Continuing finger arithmetic from Part Six. This one is called Part Seven. It is the eighth part in the series.
Ten's Compliments. Back in Part Six, we added 7 + 8. We set 7, and added 8 by adding 3 then 5. Adding 3 involved a carry, generating an addition of 5 while remembering that we still have to add 5. Very complicated. This Ten's Compliments idea reduces the steps, and having to remember upcoming steps. It is similar to Five's Complements, introduced in Part Three.
The Ten's Compliment of a number is the number you add to get ten. For now, we'll only use the Ten's Compliment of numbers greater than five. So, the Ten's Compliment of six is four. The Ten's Compliment of seven is three. The Ten's Compliment of eight is two. And the Ten's Compliment of nine is one.
So how does this help? Let's return to the dreaded seven plus eight example. Start with two fists, then set two right hand fingers and the thumb. You'd like to add eight, which is five plus three, but you don't have three to add. Eight is ten minus two (the Ten's Compliment of eight is two). Subtract the Ten's Complement, which is done by subtracting both right fingers. Then add ten by adding a finger to the left hand. Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers). Again, we added 7 + 8, which is 7 - 2 + 10.
How about six plus seven from the last lesson? You do this the same way it was done in the previous lesson. When you have six set, you don't have three fingers to subtract, and you do have two fingers to add. The way it works is that you always have exactly one of these options.
The relevant examples are 6 + 9, 7 + 9, 8 + 9, 9 + 9, 7 + 8, 8 + 8, 9 + 8, 8 + 7, 9 + 7, 9 + 6.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This is the same link as in the previous lesson.
Technically, we really introduced the Ten's Compliment of five, which is five in Part Five. It wasn't called that, and it just seems simpler to treat it as a special case.
Stay tuned for the introduction of two digit addition.
Friday, June 30, 2006
Tuesday, June 27, 2006
Finger Arithmetic Part Six
Continuing finger arithmetic from Part Five. This one is called Part Six. It is the seventh part in the series.
Single Digit Addition. No new concepts. That's not really true. We're going to combine previous concepts to handle more complicated carries. You'll need to be able to do this eventually, but these examples will be simplified in the next lesson.
We'll start with an easy example: six plus seven. Start with two fists. Set six by adding a finger and the thumb to the right hand. Seven is two plus five. Add the two of the seven by adding two fingers. You want to add the thumb, but the thumb is already set. So subtract five (the thumb) and add ten (a finger on the left hand). Read the answer: thirteen.
Let's add eight plus nine. Two fists, then set three fingers and the thumb on the right hand. Nine is five plus four. You want to add the four, but you don't have four fingers to add. So, you subtract the Five's Complement of four, which is one. You want to add the five (from the Five's Complement), but you already have that set. So, you must subtract five (the thumb) and add ten (a finger on the left hand). Then, you must go back and add the five from the nine. So add the right thumb. Read the result: seventeen.
Now, let's do the really hard one. That's right, the dreaded seven plus eight. Start with two fists, then set the two right hand fingers and the thumb. Eight is three plus one. You want to add three, but can't, so you subtract the Five's Complement of three, which is two - which is done by subtracting both right fingers. You want to add five, but already have a thumb set. So, you subtract five (the thumb) and add ten (a finger on the left hand). Now you need to go back and add the five from eight (the right thumb). Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers).
At this point, you can add any two single digit numbers. There are a few examples to try below. But none of the books have enough examples. Since you can't have too many examples, you are referred to an example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. Bookmark the link.
Single Digit Addition. No new concepts. That's not really true. We're going to combine previous concepts to handle more complicated carries. You'll need to be able to do this eventually, but these examples will be simplified in the next lesson.
We'll start with an easy example: six plus seven. Start with two fists. Set six by adding a finger and the thumb to the right hand. Seven is two plus five. Add the two of the seven by adding two fingers. You want to add the thumb, but the thumb is already set. So subtract five (the thumb) and add ten (a finger on the left hand). Read the answer: thirteen.
Let's add eight plus nine. Two fists, then set three fingers and the thumb on the right hand. Nine is five plus four. You want to add the four, but you don't have four fingers to add. So, you subtract the Five's Complement of four, which is one. You want to add the five (from the Five's Complement), but you already have that set. So, you must subtract five (the thumb) and add ten (a finger on the left hand). Then, you must go back and add the five from the nine. So add the right thumb. Read the result: seventeen.
Now, let's do the really hard one. That's right, the dreaded seven plus eight. Start with two fists, then set the two right hand fingers and the thumb. Eight is three plus one. You want to add three, but can't, so you subtract the Five's Complement of three, which is two - which is done by subtracting both right fingers. You want to add five, but already have a thumb set. So, you subtract five (the thumb) and add ten (a finger on the left hand). Now you need to go back and add the five from eight (the right thumb). Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers).
At this point, you can add any two single digit numbers. There are a few examples to try below. But none of the books have enough examples. Since you can't have too many examples, you are referred to an example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. Bookmark the link.
| 6 + 4 10 | 3 + 3 6 | 4 + 6 10 | 8 + 5 13 | 4 + 8 12 | |||||||||||||||
| 9 + 8 17 | 6 + 2 8 | 7 + 8 15 | 4 + 3 7 | 5 + 8 13 | |||||||||||||||
| 1 + 5 6 | 7 + 9 16 | 3 + 6 9 | 6 + 1 7 | 5 + 6 11 | |||||||||||||||
Wednesday, June 21, 2006
Charter School
I went to public schools through high school. I was offered the chance to go to a private high school, but turned it down. I could only see disadvantages. I wasn't interested enough to investigate the alternative.
I did OK at public school, though i can't say i was very enthusiastic. One day at home, my Dad asked me for my report card. I remembered using it as a bookmark, and went to fetch it. My Dad looked at it, then said that he'd have rather seen it than read about it in the newspaper - the honor roll. Why was that news? I was always on the honor roll. I said i'd try to show him the report card, but knew that i had so little interest in it that it would likely slip my mind.
The pace at school was slow, but i didn't mind - i was patient. Teachers saw i was bored, and gave me extra stuff to do. It did not bother me that i didn't get any credit for it. It wasn't enough. I bought a computer (in 1975, about as powerful as your watch) and taught myself machine language programming. I picked up a Japanese abacus (Soroban) and taught myself mental arithmetic. After three months, I computed a 10 digit sin(x) in my head using Taylor series. I was the only junior in the new high school calculus course.
But i would have done OK anywhere. I probably wasn't an average child after all. But where could i have excelled?
My son is in a charter school, and just finished 3rd grade. You get to go to a charter school if a parent fills out the forms and the school isn't already full.
He doesn't just get it like i did. And he won't stick with it forever like i would. So his mom and i help him out every day, and all weekend, and all summer. When the teacher calls one of us, we take it very seriously. I've gotten him through addition and subtraction. It took four years, but i've gotten him to read for enjoyment (meaning all the time). I've helped him with fractions and concepts of perimeter and area. We quiz him relentlessly on spelling, social studies and Spanish. His Mom has been, uhm, instrumental in getting him to be without peer on violin and piano.
The charter school has parents who care about their kids. After dropping their kids to the school in the morning, they'll often have discussions about school for an hour or so. I can't imagine that there is a single parent there who doesn't return a teacher's phone call right away.
I was very excited about this school after a 'parents day'. I got an appointment to sit in on a class for an hour, while my son was still in preschool. The teacher read a story to the kids, who all sat quietly in rapt attention. Even my son. Then, the kids each got out a rug, and some materials, and sat for at least twenty minutes working with them. Even my son. One child came over to the table i was sitting at. Soon a teacher came over and also sat down. The child began reading a book, out loud, fluently. It had to be 2nd grade level or better. But this was preschool.
OK, so when i was in 1st grade, i could read that well, probably better. But i was not encouraged to do so. No one else was doing it. We could pick any book out of the school's library to read, but they kept shepherding me to the See Jack Run section. So i read my older brother's books at home. Things happened in those books. You know, like real stories. At my son's charter school, it's OK to excel. This is Very exciting.
I did OK at public school, though i can't say i was very enthusiastic. One day at home, my Dad asked me for my report card. I remembered using it as a bookmark, and went to fetch it. My Dad looked at it, then said that he'd have rather seen it than read about it in the newspaper - the honor roll. Why was that news? I was always on the honor roll. I said i'd try to show him the report card, but knew that i had so little interest in it that it would likely slip my mind.
The pace at school was slow, but i didn't mind - i was patient. Teachers saw i was bored, and gave me extra stuff to do. It did not bother me that i didn't get any credit for it. It wasn't enough. I bought a computer (in 1975, about as powerful as your watch) and taught myself machine language programming. I picked up a Japanese abacus (Soroban) and taught myself mental arithmetic. After three months, I computed a 10 digit sin(x) in my head using Taylor series. I was the only junior in the new high school calculus course.
But i would have done OK anywhere. I probably wasn't an average child after all. But where could i have excelled?
My son is in a charter school, and just finished 3rd grade. You get to go to a charter school if a parent fills out the forms and the school isn't already full.
He doesn't just get it like i did. And he won't stick with it forever like i would. So his mom and i help him out every day, and all weekend, and all summer. When the teacher calls one of us, we take it very seriously. I've gotten him through addition and subtraction. It took four years, but i've gotten him to read for enjoyment (meaning all the time). I've helped him with fractions and concepts of perimeter and area. We quiz him relentlessly on spelling, social studies and Spanish. His Mom has been, uhm, instrumental in getting him to be without peer on violin and piano.
The charter school has parents who care about their kids. After dropping their kids to the school in the morning, they'll often have discussions about school for an hour or so. I can't imagine that there is a single parent there who doesn't return a teacher's phone call right away.
I was very excited about this school after a 'parents day'. I got an appointment to sit in on a class for an hour, while my son was still in preschool. The teacher read a story to the kids, who all sat quietly in rapt attention. Even my son. Then, the kids each got out a rug, and some materials, and sat for at least twenty minutes working with them. Even my son. One child came over to the table i was sitting at. Soon a teacher came over and also sat down. The child began reading a book, out loud, fluently. It had to be 2nd grade level or better. But this was preschool.
OK, so when i was in 1st grade, i could read that well, probably better. But i was not encouraged to do so. No one else was doing it. We could pick any book out of the school's library to read, but they kept shepherding me to the See Jack Run section. So i read my older brother's books at home. Things happened in those books. You know, like real stories. At my son's charter school, it's OK to excel. This is Very exciting.
Tuesday, June 20, 2006
Finger Arithmetic Part Five
Continuing finger arithmetic from Part Four. This one is called Part Five. It is the sixth part in the series.
In Part Three, we introduced the idea that sometimes you want to add something, but you have no fingers left to add. This part does that for the thumb. Here, we add five when the thumb is already set.
The first example is adding seven plus five. First, set seven. Do that by starting with a fist on both hands, adding two fingers to the right hand, then adding the right thumb. Now we want to add five. You want to add a right thumb, but your right thumb is already set. To do this, remember that 5 + 5 is the same as 5 + (10 - 5), which is rearranged as 5 - 5 + 10. Still have zero / seven on your hands? Good. Subtract five by tucking the right thumb down. Add ten by adding a finger to the left hand. Look at your hands. Read twelve.
The next example is adding six and five. First start with both fists. Set six on the right hand by adding a finger and thumb. Add five by subtracting the right thumb, and adding a finger on the left hand. Read the result: eleven.
The final example is adding nine and five. Start with both fists. Add all fingers and thumb on the right hand for nine. Subtract the right thumb and add a finger on the left hand. Read fourteen.
All examples: 5 + 5, 6 + 5, 7 + 5, 8 + 5, 9 + 5.
During the week, go over the previous lesson's examples. Stick to short practices every day. You don't have to do all the examples from all the lessons in one go. But you should sneak in all the examples for all the lessons over the course of the week. And every day should have this newest lesson.
The next lesson will get you started on single digit addition. It won't be the last word there, however. It seems that there is always something more to say.
In Part Three, we introduced the idea that sometimes you want to add something, but you have no fingers left to add. This part does that for the thumb. Here, we add five when the thumb is already set.
The first example is adding seven plus five. First, set seven. Do that by starting with a fist on both hands, adding two fingers to the right hand, then adding the right thumb. Now we want to add five. You want to add a right thumb, but your right thumb is already set. To do this, remember that 5 + 5 is the same as 5 + (10 - 5), which is rearranged as 5 - 5 + 10. Still have zero / seven on your hands? Good. Subtract five by tucking the right thumb down. Add ten by adding a finger to the left hand. Look at your hands. Read twelve.
The next example is adding six and five. First start with both fists. Set six on the right hand by adding a finger and thumb. Add five by subtracting the right thumb, and adding a finger on the left hand. Read the result: eleven.
The final example is adding nine and five. Start with both fists. Add all fingers and thumb on the right hand for nine. Subtract the right thumb and add a finger on the left hand. Read fourteen.
All examples: 5 + 5, 6 + 5, 7 + 5, 8 + 5, 9 + 5.
During the week, go over the previous lesson's examples. Stick to short practices every day. You don't have to do all the examples from all the lessons in one go. But you should sneak in all the examples for all the lessons over the course of the week. And every day should have this newest lesson.
The next lesson will get you started on single digit addition. It won't be the last word there, however. It seems that there is always something more to say.
Saturday, June 17, 2006
Finger Arithmetic Part Four
Continuing finger arithmetic from Part Three. This one is called Part Four. It is the fifth part in the series.
Bigger numbers are added to small numbers. It's an easy lesson that introduces thinking of bigger numbers as the sum of two smaller numbers. One of the smaller numbers is always five. In fact, when you set one of these numbers on a hand, the thumb is the five, and the fingers represent the other small number.
Let's say you have one, and want to add seven. For the moment, set seven on one hand. Make a fist. Add two fingers. Add the thumb. Seven is five plus two. So we can add these parts one at a time. Here are the steps. We're adding one plus seven. Set one by making a fist on the right hand, then add one finger. Add the 'two' of the seven by adding two fingers. Then add the five of the seven by adding the thumb. Read the answer. Uhm, let's see. There's a thumb. There are three fingers. That's eight.
Now we'll add three plus six. Set three by making a fist and adding three fingers. Six is five plus one. Add one by adding a finger. Add five by adding a thumb. Read the answer. Nine.
Try two plus seven. Set two. Add the two. Add the five. Read the result (nine). You did say it out loud, right?
Three plus five. Make a fist. Add three fingers. Add the thumb.
All of the examples: 0 + 5, 0 + 6, 0 + 7, 0 + 8, 0 + 9, 1 + 5, 1 + 6, 1 + 7, 1 + 8, 2 + 5, 2 + 6, 2 + 7, 3 + 5, 3 + 6, 4 + 5. Try them all.
Keep practicing Part Three during the week. It takes a bit for the Five's Complements to stick in your head. We'll need to expand on this idea soon. We're trying to keep it down to one new idea a week. However, you need to remember all the old lessons to get it all together.
Bigger numbers are added to small numbers. It's an easy lesson that introduces thinking of bigger numbers as the sum of two smaller numbers. One of the smaller numbers is always five. In fact, when you set one of these numbers on a hand, the thumb is the five, and the fingers represent the other small number.
Let's say you have one, and want to add seven. For the moment, set seven on one hand. Make a fist. Add two fingers. Add the thumb. Seven is five plus two. So we can add these parts one at a time. Here are the steps. We're adding one plus seven. Set one by making a fist on the right hand, then add one finger. Add the 'two' of the seven by adding two fingers. Then add the five of the seven by adding the thumb. Read the answer. Uhm, let's see. There's a thumb. There are three fingers. That's eight.
Now we'll add three plus six. Set three by making a fist and adding three fingers. Six is five plus one. Add one by adding a finger. Add five by adding a thumb. Read the answer. Nine.
Try two plus seven. Set two. Add the two. Add the five. Read the result (nine). You did say it out loud, right?
Three plus five. Make a fist. Add three fingers. Add the thumb.
All of the examples: 0 + 5, 0 + 6, 0 + 7, 0 + 8, 0 + 9, 1 + 5, 1 + 6, 1 + 7, 1 + 8, 2 + 5, 2 + 6, 2 + 7, 3 + 5, 3 + 6, 4 + 5. Try them all.
Keep practicing Part Three during the week. It takes a bit for the Five's Complements to stick in your head. We'll need to expand on this idea soon. We're trying to keep it down to one new idea a week. However, you need to remember all the old lessons to get it all together.
Friday, June 16, 2006
Make Mine a Double
Yesterday, i had a headache. It's a rare thing for me. I asked around at the office, and someone had some Motrin. It did the trick. In retrospect, it is possible i just needed a drink of water. Next time, i'm going to try the new double strength placebo.
Thursday, June 15, 2006
Phone Cord
I've run a research project to determine the answer to a question burning in the hearts of many: What is the minimum number of strings or ropes or cords that it takes to create a tangled spaghetti mess?
The answer appears to be one.
And you may have evidence of this within a small number of inches from where you sit. Look at the nearest phone cord. If it is anything like mine, it is a tangled mess. Every few days, i take the phone off the hook, dangle it by the cord, and let it unwind. Despite low use, and always putting it down without twisting it once, the cord is basically always a twisted mess.
But not at home. It's a cordless phone there.
I had to look up the spelling in a dictionary. Apparently, a phone chord is some sort of musical idea. It's an idea that rings a Bell.
The answer appears to be one.
And you may have evidence of this within a small number of inches from where you sit. Look at the nearest phone cord. If it is anything like mine, it is a tangled mess. Every few days, i take the phone off the hook, dangle it by the cord, and let it unwind. Despite low use, and always putting it down without twisting it once, the cord is basically always a twisted mess.
But not at home. It's a cordless phone there.
I had to look up the spelling in a dictionary. Apparently, a phone chord is some sort of musical idea. It's an idea that rings a Bell.
Wednesday, June 14, 2006
Caffeine
A few years ago, i developed arthritis in my shoulders. Call it bursitis. I could not raise my right arm higher than level. Cured, but now years later, i still reach for high shelf items with my left arm.
I was cured by stopping my intake of caffeine. I used to drink nearly a half gallon of Mt. Dew a day, though not on weekends. As my symptoms got worse, i noticed that it wasn't as bad on Sunday night as the rest of the week. As an experiment, i switched to Sprite and things improved. A month later, i had a cup of coffee, and it hurt for four days. No doubt about it. Caffeine. After ten months of abstinence, my symptoms rapidly vanished. Caffeine is a very stable chemical.
I asked around, and even doctors told me that there was no connection. Feh. Eventually i learned that caffeine can interfere with the body's intake of calcium. Now, the joints are affected first. Then the bones. So, i wondered if caffeine was big in osteoporosis.
It International Osteoporosis Foundation recently held a big congress (convention). Lots of risk factors for osteoporosis were enumerated. Their web site has a page on prevention. Caffeine is mentioned once, along with salt. You could easily miss it. At least it's mentioned.
The thing is, when i've talked to people at risk for osteoporosis, like older women, they can't imagine giving up caffeine. They say that they drink decaf, but they have no idea how much caffeine is in it. And, it can vary by a factor of ten. And, products with caffeine don't have to say how much is in it. And, i'm pretty smart, but i have no idea how to perform a test to find out. I got through high school chemistry (with an A), but haven't had much since.
Caffeine is addictive. It's subtle. It won't let go of you, even after years of abstinence. The effects appear to be cumulative.
So i had this problem with my right foot. I thought my shoes were causing discomfort. I thought it was the way i was walking. But now i know that it is just taking longer to heal than other parts of my body. It's arthritis.
I was cured by stopping my intake of caffeine. I used to drink nearly a half gallon of Mt. Dew a day, though not on weekends. As my symptoms got worse, i noticed that it wasn't as bad on Sunday night as the rest of the week. As an experiment, i switched to Sprite and things improved. A month later, i had a cup of coffee, and it hurt for four days. No doubt about it. Caffeine. After ten months of abstinence, my symptoms rapidly vanished. Caffeine is a very stable chemical.
I asked around, and even doctors told me that there was no connection. Feh. Eventually i learned that caffeine can interfere with the body's intake of calcium. Now, the joints are affected first. Then the bones. So, i wondered if caffeine was big in osteoporosis.
It International Osteoporosis Foundation recently held a big congress (convention). Lots of risk factors for osteoporosis were enumerated. Their web site has a page on prevention. Caffeine is mentioned once, along with salt. You could easily miss it. At least it's mentioned.
The thing is, when i've talked to people at risk for osteoporosis, like older women, they can't imagine giving up caffeine. They say that they drink decaf, but they have no idea how much caffeine is in it. And, it can vary by a factor of ten. And, products with caffeine don't have to say how much is in it. And, i'm pretty smart, but i have no idea how to perform a test to find out. I got through high school chemistry (with an A), but haven't had much since.
Caffeine is addictive. It's subtle. It won't let go of you, even after years of abstinence. The effects appear to be cumulative.
So i had this problem with my right foot. I thought my shoes were causing discomfort. I thought it was the way i was walking. But now i know that it is just taking longer to heal than other parts of my body. It's arthritis.
Tuesday, June 13, 2006
Finger Arithmetic Part Three
Continuing finger arithmetic from Part Two. This one is called Part Three. It is the forth part in the series. Five's Complements are introduced. Clear as mud? Let's get started!
The Five's Complement of a number is the number you add to get five. So, the Five's Complement of one is four. That's because one plus four is five. Likewise, the Five's Complement of four is one. The other pair is two and three. The Five's Complement of two is three. Two plus three is five. And the Five's Complement of three is two.
Armed with this new knowledge, we tackle adding slightly bigger numbers. The very first example is 3 + 3. Start with a fist on the right hand. Put up three fingers. You want to add three fingers, but you don't have three fingers that can be added. The idea is to add five, and subtract the Five's Complement of three - which is two. So 3 + 3 = 3 + 5 - 2. However, do it in this order: 3 - 2 + 5. You have three fingers up on your right hand. Subtract two fingers, and add the thumb (five). That leaves you with your thumb (five) and one finger (one), for a total of six. Say six out loud.
The reason that the subtraction should be done first will become apparent in a later lesson. That lesson involves carries from one hand to the other. By performing the steps in this order, you can avoid ever having more than one pending operation. It is less confusing, and more reliable. Handling carries is the single biggest reason for error in traditional pencil and paper arithmetic.
Another example: 4 + 2. Start with a fist and set four fingers. The Five's Complement of two is three. So subtract three fingers. Then add the thumb for five. Read the answer out loud. Six.
Another example: 2 + 3. Start with a fist and set two fingers. The Five's Complement of three is two. Subtract two fingers and add the thumb (five). Read the answer: five. Note that you have no fingers up - just the thumb. You have five (the thumb) plus zero (no fingers). Zero is very important. Zero may mean nothing, but it isn't meaningless.
All of the examples: 1 + 4, 2 + 3, 2 + 4, 3 + 2, 3 + 3, 3 + 4, 4 + 1, 4 + 2, 4 + 3 and 4 + 4. Try them all. Don't forget to read the answer out loud.
When you are done with this lesson, practice some of the examples from previous lessons. Add small numbers. Do some counting. Remember to read the answers out loud. Practice five minutes a day. Five minutes each day for a week is worth more than twenty minutes each day for two days. And, five minutes can be squeezed into just about any schedule.
The Five's Complement of a number is the number you add to get five. So, the Five's Complement of one is four. That's because one plus four is five. Likewise, the Five's Complement of four is one. The other pair is two and three. The Five's Complement of two is three. Two plus three is five. And the Five's Complement of three is two.
Armed with this new knowledge, we tackle adding slightly bigger numbers. The very first example is 3 + 3. Start with a fist on the right hand. Put up three fingers. You want to add three fingers, but you don't have three fingers that can be added. The idea is to add five, and subtract the Five's Complement of three - which is two. So 3 + 3 = 3 + 5 - 2. However, do it in this order: 3 - 2 + 5. You have three fingers up on your right hand. Subtract two fingers, and add the thumb (five). That leaves you with your thumb (five) and one finger (one), for a total of six. Say six out loud.
The reason that the subtraction should be done first will become apparent in a later lesson. That lesson involves carries from one hand to the other. By performing the steps in this order, you can avoid ever having more than one pending operation. It is less confusing, and more reliable. Handling carries is the single biggest reason for error in traditional pencil and paper arithmetic.
Another example: 4 + 2. Start with a fist and set four fingers. The Five's Complement of two is three. So subtract three fingers. Then add the thumb for five. Read the answer out loud. Six.
Another example: 2 + 3. Start with a fist and set two fingers. The Five's Complement of three is two. Subtract two fingers and add the thumb (five). Read the answer: five. Note that you have no fingers up - just the thumb. You have five (the thumb) plus zero (no fingers). Zero is very important. Zero may mean nothing, but it isn't meaningless.
All of the examples: 1 + 4, 2 + 3, 2 + 4, 3 + 2, 3 + 3, 3 + 4, 4 + 1, 4 + 2, 4 + 3 and 4 + 4. Try them all. Don't forget to read the answer out loud.
When you are done with this lesson, practice some of the examples from previous lessons. Add small numbers. Do some counting. Remember to read the answers out loud. Practice five minutes a day. Five minutes each day for a week is worth more than twenty minutes each day for two days. And, five minutes can be squeezed into just about any schedule.
Tuesday, June 06, 2006
Finger Arithmetic Part Two
Continuing finger arithmetic from Part One. This third part is called Part Two. We start addition. It may seem as if the lesson moves slowly. Take your time. The harder stuff builds on this easy stuff.
First, we'll add one and one. Start with a fist on your right hand. Put out a finger to represent one. Add another finger. Read the answer out loud: two.
You might think we've already covered this. And you'd be right. We have added one repeatedly in order to count. In some sense, this is nothing new.
Next example. Add one plus two. Start with a fist on your right hand. Put out a finger to set one. Add two fingers to it. Read the answer out loud: three.
Next example. Add two plus two. Start with a fist on your right had. Put two fingers out to set two. Add two fingers to it. Read the answer out loud: four.
The whole set of possible examples here are: 0 + 1, 0 + 2, 0 + 3, 0 + 4, 1 + 1, 1 + 2, 1 + 3, 2 + 2, 3 + 1. Practice these all week.
Extra credit. Add ten plus twenty. Start with a fist on your left hand. Put out a finger to set ten. Add two fingers to it. Read the answer out loud: thirty.
That's small number addition. Remember to practice the drills every day. Don't forget to bring your fingers with you, everywhere. Do you have five minutes? What are you waiting for?
First, we'll add one and one. Start with a fist on your right hand. Put out a finger to represent one. Add another finger. Read the answer out loud: two.
You might think we've already covered this. And you'd be right. We have added one repeatedly in order to count. In some sense, this is nothing new.
Next example. Add one plus two. Start with a fist on your right hand. Put out a finger to set one. Add two fingers to it. Read the answer out loud: three.
Next example. Add two plus two. Start with a fist on your right had. Put two fingers out to set two. Add two fingers to it. Read the answer out loud: four.
The whole set of possible examples here are: 0 + 1, 0 + 2, 0 + 3, 0 + 4, 1 + 1, 1 + 2, 1 + 3, 2 + 2, 3 + 1. Practice these all week.
Extra credit. Add ten plus twenty. Start with a fist on your left hand. Put out a finger to set ten. Add two fingers to it. Read the answer out loud: thirty.
That's small number addition. Remember to practice the drills every day. Don't forget to bring your fingers with you, everywhere. Do you have five minutes? What are you waiting for?
Wednesday, May 31, 2006
Finger Arithmetic Part One of Many
Continuing finger arithmetic from part zero. The second part is called part one. Just as the century with the years numbered mostly in the 1900's is called the twentieth century. What a nuisance. But thinking about these issues can prepare one to be capable of dealing with all sorts of off by one errors, such as fence post errors. And, zero is the most important number. Nothing is more important than all of mathematics. Nothing.
Each hand is one digit of a two digit number.
Your right hand is the one's digit. It can count from zero to nine. Your left hand is the ten's digit. It can count from zero to ninety, by tens. This isn't a left handed or right handed thing. It's just that when you look at Arabic numbers, the least significant digit is on the right.
Make a fist with both hands. That's zero (00). Say it.
Put up a finger on your left hand. Say 'ten'. Say it out loud.
Add another finger on your left hand. Say 'twenty'. Don't by shy.
Add another finger on your left hand. Say 'thirty'. I can't hear you.
Add another finger on your left hand. Say 'forty'. Shout if you must.
Make a fist with your left hand and stick out the thumb. Say 'fifty'. That's right. Your left thumb, all by itself, is the most valuable.
Add a finger to your left hand. Say 'sixty'. It is just as important to learn to read your hands as it is to get the movements right.
Add a finger to your left hand. Say 'seventy'. If you can't read your fingers, why move them?
Add a finger to your left hand. Say 'eighty'.
Add a finger to your left hand. Say 'ninety'. That's that.
Now we'll represent some two digit numbers.
Set twenty nine. Start with zero - two fists. Stick out two fingers on the left hand. Stick out your right thumb and all four fingers. Say 'twenty nine'.
Add one. Since you have twenty nine you have to make a fist with the right hand and add a finger to the left hand. Say 'thirty'.
Set forty nine. Start with zero - two fists. Stick out four fingers on the left hand. Stick out your right thumb and all four fingers. Say 'forty nine'.
Add one. Since you have forty nine, you have to make a fist with the right hand, and add one to the left. Since you don't have one to add, make a fist and stick out your thumb. Say 'fifty'.
Now count from zero to nineteen. That's right, you start by counting from zero to nine on your right hand. Then you make a fist with the right hand and add one finger on your left hand, to get ten (10). With the left hand showing one finger, count to nine with your right hand. That's ten to nineteen. You were counting out loud, right?
More exercises. Count from zero to twenty. Count from forty to sixty. Count backwards from sixty to forty. You were counting out loud, right?
Extra credit: count by tens backwards from ninety to zero.
That's two digit counting. Remember to practice the drills every day. Don't forget to bring your fingers with you, everywhere. Do you have five minutes? What are you waiting for?
Another hint. If you have something to put your fingers on, like a table, or your knee, you can have a finger or thumb be active when it is touching. That way you don't have to look. Tactile feedback is a good thing. But remember not to get lazy and rest your hand - it messes up the current number.
An aside. I can count from zero to one thousand twenty three on my ten fingers. I don't find it handy. There are ten kinds of people in the world. Those that understand binary, and those that don't.
Each hand is one digit of a two digit number.
Your right hand is the one's digit. It can count from zero to nine. Your left hand is the ten's digit. It can count from zero to ninety, by tens. This isn't a left handed or right handed thing. It's just that when you look at Arabic numbers, the least significant digit is on the right.
Make a fist with both hands. That's zero (00). Say it.
Put up a finger on your left hand. Say 'ten'. Say it out loud.
Add another finger on your left hand. Say 'twenty'. Don't by shy.
Add another finger on your left hand. Say 'thirty'. I can't hear you.
Add another finger on your left hand. Say 'forty'. Shout if you must.
Make a fist with your left hand and stick out the thumb. Say 'fifty'. That's right. Your left thumb, all by itself, is the most valuable.
Add a finger to your left hand. Say 'sixty'. It is just as important to learn to read your hands as it is to get the movements right.
Add a finger to your left hand. Say 'seventy'. If you can't read your fingers, why move them?
Add a finger to your left hand. Say 'eighty'.
Add a finger to your left hand. Say 'ninety'. That's that.
Now we'll represent some two digit numbers.
Set twenty nine. Start with zero - two fists. Stick out two fingers on the left hand. Stick out your right thumb and all four fingers. Say 'twenty nine'.
Add one. Since you have twenty nine you have to make a fist with the right hand and add a finger to the left hand. Say 'thirty'.
Set forty nine. Start with zero - two fists. Stick out four fingers on the left hand. Stick out your right thumb and all four fingers. Say 'forty nine'.
Add one. Since you have forty nine, you have to make a fist with the right hand, and add one to the left. Since you don't have one to add, make a fist and stick out your thumb. Say 'fifty'.
Now count from zero to nineteen. That's right, you start by counting from zero to nine on your right hand. Then you make a fist with the right hand and add one finger on your left hand, to get ten (10). With the left hand showing one finger, count to nine with your right hand. That's ten to nineteen. You were counting out loud, right?
More exercises. Count from zero to twenty. Count from forty to sixty. Count backwards from sixty to forty. You were counting out loud, right?
Extra credit: count by tens backwards from ninety to zero.
That's two digit counting. Remember to practice the drills every day. Don't forget to bring your fingers with you, everywhere. Do you have five minutes? What are you waiting for?
Another hint. If you have something to put your fingers on, like a table, or your knee, you can have a finger or thumb be active when it is touching. That way you don't have to look. Tactile feedback is a good thing. But remember not to get lazy and rest your hand - it messes up the current number.
An aside. I can count from zero to one thousand twenty three on my ten fingers. I don't find it handy. There are ten kinds of people in the world. Those that understand binary, and those that don't.
Monday, May 22, 2006
Counting On Your Fingers - arithmetic part zero of several
An Anonymous reader asked about teaching children how to add on their fingers. Adding and subtracting on one's fingers undisciplined can lead to off by one errors - in either direction. This leads to a reliability (getting the right answer) of less than 33%. In the world of math, off by one is as good as off by a million - it is just as wrong. The student is discouraged, then afraid of failure. No wonder we're so bad at math. One of my high school peers walked out of the SAT exams unfinished. It was so sad. Not a damned thing to do about it then. Maybe this will help now.
Correcting simple counting isn't anything magic, it's just being careful. I won't attempt a description. What follows is a description of a technique with the power of rocket science, brought down to the simplicity of a kindergartener. It isn't dumbed down. Instead, it is broken up into consumable chunks for the student. The goal is seven second lessons. Each post is a lesson. I won't go further than partial differential equations with boundary value problems (the math that is rocket science).
Q: How high can you count on the fingers of one hand? Five?
A: You can count from zero to nine on the fingers of one hand.
Each of the four fingers are worth one. Make a fist. That is zero. For now, use your right hand. Count to four with one finger each. Some people find it easier to put the pinky up first. I use the index finger first. It doesn't matter.
Make the fist again, and stick out your thumb. The thumb is worth five. Five is just with the thumb out. You can think of this as five and zero. Add a finger with the thumb - that's six. Count from there until you have the thumb and all the fingers out. That's nine. You've just counted from zero to nine on one hand.
Now, every day for a week, perform this exercise. Don't hurry. Don't skip ahead. Stay with this exercise longer if you need to.
Start with a fist, say 'zero'. Say it out loud.
Add a finger. Say 'one'. I can't hear you.
Add a finger. Say 'two'. Shout if you must.
Add a finger. Say 'three'.
Add a finger. Say 'four'.
Make the fist again, and stick out the thumb. Say 'five'.
Add a finger. Say 'six'.
Add a finger. Say 'seven'.
Add a finger. Say 'eight'.
Add a finger. Say 'nine'.
Extra credit. Count down from nine to zero.
An aside. Zero is a number. It is perhaps the most meaningful of the numbers. After all, nothing is more important than math. We will return to zero again and again for infinity, and beyond.
Correcting simple counting isn't anything magic, it's just being careful. I won't attempt a description. What follows is a description of a technique with the power of rocket science, brought down to the simplicity of a kindergartener. It isn't dumbed down. Instead, it is broken up into consumable chunks for the student. The goal is seven second lessons. Each post is a lesson. I won't go further than partial differential equations with boundary value problems (the math that is rocket science).
Q: How high can you count on the fingers of one hand? Five?
A: You can count from zero to nine on the fingers of one hand.
Each of the four fingers are worth one. Make a fist. That is zero. For now, use your right hand. Count to four with one finger each. Some people find it easier to put the pinky up first. I use the index finger first. It doesn't matter.
Make the fist again, and stick out your thumb. The thumb is worth five. Five is just with the thumb out. You can think of this as five and zero. Add a finger with the thumb - that's six. Count from there until you have the thumb and all the fingers out. That's nine. You've just counted from zero to nine on one hand.
Now, every day for a week, perform this exercise. Don't hurry. Don't skip ahead. Stay with this exercise longer if you need to.
Start with a fist, say 'zero'. Say it out loud.
Add a finger. Say 'one'. I can't hear you.
Add a finger. Say 'two'. Shout if you must.
Add a finger. Say 'three'.
Add a finger. Say 'four'.
Make the fist again, and stick out the thumb. Say 'five'.
Add a finger. Say 'six'.
Add a finger. Say 'seven'.
Add a finger. Say 'eight'.
Add a finger. Say 'nine'.
Extra credit. Count down from nine to zero.
An aside. Zero is a number. It is perhaps the most meaningful of the numbers. After all, nothing is more important than math. We will return to zero again and again for infinity, and beyond.
Thursday, May 18, 2006
Escape
I've mentioned my hour long commute, in each direction, minimum. I fill the time listening to podcasts, music and books. There are reviews of some of these books here. My previous car has an MP3 CD player, but now an IPod Shuffle is mostly used.
This is a review of my new favorite podcast. It is a cross between books and the radio show style podcasts you might be used to. About once a week, the show presents a story with an introduction. While billed as Science Fiction, which brings to mind Captain Kirk or Asimov's three robotics laws, it also includes fantasy and even a little horror. I'd like it to be pure Science Fiction, just as i was horrified to see that other stuff on the SciFi channel. In general, i'm not a big horror fan. However, the host, Stephen Eley (whose name barely appears on his site - at least he gives himself credit when he reads), exercises some discretion. He says that the stories have to be entertaining. Yes, he more or less admits that he doesn't know what that means, but he does seem to have the same idea i have on that topic.
Episodes aren't exactly some preset length, but tend to be under 40 minutes. OK, the most recent is the longest, at 53 minutes. This fits my commute really well. Long shows are harder to consume, which was the reason i stopped listening to the Pod Father. There are also FLASH episodes, often under five minutes, and reviews of other SciFi - movies and books mostly. I really like the FLASH episodes. The format is so short that there isn't time to be bored. They tend to be very, very dense. The ideas are packed together. Why water the garden with a squirt gun if you can get a fire hose?
Maybe it's the sound quality. But I'm not reminded of the 50's radio shows, like The Green Hornet. This is better. And, unlike radio, one can listen to a show when one has the time, pause it if needed, back up and re-listen to a bit one missed, due to traffic or something.
I haven't listened to all the back issues yet. I'm still catching up. Sometimes i'll start a show, get on the treadmill and do a run until the show is over. Don't bother checking the time or distance. It'll be enough, whatever it turns out to be.
Feeling trapped? There's no escape? Try Escape Pod.
This is a review of my new favorite podcast. It is a cross between books and the radio show style podcasts you might be used to. About once a week, the show presents a story with an introduction. While billed as Science Fiction, which brings to mind Captain Kirk or Asimov's three robotics laws, it also includes fantasy and even a little horror. I'd like it to be pure Science Fiction, just as i was horrified to see that other stuff on the SciFi channel. In general, i'm not a big horror fan. However, the host, Stephen Eley (whose name barely appears on his site - at least he gives himself credit when he reads), exercises some discretion. He says that the stories have to be entertaining. Yes, he more or less admits that he doesn't know what that means, but he does seem to have the same idea i have on that topic.
Episodes aren't exactly some preset length, but tend to be under 40 minutes. OK, the most recent is the longest, at 53 minutes. This fits my commute really well. Long shows are harder to consume, which was the reason i stopped listening to the Pod Father. There are also FLASH episodes, often under five minutes, and reviews of other SciFi - movies and books mostly. I really like the FLASH episodes. The format is so short that there isn't time to be bored. They tend to be very, very dense. The ideas are packed together. Why water the garden with a squirt gun if you can get a fire hose?
Maybe it's the sound quality. But I'm not reminded of the 50's radio shows, like The Green Hornet. This is better. And, unlike radio, one can listen to a show when one has the time, pause it if needed, back up and re-listen to a bit one missed, due to traffic or something.
I haven't listened to all the back issues yet. I'm still catching up. Sometimes i'll start a show, get on the treadmill and do a run until the show is over. Don't bother checking the time or distance. It'll be enough, whatever it turns out to be.
Feeling trapped? There's no escape? Try Escape Pod.
Sunday, May 07, 2006
Lawn Mower Man
A couple years ago, there was a set of tips for saving gas. It started with giving your lawn mower a tune up. I don't know about you, but last year my lawn mower used a gallon of gas - for the entire season. So, even if a tune up resulted in increasing fuel efficiency by 100%, at most, a gallon of gas per year could be saved. This is totally negligible, even if every lawn mower in the nation received such a tune up. Now, there's nothing wrong with maintenance. I'm all about that.
Or am i? This season, my six year old lawn mower has given up the ghost. It's some sort of carburetor problem. I can squirt gas directly into the carburetor, and it will start, and run for may fifteen seconds. And, it will mow grass that whole time. Who knows what the problem is. It could be a fuel pump, or fuel filter, or any of a dozen other things. While, i could have looked at the problem over the winter (there were signs of this coming last fall), the fact is, the lawn needed mowing today, and there just isn't time to do anything about it.
I went to the store. For $100, one can get a 3.5 hp mower like the one that died. For $100, one can get a non-motorized push reel mower. So, what are the pros and cons of each?
Well, the gas powered mower is easier to use. Pull the chord, push it around, and it will do most of the work actually cutting the grass. For the most part, it cuts everything. And who cares if there are branches or rocks or whatever - the mower will chop it up and continue on.
The push reel mower provides more exercise. When the grass is very high (as it was this morning), it takes multiple passes to get the job done. Further, aren't very good when there is more than one species of grass, and in particular, it isn't very good with dandelions. I'm cool with that - i'd rather have dandelions than grass anyway. The push reel mower is also quieter. One can wear an iPod and listen to music or podcasts while mowing the lawn. One can mow early in the morning without irritating the neighbors. Maybe even late a night. Though it should be cleaned and oiled, it doesn't have to be fueled - ever. So, that once a summer trip to the gas station with the gas can is a thing of the past. Oh, yes, it saves that one gallon a year. The entire gallon. The push reel mower is also slightly smaller. It takes up a little less room in the garage for storage. There are more corners it will fit into than a gas mower. It is a simpler device. So there is a better chance
that if it breaks, it will be obvious what is wrong with it, and it will be more likely to be fixable.
And this last bit is the main reason i bought it. Six years isn't enough. It isn't the money. $17 a year rent on a mower is cheap. But if we're going to do this throw away economy concept, we've got to have some sort of reasonable recycling system. Where are the lawn mower refurbishment organizations? Can the thing just be melted down and made into cars? Or does the whole thing get tossed into the land fill, gas, oil, caked on grass and everything? No one told me what to do with the old beast.
So, maybe i'll find the original instructions. Maybe i'll call them up and order a few parts. Maybe i'll get her operational again. Maybe the new push reel mower will be the backup - patiently waiting until some kid offers to cut my lawn for $10. Or maybe, due to laziness (some call it prioritization), the gas mower will collect dust for a bit until the garage space is needed for something else.
Or am i? This season, my six year old lawn mower has given up the ghost. It's some sort of carburetor problem. I can squirt gas directly into the carburetor, and it will start, and run for may fifteen seconds. And, it will mow grass that whole time. Who knows what the problem is. It could be a fuel pump, or fuel filter, or any of a dozen other things. While, i could have looked at the problem over the winter (there were signs of this coming last fall), the fact is, the lawn needed mowing today, and there just isn't time to do anything about it.
I went to the store. For $100, one can get a 3.5 hp mower like the one that died. For $100, one can get a non-motorized push reel mower. So, what are the pros and cons of each?
Well, the gas powered mower is easier to use. Pull the chord, push it around, and it will do most of the work actually cutting the grass. For the most part, it cuts everything. And who cares if there are branches or rocks or whatever - the mower will chop it up and continue on.
The push reel mower provides more exercise. When the grass is very high (as it was this morning), it takes multiple passes to get the job done. Further, aren't very good when there is more than one species of grass, and in particular, it isn't very good with dandelions. I'm cool with that - i'd rather have dandelions than grass anyway. The push reel mower is also quieter. One can wear an iPod and listen to music or podcasts while mowing the lawn. One can mow early in the morning without irritating the neighbors. Maybe even late a night. Though it should be cleaned and oiled, it doesn't have to be fueled - ever. So, that once a summer trip to the gas station with the gas can is a thing of the past. Oh, yes, it saves that one gallon a year. The entire gallon. The push reel mower is also slightly smaller. It takes up a little less room in the garage for storage. There are more corners it will fit into than a gas mower. It is a simpler device. So there is a better chance
that if it breaks, it will be obvious what is wrong with it, and it will be more likely to be fixable.
And this last bit is the main reason i bought it. Six years isn't enough. It isn't the money. $17 a year rent on a mower is cheap. But if we're going to do this throw away economy concept, we've got to have some sort of reasonable recycling system. Where are the lawn mower refurbishment organizations? Can the thing just be melted down and made into cars? Or does the whole thing get tossed into the land fill, gas, oil, caked on grass and everything? No one told me what to do with the old beast.
So, maybe i'll find the original instructions. Maybe i'll call them up and order a few parts. Maybe i'll get her operational again. Maybe the new push reel mower will be the backup - patiently waiting until some kid offers to cut my lawn for $10. Or maybe, due to laziness (some call it prioritization), the gas mower will collect dust for a bit until the garage space is needed for something else.
Friday, May 05, 2006
Life on one end of the Belle curve
According to the BBC news, aspartame (Nutrasweet) does not cause cancer. This is is according to a report by the EFSA (the European Food Safety Authority).
For me, that's like saying that Twinkies are fat free, or that lard has no sugar. It misses the point. I'm real down on aspartame for two reasons. One is that it appears everywhere, and is often difficult to avoid. It seems that someone thinks that everyone on Earth needs it. The other is that i get what amounts to an allergic reaction to it. If my tongue becomes just wet with a diet Coke, i get a six hour migraine headache. That's a day ruining event.
That's if i'm lucky. So far, i've been lucky. I've heard that this stuff can cause strokes for some people. This is easy enough to believe, from my perspective.
So, when i'm not at home, my diet drink of choice is water. But i have to make sure it doesn't go through one of those multi button spigots. Any residual diet drink in the spigot would get into my drink, ruining my day.
This issue is bigger than me, and bigger than aspartame. The real problem is that mass production markets like to push narrow sets of products on the entire population. It seems OK to ignore the ten or fifteen percent of the population for which the product is useless. And entire industries think this way. So, something like 15% of the population is left handed. Yet 95% of camcorders are very much right handed only. The other 5% are sort of awkward ambidextrous designs. There aren't any left handed camcorders available. At the store, there may be 30 camcorder models to choose from. Presumably, each model gets about 3% of the market. While a left handed model could sweep up 15% of the market, there aren't any. People are built from a code that produces variation. The belle curves are wide. So there are adults who are too short or tall or fat for any production car. They're stuck.
For me, that's like saying that Twinkies are fat free, or that lard has no sugar. It misses the point. I'm real down on aspartame for two reasons. One is that it appears everywhere, and is often difficult to avoid. It seems that someone thinks that everyone on Earth needs it. The other is that i get what amounts to an allergic reaction to it. If my tongue becomes just wet with a diet Coke, i get a six hour migraine headache. That's a day ruining event.
That's if i'm lucky. So far, i've been lucky. I've heard that this stuff can cause strokes for some people. This is easy enough to believe, from my perspective.
So, when i'm not at home, my diet drink of choice is water. But i have to make sure it doesn't go through one of those multi button spigots. Any residual diet drink in the spigot would get into my drink, ruining my day.
This issue is bigger than me, and bigger than aspartame. The real problem is that mass production markets like to push narrow sets of products on the entire population. It seems OK to ignore the ten or fifteen percent of the population for which the product is useless. And entire industries think this way. So, something like 15% of the population is left handed. Yet 95% of camcorders are very much right handed only. The other 5% are sort of awkward ambidextrous designs. There aren't any left handed camcorders available. At the store, there may be 30 camcorder models to choose from. Presumably, each model gets about 3% of the market. While a left handed model could sweep up 15% of the market, there aren't any. People are built from a code that produces variation. The belle curves are wide. So there are adults who are too short or tall or fat for any production car. They're stuck.
Wednesday, April 19, 2006
What A Gas
In February, i was paying about $2.10 per gallon of gas, and now it's over $2.75, and that makes me pissed (it's a 30% hike in two months). Yet, i just entered the recent entries into my gas program, and discovered that my most recent three tanks of gas delivered over 43 miles per gallon (18 km/liter). What's my secret?
Start with an efficient car. My 2000 Saturn SL is a smallish 4 door sedan with a smallish 1.9 liter engine and a 5 speed manual transmission. I got it cheap because it had some damage, and over 140,000 miles (225,000 km), and my friend wanted to get rid of it. I fixed up the bumpers myself, and though they are now mostly attached with bailing wire, this job has survived two accidents already (neither was my fault - in fact, i parked the car out of the way so this sort of thing wouldn't happen). The bumpers held, and the plastic quarter panels bounced back with hardly a scratch.
Then, drive a little slower. Though the speed limit is 70 MPH (112 km/hr) in much of Michigan, it is perfectly legal to drive at 60 mph (100 km/hr). So this car, which has an EPA rating of 32 MPG (13.6 km/liter) highway, normally achieves over 40 MPG (17 km/liter). Going a little slower might be thought to cost me as much as 7 minutes in my daily commute, but with traffic jams, accidents and construction, it turns out to be hard to measure. It just doesn't matter.
Since i drive about 35,000 miles (56,000 km) a year, that would be 1,094 gallons (4,141 liters) of gas per year at 32 MPG (13.6 km/liter). But at 43 MPG (18km/liter) it's only 814 gallons (3,081 liters) - a savings of 281 gallons of gas. At yesterday's $2.799 per gallon, that would be a savings of $786.50. What would you do with an extra tax free $786.50? I'd buy a telescope.
Start with an efficient car. My 2000 Saturn SL is a smallish 4 door sedan with a smallish 1.9 liter engine and a 5 speed manual transmission. I got it cheap because it had some damage, and over 140,000 miles (225,000 km), and my friend wanted to get rid of it. I fixed up the bumpers myself, and though they are now mostly attached with bailing wire, this job has survived two accidents already (neither was my fault - in fact, i parked the car out of the way so this sort of thing wouldn't happen). The bumpers held, and the plastic quarter panels bounced back with hardly a scratch.
Then, drive a little slower. Though the speed limit is 70 MPH (112 km/hr) in much of Michigan, it is perfectly legal to drive at 60 mph (100 km/hr). So this car, which has an EPA rating of 32 MPG (13.6 km/liter) highway, normally achieves over 40 MPG (17 km/liter). Going a little slower might be thought to cost me as much as 7 minutes in my daily commute, but with traffic jams, accidents and construction, it turns out to be hard to measure. It just doesn't matter.
Since i drive about 35,000 miles (56,000 km) a year, that would be 1,094 gallons (4,141 liters) of gas per year at 32 MPG (13.6 km/liter). But at 43 MPG (18km/liter) it's only 814 gallons (3,081 liters) - a savings of 281 gallons of gas. At yesterday's $2.799 per gallon, that would be a savings of $786.50. What would you do with an extra tax free $786.50? I'd buy a telescope.
Friday, April 07, 2006
Comment Spam
Well, this blog has gotten its first comment spam. One, of all things, promotes software to remove adware, of all things. At the moment, the policy is to just delete such nonsense. You might see such spam if you have some program scan the forum via an automated RSS feed checker, or if you just happen to read such comments soon after they're posted. It isn't a perfect world. There's always some jerk out there to mess things up. On the other hand, if you simply disagree with me, but manage to stay on topic, even remotely, it stays. In Monty Python's movie Life of Brian, Brian tells the crowd whose following him You don't have to follow anybody. You're all individuals!, to which the reply was from one guy who says I'm not. Or something like that. For a favorite scene, it is always a little different when i see it compared to how i remember it. Anyway, there are a few out there who will agree with me on some topics, but at those times, this blog isn't for you.
Monday, April 03, 2006
$7,834 per year
AAA has found it's costing the average person an average of $7,834 annually to drive their car.
My car costs me about $3,300 per year, about 42% of the average. My commute is just about 35,000 miles per year, which 2.3 times farther than the 15,000 miles used by AAA. So, my per-mile cost is under a fifth of the average. Is there something wrong with my math? You decide.
Well, for one, there has never been a new car in my driveway. Purchase price is a significant fraction of the cost of operating a car. Some people buy a new car every five years, and make car payments the whole time. No payments for me. After five years, these cars have little resale value, perhaps 10% on the dollar. They still often have five years or more of service left in them, just without new car smell. If new car smell is what you want, you can buy it in spray can form cheaply.
My cars get reasonably good gas mileage. They aren't hybrids - these are used cars, after all. The old car was getting 37 Miles Per Gallon (MPG), and the new one is getting 42 MPG. What cars are these? Well, in both cases, the EPA rating is 32 MPG on the highway. My trick is to drive a little slower. How much? Drive 65 MPH rather than 70 MPH. For the new car, this saves me $500 every year, in gas alone. As a bonus, speeding tickets aren't issued for people driving slightly under the limit.
Used cars are cheaper to insure. There is no need to insure a car against theft if no one wants it, and your $500 deductible exceeds the retail value of the vehicle. Getting a car with air bags, and anti-lock breaks can reduce your liability insurance as well. Why? It's safer. Buying a safer car is a feature. Using your insurance carrier to help you buy a safe car is a good idea. Crumple zones work - just look at the insurance rates. Insurance rates, unlike statistics, don't lie.
While some car manufacturers have been saying that their new automatic transmissions are just as efficient as manual transmissions, no evidence of this has crossed my path. Efficiency means more power to the ground for a given engine, and more miles per unit fuel. Both are good. Further, there is ample evidence that manual transmissions last longer than automatic transmissions. So, it is no surprise that my last three vehicles have five speed manuals.
While some car manufacturers say that their new engines are 20% more efficient than older versions, the evidence is still that 4 cylinder engines are always more efficient than 6 or 8 cylinder engines. Smaller is more efficient. That's because cruising down the highway requires less than twenty horsepower (HP), and a 100 HP peak engine delivers twenty HP more efficiently than a 300 HP peak engine.
Many of the 4 bangers have more than enough power to get you where you need to go. For example, 135 HP is more than enough to tow a boat when the car has a 5 speed manual transmission, and the driver drives conservatively. My 1988 Mazda achieved 27 MPG towing a 1700 lb boat at 55 MPH over two tanks of gas on a trip. So it is that i'm not impressed with vehicles that get less than 27 MPG with less capability. The advantage of trailers is that you don't pay for the capability when you aren't using them. This same car routinely achieves 40 MPG on highway trips.
Perhaps none of this is for you. The really cheap way to live with old cars is to know how diagnose them. This isn't easy. It takes education, observation, and more education. Doing work yourself on cars can save two thirds of the costs, sometimes much more. For example, an engine overhaul might take 20 hours, and a $150 head kit (gaskets and such). The primary cost is time. If you count your time as zero (it's a hobby), then a $1,000 job costs $150. The hidden cost is that your garage is tied up with broken vehicles rather than with keeping your car frost free through Winter and dry in the Spring. I've paid for my garage already.
At some point, the car is just too worn out to be worth further effort. When is that? Certainly, it was long ago for my 18 year old 290,000 mile Mazda. Or is it? The cost to get it on the road again may be a few hundred dollars. That's perhaps one monthly car payment for my neighbors, and much less than getting a new one. The question is will the money buy enough time? The value of the vehicle to me is much higher than it is to anyone else. I know what's wrong with it, and what it can be depended on to perform.
Yet, at some point, there is no longer value in fixing the vehicle, even for me. What then? Donate the carcass to charity? The tax incentives are small, since the book value of the car is small. There is always dismantling it, part by part, and selling the parts on EBay.
My car costs me about $3,300 per year, about 42% of the average. My commute is just about 35,000 miles per year, which 2.3 times farther than the 15,000 miles used by AAA. So, my per-mile cost is under a fifth of the average. Is there something wrong with my math? You decide.
Well, for one, there has never been a new car in my driveway. Purchase price is a significant fraction of the cost of operating a car. Some people buy a new car every five years, and make car payments the whole time. No payments for me. After five years, these cars have little resale value, perhaps 10% on the dollar. They still often have five years or more of service left in them, just without new car smell. If new car smell is what you want, you can buy it in spray can form cheaply.
My cars get reasonably good gas mileage. They aren't hybrids - these are used cars, after all. The old car was getting 37 Miles Per Gallon (MPG), and the new one is getting 42 MPG. What cars are these? Well, in both cases, the EPA rating is 32 MPG on the highway. My trick is to drive a little slower. How much? Drive 65 MPH rather than 70 MPH. For the new car, this saves me $500 every year, in gas alone. As a bonus, speeding tickets aren't issued for people driving slightly under the limit.
Used cars are cheaper to insure. There is no need to insure a car against theft if no one wants it, and your $500 deductible exceeds the retail value of the vehicle. Getting a car with air bags, and anti-lock breaks can reduce your liability insurance as well. Why? It's safer. Buying a safer car is a feature. Using your insurance carrier to help you buy a safe car is a good idea. Crumple zones work - just look at the insurance rates. Insurance rates, unlike statistics, don't lie.
While some car manufacturers have been saying that their new automatic transmissions are just as efficient as manual transmissions, no evidence of this has crossed my path. Efficiency means more power to the ground for a given engine, and more miles per unit fuel. Both are good. Further, there is ample evidence that manual transmissions last longer than automatic transmissions. So, it is no surprise that my last three vehicles have five speed manuals.
While some car manufacturers say that their new engines are 20% more efficient than older versions, the evidence is still that 4 cylinder engines are always more efficient than 6 or 8 cylinder engines. Smaller is more efficient. That's because cruising down the highway requires less than twenty horsepower (HP), and a 100 HP peak engine delivers twenty HP more efficiently than a 300 HP peak engine.
Many of the 4 bangers have more than enough power to get you where you need to go. For example, 135 HP is more than enough to tow a boat when the car has a 5 speed manual transmission, and the driver drives conservatively. My 1988 Mazda achieved 27 MPG towing a 1700 lb boat at 55 MPH over two tanks of gas on a trip. So it is that i'm not impressed with vehicles that get less than 27 MPG with less capability. The advantage of trailers is that you don't pay for the capability when you aren't using them. This same car routinely achieves 40 MPG on highway trips.
Perhaps none of this is for you. The really cheap way to live with old cars is to know how diagnose them. This isn't easy. It takes education, observation, and more education. Doing work yourself on cars can save two thirds of the costs, sometimes much more. For example, an engine overhaul might take 20 hours, and a $150 head kit (gaskets and such). The primary cost is time. If you count your time as zero (it's a hobby), then a $1,000 job costs $150. The hidden cost is that your garage is tied up with broken vehicles rather than with keeping your car frost free through Winter and dry in the Spring. I've paid for my garage already.
At some point, the car is just too worn out to be worth further effort. When is that? Certainly, it was long ago for my 18 year old 290,000 mile Mazda. Or is it? The cost to get it on the road again may be a few hundred dollars. That's perhaps one monthly car payment for my neighbors, and much less than getting a new one. The question is will the money buy enough time? The value of the vehicle to me is much higher than it is to anyone else. I know what's wrong with it, and what it can be depended on to perform.
Yet, at some point, there is no longer value in fixing the vehicle, even for me. What then? Donate the carcass to charity? The tax incentives are small, since the book value of the car is small. There is always dismantling it, part by part, and selling the parts on EBay.
Wednesday, March 22, 2006
Using Pricewatch Effectively
Summary: I ordered a disk drive from a small distributer, and got what i wanted, when it was expected, at the price offered - roughly half the costs elsewhere, and without rebates or other nonsense. Can't beat that with a stick.
Last week, i ordered a 160 GB hard disk through Pricewatch. I settled on an offering from a company called 3btech. They had the low bid, and are reasonably nearby. Next day delivery from a big name on-line store would have been twice as costly, as was a local store (a big chain). The idea is that instead of buying into a nationwide distribution chain, go with a mom and pop shop within the range that UPS ground can cope. 3btech happens to be about two hours by car from my house. Indeed, the disk drive was ordered on Friday afternoon, and arrived on Tuesday, as expected, and hoped.
The disk drive itself does not come from a big name company. I had never heard of White Label Magnetic Data Tech. The disk drive comes with a six month warranty, so infant death can be avoided. That's as much or more than expected elsewhere.
It turns out that i already own a Western Digital 160 GB hard disk. It's about three years old, and it has been fine. Two ideas are of note. First, disk drives are really reliable for about the age of this WD drive for 24x7 use. Second, only a small fraction of my data is on backed up somewhere. So, either the new drive will be production and the old drive the mostly-offline backup, or i'll implement software mirroring. For now, i'll use the mostly-offline backup idea.
OEM drives come with zero documentation. A sticker on the drive shows the drive selection jumper settings. Once the WD drive was set to master, and this new drive to slave, the BIOS saw them both, and Linux was happy. That's all that matters.
The new drive is identical to my Western Digital 160 GB drive in size. It has the same disk geometry. This will allow easy mirroring.
The new drive appears to be the same speed as my old one. I set them both to use 32 bit DMA transfers in my system startup with a command like:
hdparm -c 1 /dev/hda
On 3btech's web site, this White Label drive says it has a 2 MB on-disk cache, rather than the WD's 8 MB cache. Will this be an issue? No. On-drive cache hit ratios are tiny under Unix systems. The OS checks its own cache first and has much more RAM. I ran studies of this in the 1980's. On-drive caches were new, and software could query the drives for cache hit statistics. On a 9 MB RAM Unix system, a 1 MB RAM on-disk cache got quite poor cache hit ratios. One could think of the on-disk cache as the 2nd MB of cache in a 2 MB cache system. The first MB gives you most of the advantage. My Linux box has 512 MB RAM, and typically allocates over 250 MB to the disk cache. After 250 MB of cache, it matters little if there is an additional 2 MB or 8 MB. The important thing for the drive is that is has RAM for track reads and writes, and perhaps read ahead and write behind (if power reserves allow guaranteed writes through power failure). Consider that after traversing an entire mounted CD, further accesses are instant, and the drive light doesn't even light up. On-disk caches were very important for DOS, and probably important for Windows 3.x, 95, 98, and Millennium. They are probably unimportant for Windows NT, 2000, XP and Vista. For best speed, go with a 15000 RPM SATA or SCSI drive, buy lots of RAM for your system, and consider RAID options. If you need speed, be prepared to pay for it. I just want space and reliability at low cost.
My requirements are for maximum space per dollar, not maximum speed. The tune2fs -l /dev/hda1 command can be used to find out how the old filesystem was built. Then, an examination of the mke2fs man page can yield other ideas. For years, my filesystems have had zero bytes reserved for root. The 5% default space requirement is, in my opinion, a pointless tax. On a 160 GB filesystem, that amounts to 8 GB. The reserve seems to be a holdover from the 4.2 BSD filesystem development studies from the early 80s. Performance tests under Linux have shown that filesystem performance is approximately the same speed when using the last 5% as it is for the rest of the drive. Another holdover is logical disk block size. The Red Hat 9 default block size is 4 KB. However, mke2fs supports the creation of filesystems with 1 KB blocks. As files are generally completely contiguous, and performance generally comes from track reads and writes, it seems reasonable that block size is irrelevant. Smaller blocks waste less space at the ends of files. The more files, the more wasted space. Finally, a quick check of the number of files (inodes) actually used can help you tune the new filesystem. Use df -i. My filesystem had 18,000,000 inodes, but used just over 1,000,000. Inodes take up space, weather used or not. Journaling is a cheap way to gain reliability. So, the command for generating the new filesystem was:
mke2fs -j -b 1024 -m 0 -N 2000000 /dev/hdb1
Once the data was copied from the old drive to the new identically sized partitions, the 6 GB partition had 1 GB more free space, and the 145 GB partition had 3 GB more free space. Compared with default values, these options yield about 7% more space, or 12 GB.
Conclusion
Great deals can be had through services like Pricewatch and low overhead vendors. Just be sure that the overhead you skip isn't overhead you need. Maybe you really need overnight delivery, vendor support, manufacturer support, or documentation. If so, my advice is to buy it. However, if you can manage to educate yourself, you can get what you want cheaper. As Harry Potter fans know, knowledge is power.
Last week, i ordered a 160 GB hard disk through Pricewatch. I settled on an offering from a company called 3btech. They had the low bid, and are reasonably nearby. Next day delivery from a big name on-line store would have been twice as costly, as was a local store (a big chain). The idea is that instead of buying into a nationwide distribution chain, go with a mom and pop shop within the range that UPS ground can cope. 3btech happens to be about two hours by car from my house. Indeed, the disk drive was ordered on Friday afternoon, and arrived on Tuesday, as expected, and hoped.
The disk drive itself does not come from a big name company. I had never heard of White Label Magnetic Data Tech. The disk drive comes with a six month warranty, so infant death can be avoided. That's as much or more than expected elsewhere.
It turns out that i already own a Western Digital 160 GB hard disk. It's about three years old, and it has been fine. Two ideas are of note. First, disk drives are really reliable for about the age of this WD drive for 24x7 use. Second, only a small fraction of my data is on backed up somewhere. So, either the new drive will be production and the old drive the mostly-offline backup, or i'll implement software mirroring. For now, i'll use the mostly-offline backup idea.
OEM drives come with zero documentation. A sticker on the drive shows the drive selection jumper settings. Once the WD drive was set to master, and this new drive to slave, the BIOS saw them both, and Linux was happy. That's all that matters.
The new drive is identical to my Western Digital 160 GB drive in size. It has the same disk geometry. This will allow easy mirroring.
The new drive appears to be the same speed as my old one. I set them both to use 32 bit DMA transfers in my system startup with a command like:
hdparm -c 1 /dev/hda
On 3btech's web site, this White Label drive says it has a 2 MB on-disk cache, rather than the WD's 8 MB cache. Will this be an issue? No. On-drive cache hit ratios are tiny under Unix systems. The OS checks its own cache first and has much more RAM. I ran studies of this in the 1980's. On-drive caches were new, and software could query the drives for cache hit statistics. On a 9 MB RAM Unix system, a 1 MB RAM on-disk cache got quite poor cache hit ratios. One could think of the on-disk cache as the 2nd MB of cache in a 2 MB cache system. The first MB gives you most of the advantage. My Linux box has 512 MB RAM, and typically allocates over 250 MB to the disk cache. After 250 MB of cache, it matters little if there is an additional 2 MB or 8 MB. The important thing for the drive is that is has RAM for track reads and writes, and perhaps read ahead and write behind (if power reserves allow guaranteed writes through power failure). Consider that after traversing an entire mounted CD, further accesses are instant, and the drive light doesn't even light up. On-disk caches were very important for DOS, and probably important for Windows 3.x, 95, 98, and Millennium. They are probably unimportant for Windows NT, 2000, XP and Vista. For best speed, go with a 15000 RPM SATA or SCSI drive, buy lots of RAM for your system, and consider RAID options. If you need speed, be prepared to pay for it. I just want space and reliability at low cost.
My requirements are for maximum space per dollar, not maximum speed. The tune2fs -l /dev/hda1 command can be used to find out how the old filesystem was built. Then, an examination of the mke2fs man page can yield other ideas. For years, my filesystems have had zero bytes reserved for root. The 5% default space requirement is, in my opinion, a pointless tax. On a 160 GB filesystem, that amounts to 8 GB. The reserve seems to be a holdover from the 4.2 BSD filesystem development studies from the early 80s. Performance tests under Linux have shown that filesystem performance is approximately the same speed when using the last 5% as it is for the rest of the drive. Another holdover is logical disk block size. The Red Hat 9 default block size is 4 KB. However, mke2fs supports the creation of filesystems with 1 KB blocks. As files are generally completely contiguous, and performance generally comes from track reads and writes, it seems reasonable that block size is irrelevant. Smaller blocks waste less space at the ends of files. The more files, the more wasted space. Finally, a quick check of the number of files (inodes) actually used can help you tune the new filesystem. Use df -i. My filesystem had 18,000,000 inodes, but used just over 1,000,000. Inodes take up space, weather used or not. Journaling is a cheap way to gain reliability. So, the command for generating the new filesystem was:
mke2fs -j -b 1024 -m 0 -N 2000000 /dev/hdb1
Once the data was copied from the old drive to the new identically sized partitions, the 6 GB partition had 1 GB more free space, and the 145 GB partition had 3 GB more free space. Compared with default values, these options yield about 7% more space, or 12 GB.
Conclusion
Great deals can be had through services like Pricewatch and low overhead vendors. Just be sure that the overhead you skip isn't overhead you need. Maybe you really need overnight delivery, vendor support, manufacturer support, or documentation. If so, my advice is to buy it. However, if you can manage to educate yourself, you can get what you want cheaper. As Harry Potter fans know, knowledge is power.
Tuesday, March 21, 2006
Caffeine
I have a high tolerance to pain. I don't even notice it. When noticed, i look for some cause and solution. Observation. Almost five years ago, the pain in my right shoulder was bad enough that I could not extend the arm higher than horizontal. I still reach for things on high shelves with my left hand. I didn't complain, but did notice that it was somewhat better on Sundays, and best on Monday mornings. What could that mean? Well, i'd experienced caffeine withdrawal on Sundays. I didn't just get headaches because i was at church. And when my Mt. Dew consumption was reduced, they went away. So, i went cold turkey, and 10 months later, was restored to full movement and the pain was gone. Arthritis in the hands and feet which i'd barely noticed, back pain, shoulder pain, all of it.
And i won't go back. Why would i grab a Dew if it will cause such misery? The reason is that caffeine is rather addictive after all, and by comparison, i have no will power to speak of. But i'm back on the wagon again, and though my hands are better, i know my right foot won't recover until August.
The current additional experiment is to see if non-impact exercise will accelerate the healing process.
And i won't go back. Why would i grab a Dew if it will cause such misery? The reason is that caffeine is rather addictive after all, and by comparison, i have no will power to speak of. But i'm back on the wagon again, and though my hands are better, i know my right foot won't recover until August.
The current additional experiment is to see if non-impact exercise will accelerate the healing process.
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