“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” – S. Gudder
When you hear the phrase “quantitative reasoning,” does it bring you back to days of high school Algebra and Calculus? Does it make you remember the anguish of learning formulas without a purpose explained to you? If so, it may be time to look rethink your presumptions about math and logic.
Students seeking a classical education study quantitative reasoning in order to better understand the world around them. Every day we are confronted with advertisements, news reports, and arguments that twist numbers for their own purposes. If you don’t understand what the manipulators are doing, you may end up making faulty decisions and holding incorrect ideas.
In part six, we discussed some of the ways people can make philosophically moral decisions. This post gives an overview of how to use quantitative reasoning to fairly evaluate claims and make sound arguments of your own.
In the field of quantitative reasoning the three most important subjects you can focus on are: logic, statistics, and economics.
Assignment #1: Master the Basics of Logic
“Logic is the anatomy of thought.” – John Locke
Logic has been called the science of reasoning. Learn the basics of logic and you’ll be prepared to evaluate the arguments of others and make sound arguments of your own.
Aristotle was one of the most important thinkers on the subject of logic. His collection of logic-related works, The Organon, is considered one of the classic texts in the field and is available online at no cost. It explains several key principles including syllogism, induction, deduction, and logical fallacies. You can read an overview of these principles and general Aristotelian logic in the Stanford Encyclopedia of Philosophy.
Because logic is a rather complicated subject, you may also want to check out a book or two about it. Most public libraries offer plenty of volumes on the topic. You may also want to look into the logic curriculum from Memoria Press . The advanced books are aimed at homeschooling high school students, but they’re in-depth enough for adults new to the subject.
Assignment #2: Learn How to Interpret Statistics
“Statistics … the most important science in the whole world: for upon it depends the practical application of every other science and of every art; the one science essential to all political and social administration, all education, all organisation based upon experience, for it only gives the results of our experience.”- Florence Nightingale
You’re likely to encounter some form of statistics every day. On the news, you’re presented with compelling figures and visual charts. In advertising, you’re told that a certain product helps with weight loss in 80% of customers or that 72% of prescription drug users “see results.” Where do these numbers come from and what do they really mean?
The purpose of statistics, as Nightingale so accurately explains above, is to help us learn from our experience. By recording and analyzing data, we can make scientifically-founded decisions about what works.
On the other hand, you’ve probably heard the old line that 99% of statistics are made up. While the media is held to some standards, statistics can be skewed and reported in a deceitful way. Learn the basics of statistics and you’ll be prepared use numbers to your advantage, identify statistics that are worth considering, and disregard unreliable figures.
Three websites offer a wealth of information on the topic:
- HyperStat Online – A casual 18-chapter online statistics handbook with links to many other resources.
- StatPrimer – A more formal statistics textbook that goes through intermediate level. Includes exercises.
- The Little Handbook of Statistical Practice – An in-depth overview of statistics from a Tufts University professor.
You may also want to check out the classic 1954 book How to Lie with Statistics by Darrell Huff. He explains:
“The secret language of statistics, so appealing in a fact-minded culture is employed to sensationalize, inflate, confuse, and oversimplify. Statistical methods and statistical terms are necessary in reporting the mass data of social and economic trends, business conditions, ‘opinion’ polls, and the census. But, without writers who use the words with honesty and understanding and readers who know what they mean, the result can only be semantic nonsense.”
The book will walk you through the essentials of how statistics are collected and where these numbers go wrong. Although the examples may be outdated, the theory remains true. An overview of similar statistic tricks can be found in this PDF article from Columbia.
Assignment #3: Learn How the World of Economics Works
In today’s tough times, no one would argue against the importance of a solid education in economics. In fact, if professionals had paid attention in econ, they may have seen the warning signs years earlier.
Even if you’re not interested in the finance industry, understanding the basics of economics can help you interpret what is happening in the nation and guide your financial decision-making.
Fortunately, there are many no-cost resources for the self-educated economics student:
- A downloadable textbook, Introduction to Economic Analysis, is available in PDF format from a California Institute of Technology professor.
- About.com Economics gives a solid overview of the basics and publishes a blog connecting current events to economic principles.
- MIT offers dozens of free, opencourseware classes on the subject of economics.
If you’re looking for a more light-hearted way to get started with the subject, you may want to check out the ever-so-popular book Freakonomics by Steven D. Levitt. He explains the work of economists through a variety of compelling examples. The related Freakonomics blog is also an interesting read.
In Conclusion
Many people grow up thinking that quantitative reasoning skills are irrelevant to their lives. But, the subjects of logic, statistics, and economics can be used to help anyone better understand the world.
Next week: Science
9 Comments on "Ivy League Education at Home Part 7: Quantitative Reasoning"
The carnegie-mellon free open learning initiative courses are some of the best I’ve seen for learning basic logic and statistics:
logic:
http://oli.web.cmu.edu/openlearning/forstudents/freecourses/logic
statistics:
http://oli.web.cmu.edu/openlearning/forstudents/freecourses/statistics
http://oli.web.cmu.edu/openlearning/forstudents/freecourses/csr
I wouldn’t recommend economics directly after learning logic and statistics.
Much of real economics depends on mathematics in the field known as “analysis”
which includes as it’s most practically important sub-part probability.
A good place to start with analysis (for the real numbers) is:
http://web01.shu.edu/projects/reals/reals.html
You might want to learn calculus first, in which case I recommend Evgeny Shchepin’s Uppsula Lecures on calculus:
http://www.pdmi.ras.ru/~olegviro/Shchepin/index.html
Armed with a decent understanding of analysis, you will be less likely
to be suckered by economic models (there are at least two contradictory economic
models for any given economic issue). They also use mathematics liberally and
often incorrectly to both justify and obfuscate their reasoning. If you know the
mathematics, it is easier not to be distracted away from their faulty or over-simplified
assumptions.
Another extremely important part of quantitative reasoning involves computation using
computers. Any/everyone can learn to program one, and about the basics of reasoning with computers to get them to do useful things. There are several approaches to introductory courses, but the main ones are exemplified by the excellent free courses at Harvard/Stanford (Imperative languages–more real world, less fun) and MIT/Berkeley(Functional languages–more interesting, more quickly):
Harvard & Stanford:
http://www.cs50.net/
http://see.stanford.edu/see/courses.aspx (introduction to computer science courses)
MIT & Berkeley:
http://mitpress.mit.edu/sicp/
http://groups.csail.mit.edu/mac/classes/6.001/abelson-sussman-lectures/
http://webcast.berkeley.edu/course_details.php?seriesid=1906978201
http://webcast.berkeley.edu/course_details.php?seriesid=1906978233
One little piece of mathematics is so important it deserves a special mention:
the exponential function.
No one has explained what this function means for our day-to-day lives better
than Alfred Bartlett (physics prof at U Colorado):
http://www.youtube.com/watch?v=F-QA2rkpBSY
You’ve pointed out some excellent resources. Thanks, anon!
http://www.mises.org/ is a great economics site. It has daily articles and a multimedia section with a plethora of free ebooks, lectures, videos, etc.
I strongly recommend The Cartoon Guide to Statistics.
Hi Jamie! I think you’re doing an excellent job! Have been reading your blog for a few days now. Umm…I have read the Ivy League article uptil Part 7 but can’t seem to find the other parts on the site. Could you please help me with that? Thanks =)
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