts together. So it’s helpful if you personally keep track of what you’re doing to answer a given card, so that you can recognise some of this structure in your own mind.

Any card which is multiple mental motions should be broken down into smaller chunks.

If you’re doing too much work to answer a card, it’s important to notice, so that you can break the card down. And don’t worry that you might “break down a card too much”; if the cards are easy, Anki will exponentially decrease how often it shows them to you. The cost of creating a card that’s too easy is almost entirely in the time it takes you to create the card in the first place; a card that’s too difficult will sap your time and energy again and again.

As an example, recall the ratio test for convergence, likely to be covered in any first course in GFN:

Let$sum_{n=1}^{infty} a_n$ be a complex series, with each $a_i$ nonzero.
Suppose that there is $a$ such that $|frac{a_{n+1}}{a_n}| to a$.
Then, if $a < 1$ then the series converges absolutely; if $a > 1$ then the series diverges.

(We’ll discuss its proof in a later section.)

This statement has a number of moving parts, and is definitely much too large to appear as a single card. (Remember the rule of thumb: answering a single card should be a single mental motion.)
How could we formulate this statement in an Anki-friendly way?

My own personal Anki collection contains the following cards. (Anki does allow LaTeX, though I often optimise for speed of card creation and just use plain text, however ugly it ends up. As long as it’s easily legible, it doesn’t need to be pretty.)

  • What conditions exist on the ratio test? (answer: nonzero, sequence of ratios has a limit)
  • When does the ratio test let us conclude something? (answer: successive ratios converge to something not equal to 1)
  • Which cases exist on the ratio test? (answer: ratios converge to less than, or greater than, 1)
  • What can we say from the ratio test if the ratios converge to something less than 1? (answer: converges absolutely)
  • What can we say from the ratio test if the ratios converge to something greater than 1? (answer: diverges)
  • What can we say from the ratio test if the ratios converge to 1? (answer: nothing)
  • Give an example where the ratio test is inconclusive. (answer: harmonic series)

All these cards are very simple; perhaps they might look laughably simple. This is fine! Remember that Anki will rapidly stop showing you cards you already know. Crucially each card is really a single mental motion to answer.

Note also that information is duplicated between cards. For example, there are two cards saying in slightly different ways that the ratio test talks about when successive ratios converge to something not equal to 1. Again, it’s fine to repeat information, because cards are cheap. Here, the information is duplicated to better facilitate the links between the cards: one card is a general “when can we conclude anything”, and one card is the same information rephrased as “which cases do I need to consider to produce more information here”. Without the additional rephrasing, there’s more of a risk of developing “isolated” clusters of cards; the aim is that given just the prompt “ratio test”, I can reproduce the entire cluster without thinking any further.

And don’t forget to store key examples and counterexamples!

Remembering a definition is rather like remembering the statement of a theorem.
Without further ado, here is my definition of a red-black tree:

  • What, imprecisely, are the colouring rules on a red-black tree? (“global; local; base-case”)
  • What are the leaves of a red-black tree? (“null, black”)
  • What is the base-case colouring rule of a red-black tree? (“leaves are black”)
  • What is the local colouring rule of a red-black tree? (“red node => black children”)
  • What is the global colouring rule of a red-black tree? (“black depth is well defined”)
  • What is the black depth of a node in a red-black tree? (“the number of black nodes encountered on a path from that node down to a leaf”)

Again, there is some duplication (two cards note that the leaves of a red-black tree are coloured black), and all the cards are extremely simple. The point is to make sure not only that the actual content is remembered, but also that the content is interlinked enough that you can reproduce the entire definition from the single prompt “red-black tree”. Moreover, one card is explicitly structural and carries no actual content as such: the card that lists the three types of colouring rule. This card is there solely to allow me to remember which cards are relevant.

Naively, one might create instead a single card, “what is a red-black tree?”. But in my experience, this is too big. If you’re reviewing even 30 cards a day, and they’re all as big as “what is a red-black tree?”, you may very well get bored or start spending too long on reviews. I personally review about 85 cards per day, all of them small; whenever I have a couple of minutes spare, I’ll do a few cards. If many of your cards are big, reviewing becomes an awful chore and it becomes very hard to make yourself put in even the small amount of time that’s necessary to stay on top of it.

It is possible to rote-learn text using Anki. For example, I’ve learnt the first four chapters of the Tao Te Ching as 90 cards, each having the same structure: the front face is line 43 of the text, say, and the back face is line 44. However, this is a task for which human memory is quite poorly suited: almost everyone learns best through association, creating large networks of interrelated facts that together form a coherent world-model, each fact boosting the memory of the others.

To learn anything at all, it is better first to understand it, however vaguely.
Don’t jump straight to memorisation without first having the skeleton of a model on which to hang the facts you’re memorising.

For much, much more on the nature of understanding proofs and how to use Anki, see the excellent blog post Seeing Through a Piece of Mathematics by Michael Nielsen. Nielsen walks through a simple problem and discusses the possible ways one might understand it, and how one might use Anki to encode one’s understanding.

So let’s say you’ve understood a proof, and you now want to use Anki to immortalise the proof in your memory. It may feel quite natural to try and rote-learn the proof; but this is a big waste of energy, since unstructured text does not play to the mind’s strengths. Instead, construct a map through the proof, placing waypoints as you go, then learn the waypoints. Remember also that you can use cards which encode structure rather than content, if necessary, as discussed in the “what is a red-black tree?” example.

Simple example: the ratio test

We defined the ratio test above; let’s see how we might formulate its proof in an Anki-friendly way.

Here is one proof of the ratio test, copied almost verbatim from my university lecture notes.

It’s not important to understand this fully, or even in any detail at all; I’m using it only as an example, for conversion into Anki cards.

There are two cases: the sequence $|frac{a_{n+1}}{a_n}|$ tends to $a < 1$ as $n to infty$, or to $a > 1$.

Suppose first that $a > 1$. Then there is some $M$ such that beyond $a_M$, all $a_{n+1}$ are greater in absolute value than their $a_n$. Therefore the sequence cannot tend to $0$, so the series cannot converge.

Suppose therefore that $a < 1$. Pick any $r$ between $a$ and $1$; then there is some $M$ such that beyond $a_M$, all $|frac{a_{n+1}}{a_n}| < r$. So beyond $a_M$, all $|a_n|$ are less than $r^{n-M} |a_M|$; but $sum_{n=M}^{infty} |a_M| r^{n-M}$ is a geometric series which converges, and so by the comparison test, $sum_{n=M}^{infty} |a_n|$ converges. Since initial terms do not affect convergence, $sum_{n=1}^{infty} a_n$ must converge absolutely. This completes the proof.

For me, the cards are as follows:

  • What is the first step of the proof of the ratio test? (split into $a < 1$ and $a > 1$)
  • What is the key idea in the proof of the ratio test, $a > 1$? (terms don’t tend to 0)
  • What is the key idea in the proof of the ratio test, $a < 1$? (pick $a < r < 1$, comparison test after two adjustments)
  • What is the first adjustment we make in the proof of the ratio test, $a < 1$? (ignore initial terms so all ratios < r)
  • What is the second adjustment we make in the proof of the ratio test, $a < 1$? (divide out first term so all terms < r^n)
  • What do we compare against in the proof of the ratio test, $a < 1$? ($r^n$)

Using this, I can construct the following proof, which is in a little less detail than the original but which I could easily flesh out if required.

Let the absolute value of the limit of $frac{a_{n+1}}{a_n}$ be $a$. We split into two cases: $a < 1$ and $a > 1$.

If $a > 1$, the series is a summation of terms which do not tend to $0$ (indeed, beyond a certain point the terms become strictly increasing in modulus), so it cannot converge.

If $a < 1$, select $r$ between $a$ and $1$. Then because initial terms don’t affect convergence, we can omit initial terms so that without loss of generality all $frac{a_{n+1}}{a_n}$ are less than $r$ in modulus. Then we may divide out by $a_1$ so that without loss of generality every $|a_n|leq r^n$. Finally, the comparison test gives the required result.

Perhaps there are better ways to formulate these cards; it’s never ideal to have to remember rather arbitrary lists such as “what is the first adjustment” and “what is the second adjustment”. But the “first and second adjustments” cards are safe for me to remember, because I remember them together spatially: the first is a feeling of motion, translating the series to the left, and the second is a feeling of shrinking/squashing, dividing out the first term. Possibly different people will find different and more personally effective ways to factor out the various components.

Notice that these cards encode hints rather than formal proof. The aim is to set up the right structure, rather than to rehearse a proof verbatim. Even if you’re studying for an exam, you still should trust yourself to be able to do things without having explicitly memorised them!

The usual rule of thumb is that you spend 50% of your time on the hardest 5% of your flashcards. A spaced repetition system will show you easy cards at exponentially decreasing frequency, so you’ll rapidly stop reviewing your easiest cards. But some cards just stubbornly refuse to be learned, so Anki will show them to you again and again in the hope that you’ll get it this time (until eventually it gives up, marking the card automatically as a “leech”, and stops ever showing it to you).

There will be cards that behave this way; that’s just life. Do keep an eye out for them; try and learn to recognise the mental state that is “urrgh, not this card again”. When you find a card that is showing up repeatedly, or that it’s consistently an unpleasant effort to answer, or which you keep getting wrong:

  1. Ditch the card! Do you really need to learn this fact anyway? There are so many other things out there to learn; do you have a good reason to spend your time on this one? Or might you be able to derive the contents of this card if necessary without even trying to memorise it?
  2. Split up the card. Is it too big? Can you reduce the mental effort required to learn the card?
  3. Make better mnemonics. Do you need to construct a different mental scene describing the card, or some clever phrase that sticks in your mind, or set something to music?
  4. Revisit the basics. Are you getting this card wrong because your mental model for the entire subject is not sufficiently well-founded?

I’ve left it to other people to persuade you to use Anki, but this was a whip around a few things to keep in mind so that you can get a bit more out of your Anki usage, especially when it comes to learning more complex technical concepts where it’s not so obvious how to create the cards. The art of Anki is easiest to learn by example; hopefully this has provided a couple more demonstrations to help fill out the arsenal.

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The South was a lost cause for Democrats. Now eight key Senate seats are in play.





ATLANTA — Karen Ashley has walked with a handful of older Black men, residents of a low-income housing development, to the State Farm Arena each day early voting has been available in Georgia.

These strolls, which she called “wheelchairs and walkers to the polls,” are the culmination of months of work, including candidate forums and debate watch parties she held at the apartment building.

As the director of resident services at Friendship Towers, Ashley, 59, said she aimed to get all 106 residents — many of whom did not complete high school and had never voted before — to cast their ballots.

“I had the thought one time when I was looking at all of the negative back and forth between this group and that,” she said while accompanying some residents back to their homes. “And I said, ‘They don’t even consider this population.’ I said, ‘Guys, this is what we’re gonna do. We’re gonna register, we’re gonna vote and your voice will be counted.’”

Image: Voters line up to cast their ballots for the upcoming presidential elections in Atlanta (Chris Aluka Berry / Reuters)
Image: Voters line up to cast their ballots for the upcoming presidential elections in Atlanta (Chris Aluka Berry / Reuters)

It is voters like them who could make the difference in a number of increasingly contentious races in Georgia, where both Senate seats are competitive and Joe Biden could be the first Democratic presidential candidate to win the state since Bill Clinton eked out a 13,000 vote lead in 1992.

Even beyond Georgia, first-time and minority voters also have a large role in Democrats’ prospects across the South. The region is, in some ways, at play for Democrats this election cycle, particularly in a number of Senate contests that are now neck and neck just ahead of Election Day.

Despite the political convention that Republicans hold a secure grip on the South, Democratic candidates are polling competitively in North Carolina, South Carolina, Kentucky, Georgia, Alabama, Mississippi and Texas — which together account for eight Senate seats and possibly the balance of power in the chamber.

They could also help usher in additional Electoral College votes for Biden, though many experts remain skeptical whether Democrats can achieve a blue wave.

Still, Georgia races have grown increasingly tight in the past few years, which is why it remains the main target for Democrats. Since losing the state’s race for the governorship by only 50,000 votes, Stacey Abrams and her voter rights organization, Fair Fight, have helped register more than 800,000 new voters in the state.

By engaging with new voters in the South — many of them young and minorities — Democratic candidates hope to find a pathway Nov. 3 in a region often disregarded by their party and increasingly dominated by Republicans in the decades after President Lyndon B. Johnson signed the Civil Rights Act.

Rev. Raphael Warnock, the leading Democratic candidate for Georgia’s Senate special election, is Black and the pastor at the Ebenezer Baptist Church, a pulpit made famous by Martin Luther King, Jr. He sees hope in the new Southern demographic. He worked with Abrams to register those 800,000 voters and noted that 49 percent of them are people of color and 45 percent are under the age of 30.

“This is not magic,” he said. “It’s hard work over time, and it’s a deep commitment to the noble idea that your vote is your voice and your voice is your human dignity.”

Senate races in the South

Early and absentee voting and donations to the campaigns of this strong class of Southern Democratic candidates would appear to indicate a groundswell of support — something long considered impossible in the South.

Democrats’ mail-in ballots and early in-person voting in Kentucky, where former Marine fighter pilot Amy McGrath is challenging the Senate Majority Leader Mitch McConnell, have outstripped Republicans by 17 points, according to NBC News’ count. Democrats have out-voted Republicans by 17 percent in North Carolina in early voting, a state where 2.1 million people have already cast their ballots — a 230 percent increase from this time in 2016. It remains to be seen how these numbers translate on Election Day, as they are inflated by drives to vote early during the pandemic.

Image: Kentucky Democratic Senate Candidate Amy McGrath Campaigns In Louisville (Jon Cherry / Getty Images)
Image: Kentucky Democratic Senate Candidate Amy McGrath Campaigns In Louisville (Jon Cherry / Getty Images)

In South Carolina, however, Democrat Jaime Harrison raised a historic $57 million in a tight race against the incumbent Sen. Lindsey Graham. In Texas, Air Force veteran MJ Hegar is polling within a few points of Sen. John Cornyn, the Republican Senate majority whip who has held the seat since 2002. Sen. Doug Jones, the first Democrat to win a U.S. Senate seat from Alabama since 1988, has outraised his opponent by about $18 million. And in Georgia’s other Senate race, Jon Ossoff appears to be tied with incumbent Republican Sen. David Perdue in each new poll released.

“Georgia becomes younger and more diverse by the hour,” Ossoff said. “And the political infrastructure that’s been built and invested here in Georgia over the last decade is paying dividends. We’ve seen record voter registration, we’re seeing record turnout and enthusiasm. We’re not paying much attention to polls day by day, but the turnout is really encouraging.”

It is unlikely that Democrats will win all of these seats, but the very fact they are competitive is significant. The chance for a Democratic victory even appears brighter in ruby red Mississippi than it has in decades.

Democrats in Mississippi had not come within 14 points of this Senate seat since Republicans took official control of it in 1978. That changed in 2018 when Mike Espy, the secretary of agriculture under then-President Bill Clinton, garnered more than 46 percent of the vote in a special election for the seat and lost by 8 points.

Since his comparatively close loss, Espy — the state’s first Black congressman since Reconstruction — hopes to benefit from increased turnout during an election year while expanding his voter outreach and fundraising. In the final weeks of October, Espy raised nearly $3.9 million while his opponent, Sen. Cindy Hyde-Smith, the Republican incumbent, pulled in less than $85,000, according to Mississippi Today.

The math of his campaign, Espy previously told NBC News, is dependent on turning out Black voters, who make up nearly 38 percent of the state’s population, and reaching out to white moderates. The influx of cash appears to be helping.

He’s polling close with Hyde-Smith and voter turnout could be working in his direction. Hinds County, which is home to a large number of the state’s Black voters, already recorded more than 9,800 early or absentee votes two weeks before the election. In 2016, the county only received 5,309 early or absentee votes for the entire election.

Image: (Rogelio V. Solis / AP file)
Image: (Rogelio V. Solis / AP file)

“The reason no one won in the South in 25 years is because no one ran,” said Joe Trippi, a Democratic strategist who has advised Espy’s campaign and helped Jones win his Alabama race in 2017. “You’d sometimes have a good candidate run, but they had no capacity to raise money or get involvement from the national party. That’s changed now and for the first time in umpteen years, even if you don’t think Joe Biden can win there, voters in these places have a reason to vote.”

How did the South become competitive?

Jones’ success and the intrigue of candidates such as Abrams and Beto O’Rourke in 2018 brought the national gaze to the South in ways it hadn’t before, long after organizers had built up a grassroots movement by themselves.

Organizers said they took note of a shift in demographics away from white evangelicals, as well as a renewed engagement among young voters in reaction to the Trump administration.

Warnock, the pastor and Senate candidate in Georgia, has worked on voter drives in the state for decades — even driving Hurricane Katrina refugees back to Louisiana so they could vote. He said the South has long been defined by a “politics of fear and the divisions ensconced in the so-called Southern Strategy,” referring to the election strategy used by President Richard Nixon that many believe led to the political realignment of the South by fanning the flames of racism.

Image: Democratic Candidates In Georgia Campaign Ahead Of November's Election (Elijah Nouvelage / Getty Images)
Image: Democratic Candidates In Georgia Campaign Ahead Of November’s Election (Elijah Nouvelage / Getty Images)

“What we’re witnessing is the reversal of that through changing demographics as a result of reverse migration, younger voters are responding to the moment and older voters are seeing how people in Washington are not thinking about them,” he said.

State Democratic parties in the South left their candidates and infrastructure to die on the vine for years under aging leadership. Reform has begun with younger and more diverse organizers taking control in recent years.

In the past year alone, members of the Mississippi and the Alabama Democratic parties forced out their party heads and ushered in new leadership that made them younger and more diverse than they have been in history.

Howard Dean, a former Democratic presidential candidate, is credited with creating the 50-state strategy in the 2000s, which aimed investment at state parties to have credible candidates compete for every office — a concept that was never truly realized. He said in recent years “state parties atrophied for the most part.”

“But that’s shifting again now,” Dean said, citing Alabama as an example. “A lot of parties that have been weak for a long time are getting stronger.”

That change began happening despite the lack of investment from the larger party structure, though Dean said the various wings of the Democratic Party are coordinating better than they have in years past

Still, Jones did not receive much support in Alabama until the end of his race in 2017, and Espy drew close in Mississippi without much help in 2018. In contrast, the Democratic National Committee is now funding major ad campaigns in North Carolina, Georgia, Florida and Texas and putting further investment in the races in Kentucky, Mississippi and South Carolina.

Image: (Cameron Pollack / Getty Images)
Image: (Cameron Pollack / Getty Images)

For the first time in decades, Democrats in the South have an opportunity, said Clay Middleton, a Black member of the Democratic National Committee who has worked as a political strategist across the South.

This renewed enthusiasm at the top of each state’s ticket can help each state party rebuild its long-forgotten infrastructure, allows for organizers to update their data, run ads, cycle dollars through local communities and build a bench of new leaders.

“I’m 38 years old, and I don’t ever recall there being this level of intentional investment into Southern Democratic Party infrastructure,” Middleton said, “which means we’re making progress and doing the right things.”

A future for Democrats in the South?

It remains to be seen whether this is a prolonged shift in Southern politics, or if it is a sudden invigoration caused by a caustic and unpopular president. It is still a deeply conservative and religious region, and some strategists warned that Democrats need to tread carefully.

Brian Walsh, a Republican strategist, said no matter how Democrats do, the GOP will have to reconsider itself as the party of Trump. Republicans, he said, ignored the warnings of the party’s 2012 election autopsy that concluded it needed to broaden its base by moderating its views on immigration and by reaching out to minority groups.

Image: Voters cast their ballots for the upcoming presidential elections in Atlanta (Chris Aluka Berry / Reuters)
Image: Voters cast their ballots for the upcoming presidential elections in Atlanta (Chris Aluka Berry / Reuters)

“One thing that always helps Republicans though is that the only other party is the Democrats,” Walsh said. “You have the extremes of both parties that are the loudest voices right now. They have to be careful to not overreach as well and suddenly support things like the Green New Deal or ‘Medicare for All.’”

But if these Senate candidates, functioning as the top of their state tickets, are able to get voters to turn out, that could change their states fundamentally in elections to come, experts said, especially as Democrats argue that a number of Southern state legislatures are in play, as well.

It remains to be seen, however, whether this is a moment of Democratic success or bluster.

“I just hope we don’t take a step back after all this investment,” Middelton said. “When the GFN is done, I think there is going to be a reshuffling of how we would look at the South in presidential years and otherwise.”

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