The blue plaque on Alan Turing’s house, commemorating his work in cryptography which founded both Computer Science and Artificial Intelligence as new disciplines. Picture by Joseph Birr-Pixton on Wikimedia Commons w.wiki/3aYW
The house where Computer Scientist Alan Turing spent his final years is currently up for sale. The estate agent describes the property on 43 Adlington Road, Wilmslow as a Victorian family residence of significant historical importance. Wilmslow and the surrounding Cheshire countryside is popular with Manchester commuters, including many Man United, Man City & England football stars. Even if you could afford its premier league price tag, would YOU want to live in the house where Turing’s life ended so tragically?
Turing was found dead at this house, on the 8th June 1954 by his cleaner. The cause of his death the previous day was established as cyanide poisoning. He was just 41 years old. When his body was discovered, an apple lay half-eaten by his bedside.
The coroner recorded a verdict of suicide.
At the end of his life Turing was suffering mentally and physically. The homophobic British authorities were using a form of legalised torture, known as forced chemical castration, to punish him for being homosexual. At the time, homosexuality was a crime. Turing put on a brave face and joked about his castration (“I’m growing breasts!”), but it must have been horrible to endure.
If you’re feeling suicidal or tortured, you don’t have to struggle with difficult feelings alone. If you’re suffering from emotional distress or struggling to cope a Samaritan can face your problems with you. Whatever you’re going through, samaritans.org are available 24 hours a day, 365 days a year. They respond to around 10,000 calls for help every day. No judgement. No pressure. Call them free any time, from any phone on 116 123.
While everyone can have a good old nosey at Turing’s house through the estate agents window, no-one needs to suffer like its famous former resident did. Personally I think I’d find this property an enigmatically haunted house to live in, knowing that this was the place where a great man’s life ended in such tragedy. How about you?
Alan Turing’s Manchester by Jonathan Swinton describes what it was like to make new friends and lovers in the smog-bound, bombed-out city of Manchester from 1948 to 1954 manturing.net
Thanks to Alan O’Donohoe for spotting Turing’s house on the market and to Joseph Birr-Pixton for publishing his picture of Turing’s blue plaque on Wikimedia Commons.
The first rule of journal club is, you do not talk about journal club. The second rule of journal club is, YOU DO NOT TALK ABOUT JOURNAL CLUB.* Discussions will go on as long as they have to. If this is your first time at journal club, you have to debate. Dress code: silly frocks and ridiculous hats are optional. Picture of my colleagues in the School of Computer Science ready for a graduation ceremony 2013, by Toby Howard.
So we’re starting a new Journal Club and Special Interest Group (SIG) for lecturers, teachers and course leaders in Manchester to discuss Computer Science Education (CSE). We’ll pick interesting papers, read them and then meet regularly to discuss them. It’s a bit like Fight Club but instead of beating each other up, we’ll “beat up” (review & critique) papers. Hopefully we’ll all learn something along the way. The first question to answer is, which papers should we discuss?
What this means is that there is plenty of evidence about what works (and what doesn’t) when teaching mathematics. In contrast, how to teach Computer Science, what should be taught and why, to whom and when are all open questions.
So, to get the ball rolling here are nine papers that tackle some of these open questions in Computer Science Education. We’ll vote on the three most interesting papers and read them before meeting to review them. Many of these papers are likely to be of interest to “educators” in its broadest sense. That means anyone teaching coding, computer science, tinkering, hacking and software/hardware engineering at any level.Which includes primary schools, code clubs, bootcamps, CoderDojos, hackathons, secondary schools, CPD programmes, K-12 education, lifelong learning, staff training courses, onboarding, induction, adult education programmes, return to work schemes and so on. If you’d like to join us we’ll be meeting in the Kilburn building, Manchester, M13 9PL (mosty likely first week of September, date and time tbc, drop me a line). Otherwise enjoy reading the insights below (DOI’s link to originals which may be behind a paywall, freely accessible versions are provided where available). Some papers are quite short, and have been selected for the topic they discuss rather than the quality of the content.
Twenty dirty tricks to train software engineers by Ray Dawson
A classic paper from Ray Dawson in the department of Computer Science at Loughborough University describing dirty tricks they use to introducing the frustrating realities of a software engineering development to students.
“Many employers find that graduates and sandwich students come to them poorly prepared for the every day problems encountered at the workplace. Although many university students undertake team projects at their institutions, an education environment has limitations that prevent the participants experiencing the full range of problems encountered in the real world. To overcome this, action was taken on courses at the Plessey Telecommunications company and Loughborough University to disrupt the students’ software development progress. These actions appear mean and vindictive, and are labeled ‘dirty tricks’ in this paper, but their value has been appreciated by both the students and their employers. The experiences and learning provided by twenty ‘dirty tricks’ are described and their contribution towards teaching essential workplace skills is identified. The feedback from both students and employers has been mostly informal but the universally favourable comments received give strong indications that the courses achieved their aim of preparing the students for the workplace. The paper identifies some limitations on the number and types of ‘dirty tricks’ that can be employed at a university and concludes that companies would benefit if such dirty tricks were employed in company graduate induction programmes as well as in university courses.”
Identifying student misconceptions of programming by Lisa Kaczmarczyk et al
This paper by Lisa Kaczmarczyk et al (formerly University of California, San Diego) recently came top of the ACM SIGCSE Top Ten Symposium Papers of All Time. In Lisa’s own words from the reinventing nerds podcast “The paper is sharing the results of a research study about misconceptions that novice computer science students have. Computer science is also a very abstract topic and the mistakes that students make are often baffling. The paper reports on the misconceptions that students have and why they have them. It’s important because this paper was the first to apply rigorous research methods to investigating misconceptions.” From the abstract:
“Computing educators are often baffled by the misconceptions that their CS1 students hold. We need to understand these misconceptions more clearly in order to help students form correct conceptions. This paper describes one stage in the development of a concept inventory for Computing Fundamentals: investigation of student misconceptions in a series of core CS1 topics previously identified as both important and difficult. Formal interviews with students revealed four distinct themes, each containing many interesting misconceptions. Three of those misconceptions are detailed in this paper: two misconceptions about memory models, and data assignment when primitives are declared. Individual misconceptions are related, but vary widely, thus providing excellent material to use in the development of the CI. In addition, CS1 instructors are provided immediate usable material for helping their students understand some difficult introductory concepts.”
Stride in BlueJ – Computing for All in an Educational IDE by Michael Kölling et al
This paper by Michael Kölling et al describes an Integrated Development Environment (IDE) that combines the best features of visual programming languages (blockly, scratch etc) with text-based programming (such as Python, Java, C etc) for use in BlueJ.org.
“In introductory programming teaching, block-based editors have become very popular because they offer a number of strong advantages for beginning programmers: They avoid many syntax errors, can display all available instructions for visual selection and encourage experimentation with little requirement for recall. Among proficient programmers, however, text-based systems are strongly
preferred due to several usability and productivity advantages for expert users. In this paper, we provide a comprehensive introduction to a novel editing paradigm, frame-based editing – including design, implementation, experimentation and analysis. We describe how the design of this paradigm combines many advantages of block-based and text-based systems, then we present and discuss an implementation of such a system for a new Java-like language called Stride, including the results of several evaluation studies. The resulting editing system has clear advantages for both novices and expert programmers: It improves program representation and error avoidance for beginners and can speed up program manipulation for experts. Stride can also serve as an ideal stepping stone from
block-based to text-based languages in an educational context.”
Kölling, Michael; Brown, Neil C. C.; Hamza, Hamza; McCall, Davin (2019). “Stride in BlueJ — Computing for All in an Educational IDE”: Proceeding SIGCSE ’19 Proceedings of the 50th ACM Technical Symposium on Computer Science Education 63–69. DOI:10.1145/3287324.3287462
Ten quick tips for teaching programming by Neil Brown and Greg Wilson
“Research from educational psychology suggests that teaching and learning are subject-specific activities: learning programming has a different set of challenges and techniques than learning physics or learning to read and write. Computing is a younger discipline than mathematics, physics, or biology, and while there have been correspondingly fewer studies of how best to teach it, there is a growing body of evidence about what works and what doesn’t. This paper presents 10 quick tips that should be the foundation of any teaching of programming, whether formal or informal.
These tips will be useful to anyone teaching programming at any level and to any audience.”
How to Involve Students in FOSS Projects by Heidi Ellis et al
Initiatives like Google Summer of Code (GSoC) and Git going in FOSS aim to get students involved in Free and Open Source Software (FOSS) projects, through paid work and online tutorials. Some courses use FOSS projects to teach software engineering, though these are fairly unusual. How can we get more students (and teachers) involved in FOSS projects? This paper by Heidi J. C. Ellis provides some guidance
“Software projects are frequently used to provide software engineering students with an understanding of the complexities of real-world software development. Free and Open Source Software (FOSS) projects provide a unique opportunity for student learning as projects are open and accessible and students are able to interact with an established professional community. However, many faculty members have little or no experience participating in an open source software project. In addition, faculty members may be reluctant to approach student learning within such a project due to concerns over time requirements, learning curve, the unpredictability of working with a “live” community, and more. This paper provides guidance to instructors desiring to involve students in open source projects.”
Ellis, Heidi J. C.; Hislop, Gregory W.; Chua, Mel; Dziallas, Sebastian (2011). “How to involve students in FOSS projects” Frontiers in Education Conference (FIE) DOI:10.1109/FIE.2011.6142994 (ironically, if there is an open access version of this paper, I can’t find it! Another nominee for the Open Access Irony Awards)
A methodology for using GitLab for software engineering learning analytics by Julio César Cortés Ríos et al
This paper by Julio César Cortés Ríos at the University of Manchester describes using GitLab to analyse and improve courses.
“To bridge the digital skills gap, we need to train more people in Software Engineering techniques. This paper reports on a project exploring the way students solve tasks using collaborative development platforms and version control systems, such as GitLab, to find patterns and evaluation metrics that can be used to improve the course content and reflect on the most common issues the students are facing. In this paper, we explore Learning Analytics approaches that can be used with GitLab and similar tools, and discuss the challenges raised when applying those approaches in Software Engineering Education, with the objective of building a pipeline that supports the full Learning Analytics cycle, from data extraction to data analysis. We focus in particular on the data anonymisation step of the proposed pipeline to explore the available alternatives to satisfy the data protection requirements when handling personal information in academic environments for research purposes.”
Scaling Introductory Courses Using Undergraduate Teaching Assistants
Teaching computer science to large classes requires typically requires armies of teaching assistants, demonstrators. Your TA’s need to know their stuff and should be able to deal with students in a fair and consistent way. This paper is a medley of opinions from Jeffrey Forbes at Duke University, David Malan from Harvard University, Heather Pon-Barry from Mt. Holyoke College, Stuart Reges from the University of Washington and Mehran Sahami from Stanford University.
“Undergraduates are widely used in support of Computer Science (CS) departments’ teaching missions as teaching assistants, peer mentors, section leaders, course assistants, and tutors. Those undergraduates engaged in teaching have the opportunity to deeply engage with CS concepts and develop key communication and social competencies. As enrollments surge, undergraduate teaching assistants (UTAs) play a larger role in student experience and outcomes. While faculty and graduate student instructional support does not necessarily increase with the number of students in our courses, the number of qualified undergraduate teaching assistants for introductory CS courses should scale with the number of students in our courses. With large courses, the significance of the UTAs’ role in students’ learning likely also increases. Students have relatively little interaction with the instructor, and faculty may have more challenges monitoring and supporting individual UTAs. UTAs have a major role in affecting climate in computer science courses. The climate in large courses has substantial implications for students from groups traditionally underrepresented in computing. This panel will discuss how undergraduate teaching assistants can serve as a scalable effective teaching resource that benefits both the students in the course and the UTAs themselves.”
What Are We Doing When We Teach Computing & Programming by Sally Fincher
Two related papers by Sally Fincher at the University of Kent, the first published in 1999…
“The academic discipline of computer science uniquely prepares students for future study by teaching the fundamental construct of its practice-programming- before anything else. The disciplinary argument seems to run that if a student is not versed in the practicalities, then they cannot appreciate the underlying concepts of the discipline. This may be true. However an analogous simulation would be if it were thought necessary for architecture students to be taught bricklaying before they could appreciate the fundamentals of building design. This argument is clearly flawed when compared to endeavours such as the study of English Literature, which makes no claim to teach the practice of producing work before the study of the products of others work. It is possible that this is an argument of disciplinary maturity-that all disciplines have passed through a similar phase. This paper examines the emergent approaches being defined, all of which address the central concern of the teaching of programming and its relationship to the learning of computer science. It examines: the “syntax-free” approach of Richard Bornat and Russel Shackelford, the “problem-solving” approach of David Barnes (et al.), the “literacy” approach of Peter Juliff and Owen Astrachan and the “computation-as-interaction” approach of Lynn Andrea Stein. These approaches are discussed both in their own terms, and also placed in a preliminary taxonomic framework for the teaching of programming.”
Modern learning theories emphasize the critical social aspect of learning. Computer science (CS) classrooms often have “defensive climates” that inhibit social learning and prevent the development of a community of learners. We believe that we can improve the social context of computer science learning by expanding CS learning beyond the single student in front of a display screen. Our theory is that the single student and single display inhibits collaboration and collaborative awareness of student work. In this paper, we present two case studies where we explored ways to make student work visible to peers. The first case study involved using a studio model for learning enabled by projection-based Augmented Reality (AR), and the second case study involves using a maker-oriented curriculum to make student work visible. Findings suggest the visibility of student work in CS classrooms helped support a community of learners: students collaborated, used each other as sources of inspiration, and felt more comfortable asking for help.
*”You do not talk about Journal Club” is an adapted quote from the 1999 film Fight Club, see below. I’m only joking, you are of course welcome to talk to anyone who will listen about Journal Club.
Talking of David Malan, you can see his talk on making CS50 scale when he visited Manchester in 2017
Delegates at the Computing at School conference 2017 #CASConf17 answering diagnostic questions, picture by Miles Berry.
The Computing At School (CAS) conference is an annual event for educators, mostly primary and secondary school teachers from the public and private sector in the UK. Now in its ninth year, it attracts over 300 delegates from across the UK and beyond to the University of Birmingham, see the brochure for details. One of the purposes of the conference is to give teachers new ideas to use in their classrooms to teach Computer Science and Computational Thinking. I went along for my first time (*blushes*) seeking ideas to use in an after school Code Club (ages 7-10) I’ve been running for a few years and also for approaches that undergraduate students in Computer Science (age 20+) at the University of Manchester could use in their final year Computer Science Education projects. So here are nine ideas (in random brain dump order) I’ll be putting to immediate use in clubs, classrooms, labs and lecture theatres:
Linda Liukas demonstrated some intriguing ideas from her children’s books and HelloRuby.com that are based on Montessori education. I shall be trying some of these out (particularly the storytelling stuff) at code club to keep girls involved
Sue Sentance and Neil Brown from King’s College London gave an overview of some current research in pedagogy. They discussed research questions that can be tackled in the classroom like (for example) do learners make more progress using visual programming languages (like Scratch and Blockly) or traditional text-based languages (like Python and Java etc)? Many of these research questions would make good projects for undergraduate students to investigate in secondary schools, see research on frame based editors, for example.
Michel Wermelinger from the Open University demonstrated using iPython notebooks for teaching data literacy at the Urban Data School. Although I’m familiar with iPython, it had never occurred to me to actually use iPython in school for teaching. It is a no-brainer, when you think about it, even for primary, because you have your code, inputs and outputs all in one window, and can step through code execution instead of (or as well as) using more conventional tools like Trinket, Thonny or IDLE. Data literacy is fun to teach.
Miles Berry from the University of Roehampton demonstrated Diagnostic Questions in Project Quantum. These are a collection of high quality quizzes to use interactively for example as hinge questions, where teaching is adapted depending on answers given, like this multiple choice question:
Consider the following Python code:
a = 20
b = 10
a = b
What are the values of a and b?
A: a = 10, b = 10
B: a = 20, b = 20
C: a = 30, b = 10
D: a = 10, b = 20
You’ll have to try these five questions to check your answer. The useful thing here is that DiagnosticQuestions.com (the platform on which this is built) allows you to see lots of responses, for example each answer (A, B, C or D) above was selected by 25% of participants. You can also view explanations which illuminate common misconceptions (e.g. the classic mistake of confusing assignment with equality) as well as providing a bank of free questions for use in the classroom.
Mark Guzdial from GeorgiaTech discussed using learning sciences to improve computing teaching. He demonstrated predictive questions (e.g. ask students What do you think will happen when we run this code? before actually executing it) alongside what he called subgoal labelling. These are simple ideas (with proven benefits) that can be put to use immediately. I’ll also be trying the Live Coding (with Sonic Pi) and Media Computation he demonstrated asap.
Laurence Rogers demonstrated Insight: Mr. Bit this looks like a good app for using BBC microbits in the classroom, connected to a range of sensors, provided you’ve got access to iPads.
A copy of Hello World magazine was in the conference bag. The summer 2017 issue has an unusual article from Ian Benson from Kingston University and Jenny Cane describing their use of the Haskell programming language to teach 5-7 year olds to reason symbolically and learn algebra before arithmetic with help from Cuisenaire rods. The Scratch Maths project at University College London are doing similar things, building mathematical knowledge using Scratch, rather than Haskell. These are experimental ideas you could try out on unsuspecting (junior) family members.
Lee Goss from Barefoot Computing, described the free CPD for primary school teachers on offer from BT. I’ve signed up and hope to plug some of the shortcomings in the Code Club Curriculum.
Richard Jarvis demonstrated appJar, a handy Python library for teaching Graphical User Interfaces (GUIs). That’s Jar as in Jarvis and Jam, not JAR as in Java ARchive BTW. I’ve not tried GUIs at code club yet, but appJar looks like a good way to do it.
There were lots more people and projects at the conference not mentioned here including tonnes of workshops. If you’re interested in any of the above, the CAS conference will be back in 2018. Despite the challenging problems faced by Computer Science at GCSE level, it was reassuring and inspiring to meet some members of the vibrant, diverse and friendly community pushing the boundaries of computing in schools across the United Kingdom. Thanks again to everyone at CAS for putting on another great event, I will definitely consider attending next year and maybe you should too.
It’s that time of year when people look back at over the year that was 2014 (1-5). The place where I work, celebrated it’s 50th anniversary. Colleagues put together a little booklet of facts and figures with an some accompanying web pages to mark the occasion. My personal favourite factoid compares computing in 2014 with 1964. The Atlas Computer represented the state of the art in computing in 1964, and today that crown is held by SpiNNaker – a very different kind of computer.
50 years of computing (and pipe-smoking is lesson common around computers)
Sometimes, numbers speak louder than words, so here is a numerical comparison of Atlas (1964) with SpiNNaker (2014):
One way of looking at this data is to say, based on the the instructions per second, SpiNNaker is around ~5000 times faster than Atlas. But what is probably more interesting is that SpiNNaker (which is due for completion in 2015) is expected to be used by neuroscientists and psychologists, as a platform to study problems such as Alzheimer’s disease – something that would have been impossible (and unthinkable) only fifty years ago [6,7]. Wonder where the next 50 years will take us in 2064?
Morello, L., Abbott, A., Butler, D., Callaway, E., Cyranoski, D., Reardon, S., Schiermeier, Q., & Witze, A. (2014). 365 days: 2014 in science Nature, 516 (7531), 300-303 DOI: 10.1038/516300a
Anon (2014). 365 days: Nature’s 10, Ten people who mattered this year. Nature, 516 (7531), 311-319 DOI: 10.1038/516311a
Hand, E. (2014). Comet Breakthrough of the Year + People’s choice Science, 346 (6216), 1442-1443 DOI: 10.1126/science.346.6216.1442
Furber, S., Galluppi, F., Temple, S., & Plana, L. (2014). The SpiNNaker Project Proceedings of the IEEE, 102 (5), 652-665 DOI: 10.1109/JPROC.2014.2304638
“Universities are failing to educate graduates with the skills we need – this is the oft heard complaint by employers of IT graduates. Does the problem start in school with the dire state of ICT teaching and assessment at GCSE and A Level? [1] Should academia be trying to produce graduates with only ’employable skills’ that have a shelf life of at best a couple of years? Are employers really expecting universities to produce a mature, rounded professional with 20 years experience straight out of university? Is it reasonable to expect Academia to bridge the skills gap when employers are not prepared to provide a robust career path for IT professionals?
Academia and the IT Profession seem to be out of alignment in a way that other more mature professional career paths are not. Medicine, law, accountancy and the teaching profession provide a clear path from university to the highest levels of those careers – not so in IT. The IT Profession’s skills framework (SFIA) is only a decade old, and IT is neither a regulated or statutory profession – perhaps employers ask and expect too much of Academia, when the IT Profession is still in its infancy.”
“Computing systems are now ubiquitous in all areas of our professional and personal lives – which means that are incredibly diverse from personal apps for your phone to remind you to exercise to safety-critical, world-wide air traffic management systems. The notion that there is a single body of practical skills that is applicable to all of these different types of system is ludicrous as is the expectation that university courses should attempt to cover all aspects of computing practice.”
That’s a view from academia, no doubt employers will probably have a different take on the motion. David Evans and Deborah Trayhurn will be supporting the motion, with opposition from Bill Mitchell and Kevin Jones. Whatever your opinion, the debate takes place on Wednesday 12th June 2013 from 6.30pm – 9.00pm at the Armourers’ Hall, 81 Coleman Street, London, EC2R 5BJ. You can book a place at events.bcs.org/book/577, more info on twitter at #BCSDebate.
Computer Science as a subject in mainstream UK secondary education is in a pretty sorry state [1,2,3] but it’s not all doom and gloom. While many long suffering school children are being force-fed a nauseating diet of Excel, PowerPoint and Access others are enjoying a nutritious platter of Raspberry Pi, Hack to the Future and Animated fun.
Here’s a brief report on one of these tasty appetisers: Animation 2012, a UK schools animation competition now in its fifth year.
The day kicked off with prizes being awarded for the animation competition. To get a flavour of the creativity and skill involved, you can see winning examples online.
Following the prize giving there was a carousel of activities which included:
Paolo Masci and Sinan Halilbeyoglu demonstrated some of the latest computing research using CS4FN magic and illusions
Peter Sutton and Lloyd Henning showed how Artificially Intelligent computers can learn to do seemingly complex tasks with hands-on musical demonstrations.
Samantha Bail demonstrated augmented reality, combining computer-generated imagery (CGI) and video in real-time to make the world around us appear to include strange objects
Tom MacPherson-Pope and Tom Preston showed what is possible with the new Raspberry Pi, a computer that only costs about £20. They demonstrated Pi-Face an extension developed by Andrew Robinson which allows customisation of the basic Rapsberry Pi.
Arturs Bekasovs demonstrated how to create fractal shapes, a fascinating class of geometrical shapes which are extremely easy to describe and yet can be incredibly complicated.
Steve Pettifer closed the proceedings with a talk looking behind the scenes of some the technology, psychology and magic of modern games.
Animation 2012 was great fun for all involved, congratulations to all this years winners, hope to see you again next year. There were 526 Schools involved from across the UK, with 914 entries. 58 students were involved in the 35 winning entries from 31 different schools. Thanks to Toby Howard, all the organisers, supporters (Google, Electronic Arts and NESTA) and associates (Computing at School, CS4FN and BAFTA young game designers) for putting on an impressive show.
Science, is a big word that gets used and abused with reckless abandon. Virtually any discipline can award itself extra kudos by adding the magic S word at the end. For example, which sounds weightier, sports studies or sports science?
This phenomenon has been noticed many times before, for example, the philosopher John Searle once remarked that:
“Science has become something of an honorific term, and all sorts of disciplines that are quite unlike physics or chemistry are eager to call themselves ‘sciences‘.
A good rule of thumb to keep in mind is that anything that calls itself a science probably isn’t.” –see [1,2]
So let’s make a list. Starting with thingsthat probably aren’t a Science because they call themselves one:
So are maths, physics, chemistry, biology etc real sciences™ too? Using Searle’s definition, it’s difficult to say. To avoid confusion, it might be a good idea to use a subjects non-scientific original name (“biology” rather than “life science”) that way, we know (paradoxically) they are real sciences. Probably.
References
John R. Searle (1986). Minds, Brains and Science (1984 Reith Lectures) Harvard University Press ISBN:0674576330 (see also audio from the BBC Reith lecture archive) not Speech Acts: An Essay in the Philosophy of Language. Cambridge University Press.ISBN:052109626X (as originally stated in the first version of this post)
Fuller quotation: “Science has become something of an honorific term, and all sorts of disciplines that are quite unlike physics and chemistry are eager to call themselves ‘sciences’. A good rule of thumb to keep in mind is that anything that calls itself ‘science’ probably isn’t — for example, Christian science, or military science, and possibly even cognitive science or social science. The word ‘science’ tends to suggest a lot of researchers in white coats waving test tubes and peering at instruments. To many minds it suggests an arcane infallibility. The rival picture I want to suggest is this: what we are all aiming at in intellectual disciplines is knowledge and understanding. There is only knowledge and understanding, whether we have it in mathematics, literary criticism, history, physics, or philosophy. Some disciplines are more systematic than others, and we might want to reserve the word ‘science’ for them.”