Mar 2, 2017

Arithmetic vs Reality: The Sawdust Principle

I thought about calling this post "The Sum is Less than the Whole". I also thought about calling it "2/1 < 2". Changed my mind at the last second. This whole post is about how misusing simple arithmetic can really mess things up. I had this lesson drilled into me in junior high school wood shop class. We actually had a lecture about measuring and sawing and error. Didn't see anything like that in a math class until I was in grad school. That just isn't right.

Try this: Take two boards of the same length and cut one of them into two parts. Is the length of the two cut boards lined up end to end the same as the length of the uncut board? The answer is NO. The sum of the lengths of the cut pieces are less than the length of the uncut board. The lost length is on the floor as sawdust. Hence the name "The Sawdust Principle." Many processes are lossy. On the other hand, arithmetic gives precise answers. But, if you do the math with out factoring in the sawdust. Your precise answer will be precisely wrong.

Let's try another example: Let's say I need 5 boards exactly 1 foot long. (Sorry about not using metric units.) I set up my table saw to cut sections that are exactly that length. The process of squaring up a table saw and setting the distance just right is not as simple as it sounds so I will run a test cut or three to make sure I am cutting exactly the length I want. Using good old arithmetic I grab a 5 foot board and start cutting it up. After all 5/1=5. That is, I trust arithmetic and forget about the reality of sawdust. What happens?

After 4 cuts I have 4 boards that are the correct length and a piece of scrap that is just about a half inch too short. Why is it too short? The kerf (yes, that is a real word that means the width of a cut) of my current blade is right around an 1/8 of an inch. That means that after 4 cuts about a 1/2 inch of board has been turned into sawdust. You have to remember the sawdust.

Here is the thing, arithmetic only works when you use it correctly. We humans make the mistake of ignoring small losses and discrepancies because we just really do not see them. That mistake lets tiny bits of error build up until it becomes a real, sometimes dangerously large, mistake. Or, as I learned when studying numerical analysis: Error accumulates. Sawdust piles up on the floor.

Do you worry about the milk that sticks to the side of a measuring cup when you are making biscuits? Do you worry about the variation in the size of "large" eggs when you are scrambling them? No, and No. For very good reasons we are used to ignoring small errors in measurement. But, if you are making biscuits and scrambled eggs by the ton the small errors start to add up to real money.

The sawdust principle is a specific example of a general principle, the misapplication of knowledge. In the examples arithmetic is misapplied. There is no question the 5/1=5 which is why I picked a 5 foot board to cut up. The problem is that I forgot about the kerf. The kerf is so small we want to just ignore it. We should have asked what (1 + kerf) * 5 equals. We used perfectly valid arithmetic, the way we used it was wrong.

Misapplication of perfectly valid knowledge will mess you up every time. There is an old saying that covers this concept and a bit more:
  1. Data is not information.
  2. Information is not knowledge.
  3. Knowledge is not wisdom.
The examples I have given show what happens when we lack the wisdom to select how to properly apply knowledge.

Ignoring small absolute errors when measuring largish amounts usually doesn't cause any problem because the error is a tiny percentage error too. The habit of ignoring small absolute errors will really bite you when they are a large percentage error. There is a real difference between percentage error and absolute error. An error of 0.06 ML (milliliter, see I can use metric!) is nothing to worry about when measuring liters. When you are measuring fractions of a milliliter 0.06 ML is a large percentage error and significant. Percentage versus Absolute you have to recognize the difference.  Context makes the difference. People I deal with constantly make the mistake of thinking that a small absolute error is meaningless, even when the tiny value is a large percentage error.

Recently I ran into 2 pharmacists who do not understand this concept. I'm not picking on pharmacists, well not more than a little bit. I will say that I have found myself frustrated several times by people who just could not see the error they were making or just refused to believe the correct math when I showed it to them. I normally don't care if idiots want to stay idiots, but pharmacists can really hurt me. I have cutaneous t-cell lymphoma (CTCL), diabetes, ocular lattice degeneration, and a prostate that is no longer my friend. I really need my meds. I spend way to much time at the pharmacy. 

What happened is that I have a prescription for a controlled substance that is good for my mind and my prostate gland. If you have ever had a prostate infection you know how much I want this medication. Really... imagine one of your most favorite body parts doing its best job to emulating a rotting, swelling, porcupine. Oh, ouch? Hand me that catheter I need to pee.

I have to inject exactly 0.5 ML of my medication every five days. I get the medication in a 10 ML vial. Because it is a controlled substance pharmacists have very good reasons for making sure I don't have a chance to abuse it or get any extra that I could sell on the street. As soon as you have legal access to a controlled substance you are immediately assumed to be an addicted drug dealer. Now, that is often true of pharmacists... and some patients. Me? No. Pharmacists? Yes, too often. That is why they can go to jail for filling prescriptions.

So the problem is that the pharmacists believe that given my prescription a 10 ML vial gives me 20 doses and should cover me for 100 days. Except for the sawdust effect. If you just look at a syringe you see some empty space between the end of the plunger and the end of the needle. It is a very small space. No matter how big or how small the dose you load into the syringe that small gap space has to be filled too and the medication in that gap is wasted. That is, a syringe has a kerf!

The kerf on my table saw is about 1/8 inch. To the best of my ability to measure the kerf, the waste, from the syringes I use is 0.06 ML. That is a tiny volume. Easy to assume it can be safely ignored. But in this case that is 12% of the size of the dose. That means that for every dose I inject roughly 1/8th of a dose is wasted. Turns out I can can only get 17 doses from a 10 ML vial. So a vial only covers me for 85 days. Not good. I see problems coming.

Not to worry. Turns out I have to get a new prescription every time I get the medication. No refills allowed by law. So, no problem. I just get a new prescription. Pharmacists usually fill new prescriptions with no questions. Well, they do when you are an established customer, the doctor is local, the pharmacist is in a good mood, and he knows how a syringe really works

So, I have been filling my prescription at the same place for quite a few years. For lack of knowledge of sawdust and syringe operation the last time I tried to fill it the pharmacist refused to fill the prescription. As far as he was concerned I was getting a refill way too early. I tried to explain the situation to him. My doctor tried to explain the situation to him. I got CVS to call him and he refused... I talked to a "corporate pharmacist" at CVS who told me I had received at 100 day supply. No thought need apply to their opinion. No explanations allowed. Reality need not interfere with their decision. To make matters worse the fact that I complained was reason enough for CVS to tell me they do not want my business and to call my doctor and tell him the same thing. Wow. All because I tried to explain how a syringe works.

I guess I should mention that my doctor had a nurse call the pharmacist and give him the same explanation I did. He didn't believe her either. 

The story gets worse from there. My lawyer says that even though I have a good basis for a suit it would cost more to sue than I could recover.... So, it is not even worth the fun suing the dumb shits. Anyway, I filled the prescription at the Walgreens across the street. 

The best part of this is realizing how many people who are supposed to be highly educated "professionals" who are trusted to protect my health don't know how to use arithmetic. Amazing, disturbing, disgusting, horrifying... I want to puke just thinking about it. In fact, just writing about it makes my prostate ache.

It would not have been so frustrating if I could have gotten even one of these pharmacists to look at a syringe or actually test and measure the syringe loss. I have found that truly stupid people are usually smart enough to refuse any opportunity to learn.

On the other hand, only 3 (these 2 and 1 other) of all the many pharmacists I have had to deal with showed this lack of knowledge of syringe fundamentals. I have never met a nurse who didn't know about syringe lossage. I have run into a few doctors who didn't but a couple of minutes of explanation and they got it...

The only thing worse than getting older is not getting older. I feel much better now. Time to go take some pills, and one of my other 3 or more daily shots. I get lots of experience filling and using syringes.

BTW, I have not only calculated how many doses I get from a 10 ML vial I have counted them. I keep a daily log of my medications and several other vital stats. (I have found I do a much better job than my Doctors on tracking my long term health trends. You see, I want to get really really old and Doctors in the US get paid for services, like all other piece rate workers. They do not get paid for keeping me alive.) I get the number of doses I calculated. That is, theory is backed up by experiment. Theory must be substantiated by experiment... ALWAYS.


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