Due to a sudden, unexpected passing in the family a few years ago and another more recently and my subsequent (mental) health issues stemming from that, I was unable to download this book in time to review it before it was archived as I did not visit this site for several years after the bereavements. This means I can't leave an accurate reflection of my feelings towards the book as I am unable to read it now and so I am leaving a message of explanation instead.

I am now back to reading and reviewing full time as once considerable time had passed I have found that books have been helping me significantly in terms of my mindset and mental health - this was after having no interest in anything for quite a number of years after the passings.

Anything requested and approved will be read and a decent quality review written and posted to Amazon (where I am a Hall of Famer & Top Reviewer), Goodreads (where I have several thousand friends and the same amount who follow my reviews) and Waterstones (or Barnes & Noble if the publisher is American based). Thank you for the opportunity and apologies for the inconvenience.

PARTIAL TRUTHS

“Although simple in concept the prosaic function has complex nuances,” James Zimring writes in the book Partial Truths: How Fractions Distort our Thinking. As it happens, this is just a very polite way of saying that fractions trip us up all the time. Anything expressed as a fraction (probabilities, anyone?) is uniquely situated to confuse even the best of us.

Why is that? In his book, Zimring discusses several conjectures by way of explanation:

- Humans are hard wired to think both in terms of whole numbers.

- When dealing with fractions, we are prone to make the error of either getting the numerator or denominator wrong (or both).

- We have built-in cognitive biases (such as confirmation bias) that make it harder for us to process fractions correctly.

No doubt, it’s an interesting perspective on the matter, and Zimring makes a very compelling if occasionally obtuse case of it in Partial Truths. The book's best parts are where Zimring gamely deconstructs the matter and frames the issue in thought-provoking ways. He asks, for instance: “if humans really are so cognitively flawed, if we observe incorrectly, and if we think illogically, then how can we explain how effective humans are at using reason to make tools, solve problems, develop advanced technologies, and basically take over the world?” Later on, he brings he crux of his book to its necessary conclusion by asking, in essence, how come natural selection hasn’t weeded out our weakness with fractions by now. Certainly, these and many other examples will tickle the mental muscles of anyone keen on giving their critical thinking skills a workout.

Yet because it is at the end of the day a book about math, as stated the book can be occasionally confusing, particularly in those chapters where Zimring “debunks” flaws in thinking. As an example, a chapter on the perceived impossibility of winning the lottery boiled down to the point that such an achievement is more likely than we think, yet over-elaborates. The more math-inclined among the readership may also be puzzled why certain concepts that would be useful to helping understand probabilities better—like p-values and the difference between Type I and II errors—are left until late.

Nevertheless, as mathematics (or mathematics-adjacent) treatises go Partial Truths is as reader-friendly and interesting as they come.

Partial Truths is not a mathematics book, and I confirm this as someone who is very afraid of math. Instead, it is a book about how math, specifically fractions, is wielded and and twisted to reflect the way we see the world. Lies? Distortion? Yes, these do exist, but most of the time, these are the outliers or extreme examples of the biases and slivers that have long governed our minds before someone even said things out loud. I never thought I would like math this way, and I appreciate James Zimring for creating an informative yet enjoyable read. I love how approachable the language is in this book, and it is very readable for even the staunchest hater of math in their school days (that would be me).

To be human is to be biased, and that is a necessary thing that often needs correcting. That's the essence of James Zimring's Partial Truths. From the trivial to the important, people look at things the wrong way, come to erroneous conclusions, and stand by their ignorance and insist on it for everyone else.

It doesn't sound like such a brilliant species when it's put that way, and Zimring spends a lot of time on Darwin, evolution and natural selection, which themselves are the objects of much misinformation and erroneous implementation. His own conclusion is that natural selection does not favor brilliance; it favors the successful in reproducing. And humans have exceeded all needs and expectations in that domain. Smarts is just a nice-to-have that our brains tend to inhibit.

The book starts off gently, a little too gently for my tastes, as Zimring patiently explains how everyone looks at fractions wrong. He cites the now age-old story of how A&W tried to outdo McDonalds' quarter pounder with a third pounder. It failed, because surveys said people thought 1/3 was smaller than 1/4, because three is smaller than four. Chalk up another win for the school system.

From there, it is on to automobile crashes versus airplane crashes, where everyone thinks it is far safer to drive than to fly. I hope we all know the truth is precisely the opposite (but I'm not betting my own money on it). It was just not what I expected to read.

Then there's an examination of lotteries, where customers focus on winning, looking at the morass through rose-colored glasses. The odds of winning the Powerball are 1 in 292 million. There are typically more than 150 million tickets sold for each drawing, and it can go months without a winner. The way Zimring looks at it, 300 million people a week don't win the lottery. Or, to put it even more dramatically, a customer buying a ticket for every Powerball drawing should expect to win once every 2,807,692 years. But customers never look at it that way. All they see is winners. And they expect to be one one day.

This however, is not the partial truth I (thought I) was here for. Lotteries and quarter pounders are not what I wanted to explore in this era of alternative facts, fake news and civilian slaughter dressed up as an "operation" of "denazification".

It was getting time to throw the book against the far wall and curse myself for agreeing to review it, but Zimring turns it all around. The stories changed from the hoary old to the new, relevant and relatable. And entertaining.

Zimring ventures into the psychic world, where mindreaders continually shock audiences when they spell out some bizarre scenario and an audience member stands and claims it, and demands to know how the psychic knew. Well, the psychic didn't know, but in a large crowd, the odds of someone relating to any situation are quite good. Even if they have to rationalize a lot to make it fit. (It's what readers do with horoscopes every day.)

Another psychic trick is to pretend to almost see the name of a relative of the victim's, beginning with a J, M, S or D. Most Anglo-Saxon names begin with these letters, and if the victim has the average 40 relatives, it's easy for the psychic to hit paydirt. The actual odds that the victim will not have a relative with such a name is one in 276, or .0036 of the time, Zimring says. Psychics play the odds, something everyone should learn.

And then it's the old: in any group of 30, at least two will have the same birthday trick. This is because most people are born in a five month range from fall to spring. The other seven months are hardly represented at all by comparison. Humans are subject to the seasons, including the mating season, the phases of the moon, and the seasons of the year. Spring fever and May weddings are real and standard phenomena for humans. The result is a compressed birthing season.

I loved the quote Zimring obtained from one psychic, (comedian) Mark Edward: "If psychics were real, they wouldn't need to ask even a single question. They would just know." Instead, it is an endless stream of questions and feedback to refine the result and nail the victim with facts s/he could not possibly know.

From psychics he turns to New Age fads, treatments, crystals and beliefs. The innate biases kick in, and otherwise intelligent people hook themselves into supporters and believers. Lying with fractions, which is the common thread throughout the book, is rampant. By making the denominator smaller (by ignoring selected studies, test and reports, or say, segments of the population), the resulting success story becomes inflated and mightily impressive, numerically. Such results must therefore have the force of truth behind them, one would think. Or so people assume. That's how New Age treatments establish themselves as truth.

This, Zimring says, is also the calling card of Big Tobacco, which funded all kinds of studies in order to prove tobacco didn't kill, but only reported the ones that had results it liked. It suppressed the rest, because that was the Big Tobacco deal: we will fund your study, but we retain exclusive rights to publish.

My own favorite example of this lying by omission is the more recent full page ad campaign against recognizing climate change, signed by over 33,000 scientists, an impressive showing. Who were all these scientists who had suddenly spoken up after decades of silence? It turns out they were mostly computer science grads. Out of millions, the sponsors found 33,000 to support their view, never mind that it wasn't their field. But it was their title, and that's all they needed.

My favorite chapter deals with God The Designer. Any time something is amazing, or fits perfectly, or threads a needle through complexity, people like to claim there was an eternal intelligent designer who did that, and that there is no other possible explanation. As Zimring puts it:

"Those who marvel at the fine-tuning of life might as well sit and marvel at how precisely the concrete in a pool fits around the shape of the water in it, and how amazingly perfectly the water fits the pool, even with twists and turns and small cracks. What are the odds of this happening, and not just for one pool , but for every pool! No, given how precisely pools fit the shape of the water and the water fits the pool, clearly an advanced intelligence with astounding engineering and precision designed each body of water and each pool to fit each other perfectly, molecule by molecule and atom by atom. Anything else is be so improbable as to be absurd."

But what it boils down to is the lottery fallacy again - looking at the situation's figures backwards. By examining the size of the universe and how it is populated, Zimring shows how it is all but impossible for an intelligent designer to exist or work its magic at the smallest level of every planet. Just because "we" don't have an answer, an understanding of how things work, does not mean some non-human super being is solely responsible: "Evolution is essentially a self-adjusting fraction that guarantees that life is fine-tuned to itself and its environment."

And Zimring is far from alone in this view. He cites Roger Penrose, a world-renowned physicist, who calculated that the original phase-space volume of the universe would be 1 to the power 10 and then to the power of 123. As Penrose explained: "This now tells us how precise the Creator's aim must have been...One could not possibly even write the number down in full...It would be a 1 followed by 10 to the 123rd power of successive 0s! Even if we were to write a 0 on each separate proton and on each separate neutron in the entire universe - and we could throw in all the other particles as well for good measure - we should still fall far short of writing down the figure needed."

These are the kinds of odds you find against there being an intelligent designer managing the birth of the universe. He calls the argument for an intelligent designer "inference to the best explanation." It is a common tactic, and it obviously works, but it is one that is never testable, let alone provable "unless the number of possible explanations is limited." And when it comes to the universe, there are no such limits, he says.

Similarly, the odds of this being one of several universes, that is, a single universe in the multiverse, suffers the same fate: "While interesting, the multiverse hypothesis remains a weak explanation of the fine-tuned universe." Or, as Zimring most elegantly puts it: "The rules of the world are working exactly as we understand them, but we are mistaking the highly likely for the virtually impossible." In everything from lotteries to intelligent designers, we get the fractions wrong.

Where does an author go after dismissing a Creator and the multiverse? For me the book should have ended there, on a high and bold note, encompassing religion, the whole universe and beyond. But Zimring keeps plowing onward, or more accurately, backward. In a terribly anticlimactic finish, he returns to psychological studies and the manipulation of fractions. He discusses how debiasing may or may not improve things, and how some human subjects walk back their extreme positions when asked for details on how they got there.

Not nearly as interesting as dissing God mathematically.

The human mind operates all kinds of traps and detours that psychologists love to catalog and test. The mind applies biases to everything we see and evaluate. These biases have fed untold thousands of undergrads their beer money, as grad students continue to tease out exactly how and when these biases appear, in endless studies. The biases go by very common and descriptive names: availability bias, confirmation bias, hindsight bias, knew-it-all-along bias, cherry-picking bias, and conformity bias, for example, all of which are examined in the book. They are why two people reading the same text can disagree as to what it says and means. They are why it takes 12 jurors to make a decision, after possibly weeks of argument, diplomatically called deliberation. They are the spice of life, Zimring says. And we probably wouldn't get anywhere without them.

So while Zimring scores with dramatic and proper applications of math, the book is a lot of up and down instead of a powerful build, in my unbiased opinion.

David Wineberg

Solid Exposition Of Its Premise. This book is pretty well exactly what its title says it is: an examination of cognitive biases, with fractions as the common access point to all of them. Thought of in this manner, the book is solid, though on its overall points - many political, including repeated attacks on the 45th President of the United States - your mileage will vary considerably. Indeed, on many of the issues Zimring examines, his overall consideration of the issue at hand is actually limited by his devotion to fraction-based thinking, at least within the confines of this text. Ultimately, this book is more a rare take on cognitive biases than anything truly mathematical, and the math here really is simplified such that pretty well anyone capable of reading the text itself can follow the math easily enough. The bibliography clocks in at around 20% of the overall text, which is close enough to the average of similar texts in my experience to be acceptable. Recommended.

NOTE: NEEDS MORE MATH. I know! It's such a weird note to have. Who wants *more* math in a book, right?!

Well, sometimes, I think most of us do.

Despite its subtitle ("How Fractions Distort Our Thinking") "Partial Truths" contains no math at all, except the little that is necessary to explain what a fraction is.

The core of the book, however, is a discussion of biases, interpreted as misperceived fractions. For example, if you read about a topic, but reject a number of texts simply because they don't align with your point of view, you might come off thinking that a greater proportion of evidence supports your preferred point of view than not.

This is an interesting point of view, but I don't feel it's sufficient in and of itself to make "Partial Truths" a great book. In fact, it sometimes feels like the author wanted to discuss current events (the war in Irak) and phenomena (New Age), and used the opportunity of his ideas to do so. This is alright (we're all allowed to have pet peeves), but these points were expanded to the detriment of the book's supposed topic.

Why I think this needs more math: in defense of dry material

I know many people hated math in school. It's dry. It's abstract. It's a bit like pulling teeth, especially if you do it day after day, in exercises that seem to make no sense and never have anything to do with the real world.

But what math does is speak about underlying rules; while we don't always find knowing those rules useful, they can occasionally come in handy.

If you only sell apples, it's useful to know that if you have 2 apples and get 3 more apples, you're going to have 5 apples. But if you diversify and start selling more types of fruit, 2 + 3 = 5 can be an abstract idea that's very nice to know, because you can apply it to all your fruit.

This holds true for all math. Most of us don't usually need complicated formulas, but every once in a while, they can help us so we don't need to eyeball things and discover if we were right or wrong by trial and error.

A book such as this one has many advantages over a classroom setting. It doesn't need to address all of math; it doesn't need to prepare readers for exams; and it can afford to take things slowly and leisurely in a way teachers can't because they're always pressed for time and results. Thus, to keep things artificially math-free when discussing math feels like the wrong choice.

For example, "Partial Truths" mentions probabilities a few times, but they're never discussed, except to be described as "fractions". I find this odd; probabilities are their own can of worms. They're not immediately intuitive. In fact, if you don't know more about them, they can look like magic.

The odds of getting heads when flipping a coin is 1/2. What are the odds of getting heads at least one time if I flip the coin twice? 3/4. What about the odds of getting heads at least once if I flip the coin thrice? 7/8.

Let's make it more complicated! If you have a trait that appears in 1/300 people, and you have 300 people in the room, what are the odds that at least one person has that trait? A friend who actually remembers math formulas calculated the probability for me: it's about 63%. Slightly less than 2 out of 3 chances. But come on, 1 chance in 300 people, and you have 300 people, what's going on? Why is this so surprisingly low? How is it calculated?

Zimring doesn't discuss this and, because this is a review, neither will I (regrettably). But it's pretty cool, and if you aren't required by exams to actually fiddle with the numbers, the underlying explanation is interesting enough to be worth looking up.

Let's talk about the book as a whole

There's little here you won't find in other books; there's a high probability (heh) that you'll have heard of cherry picking, confirmation bias and the rest before. Zimring has a slightly new perspective on them (seeing them as fractions), and applies it in various domains. Some details were novel to me, and some observations were interesting, but all in all I feel like the topic has unrealized potential.

I enjoyed this book. The book is really about biases but uses fractions as a discussion point. There is not a lot of math in the book; what little there is, is explained very well. The book has a conversational tone and the author shares some personal perspectives, which I usually appreciate. The writing is quite compelling, with some humor and clever wording. The endnotes are also worth reading, however, the endnotes that contain clarifications on the text are mixed in with the endnotes that only contain references and citations. I find this annoying in many books. I much prefer that clarifications or explanations appear as footnotes on the same page as the content. I quickly stopped checking the endnotes but scanned through them at the end and many were worthwhile reading. While the pacing of the book was quite good overall, I found that the book slowed down when the discussion turned to cognitive psychology. Nonetheless, the book was so good overall that it still merits 5 stars. Thank you to Netgalley and Columbia University Press for the advance reader copy.