The Laws of Small Numbers
Big inputs make big mistakes; small inputs make small mistakes.”
That is the first thing my friend Kanji Ishikawa says to himself each
morning on arising. It is his mantra, the single most important thing
he knows about diabetes.
Kanji is the oldest surviving type 1 diabetic in Japan (he is, by the
way, younger than I, but afflicted with numerous long-term diabetic
complications because of many years of uncontrolled blood sugars). Many
biological and mechanical systems respond in a predictable way to small
inputs but in a chaotic and considerably less predictable way to large
inputs. Consider for a moment traffic. Put a small number of automobiles
on a given stretch of highway and traffic acts in a predictable fashion:
cars can maintain speed, enter and merge into open spaces, and exit
with a minimum of danger. There’s room for error. Double the number
of cars and the risks don’t just double, they increase geometrically.
Triple or quadruple the number of cars and the unpredictability of a
safe trip increases exponentially.
The name of the game for the diabetic in achieving blood sugar normalization
is predictability. It’s very difficult to use medications safely unless
you can predict the effect they’ll have. Nor can you normalize blood
sugar unless you can predict the effects of what you’re eating. If you
can’t accurately predict your blood sugar levels, then you can’t
accurately predict your needs for insulin or oral blood sugar–lowering
agents. If the kinds of foods you’re eating give you consistently unpredictable
blood sugar levels, then it will be impossible to normalize blood sugars.
One of the prime intents of this book is to give you the information
you need to learn how to predict your blood sugar levels and how to
ensure that your predictions will be accurate. Here the Laws of Small
Numbers are exceedingly important.
Predictability. How do you achieve it?
THE LAW OF CARBOHYDRATE ESTIMATION
The old American Diabetes Association (ADA) dietary recommendations
allowed 150 grams of carbohydrate per meal. This, as you may know by
now, is grossly excessive for people trying to control their blood sugars.
Here is one reason why.
Typically, 150 grams of carbohydrate would be a good-sized bowl of
cooked pasta. You may think that by reading the ingredients label on
the package you can precisely compute how much of the dry pasta you
must weigh out to dispense exactly 150 grams of carbohydrate. Now, if
you’re a nonobese type 1 diabetic who weighs 150 pounds (68 kilograms)
and makes no insulin, 1 gram of carbohydrate will raise your blood sugar
by about 5 mg/dl. By using methods that we’ll later describe, you can
calculate exactly how much insulin you must inject to keep your blood
sugar at the same point after the meal as it was before the meal. This
may sound elegant, but it will rarely work for a highcarbohydrate meal.
What neither the ADA nor the package tells you is that food producers
are permitted a margin of error of plus or minus 20 percent in their
labeling of ingredients. Furthermore, many packaged products—for example
vegetable soup—cannot even match this error range, in spite of federal
labeling requirements. So even if you perform the necessary calculations,
your blood sugar after the meal can be off by a carbohydrate error of
5 mg/dl multiplied by ± 30 grams (± 20 percent of 150
gm), or by a whopping ±150 mg/dl for just this one meal. If your
target blood sugar level is approximately 85 mg/ dl, you’ve now got
a blood glucose level anywhere between 235 mg/dl and 0 mg/dl. Either
situation is clearly unacceptable.
Let’s try another example. Say you’re a type 2 diabetic, obese, and
make some insulin of your own but also inject insulin. You’ve found
that 1 gram of carbohydrate only raises your blood sugar by 3 mg/dl.
Your blood sugar would be off by ±90 mg/dl. If your target blood
sugar value is, say, 90 mg/dl, you’re looking at a postmeal blood sugar
level of anywhere from 180 mg/dl to 0 mg/dl.
That’s one of the many problems with the ADA guidelines. Big inputs
and big uncertainty.
But if you eat an amount of carbohydrate that will affect your blood
sugar by one-tenth of that margin of error, then you’re going to have
a much simpler time of normalizing blood sugar levels. My diet plan,
which we will get into in Chapters 9–11, aims to keep these margins
in the realm of ±10–20 mg/dl. How do we accomplish this? Small
inputs. Eating only a tenth of a serving of pasta is not the answer.
Even small amounts of some carbohydrates can cause big swings in blood
sugar. And anyway, who would feel satisfied after such a small serving
of pasta? The key is to eat foods that will affect your blood sugar
in a very small way.
Small inputs, small mistakes. Sounds so simple and straightforward
that it may make you want to ask why no one has told you about it before.
Say that instead of eating pasta as the carbohydrate portion of your
meal, you eat salad. If you estimate 2 cups of salad to total 12 grams
of carbohydrate and are off not by 20 percent but by 30 percent, that’s
still an uncertainty of only 4 grams of carbohydrate—a maximum potential
20 mg/dl rise or fall in blood sugar. A big bowl of pasta for a couple
of cups of salad? Not much of a trade, you may say. Well, we don’t intend
that you starve. As you decrease the amount of fast-acting carbohydrate
you eat, you can often simultaneously increase the amount of protein
you eat. Protein can, as you may recall, also cause a blood sugar rise,
but this takes place much more slowly, to a much smaller degree, and
is more easily covered with medication.
In theory, you could weigh everything you eat right down to the last
gram and make your calculations based on information provided by the
manufacturer or derived from some of the books we use. This information,
as noted above, is only an estimate, with considerable margin for error.
You will have only a vague idea of what you’re actually consuming, and
of the effect it will have on blood sugar.
The idea here is to stick with low levels of slow-acting, nutritious
carbohydrates. In addition, stick with foods that will make you feel
satisfied without causing huge swings in blood sugar. Simple.
THE LAW OF INSULIN DOSE ABSORPTION
If you do not take insulin, you can skip this section.
Think again of traffic. You’re driving down the road and your car drifts
slightly toward the median. To bring it back into line, you make a slight
adjustment of the steering wheel. No problem. But yank the steering
wheel and it could carry you into another lane, or could send you careening
off the road.
When you inject insulin, not all of it reaches your bloodstream. Research
has shown that there’s a level of uncertainty as to just how much absorption
of insulin actually takes place. The more insulin you use, the greater
the level of uncertainty.
When you inject insulin, you’re putting beneath your skin a substance
that isn’t, according to your immune system’s way of seeing things,
supposed to be there. So a portion of it will be destroyed as a foreign
substance before it can reach the bloodstream. The amount that the body
can destroy depends on several factors. First is how big a dose you
inject. The bigger the dose, the more inflammation and irritation you
cause, and the more of a “red flag” you send up to your immune system.
Other factors include the depth, speed, and location of
Your injections will naturally vary from one time to the next. Even
the most fastidious person will unconsciously alter minor things in
the injection process from day to day. So the amount of insulin that
gets into your bloodstream is always going to have some variability.
The bigger the dose, the bigger the variation.
A number of years ago, researchers at the University of Minnesota demonstrated
that if you inject about 20 units of insulin into your arm, you’ll get
on average a 39 percent variation in the amount that makes it into the
bloodstream from one day to the next. They found that abdominal injections
had only a 29 percent average variation, and so recommended that we
use only abdominal injections. On paper that seems fine, but in practice
the effects on blood sugar are still intolerable. Say you do inject
20 units of insulin at one time. Each unit lowers the blood sugar of
a typical 150-pound adult by 40 mg/dl. A 29 percent variability will
create a 7-unit discrepancy in your 20-unit injection, which means a
280 mg/dl blood sugar uncertainty (40 mg/dl x 7 units). The result is
totally haphazard blood sugars and complete unpredictability, just by
virtue of the varying amounts of insulin absorbed. Research and my own
experience demonstrate that the smaller your dose of insulin, the less
variability you get. For type 1 diabetics who are not obese, we’d ideally
like to see doses anywhere from ¼ unit to 6 units or at the most
7. Typically, you might take 3–5 units in a shot. At these lower doses,
the uncertainty of absorption approaches zero, so that there is no need
to worry about whether you should inject in your arm or abdomen or elsewhere.
I have a very obese patient who requires 27 units of long-acting insulin
at bedtime. He’s so insulin-resistant that there’s no way to keep his
blood sugar under control without this massive dose. In order to ameliorate
the unpredictability of large doses, he splits his bedtime insulin into
four small shots given into four separate sites using the same disposable
syringe. As a rule, I recommend that a single insulin injection never
exceed 7 units.
THE LAW OF INSULIN TIMING
Again, it’s very difficult to use any medication safely unless you
can predict the effect it will have. With insulin, this is as true of
when you inject as it is of how much you take. If you’re a type 1 diabetic,
fastacting (regular) insulin can be injected 40–45 minutes prior to
a meal tailored to your diet plan to prevent the ensuing rise in blood
sugar. Regular, “fast-acting” insulin, despite its designation, doesn’t
act very fast, and cannot come close to approximating the phase I insulin
response of a nondiabetic. To a lesser degree this is also true of the
new, faster-acting lispro (Humalog) or aspart (Novolog) insulins. Still,
these are the fastest we have. Small doses of regular start to work
in about 45 minutes and do not finish for at least 5 hours; lispro starts
to work in about 20 minutes and also takes at least 5 hours to finish.
This is considerably slower than the speed at which fast-acting carbohydrate
raises blood sugar.