In my opinion, there are a lot of problems with how we teach math. The first is that we only teach the decimal system. Really, a lot of math is just easier to do in oct or hex. In fact, all math is really easy when you change the system to another base. What's 16^4? 0x10000 (0x does not mean 0*, it's short hand for hex).
The second is that we don't start with 0 when teaching kids to count. We really should. So, 0,1,2,3,4,5,6,7,8,9. After that, you add another number to the front: 10, 11, 12... Same things with Oct: 0,1,2,3,4,5,6,7,10,11,12,13... Same thing with hex: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10,12,13... Understanding this from Kindergarten would make math so much easier later on.
We also don't teach logic. This is a big one for me. Logic is the basis for rational thought, but it's also the first step in any mathematical problem. Logic is the difference between going about a problem the hard way and the easy way. Take the above problem. 16x16x16x16 is a pretty big number. I have it memorized from years of doing programming. Computers calculate in binary (well, they do everything in binary...), with data clustered into 8-bit increments called Bytes. Half of a byte is a nibble, and thus this is 4 bits. 2^4 is 16 values (0-15). Every bit doubles the number of values, so 8 bits is 256 (16x16). 16 bits is thus 256x256, 65536. Looking at the problem in binary, that's (2^4)^4, or 2^16. I can write that in a large number of ways. I can write it as 1000000000000000 in binary, 200000 base 8, 10000 base 16. However, the simplest is hex. 16 = 0x10. 10^4 is 10000. Done. I could spend a lot of time calculating in dec, or I could convert to hex and be done. This of course is a simplistic and math-centric use of logic.
Perhaps my biggest problem is that we don't teach why. It took till calculus to learn where 4/3*pi*r^3 comes from. Until then, we're asked to just memorize formulas. I never did memorize formulas well. If I understood something, I was good, but wrote memorization of formulas didn't work for me. I failed some math tests in 3rd grade because they were memorizing multiplication tables. I could do multiplication, but not as quickly as the other students could write the answers to pre-memorized tables. I kept running out of time.
the problem reversed when we started division. Because I truly understood multiplication (didn't just memorize tables), I immediately understood division. Then comes fractions. Most students dread fractions at first. Why? Because they don't understand them. 10/4 is 10 divided by 4. If you know division, you know fractions, it's just a different way of writing the problem. In fact, I prefer fractions to division. It'd hate to write out in decimal 13/9, but I can simplify that to 1 4/9 in a heart been and keep going...
Over-all, there's a belief that children can't understand complicated material. We start teaching simple material and make is more complicated as we go. The problem is, it's like making a foundation out of packed dirt because that's all you need for a hut, and then building a house on it. Really, we should spend more time teaching the basics: how numbers work, and then teaching the rest would take much less time.
Saturday, July 11, 2015
Saturday, July 4, 2015
Imigration
Donald Trump, playing his usual role of Court Jester, put on quite a show with his stump speech. If I were to believe him, everything wrong with America is an immigrant's fault. Well, that may be true (just ask the Native Americans, with whom I share some blood), but in the context of his speech, far from it. Is he right about some of it? Yes. Most immigrants from Mexico are not well educated. They don't have a lot of money. I know some that are, but most are not.
Does the constant ingress of uneducated, possibly unskilled, impoverished people hurt the economy? Yes. Are the people worthless? No. Go back a hundred years (not that long ago) and ask a New York native about the Irish. Things have changed in 100 years, but not the rhetoric.
I'm not a huge fan of immigration, I'll come right out and say. I don't like Mexican culture. I don't like Mexican music. I HATE the way the Catholic church has worsened the poverty by discouraging birth control. Unlike the Irish, most of the new immigrants can't even speak English, and rather than learn, states have pandered to them by providing services in Spanish.
Building a wall for billions of dollars, and patrolling the border for millions more per year, while great for local businesses and those who take the job, is not the way to discourage immigration. No one who, as things are, risks all they have to get across the border, is going to be the slightest bit more deterred by a fence. That, and militarizing the border doesn't do great things to our diplomatic relationship with our neighbors.
If we really want people stop coming here, maybe we should help them find good-paying jobs in their own country, where their family lives, where they share a culture and a language, and where they really want to be. In short, to fix the burden immigrants put on the U.S. economy, maybe we should help fix Mexico's?
Let's be fair about this: a lot of Mexico's economic woes are our fault, as is much of the border violence. Mexico, unlike the U.S. outlaws private ownership of firearms. Many (perhaps most) of the weapons the drug cartels use, come from the U.S. On the flip side, most of the drugs those cartels profit from are sold in the U.S. Why? Because it's illegal to grow, produce, or sell them here, resulting in a black market ripe for exploitation.
So to start, we can end the War on Drugs, which, like most of our "Wars' since Vietnam, has succeeded in producing better drug lords, more refined drugs, and steeper profit margins, but has utterly failed to achieve it's goals of a drug-free U.S. By drugs here, I am referring, of coarse, to those not produced and distributed by big pharmaceuticals (well, not anymore at least).
Once the black market has dried up (because it's cheaper to produce in desert-rich west Texas than ac cross the boarder with the check points and all), profits will plummet for the cartels, and mos of them will go on to more lucrative endeavors. With a stabilized border, we can proceed to sending teachers to the border villages to help increase over-all education. Like we do in Japan, we can teach them English while we're at it...
Ultimately, as Mexico's economy improves (and someone finances free condoms), there will be far less immigration into the U.S. Then, the economic burden of the local immigrants will decrease. This does, of coarse, mean no more slave labor for local corporations to exploit, more expensive construction costs, and more expensive imported Mexican clothes (have you looked at the Made In tag on that shirt?). Overall, the bottom range wages will go up with less unskilled workforce willing to work for peanuts, but general expenses will go up.
Ultimately, however, as long as it's cheaper to provide goods and services elsewhere, investor conscious CEOs will keep moving those services to the least expensive locations. So while local wages will increase in the short run, available jobs may ultimately decrease. See, the problem isn't the immigrants, it's free trade and multi-national corporations. More than that, the problem is the stock market and it's dependence on not increasing profitability, but increases in the increasing of profitability.
For those that don't understand, I'll fill you in. A company goes public by selling a portion of the company to investors at large (the stock market). The value of the stock is based on the demand for it, which is in turn determined by the risk / reward ratio of the purchase. That is, does the value of the stock increase or decrease, and by how much how quickly?
A company that shows a profit then must either invest the profit in itself (theoretically driving up the value of the stock), or give holders a portion of the profit. If more stock is needed, then it may be split, resulting in a return to the holder of half the value of stock (a dividend).
So as a company is becoming bigger, and more profitable, stock purchases increase, resulting in more available cash, potentially increasing the bottom line, and driving up the value of the stock. The problem is, this upward trend is not infinitely sustainable. Eventually, the profit will stagnate. Now, that isn't the company actually losing money. That isn't even the company showing expenses in excess of income (in the red). That's simply the company not growing at it's previous rate. At this point, the stock can only decrease in value (unless it's split, which can be expensive). This results in a high risk but low reward environment for the value of the stock (high value, as it's grown, but the value could decrease). Investors start liquidating the stock, and the value plummets. Now, this isn't really a problem for a company, as it's already got the capital from the initial investments and subsequent purchases, but it is for the majority stock holders. The "board" then must act to stop the free fall. They must cut costs to increase the profitability of the company. They will inevitably hire a CEO that will destroy the company in order to re-value the stock. By this I mean that they will sell off assets, fire good people, and move local operations to cheaper countries (where the product will likely suffer from quality control lapses and low worker enthusiasm). In the process, however, the profit of the company will skyrocket resulting in a new stock value surge. During this time the smart investors will slowly sell off their shares and find something new. The company will then have a second crash due to lack of any useful assets, and may or may not get re-built by a new CEO. Meanwhile the CEO who destroyed the company will be hired by another board in a similar position after being let go with a huge severance package. This is capitalism at it's more corrupt. Well, almost most corrupt.
This process is fueled by free trade, where the company can simply move operations to less expensive locations rather than investing in local resources. It's largely responsible for the rising economic inequality, and a number of recessions. Just think of the dotcom bust, as a leading example. It's fueled by America's love for gambling (really, the stock market is a form of gambling).
The problem is several-fold. First, fewer jobs in the U.S. and more people looking for them means that, in a free market, wages are suppressed. The same effect, in reverse, is what drives the move. Lots of people in few jobs have already suppressed wages in the new location. Because wages are low, the populous will never have access to education and other tools to get out of poverty, and wages will remain low. If they don't, the company will find somewhere new with low wages to exploit.
We live in a global economy, and this is a global issue. As Americans we take for granted our quality of life. Ask a laborer in a factory in China or working at one of the call centers everyone hates in India, and they'll tell you about their living conditions that will but all but the poorest Americans to shame. They're the lucky ones that have jobs, too. The absurdity, though, is that this is all means by which a few elites get exuberantly wealthy and use that wealth and influence to craft economic policies to their liking.
As American, we can't change the laws in India or China, but we can tariff the shit out of their goods, making it less expensive to make in the U.S. than import (and helping the tax base a lot, too). However, that means that $10 shirt will be $25 and we can't have that...
Does the constant ingress of uneducated, possibly unskilled, impoverished people hurt the economy? Yes. Are the people worthless? No. Go back a hundred years (not that long ago) and ask a New York native about the Irish. Things have changed in 100 years, but not the rhetoric.
I'm not a huge fan of immigration, I'll come right out and say. I don't like Mexican culture. I don't like Mexican music. I HATE the way the Catholic church has worsened the poverty by discouraging birth control. Unlike the Irish, most of the new immigrants can't even speak English, and rather than learn, states have pandered to them by providing services in Spanish.
Building a wall for billions of dollars, and patrolling the border for millions more per year, while great for local businesses and those who take the job, is not the way to discourage immigration. No one who, as things are, risks all they have to get across the border, is going to be the slightest bit more deterred by a fence. That, and militarizing the border doesn't do great things to our diplomatic relationship with our neighbors.
If we really want people stop coming here, maybe we should help them find good-paying jobs in their own country, where their family lives, where they share a culture and a language, and where they really want to be. In short, to fix the burden immigrants put on the U.S. economy, maybe we should help fix Mexico's?
Let's be fair about this: a lot of Mexico's economic woes are our fault, as is much of the border violence. Mexico, unlike the U.S. outlaws private ownership of firearms. Many (perhaps most) of the weapons the drug cartels use, come from the U.S. On the flip side, most of the drugs those cartels profit from are sold in the U.S. Why? Because it's illegal to grow, produce, or sell them here, resulting in a black market ripe for exploitation.
So to start, we can end the War on Drugs, which, like most of our "Wars' since Vietnam, has succeeded in producing better drug lords, more refined drugs, and steeper profit margins, but has utterly failed to achieve it's goals of a drug-free U.S. By drugs here, I am referring, of coarse, to those not produced and distributed by big pharmaceuticals (well, not anymore at least).
Once the black market has dried up (because it's cheaper to produce in desert-rich west Texas than ac cross the boarder with the check points and all), profits will plummet for the cartels, and mos of them will go on to more lucrative endeavors. With a stabilized border, we can proceed to sending teachers to the border villages to help increase over-all education. Like we do in Japan, we can teach them English while we're at it...
Ultimately, as Mexico's economy improves (and someone finances free condoms), there will be far less immigration into the U.S. Then, the economic burden of the local immigrants will decrease. This does, of coarse, mean no more slave labor for local corporations to exploit, more expensive construction costs, and more expensive imported Mexican clothes (have you looked at the Made In tag on that shirt?). Overall, the bottom range wages will go up with less unskilled workforce willing to work for peanuts, but general expenses will go up.
Ultimately, however, as long as it's cheaper to provide goods and services elsewhere, investor conscious CEOs will keep moving those services to the least expensive locations. So while local wages will increase in the short run, available jobs may ultimately decrease. See, the problem isn't the immigrants, it's free trade and multi-national corporations. More than that, the problem is the stock market and it's dependence on not increasing profitability, but increases in the increasing of profitability.
For those that don't understand, I'll fill you in. A company goes public by selling a portion of the company to investors at large (the stock market). The value of the stock is based on the demand for it, which is in turn determined by the risk / reward ratio of the purchase. That is, does the value of the stock increase or decrease, and by how much how quickly?
A company that shows a profit then must either invest the profit in itself (theoretically driving up the value of the stock), or give holders a portion of the profit. If more stock is needed, then it may be split, resulting in a return to the holder of half the value of stock (a dividend).
So as a company is becoming bigger, and more profitable, stock purchases increase, resulting in more available cash, potentially increasing the bottom line, and driving up the value of the stock. The problem is, this upward trend is not infinitely sustainable. Eventually, the profit will stagnate. Now, that isn't the company actually losing money. That isn't even the company showing expenses in excess of income (in the red). That's simply the company not growing at it's previous rate. At this point, the stock can only decrease in value (unless it's split, which can be expensive). This results in a high risk but low reward environment for the value of the stock (high value, as it's grown, but the value could decrease). Investors start liquidating the stock, and the value plummets. Now, this isn't really a problem for a company, as it's already got the capital from the initial investments and subsequent purchases, but it is for the majority stock holders. The "board" then must act to stop the free fall. They must cut costs to increase the profitability of the company. They will inevitably hire a CEO that will destroy the company in order to re-value the stock. By this I mean that they will sell off assets, fire good people, and move local operations to cheaper countries (where the product will likely suffer from quality control lapses and low worker enthusiasm). In the process, however, the profit of the company will skyrocket resulting in a new stock value surge. During this time the smart investors will slowly sell off their shares and find something new. The company will then have a second crash due to lack of any useful assets, and may or may not get re-built by a new CEO. Meanwhile the CEO who destroyed the company will be hired by another board in a similar position after being let go with a huge severance package. This is capitalism at it's more corrupt. Well, almost most corrupt.
This process is fueled by free trade, where the company can simply move operations to less expensive locations rather than investing in local resources. It's largely responsible for the rising economic inequality, and a number of recessions. Just think of the dotcom bust, as a leading example. It's fueled by America's love for gambling (really, the stock market is a form of gambling).
The problem is several-fold. First, fewer jobs in the U.S. and more people looking for them means that, in a free market, wages are suppressed. The same effect, in reverse, is what drives the move. Lots of people in few jobs have already suppressed wages in the new location. Because wages are low, the populous will never have access to education and other tools to get out of poverty, and wages will remain low. If they don't, the company will find somewhere new with low wages to exploit.
We live in a global economy, and this is a global issue. As Americans we take for granted our quality of life. Ask a laborer in a factory in China or working at one of the call centers everyone hates in India, and they'll tell you about their living conditions that will but all but the poorest Americans to shame. They're the lucky ones that have jobs, too. The absurdity, though, is that this is all means by which a few elites get exuberantly wealthy and use that wealth and influence to craft economic policies to their liking.
As American, we can't change the laws in India or China, but we can tariff the shit out of their goods, making it less expensive to make in the U.S. than import (and helping the tax base a lot, too). However, that means that $10 shirt will be $25 and we can't have that...
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