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
Friday, April 24, 2009
Wednesday, April 8, 2009
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.
Stay radical.
Friday, April 3, 2009
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.
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.
Thursday, April 2, 2009
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.
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.
Wednesday, March 18, 2009
Reason # Nineninenine to own a Calculator
I know you've been working hard this week and reading a lot so I'll keep this brief. Here's one final PSSA style question:
Why in Mathopolis would you get one of these?
a. You need a clock.
b. You've got mad math skills and you want to practice them.
c. You like Nines.
d. You are so cool your friends need to wear a sweater when they hang out with you.
This one is from the Triple Nine Society (if you search for that you can find out more info.)
Stay radical!
Sunday, March 15, 2009
A Day Late, but Still Irrational
A good friend of mathematical accuracy, Adam, sent us this gem in honor of Pi Day (3/14). Come to think of it, Adam is a fabulous name- one of the few that implies a mathematical operation.
If a mathematical superhero didn't have the ability to fly, they'd surely be driving this model- the Mazda Mathmobile.
If a mathematical superhero didn't have the ability to fly, they'd surely be driving this model- the Mazda Mathmobile.
Thursday, March 12, 2009
Winter Comes to an End, but Bad Math Doesn't
Next week is the start of PSSA season. I guess that means we get to hunt the PSSAs. Wouldn't that be great. Anyways, I have no idea what the weather will be next week, but I hope the temperatures (and attitudes) stay positive.
Since the Mathman morning announcements have been reduced like the greatest common factor between the numerator and denominator (i.e. cancelled) for a while, I've had some time to head out into the "real world" and fight bad math at every intersection.
It didn't take long for me to find this example:
Wow. Sounds like a fabulous toy (THAT YOU SHOULD NEVER BRING TO SCHOOL). I mean, who wants to take the effort to throw a snowball?
Anyways, If I'm going to plop down >$20 on a piece of plastic I want to know how well it works. So I went looking for some information and found:
Ad copy #1:
The 50 Foot Snowball Launcher.
STOP RIGHT HERE! 50 FOOT SNOWBALLS! RADICAL!
This toy blaster makes and launches softball-sized snowballs up to 50', allowing rapid, long-range assaults during neighborhood snowball confrontations.
Wait a second... It doesn't launch 50 foot snowballs, it launches smaller snowballs up to 50 feet. That's a bummer.
Ad copy #2:
Snowball Blaster by Wham-O
*Snowball Maker/ Launcher
*Makes and launches Snowballs up to 80 feet (24 meters)
*Compelling Box Packaging
So does it launch snowballs 50 feet or 80 feet (24 meters)?
Ad copy #3:
Product Description:
Protect your turf and defend your snow fort with a snowball maker and launcher
Snow toy makes and launches Snowballs up to 50 feet (16 meters)
By this point I was really confused. The numbers don't match.
Why?
A: My guess is probably poor font choice. When I looked at the actual package it appeared to say "80ft (16m)". This advertising ploy was pure genius. That's because 80 feet is much farther than 16m. Here's some math:
Since 1 meter = 39.37 inches it follows that
1 m .... ..... 16 m
----------- = --------- = (approx.) 52.5 ft.
39.37 in.... 629.92 in
We could also check the 80 feet and figure out how many meters that is.
Since 1 in = 2.54 cm, 12 in (1 ft) = 30.48 cm. So,
1 ft.... .... 80 ft
----------- = --------- = (approx.) 24.4 m
30.48 cm.. 2438.4 cm
The poor font choice for the 5 or 8 made the 50 or 80 very confusing. The PSSA graders probably would have ruled that "ILL" for illegible. Definitely less than a proficient score would be awarded to this product.
In conclusion, since you CAN'T use this at school, why bother paying >$30 for something so impractical? Something that would be much handier (and much less money) would be a scientific calculator with a fraction button. That, coupled with a bit of conversion common sense (CCS) would allow you to figure out that the claims made for this toy are at best confusing.
Keep your eyes open, #2 pencils sharp, and leave the snowballs at home.
Until next time,
Stay radical.
Since the Mathman morning announcements have been reduced like the greatest common factor between the numerator and denominator (i.e. cancelled) for a while, I've had some time to head out into the "real world" and fight bad math at every intersection.
It didn't take long for me to find this example:
Wow. Sounds like a fabulous toy (THAT YOU SHOULD NEVER BRING TO SCHOOL). I mean, who wants to take the effort to throw a snowball?
Anyways, If I'm going to plop down >$20 on a piece of plastic I want to know how well it works. So I went looking for some information and found:
Ad copy #1:
The 50 Foot Snowball Launcher.
STOP RIGHT HERE! 50 FOOT SNOWBALLS! RADICAL!
This toy blaster makes and launches softball-sized snowballs up to 50', allowing rapid, long-range assaults during neighborhood snowball confrontations.
Wait a second... It doesn't launch 50 foot snowballs, it launches smaller snowballs up to 50 feet. That's a bummer.
Ad copy #2:
Snowball Blaster by Wham-O
*Snowball Maker/ Launcher
*Makes and launches Snowballs up to 80 feet (24 meters)
*Compelling Box Packaging
So does it launch snowballs 50 feet or 80 feet (24 meters)?
Ad copy #3:
Product Description:
Protect your turf and defend your snow fort with a snowball maker and launcher
Snow toy makes and launches Snowballs up to 50 feet (16 meters)
By this point I was really confused. The numbers don't match.
Why?
A: My guess is probably poor font choice. When I looked at the actual package it appeared to say "80ft (16m)". This advertising ploy was pure genius. That's because 80 feet is much farther than 16m. Here's some math:
Since 1 meter = 39.37 inches it follows that
1 m .... ..... 16 m
----------- = --------- = (approx.) 52.5 ft.
39.37 in.... 629.92 in
We could also check the 80 feet and figure out how many meters that is.
Since 1 in = 2.54 cm, 12 in (1 ft) = 30.48 cm. So,
1 ft.... .... 80 ft
----------- = --------- = (approx.) 24.4 m
30.48 cm.. 2438.4 cm
The poor font choice for the 5 or 8 made the 50 or 80 very confusing. The PSSA graders probably would have ruled that "ILL" for illegible. Definitely less than a proficient score would be awarded to this product.
In conclusion, since you CAN'T use this at school, why bother paying >$30 for something so impractical? Something that would be much handier (and much less money) would be a scientific calculator with a fraction button. That, coupled with a bit of conversion common sense (CCS) would allow you to figure out that the claims made for this toy are at best confusing.
Keep your eyes open, #2 pencils sharp, and leave the snowballs at home.
Until next time,
Stay radical.
Tuesday, March 10, 2009
I <3 Doing Things the Hard Way
"I used my calculator."
I would be willing to bet this is most frequently used statement in the math classes around BJHS. This little phrase has become the new magic word, bumping "Please" off of the #1 spot. (I realize the phrase is more than one word, but the fluidity with which many say "I used my calculator" makes it almost one word.) The truth of the matter is, statistically speaking, over 1/3 of the Junior High students cannot use this phrase truthfully.
The BJHS Math Dept. (otherwise known as The Department of Accuracy and Justice) has collected data about calculator ownership from all of the homerooms throughout the school. The results: at least 470 students out of 1300 (rounded to the nearest 100) don't own a calculator.
470
---- = .3615 = 36% cannot use the statement "I used MY calculator." accurately.
1300
The strange thing is that many students would have difficulty in calculating the decimal and percent above without a calculator.
What is also puzzling about this situation is how many of the BJHS students own cell phones or iPod/ mp3 players compared to those who own a calculator. It's perplexing because nobody uses "I used my cell phone." or "I used my iPod." to describe how they solved a math problem. It's really weird that people wouldn't own a calculator as they probably have math homework around 4 out of 5 days (80%) of the week.
All of these observations don't even account for the fact that a scientific calculator with a fraction (A b/c) button only costs $10-$15 and is so much more useful throughout the school day than either a cell phone or mp3 player. Owning and using your OWN calculator may even make math a bit easier for you- that is unless you have mathematical superpowers which allow you to calculate at the speed of light (approximately 186,000 miles per second).
So let's summarize: Cost < a monthly cell phone bill. Usefulness > an iPod. It sounds like calculator ownership is something everyone should experience.
So the message is: If you really love doing math for fun DON'T own a calculator. It will take you a lot longer to do your math work so you'll feel a sense of accomplishment knowing you did ALL the work and didn't take the easy way out.
I would be willing to bet this is most frequently used statement in the math classes around BJHS. This little phrase has become the new magic word, bumping "Please" off of the #1 spot. (I realize the phrase is more than one word, but the fluidity with which many say "I used my calculator" makes it almost one word.) The truth of the matter is, statistically speaking, over 1/3 of the Junior High students cannot use this phrase truthfully.
The BJHS Math Dept. (otherwise known as The Department of Accuracy and Justice) has collected data about calculator ownership from all of the homerooms throughout the school. The results: at least 470 students out of 1300 (rounded to the nearest 100) don't own a calculator.
470
---- = .3615 = 36% cannot use the statement "I used MY calculator." accurately.
1300
The strange thing is that many students would have difficulty in calculating the decimal and percent above without a calculator.
What is also puzzling about this situation is how many of the BJHS students own cell phones or iPod/ mp3 players compared to those who own a calculator. It's perplexing because nobody uses "I used my cell phone." or "I used my iPod." to describe how they solved a math problem. It's really weird that people wouldn't own a calculator as they probably have math homework around 4 out of 5 days (80%) of the week.
All of these observations don't even account for the fact that a scientific calculator with a fraction (A b/c) button only costs $10-$15 and is so much more useful throughout the school day than either a cell phone or mp3 player. Owning and using your OWN calculator may even make math a bit easier for you- that is unless you have mathematical superpowers which allow you to calculate at the speed of light (approximately 186,000 miles per second).
So let's summarize: Cost < a monthly cell phone bill. Usefulness > an iPod. It sounds like calculator ownership is something everyone should experience.
So the message is: If you really love doing math for fun DON'T own a calculator. It will take you a lot longer to do your math work so you'll feel a sense of accomplishment knowing you did ALL the work and didn't take the easy way out.
Thursday, March 5, 2009
How Good is Your Memory?
So you think iPhone is the greatest thing ever.
Think again.
A long time ago-in a galaxy far, far, away, people thought they had the greatest video game system ever. The year was 1977. While that may sound like the age of the dinosaur for those of you who can't remember life without texting or cell phones, it's not really that long ago. As a matter of fact, statistically speaking, you'll probably live longer than 2 billion seconds or over twice that amount of time.
Anyways, in 1977, the first successful home video game systems came into play. (I know some of you can't imagine life without video games, but people did survive.) The first widely available video game system was the Atari (later to be called the Atari 2600). The Atari was out long before any of the Playstations, Nintendos, or XBoxes. If you don't know what I'm talking about, look up "Atari" sometime when you're not texting inequalities on your phone. (Example: Dude, 1<3 Don't Stop Believing - it's my favorite song on my iPod- it is so da bomb).
You may ask, "Why would I care about 1977? That's like, last century." Well, stick with me young Jedi for you have a lot to learn. (-not only did the Atari come out in 1977, but Star Wars did as well.)
Ok, so why was the Atari so revolutionary (even if it was 1977)? I'm glad you asked.
The Atari cartridge was revolutionary because it had 4K of memory. That's 4,000 bytes (actually 4,096, but we're going with 4,000). Remember from typing class that 1 character equals about one byte. For 1977 that was pretty amazing. For 2009, that's pretty lame because the basic iPhone has 4GB of memory.
So the PSSA style question is: "How many Atari cartridges would fit on an iPhone?"
A. A whole lot. (or ITL)
B. IDK. (otherwise known as ITL)
C. I'm not quite sure, but 1 <3 learning so let's figure it out.
D. Don't select this choice, it's just on here to be a distraction. (or ITL to read and eliminate this choice)
I hope you chose "C."
First of all some background information: (this would be on a formula sheet, padawan)
1K = 1000 bytes
1MB = 1000K
1GB = 1000MB
Now to use the force (i.e. math) to figure things out: (note the ..... are just placeholders because Mathman stinks at page formatting in html.)
1 cartridge..... C cartridges
--------------- = ------------
4 K............... 1000K
Solving for C (by using cross products and proportions) gives us:
1*1000=1000
1000/4=250 cartridges in 1000K (or 1MB)
Now,
250 cartridges..... N cartridges
------------------- = ---------------
1 MB ................ 1000 MB
Solving for N gives,
250*1000=250000
250000/1=250000 cartridges in 1000MB (or 1GB)
Since the iPhone we're comparing to is 4GB, that would hold 250,000*4 = 1,000,000 Atari cartridges.
Big deal, you say, the iPhone I want is still the greatest thing EVER.
For now.
Let me leave you with the next up and coming unit of measure. The terabyte (TB) is coming and it's 1000GB. It's going to make your iPhone go the way of the Atari.
Think again.
A long time ago-in a galaxy far, far, away, people thought they had the greatest video game system ever. The year was 1977. While that may sound like the age of the dinosaur for those of you who can't remember life without texting or cell phones, it's not really that long ago. As a matter of fact, statistically speaking, you'll probably live longer than 2 billion seconds or over twice that amount of time.
Anyways, in 1977, the first successful home video game systems came into play. (I know some of you can't imagine life without video games, but people did survive.) The first widely available video game system was the Atari (later to be called the Atari 2600). The Atari was out long before any of the Playstations, Nintendos, or XBoxes. If you don't know what I'm talking about, look up "Atari" sometime when you're not texting inequalities on your phone. (Example: Dude, 1<3 Don't Stop Believing - it's my favorite song on my iPod- it is so da bomb).
You may ask, "Why would I care about 1977? That's like, last century." Well, stick with me young Jedi for you have a lot to learn. (-not only did the Atari come out in 1977, but Star Wars did as well.)
Ok, so why was the Atari so revolutionary (even if it was 1977)? I'm glad you asked.
The Atari cartridge was revolutionary because it had 4K of memory. That's 4,000 bytes (actually 4,096, but we're going with 4,000). Remember from typing class that 1 character equals about one byte. For 1977 that was pretty amazing. For 2009, that's pretty lame because the basic iPhone has 4GB of memory.
So the PSSA style question is: "How many Atari cartridges would fit on an iPhone?"
A. A whole lot. (or ITL)
B. IDK. (otherwise known as ITL)
C. I'm not quite sure, but 1 <3 learning so let's figure it out.
D. Don't select this choice, it's just on here to be a distraction. (or ITL to read and eliminate this choice)
I hope you chose "C."
First of all some background information: (this would be on a formula sheet, padawan)
1K = 1000 bytes
1MB = 1000K
1GB = 1000MB
Now to use the force (i.e. math) to figure things out: (note the ..... are just placeholders because Mathman stinks at page formatting in html.)
1 cartridge..... C cartridges
--------------- = ------------
4 K............... 1000K
Solving for C (by using cross products and proportions) gives us:
1*1000=1000
1000/4=250 cartridges in 1000K (or 1MB)
Now,
250 cartridges..... N cartridges
------------------- = ---------------
1 MB ................ 1000 MB
Solving for N gives,
250*1000=250000
250000/1=250000 cartridges in 1000MB (or 1GB)
Since the iPhone we're comparing to is 4GB, that would hold 250,000*4 = 1,000,000 Atari cartridges.
Big deal, you say, the iPhone I want is still the greatest thing EVER.
For now.
Let me leave you with the next up and coming unit of measure. The terabyte (TB) is coming and it's 1000GB. It's going to make your iPhone go the way of the Atari.
Tuesday, March 3, 2009
Stop Me if You've Heard This One Before
Here's a joke for you:
Bill Gates walks into a room and everyone becomes a millionaire, on average.
Hilarious, huh?
I see the mail piling up right now: "Dear Mathman. I don't get the joke." or "Dear Mathman, it's too hard to understand that joke." or even, "Dear Mathman, that's a dumb joke. Pencil tapping is waaayyy cooler." (maybe if you're actually really good at pencil tapping)
Well, it isn't a dumb joke, because you have to understand the three M's to get it. What are the three M's you ask. Is that, like, 150% better than Eminem? (most certainly). Do they melt in your mouth, not in your hands? (It does take a long time in the microwave to melt the candy shell, but that's a story for another time.)
The three M's are measures of central tendency, or the mean, median, and mode. Measures of central tendency (the three M's), refer to "average". Most people get the mode. That was a bit of a joke in itself as mode refers to the most frequent data values in a set. That doesn't help us much with the Bill Gates joke since he's probably the only one person in the room with enough money to buy a planet.
The median refers to the middle value of a data set. Once again, since Mr. Gates is only one data value, one person with no money in their pockets would cancel his cash right out.
That leaves mean as being the only hope to make this joke funny. Never underestimate the power of an outlier. A quicky wiki left me with Bill being worth somewhere around $58 billion in 2008. That's $58,000,000,000 in standard notation or 5.8 x 10 to the 10th power dollars. Do you realize how big that is? That's 58,000 groups of $1,000,000 each. That's enough cash to pay someone (who's awesome at it) to pencil tap for you while you do your math homework.
Since it takes $1,000,000 to be a millionaire, Bill Gates could offset 57,999 other people in the room who wouldn't even have enough money to buy their own pencil to tap and pull the mean to $1,000,000 a piece. That would buy a whole lot of pencils for each person so they could stop absconding them from Mr. Krack's pencil box.
Here's the definiton for mean:
sum of all the values
--------------------------- = mean
total number of entries
In our case:
$58,000,000,000
------------------------ = $1,000,000
58,000
Just to put that in perspective: Heinz Field seats 64,000 people. That means we'd need 64,000-58,000 = 6,000 more millions of dollars to make everyone in Heinz Field (on average) a millionaire. That amount of money we'd need to spread over 63,999 people is 6,000 x $1,000,000 = $6,000,000,000. So the average amount those (other than Bill Gates) 63,999 people would need is $6,000,000,000 / 63,999 = $93,751.46. I'm taking a guess here that most people don't have this much money kicking around. (Personally, I am good for the $.46 of my share.)
To me that makes this problem even more interesting since Bill himself could cover 58,000 out of the 64,000 people in the stadium and most likely we still wouldn't be able to make everyone in the stadium millionaires since we wouldn't have enough money.
One man has the capability to make the "average" of:
58,000
----------- = 90.625%
64,000
of the population of Heinz Field millionaires, while the rest of us 63,999 people would have a hard time covering the remaining 9.375% of the money to raise the average of the population of Heinz Field to the status of millionaires.
Bill Gates walks into a room and everyone becomes a millionaire, on average.
Hilarious, huh?
I see the mail piling up right now: "Dear Mathman. I don't get the joke." or "Dear Mathman, it's too hard to understand that joke." or even, "Dear Mathman, that's a dumb joke. Pencil tapping is waaayyy cooler." (maybe if you're actually really good at pencil tapping)
Well, it isn't a dumb joke, because you have to understand the three M's to get it. What are the three M's you ask. Is that, like, 150% better than Eminem? (most certainly). Do they melt in your mouth, not in your hands? (It does take a long time in the microwave to melt the candy shell, but that's a story for another time.)
The three M's are measures of central tendency, or the mean, median, and mode. Measures of central tendency (the three M's), refer to "average". Most people get the mode. That was a bit of a joke in itself as mode refers to the most frequent data values in a set. That doesn't help us much with the Bill Gates joke since he's probably the only one person in the room with enough money to buy a planet.
The median refers to the middle value of a data set. Once again, since Mr. Gates is only one data value, one person with no money in their pockets would cancel his cash right out.
That leaves mean as being the only hope to make this joke funny. Never underestimate the power of an outlier. A quicky wiki left me with Bill being worth somewhere around $58 billion in 2008. That's $58,000,000,000 in standard notation or 5.8 x 10 to the 10th power dollars. Do you realize how big that is? That's 58,000 groups of $1,000,000 each. That's enough cash to pay someone (who's awesome at it) to pencil tap for you while you do your math homework.
Since it takes $1,000,000 to be a millionaire, Bill Gates could offset 57,999 other people in the room who wouldn't even have enough money to buy their own pencil to tap and pull the mean to $1,000,000 a piece. That would buy a whole lot of pencils for each person so they could stop absconding them from Mr. Krack's pencil box.
Here's the definiton for mean:
sum of all the values
--------------------------- = mean
total number of entries
In our case:
$58,000,000,000
------------------------ = $1,000,000
58,000
Just to put that in perspective: Heinz Field seats 64,000 people. That means we'd need 64,000-58,000 = 6,000 more millions of dollars to make everyone in Heinz Field (on average) a millionaire. That amount of money we'd need to spread over 63,999 people is 6,000 x $1,000,000 = $6,000,000,000. So the average amount those (other than Bill Gates) 63,999 people would need is $6,000,000,000 / 63,999 = $93,751.46. I'm taking a guess here that most people don't have this much money kicking around. (Personally, I am good for the $.46 of my share.)
To me that makes this problem even more interesting since Bill himself could cover 58,000 out of the 64,000 people in the stadium and most likely we still wouldn't be able to make everyone in the stadium millionaires since we wouldn't have enough money.
One man has the capability to make the "average" of:
58,000
----------- = 90.625%
64,000
of the population of Heinz Field millionaires, while the rest of us 63,999 people would have a hard time covering the remaining 9.375% of the money to raise the average of the population of Heinz Field to the status of millionaires.
Friday, February 27, 2009
Possibilities vs. Probabilities
Citizens of the Junior High: The PSSAs are coming soon. That can only mean one thing:
Free breakfast.
You've probably heard the saying, "There's no such thing as a free lunch." Well, that's because there are way too many possibilities for breakfast.
Lets's consider the options you had for choosing your breakfast: Orange or apple juice (much to the dismay of Mathman, espresso isn't one of the options here) and a breakfast item of a Cocoa Puffs cereal bar, Trix cereal bar, cinnamon sugar donut, apple, banana, or the ubiquitous "Honey Bun".
If we were to quickly calculate the possibilities for the number of breakfasts we'd have:
Orange juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"
Apple juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"
So there are 12 possibilities for breakfast.
There's a simpler way of finding out how many ways to choose breakfast. Think about it 2 ways for juice, 6 breakfast items = 12 possibilities.
2 and 6 to get 12. Multiplication must be the secret operation.
Now, we can also consider that picking a juice doesn't effect the choice of a menu item. So choosing a juice and a breakfast item are independent events.
Now that we have considered the possibilities, let's consider the probability of choosing a particular breakfast. Let's look for P(apple juice, Trix cereal bar). The P() stands for probability of what's in the (). The P(apple juice, Trix cereal bar) is 1 result of 12 possibilities or a 1/12 chance. We could also get here by taking the P(apple juice)= 1/2 and P(Trix cereal bar) = 1/6. Once again, use the secret operation of multiply to get 1/12.
So the odds of getting Mathman's favorite breakfast of espresso and chocolate chip and banana pancakes is P(espresso, banana pancakes) = 0*0 = 0 since the P(espresso)=0 and the P(banana pancakes)=0.
Let's end on a positive note: the P(staying radical)= 1 or 100%. That's the only way to be.
Free breakfast.
You've probably heard the saying, "There's no such thing as a free lunch." Well, that's because there are way too many possibilities for breakfast.
Lets's consider the options you had for choosing your breakfast: Orange or apple juice (much to the dismay of Mathman, espresso isn't one of the options here) and a breakfast item of a Cocoa Puffs cereal bar, Trix cereal bar, cinnamon sugar donut, apple, banana, or the ubiquitous "Honey Bun".
If we were to quickly calculate the possibilities for the number of breakfasts we'd have:
Orange juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"
Apple juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"
So there are 12 possibilities for breakfast.
There's a simpler way of finding out how many ways to choose breakfast. Think about it 2 ways for juice, 6 breakfast items = 12 possibilities.
2 and 6 to get 12. Multiplication must be the secret operation.
Now, we can also consider that picking a juice doesn't effect the choice of a menu item. So choosing a juice and a breakfast item are independent events.
Now that we have considered the possibilities, let's consider the probability of choosing a particular breakfast. Let's look for P(apple juice, Trix cereal bar). The P() stands for probability of what's in the (). The P(apple juice, Trix cereal bar) is 1 result of 12 possibilities or a 1/12 chance. We could also get here by taking the P(apple juice)= 1/2 and P(Trix cereal bar) = 1/6. Once again, use the secret operation of multiply to get 1/12.
So the odds of getting Mathman's favorite breakfast of espresso and chocolate chip and banana pancakes is P(espresso, banana pancakes) = 0*0 = 0 since the P(espresso)=0 and the P(banana pancakes)=0.
Let's end on a positive note: the P(staying radical)= 1 or 100%. That's the only way to be.
Thursday, February 26, 2009
It's All in the Merchandising
Introducing our new weapon in the fight against ignorance:
Welcome the Algebratz.
I've read the PSSA manuals. I see nothing against using the Algebratz.
Welcome the Algebratz.
I've read the PSSA manuals. I see nothing against using the Algebratz.
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