I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA.
"Geometric Algebra Primer" by Jaap Suter Gives a gentle introduction and reference for the basic GA operations.
"3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne Gives a hands-on, step-by-step tutorial using the free open-source GA visualization software GA Viewer. This tutorial uses the conformal model which is more advanced than the regular 3-D model. Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd.
I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing General Relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA.
"Geometric Algebra Primer" by Jaap Suter Gives a more gentle introduction and reference for the basic GA operations.
"3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne Gives a hands-on, step-by-step tutorial using their free open-source GA visualization software, "GAViewer". This tutorial uses the conformal model which is more advanced than the regular 3-D model. (2 extra dimensions, of a very odd but useful type) Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd. (The 2nd edition is worth getting on paper. It has some very useful reference pages not available online, and many corrected errata.)
Facebook is not news. Facebook is not for nerds, it is for fools. What we need is not more Facebook folderol, but a script that will mod -3 (idjit) anybody who is damn fool enough to even entertain the notion of having a Facebook account.
"IQ tests are not valid in this regard because you don't test for the right things: They don't test for long-term strategy and thinking ahead months, years or even decades."
Yeah, I was just thinking: this is just like Natalie Portman, covered in hot grits, except without the grits. Or Natalie Portman. Imagine a Beowulf cluster of those, and you've got a really big empty space.
I dunno... using over-proof-vodka-and-nitrous-oxide rockets seemed like a good design idea at the time, but it might somehow have had some indirect effects on quality control....
Well that's one way of thinking about it, but it seems backwards. Yes you can span the whole range from a supernova to the inside of a coal seam using just 1 bit, but typically dynamic range is measured in stops or bits (essentially the same thing, a power of two in light intensity), and what we want to know is the range of different gradations that can be distinguished.
The extra values are actually always mostly in the highlights. Sensors are linear. The brightest stop (of between 8-14 stops of dynamic range in a digital camera) always has half the values, the next stop has another quarter, the next another eighth. The top three stops (highlights to upper midtones) has 7/8ths of the codes. For an 8-bit per channel device that leaves 32 codes to represent all the data in the bottom 5 to 11 stops of dynamic range, which leads to noise, dithering, banding and other artifacts. With 16 bits per channel there are 8192 codes for that lower region (and 57,343 for the upper stops), so that's the same factor increase for both ranges (256x), but the extra midtone and shadow information matters more - we can visually distinguish (with our log-sensitive eyeballs) more than 32 shades in that lower range, while 224 codes for the upper range is far closer to adequate. In that way, you're right about most of the useful new codes going to the darker areas.
The effective black level is set by the noise floor, which is mostly an inverse function of the size of the pixels plus a set amount of read noise for each readout. The white level in photometric terms is limited most directly by the pixel full-well capacity, and the amount of light excluded from the camera, so there is a lot more room to capture brighter things than fainter things - we can always cut out more light, even if it means going to a pinhole camera with a welding-mask filter, while we can't improve the noise floor much or gain more information from longer exposures past a certain point. Most of the increase in dynamic range comes from the highlights, most of the useful increase comes from the shadows.
Yes. A digital photo can have a dynamic range of over 12 stops in each channel, even 14 on a really good camera. Half the light level codes in a channel are in the brightest stop, e.g. 1024 of 2048 for a 12 stop dynamic range. There is no point in shooting RAW format with its additional dynamic range if you're going to edit it in a lousy 8 bits per pixel.
I wish programs for monitors and cameras would not say DPI. It's PPI, pixels per inch, which is not at all the same thing as the DPI that a printer produces.
"US Manufacturing output was at an all-time high immediately before the current recession"
What, in nominal dollars? Or counting the profits of offshoring by US companies? Or the non-productive consumable goods like bombs and land mines? Or McDonald's? (No, really!) Or counting products assembled in the US from foreign parts? Yeah, when 90% of the product and 2% of the cost come from China, the accounting makes that US-assembled product look like we're making stuff, but it isn't true. Sandwiches and paper plates do not count as manufacturing, either. What does US durable goods production look like after deducting the partially-finished foreign parts component, that's the real story.
When it gets down to it — talking trade balances here — once we've brain-drained all our technology into other countries, once things have evened out, they're making cars in Bolivia and microwave ovens in Tadzhikistan and selling them here — once our edge in natural resources has been made irrelevant by giant Hong Kong ships and dirigibles that can ship North Dakota all the way to New Zealand for a nickel — once the Invisible Hand has taken away all those historical inequities and smeared them out into a broad global layer of what a Pakistani brickmaker would consider to be prosperity — y'know what? There's only four things we do better than anyone else: music movies microcode (software) high-speed pizza delivery
-Neal Stephenson, Snow Crash
(but we've given up on high-speed pizza delivery, and the microcode is draining away, too.)
Funny, I didn't see 20% real unemployment in the 1950s, either.
If you ship your production overseas, your process engineering, your design, your support, your sales and ultimately your whole economy will follow. Without a broad earnings base among the population, who will be able to buy your products? Not the ~90% of the population with shrinking earnings. And once everything is overseas, why does the overseas supplier need the US company who was doing the outsourcing? They just take the market from that hollowed-out US shell.
No, it isn't like that at all - these particular laws were bought and paid for by the corporations expressly to give themselves power at the expense of their employees' natural rights.
But performance on most subscales of IQ tests is at its maximum at age 16. Vocabulary and knowledge continue to improve at a glacial pace up to 40. The frontal lobe changes do not necessarily show improvement, but only change (and the changes are negligible).
"It's not merely a coincidence..." No, low education, poverty and criminality all usually flow from the common factor being genetically or otherwise permanently low IQ. Such people can benefit if they have classes tailored to their level, but putting them in with the average and above average students just holds everybody back. Low IQ people are by definition slower to learn, so their education should not waste time on things they will never need or understand, but rather focus on getting them prepared for life - practical rules of thumb, good habits, handing their own finances, being employable at something, knowing when they should get advice rather than trying to figure things out on their own. Most of them would do better to have experience working or being apprenticed after about 16 than further intensive schooling - they could do half-time at school and still get all they were likely to get out of the experience.
They wouldn't have to be forced to go to these mini-prisons if school weren't 90% bullshit. Even the dumb kids realize it. The solution isn't force, and raising kids in day-camp prisons but getting rid of the force and replacing the bullshit with something useful and interesting. Read John Taylor Gatto's work for what is wrong with schools, how things used to be different and how things could be improved.
You seem to think that a business should arbitrarily compensate capital at above market rates, despite not actually needing that capital, while being entirely dependent on - indeed having no existence as a going concern without - the work of its employees. Capital does not produce profit, it chases it. Employees are the source of profit in established businesses. They are people, not interchangeable widgets bought by the great-gross. They, not the stockholders, are the company.
Capital, on the other hand, is just ledger entries in a computer at Cede & Co., born out of loans to brokerages not backed by deposits but ultimately by other loans made by the Federal reserve to its stockholders, the big banks who get to spend the inflated money supply first, before prices rise. It's a scam, the market isn't free, but totally managed for the benefit of bankers creating money from thin air. These thieves don't deserve greater rewards, power and respect than the people who actually make real value with their work, but dupes keep repeating the class-war propaganda of the thieves' wholly owned mouthpieces.
So people should take whatever the employer offers? No bargaining? Capital should gang up into collectives to bargain, that doesn't distort the market, but labor should not? After all the corporation is free to fire them all, or lock them out, right? But they don't, because they can't find that many replacements quickly enough to prevent a quarterly loss at the least. And in the middle of the great recession, you really think 45,000 people with specialized skills can all go out at once and find new jobs, when there are already ten million out looking for work? Verizon is doing well enough to pay over $50M to its top 5 executives a year (speaking of squeezing out undeserved money), to make good, increasing profits, yet they don't make enough to be able to afford to meet the obligations that they had previously been meeting? You do realize that no innovation or research is done by top telecom management, right? And that all the work of actually making the phones and DSL work is done by non-management employees, right? And that the issue is not employees squeezing undeserved money but Verizon not wanting to continue to pay the same health insurance that they had been paying, just because they thought they could get away with it?
The top 10% in wealth own over 81% of all stocks, 98% of other financial securities and over 93% of all business equity. from: Wolff, E. N. (2010). Recent trends in household wealth in the United States: Rising debt and the middle-class squeeze - an update to 2007. Working Paper No. 589. Annandale-on-Hudson, NY: The Levy Economics Institute of Bard College
Unless one owns at least several percent of a business, you have no effective say in how it is run (CEOs excepted, of course.) The money paid to CEOs is simply a warm gesture of respect to themselves. Stockholders have no effective say when it is the management sets the slate of board candidates and votes all the shares that didn't send in a proxy. The board members want to keep their sinecures, so they go along with whatever the CEO wants for himself, using the cover of a compensation committee and a consultant who can be relied upon to deliver the answer the customer wants.
And how much covert sabotage was conducted by management, by policy? Those confusing tariffs that keep services secret and obligations obtuse didn't write themselves, you know. The apparently nonsensical procedures that create bureaucratic run-arounds are there for a reason - management evading obligations to provide the service people paid for. The overpriced equipment from incestuous vendor relationships cuts the service that can be provided for everyone. The lack of good troubleshooting tools for techs, even when such tools are relatively cheap means things stay broken. (Actually fixing things is too expensive, right? We'll have our field boys just fixat it, armed with nothing much more sophisticated than a voltmeter, then game the intentionally stupid metrics we ourselves set to make it look like we still provide service.) The lobbying that prevents competitors from gaining a toehold defrauds everyone, the whole public, and destroys the potential livelihoods of those who would have worked for the competitors and the capital of their investors. Union strikes have never committed a tenth the sabotage as results from management's everyday practices.
Slashdot Mirror
Apologies for the double post. The first post disappeared after leaving the page and returning, ^-F didn't find "geometric" anywhere on the page. (?!)
I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald
Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA.
"Gravity, Gauge Theories and Geometric Algebra" by Anthony Lasenby, Chris Doran, Stephen Gull
General Relativity using GA - interestingly, curved space-time is not required using GA.
"Primer on Geometric Algebra for introductory mathematics and physics" by David Hestenes
Another good intro, much less dense than Macdonald's, with more diagrams and basic applications.
"Geometric Algebra Primer" by Jaap Suter
Gives a gentle introduction and reference for the basic GA operations.
"3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne
Gives a hands-on, step-by-step tutorial using the free open-source GA visualization software GA Viewer. This tutorial uses the conformal model which is more advanced than the regular 3-D model. Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd.
I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing General Relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald
Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA.
"Gravity, Gauge Theories and Geometric Algebra" by Anthony Lasenby, Chris Doran, Stephen Gull
General Relativity using GA - interestingly, curved space-time is not required using GA.
"Primer on Geometric Algebra for introductory mathematics and physics" by David Hestenes
Another good intro, much less dense than Macdonald's, with more diagrams and basic applications.
"Geometric Algebra Primer" by Jaap Suter
Gives a more gentle introduction and reference for the basic GA operations.
"3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne
Gives a hands-on, step-by-step tutorial using their free open-source GA visualization software, "GAViewer". This tutorial uses the conformal model which is more advanced than the regular 3-D model. (2 extra dimensions, of a very odd but useful type) Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd. (The 2nd edition is worth getting on paper. It has some very useful reference pages not available online, and many corrected errata.)
No, the usual math completely obscures the "why". The "why" of GR can only be understood WITHOUT the gratuitously ugly tensor formulation.
Facebook is not news. Facebook is not for nerds, it is for fools. What we need is not more Facebook folderol, but a script that will mod -3 (idjit) anybody who is damn fool enough to even entertain the notion of having a Facebook account.
Like the law that says you can't maintain a picket line.
"IQ tests are not valid in this regard because you don't test for the right things: They don't test for long-term strategy and thinking ahead months, years or even decades."
Nor do brain scans.
Yeah, I was just thinking: this is just like Natalie Portman, covered in hot grits, except without the grits. Or Natalie Portman.
Imagine a Beowulf cluster of those, and you've got a really big empty space.
I dunno... using over-proof-vodka-and-nitrous-oxide rockets seemed like a good design idea at the time, but it might somehow have had some indirect effects on quality control....
"...has taken 12 years to build. But in theory, it's 90% done ..."
So we should check back in 2024 or so, then, I guess?
Well that's one way of thinking about it, but it seems backwards. Yes you can span the whole range from a supernova to the inside of a coal seam using just 1 bit, but typically dynamic range is measured in stops or bits (essentially the same thing, a power of two in light intensity), and what we want to know is the range of different gradations that can be distinguished.
The extra values are actually always mostly in the highlights. Sensors are linear. The brightest stop (of between 8-14 stops of dynamic range in a digital camera) always has half the values, the next stop has another quarter, the next another eighth. The top three stops (highlights to upper midtones) has 7/8ths of the codes. For an 8-bit per channel device that leaves 32 codes to represent all the data in the bottom 5 to 11 stops of dynamic range, which leads to noise, dithering, banding and other artifacts. With 16 bits per channel there are 8192 codes for that lower region (and 57,343 for the upper stops), so that's the same factor increase for both ranges (256x), but the extra midtone and shadow information matters more - we can visually distinguish (with our log-sensitive eyeballs) more than 32 shades in that lower range, while 224 codes for the upper range is far closer to adequate. In that way, you're right about most of the useful new codes going to the darker areas.
The effective black level is set by the noise floor, which is mostly an inverse function of the size of the pixels plus a set amount of read noise for each readout. The white level in photometric terms is limited most directly by the pixel full-well capacity, and the amount of light excluded from the camera, so there is a lot more room to capture brighter things than fainter things - we can always cut out more light, even if it means going to a pinhole camera with a welding-mask filter, while we can't improve the noise floor much or gain more information from longer exposures past a certain point. Most of the increase in dynamic range comes from the highlights, most of the useful increase comes from the shadows.
Yes. A digital photo can have a dynamic range of over 12 stops in each channel, even 14 on a really good camera. Half the light level codes in a channel are in the brightest stop, e.g. 1024 of 2048 for a 12 stop dynamic range.
There is no point in shooting RAW format with its additional dynamic range if you're going to edit it in a lousy 8 bits per pixel.
I wish programs for monitors and cameras would not say DPI. It's PPI, pixels per inch, which is not at all the same thing as the DPI that a printer produces.
The dabblers complain about GIMP, the pros ignore it entirely, and with good reason.
"US Manufacturing output was at an all-time high immediately before the current recession"
What, in nominal dollars? Or counting the profits of offshoring by US companies? Or the non-productive consumable goods like bombs and land mines? Or McDonald's? (No, really!) Or counting products assembled in the US from foreign parts? Yeah, when 90% of the product and 2% of the cost come from China, the accounting makes that US-assembled product look like we're making stuff, but it isn't true. Sandwiches and paper plates do not count as manufacturing, either. What does US durable goods production look like after deducting the partially-finished foreign parts component, that's the real story.
When it gets down to it — talking trade balances here — once we've brain-drained all our technology into other countries, once things have evened out, they're making cars in Bolivia and microwave ovens in Tadzhikistan and selling them here — once our edge in natural resources has been made irrelevant by giant Hong Kong ships and dirigibles that can ship North Dakota all the way to New Zealand for a nickel — once the Invisible Hand has taken away all those historical inequities and smeared them out into a broad global layer of what a Pakistani brickmaker would consider to be prosperity — y'know what? There's only four things we do better than anyone else:
music
movies
microcode (software)
high-speed pizza delivery
-Neal Stephenson, Snow Crash
(but we've given up on high-speed pizza delivery, and the microcode is draining away, too.)
Funny, I didn't see 20% real unemployment in the 1950s, either.
If you ship your production overseas, your process engineering, your design, your support, your sales and ultimately your whole economy will follow. Without a broad earnings base among the population, who will be able to buy your products? Not the ~90% of the population with shrinking earnings. And once everything is overseas, why does the overseas supplier need the US company who was doing the outsourcing? They just take the market from that hollowed-out US shell.
So no affordable health care or jobs then. And we all know how well the housing thing worked out.
No, it isn't like that at all - these particular laws were bought and paid for by the corporations expressly to give themselves power at the expense of their employees' natural rights.
But performance on most subscales of IQ tests is at its maximum at age 16. Vocabulary and knowledge continue to improve at a glacial pace up to 40. The frontal lobe changes do not necessarily show improvement, but only change (and the changes are negligible).
"It's not merely a coincidence..."
No, low education, poverty and criminality all usually flow from the common factor being genetically or otherwise permanently low IQ. Such people can benefit if they have classes tailored to their level, but putting them in with the average and above average students just holds everybody back. Low IQ people are by definition slower to learn, so their education should not waste time on things they will never need or understand, but rather focus on getting them prepared for life - practical rules of thumb, good habits, handing their own finances, being employable at something, knowing when they should get advice rather than trying to figure things out on their own. Most of them would do better to have experience working or being apprenticed after about 16 than further intensive schooling - they could do half-time at school and still get all they were likely to get out of the experience.
They wouldn't have to be forced to go to these mini-prisons if school weren't 90% bullshit. Even the dumb kids realize it. The solution isn't force, and raising kids in day-camp prisons but getting rid of the force and replacing the bullshit with something useful and interesting. Read John Taylor Gatto's work for what is wrong with schools, how things used to be different and how things could be improved.
You seem to think that a business should arbitrarily compensate capital at above market rates, despite not actually needing that capital, while being entirely dependent on - indeed having no existence as a going concern without - the work of its employees. Capital does not produce profit, it chases it. Employees are the source of profit in established businesses. They are people, not interchangeable widgets bought by the great-gross. They, not the stockholders, are the company.
Capital, on the other hand, is just ledger entries in a computer at Cede & Co., born out of loans to brokerages not backed by deposits but ultimately by other loans made by the Federal reserve to its stockholders, the big banks who get to spend the inflated money supply first, before prices rise. It's a scam, the market isn't free, but totally managed for the benefit of bankers creating money from thin air. These thieves don't deserve greater rewards, power and respect than the people who actually make real value with their work, but dupes keep repeating the class-war propaganda of the thieves' wholly owned mouthpieces.
So people should take whatever the employer offers? No bargaining? Capital should gang up into collectives to bargain, that doesn't distort the market, but labor should not? After all the corporation is free to fire them all, or lock them out, right? But they don't, because they can't find that many replacements quickly enough to prevent a quarterly loss at the least. And in the middle of the great recession, you really think 45,000 people with specialized skills can all go out at once and find new jobs, when there are already ten million out looking for work? Verizon is doing well enough to pay over $50M to its top 5 executives a year (speaking of squeezing out undeserved money), to make good, increasing profits, yet they don't make enough to be able to afford to meet the obligations that they had previously been meeting? You do realize that no innovation or research is done by top telecom management, right? And that all the work of actually making the phones and DSL work is done by non-management employees, right? And that the issue is not employees squeezing undeserved money but Verizon not wanting to continue to pay the same health insurance that they had been paying, just because they thought they could get away with it?
The top 10% in wealth own over 81% of all stocks, 98% of other financial securities and over 93% of all business equity.
from: Wolff, E. N. (2010). Recent trends in household wealth in the United States: Rising debt and the middle-class squeeze - an update to 2007. Working Paper No. 589. Annandale-on-Hudson, NY: The Levy Economics Institute of Bard College
Unless one owns at least several percent of a business, you have no effective say in how it is run (CEOs excepted, of course.) The money paid to CEOs is simply a warm gesture of respect to themselves. Stockholders have no effective say when it is the management sets the slate of board candidates and votes all the shares that didn't send in a proxy. The board members want to keep their sinecures, so they go along with whatever the CEO wants for himself, using the cover of a compensation committee and a consultant who can be relied upon to deliver the answer the customer wants.
And how much covert sabotage was conducted by management, by policy? Those confusing tariffs that keep services secret and obligations obtuse didn't write themselves, you know. The apparently nonsensical procedures that create bureaucratic run-arounds are there for a reason - management evading obligations to provide the service people paid for. The overpriced equipment from incestuous vendor relationships cuts the service that can be provided for everyone. The lack of good troubleshooting tools for techs, even when such tools are relatively cheap means things stay broken. (Actually fixing things is too expensive, right? We'll have our field boys just fixat it, armed with nothing much more sophisticated than a voltmeter, then game the intentionally stupid metrics we ourselves set to make it look like we still provide service.) The lobbying that prevents competitors from gaining a toehold defrauds everyone, the whole public, and destroys the potential livelihoods of those who would have worked for the competitors and the capital of their investors. Union strikes have never committed a tenth the sabotage as results from management's everyday practices.