In my last little rant about 212:The Extra Degree, I described how the main thing that offended me about the whole movement was the ill-informed metaphor they use. I hate a bad metaphor based on bad reasoning. That got me thinking of the times I’ve been told that "logic betrays us" by which the person saying it usually means that "common sense" often provides superior information to logic. Let me be the first genius to tell you that a little bit of common sense should tell you that isn’t true. Saying logic betrays us is like saying hammers betray us. Hammers betray us when we try to use them to drive machine screws into sheet metal, but for sinking a nail into a piece of wood, a framing hammer is a damn reliable tool. Logic too is an utterly dependable tool: you can depend on it to bring you to solid conclusions if it is used well and based on good assumptions. You can, on the other hand, depend on it to bring you to the most absurd conclusions if used incorrectly or if you start from faulty assumptions. In this age of American unreason (see Susan Jacoby, The Age of American Unreason or Chris Mooney, The Republican War on Science) I guess it’s necessary to point that out.

Malcolm Gladwell made a big splash with Blink: The Power of Thinking Without Thinking, a book that argues that often our gut reactions can get us to the same result as considered reflection, but much quicker and with surprising reliability. I don’t refute that and it’s often true, though my favorite book that makes that point is Gavin de Becker’s The Gift of Fear (a great read). In any case, under some circumstances where we have a need to process lots of information quickly (fighting a structure fire, escaping a rapist), our instinct is often a better guide than reason because we may not have time to apply our reason before we get killed, but subconscious processing in our minds often finds a viable solution rapidly. Damn useful. But I see the idea extended in support of unreason and the belief that our gut reactions trump considered reflection (and I don’t blame Gladwell for that). If there’s time to consider and reflect and, more importantly, to test, that’s better. Always.

Logic by its very nature can be neither loyal nor disloyal, and therefore can never betray. Whenever you hear that we cannot trust reason, be prepared because you are about to be fed some bullshit, perhaps innocuous, perhaps dangerous. Reason cannot always provide a satisfactory answer to our questions, our needs and our hopes. It’s not always the solution, but it never betrays us. We cannot always trust to reason, but we can always trust reason.

I remember in particular two cases in particular from my late teens where I was told that logic is a poor guide and I was told this in contexts where you would least expect it: in the preface to a book of logic puzzles and in a philosophy class in college.

The fake syllogism.

I was in a philosophy class taught by a great and inspiring teacher, but not a man whose logical faculties were not highly developed. He was making the argument that the Nazis used logic to show that because Jews were bad, Nazis were good. The syllogism he gave was this one:

Proposition 1: All Jews are bad.
Proposition 2: We are not Jews.
Conclusion: Therefore we are good.

I don’t refute that this is part of appeal of anti-semitism for the Nazis and others, but it has nothing to do with logic. A fundamental aspect of a syllogism is that any terms can be replaced and it still makes sense as long as the propositions are equivalent. Again, logic is neither loyal or disloyal, merely a tool. So that syllogism is the same as this one:

Proposition 1: All elephants have eyes.
Proposition 2: We are not elephants.
Conclusion: Therefore we do not have eyes.

In any undergraduate class, 10% are paying close attention to what the teacher is saying and really understanding it, 10% are utterly confused and lost, and the other 80% are having sexual fantasies. That’s been proven. Miraculously, on the day in question, yours truly was in the 10% who were paying attention. So I pointed out the problem with the syllogism and was told by some very smart people, including the professor and someone who is now a top cardiologist, that I wasn’t getting it. "It’s a simple syllogism" I was told. No, it was a faulty syllogism, and potent as such, but it was unreason that allowed such lies to be perpetrated, not reason. Reason did not betray the Jews, unreason betrayed them.

Of steam and ice.

This one is less harmful and absolutely analogous to the 212: The Extra Degree folly.

James Fixx, who wrote The Complete Book Of Running, a major bestseller in 1970s that helped popularize running, also wrote the lesser-known Games for the Super Intelligent. I owned it, but my pride is not such that I bought it. It was a gift. A joke I think. In any case, that book or its sequel asserted in the preface that fun as the logic games within may be, sometimes logic betrays us and is a poor guide. If I remember right, he pointed out that a cocktail had about 350 calories (I’m making up the number — it may have been, but the principle and the error will be the same). Now, he pointed out that it takes 80 calories per gram to melt ice. So, he reasoned, with a bit of ice in your drink, you would be at break even. With less than five grams, less than a quarter ounce, you should be able to drink cocktails all day long and lose weight like crazy. The logic is ironclad, but alas, in practice, it isn’t so. Logic, thus fails us.

Except, of course, that dietary calories are actually measured in kilocalories. So in point of fact, if your drink has 350 calories, that gin and tonic is actually 350,000 calories. So to balance that out, you would need to eat three kilograms of ice (80 calories per gram to melt it and 37 calories per gram to heat it up to body temperature comes out to 117 calories per gram, divided into 350,000 calories yields 2991 grams). So the not-so-intelligent but nevertheless diligent fact-checkers realize that they’re going to need a hell of an ice maker to keep up with their weight loss program.

But this is not meant as a weight-loss guide. I just want to point out two things.

1. Logic does not betray us. We betray logic by feeding in poor assumptions and by failing to reason logically from otherwise good (or bad, in the case of the Nazis) assumptions.
2. It is the belief that logic can betray us that creates the opening for illogic. If you believe that reason can fail, that gut reactions trump logical arguments, that common sense is a better guide, you create the conditions where you don’t ask the right questions, where you let bad answers stand and, ultimately, you make bad decisions.

If your gut reaction tells you something seems wrong, then you need to question it and put it to the test of reason. But here’s the thing: if your gut reaction tells you that something is right, then you need to question it and put it to the test of reason. That’s what separates research from reverie, scholars from pundits, facts from opinion, staring from blinking and, while we’re at it, creationism from science.

Telecommuting from my mountain hideaway, I’m blessed to be insulated from most biz-speak. I depend on my visits with my brother to tell me about the latest trends in useless business mumbo jumbo. As a former engineer and business strategist for HP and current executive leadership coach for HP, IDX and GE (he only works for companies that go by acronyms apparently) and now on his own, he hears a lot of it. Also, his in-laws are mostly real-estate agents, a profession that generally has a gluttonous appetite for devouring motivational speakers and such. So he’s virtually a certified expert on biz-speak mumbo jumbo.

Anyway, I was telling him something and he made some sarcastic response along the lines of "Yeah, 212!" I had no idea what this was until he explained to me the mathematically and scientifically challenged metaphor behind 212: The Extra Degree.

Motivational speakers tend to be mathematically challenged. The proper sports lingo requires that one give 110% or even 200% (100% psychological and 100% physical). Of course, anyone who tells you to give 110% is, ipso facto, full of crap or a very poor mathematician. Anyway, these people, who espouse the so-called 212 principle preach instead of the gospel of giving just a little bit more. They love to say things like you’ll see in the YouTube video such as:

• From 2000 to 2006, the average difference in PGA victories was 1.71 strokes.
• In the 2004 Olympics, the 200m freestyle swim had margin of victory of .43 seconds (hey, in 2008, some swim events had a margin of victory of .01 seconds).

The unreasoning goes like this. If you have some water on the stove and you start adding heat, you take it from room cold water right out of the tap to 211 degrees and pretty much nothing happens. But if you go just a little farther, to 212 degrees, there is a state change, the water boils, real action takes place, nothing is the same. That little change makes all the difference. So in your sport/life/business/blog you have to keep pushing because sometimes you’re at 211 degrees without really knowing it and if you can go just a bit farther, success, riches, sex and unlimited ice cream await you.

There is the minor problem that when you take water from 211 degrees to 212 degrees, in fact nothing changes under standard, idealized conditions (i.e. the thermodynamic equivalent of the frictionless surface used in mechanics). This then leads us into the major problem of taking water from 212 degrees in liquid form, to 212 degrees in vapor form. Since the latent heat of vaporization is roughly 540 calories per gram, depending on conditions, it turns out that the state change effect, which is "just a little farther", is in fact a hell of a lot of work. So to keep it all in metric, if the water out of your tap is 20 degrees, it takes 80 calories per gram to heat it to the boiling point. But, to actually get it to boil takes almost seven times the energy that it took to get it there. So you think you’re almost there, you’ve almost reached that pinnacle of unlimited ice cream, but whatever it took you to get where you are, you now have to be prepared to plow 6.75 times as much energy into it to achieve the state change.

In my experience as a historian, this pretty much correlates with what it really takes to push through to boiling and become one of the best at what you do. I read old manuscripts which can be very difficult to decipher. To get to the point where you can read 90% of the words and get the vague sense takes a couple of months. To be able to read 99% takes perhaps a year or two and you get the meaning right in 99.9% of the cases. To get to the point where you can decipher 99.9% of the words and are considered a leading expert and people come to you for help and advice seems to take some natural apptitude, dogged determination and over a decade of focussed effort. For most people it simply isn’t worth it to push form 211 to 212 degrees because of the massive amount of energy it takes to achieve state change.

Adapted from the Wikipedia article on Asymptotes

Put another way, excellence is asymptotic in my experience. An asymptote is a curve that approaches a line, but will never touch it. In other words, the trip from beginner to not bad goes pretty fast, the trip from not bad to damn good takes quite a while and the trip from damn good to perfect can’t be attained. Now, you might at this point say that I’m missing the point, that the metaphor works in that there’s a point where you break through and stand out from the crowd and magic happens. I understand that, but when you take into account the actual physics of boiling water, the metaphor makes a lot more sense.

I remember a great magician I used to like to watch on the streets. Someone came up to him and said "You’re really good." He said, "No, I’m great. Do you know the difference?" The difference is that it only took him 80 calories to be good. But long years of trial and practice, the investment of another 540 calories made him great. From incompetence to competence takes 80 calories. From competence to excellence takes 540 calories.

Marshall Goldsmith sees it altogether differently. He argues that it’s not that the amount of effort required for the state change is massively different, but that more of the same will typically not get you there at all. He’s the author of the top-selling success guide What Got You Here Won’t Get You There: How Successful People Become Even More Successful. To stay with the 212 metaphor, Goldsmith thinks that it actually takes different skills to make a huge leap like the one from liquid to gas than the skills it took to get you from cold to hot.

Reason has failed the 212ers not because of flawed logic but because of bad information with the consequence that they don’t know when to give up. They don’t know that they’ve become competent but have neither the drive nor the aptitude to become excellent. I’m not, by the way, saying I do. I sing the praise of mediocrity in most endeavours (alas, that’s another topic, but I am not being facetious). I only strive for excellence in a couple of areas and, through long practice and much suffering, I have perhaps arrived in one or two areas. Mostly, though, I accept mediocrity for the simple reason that I understand how many calories are required for a state change and I know that I can only pour those calories into a few things and I had better be damn sure they really matter. 540 calories hurts! And if Marshall Goldsmith is right, more won’t help anyway. What is required is different.

Is it worth it to try to make the water boil?