Customer Reviews

Mathsemantics: Making Numbers Talk Sense

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The author is "an expert" - someone who knows something and can explain it to and/or use it for those who can't - or just don't - on their own.

I am a high school math teacher and community college and high school computer teacher. MacNeal THRILLED me with his insight into something that may be part of the problem with education the way we do it. Look for his connection of Piaget's work on the development of children's and adults' abilities through necessary stages with the Chinese language and with the teaching of math.

I have had more successes with some of my students because of MacNeal and his book.

I enjoyed this book. It's humorous, and addresses how humans learn, not how teachers would like them to learn. It's compared to Paulos' INNUMERACY, but it doesn't have Paulos' arrogance and condescension. I enjoyed that, too, so consider this a good companion book.

This is one of my favorite books of its kind. It deserves a place on the shelf next to Paulos's _Innumeracy_. _Mathsemantics_ is a highly readable, insightful, conversational, anecdotal, fascinating discussion of the ways people apply (or fail to apply, or misapply) mathematical thinking to real world situations, and why they have trouble mixing math and language.

I teach British literature and love Scott, Austen, Wodehouse, and Hardy. I thouroughly enjoy the murders mysteries of Rex Stout and Dorothy Sayers. So why am I reviewing a book about math? Because it is one of the finest books I have ever read.

This book bridges the gap between the right and left brains. While its subject matter includes some advanced concepts, they are expressed so articulately that they are accessible to virtually everyone.

This is not a book for educators or students alone. Everyone should read it.

As an educator with a primary school child, I've read many books on numeracy. This is one of the very best. It's lively, engaging, grounded in theory and practice and clearly reflects a lifetime of reflection. MacNeal weaves in many examples from real life, together with instructive and sometimes humorous and touching anecdotes about his own childhood.

As a fan of general semantics, I enjoyed this. What is 2 apples plus 3 oranges? The author uses simple questions like this to illustrate use and misuse of numbers. Most maths teaching ignores the meaning of numbers, but this short book shows lucidly how an understanding of the process of abstraction can help us avoid using numbers irrationally. Recommended, though I suggest reading in conjunction with Hayakawa's Language in Thought and Reality (the most readable book on general semantics).

This book is a treat for anyone interested in math, words, analysis, and problem solving. Analysis is an art, and the author shows how numbers and words can present or hide the problem.

The author builds the book around a set of problems he collected or invented over 20 years to help him hire people to work in his business. The problems turn out to be arenas where common sense does battle with dumb rules ("you can't add apples and oranges") and the art of definition (a passenger, a trip, a ticket, a traveler, and an airplane seat are different entities).

This is also a funny book! The problems are interesting and concrete. The book is structured, too, so the reader easily gets a chance to hack away at the problem, and also see how other folks have done solving the problem over the last 20 years. (The explantions some folks give to explain their answers are sometimes screamingly funny, but always interesting.)

This book is a fun read. It would also make a great companion text in a high school or college math or analysis course.

A text best suited (and by evidence of what was written) originally written for auditory learning-style folks who have trouble with mathematics. However, it is benificial as a groundwork for exploring the ramifications of the differences between the oldest forms of representation: numbers and words. By no means a comprehensive text on the subject, it is a good beginning place for further explorations.

Edward MacNeal (1994) an airline business consultant, introduces Mathsemantics (Science of Mathematical semantics) as an extensional (factual evaluating) language for proper evaluating. Showing via job application tests taht maths incompetence often results from semantic mis-understandings; like any language, requiring familiarity.
What Jean Piaget (1926) found in children. Alfred Korzybski (1933) showed persisted via an education in Aristotle's (c. 350 B.C.) 'intensional' ('subject-predicate', false-to-facts 'universalizing') linguistic structure ('logic'), reversing the empirical evaluating order (event-perceiving-insight-formulating), consequently allowing 'identifying' 'meanings' (words) with perceivings, etc.
Whilst our mathematical education mostly fails to solve these semantic problems, involved in applying numbers to events. For example, we may expect that calculations have only one answer, despite measuring involves approximating (rounding-up, etc) involving estimates (probabilities). Further Greeks like Parmenides (c. 480 B.C.) did not accept zero as a number, 'reasoning': "non-being could not be, because it was a logical impossibility". Thus unsurprisingly, many tend to round-up to 1 rather than 0!
Infact Kurt Godel (1940) found no mathematical system can be complete-nor-consistent. As Korzybski (1933, 1936) asserted: "map is not the territory...is not all the territory...is self-reflexive (speak of map of map, etc)".
Korzybski (1933) asserted that by extensionalizing to events, we find context. However MacNeal continues that units (unity) entail convenient 'categories' representing events despite that a name tells us nothing-about-nor-is-the-thing. MacNeal argues that we cannot do without 'addition', suggesting that we can 'add' different changing things under combined units: "2 apples + 5 oranges = 7 fruit".
Yet MacNeal the General Semanticist (Korzybski (1933), Science of values, hence evaluating), avoids the fact that events, abstracting processes, etc., are not 'additive', involving Korzybski's (1933) non-elementalistic, functional (non-linear-asymmetry-non-additive), more-or-less emergent wholes. As Korzybski (1933) argued water, having new emergent characteristics, is not the 'sum' of an oxygen atom 'plus' two hydrogen atoms.
Therefore,

C = A + B

becomes,

C = f (A, B)

Let alone that 'classifying' entails 'identifying'.

MacNeal makes a strong case that a proper understanding of mathematics requires thinking skills that our schools have not yet even identified. The author fills this book with examples of basic mistakes that "educated" people often make when using or even talking about numbers.

MacNeal argues convincingly that using mathematics properly goes far beyond being able to manipulate numbers. Mathematics is a language that helps us understand the real world. Divorcing this language from spoken languages, such as English, fails to teach students how to use and think about issues that relate to mathematics. (And that certainly includes a multitude of topics!)

"Mathsemantics" also provides a practical method of learning to make estimates. The author provides many examples of how to use information that we do have to make reasonable estimates regarding information that is unavaialable to us.

If I were a high school or college instructor...of almost any subject...I would (easily) find a way to make "Mathsemantics" required, relevant reading. This book provides so much more value than most of the "best-selling" books that you will read and hear about.