I burned out in my 50s and followed an old dream to become a math teacher, which was the hardest thing I've ever done professionally (much harder than software) and didn't go so well because I was only good at the teaching part of teaching. So I became a math and computer science tutor. I don't earn what I used to but I'm doing pretty well and I've never had so much fun earning a living. It helps that I also have a math degree; I get very little demand for computer science tutoring. And since I do miss writing software and wanted to learn Ruby, I rolled my own accounting system, about 5% of which is in Google Script (to export my tutoring calendar to a spreadsheet) and the rest in Ruby. That was fun!
I still don't see how this is trigonometry. When solving a right triangle and you have two of the sides, you can find the third side using the Pythagorean Theorem, without trigonometry. That's pretty much what this system does, normalized so the long leg is 1. The way they did it, taking advantage of terminating sexagesimal fractions coupled with an impressive collection of Pythagorean triples, is certainly amazing, given how long ago this was done, and it might have been extremely useful, but I wouldn't call it trigonometry since it's silent about the angles.
Agreed. In the video, they keep saying that this trigonometry is "different" from modern trigonometry because it's based on ratios, not angles. Hogwash! Modern trigonometry is all about ratios, but in relation to angles. It might be interesting to study triangle ratios without reference to angles, but it's the relationships between the angles and the ratios that makes it trigonometry. If you can't figure out how high up a wall a 10' ladder goes at a 70 angle, it's not trigonometry!
Human sexuality is bimodal, not absolute: most of us are quite obviously male or female but some of us aren't. There is no sharp dividing line in nature; anybody who wants a sharp line will have to invent one.
In this age, when most electronic devices live on low voltage DC, why do we keep building them to plug into AC power, with all that lost energy and lost space taken up by bricks and other power supplies?
Instead, why haven't we standardized on some standard DC power plug, maybe with +5V and +12V, with some minimum power cleanliness? Houses and office buildings could be wired with that alongside AC, and people could buy power strips that plug into AC and provide many standard DC outlets (old houses would not have to be rewired). Then many devices wouldn't need power supplies at all, and others would need much more minimal power supplies that would just clean it up and maybe alter the voltage level to its own purposes. I know that DC doesn't travel well for long distances, so still only AC would come to the house/building, but I'd rather have one big, efficient brick in the basement, or one medium-sized, efficient brick in my office, than zillions of little inefficient bricks all over the place.
I guess we kind of have some standards like this, because you can buy 12V stuff for off-grid homes and there's the "cigarette lighter" adapter for cars, and another one for airplanes. But still most stuff we buy plugs into AC.
Imagine a world with no power bricks, and smaller, quieter PCs, tiny phone/camera chargers, etc.
Presumably because of economies of scale, the AC/standard DC adapters could be built to be smart enough to consume not much more power than they emit.
Why haven't we done this? Couldn't a relatively small coalition of big manufacturers do something like this to add value to their products and reduce their costs at the same time?
I admit to being an analog electronics moron so there must be something I'm missing.
Er, if a gazillion youtube users were to film molecules exhibiting brownian motion, and if those users were to post the tiny fraction of that video that is amusing, I'll bet those molecules could be "scientifically proven" to dance too.
Another point on how to read math books: Read them actively and conversationally. Authors usually say things a certain way, or order things a certain way, for a reason. Always ask, "why?" Why are they teaching me this? Why is this section after that section? Why did they use those words as opposed to some other words? Talk to the author in your head. Often the author will answer you if you read carefully enough and think hard enough.
Also, whenever they state a theorem, before reading the proof, try to prove it on your own. Even if you don't succeed, you will be able to read the proof much better for having tried. And as one of my great college professors said, "always read with pencil!" It's easy to get lulled into skimming over this stuff but then you'll miss a lot.
With most theorems, the proof is a lot of symbol manipulation plus one or two key insights. Go over the proof to find the key insights.
The key in all of education, and math in particular, is in what educators call constructivism. Basically this theory says that you learn best when you feel like you are inventing what you are learning. Of course this isn't really possible because we have a lot of intellectual history behind us and there's no way one person could invent a small fraction of it. But a good book or teacher will guide you enough so that, with your help, you can get that sensation of "discovering" of exactly what they are trying to tell you. But this kind of learning requires that you try to actively construct what you are learning rather than passively trying simply to take it in.
There's more theory that emphasizes the social nature of learning which suggests that you should not try to do this all on your own.
Why has it become verboten for anything smaller than a laptop to have a clamshell keyboard? Sure, there are a few Zaurus models, and probably a few I don't know or have forgotten, but for the most part, small computers have integrated or slide-out keyboards which are way too small and which don't protect the screen, or no keyboard at all! You need to protect the screen, and you need to type! What's the problem?
Another thing online newspapers never think about: Links! So many times online newspaper articles refer to other articles, people, places, companies etc but don't bother with hotlinks. I wonder if this is just because coming up with decent links takes time and money or if they are afraid of making their online newspaper more valuable than their paper newspaper.
This is clearly a defensive response to the fact that people are getting tired of the Microsoft tax and Microsoft dependence caused by using de facto Microsoft "standards", e.g. the state of Massachusetts moving to ODF.
It's also clear that, while they may "open" the file formats, like other Microsoft "standards", the documentation will be incomplete enough and obscure enough that it will be virtually impossible to ensure Office compatibility by coding from spec. So Microsoft would get a PR win and a big bullet point in competing with ODF, without actually giving anything up.
I guess there are lots of concepts of "god". I'll talk about a god who is an intentional being who created us and who cares what we do.
If you accept evolution, you must accept that we were not created in any meaningful sense. What about a Deist God who set the Universe in motion, tweaking the laws and constants to favor some kind of evolution? But it's hard to imagine such a laissez-faire creator having strong opinions about what we should do; if he cared he'd have taken an active role in our design! Surely, for example, if this god wanted us to follow the golden rule, that god (who could create a whole universe, after all) could and would have intervened on this one little planet to make us better at it! But evolution says this didn't happen.
If you think there might be some god that is consistent with evolution, what kind of god would that be? How would you reconcile the scientific fact of this god's laissez-faire attitude towards the emergence of life with any godlike caring about the results?
The Vatican supports evolution because it makes perfect sense (evolution never says there is no God, God could be directing evolution).
You are actually spouting ID here, not Darwinian evolution. A key component (perhaps the key component) of Darwinian evolution is that it is purposeless. That's what makes it one of the great scientific theories ever, because it escapes the infinite regress (who designed the designer?)
The Catholic Church, as well as religious people all over the world, hope that people don't notice the purposelessness of evolution. Because once you accept this scientific theory (and you really must, or else lose the last century and a half of biology) you must accept that either there is no god or whatever god does exist is so inscrutable that it is impossible to know anything about it. Either of these is tantamount to atheism. Get used to it!
Despite the wishful thinking of Gould and many others, science has challenged religious assertions since Copernicus at least. Darwin's was a big one, but there have been many others. Religionists need to just get over the hoax of theology and be content with culture, ethics, and collecting money.
If schools know what's good for them, they should make corporate whoring grounds for dismissal. The last thing students need is corporate whores posing as friends.
regarding the wider scope of Intellegent Design, why does that necessarily have to conflict with the established theory of evolution?
Because evolution posits random mutation and natural selection! If there's one fact to take from the theory of evolution, it's that evolution is purposeless! If you believe that what you call "evolution" is a tool of God, you are not talking about Darwinian evolution. You really are talking about so-called Intelligent Design. And that opinion may be comfortable for you, but it is simply not borne out by the last century of biology.
Check out some Richard Dawkins quotes on this subject, e.g. this one: "Certainly I see the scientific view of the world as incompatible with religion."
This is basically Legato Prestoserve (introduced around 1989) packaged with a disk drive. Prestoserve used battery-backed NVRAM instead of flash. It was typically installed on servers, and its main purpose was not power conservation but rather accelerating an NFS server by committing writes to stable storage without waiting for the hard drive. But the idea is similar: a persistent disk cache.
This may not be worth much more than the pixels it's printed on, but a Business Week poll that asks what browser you'll be using in six months currently has Firefox at 48% against "Explorer" at 32%. "Mozilla" is listed separately at 10% so if you take Mozilla and Firefox together that's a nice lead. Opera is sitting at 3.5%.
Seems to me we could fairly easily do a pretty good job of verifying the vote. Here's how we'd handle a single vote for a single community of voters (whether a precinct or the whole country):
Each vote gets stored in a database, and voter information gets stored elsewhere in the database, but no connection is made in the db between vote and voter
Every voter gets handed an electronically signed copy of his vote and the database index of his vote
After the election, the database becomes public and freely redistributed
Here are some consequences:
Using any copy of the database, anyone can add up the votes themselves
Any voter can verify that his vote was counted by looking it up with his index, and can prove his vote to a third party by using the signed copy
Anyone can proofread the list of voters for dead or otherwise illegal voters, e.g. by comparing with other databases like phone books
Your vote remains secret unless you choose reveal its key
There are a few problems with this; for one thing I don't know if whether a given person has voted is supposed to be public information; for another it would be hard to look for illegal voters. But I think this is a big improvement over the black box we have now!
Who are you or that priest to say that God created the world?
The fuss is that if your morality starts with a wacky 2000-year-old book, and that the benefits of moral behavior accrue in an undetectable and unfalsifiable realm, then you can end up with a perverse morality that causes overpopulation, poverty, disease, suffering and death, to say nothing of raped children.
There is no evidence that there is a god. New evidence, like that which started this conversation, keeps arriving in support of god-free scientific explanations of things formerly attributed to one god or other. We all need to open up our eyes to the obvious truth and let morality start and stop, on this planet, with each other.
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I burned out in my 50s and followed an old dream to become a math teacher, which was the hardest thing I've ever done professionally (much harder than software) and didn't go so well because I was only good at the teaching part of teaching. So I became a math and computer science tutor. I don't earn what I used to but I'm doing pretty well and I've never had so much fun earning a living. It helps that I also have a math degree; I get very little demand for computer science tutoring. And since I do miss writing software and wanted to learn Ruby, I rolled my own accounting system, about 5% of which is in Google Script (to export my tutoring calendar to a spreadsheet) and the rest in Ruby. That was fun!
I still don't see how this is trigonometry. When solving a right triangle and you have two of the sides, you can find the third side using the Pythagorean Theorem, without trigonometry. That's pretty much what this system does, normalized so the long leg is 1. The way they did it, taking advantage of terminating sexagesimal fractions coupled with an impressive collection of Pythagorean triples, is certainly amazing, given how long ago this was done, and it might have been extremely useful, but I wouldn't call it trigonometry since it's silent about the angles.
Agreed. In the video, they keep saying that this trigonometry is "different" from modern trigonometry because it's based on ratios, not angles. Hogwash! Modern trigonometry is all about ratios, but in relation to angles. It might be interesting to study triangle ratios without reference to angles, but it's the relationships between the angles and the ratios that makes it trigonometry. If you can't figure out how high up a wall a 10' ladder goes at a 70 angle, it's not trigonometry!
Does this mean that pi is slightly lower (43/14 ~ 3.07) in space?
Kids naturally learn languages best when they are young, and math is a language. Sadly, though, few elementary school teachers are native speakers.
(Disclosure: I'm a math educator too.)
Human sexuality is bimodal, not absolute: most of us are quite obviously male or female but some of us aren't. There is no sharp dividing line in nature; anybody who wants a sharp line will have to invent one.
In this age, when most electronic devices live on low voltage DC, why do we keep building them to plug into AC power, with all that lost energy and lost space taken up by bricks and other power supplies?
Instead, why haven't we standardized on some standard DC power plug, maybe with +5V and +12V, with some minimum power cleanliness? Houses and office buildings could be wired with that alongside AC, and people could buy power strips that plug into AC and provide many standard DC outlets (old houses would not have to be rewired). Then many devices wouldn't need power supplies at all, and others would need much more minimal power supplies that would just clean it up and maybe alter the voltage level to its own purposes. I know that DC doesn't travel well for long distances, so still only AC would come to the house/building, but I'd rather have one big, efficient brick in the basement, or one medium-sized, efficient brick in my office, than zillions of little inefficient bricks all over the place.
I guess we kind of have some standards like this, because you can buy 12V stuff for off-grid homes and there's the "cigarette lighter" adapter for cars, and another one for airplanes. But still most stuff we buy plugs into AC.
Imagine a world with no power bricks, and smaller, quieter PCs, tiny phone/camera chargers, etc.
Presumably because of economies of scale, the AC/standard DC adapters could be built to be smart enough to consume not much more power than they emit.
Why haven't we done this? Couldn't a relatively small coalition of big manufacturers do something like this to add value to their products and reduce their costs at the same time?
I admit to being an analog electronics moron so there must be something I'm missing.
If $4 is too much, and if you buy stuff like lettuce in a grocery store, you often get a pretty good velcro-ish strip with each head of lettuce.
Er, if a gazillion youtube users were to film molecules exhibiting brownian motion, and if those users were to post the tiny fraction of that video that is amusing, I'll bet those molecules could be "scientifically proven" to dance too.
Pi does equal 3. The Bible says so.
Another point on how to read math books: Read them actively and conversationally. Authors usually say things a certain way, or order things a certain way, for a reason. Always ask, "why?" Why are they teaching me this? Why is this section after that section? Why did they use those words as opposed to some other words? Talk to the author in your head. Often the author will answer you if you read carefully enough and think hard enough.
Also, whenever they state a theorem, before reading the proof, try to prove it on your own. Even if you don't succeed, you will be able to read the proof much better for having tried. And as one of my great college professors said, "always read with pencil!" It's easy to get lulled into skimming over this stuff but then you'll miss a lot.
With most theorems, the proof is a lot of symbol manipulation plus one or two key insights. Go over the proof to find the key insights.
The key in all of education, and math in particular, is in what educators call constructivism. Basically this theory says that you learn best when you feel like you are inventing what you are learning. Of course this isn't really possible because we have a lot of intellectual history behind us and there's no way one person could invent a small fraction of it. But a good book or teacher will guide you enough so that, with your help, you can get that sensation of "discovering" of exactly what they are trying to tell you. But this kind of learning requires that you try to actively construct what you are learning rather than passively trying simply to take it in.
There's more theory that emphasizes the social nature of learning which suggests that you should not try to do this all on your own.
"Let them eat cake!"
...fetch speech?
Why has it become verboten for anything smaller than a laptop to have a clamshell keyboard? Sure, there are a few Zaurus models, and probably a few I don't know or have forgotten, but for the most part, small computers have integrated or slide-out keyboards which are way too small and which don't protect the screen, or no keyboard at all! You need to protect the screen, and you need to type! What's the problem?
Another thing online newspapers never think about: Links! So many times online newspaper articles refer to other articles, people, places, companies etc but don't bother with hotlinks. I wonder if this is just because coming up with decent links takes time and money or if they are afraid of making their online newspaper more valuable than their paper newspaper.
This is clearly a defensive response to the fact that people are getting tired of the Microsoft tax and Microsoft dependence caused by using de facto Microsoft "standards", e.g. the state of Massachusetts moving to ODF.
It's also clear that, while they may "open" the file formats, like other Microsoft "standards", the documentation will be incomplete enough and obscure enough that it will be virtually impossible to ensure Office compatibility by coding from spec. So Microsoft would get a PR win and a big bullet point in competing with ODF, without actually giving anything up.
I guess there are lots of concepts of "god". I'll talk about a god who is an intentional being who created us and who cares what we do.
If you accept evolution, you must accept that we were not created in any meaningful sense. What about a Deist God who set the Universe in motion, tweaking the laws and constants to favor some kind of evolution? But it's hard to imagine such a laissez-faire creator having strong opinions about what we should do; if he cared he'd have taken an active role in our design! Surely, for example, if this god wanted us to follow the golden rule, that god (who could create a whole universe, after all) could and would have intervened on this one little planet to make us better at it! But evolution says this didn't happen.
If you think there might be some god that is consistent with evolution, what kind of god would that be? How would you reconcile the scientific fact of this god's laissez-faire attitude towards the emergence of life with any godlike caring about the results?
The Vatican supports evolution because it makes perfect sense (evolution never says there is no God, God could be directing evolution).
You are actually spouting ID here, not Darwinian evolution. A key component (perhaps the key component) of Darwinian evolution is that it is purposeless. That's what makes it one of the great scientific theories ever, because it escapes the infinite regress (who designed the designer?)
The Catholic Church, as well as religious people all over the world, hope that people don't notice the purposelessness of evolution. Because once you accept this scientific theory (and you really must, or else lose the last century and a half of biology) you must accept that either there is no god or whatever god does exist is so inscrutable that it is impossible to know anything about it. Either of these is tantamount to atheism. Get used to it!
Despite the wishful thinking of Gould and many others, science has challenged religious assertions since Copernicus at least. Darwin's was a big one, but there have been many others. Religionists need to just get over the hoax of theology and be content with culture, ethics, and collecting money.
If schools know what's good for them, they should make corporate whoring grounds for dismissal. The last thing students need is corporate whores posing as friends.
regarding the wider scope of Intellegent Design, why does that necessarily have to conflict with the established theory of evolution?
Because evolution posits random mutation and natural selection! If there's one fact to take from the theory of evolution, it's that evolution is purposeless! If you believe that what you call "evolution" is a tool of God, you are not talking about Darwinian evolution. You really are talking about so-called Intelligent Design. And that opinion may be comfortable for you, but it is simply not borne out by the last century of biology.
Check out some Richard Dawkins quotes on this subject, e.g. this one: "Certainly I see the scientific view of the world as incompatible with religion."
This is basically Legato Prestoserve (introduced around 1989) packaged with a disk drive. Prestoserve used battery-backed NVRAM instead of flash. It was typically installed on servers, and its main purpose was not power conservation but rather accelerating an NFS server by committing writes to stable storage without waiting for the hard drive. But the idea is similar: a persistent disk cache.
TouchStream kb and iGesture pad look like interesting products. But for a shorter learning curve, a generic touchpad solves some of the same problems, and can be integrated into an ergo keyboard.
This may not be worth much more than the pixels it's printed on, but a Business Week poll that asks what browser you'll be using in six months currently has Firefox at 48% against "Explorer" at 32%. "Mozilla" is listed separately at 10% so if you take Mozilla and Firefox together that's a nice lead. Opera is sitting at 3.5%.
Remember when there was a "browser market"?
Make sure to cast your vote!
Seems to me we could fairly easily do a pretty good job of verifying the vote. Here's how we'd handle a single vote for a single community of voters (whether a precinct or the whole country):
Here are some consequences:
There are a few problems with this; for one thing I don't know if whether a given person has voted is supposed to be public information; for another it would be hard to look for illegal voters. But I think this is a big improvement over the black box we have now!
Who are you or that priest to say that God created the world?
The fuss is that if your morality starts with a wacky 2000-year-old book, and that the benefits of moral behavior accrue in an undetectable and unfalsifiable realm, then you can end up with a perverse morality that causes overpopulation, poverty, disease, suffering and death, to say nothing of raped children.
There is no evidence that there is a god. New evidence, like that which started this conversation, keeps arriving in support of god-free scientific explanations of things formerly attributed to one god or other. We all need to open up our eyes to the obvious truth and let morality start and stop, on this planet, with each other.