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.
Wednesday, May 31, 2006
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.
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