Binary (Base 2)- Either You Get it or You Don't.

Dear Mathman,

I heard this joke in math class the other day:

“There are only 10 types of people in this world- those who understand binary and those who don’t.”

I’m one of the types of people who doesn’t get it. Please help.

Thanks,
Sly T. Lee Confused



Dear Sly,

Thanks for asking for help. That is a great skill more of us need to use. BTW, you sure know how to tell a joke. I just had to pick myself up off the floor. I laughed myself right out of my chair. Keep them coming.

Anyways, this joke revolves around understanding the binary system. You might not realize it, but we both needed the binary system to even see this blog entry. Huh? As a matter of fact, you’re using the binary system anytime you use anything powered by electricity. Anything.

The binary system is based on the prefix “bi”. Do you know what number “bi” is referring to? Hint: think bicycle. I hope you figured out “Bi” means “two”. So the binary system is counting system based on the number 2. A bit lost? Let’s go back to the electricity example for a second. . Think about the common light switch. There are only two options, on or off. The electricity flows or it doesn’t (we’re ignoring dimmer switches to keep it simpler).

Any electronic device is broken down into a whole lot of light switches that are on or off. Fortunately for us, many of these switches have been shrunken down to a microscopic level. If they hadn’t, this computer that I’m typing on would take up a fair amount of real estate here in Mathopolis. Ah, the wonders of modern science.

Enough of science, let’s get back to math:

We’re not used to the simplicity of the binary system, we’re used to a much more complex system of keeping track of numbers. Our system is base 10 and is called the decimal system. It’s worth it to think about this for a minute so we can understand and appreciate the binary system a bit more. The decimal system revolves around 10 possibilities for each digit (single number). You know these possibilities as 0,1,2,3,4,5,6,7,8, and 9 (that was fun to type from the top of the keyboard). We know the place values in our system as “ones”, “tens”, “hundreds”, “thousands”, “ten thousands”, and so on. Think of a number to keep this straight:

67,890 is 6 ten thousands, 7 thousands, 8 hundreds, 9 tens, and 0 ones.

In our decimal system the number 10 is made up of 1 tens and 0 ones. When we write a number we start with the lowest value for a digit, 0, and work our way through the digits until we get to the highest value, 9. If we have to go higher than 9 we add the next place value and use a 0 to hold the first place value. We’re so used to doing this automatically we don’t think about it anymore.

The binary system works the same way. We start with a 0 in the first place value and count up until we hit the largest digit, then we add the next place value and start over. So, the number 0 in binary is 0. The number 1 in binary is 1. The number 2 in binary exceeds the highest digit for first place value so we need to add the second place value.

In base 2 (binary), the number 2 is written as 10. The place values go ones, twos, fours, eights, and so on. In the decimal system the place values are: 10^0=1, 10^1=10, 10^2=100, 10^3=1000, and so on. In the binary (base 2) system, the place values are: 2^0=1, 2^1=2, 2^2=4, 2^3=8, and so on. You count the same: 1,2,3,4,5,6,7,8,9,10,11, etc. but the numbers are written differently. This is like a foreign language for math.

Now, take a moment and reread the joke. Is it funny yet? If we wrote it without the 10 in binary, which really is the counting number 2, it wouldn’t be nearly as funny:

“There are only 2 types of people in this world- those who understand binary and those who don’t.”


Stay radical,
Mathman

Whoa, Math AND Science

Reuben Margolin definitely has mathematical and scientifical (?) superpowers. He probably won his school's science fair as a student.



Stay radical.

Being Careless Can Stink.

Recently a lot of math classes have been dealing with percents and sale prices. For some reason, many people have problems with percent problems. I guess they are called “problems” for a reason, but really they’re not that hard to solve- IF you read carefully. Most of the time errors occur it is due to careless mistakes in either not writing down the work, or reading the problem incorrectly.

We can deal with the first situation rather quickly: show your work on paper. Percent problems go with proportions like cheese goes with pizza. Be careful to match the original amount to the 100 in the denominators of each side of the proportion, and keep the percent over the 100 and you’re set. If you don’t know what I’m talking about when I say, “proportion”, look at the previous blog entries below.

The second case is actually the first thing that should happen when you’re starting the problem. Just like my last blog entry said, take your time to read carefully the first time and you’ll save time in the long run. Even with careful reading though, some people still struggle. Most of the time I’ve found this is due to confusion over one little letter. This letter is crucial to the meaning of the problem and the work involved in finding its solution.

How can one stinking letter be so powerful you ask? What is this powerful letter?

A: “f”

The letter “f” has the power to change “of” to “off”. If the problem is “10% of the original price”, the answer will turn out to be less than ½ of the original amount. If the letter is “10% off the original price”, the answer will end up being more than ½ of the original price. People will flock to a sale of "10% of" as it can also be interpreted as "90% off".

One little letter = one big difference.

If you aren’t careful with that one little letter “f” then “art” takes on an entirely new meaning.

That stinks. Read carefully.



Stay radical.

Girls (and Boys) Just Wanna Have Fun...

Recently, I’ve come to the conclusion that many students secretly love doing math work. This is exciting. I can’t say, “Everybody loves doing math work” because that would imply 100% of the students love doing math work. It is very difficult to account for 100% of anything, let alone everybody, but there is a lot of evidence to support my stance.

Let me explain:

If you like doing something, you’ll spend time doing it. The more you like it, the more you’ll make it a priority. For instance, if you like playing video games, you’ll often trade sleep for the experience of saving the princess or ridding the planet of aliens. If you like inequalities, you’ll write them on the back of your hand ( 1<3 …). As a side note, these inequalities usually express a commitment to a unit rate of humans. For example: 1<3 Clarence. Also interesting is that what follows the <3 should, according to proper English, be plural but seldom is. Of course, some people prefer 1<3 ?, which as far as plurality goes, is ambiguous. This has been an interesting tangent, but now back to our regularly scheduled program…

If spending time doing something = fun then a lot of students enjoy some things that are a bit puzzling to me. For instance, some students enjoy being yelled at by their parents. These students must enjoy it because they invest time in being yelled at. They know their parents will nag them to do something that they are required to do on a regular basis. They don’t do what their parents ask them to do the first time, or the second, or the third, or the nth time (when n>3). What most of these students don’t realize is that each time their parents nag them it takes more of the student’s personal time that could be spent on video games or inequalities (or getting better at pencil tapping by practicing to YouTube videos). Since it’s taking up their time, and they could have made a choice to not be nagged by doing what they knew needed done in the first place, these students must view being nagged as fun.

Now this is bizarre behavior, but it’s not as strange as those students who secretly love math. On the surface these students may say, “I hate math”, but deep down their actions show otherwise. They could save a bundle of time if they used a bit of common sense, but they’re having fun doing (and redoing) things the hard way.

I hear the question now, “Mathman, what in the 2nd prime numbered planet from the sun do you mean?”

A: These students think that they’re taking the easy way out by saying: “I did it in my head” or “I did it on my calculator” or “I used another piece of scratch paper, but my little sister feels the need for more fiber in her diet so she ate it.” What he (used as the indefinite pronoun) doesn’t realize is that, in the end, math teachers are a stubborn lot and WILL require him to “Show your work” or “Explain your answer”. So the person who answered “IDK”, “?”, or “ITL” will, in fact, be spending more time on the problem then necessary. He could have put the effort into solving the problem correctly the first time, but instead chose the path that required not just solving the problem, but the path of extra writing by putting down the wrong answer in the first place. What’s the clincher in the whole deal though is that he also must like being nagged by his math teacher. Why? The student could have saved time by reading the directions and solving the problem correctly in the first place. Instead he chose to have the math teacher tell him to do it again (and again, and again, …).

Some people sure have strange ideas of what constitutes fun.

Maybe we need shirts:

1 <3 Math.

Or

1<3 Redoing things that I could have done right the first time.



Stay radical.