Table of Contents
Week 2. Abstractions
This week is all about grouping, classifying, generalizing, and calculating, and generally how to turn encounters with people and things into knowledge that can be considered in the form of knowledge. We will discuss how to find and use abstractions in different forms of texts, from ancient clay tablets to vernacular books to computer code. We will try to understand a 600 year old fart joke.
What to do during week 2
- Please Please complete the Time-Sensitive bureaucratic task from week 1 (confirming your marking option). We cannot learn about bureaucracies in the history of science until we have some this bit of bureaucratic experience ourselves!
- Whole-class learning takes place at our lecture theatre on Tuesday and Thursday.
- Thursday features a guest conversation with Dr Richard Oosterhoff.
- Tutorials start this week! Yours will be either Tuesday or Wednesday. Please see announcements from the course administrator.
- Continue your reading and writing. Have a proper look (even if it is a very quick proper look) at three or more sources from the resource list. Set yourself a time limit and find out as much as you can in the time that you have. Find something that makes you think and that you want to read.
- Use the Exercises and Proofs below to guide your engagement and test your understanding.
- Sign up for special out-of-lecture small group activities for weeks 3 and 5/6; these have capacity limits so we need to divide up into groups. Note week 5/6 activity may be rearranged or cancelled due to strike (but please sign up for now so we know who is interested and on the hope of a negotiated end to the strike!).
- Next Tuesday there will be an optional activity at the National Museum of Scotland that you can do on your own (any day/time) or in a small group. Sign-up to be matched to classmates to do this as a small group in the first hour of class time.
- Next Thursday there will be a chance for a hands-on look at the notebooks of Charles Lyell at the Centre for Research Collections on the top floor of the main library. Limited to 10 students at a time for 15-minute time slots, so please sign up if interested. You will leave class for those 15 minutes (plus however long it takes you to walk to the library and back). There will be an alternative (or additional!) online activity with the letters of Charles Darwin.
- Later on there will be a chance to visit the Edinburgh Anatomical Museum. This is a closed collection at the university used mainly by medical students and staff at the university, and requires special arrangements to view. Please sign up to visit during class time in week 6 or 7, note dates have been updated since this was first posted to avoid having to worry about strike issues.
A pdf! Unit 2: Abstractions
Spend a short amount of time thinking about these questions and practice putting your ideas into writing.
- This week, pay attention to the numbers around you. Where do they appear? What do they tell you? How do you use them in your life? What makes it possible for you to use them? Where did they come from? How did you learn to recognize them and use them? Make some lists of different places where you encounter numbers and the kinds of numbers you encounter there, and note some answers to these questions about them.
- Perform an easy calculation by hand (any easy calculation!). What makes it easy? What makes it a calculation? How do you know when you have performed it correctly? What skills or techniques did you use? Now perform a difficult calculation by machine (computer, calculator, smartphone, etc.). What makes it difficult? What makes it a calculation? How do you know if you have performed it correctly? What skills or techniques did you use? What kinds of calculations can machines do that hands cannot, and what can hands do that machines cannot?
At the end of this week, after you have had your first tutorial and have seen some more of the course, revisit the goals you wrote down in week 1 and make any updates and adjustments.
If you are enrolled for a numerical mark, identify what mark you want to get and look at the marking criteria to understand what that will require.
How to Use a Text
Choose a reading excerpt and do the How to Use a Text exercise. Bring questions about this to your tutorial (this week or next week).
Read what your classmates have shared and try to make at least one edit in the Florilegium. Use the example page to test things out if you are not feeling like adding to an existing substantive page or creating a new one. You will need to use the login instructions posted on Learn and discussed in week 1.
Be creative. Share readings from the Resource List you found exciting. Compare your perspectives based on your background and subject areas. Find ways to make each other's experience of the course better, together.
The three readings at the top of this week's list spotlight three major topics for our theme of Abstractions: the changing relationship between quantification and society in the ancient world (Robson), mathematical theories of nature as a result of specific cultures of learning (Warwick), and the relationship between creativity and material objects in the history of calculation (Jones).
Verran connects last week's readings on anthropological methods for understanding the cultural basis of logic and science. A set of readings explore mathematical abstractions and their social and political contexts in different periods of Chinese history (Elman, Hart, Bréard). Netz, Rampling, Oosterhoff, and Terrall examine different settings of learning that brought different values and approaches to creating and transforming abstractions in Europe and the Mediterranean. Olesko and Kaiser respectively examine the contexts and practices of theoretical physics in the 19th and 20th centuries.
Another group of readings considers the history of computing and information. Daston's lecture is a good way into the backstory of the machine-dominated history of the topic. Mullaney, Agar, Hicks, McNeill, Kline, Abbate, and Rankin explain computing's relationship to government, politics, communication, gender, labour, language, and other major conditions and considerations.
The final group of readings is about the history of calculus and some of its legacies in mathematics and beyond. Katz and Alexander look for pre-Newtonian ideas that made a difference; Iliffe's volume is a resource for exploring Newton's world, while Guicciardini, Shank, and Grabiner trace the major challenges of interpreting and reimagining the calculus after Newton. Grattan-Guinness and collaborators focus on the somewhat longer history of modern calculus from a mathematical perspective. Mazzotti, Rankin, and McNeill (together with Warwick Terrall noted above) develop gender as a specific dimension. Richards discusses the relationship between new mathematics, education, philosophy, and the world in the 19th century, and Steingart's book takes up related questions in the 20th century.
A. Abstractions are often based on the idea of removing people and their ideas from the material world, but they depend all the same on people and objects in specific historical contexts. Discuss one or more examples of the material conditions and tools used to produce abstractions and to give them meaning.
B. It is one thing to transfer a physical object from one person to another and quite another thing to transfer an idea or abstraction. Identify one or more examples of abstractions moving between people and contexts and discuss what circumstances supported this movement.
C. There are many examples in the lectures and readings this week of abstractions being associated with particular social and cultural values. Choose one such example and explain its relationship between abstractions and values, or compare and contrast two such examples.
D. Comparing at least two specific historical contexts, discuss how the meaning, tools, and uses of calculation can differ in the history of science.
For each of these questions, it will be helpful to consider universities, noble courts, salons, observatories, or other specific settings organised in various ways at various points in history for producing and moving abstractions.