Stop Freaking Out About Ebola (Because: Math)



When I read Richard Preston’s The Hot Zone in the mid-1990s, I was terrified. This was the first I had heard of a scary new disease called ebola. I was working for an AIDS Service Organization at the time, so I understood — better than most — how blood-borne infectious diseases are contracted. Still, the images of how the victims of this virus die are still with me. Horrifying.

But I’m not at all afraid of ebola today. Not one little bit. Why? Math.

It’s difficult for ebola to spread. Really difficult. Like HIV, the ebola virus only lives in bodily fluids, including blood, saliva, mucus, vomit, semen, breast milk, sweat, tears, feces and urine. (HIV is only transmitted through four bodily fluids: semen, vaginal fluids, breast milk and blood.) Transmission can occur when infected bodily fluids come into contact with a person’s eyes, mouth or nose, or an open wound or abrasion.

Compare this to measles, which is transmitted through the air. The measles virus lives in the mucus lining of the nose. A sneeze or cough can release virus-infected droplets into the air. Breathe in the air with little measles droplets, and unless you’ve been vaccinated, it’s very likely you’ll see a tell-tale rash in a few days.

Since measles is highly contagious for four days before symptoms appear, a person can transmit the virus without even knowing he has it himself. According to the CDC, measles is so contagious that if one person has it, it will spread to 90 percent of the people who come in contact with that person (if they are not already immune, thanks to the vaccine).

It’s All About the R0

The way a virus is transmitted helps determine how contagious the disease is. And the big deal here is something called R0 or “reproduction number” (also called “r-naught”). R0 is the number of people that one infected person will likely infect during an outbreak.

Those of us of a certain age might remember a shampoo commercial that illustrates this perfectly.

Like Fabrerge Organics shampoo, ebola’s R0 is 2. When one person contracts ebola, it is likely that two others will become infected. Yes, those numbers add up — and they have in parts of Africa.

Now take a look at measles, with an R0 of 18. When one person gets measles, it’s likely that 18 people around him do too. Then each of those 18 people spread the virus to 18 more people. In one generation of this infection, 18 x 18 (324) have contracted measles. That’s compared to only 2 x 2 (4) people who will likely contract ebola in one generation of the infection. In fact, measles is still one of the leading causes of death in children around the world. According to the WHO:

Measles is still common in many developing countries – particularly in parts of Africa and Asia. More than 20 million people are affected by measles each year. The overwhelming majority (more than 95%) of measles deaths occur in countries with low per capita incomes and weak health infrastructures.

But measles is not a major threat in the U.S., and we all know why — the measles vaccine. Ebola has no vaccine, but a relatively strong health care system in our country and its very low R0 makes ebola a low threat, compared to other viruses, like HIV and certain strains of influenza.

The scary thing about ebola is not how quickly it spreads but how basic medical care can keep it from spreading. We have that basic care here in the U.S. Large swaths of Africa do not.

And along with a low R0, the ebola virus has a relatively short infectious period — about a week. On the other hand, HIV is infectious for years and years — many of those years while the infected person has no symptoms or does not even test positive on an HIV test. The relationship between time and infection matters, too.

You Should Worry About Other Things Instead

For example, the National Institutes of Health (NIH) reports that each year, about 5,000 people under the age of 21 die in alcohol-related incidents, including car crashes, falls, burns, homicides, suicides and alcohol poisoning.

According to the Federal Reserve, Americans held $229.4 billion in consumer credit (outstanding household debt, including credit cards and loans) in July 2014.

The global sea level is rising at alarming rates, according to the National Oceanic and Atmospheric Administration (NOAA). Before 1900, these levels remained constant. Since 1900, the levels have risen 0.04 to 0.1 inches per year. But beginning in 1992, that rate climbed to 0.12 inches per year. This translates to much greater likelihood of flooding in coastal areas (including the neighborhood where I lived for 10 years).

And we should be concerned about ebola in Africa, mainly because we can do something about the higher rates of ebola infection and deaths there.

But ebola in the United States? Really, this shouldn’t be a worry for you. Let the math ease your mind.

Photo Credit: CDC Global Health via Compfight cc

Math at Work Monday: Kelly the Virtual Assistant



This world is spinning fast, and a lot of things are changing.  Today’s interview is with Kelly Case of Time on Hand Services.  She is a virtual assistant or VA – in fact, she’s my VA!  Without Kelly, this blog would be empty most of the time. She also lays out my newsletter and does lots of research for me. 

Can you explain what you do for a living?

I have my own business that provides administrative services to other companies.  These companies vary in size and may be located anywhere in the world.  Thanks to the internet, there is less and less need for your assistant to be in the physical office with you.  My clients enjoy the freedom of having a virtual assistant. They don’t have to provide office space, computer equipment, or benefits.  They decide how many hours they want me to work for them each month and then assign tasks to me at their convenience.  These tasks vary widely.  I do bookkeeping, email management, calendar management, blog management, proofreading, data entry, travel planning, transcription, customer service, email marketing, website design, and more.

When do you use basic math in your job?

I use math just about every day, for my own virtual assistance business as well as for the businesses of my clients.  I use math when doing invoicing, payroll, travel planning, and bookkeeping.  For instance, when reconciling credit card or checking accounts, I must use math to make sure the credits and debits match the bank statement.  When invoicing, I use math to make sure I’m charging their clients or mine the right amounts or percentages.  A customer of my client may agree to make three monthly payments to the client for a certain product.  I split the payment into thirds and charge at the appropriate time.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

Yes, I use the calculator function on my computer whenever I need to calculate long lists of numbers to prevent human error.  I usually do it twice to be sure I come up with the same answer each time.  I also use Microsoft Excel to keep track of credits and expenses for my clients’ check registers. Quickbooks is used often for the bookkeeping aspect as well.

How do you think math helps you do your job better?

I’m not sure that it helps me do it better, but it enables me to do my job.  I wouldn’t be able to invoice, do payroll, or keep books without the use of math.  Numbers are an integral part of our daily lives and work places.  And, where there are numbers, there is math.

How comfortable with math do you feel? Does this math feel different to you ?

I am extremely comfortable with math.  The type of math I use in my job is very elementary and basic for me.

What kind of math did you take in high school? Did you like it/feel like you were good at it?

I enjoy math very much.  In high school, I got As in math and was asked by friends to do their homework assignments for them.  In fact, I enjoy it so much I took math as one of my college electives because I knew it would be an easy A for me.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pickup using the skills you learned in school?

No, I didn’t need to learn any new math skills per se.  I just had to learn the different programs that I use to do the math, like Quickbooks or an online payroll service.

More and more writers, like me, are hiring virtual assistants. This allows us to focus on our writing, and for me, it means having a detail person on my team. Have a question for Kelly or interested in learning more about her services?  Check her out at Wondering how you can use a virtual assistant in your business? Ask in the comments section.

Photo Credit: Philippe Put via Compfight cc

Is Math Creative?

Is math creative?

As a math major in college, I was required to take a computer programming class. In retrospect, the reasoning made perfect sense: successful programming follows a natural logic, very much the same way math does. But at the time, I was resentful, and a little scared.

Sure enough, I was lost by week two. I enlisted in some tutoring from a dear friend in my section. And she demonstrated to me a completely different way of structuring the code. Her process made much more sense than the methods taught by our instructor, so I adopted it. Three days later, I sat in shock, as the prof announced that some of our assignments looked suspiciously similar.

Let me be clear: I had not copied my friend’s coding. I had identified with her way of thinking and modeled my code after her approach. But it was such out-of-the-box thinking, I understood why the prof thought we were cheating. And sadly, instead of talking to him about it, I simply reverted back to his methods. Yeah, I didn’t get much out of that class.

My friend demonstrated some amazing creativity in her approach to coding. She did this in all of her math classes as well — for which she was greatly rewarded. I learned from her that thinking creatively is critical for succeeding in math of any kind. And I mean any kind — from proving Fermat’s Last Theorem to finding out how many gallons of Symphony in Blue you need to paint your living room.

Too often, math is described in black-and-white terms. There’s a right and a wrong answer. There’s a step-by-step process to follow. If you think of math this way, it’s no wonder. Most of us were taught that math is about a right answer.

But those teachers were wrong. Sure, the right answer is important, but just like those inspirational posters say, it’s all about the journey. How you get to your answer is just as important as the right answer.

And that’s where creativity comes in. Because we all access this information in different ways. Some of us are visual. Some of us need time to think. Some of us like to talk things out. Those of us with true numeracy use creative methods for solving ordinary problems. Take 23 x 6, for example.

Most of the world would stack these numbers up, multiply 6 by 3 and then 6 by 2, add (remembering to align the numbers properly) and get 138. But there are many other ways. I like this one:

23 x 6 = (20 + 3) x 6

                       = (20 x 6) + (3 x 6)

         = 120 + 18

          = 138

With that method, I can do the problem in my head!

But you don’t need to solve the problem that way. Come up with your own process. Be bold! Set off on your own! Be creative!

So in answer to the question, Is math creative? YES! You’ve just got to access your own out of the box thinking.

Photo Credit: Yuri Yu. Samoilov via Compfight cc

Do you agree that math is creative? Why or why not? What examples of creativity (or lack thereof) can you share?

Math at Work Monday: Joe the Platform Consultant


In the IT field, there are many machines and programs that are really confusing and difficult to understand. Not only do we have to trust and depend on these machines, but also the people who service them. Joe Thompson is one of the good guys. He provides assistance to the users and companies when they need it most. From consulting to maintenance, Joe and his colleagues are there for us when our technology isn’t working quite right. (Joe is also one of my former geometry students. It’s been great to reconnect with him and see how accomplished he is now!)

Can you explain what you do for a living?

Red Hat’s consultants help customers get our products working when they have specific needs that go beyond the usual tech support.  We are essentially advanced computer system administrators on whatever our customers need us to be to get Red Hat’s products to work for them.  Common consulting gigs are setting up Red Hat Satellite to manage the customer’s servers, or doing performance tuning to make things run faster or a “health check” to verify things are running as efficiently as possible.

We just put out a marketing video about our consulting for public-sector clients, actually:

(We do more than just public sector and cloud, of course.)

When do you use basic math in your job?

The most common is when tuning a system to perform well, or configuring various things.  Unit conversions and base conversions are especially important.

IT has a long-running math issue actually: does “kilo” mean “1000” (a round number in base 10), or “1024” (a round number, 10000000000, in base 2)?  There are various ways people try to indicate which is intended, like using a capital K vs. a lowercase k, or using KiB vs. KB.  This matters in a lot of cases because when you get up into large data sizes, the difference between round numbers in base 10 and base 2 gets pretty big.  A 1-TB hard drive (a typical size today, maybe even a little small) is a trillion bytes — 1000 to the fourth power, not 1024 to the fourth power.  The difference is about 10% of the actual size of the drive, so knowing which base you’re dealing with is important.

Then there are units that have to be converted.  A common adjustment for better performance is tweaking how much data is held in memory at a time to be transmitted over the network, which is done by measuring the delay between two systems that have to communicate.  Then you multiply the delay (so many milliseconds) by the transmission speed (so many megabits or gigabits per second) and that gives the buffer size, which you have to set in bytes (1 byte = 8 bits) or sometimes other specified units.

Sometimes software writers like to make you do math so they can write their code easier.  If a program has options that can either be on or off, sometimes a programmer will use a “bitfield” — a string of binary digits that represent all the options in a single number, which is often set in base 10.  So if you have a six-digit bitfield and want to turn off everything but options 1 and 6, you would use the number 33: 33 = 100001 in binary.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

I’ve always done a lot of arithmetic in my head and I can at least estimate a lot of the conversions without resorting to a calculator.  I’ll break out the calculator if the math is long and tedious though, like averaging a long column of numbers, or if I need a precise answer quickly on something like how many bytes are in 1.25 base-10 gigabits — I can do the billion divided by 8 and come out with 125 million bytes per base-10 gigabit, and then multiplying by 1.25 I know I’m going to be in the neighborhood of 150 million bytes, but I need the calculator to quickly get the exact answer of 156250000 bytes.  If I’m on a conference call about that kind of thing I’ll use the calculator more than otherwise.

Google introduced a new feature a couple of years ago that will do basic math and unit conversions for you, so if I’m deep into things or just feeling lazy I can also just pull up a web browser and type “1.25 gigabits in bytes” in the search bar, and Google does it all for me.  But recently I noticed I was reaching for the calculator more, and arithmetic in my head was getting harder, so I’ve been making a conscious effort to do more head-math lately.

How do you think math helps you do your job better?

Without math, I couldn’t do my job at all :)  Even so little a thing as figuring out how long a file will take to transfer takes a good head for numbers.  As soon as you dig under the surface of the operating system, it’s math everywhere.

How comfortable with math do you feel? Does this math feel different to you ?

I’m pretty comfortable with math.  A lot of my off-time hobbies touch on computers too so it’s a lot of the same math as work even when I’m not working.

What kind of math did you take in high school? Did you like it/feel like you were good at it?

I took the standard track for an Advanced Studies diploma from grades 8-11 (Algebra I, Geometry, Algebra II, Advanced Math), plus AP Calculus my senior year, and always did well. I didn’t expect to like Geometry going in because it’s not one-right-answer like a lot of math, but I ended up enjoying the logical rigor of proofs.  (Though I do recall giving my Geometry teacher fits on occasion when my proofs took a non-standard tack…)

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pickup using the skills you learned in school?

Most of it was learned in school, although base conversion isn’t something we spent a lot of time on.  I got good at it through long, frequent practice as you might guess…

Do you have a question for Joe? Send me your question and I will forward it to him.

Photo Credit: Dan Hamp via Compfight cc

The Brain Ordered: A review of The Organized Mind

The Organized Mind

These days I’m devouring just about any writing I can find that features the cross section between neurology, sociology and psychology. Daniel Pink’s Drive completely changed my mind and confirmed my suspicions about how motivation actually works. And now The Organized Mind by behavioral neurologist Daniel Levitin has helped me better understand how the brain helps us organize our time, thoughts and things — and how our brains can get in the way.

It’s a big book. And parts of it are very dense, including sections that explain the anatomy of the brain and almost an entire chapter devoted to the probabilities of medical outcomes. But the rest of the book is quite narrative, with funny and relatable examples. This science and geek loved it all.

For me, the takeaways were in productivity and learning. It’s not fair to boil it all down to two categories, but I will. At the same time, I’ll point out how all of this relates to math, with a few quotes from Levitin‘s book.

What the Brain Does Well


Turns out the brain is perfectly designed for identifying similarities and differences.

In the last few years, we’ve learned that the formation and maintenance of categories have their roots in known biological processes in the brain. … Theoretically, you should be able to represent uniquely in your brain every known particle in the universe, and have excess capacity left over to organize those particles into finite categories. Your brain is just the tool for the information age.

Where’s the math in that? Everywhere. It could be argued that math is the study of categories. Start with our number system. Positive numbers that are not fractions and decimals fall in the category of whole numbers. Add negative numbers to that group, and you’ve got integers. (And so on.) Or you can group numbers as prime and not prime or even and odd. Graphs of equations can be lines or curves — and some curves are parabolas, while others are circles. See where I’m going with this?

This is all good news. Because the brain is so excellent at forming and maintaining categories, your brain was made for math.


But how can we make sure we remember all of these categories?

The last two decades of research on the science of learning have shown conclusively that we remember things better, and longer, if we discover them ourselves rather than being told them explicitly.

This idea has huge implications for math education. For the most part, approaches to teaching math fall in one of two categories (see what I did there?): telling and discovering. Most of us who grew up in the 70s and 80s learned math through the “telling” method. The teacher gave a lecture, demonstrating how to perform a skill, and asking students to practice the steps shown in the lesson. Discovery turns this process on its head, giving students the opportunity to figure things out on their own, even finding new ways to solve problems. When they can discover ideas on their own, students have a much better shot at remembering what they’ve learned.

Of course discovery is messy and difficult, which brings us to ways that our brain gets in the way.

What the Brain Doesn’t Do Well


This idea from Levitin blew my mind. Apparently it’s a proven fact that people don’t manage frustration well. It’s why we procrastinate, and that feeling of frustration is rooted in our brains.

The low tolerance for frustration has neural underpinnings. Our limbic system and the parts of the brain that are seeking immediate rewards come into conflict with our prefrontal cortex, which all too well understand the consequences of falling behind. Both regions run on dopamine, but the dopamine has different actions in each. Dopamine in the prefrontal cortex causes us to focus and stay on task; dopamine in the limbic system, along with the brain’s own edogenous opiods, causes us to feel pleasure.

Then we play into this automatic system with two “faulty beliefs: first, that life should be easy and second, that our self-worth is dependent on our success.” So, when the going gets tough, we quit — shoot for an easier option.

Unfortunately, this is just something we need to fight against. And Levitin has some great strategies to offer. At the same time, I felt very validated in my instinct to choose low-hanging fruit, rather than reaching for loftier goals. That also goes for the math student who is immediately frustrated by assignments he can’t understand, and the grownup who always lets someone else split the restaurant tab.


For years I’ve struggled with my inability to internalize the concepts of probability, so I was really relieved to learn that my brain is wired this way.

Cognitive science has taught us that relying on our gut or intuition often leads to bad decisions, particularly in cases where statistical information is available. Our guts and our brains didn’t evolve to deal with probabilistic thinking.

No wonder I have to work so hard to understand the probability I’ll suffer from a medication’s side effects or even the chance I’ll win in Roulette. Unlike categorizing, my brain isn’t set up to have an intuition about probability. (This isn’t to say that others can’t find calculate probabilities quickly, of course.)

Of course much depends on our understanding of probability, including life-and-death situations, like choosing the right medical treatment. It’s important to think about these things in a clear and focused way. That’s one reason Levitin spends so many pages on something called FourFold tables. (More on those in a later post.)

I encourage you to pick up a copy of The Organized Mind. (No, you can’t borrow mine; I’ve been referring to it over and over since I finished reading!) It’s a great look at how we can maximize the things our brains do well and work against the tricks our brains play on us — to be better organized and productive, while learning and using math.

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Have you read Daniel Levitin’s book? If so, what did you think? Share your comments and questions.