Actually the entire post was devoted to the 2nd half of your comment. The point was, the current developed nations are pretty much all in the same boat as 'standard of living' goes. There are no horrors to avoid when swapping between them. There are only slight differences. And this happens DESPITE the large differences in taxation. Perhaps taxation is only a piece of the puzzle and there are a great number of other factors to include.
Thank you. You're correct. The gapminder tax statistics don't seem to count taxation at all levels of government. I thought it did.
I wonder about the reliability of the other statistics now. If just the tax statistics are incorrect, then only that part about the amount Germany and US are taxed would be wrong. Everything else would stand.
Do you have more reliable statistics you could point me to in regards to Life expectancy, Infant Mortality, Income per person? Or are they correct?
Are you saying that poor health care caused these babies to be born earlier? If so, how?
Are you saying that good health care allowed for the birth of babies that wouldn't normally have been born?
Or are you saying that 'infant mortality' rates are skewed by other factors that have little to do with health care?
I've heard that different countries define 'live birth' differently which may skew things. The US defines it as the instant the baby is fully out, even if it dies seconds later. I believe some other countries don't consider this a live birth, and therefore it doesn't contribute to infant mortality statistics.
This is why I put "in developed nations" into that sentence. I figured the income disparity would be low in them. Just as the wikipedia article you linked states on the 'Correlation with per-capita GDP' section: "rich countries generally have lower Gini indices (under 40)"
I could argue that.4 and.36 are close enough, however.4 and.24 are not. My thinking appears to be outdated. The US was with the pack in the 80s and early 90s, but now there's a clear difference. From the wikipedia article you linked: "the U.S.A, Hongkong and Singapore being rich exceptions with high Gini coefficients." You were right.
I'm now very curious as to why this disparity steadily grew since the early 80s. If you have an idea as to the reason, please let me know your thoughts.
I appreciate your response, but far too often people are arguing points on common misconceptions of the world. This is where I asked you to site your source that the USA has lower standards of living than these higher taxed countries.
You've defined your grounds for 'standard of living' now, but you haven't given citation as to where you got the idea that USA has lower standard of living than other countries. So I did a little groundwork and found a source of the statistics you mentioned.
I compared tax revenue (% of GDP) to the first 3 grounds you listed. Click on the links to show interactive flash graphs of the statistics.
In 2006 the USA has an expectancy of 78. The highest in the world is 81. There are many developed countries in between. A 3 year difference is almost statistically insignificant and it's reasonable to say that all of these countries can be grouped as 'high life expectancy'. The difference is within an error margin which can be attributed to things like culture and diet.
The USA is behind other developed nations here at 0.006% infant mortality. Most developed nations are 0.004% and Iceland leads with 0.002%. Note that Germany is taxed lower than the USA and still beats the USA by 0.002%. Also note that New Zealand's tax revenue is very high (34% compared to 12% of USA) and only beats USA by 0.001%. Again it could be judged that these differences are small enough to be attributed to factors other than taxation.
There are some poverty indicators on the graph that you can play with as well, but income per person is a fairly reasonable way to assess how well the citizens are doing financially in developed nations. Feel free to counter with poverty statistics you may find.
Here USA leads the pack. In 2004, 2 oil producers (Qatar & Kuwait) and Norway and Luxemburg beat it. Macao gets ahead in 2006. Note that all of these countries are extremely small in comparison to the USA.
Note that the USA is near the bottom of tax revenue of the developed countries. Yet the differences when comparing higher taxed countries with hard statistics of the criteria you mentioned are next to nothing. The other 2 criteria (happiness & leisure) are often minefields when talking about "reliability" and often depend on who is taking the survey. Broadband availability (while may greatly raise the happiness of you or I) is not usually a factor when considering 'standard of living'.
On a related note, I highly suggest this video by a Swedish s
I'd love to have the title "Director of Penetration Testing", but can only think of 2 types of jobs where the title is appropriate. And I don't have the stamina for either.
I think that's wonderful that you had that talk. I think we're actually agreeing here. I mentioned, "unless you tell them otherwise" in the beginning and reinforced it with "unless someone tells them otherwise" at the end. I was refering to exactly what you're talking about.
Children before 6 can most definitely reason. And you can appeal to that reason to teach the difference between what's real and what's not. There's just a radical change in the _way_ that they reason after 6. One of the changes is this natural skepticism that you mentioned. I refered to it as 'doubt' but I think 'skepticism' fits much more eloquently.
Anyway, I would love to read what you read on the persistence of memory. Are there sources you can point me to?
Actually, a normal human being begins to be able to distinguish fantasy from reality at 6 yrs of age. Before that they take everything literally unless you tell them otherwise (which is why the "I got your nose!" game works so well).
Before 6, if you tell them bears live in the forest and dragons live in caves, they make no distinction. This is why many developmental psychologists suggest avoiding fantasy before 6.
At around 6 (give or take), their brain chemistry begins to change and they glide into a stage where they have the ability to doubt. Between 6 - 12 yrs, you'll often hear them ask "Really?!?" after telling them something fantastic. You won't hear that very much beforehand. Before that, they'll take everything as fact (unless someone tells them otherwise).
Perhaps some investments take 20 years of net profits to make paying for the R & D worthwhile.
Perhaps if there was no possibility to patent steam engine developments, the producers wouldn't have started selling them until they were sure they could make a product that wouldn't be reverse engineered immediately. If it could, someone else may start producing and push them out of business almost immediately.
It's like the Wright brothers waiting on the patent (a couple of comments above) before they announced they could fly. They'd have little incentive to show the world, if any company with more capital could push them out of business immediately.
20 years is too long for a lot of things, especially today when innovation in some technologies goes so quickly. But perhaps it would be better to 'revise' the system to be up-to-date with current technologies and not 'obliterate' the entire thing.
If they're so smart maybe they should wake up and take the time to learn a little more about what they're buying.
I do not want to live in a society where it's deemed okay to scam someone because they don't have sufficient background knowledge.
Nor do I want to live in a society where the people who were scammed are blamed because they didn't learn about the scam before it happened. However, they should be accountable if the subject is common knowledge and they know what they're getting into. What DRM truly does is not common knowledge, especially among people over 30.
I have very intelligent friends, usually over 30, that just have no idea about computers, and frankly don't care. It's as interesting to them as how their toaster works. They come to me with their computer issues and the phrase I hear often is, "I hate this. Technology is supposed to make life easier."
They're frustrated and rightfully so. Some will undoubtedly buy into crap like this, and not understand why they can't have their music anymore. They'll get frustrated, angry, or cry, and try silly things to put the music on their computer or new phones. Another phrase I hear often: "I was up half the night trying to get this to work."
The people who sell things like this are putting out a product they know to be inferior. They rationalize it with ideas like, "people have a choice" and "people may actually prefer this layout and never realize the drawbacks."
But in the end, my friends would have a bought a better product for less if this crap hadn't been around. And when they can't do what they thought they should be able to do, they don't know why, and they get very upset. Crap like this ruins the days of many, many people. It's avoidable and it's the fault of people who put plans like this into action.
They're screwing people over to make a buck, plain and simple.
Thank you Dave. This was well researched. I see this topic come up often, and what you said is often ignored. And though I've heard it before, this was well written.
I've copied and may post this (and give you credit unless you object) if I see the same kind of misinformation and 1-sided thinking come up in the future.
It would also be nice for whale communication, seeing as their ability to communicate over vast distances of ocean is significantly reduced by the background noise coming from mechanical engines in the water.
While I agree with your overall point, it reminded me of a conversation I had with a friend, TODAY.
Me: How do you like Windows Vista?
Her: I don't have Vista.
Me: (confused pause) Yeah you do, I saw it on your laptop.
Her: No, I have Open Office.
Me: Oh I see. No Vista is the operating system on your computer.
Her: (starts to get a little annoyed) No, it's not on there is it? I thought they didn't put it on. I have Open Office or whatever instead and I don't like it, there are things you can't do.
Me: You're talking about Microsoft Office. That's something you'd have to buy extra. Vista is an operating system. (I try to explain what an operating system is versus programs like Office.)
Her: Vista comes with the computer? I used to have Write or something, but now I can only use Open Office.
Me: (Tries again for a longer time, talking about running files, moving files, GUI, taskbar, etc. Nothing's working. Somehow I get into): "...so you see, this book here is the physical hardware and this plastic slip on top is the operating system, and then all the spaghetti on top of that is all the programs it can run, but the programs can't talk to the book without the plastic sheet translating in between..."
Somehow, the spaghetti explanation seemed to work (@_@)
Just like:
Microsoft is the company that produces Windows.
Apple is the company that produces OS X.
Ubuntu is the most popular desktop version of Linux, probably because there's a large focus on being user friendly. One of their main slogans is: "Linux for human beings".
McDonalds Files Patent for Hamburger that Eats Itself.
The New York Times Files Patent for Newspaper that Reads Itself and then Complains to Self about it's Left-wing Bias.
Internet Forum Trolls File Patent for Web Browser that Rick Roll's Itself.
It seems a lot of single player RTS campaigns these days are basically tutorials for multiplayer. They slowly introduce new units and situations until the last board when you use all of them. Next step is multiplayer =P
First of all, let me say I was taught in the same traditional method as you were. And I believe you and I have extremely clear ways of thinking. And that we, as we are now, can or may reach our highest mental ability possible. What childhood developmental psychologists study, is what is the most effective way to get there. In other words, the means, and not the ends.
However, it is not an analogy. I also probably would have thought it was an analogy a few years ago, if you asked me. But arithmetic, geometry, and algebra are all ways of looking at the same thing.
What we have in the real world is matter. If we physically have a unit and another unit, we call it 2. The digit 2 is single digit. It's a single symbol we use to describe two units of matter. It's an abstraction of the concrete.
You cannot get much further in math if you can't make this abstraction. Abstraction is very important. Thinking abstractly comprises most of what we teach. The idea is to build upon layers of well known abstraction, starting from as close to concrete as possible and building from there. Hence, "breaking it down".
Length is a physical real world characteristic. Perhaps there is a quantum size we can't get smaller than, such as Planck's constant. Perhaps our world is analogue and we can divide until infinity. If this is the case it's all the more miraculous that we have size at all, in spaces that are infinitely small.
Just as we can say a unit and another unit is 2, we can say a unit of length and another unit of length are 2. The first 2 describes quantity, and the second 2 describes quality (or quantity of size if you'd like).
Variables such as (a + b + c) are another layor of abstraction of digits like (1 + 2 + 3).
So I very much see where you come from, and I personally also find it easier to think abstractly in many situations. But the reason we see these things as different is because we're so used to thinking of the same thing is 2 different abstract ways. Or "looking the same thing in a different light".
For someone whose level of abstraction is that of an elementary student, it is far easier to fully grasp a concept if shown by the most concrete method possible, only using abstraction they are comfortable with. Once they're extremely comfortable with "playing" with numbers, the concepts that go along with that should be introduced. For example, it's probably best not to reconstruct (a + b + c)^5 in 3 dimensional space.
But to what extent do the most fundamental game mechanics limit the more complex end-game play?
None. Follow me here. They're correlating complexity with difficulty and the 2 often do seem to go together, but what complexity really goes with is time it takes to learn. If complexity is broken up into its smallest pieces, the difficulty only comes with unclear presentation, presenting too many pieces at once, or presentation when there is no motivation to learn.
I'm in the education profession and I used to be addicted to MMOs, including a lot of WoW (but luckily got out just before WotlK). Learning curves are something I deal with every day (and MMOs used to be =p). It's all a matter of teaching. I'll use WoW as my example.
WoW does a very good job at teaching most of its game, but if you look closely, it doesn't guide players through a few things; for example talent builds and rotations. And this is where it's very easy to see and divide crap players with people that have spent time on forums learning about their class. People on countless sites (like elitist jerks for example) had volumes of arguments, spreadsheets, graphs, etc devoted to these things. Although any high level character can easily get by in almost every aspect of the game, to maximize the potential of a class is something else entirely. As a raid leader or for PvP, there were a number of times where I'd be much more inclined to take people who I knew understood the mechanics over someone whose gear was better. The initial point being, WoW is not simplistic, but it looks that way because they teach many aspects of it well, and they let people get away with being crappy at the other aspects without detriment.
That's not to say it couldn't be more complex. But that's not the point. Back in BC days, when you met a level 70 hunter talking about theoretically being able to lay up to 5 traps within a certain number of seconds when specced a certain survival spec and managing cooldowns properly, versus some guy's wife that takes over his hunter for a bit during a raid while he deals with an emergency at work, the difference is profound.
The point is to break complexity up into it's smallest pieces, present it clearly, motivate, and don't overwhelm with too much at once. Dish it out over time.
The first thing anyone needs to know is how to move around. Then go onto how to interact with the world. But in an MMO where there are a bajillion ways to interact, don't go over it all at once. If you need to know A & B for a task, first give a task that shows A, then a task that shows B, then give the task that puts them together.
Some games do this with giving some sort of documentation at some point during the game. They give you a bunch of text, or a sensei, teaching you A-Z and then they thrust you into situations that use many of the techniques. Those techniques go from easy to harder, combining more and more as you go along, and you're usually allowed to go back to the documentation if you need it. But there is rarely the "isolation of concept" in this method. I remember an instructor in FF8 telling me to read instructions about the system on the computer terminal, and a similar 'instructor' in FF7 thinking about it. But it was rarer in games like the Legend of Zelda.
In real life schools, we also often make these mistakes. We often immediately give the abstraction of concepts (eg: mathematical formulas) instead of first showing their real world equivalents. Or we give multiple concepts at once that can be broken down further (sometimes because we can't see that they can be). Or we don't motivate. Or we overwhelm with new concepts before the foundation has been able to sink in. A number of educators, (eg: Montessori), have been trying to get public schools to realize this for about 100 years, and it _is_ changing. But slowly.
Take the Pythagorean Theorem for example. This is something that is normally gone into depth in high school,
As for rotation, I think it's something like this:
Find an object in the sky. Figure out it's position. A number of days/weeks/years later, look at it again. Figure out it's new position. See how far it traveled and how long it took. Repeat for as many objects in the galaxy as possible.
As for mass, I would guess it has something to do with using spectrometers to get good ideas about out how much of each element is out there. We already know the mass of these elements. Also looking at movement again, we can see how gravitational forces act on the galaxies around us.
Then of course, we build complex mathematical models that coincide with what we observe. This is why people suspect there's a thing called Dark Matter. We see the gravity of galaxies and galaxy clusters curving the light of galaxies behind them a lot more than they should be. We think we know what gravity they should have because of their observed masses. Where's all this extra curve coming from?! It's almost as if the galaxy is surrounded in a bubble of more mass! ZOMG Dark matter! Oh yeah, and the edges of galaxies spin a lot faster than they should. Why? Because they're in a sphere of Dark matter of course!! Yeah, it's pretty shaky, but some thing(s) or force(s) is/are adding more gravitational effect and keeping those edges speedy.
Slashdot Mirror
Actually the entire post was devoted to the 2nd half of your comment. The point was, the current developed nations are pretty much all in the same boat as 'standard of living' goes. There are no horrors to avoid when swapping between them. There are only slight differences. And this happens DESPITE the large differences in taxation. Perhaps taxation is only a piece of the puzzle and there are a great number of other factors to include.
Thank you. You're correct. The gapminder tax statistics don't seem to count taxation at all levels of government. I thought it did.
I wonder about the reliability of the other statistics now. If just the tax statistics are incorrect, then only that part about the amount Germany and US are taxed would be wrong. Everything else would stand.
Do you have more reliable statistics you could point me to in regards to Life expectancy, Infant Mortality, Income per person? Or are they correct?
Are you saying that poor health care caused these babies to be born earlier? If so, how?
Are you saying that good health care allowed for the birth of babies that wouldn't normally have been born?
Or are you saying that 'infant mortality' rates are skewed by other factors that have little to do with health care?
I've heard that different countries define 'live birth' differently which may skew things. The US defines it as the instant the baby is fully out, even if it dies seconds later. I believe some other countries don't consider this a live birth, and therefore it doesn't contribute to infant mortality statistics.
This is why I put "in developed nations" into that sentence. I figured the income disparity would be low in them. Just as the wikipedia article you linked states on the 'Correlation with per-capita GDP' section: "rich countries generally have lower Gini indices (under 40)"
.4 and .36 are close enough, however .4 and .24 are not. My thinking appears to be outdated. The US was with the pack in the 80s and early 90s, but now there's a clear difference. From the wikipedia article you linked: "the U.S.A, Hongkong and Singapore being rich exceptions with high Gini coefficients." You were right.
I could argue that
I'm now very curious as to why this disparity steadily grew since the early 80s. If you have an idea as to the reason, please let me know your thoughts.
You've defined your grounds for 'standard of living' now, but you haven't given citation as to where you got the idea that USA has lower standard of living than other countries. So I did a little groundwork and found a source of the statistics you mentioned.
I compared tax revenue (% of GDP) to the first 3 grounds you listed. Click on the links to show interactive flash graphs of the statistics.
Life Expectancy at Birth
In 2006 the USA has an expectancy of 78. The highest in the world is 81. There are many developed countries in between. A 3 year difference is almost statistically insignificant and it's reasonable to say that all of these countries can be grouped as 'high life expectancy'. The difference is within an error margin which can be attributed to things like culture and diet.
Infant Mortality Rate
The USA is behind other developed nations here at 0.006% infant mortality. Most developed nations are 0.004% and Iceland leads with 0.002%. Note that Germany is taxed lower than the USA and still beats the USA by 0.002%. Also note that New Zealand's tax revenue is very high (34% compared to 12% of USA) and only beats USA by 0.001%. Again it could be judged that these differences are small enough to be attributed to factors other than taxation.
Income per person
There are some poverty indicators on the graph that you can play with as well, but income per person is a fairly reasonable way to assess how well the citizens are doing financially in developed nations. Feel free to counter with poverty statistics you may find.
Here USA leads the pack. In 2004, 2 oil producers (Qatar & Kuwait) and Norway and Luxemburg beat it. Macao gets ahead in 2006. Note that all of these countries are extremely small in comparison to the USA.
Note that the USA is near the bottom of tax revenue of the developed countries. Yet the differences when comparing higher taxed countries with hard statistics of the criteria you mentioned are next to nothing. The other 2 criteria (happiness & leisure) are often minefields when talking about "reliability" and often depend on who is taking the survey. Broadband availability (while may greatly raise the happiness of you or I) is not usually a factor when considering 'standard of living'.
On a related note, I highly suggest this video by a Swedish s
"facilitating higher standards of living" [citation needed] along with [unambiguous definition of 'higher standards of living']
I'd love to have the title "Director of Penetration Testing", but can only think of 2 types of jobs where the title is appropriate. And I don't have the stamina for either.
I'll keep my alcohol. Years of private studies show loss of fear and suppression of bad memories.
I think that's wonderful that you had that talk. I think we're actually agreeing here. I mentioned, "unless you tell them otherwise" in the beginning and reinforced it with "unless someone tells them otherwise" at the end. I was refering to exactly what you're talking about.
Children before 6 can most definitely reason. And you can appeal to that reason to teach the difference between what's real and what's not. There's just a radical change in the _way_ that they reason after 6. One of the changes is this natural skepticism that you mentioned. I refered to it as 'doubt' but I think 'skepticism' fits much more eloquently.
Anyway, I would love to read what you read on the persistence of memory. Are there sources you can point me to?
Actually, a normal human being begins to be able to distinguish fantasy from reality at 6 yrs of age. Before that they take everything literally unless you tell them otherwise (which is why the "I got your nose!" game works so well).
Before 6, if you tell them bears live in the forest and dragons live in caves, they make no distinction. This is why many developmental psychologists suggest avoiding fantasy before 6.
At around 6 (give or take), their brain chemistry begins to change and they glide into a stage where they have the ability to doubt. Between 6 - 12 yrs, you'll often hear them ask "Really?!?" after telling them something fantastic. You won't hear that very much beforehand. Before that, they'll take everything as fact (unless someone tells them otherwise).
Perhaps some investments take 20 years of net profits to make paying for the R & D worthwhile.
Perhaps if there was no possibility to patent steam engine developments, the producers wouldn't have started selling them until they were sure they could make a product that wouldn't be reverse engineered immediately. If it could, someone else may start producing and push them out of business almost immediately.
It's like the Wright brothers waiting on the patent (a couple of comments above) before they announced they could fly. They'd have little incentive to show the world, if any company with more capital could push them out of business immediately.
20 years is too long for a lot of things, especially today when innovation in some technologies goes so quickly. But perhaps it would be better to 'revise' the system to be up-to-date with current technologies and not 'obliterate' the entire thing.
If they're so smart maybe they should wake up and take the time to learn a little more about what they're buying.
I do not want to live in a society where it's deemed okay to scam someone because they don't have sufficient background knowledge.
Nor do I want to live in a society where the people who were scammed are blamed because they didn't learn about the scam before it happened. However, they should be accountable if the subject is common knowledge and they know what they're getting into. What DRM truly does is not common knowledge, especially among people over 30.
I have very intelligent friends, usually over 30, that just have no idea about computers, and frankly don't care. It's as interesting to them as how their toaster works. They come to me with their computer issues and the phrase I hear often is, "I hate this. Technology is supposed to make life easier."
They're frustrated and rightfully so. Some will undoubtedly buy into crap like this, and not understand why they can't have their music anymore. They'll get frustrated, angry, or cry, and try silly things to put the music on their computer or new phones. Another phrase I hear often: "I was up half the night trying to get this to work."
The people who sell things like this are putting out a product they know to be inferior. They rationalize it with ideas like, "people have a choice" and "people may actually prefer this layout and never realize the drawbacks."
But in the end, my friends would have a bought a better product for less if this crap hadn't been around. And when they can't do what they thought they should be able to do, they don't know why, and they get very upset. Crap like this ruins the days of many, many people. It's avoidable and it's the fault of people who put plans like this into action.
They're screwing people over to make a buck, plain and simple.
Thank you Dave. This was well researched. I see this topic come up often, and what you said is often ignored. And though I've heard it before, this was well written.
I've copied and may post this (and give you credit unless you object) if I see the same kind of misinformation and 1-sided thinking come up in the future.
..."Abobe"?!
It's not a misspelling. They're publishing the protocol for their warez versions. Hopefully it will be compatible with my Abobe Fotoshop and Akrobat.
Might be nice for whale-watching and the like
It would also be nice for whale communication, seeing as their ability to communicate over vast distances of ocean is significantly reduced by the background noise coming from mechanical engines in the water.
You give them too little credit.
While I agree with your overall point, it reminded me of a conversation I had with a friend, TODAY.
Me: How do you like Windows Vista?
Her: I don't have Vista.
Me: (confused pause) Yeah you do, I saw it on your laptop.
Her: No, I have Open Office.
Me: Oh I see. No Vista is the operating system on your computer.
Her: (starts to get a little annoyed) No, it's not on there is it? I thought they didn't put it on. I have Open Office or whatever instead and I don't like it, there are things you can't do.
Me: You're talking about Microsoft Office. That's something you'd have to buy extra. Vista is an operating system. (I try to explain what an operating system is versus programs like Office.)
Her: Vista comes with the computer? I used to have Write or something, but now I can only use Open Office.
Me: (Tries again for a longer time, talking about running files, moving files, GUI, taskbar, etc. Nothing's working. Somehow I get into): "...so you see, this book here is the physical hardware and this plastic slip on top is the operating system, and then all the spaghetti on top of that is all the programs it can run, but the programs can't talk to the book without the plastic sheet translating in between..."
Somehow, the spaghetti explanation seemed to work (@_@)
Canonical is the company that produces Ubuntu.
Just like:
Microsoft is the company that produces Windows.
Apple is the company that produces OS X.
Ubuntu is the most popular desktop version of Linux, probably because there's a large focus on being user friendly. One of their main slogans is: "Linux for human beings".
McDonalds Files Patent for Hamburger that Eats Itself.
The New York Times Files Patent for Newspaper that Reads Itself and then Complains to Self about it's Left-wing Bias.
Internet Forum Trolls File Patent for Web Browser that Rick Roll's Itself.
Playstation 3 cries in a corner. Parents sue for therapy bills.
or people will start to read books.
It seems a lot of single player RTS campaigns these days are basically tutorials for multiplayer. They slowly introduce new units and situations until the last board when you use all of them. Next step is multiplayer =P
First of all, let me say I was taught in the same traditional method as you were. And I believe you and I have extremely clear ways of thinking. And that we, as we are now, can or may reach our highest mental ability possible. What childhood developmental psychologists study, is what is the most effective way to get there. In other words, the means, and not the ends.
However, it is not an analogy. I also probably would have thought it was an analogy a few years ago, if you asked me. But arithmetic, geometry, and algebra are all ways of looking at the same thing.
What we have in the real world is matter. If we physically have a unit and another unit, we call it 2. The digit 2 is single digit. It's a single symbol we use to describe two units of matter. It's an abstraction of the concrete.
You cannot get much further in math if you can't make this abstraction. Abstraction is very important. Thinking abstractly comprises most of what we teach. The idea is to build upon layers of well known abstraction, starting from as close to concrete as possible and building from there. Hence, "breaking it down".
Length is a physical real world characteristic. Perhaps there is a quantum size we can't get smaller than, such as Planck's constant. Perhaps our world is analogue and we can divide until infinity. If this is the case it's all the more miraculous that we have size at all, in spaces that are infinitely small.
Just as we can say a unit and another unit is 2, we can say a unit of length and another unit of length are 2. The first 2 describes quantity, and the second 2 describes quality (or quantity of size if you'd like).
Variables such as (a + b + c) are another layor of abstraction of digits like (1 + 2 + 3).
So I very much see where you come from, and I personally also find it easier to think abstractly in many situations. But the reason we see these things as different is because we're so used to thinking of the same thing is 2 different abstract ways. Or "looking the same thing in a different light".
For someone whose level of abstraction is that of an elementary student, it is far easier to fully grasp a concept if shown by the most concrete method possible, only using abstraction they are comfortable with. Once they're extremely comfortable with "playing" with numbers, the concepts that go along with that should be introduced. For example, it's probably best not to reconstruct (a + b + c)^5 in 3 dimensional space.
But to what extent do the most fundamental game mechanics limit the more complex end-game play?
None. Follow me here. They're correlating complexity with difficulty and the 2 often do seem to go together, but what complexity really goes with is time it takes to learn. If complexity is broken up into its smallest pieces, the difficulty only comes with unclear presentation, presenting too many pieces at once, or presentation when there is no motivation to learn.
I'm in the education profession and I used to be addicted to MMOs, including a lot of WoW (but luckily got out just before WotlK). Learning curves are something I deal with every day (and MMOs used to be =p). It's all a matter of teaching. I'll use WoW as my example.
WoW does a very good job at teaching most of its game, but if you look closely, it doesn't guide players through a few things; for example talent builds and rotations. And this is where it's very easy to see and divide crap players with people that have spent time on forums learning about their class. People on countless sites (like elitist jerks for example) had volumes of arguments, spreadsheets, graphs, etc devoted to these things. Although any high level character can easily get by in almost every aspect of the game, to maximize the potential of a class is something else entirely. As a raid leader or for PvP, there were a number of times where I'd be much more inclined to take people who I knew understood the mechanics over someone whose gear was better. The initial point being, WoW is not simplistic, but it looks that way because they teach many aspects of it well, and they let people get away with being crappy at the other aspects without detriment.
That's not to say it couldn't be more complex. But that's not the point. Back in BC days, when you met a level 70 hunter talking about theoretically being able to lay up to 5 traps within a certain number of seconds when specced a certain survival spec and managing cooldowns properly, versus some guy's wife that takes over his hunter for a bit during a raid while he deals with an emergency at work, the difference is profound.
The point is to break complexity up into it's smallest pieces, present it clearly, motivate, and don't overwhelm with too much at once. Dish it out over time.
The first thing anyone needs to know is how to move around. Then go onto how to interact with the world. But in an MMO where there are a bajillion ways to interact, don't go over it all at once. If you need to know A & B for a task, first give a task that shows A, then a task that shows B, then give the task that puts them together.
Some games do this with giving some sort of documentation at some point during the game. They give you a bunch of text, or a sensei, teaching you A-Z and then they thrust you into situations that use many of the techniques. Those techniques go from easy to harder, combining more and more as you go along, and you're usually allowed to go back to the documentation if you need it. But there is rarely the "isolation of concept" in this method. I remember an instructor in FF8 telling me to read instructions about the system on the computer terminal, and a similar 'instructor' in FF7 thinking about it. But it was rarer in games like the Legend of Zelda.
In real life schools, we also often make these mistakes. We often immediately give the abstraction of concepts (eg: mathematical formulas) instead of first showing their real world equivalents. Or we give multiple concepts at once that can be broken down further (sometimes because we can't see that they can be). Or we don't motivate. Or we overwhelm with new concepts before the foundation has been able to sink in. A number of educators, (eg: Montessori), have been trying to get public schools to realize this for about 100 years, and it _is_ changing. But slowly.
Take the Pythagorean Theorem for example. This is something that is normally gone into depth in high school,
As for rotation, I think it's something like this:
Find an object in the sky. Figure out it's position. A number of days/weeks/years later, look at it again. Figure out it's new position. See how far it traveled and how long it took. Repeat for as many objects in the galaxy as possible.
As for mass, I would guess it has something to do with using spectrometers to get good ideas about out how much of each element is out there. We already know the mass of these elements. Also looking at movement again, we can see how gravitational forces act on the galaxies around us.
Then of course, we build complex mathematical models that coincide with what we observe. This is why people suspect there's a thing called Dark Matter. We see the gravity of galaxies and galaxy clusters curving the light of galaxies behind them a lot more than they should be. We think we know what gravity they should have because of their observed masses. Where's all this extra curve coming from?! It's almost as if the galaxy is surrounded in a bubble of more mass! ZOMG Dark matter! Oh yeah, and the edges of galaxies spin a lot faster than they should. Why? Because they're in a sphere of Dark matter of course!! Yeah, it's pretty shaky, but some thing(s) or force(s) is/are adding more gravitational effect and keeping those edges speedy.