In the US, export control is regulated by the Bureau of Industry and Security, a division of the Department of Commerce. The list of controlled technologies is here; see the relevant "Category" at the bottom of the page.
Note that "export" has a specific definition that includes "technology", and one may violate these regulations by merely telling a foreign national of the "wrong" country about a controlled technology, even if both of you are inside the US: Actual transport of a physical object across a national border is not required to violate these regulations.
He does not have "actually filed criminal charges against him." RTFA: "Assange is wanted for questioning in [Sweden] over allegations of sexual impropriety made by two women. He has not been charged with any offence and has offered to answer any questions the prosecutors may have."
Not advertised: if the utility company is having trouble making money or needs a place to sink their spinning reserves during off-peak demand, they can use SG to raise the delivered voltage to end customers. Your lights will burn a little brighter, but you probably won't notice. It will also cost you a little bit more. Too bad.
If you think your utility is purchasing extra fuel because it's having trouble making money, either you or it is living in a dreamworld, and I know which way to bet. The utility does have "a place to sink [its] spinning reserves during off-peak demand": It's called the "off" mode -- when it costs the least per hour -- or the "sell" mode, when it sells its electricity to another utility that needs it to handle its peak demand. Peak generating capacity is always far more expensive to run than off-peak generating capacity, and no utility rate structure with which I am familiar fully captures those costs.
Not advertised: the utility can replace fast-response generators like natural gas with slower response generators like coal, because they don't need as much fast response generation capacity to deal with their now smaller peaks. Of course, coal has a bigger carbon footprint than gas. Too bad.
The slowest-response generators are powered by nuclear reactors, which have an even lower carbon footprint. It's ideal in most regions of the US to operate the nuclear plants 24/7, then run the gas plants as needed. We can have a long thread on the pros and cons of coal-fired power plants (of which I won't take part), but in the US at least the environmental costs of coal are becoming significant.
I've heard of electromagnetic frequency radiation, but not electromagnetic FREQUENTLY radiation. What is this?
Some types of electromagnetic energy, like cable TV signals, remain inside the equipment that generated them, or travel inside shielded transmission lines, for most of their existence, only radiating briefly when they pass by an opening in a case or somebody unplugs a cable. That's electromagnetic INFREQUENTLY radiation.
Other types of electromagnetic energy, like cellular telephone signals, easily escape their generating equipment, and spend the majority of their existence radiating freely in the environment, only occasionally becoming recaptured by a nearby antenna or recalcitrant cerebrum. That's electromagnetic FREQUENTLY radiation.
Because of the expense, very few smart meter systems use PLC (usually known as Broadband over Power Lines, or BPL, in the US). It's expensive to have to bypass all the transformers and other kit in the power grid that wasn't designed to pass communications in the first place, which is fortunate because PLC is nasty to the RF environment -- all those unshielded, long, high, conductors radiate. However, the great majority of smart meter systems with which I am familiar use either licensed channels in the UHF or 800/900 MHz land mobile bands, or use the unlicensed 868/900 or 2400 MHz ISM bands, and they're no more likely to cause interference than any other user of the spectrum.
I like that development method, too, but it does move the variable from "ship date" to "customer features". Often, as Spolsky promotes, it's a good way of doing things, since the features are not promised in advance. Sometimes, however, projects start with an agreement on just what the features are to be, and it's difficult some time later to make the unilateral decision to delay them to later releases. Without, of course, affecting payment schedules and company cash flow....
I have seen variants in which a company has two development teams, "June" and "December". Team June starts its project every 1 July, and ships every 30 June. Team December starts its project every 1 January, and ships every 31 December. If a team runs into a development snag that threatens to delay it past its due date, the feature or technology is excised from the project and placed with the following team, which then has an additional six months to work the problem. This works well for both hardware and software development (frequent new product introductions, snazzy features that work when introduced, etc.), if one has the cash to simultaneously fund two development teams.
In the real world, the longer you let someone hold your money, the better return you get. (Note the increasing coupon with increasing maturity.) This isn't some kind of academic use of the Law of Compound Interest, or some Wall Street quant's way of finding a microsecond's inequality in the market (which is, of course, the exception that proves the rule; it's called an "inequality" precisely because it's an unusual situation in which the short-term return is unexpectedly high).
Also, I did say that "[y]ou have better options and get a better return on your investment if you invest $100,000 than if you invest $1,000." It's even more true if you invest a million -- assuming you have one, of course, which is the subject under discussion.
If you truly are working for a small software development company, cost may not be the issue. Frequently (I may even say universally) the issue facing the owners of small companies is not cost, or even profitability, but cash flow -- making sure that there is enough money coming in to make the next big expense coming up (frequently payroll). In small companies there typically aren't the cash reserves available to spend on unanticipated expenses or program delays. The boss may even agree with you that the overall cost would be reduced if software testing were introduced, but may not "want to invest the time and money" because the company does not have the cash available to make the investment.
For example, the software you're working on needs to ship by the end of January to receive payment from the customer by the end of February, so that payroll can be made in March. If bug-fixing stops in January for development of the bug-fixing program, the customer doesn't get his software until the end of February, so he doesn't pay until the end of March and so payroll is missed that month. Having fewer bugs in the long term has to be balanced by the need to stay in business until the "long term" is reached.
It's like anything else in finance: You have better options and get a better return on your investment if you invest $100,000 than if you invest $1,000, but if you don't have $100,000, it doesn't much matter -- you do what you can with the resources you have available. Similarly, you get a better return if you're able to invest your money for a year than if you must have it back in a week. (The guy who said "time is money" actually knew something.) This trade between cash flow and long-term efficiency (leading, one hopes, to profitability), i.e., knowing when and how much to invest, is the real art of business management.
The solution to your problem? IMHO, incremental investment. I agree with those above who suggest implementing tests for new bugs found. This should enable you to begin to work more efficiently over time, without substantially delaying current work, while collecting metrics (I know, I know...) that can help quantify the cost of the bug re-work. Once a substantial body of tested bugs has been collected, one can institute a formal testing program (preferably by including it in the next project, so that it is a planned expense) as a cost reduction, since by then it should speed up development work over the ad hoc method then in place.
The important question to ask is, "what could such a chip be economically used for?"
Unless one is developing something for military or other national security-type purposes, where cost is typically significantly less important than attaining the ultimate in performance (however "performance" is defined in the application), the question typically is, "what's the cheapest way to do X?"
If, as is frequently the case, X is defined as "power the chip," one has an interesting economic quandary: In terms of money/area, conventional solar cells, especially amorphous solar cells, are about the cheapest form of silicon known to man. Using this new technology, though, these solar cells would be replaced by area on an integrated circuit, which is about the most expensive form of silicon known to man. Worse, the power consumed by the electronics must be minimized ("below 1 milliwatt"), so one is pressured into using very fine-lithography silicon, which is the most expensive form of silicon known to man.
The only way I can see that one wins on cost with this technology is if one has electronics that are so low-powered that they can be powered by an amorphous solar cell with an area equal to that of the circuitry itself. If you need a point of reference on the practicality of this requirement, I point you to your average solar-powered calculator, which has a solar cell area of several cm^2, and an active circuit area of probably less than 5 mm^2.
If, however, X is defined as "power the chip with a monolithic structure," perhaps for acceleration, board area, or other system-level requirements, then using external solar cells is prohibited (by the terms of the game), and then this technology begins to look more appealing. Even then, however, I would wonder if it wouldn't be easier to use chip stacking or similar technology to put a solar cell on a chip, since then each die could be processed in a manner optimum for its purpose (solar cell or integrated circuit). And, of course, you're still left with the problem of getting sufficient power from such a small area.
If you've never seen one of these patent lawsuits, they start by going through each claim (that the petitioner claims infringement), and identifies how the infringing technology contains each element of the claim. The easiest way to have such a suit dismissed is to have at least one element different (or missing) in the supposedly-infringing technology. In the case of method claims, as the GP says, just do one step differently.
As an example, the issued patent (6,053,823) has only one independent claim, which has the elements (steps) of:
-------- - adding the rank of each participating team from a first poll to the rank of each team in a second poll to obtain an initial overall rank; [element 1]
- assigning a final rank for each team, with the lowest sum of the initial overall rank constituting the highest rank, and the highest sum from the initial overall rank constituting the lowest rank; [element 2]
- conducting a championship tournament with at least the three teams having the highest final rank, comprising the steps of:
- conducting at least a first round of events to determine the two teams to play in a championship game; and
- conducting a championship game with the two teams determined from the previous round of events, to determine a champion. [element 3] --------
So to start out we see that this method requires adding the rank of each team from a couple of polls. Don't use polls? No infringement. Don't add the rankings from the two polls to establish the initial overall rank? No infringement.
Secondly, a final rank for each team must be calculated, with the highest and lowest ranks determined as described. Don't have a final rank for each team? No infringement. Determine highest and lowest differently? No infringement.
Finally, a championship tournament must be held with at least the three teams having the highest final rank, which must also have the two steps of (1) a first round of "events" to determine the two teams to play in the championship game, and (2) playing the championship game. Have only two teams in the tournament? No infringement. Don't have a first round of events? No infringement.
As I hope you can see, there are lots of ways (I've identified only a few) to have a playoff that avoids this patent. What the headline to the linked article should say is, "One Method of College Football Playoffs Patented."
The best circuit analogy I've seen to this switching between a distinct pair of alternatives is a delta-sigma analog-to-digital converter (or sigma-delta converter, depending on your dialect). This converter takes an analog signal input, but the output is only one of two values, 1 or 0. The long-term average of the output pulses is equal to the input analog voltage, but at any given instant the output is at one of the rails (1 or 0).
It's like saying that at any instant the US government is controlled by Democrats or Republicans, but the long-term average (representing the input to the system, i.e., the wishes of the people) is somewhere between these extremes. Or the old argument about whether a company should be organized around functions (having, e.g., an engineering department, a sales department, etc., each handling all products) or products (having, e.g., a Product A division, a Product B division, etc., each handling all functions). Each new CEO switches the company from one to the other, while the optimum is some unattainable blend of the two. (Don't mention matrix management.)
Interestingly, one of the most prized features of delta-sigma converters is that their noise is "shaped", that is, pushed to higher frequencies out of band, so it can be easily filtered. This greatly increases the performance attainable with a given technology. Every time I hear protest voices in democratic governments, or organizational griping by corporate salarymen, I always pause to wonder if I am listening to this feature of the converter, too. And whether I should filter it.
Good point -- you're right. It also has the same problem: While one needs to know basic facts about what happened and when in order to have a discussion of past events, the real fascination is in understanding why these events happened, or why so-and-so did such-and-such. Unfortunately, most classes never get past the rote memory of the facts, and stage 2 never happens.
If you learn basketball you have a 0.001% chance of becoming a multimillionaire , or you'll be another poor modern peasant. But at least you have a chance.
If you learn math your career will either be asking if they want fries with that, or possibly a few short years before your job moves to the east and you'll be another poor modern peasant. No chance at all.
Not quite. If you learn basketball instead of math, you have a 99.999% chance, using your numbers, of not becoming a multimillionaire and of not holding a quality job, since you also didn't learn math.
If you learn math, you'll at least be more employable than all but 432 of the guys that learned basketball (that being the number of players in the NBA), since they didn't learn math.
I note in passing that the value of a 0.001% chance at $10 million is only $100. Math helps in making career decisions, too.
I don't disagree (having taught myself), but it does become a self-fulfilling prophecy: The group of already highly-motivated students becomes smaller and smaller with every semester of unstimulating classes.
It certainly is difficult to teach the mechanics that are necessary to perform mathematics, like manipulation of fractions, while simultaneously retaining the "why is this like that?" fascination with the subject.
I honestly can not understand where there can be "beauty" in a mathematical expression that covers the entire blackboard.
No one else can, either.
The beauty is in the simple relations between apparently unrelated things that, while provably true, still seem magical and mysterious. One example:
You're probably aware that the ratio of the circumference to the diameter of a circle has been given a special name, pi. This is a practical, useful thing that seems purely geometric; you can measure the diameter of a circular hole, multiply by pi, and get the circumference of the hole. Fine.
Well, it was shown in the 17th Century (!) that pi is also equal to four times (one, minus a third, plus a fifth, minus a seventh, plus a ninth,... , on out forever). In fact there are many series of integers that are related to pi.*
Now, why would this be? What does the ratio between the circumference and the diameter of a circle have to do with the "counting numbers"? Why should there be any relationship at all? After centuries of puzzling, no one knows. ________ * My personal favorite was proven by Euler in the 18th Century: pi squared, divided by six, is equal to one over one squared, plus one over two squared, plus one over three squared,... , on out forever. What does pi have to do with the inverse squares of the integers?!?
Math [is] misunderstood because it's hard, and that's why people have misconceptions about it. [The u]nderstanding of math require[s] considerable effort and concentration which most people tend to avoid if possible.
Look, that's just flat wrong. When I was in grade school, the same people who wouldn't do their math homework would then go to the gym and shoot baskets for three hours every day. When I asked why, they would say "math is hard, it's either right or its wrong, and to be any good at all takes considerable effort." When I told them I felt the same way about shooting a basketball, and if they spent the same amount of time in a math book as they do in the gym they'd be stars at math, all I would get was funny looks. I never could understand how such people would work so hard at learning one thing -- basketball -- that they'd sweat, be out of breath, and have to take a shower afterwards, and then turn around and say that learning math was hard!
Like learning anything else (including basketball), if learning math is hard, you're learning it incorrectly, and need better instruction.
-- The parenthetical comment "(if it was done right!)" in "Ready For The Big Play" should, of course, be, "(if it were done correctly!)"
-- References in "Cargo Cult Education" to the "south Pacific" should be to the "South Pacific"
-- Also in "Cargo Cult Education", "But of course nothing came. (except, eventually, some anthropologists!)" should be, "But of course nothing came (except, eventually, some anthropologists!)."
This is by far the best defense of mathematics I've ever read. It's a shame that the poor quality of grade school math education has made it necessary, though. Can one imagine a similar essay on any other subject? Only math is so poorly taught.
Please do submit again. A thick skin is sometimes needed at first, but you'll get the customs down soon enough, and a high-quality submission like yours is always appreciated.
Slashdot Mirror
In the US, export control is regulated by the Bureau of Industry and Security, a division of the Department of Commerce. The list of controlled technologies is here; see the relevant "Category" at the bottom of the page.
Note that "export" has a specific definition that includes "technology", and one may violate these regulations by merely telling a foreign national of the "wrong" country about a controlled technology, even if both of you are inside the US: Actual transport of a physical object across a national border is not required to violate these regulations.
He does not have "actually filed criminal charges against him." RTFA: "Assange is wanted for questioning in [Sweden] over allegations of sexual impropriety made by two women. He has not been charged with any offence and has offered to answer any questions the prosecutors may have."
Who let the word out?!?
Ah, you must be in the UK.
If you think your utility is purchasing extra fuel because it's having trouble making money, either you or it is living in a dreamworld, and I know which way to bet. The utility does have "a place to sink [its] spinning reserves during off-peak demand": It's called the "off" mode -- when it costs the least per hour -- or the "sell" mode, when it sells its electricity to another utility that needs it to handle its peak demand. Peak generating capacity is always far more expensive to run than off-peak generating capacity, and no utility rate structure with which I am familiar fully captures those costs.
The slowest-response generators are powered by nuclear reactors, which have an even lower carbon footprint. It's ideal in most regions of the US to operate the nuclear plants 24/7, then run the gas plants as needed. We can have a long thread on the pros and cons of coal-fired power plants (of which I won't take part), but in the US at least the environmental costs of coal are becoming significant.
Some types of electromagnetic energy, like cable TV signals, remain inside the equipment that generated them, or travel inside shielded transmission lines, for most of their existence, only radiating briefly when they pass by an opening in a case or somebody unplugs a cable. That's electromagnetic INFREQUENTLY radiation.
Other types of electromagnetic energy, like cellular telephone signals, easily escape their generating equipment, and spend the majority of their existence radiating freely in the environment, only occasionally becoming recaptured by a nearby antenna or recalcitrant cerebrum. That's electromagnetic FREQUENTLY radiation.
Anything else?
It sounds like you're mixing up two technologies -- wireless smart meters and power line communication. The two are orthogonal and independent.
Because of the expense, very few smart meter systems use PLC (usually known as Broadband over Power Lines, or BPL, in the US). It's expensive to have to bypass all the transformers and other kit in the power grid that wasn't designed to pass communications in the first place, which is fortunate because PLC is nasty to the RF environment -- all those unshielded, long, high, conductors radiate. However, the great majority of smart meter systems with which I am familiar use either licensed channels in the UHF or 800/900 MHz land mobile bands, or use the unlicensed 868/900 or 2400 MHz ISM bands, and they're no more likely to cause interference than any other user of the spectrum.
Merci pour vos commentaires, et toutes mes excuses pour mon mauvaise connaissance de la langue française.
I like that development method, too, but it does move the variable from "ship date" to "customer features". Often, as Spolsky promotes, it's a good way of doing things, since the features are not promised in advance. Sometimes, however, projects start with an agreement on just what the features are to be, and it's difficult some time later to make the unilateral decision to delay them to later releases. Without, of course, affecting payment schedules and company cash flow....
I have seen variants in which a company has two development teams, "June" and "December". Team June starts its project every 1 July, and ships every 30 June. Team December starts its project every 1 January, and ships every 31 December. If a team runs into a development snag that threatens to delay it past its due date, the feature or technology is excised from the project and placed with the following team, which then has an additional six months to work the problem. This works well for both hardware and software development (frequent new product introductions, snazzy features that work when introduced, etc.), if one has the cash to simultaneously fund two development teams.
In the real world, the longer you let someone hold your money, the better return you get. (Note the increasing coupon with increasing maturity.) This isn't some kind of academic use of the Law of Compound Interest, or some Wall Street quant's way of finding a microsecond's inequality in the market (which is, of course, the exception that proves the rule; it's called an "inequality" precisely because it's an unusual situation in which the short-term return is unexpectedly high).
Also, I did say that "[y]ou have better options and get a better return on your investment if you invest $100,000 than if you invest $1,000." It's even more true if you invest a million -- assuming you have one, of course, which is the subject under discussion.
If you truly are working for a small software development company, cost may not be the issue. Frequently (I may even say universally) the issue facing the owners of small companies is not cost, or even profitability, but cash flow -- making sure that there is enough money coming in to make the next big expense coming up (frequently payroll). In small companies there typically aren't the cash reserves available to spend on unanticipated expenses or program delays. The boss may even agree with you that the overall cost would be reduced if software testing were introduced, but may not "want to invest the time and money" because the company does not have the cash available to make the investment.
For example, the software you're working on needs to ship by the end of January to receive payment from the customer by the end of February, so that payroll can be made in March. If bug-fixing stops in January for development of the bug-fixing program, the customer doesn't get his software until the end of February, so he doesn't pay until the end of March and so payroll is missed that month. Having fewer bugs in the long term has to be balanced by the need to stay in business until the "long term" is reached.
It's like anything else in finance: You have better options and get a better return on your investment if you invest $100,000 than if you invest $1,000, but if you don't have $100,000, it doesn't much matter -- you do what you can with the resources you have available. Similarly, you get a better return if you're able to invest your money for a year than if you must have it back in a week. (The guy who said "time is money" actually knew something.) This trade between cash flow and long-term efficiency (leading, one hopes, to profitability), i.e., knowing when and how much to invest, is the real art of business management.
The solution to your problem? IMHO, incremental investment. I agree with those above who suggest implementing tests for new bugs found. This should enable you to begin to work more efficiently over time, without substantially delaying current work, while collecting metrics (I know, I know...) that can help quantify the cost of the bug re-work. Once a substantial body of tested bugs has been collected, one can institute a formal testing program (preferably by including it in the next project, so that it is a planned expense) as a cost reduction, since by then it should speed up development work over the ad hoc method then in place.
what could such a chip be used for?
The important question to ask is, "what could such a chip be economically used for?"
Unless one is developing something for military or other national security-type purposes, where cost is typically significantly less important than attaining the ultimate in performance (however "performance" is defined in the application), the question typically is, "what's the cheapest way to do X?"
If, as is frequently the case, X is defined as "power the chip," one has an interesting economic quandary: In terms of money/area, conventional solar cells, especially amorphous solar cells, are about the cheapest form of silicon known to man. Using this new technology, though, these solar cells would be replaced by area on an integrated circuit, which is about the most expensive form of silicon known to man. Worse, the power consumed by the electronics must be minimized ("below 1 milliwatt"), so one is pressured into using very fine-lithography silicon, which is the most expensive form of silicon known to man.
The only way I can see that one wins on cost with this technology is if one has electronics that are so low-powered that they can be powered by an amorphous solar cell with an area equal to that of the circuitry itself. If you need a point of reference on the practicality of this requirement, I point you to your average solar-powered calculator, which has a solar cell area of several cm^2, and an active circuit area of probably less than 5 mm^2.
If, however, X is defined as "power the chip with a monolithic structure," perhaps for acceleration, board area, or other system-level requirements, then using external solar cells is prohibited (by the terms of the game), and then this technology begins to look more appealing. Even then, however, I would wonder if it wouldn't be easier to use chip stacking or similar technology to put a solar cell on a chip, since then each die could be processed in a manner optimum for its purpose (solar cell or integrated circuit). And, of course, you're still left with the problem of getting sufficient power from such a small area.
You mean Disneyworld. It's the guys at Vandenberg that have to avoid the nuns and orphans on their way to Disneyland (still no picnic).
No, the GP is absolutely right.
If you've never seen one of these patent lawsuits, they start by going through each claim (that the petitioner claims infringement), and identifies how the infringing technology contains each element of the claim. The easiest way to have such a suit dismissed is to have at least one element different (or missing) in the supposedly-infringing technology. In the case of method claims, as the GP says, just do one step differently.
As an example, the issued patent (6,053,823) has only one independent claim, which has the elements (steps) of:
--------
- adding the rank of each participating team from a first poll to the rank of each team in a second poll to obtain an initial overall rank; [element 1]
- assigning a final rank for each team, with the lowest sum of the initial overall rank constituting the highest rank, and the highest sum from the initial overall rank constituting the lowest rank; [element 2]
- conducting a championship tournament with at least the three teams having the highest final rank, comprising the steps of:
- conducting at least a first round of events to determine the two teams to play in a championship game; and
- conducting a championship game with the two teams determined from the previous round of events, to determine a champion. [element 3]
--------
So to start out we see that this method requires adding the rank of each team from a couple of polls. Don't use polls? No infringement. Don't add the rankings from the two polls to establish the initial overall rank? No infringement.
Secondly, a final rank for each team must be calculated, with the highest and lowest ranks determined as described. Don't have a final rank for each team? No infringement. Determine highest and lowest differently? No infringement.
Finally, a championship tournament must be held with at least the three teams having the highest final rank, which must also have the two steps of (1) a first round of "events" to determine the two teams to play in the championship game, and (2) playing the championship game. Have only two teams in the tournament? No infringement. Don't have a first round of events? No infringement.
As I hope you can see, there are lots of ways (I've identified only a few) to have a playoff that avoids this patent. What the headline to the linked article should say is, "One Method of College Football Playoffs Patented."
The best circuit analogy I've seen to this switching between a distinct pair of alternatives is a delta-sigma analog-to-digital converter (or sigma-delta converter, depending on your dialect). This converter takes an analog signal input, but the output is only one of two values, 1 or 0. The long-term average of the output pulses is equal to the input analog voltage, but at any given instant the output is at one of the rails (1 or 0).
It's like saying that at any instant the US government is controlled by Democrats or Republicans, but the long-term average (representing the input to the system, i.e., the wishes of the people) is somewhere between these extremes. Or the old argument about whether a company should be organized around functions (having, e.g., an engineering department, a sales department, etc., each handling all products) or products (having, e.g., a Product A division, a Product B division, etc., each handling all functions). Each new CEO switches the company from one to the other, while the optimum is some unattainable blend of the two. (Don't mention matrix management.)
Interestingly, one of the most prized features of delta-sigma converters is that their noise is "shaped", that is, pushed to higher frequencies out of band, so it can be easily filtered. This greatly increases the performance attainable with a given technology. Every time I hear protest voices in democratic governments, or organizational griping by corporate salarymen, I always pause to wonder if I am listening to this feature of the converter, too. And whether I should filter it.
Good point -- you're right. It also has the same problem: While one needs to know basic facts about what happened and when in order to have a discussion of past events, the real fascination is in understanding why these events happened, or why so-and-so did such-and-such. Unfortunately, most classes never get past the rote memory of the facts, and stage 2 never happens.
I might throw in one other: Civics. (Or grammar.)
If you learn basketball you have a 0.001% chance of becoming a multimillionaire , or you'll be another poor modern peasant. But at least you have a chance.
If you learn math your career will either be asking if they want fries with that, or possibly a few short years before your job moves to the east and you'll be another poor modern peasant. No chance at all.
Not quite. If you learn basketball instead of math, you have a 99.999% chance, using your numbers, of not becoming a multimillionaire and of not holding a quality job, since you also didn't learn math.
If you learn math, you'll at least be more employable than all but 432 of the guys that learned basketball (that being the number of players in the NBA), since they didn't learn math.
I note in passing that the value of a 0.001% chance at $10 million is only $100. Math helps in making career decisions, too.
I don't disagree (having taught myself), but it does become a self-fulfilling prophecy: The group of already highly-motivated students becomes smaller and smaller with every semester of unstimulating classes.
It certainly is difficult to teach the mechanics that are necessary to perform mathematics, like manipulation of fractions, while simultaneously retaining the "why is this like that?" fascination with the subject.
I honestly can not understand where there can be "beauty" in a mathematical expression that covers the entire blackboard.
No one else can, either.
The beauty is in the simple relations between apparently unrelated things that, while provably true, still seem magical and mysterious. One example:
You're probably aware that the ratio of the circumference to the diameter of a circle has been given a special name, pi. This is a practical, useful thing that seems purely geometric; you can measure the diameter of a circular hole, multiply by pi, and get the circumference of the hole. Fine.
Well, it was shown in the 17th Century (!) that pi is also equal to four times (one, minus a third, plus a fifth, minus a seventh, plus a ninth, ... , on out forever). In fact there are many series of integers that are related to pi.*
Now, why would this be? What does the ratio between the circumference and the diameter of a circle have to do with the "counting numbers"? Why should there be any relationship at all? After centuries of puzzling, no one knows. ... , on out forever. What does pi have to do with the inverse squares of the integers?!?
________
* My personal favorite was proven by Euler in the 18th Century:
pi squared, divided by six, is equal to one over one squared, plus one over two squared, plus one over three squared,
Math [is] misunderstood because it's hard, and that's why people have misconceptions about it. [The u]nderstanding of math require[s] considerable effort and concentration which most people tend to avoid if possible.
Look, that's just flat wrong. When I was in grade school, the same people who wouldn't do their math homework would then go to the gym and shoot baskets for three hours every day. When I asked why, they would say "math is hard, it's either right or its wrong, and to be any good at all takes considerable effort." When I told them I felt the same way about shooting a basketball, and if they spent the same amount of time in a math book as they do in the gym they'd be stars at math, all I would get was funny looks. I never could understand how such people would work so hard at learning one thing -- basketball -- that they'd sweat, be out of breath, and have to take a shower afterwards, and then turn around and say that learning math was hard!
Like learning anything else (including basketball), if learning math is hard, you're learning it incorrectly, and need better instruction.
Brilliant -- a live version of "A Pathway into Number Theory". That's the kind of teaching for which awards should be given.
-- The parenthetical comment "(if it was done right!)" in "Ready For The Big Play" should, of course, be, "(if it were done correctly!)"
-- References in "Cargo Cult Education" to the "south Pacific" should be to the "South Pacific"
-- Also in "Cargo Cult Education", "But of course nothing came. (except, eventually, some anthropologists!)" should be, "But of course nothing came (except, eventually, some anthropologists!)."
This is by far the best defense of mathematics I've ever read. It's a shame that the poor quality of grade school math education has made it necessary, though. Can one imagine a similar essay on any other subject? Only math is so poorly taught.
Please do submit again. A thick skin is sometimes needed at first, but you'll get the customs down soon enough, and a high-quality submission like yours is always appreciated.
... when the time comes for the kids to grow up, we'll just sell them as slaves to the Chinese.
...but they'll be illiterate. Would the Chinese want them?