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Without evidence of benefit, an intervention should not be presumed to be beneficial or safe.

- Rogue Medic

What Math Do We Need To Know?

Fri, 10 Jul 2009 00:28:52 -0400 by

An interesting and very short – less than 3 minutes – presentation from a professor of mathematics about what we should be teaching in math class.

I can’t leave you hanging like that without telling you a little bit about what 2 standard deviations means. But first you should read what he said in, If Arthur Benjamin got an extra minute on stage ….

Now to what 2 standard deviations means. This is easiest if you look at a bell curve. Bell curves only represent normal distribution. You’ve seen this curve before.

Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for 68.27 % of the set; while two standard deviations from the mean (medium and dark blue) account for 95.45%; three standard deviations (light, medium, and dark blue) account for 99.73%; and four standard deviations account for 99.994%. The two points of the curve which are one standard deviation from the mean are also the inflection points.[1]

Here is another way of looking at the same information, just rotated to the side


The red circles with tails are the Greek letter Sigma, which is the symbol for standard deviation. The data points (dots) on the left are far too few to produce the smooth curve that appears on the right (which is just the bell curve from above with different colors and flipped on its side, so that the standard deviation bars approximately match). No the numbers on the left are not grades of a class from paramedic school before grading on a curve.

Why is it important to understand the concept of 2 standard deviations?

Anything outside of 2 standard deviations is unlikely. Anything outside of 3 standard deviations is rare.

In the video, he mentions the financial mess. One of the big problems was that bankers were making sub-prime loans that initially were just a tiny part of their business. As long as they remained a tiny part of the business, that was not a problem. Grouped in with an overwhelming number of safer loans, they would not present a huge problem, even if they all failed at once.

Mortgage writers were apparently ignoring the increasing proportion of loans that were sub-prime. They went from between 2 and 3 standard deviations to around 1 standard deviation. now it did not even take a coordinated failure of these loans to cause a huge problem, but the mortgage writers kept acting as if things had not changed. They were making their consistent commission. They were selling the risk to people with even less understanding of statistics. On the other hand, they were selling a risky asset, rather than keeping it as an investment. So, maybe they were not so unaware.

When the problem loans were only a few percent of business, the risk was small. You can see from the bell curve, that only a little of the shaded area is there. As the percent of problem loans increased, the chance of many failing at the same time increased. It was not a question of if, but when.

Things changed. Not a little bit, but a lot. The change was ignored.

We do the same thing in EMS in many ways.

We claim that some risk is small, insignificant.

We do this for many things.

We ignore the accumulation of rare, or just unlikely, risks.

We act surprised when the inevitable happens.

We blame someone else.

Footnotes:

^ 1 Standard Deviation
All of the graphs are from Wikipedia.
Article

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Filed Under: Critical Judgment, Heresy, Math Tagged With: , ,

Confidence Intervals I

Tue, 24 Feb 2009 18:40:34 -0500 by
In my last post, Evidence Based Medicine Discussion – Hijacked from Ambulance Driver, I wrote about the 95% Confidence Interval (CI). In the comments, Vince wrote:

I’m a little late to the party, since my blog-perusing time has been stolen from me of late. I will not begin heroics on our equine friend with lividity, I just have one comment to your statement,

That is the purpose of the 95% Confidence Interval. Unless it is calculated incorrectly, due to a misunderstanding of what is being measured, or a misunderstanding of what variables are relevant, the research should only have a one-in-twenty chance of misrepresenting the conclusion.

I assume you were just typing at 100 miles/hr but it is a point worth clearing up.

Well, typing faster than I think, perhaps 100 millimeters per hour (one of the reasons I don’t post more often), but I did ponder over the use of the word conclusion. I could not come up with a more appropriate word at the time and I never returned to it, although I should have.

Confidence Intervals are not any type of guarantee of conclusions at all! As I am sure you are aware, CI represents the probability that the data are somehow correlated to a phenomena and not just the result of “statistical randomness”, inasmuch as the selected group will represent (statistically) the larger population.

You are correct. I was trying to qualify that by excluding the things that would lead to incorrectly drawn conclusions. I was giving a bit too much importance to the conclusion. I was trying to make a point about one thing that is not well understood. I was trying to simplify things. I did a poor job.

BY NO MEANS does a CI of 95% (or 99% for that matter) guarantee anything about VALID CONCLUSIONS.*

Unfortunately, many studies with >95% CI’s have 100% chance of misrepresenting conclusions!

This is true. This is one area of research that provides me with so much to write about. When researchers are measuring the wrong thing, or trying to measure the right thing, but not effectively controlling for variables, the results probably will have no more than a random chance of producing information about anything, except How not to do research.

Several factors play a role in the ability to made a valid conclusion from any collection of data. Not least of these are the actual study design, inclusion(exclusion) criteria, experimental methodology,..etc etc ….but just to clarify- Confidence Interval is merely a testament to the chances that the data are related to an observed pattern and not just random- and speaks to how the measured group potentially scales up.

Yes. I tried to work that into my description of conclusions, but I only ended up complicating things. The researchers may claim that the data gives a 95% CI, but they may not be measuring the right things, so, their claim of a 95% CI may be the weakest point of a study. If the researchers do not adequately control for all relevant variables, it may not matter how much data they have, they are not any more likely to be measuring relevant data than would some conspiracy theorist.

To quote one of my favorite curmudgeons,

“There are Lies, Damn Lies, and Statistics.”

Was that Jenny Killer McCarthy?

The important thing to point out about the 95% CI is that it does mean that, if the research is properly designed, there is less than a 5% chance that the data are due to chance.

This does not mean that 5% of research will come to the opposite conclusion. This does not even mean that 5% of the research will have data that differs from what accurately represents the observable data. It means that, if the variables are understood, the research is properly designed, the study is carried out without significant deviations from the study protocol, . . . , then the data have less than a 5% chance of coming out as they do purely by chance.

The differences in the size of studies mean that a study can have greater than 95% CI, but be several times smaller than another greater than 95% CI. The idea that 1 in 20 studies will come to the opposite conclusion, is a misunderstanding of the meaning of the Confidence Interval.

* [As an aside, if it is the last thing I am going to do I am getting a “Correlation does not equal Causation” tattoo]

You are old enough to make these decisions on your own. I would recommend using this at the appropriate time. Maybe as a bet. And there are several science tattoo blogs that might be interested in having you show a bit of skin. Don’t be offended if they are only interested in the skin with the tattoo.

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Filed Under: Critical Judgment, Heresy, Math, Research, Science Tagged With: , ,

Up to a Maximum of X Times vs. Titration

Fri, 11 Jul 2008 00:30:00 -0400 by
Over at Ridin’ the Bus, Gertrude was writing Who’s teaching the teachers? Well, my answer is that the teaching jobs are often as political as the desirable EMS jobs. Squad Y is a bunch of people friendly with So-and-So. Squad B is a bunch of people friendly with Whojamacallit. Whether these are 911 jobs, critical care jobs, flight medic/nurse jobs, or anything else does not matter. There is more of an old boy network involved than a critical examination of the qualifications of a job candidate. Teaching is no different.

The current teachers are not necessarily those who excelled in medic school, or EMT school, when they attended. They might not have learned things all that well, when they were in school. The instructor may have modified his understanding since then, but that does not mean that it was for any medical reason. A lot of what is taught is pure speculation.

I described this in several posts A, B, C, D, and E. I reference it in several others. We are poorly educated. The educators often do not know what they are doing well enough to be teaching it.

An excellent example of this is cardioversion. I have never seen anyone else do a good job of teaching cardioversion. That does not mean that it does not happen, but it is not encouraging that I do not see it taught well. ACLS (Advanced Cardiac Life Support) encourages us to just review the material, since the students are already supposed to be familiar with everything. How many nurses going to their first ACLS class have any experience with cardioversion? This is not something that you learn to do well from a book or a blog. You learn it by using the paddles, turning on the synchronizer, and delivering shocks to a mannequin or to a patient. Too many people learn, during their first cardioversion, that they never really understood cardioversion.

Anyway, the topic of Gertrude’s post was the rules that are taught to us. Her example is when a student asked her for the maximum number of times a patient can be suctioned.

Think about this.

Why do we suction patients?

We suction them because there is something in the airway that may interfere with ventilation. It may be a potential obstruction. It may be a partial obstruction. It may be a complete obstruction.

As long as we do what we can to maintain oxygenation, there is no maximum. For the complete obstruction, there is no reason to pause and ventilate in between suction attempts, or to limit the length of suctioning, unless there is the possibility that you have cleared, or partially cleared, the obstruction.

One of the other instructors had given them a number. What is a good number for this? 3? 5? 23? The patients weight in kilograms, divided by their SpO2 percent, multiplied by the number of synapses actually transmitting information in that instructor’s brain?

How about until the portable battery runs out? But remember there are other ways of creating suction – a large syringe, a bulb syringe from the OB kit, scooping things out of the airway, gravity, a vacuum cleaner in the residence. Who really cares how you do it, if you are able to provide the airway the patient needs?

Why do we feel the need to have a number? A limit on what we can do?

People like externally imposed limits. The idea of being responsible for making intelligent decisions is something that many people flee from.

“Responsibility? Just tell me what I have to do to avoid getting in trouble.”

“As long as I follow the protocol, I won’t get in trouble.”

Of course, if the protocol does not apply to your patient, or if you follow the wrong protocol (because you ignored assessment in favor of memorization of protocols) you might kill your patient in your devotion to keeping out of trouble.

Maximum of 3 NTG (NiTroGlycerin, overseas GTN – GlycerylTriNitrate).

Why?

Most likely because the AHA wants you to switch the patient to IV NTG as soon as possible. Not exactly common in the prehospital setting, but a very good idea. NTG is a drug that needs to be titrated. A maximum number prevents titration, so people teaching these maximums should not be teaching. Titration is adjusting the dose based on the response of the patient. Almost all EMS drugs need to be titrated.

Does a response mean that you stop? No, but you take that information into consideration in your continuing doses. Sometimes it will mean to stop. NTG + Syncope is more than a subtle hint to stop NTG. After blood pressure returns, then you may resume cautiously (perhaps after running a liter into the patient) or you may decide not to give any more, but initially your response should be to stop.

Atropine is not a titration drug. Fast push, a minimum adult dose of 0.5 mg and a maximum dose of 0.03 mg/kg if stable, 0.04 mg/kg if unstable. With atropine, you may get the opposite result of what you want, if you give it slowly or if you do not give enough. Another non-titration drug is adenosine. Also fast push. Maximum of 3 doses – 6 mg, 12 mg, and another dose of 12 mg. Glucagon is another drug not generally titrated (many places do not even carry more than one dose).

Some titration drugs:

Oxygen – titrate to adequate oxygenation.

Dextrose 50% in Water – titrate to adequate saccharinity.

Dopamine and dobutamine are given as drips, the dosage formula is for calculating a starting dose and for understanding the maximum dose rate, which does not mean that you stop, only that you stop increasing the dose rate.

NTG – I have given over 50 sprays (over 20 mg) to a single CHF patient on one call and the blood pressure never dropped below 200 mm/hg systolic. Maximum of 3? Not a chance.

Albuterol (Salbutamol overseas)- if the patient is not able to breathe adequately, we continue giving albuterol, but we add other beta 2 agonists, maybe some magnesium and methylprednisolone. There are some who will even tell you that you may not give albuterol to a tachycardic or hypertensive patient, since it is not completely selective for beta 2 and might make things worse. Yes, it will stimulate the heart to work harder, but if it opens the airways, the pressure and heart rate will come down in spite of that stimulus. If it doesn’t open the airways, the side effects are not the patient’s primary concern, not even a secondary concern.

Fentanyl/dilaudid/morphine – no minimum dose and no maximum dose. Only the response to treatment matters. No maximum of 6 mg, or 10 mg, or 20 mg, or even 100 mg of morphine (about 60 mcg/100 mcg/200 mcg/1 mg for fentanyl; 0.75 mg/1.25 mg/2.5 mg/12.5 mg for dilaudid). Anyone who tells you otherwise is a liar and/or incompetent.

Midazolam/lorazepam/diazepam – no minimum dose and no maximum dose. Only the response to treatment matters. No maximum of 5 mg, or 10 mg, or 20 mg, or even 100 mg of midazolam . . . .

Diltiazem is a slow push medication that has standard doses (0.25 mg/kg for the initial dose and 0.35 mg/kg for a repeat). If you are giving it slowly it isn’t just to minimize the side effects, but also to observe for side effects that would discourage you from continuing with the dose. Diltiazem is often given to little old people, who may not give much warning before dropping their blood pressure significantly. I like to keep them sitting up and talking to me while I slowly (over 5 minutes, not the recommended 2 minutes) push the diltiazem. If they are sitting up, the part of the body most likely to show signs of decreased perfusion is the brain – sooner than a repeat blood pressure, sooner than skin sign changes. If the behavior changes in any way, I stop and I do not give any more until after I have satisfied myself that this is not a sign of an adverse reaction. I can always give more later, but most likely it is an adverse reaction.

Naloxone – no minimum dose and no maximum dose. I like to give 20 mcg to 40 mcg at a time. Response is what tells me when to stop.

These are just some of the drugs that are only appropriately given when titrated.

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By Rogue Medic
Filed Under: ACLS, Adenosine, Airway Management, Assessment, Atropine, Cardioversion, Critical Judgment, Fentanyl, GTN, Heresy, Math, Midazolam, Morphine, Naloxone, NTG

The Happy Hospitalist: Happy’s Gone Lost His Mind

Sun, 15 Jun 2008 17:31:00 -0400 by

The Happy Hospitalist: Happy’s Gone Lost His Mind: “What do we have. Currently, we have a health care system that costs over 2 trillion dollars a year to operate. It is 15% of our economy. Half of that is government gravy train money. Some would argue, we need expensive health care to keep our economy from collapsing. That 2 trillion dollars funds millions and millions of Americana’s retirement, college savings, mortgages, SUVs and t-bone steaks. Removing a significant chunk would collapse the economy. The only problem is, that money is being spent in all the wrong ways. And we are printing money to support a system that is collapsing on its own weight.”

The most obvious recent examples of this were:

Enron. If only everybody had kept buying the stock and ignored the problems, the stock price would have stayed up. Of course, since the problems were fraud and criminals should not be allowed to continue their swindles, this should not have been allowed to continue. Happy makes a great case for Medicare being the same kind of fraud. We discourage thinking, but encourage thoughtless action. Probably not even the second best plan available to us.

The NASDAQ bubble. It was over 5,000 in March, 2000. It is less than half of that now, but its low point was at 1,140 in October, 2002 – losing almost 4/5 of its value. In the housing market this would be a quarter million dollar house dropping to $50,000. The housing market hasn’t seen really bad. NASDAQ was receiving a lot of money to prepare for Y2K. An idea that would have been ridiculed anywhere sensible people debated things, but all of this money drove the NASDAQ to obscene height. When the money ran out, the buying pressure did, too. Without buyers, there is nothing to support prices. Y2K is another example of paranoiacs bringing about great destruction in their devotion to the lie “You can’t be too safe.”

Housing. We are now trying to get the government to help out people who spent too much for their homes. Apparently, making a profit on housing is a right. If only the oil companies made houses their profits would be safe. When oil comes back down, and it will. The oil companies may be right back to depending on government hand outs to survive. A big part of the support for oil prices is the construction going on in China in preparation for the Olympics. Once the Olympics are over, will there be as much growth? I don’t think so. Is this an appropriate analogy to the Y2K fiasco? I don’t know. Food costs have been climbing too.

There is an interesting comparison between China in 2007 and the NASDAQ in 2000. The article was right, just early. They predicted that the Chinese market was at its peak, when it hadn’t even hit 4,500, yet. Later in 2007 it got above 6,000. Since then it has not resembled the missile launch that excited everyone. Now it looks more like a drunk on roller skates. It isn’t a question of if he will fall, just how bad it will be before he stops. It is under 3,000 – less than half of what it was at its peak.

Excesses need to be corrected. When they form a bubble, as these did, the correction is much more painful than it would be otherwise. If the government doesn’t straighten out the Medicare mess and the other monetary misadventures they are leading us on, we will have much bigger problems than mortgage and fuel payments.

His solution reminds me of Utopia by Thomas More. It was never meant to be a real place, so the title came from the Greek for nowhere. Is Happy’s solution more practical? I don’t know, but does anyone in government relinquish the power of the purse voluntarily?

How much do we have to lose by ignoring the problem, or just continuing to patch the more obvious holes? Too much.

Health care is a mess. People have no idea of what the costs really are, so they have no incentive to control costs. Maybe this would help. We need to stop worrying about disrupting the status quo.

Maintaining the status quo will kill us. The only status quo people are corpses. For them, things can’t get any worse.

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By Rogue Medic
Filed Under: Critical Judgment, Heresy, Irrational Government Oversight, Math

More Bad Airway Instruction.

Fri, 04 Apr 2008 15:17:00 -0400 by
 
Entertainment from PALS (Pediatric Advanced Life Support) classes?

How about pediatric intubation?

Kids are pretty scary, especially when they are really sick.

Then the idea of doing math while preparing to intubate a child is less than appealing to you?

Absolutely. Why would I want to do that?

Well, the PALS teaching includes using a formula:
 

 

Endotracheal Tube Size

The internal diameter of the appropriate endotracheal tube for a child will roughly equal the size of that child’s little finger, but this estimation may be difficult and unreliable.33,34 Several formulas such as the ones below allow estimation of proper endotracheal tube size (ID, internal diameter) for children 1 to 10 years of age, based on the child’s age:

Uncuffed endotracheal tube size (mm ID) =(age in years/4) + 4

In general, during preparation for intubation using the above formula, providers should have the estimated tube size available, as well as uncuffed endotracheal tubes that have internal diameters that are 0.5 mm smaller and 0.5 mm larger than the size estimated ready at the bedside for use.

The formula for estimation of a cuffed endotracheal tube size is as follows30:

Cuffed endotracheal tube size (mm ID) = (age in years/4) + 3 [1]

 

They include at least one test question to stress the importance of this.

Then in the last sentence in that section – the only sentence I did not include above – they write:
 

Endotracheal tube size, however, is more reliably based on a child’s body length. Length-based resuscitation tapes are helpful for children up to approximately 35 kg.35 [1]

 

I still get people arguing with me that the formula is more accurate than the length-based tape. They argue that the child’s airway grows at a rate determined by the formula, regardless of how quickly the rest of the body grows. The tape accounts for this difference, the formula caters to fools.

What is a length-based resuscitation tape?
 


 

This image is from the FDA Patient Safety News from October 2004 a bit more than half way down the page.[2]

You need to get a length-based resuscitation tape (Broselow or generic), become familiar with the tape, become familiar with the information that is on the tape, and use the tape a few times to feel comfortable with it.

This is a way to avoid having people calculate formulas or guess at weights when dealing with unstable children. Most doctors don’t calculate well under these circumstances. The same is true for nurses, medics, and even mathematicians. It is a very bad idea to avoid using something that simply and more accurately arrives at the answer.

Except when intubating during PALS.

Why?

Maybe they needed to get another multiple choice question for the test. Why try to explain dangerous foolishness?

Looking at the tape, you can see the Red to Head attempt to avoid confusion can be confusing in itself. There is a red section of the tape for 8 – 9 kg patients.

Nobody would make that mistake.

Nobody properly trained and supervised by competent people would, but the FDA does not look at things that way. Instead they try to require a fool proof tool. Only a fool would do that. Nobody has made the FDA fool proof.

Dr. Deborah Peel must love them, since they approach things the same way.[3],[4]

Here is what the FDA wrote:
 

Determining the dose of medication to give a child in an emergency can be a challenge. In most cases the dose is based on the child’s weight, and this can be very difficult to estimate. Even parents can be far off the mark when they’re asked their child’s weight. And even if the estimate is accurate, there’s the added chore of looking up the dose for a child of that weight.

Some clinicians avoid these difficulties by using a Broselow Tape, which measures the child from head to toe and uses this measurement to estimate the child’s weight, and thus the dose. The tape is divided into color-coded segments based on the child’s length, and each of the colored segments shows the approximate weight for that length child, along with the dose for commonly used emergency drugs for children of that weight. [2]

 

Here is one of the problems. They act as if the only way to measure the child is to start at the head and stretch the tape down to the feet. Would it be wrong, or unanticipated, to start at the fee and move to the head? What part of the body would a podiatrist start at?

The only thing that matters, whether you start at the feet or start at the head, is that the bright red/orange color on one end of the tape is the starting point. Starting at the other end of the tape is wrong – you will be using a different measurement.

You can use this tape for finding the dose of common resuscitation drugs and for finding the size of various pediatric equipment, such as an endotracheal tube.
 

But errors are often made using Broselow tapes. In a recent Medication Safety Alert, the Institute for Safe Medication Practices notes that the tapes can be placed alongside the child upside down, which would give the wrong length for the child and thus the wrong dose.[2]

 

It does not matter if the tape is “right side up,” what matters is that you start from the bright red/orange color on one end of the tape. The other end of the tape does not have this. It gets worse.
 

ISMP also says that the 1998 edition of the tape can be confusing in several respects, and that some of these problems were corrected in the newer 2002 version. They also point out that errors can occur if physicians wrongly assume that the listing of drugs on the tape means that they’re to be given in sequence. [2]

 

If you are a doctor and you don’t know anything about resuscitation get out of the way of the people who do. No amount of fool proofing will work for you. You are a danger to everyone else present. The same is true for nurses and medics who don’t know what they are doing.

If you do not know what medications to give, don’t give any medications.

If you are giving medications in the order that they are listed on the tape you are a dangerous idiot and should be bundled up and sent to Osama bin Laden as a Hanukkah present for him to torture.

Subtle.

I do what I can.

Of course, if you do not know the difference between the 8 – 9 kg section of the tape and the part marked MEASURE FROM THIS END, you probably don’t know what medication to give, when to give a medication, or why to give a medication.
 

Here are some of the measures ISMP recommends to prevent errors when using Broselow tape.

First, replace outdated Broselow tapes with the most recent edition, issued in 2002.

To prevent using the tapes upside down, hang them with the red arrow that says “Measure from this end” at the top. Teach staff to remember “RED TO HEAD” when placing the tape alongside the child’s body. [2]

 

And they repeat their misleading suggestion.
 

And if the tape is laminated in plastic, be sure the plastic doesn’t extend beyond the red arrow, which could change the measurement starting point.

For in-service training on how to properly use Broselow tapes, the Duke University Medical Center has a comprehensive programmed instruction course under its program for enhancing pediatric safety. [2]

 

A comprehensive programmed instruction course?

Give them the tape, let the doctors, nurses, and medics ask questions. Let them use the tape. Correct them when they make mistakes. As long as they do not resemble 2 monkeys with a football, things are pretty good.

Or is that too comprehensive for such a fine medical and educational institution.

Duke did a study that found that morphine is bad for chest pain, suggested that only NTG (nitroglycerin) should be used for the chest pain. Meanwhile, other researchers at Duke are trying to show that NTG is bad for chest pain. Does anyone at Duke communicate?
 

More on length based resuscitation tapes here:

A Pediatric Bag Separate From the Adult Gear

Weight based tube size here:

Bariatric Endotracheal Tubes for Adults?

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Footnotes:

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[1] Endotracheal Tube Size
2005 American Heart Association Guidelines for Cardiopulmonary Resuscitation and Emergency Cardiovascular Care
Part 12: Pediatric Advanced Life Support
Breathing: Oxygenation and Assisted Ventilation
Free Full Text from Circulation

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[2] FDA Patient Safety News from October 2004
FDA
Archived FDA Patient Safety News
Link to PDF of archived printed information from October 2004 that does not include the image in its current form.

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[3] Deborah Peel is the antidote to HIPAA
Mon, 17 Mar 2008
Rogue Medic
Article

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[4] Calling Dr. Deborah Peel – Anyone Home?
Wed, 26 Mar 2008
Rogue Medic
Article

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By Rogue Medic
Filed Under: Critical Judgment, Heresy, Intubation, Irrational Government Oversight, Math, NTG, PALS

Reporters – not just for target practice

Sat, 29 Mar 2008 00:41:00 -0400 by
Suppositories kill deadliest malaria parasites fast

Some headlines just make you smile.

How do they get the suppository in the parasite?

Oh! . . . . Never mind.

Suppositories derived from sweet wormwood kill the deadliest malaria parasites quickly and offer a stop-gap treatment for people in remote areas until they can reach a hospital, researchers said on Friday.

“stop-gap treatment” 🙂

Wormwood is the source of absinthe, which is now legal again – sort of.

It is sad that the understanding of statistics seems to escape most people:

The disease kills a child every 30 seconds

As if they are lined up and taken to an abattoir at a scheduled time.

It should read that: “On average, the disease kills a child every 30 seconds.” This clown is paid to write this poorly, but I did get a giggle out of the unintentional(?) humor.

By Rogue Medic
Filed Under: Heresy, Humor, Math
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