I have decided to do a short series on window managers I have used. I titled this OS Review, because most people don't realize there is a difference between a window manager and an operating system, and because, in the case of Windows 10, it is the OS as well. Most of these will be Linux window managers, but because I have primarily been using Windows 10 recently, I am starting with it.
I have been using Windows 10 since early January. That makes it about 5 months. For some context, before that, I used Linux primarily, and I went through several window managers over the last several years. I bought a new laptop at the beginning of the year, and after some research, I decided to give Windows 10 a try. I have not used Vista, practically at all, I used Windows 7 a bit at work, and I also skipped over Windows 8. I have used Windows XP off and on since it was originally released (and I am still using it on another machine, for playing games). I chose to try Windows 10, because it is almost as light weight and as stable as XP, and it does not have the tons of worthless features that started with Vista and continued into Windows 7. In short, in my opinion, Windows 10 is the first version of Windows that is actually better than XP, since XP itself (the later DOS versions of Windows still beat XP in my opinion).
My research indicated that Windows 10 Home and Pro both included "features" that I will not tolerate. The big one is mandatory updating. When an update is released, the OS will give you two options: You can install and restart now, or you can install and restart in exactly 30 minutes. Once at work, we had an online meeting scheduled from 2pm to 3pm. At precisely 1:58pm, an update was released. We had to choose between installing immediately and being late to the meeting, or installing in 30 minutes and interrupting the meeting. This is a bad thing. More recently, a professional gamer had an update cut him off in the middle of an important game. This is also a bad thing. (If you cannot see it, imagine the stadium kicking everyone out for 10 minutes in the middle of a Super Bowl game, to install a new score board.) The operating system should not control the user's schedule, and it should never force a restart without the consent of the user.
So, the first thing I did when I got my new laptop was to wipe the disk and install Windows 10 Enterprise. (I work at an educational institution that provides access to this at no cost to employees.) This version allows the user to schedule the update and restart for any time, though it is still not very forgiving if you pick a bad time yourself (for example, maybe you end up having to deal with a server emergency at 3:00am). Still, this is way better than the other versions.
Windows 10 is very good for an MS product. For the first few months, it never crashed. Then it crashed twice, which is unacceptable for an operating system but way better than previous Windows operating systems. The Intel video driver crashes regularly (this is Lenovo's fault, for not updating it to a newer version), but miraculously, Windows does not crash. It actually recovers, giving me a notification that the driver crashed and has been restarted. This is a huge step forward for Windows.
One of my favorite features in Windows 10 is Cortana. I have tried to add voice control to Linux, but it is just too young at this point. Cortana is a lot of fun, but sadly, she is very limited. You can start applications with her, but she cannot handle any ambiguity. If a command is ambiguous, she will give a list of matching options, but by the time you figure out which one you need, it would have been faster and easier to use the keyboard. The one thing Cortana is good at is web searches. Getting her to use Google with Firefox was a pain (she uses Edge and Bing, the MS "decision engine" that is really just a thinly veiled advertising scheme, by default), but at least it is possible. Of course, if she misunderstands a command, here comes Google (or Bing), whether you wanted it or not! Honestly, it is just faster to type your search into the browser directly. In addition, you cannot add custom commands to Cortana, which further undermines her value. I have found myself relying on Cortana less and less, because she is just not that useful. She could be useful, but it is going to take some work from MS to make her into a real input device. The one thing I still use Cortana for is scheduling reminders. I have this nice wind up pendulum wall clock that has to be wound regularly, so I set up a weekly reminder to wind it. If course, even this is not ideal. This clock is a 20 day clock, so really it only needs to be wound about twice a month, but Cortana cannot handle that. She cannot even handle every other week. So I have a weekly reminder, and sometimes I skip it (though never twice in a row). Yeah, Cortana needs work.
Another thing I like about Windows 10 is the system tray clock application that can display both the time and the date. In fact, I dumped the LXDE Linux window manager because it failed on this one. This is a big deal for me. I don't bother to memorize the date, because it changes too often (over 350 times a year, in fact). Having it sitting there right under the time is invaluable to me. Of course, I also like to use my computer clock to time things; unfortunately, Windows 10 does not have any option for displaying seconds. Yeah, turns out MS cannot do anything 100% right. (They say updating the clock every second would slow the computer down too much. I have experience with very many Linux systems that disprove this claim.)
To top off what I like about Windows 10, is the virtual desktops. I have been a regular Linux user for over 15 years now. Every Linux system I install has 4 virtual desktops. This works very well for my normal workflow. Windows XP had a PowerToy that could add this functionality, but it was not very good. Windows 10 boasts fully functional virtual desktops. Remember how I said MS cannot do anything 100% right though? Their failure with this feature is the inability to add keybindings to go to a specific desktop. They have designed the virtual desktop system with the assumption that the typical user will constantly add and remove desktops as needed. Unfortunately, it turns out most people don't do this. People who use virtual desktops tend to use desktops for dedicated tasks. For example, I tend to use my first desktop for my highest priority work. My second one will be for keeping documentation open and ready. The third will be for very low priority stuff that I just want to keep alive (a browser video game, for example). The fourth is usually left empty, just in case I need it for something not in those categories (maybe someone needs to check their email on my computer). Because of this, I find it very valuable to be able to switch to a specific desktop instantly, with one command. Windows 10 does not provide any way to do this. On my old laptop, I can switch to a desktop by pressing Win+Fx, where x is the desktop number. If my wife needs to check her email, I hit Win+F4. If I am working and I need to glance at documentation, Win+F2, and then Win+F1 to get back to my work. In Windows 10, it is Ctrl+Win+left or Ctrl+Win+right to cycle through desktops. If I need to go to desktop 4, it is Ctrl+Win+right+right+right, and I have to watch two desktops I don't currently care about whiz by. Not only is this confusing, it is so unintuitive that I don't end up using desktops 3 and 4 very much, which cuts into my productivity. In addition, the Windows hotkeys are too close to hotkeys that do other things. If you accidentally press Ctrl+Alt, pressing left or right will changes your screen orientation (my wife had this happen, and she was only using one desktop). If you accidentally press up or down instead of left or right, it will minimize or maximize the current window. If you trip over spacebar, it can change something somewhere that will make it so your keyboard no longer registers certain letter keys (this is manufacturer specific, I believe, but it is really frustrating). This particular combination is both slow and prone to errors that have serious effects on productivity. It would be trivial for MS to add the ability to bind specific key combinations to specific desktops, but they just assume that no one wants that, despite the fact that it has been a common Linux convention for over a decade. At this point, they are also ignoring constant pleas on their forums for this feature as well.
Aside from the two crashes, there is really only one seriously bad thing I have to say about Windows 10: The unicode support sucks. On their website, MS has an article about code pages. MS DOS did not have support for millions of characters, so instead it used code pages, which offered a way to select a specific set of 256 characters. This allowed MS DOS to handle many different languages, albeit, only one at a time. As the internet got big, it became more important for computers to be able to handle all languages at once, and unicode was born. According to MS, code pages are "legacy", which means, they are only supported so old programs that use them will still work. Their documentation says that modern programs should support unicode, instead of code pages. Of course, at the same time as telling everyone else to use unicode, here is MS, in 2016, still using code pages in their own OS! The terminal program, run with the command "cmd", is still using code pages, which makes it very difficult to do anything with a filesystem that is using non-English characters (Japanese, for instance). To mitigate this, MS provides code page 65001, for unicode, but it is buggy, and it is not the default. Even worse, the default terminal font does not actually contain many foreign characters, so they all display as boxed question marks, even if you do set the terminal to unicode. And, even worse than that, the terminal is so picky about character width in fonts that it is nigh on impossible to get it to use a font with foreign characters, even if you hack the registry to add more font options. My specific experience is with Japanese, which requires most of its characters to be twice as wide as normal English characters, just to be readable. I spent many hours of research over two days trying to find a solution, and nothing would work. Thanks MS. Wish they would take their own advice.
Honestly though, if foreign language is not a significant issue for you, Windows 10 is the best version of Windows since 3.11 (ok, it may even beat that). MS has finally added a lot of very useful features that Linux has had for over 15 years now. Cortana is a really good start for voice control. The virtual desktops are better than they were in the XP PowerToy (but still need work to compete with what Linux has had for over a decade). It also crashes less, and it seems to handle driver crashes (historically the most common source of blue screens in Windows) much more gracefully than in the past. It is lighter than most versions of Windows since XP, and the PC interface is not designed exclusively for phones and tablets. Windows 10 is not a bad OS for the average American, if you can afford the Enterprise version, or if you can put up with your computer dictating its own update schedule.
If you are not using English exclusively though, you might want to consider Linux or even Mac. Some Windows applications have decent unicode support, but Windows itself does not. Neither cmd.exe nor PowerShell has sufficient unicode support to work with most foreign languages by default, and neither of them can handle Japanese, Chinese, Korean, or any other language where characters must be wider than English to be readable. If you are in this category though, you probably already know this. If you are just starting to need this (in my research, I found several businesses who were starting to work with people overseas that were affected by this problem), you should be aware that you are out of luck. MS just does not care about you, and your only solutions involve using a more modern OS, like Linux or even Mac OS X.
That was the conclusion, but I would like to share the aftermath of my experience with Windows 10, for anyone that is interested. I am currently working on learning Japanese. I want to learn both the spoken and written forms of the language. I recently bought some stickers I can put on my keyboard, so I can see what Japanese characters will be printed when I use my keyboard in Windows IME mode (or in Japanese mode in Linux). I am also looking into buying an actual Japanese keyboard. As such, Japanese support, and more broadly, unicode support (I am not stopping at just Japanese), is essential to me. Around the time I started this endeavor, I discovered that Enlightenment, my long time favorite Linux window manager that has always been missing just enough important features that I was never able to use it, is now mature enough to be in a popular Linux distribution. I am not going to use that distro (I'll discuss that in a future OS Review), but I decided it was time to try it out again. To my happy surprise, it is just as awesome as it used to be, and it seems to meet my needs now. Linux in general has excellent unicode support and has had it for many years. This problem with unicode support came to the front about 2 days after finding the Enlightenment is still going strong. So today, I tested Enlightenment, with a serious eye on dumping Windows again, and so far, it is great. The only other roadblock is whether or not Debian has updated to a Linux kernel that supports my wireless card, and honestly, I am not sure I would be opposed to compiling the most recent kernel myself if Debian has not done it yet.
15 May 2016
01 May 2016
The Search for Perpetual Motion
Perpetual motion has been a sort of holy grail of science since the discovery of momentum, inertia, velocity, and similar ideas from classical physics (electromagnetism gave it a major boost). Around the same time though, the Laws of Thermodynamics were conceived, which state that perpetual motion machines are impossible, because the energy in a closed system cannot increase, and entropy cannot decrease, which means that any organized motion will eventually decay to nothing as it radiates thermal energy (from friction, in most cases). This proof, however, has not stopped the search. Any kind of working perpetual motion machine would prove that it is possible for a closed system to either increase in total energy or at least for entropy to decrease, and this essentially means that we could create devices that would create free energy. This is, essentially, a search for gold, and many people are willing to doubt the proof against it if there is a promise of riches at the end of the rainbow. Of course, this search is so absurd that the U.S. Patent Office will not even consider patents for perpetual motion machines. Until about 10 minutes ago, I was of the opinion that we would be better off if everyone would just give up on this fool's errand and do something useful with their time. What happened 10 minutes ago, however, is that I realized several things.
The first thing I realized is that science cannot prove anything definitively (I already knew this, but I applied it to this problem in that moment). The closest science can get to proof is to disprove all other possibilities, but even then, it stands on shaky ground. The fact is, science proves things by observation. The Laws of Thermodynamics are not literally proven physical laws. They are statements about what has been observed. The Laws of Thermodynamics state that we have never observed conservation of energy to be violated and we have never observed entropy to decrease in a closed system, given an enormous number of observations. This is the closest science can get to proof, but it does not mean that it can never happen. Perhaps there is some very specific situation where conservation of energy can be violated or where entropy can decrease in a closed system. Until every possible situation has been tested, the Laws of Thermodynamics are just widely accepted theories that apply to every situation that has been tested. In other words, we don't actually have solid proof that perpetual motion and free energy are impossible.
Now, I don't want to imply that I think perpetual motion is possible, and I certainly am not trying to suggest that we should put more resources into this endeavor. Given how much effort has been spent on this without any progress, odds are that even if it is possible, the situation required is so complex or otherwise difficult to discover that we will probably never discover it. Of course, it is also possible that we just don't have the technology to do it, but if this is the case, it will likely be solved as soon as we develop that technology. The fact is, it probably does not matter if perpetual motion is possible or not, because we probably would have found it already if it is something we have the means to do.
The second thing I realized is that the work done on perpetual motion machines has produced value. A great number of very useful inventions have drawn from discoveries and ideas found while trying to make perpetual motion machines. Now, I said that we probably don't need to put more resources into this search, but this is where more resources might really produce useful things. In fact, we are already seeing useful ideas come from the search for free energy, beyond just perpetual motion. There are many people experimenting with "crystal cell" batteries that seem to be able to continuously produce very small electric currents for far longer than standard batteries can last even in storage. The hope is that these batteries can be improved and scaled up to produce large amounts of energy for very long periods of time, but even if this fails, there are plenty of applications for very long life, low current batteries, and the number of applications will only increase as we improve the energy efficiency of technology. As long as people are constantly trying new things, we will see new discoveries, even if the end goal is impossible.
There are two reasons we should continue the search for perpetual motion and free energy. The first is that maybe it is possible, and we have just not found it yet. The second, more important reason, is that this search can provide us with very valuable knowledge and discoveries, even if we never reach the goal. This second reason may even be sufficiently valuable to encourage or even help fund the search.
The first thing I realized is that science cannot prove anything definitively (I already knew this, but I applied it to this problem in that moment). The closest science can get to proof is to disprove all other possibilities, but even then, it stands on shaky ground. The fact is, science proves things by observation. The Laws of Thermodynamics are not literally proven physical laws. They are statements about what has been observed. The Laws of Thermodynamics state that we have never observed conservation of energy to be violated and we have never observed entropy to decrease in a closed system, given an enormous number of observations. This is the closest science can get to proof, but it does not mean that it can never happen. Perhaps there is some very specific situation where conservation of energy can be violated or where entropy can decrease in a closed system. Until every possible situation has been tested, the Laws of Thermodynamics are just widely accepted theories that apply to every situation that has been tested. In other words, we don't actually have solid proof that perpetual motion and free energy are impossible.
Now, I don't want to imply that I think perpetual motion is possible, and I certainly am not trying to suggest that we should put more resources into this endeavor. Given how much effort has been spent on this without any progress, odds are that even if it is possible, the situation required is so complex or otherwise difficult to discover that we will probably never discover it. Of course, it is also possible that we just don't have the technology to do it, but if this is the case, it will likely be solved as soon as we develop that technology. The fact is, it probably does not matter if perpetual motion is possible or not, because we probably would have found it already if it is something we have the means to do.
The second thing I realized is that the work done on perpetual motion machines has produced value. A great number of very useful inventions have drawn from discoveries and ideas found while trying to make perpetual motion machines. Now, I said that we probably don't need to put more resources into this search, but this is where more resources might really produce useful things. In fact, we are already seeing useful ideas come from the search for free energy, beyond just perpetual motion. There are many people experimenting with "crystal cell" batteries that seem to be able to continuously produce very small electric currents for far longer than standard batteries can last even in storage. The hope is that these batteries can be improved and scaled up to produce large amounts of energy for very long periods of time, but even if this fails, there are plenty of applications for very long life, low current batteries, and the number of applications will only increase as we improve the energy efficiency of technology. As long as people are constantly trying new things, we will see new discoveries, even if the end goal is impossible.
There are two reasons we should continue the search for perpetual motion and free energy. The first is that maybe it is possible, and we have just not found it yet. The second, more important reason, is that this search can provide us with very valuable knowledge and discoveries, even if we never reach the goal. This second reason may even be sufficiently valuable to encourage or even help fund the search.
23 April 2016
Art Perfected
The Japanese katana was perfected over hundreds of years. This is just an example. There are plenty of things that modern society treats as perfected. The Japanese katana is just one of many. As I watched a few videos today on the ancient art of katana making, and I heard this phrase applied to the weapon, I began to wonder, exactly when was this art perfected?
I believe that claiming some art or craft has been perfected is a cop out. Consider, Masamune, who lived from the mid 1200s to the mid 1300s, according to most scholars, is credited with inventing many of the techniques that are still used in katana making today. Modern katanas are not still made exactly the way that Masamune made them though. According to scholars as well as Japanese lore, improvements were still being made to the process and to the end product for many centuries after that. In fact, general consensus seems to hold that the art of katana making reached perfection sometime between the 1600s and the 1800s (though, it is possible that improvements were still being made into the early 1900s). All traditionally crafted modern katanas use approximately the same process used to make the weapons around 150 to 200 years ago and possibly as far back as 400 years ago. The question is, why did the improvements stop?
Scholars, historians, artisans, and other experts will claim that the art of katana making was perfected, and improvements were unnecessary or even futile. The question I have is, what if Masamune had thought that the art of Japanese sword making was perfected before his time? We would not even have the katana, if Masamune had just given up and abandoned his experimentation that lead to a significantly superior blade. Now, keep in mind that the katana is just one example here. How many crafts have been "perfected" prematurely? What are we missing when we walk away because we think there is no longer room for improvement?
I believe I know the reason that people tend to do this. Most historians seem to believe that the katana had reached perfection sometime between the 1600s and the 1800s, but I think that this consensus was actually reached later than this. Before this time, individual katanas were often considered perfect, as an extension of the spirit of the owner, but there were still experimental techniques and techniques that were not agreed upon by the masters, in the art of making the weapons. The samurai class began to fall around the time guns were introduced to Japan, because an untrained peasant with a gun could fell a samurai warrior with a lifetime of training with hardly any effort. World War II was the major turning point in Japan for the art of sword making. This is often regarded as the completion of the fall of the samurai. I believe that the word "perfect" shifted from being applied to individual weapons to the art of sword making in general during this time. By the end of WWII, sword making had become something of an obsolete craft. This is when it finally changed from a legitimate profession to the preservation of an ancient tradition. The art of Japanese sword making most likely shifted from a living and evolving craft to a "perfected" art when the craft became obsolete and started dying out and the focus went from the production of useful tools to the preservation of national culture.
The fact is, katana making is not a perfected art. It is an art where evolution, improvement, and progress no longer have any value. Improving the process will no longer increase the value of the weapon. No one buys katanas to kill people anymore. Collectors care more about authenticity than function, so for them, changing the process actually reduces the value of the product, even if it improves the function. Katanas are not really weapons anymore. They are collectors items, novelties, souvenirs, national treasures, and historically interesting objects, but they are not weapons. As collectors items, novelties, souvenirs,...etc., perhaps they are perfected in their current state, because any change to the process would reduce their value. As weapons though, to claim that katana making is a perfected art is the ultimate hubris. Cheap guns were used to kill off the warrior class that dedicated their lives to this weapon. The katana may be the very best close combat weapon ever created by human hands, but that does not mean that it could not be improved.
This seems to be the trend with all "perfected" crafts. They are almost always crafts that have lost all of their practical value. The are usually processes that have been automated (though, usually at the cost of quality), or products that have been replaced by something cheaper and easier to produce (again, often at lower quality). People who still do those crafts usually stick to traditional methods, but not because they cannot be improved upon. Like katanas, most "perfected" crafts are not improved upon either because there is no value in improving them, or because changing the process would reduce the value of the product, because no one is buying it for function. The real question though, is what are we missing because we are walking away too soon?
The techniques used in katana making have been applied to many modern manufacturing processes, because they result in better products. If Masamune had not introduced the technique of layering different qualities of metals to improve the differential tempering process of Japanese sword making, we might not have high quality saw blades. What if Masamune had decided that the art of Japanese sword making had already been perfected? Perhaps katanas are not valued as weapons anymore, and maybe this offers a justification for giving up on improving them further, but maybe we are missing out on something that could improve or even revolutionize many industries, because we are copping out by claiming that an art that is not as valuable as it once was is no longer worth improving at all. And, beyond just katana making, what things are we missing from all of the other "perfected" arts? Even arts that have merely been abandoned, with no claims of perfection (like blacksmithing), could be hiding valuable secrets just beyond the horizon.
No human craft or art is ever perfect. Perfection is just a made up excuse to cease improvement. Yes, it may be justified to stop improving on something that is no longer valuable, but lets be honest: We are not stopping improvement because the craft has been perfected. We are stopping because there is no longer enough value in it to justify the cost of innovation. If we cannot admit that, then perhaps the craft is still worth improving, and if it is still worth improving, let's do it and see what we discover!
Disclaimer:
(If nothing about the above offends you, feel free to stop here. The main article is finished.)
I love the art of Japanese sword making. I have studied it in some depth. The techniques involved are ingenious. Yes, we have known about them for a long time, but the original inventors of the techniques deserve recognition for their invaluable contributions to our current level of technology. I am very glad to see that the traditional methods have been preserved, and I would like to gain some experience in them. I plan to eventually forge my own katana, as close to the traditional methods as possible. In other words, I have great respect for this ancient art that produces one of the highest quality products mankind has ever made. Still, I am almost certain that there is room for improvement, because there is always room for improvement. It is a shame that we are hiding this with the claim that the art has already been perfected.
I believe that claiming some art or craft has been perfected is a cop out. Consider, Masamune, who lived from the mid 1200s to the mid 1300s, according to most scholars, is credited with inventing many of the techniques that are still used in katana making today. Modern katanas are not still made exactly the way that Masamune made them though. According to scholars as well as Japanese lore, improvements were still being made to the process and to the end product for many centuries after that. In fact, general consensus seems to hold that the art of katana making reached perfection sometime between the 1600s and the 1800s (though, it is possible that improvements were still being made into the early 1900s). All traditionally crafted modern katanas use approximately the same process used to make the weapons around 150 to 200 years ago and possibly as far back as 400 years ago. The question is, why did the improvements stop?
Scholars, historians, artisans, and other experts will claim that the art of katana making was perfected, and improvements were unnecessary or even futile. The question I have is, what if Masamune had thought that the art of Japanese sword making was perfected before his time? We would not even have the katana, if Masamune had just given up and abandoned his experimentation that lead to a significantly superior blade. Now, keep in mind that the katana is just one example here. How many crafts have been "perfected" prematurely? What are we missing when we walk away because we think there is no longer room for improvement?
I believe I know the reason that people tend to do this. Most historians seem to believe that the katana had reached perfection sometime between the 1600s and the 1800s, but I think that this consensus was actually reached later than this. Before this time, individual katanas were often considered perfect, as an extension of the spirit of the owner, but there were still experimental techniques and techniques that were not agreed upon by the masters, in the art of making the weapons. The samurai class began to fall around the time guns were introduced to Japan, because an untrained peasant with a gun could fell a samurai warrior with a lifetime of training with hardly any effort. World War II was the major turning point in Japan for the art of sword making. This is often regarded as the completion of the fall of the samurai. I believe that the word "perfect" shifted from being applied to individual weapons to the art of sword making in general during this time. By the end of WWII, sword making had become something of an obsolete craft. This is when it finally changed from a legitimate profession to the preservation of an ancient tradition. The art of Japanese sword making most likely shifted from a living and evolving craft to a "perfected" art when the craft became obsolete and started dying out and the focus went from the production of useful tools to the preservation of national culture.
The fact is, katana making is not a perfected art. It is an art where evolution, improvement, and progress no longer have any value. Improving the process will no longer increase the value of the weapon. No one buys katanas to kill people anymore. Collectors care more about authenticity than function, so for them, changing the process actually reduces the value of the product, even if it improves the function. Katanas are not really weapons anymore. They are collectors items, novelties, souvenirs, national treasures, and historically interesting objects, but they are not weapons. As collectors items, novelties, souvenirs,...etc., perhaps they are perfected in their current state, because any change to the process would reduce their value. As weapons though, to claim that katana making is a perfected art is the ultimate hubris. Cheap guns were used to kill off the warrior class that dedicated their lives to this weapon. The katana may be the very best close combat weapon ever created by human hands, but that does not mean that it could not be improved.
This seems to be the trend with all "perfected" crafts. They are almost always crafts that have lost all of their practical value. The are usually processes that have been automated (though, usually at the cost of quality), or products that have been replaced by something cheaper and easier to produce (again, often at lower quality). People who still do those crafts usually stick to traditional methods, but not because they cannot be improved upon. Like katanas, most "perfected" crafts are not improved upon either because there is no value in improving them, or because changing the process would reduce the value of the product, because no one is buying it for function. The real question though, is what are we missing because we are walking away too soon?
The techniques used in katana making have been applied to many modern manufacturing processes, because they result in better products. If Masamune had not introduced the technique of layering different qualities of metals to improve the differential tempering process of Japanese sword making, we might not have high quality saw blades. What if Masamune had decided that the art of Japanese sword making had already been perfected? Perhaps katanas are not valued as weapons anymore, and maybe this offers a justification for giving up on improving them further, but maybe we are missing out on something that could improve or even revolutionize many industries, because we are copping out by claiming that an art that is not as valuable as it once was is no longer worth improving at all. And, beyond just katana making, what things are we missing from all of the other "perfected" arts? Even arts that have merely been abandoned, with no claims of perfection (like blacksmithing), could be hiding valuable secrets just beyond the horizon.
No human craft or art is ever perfect. Perfection is just a made up excuse to cease improvement. Yes, it may be justified to stop improving on something that is no longer valuable, but lets be honest: We are not stopping improvement because the craft has been perfected. We are stopping because there is no longer enough value in it to justify the cost of innovation. If we cannot admit that, then perhaps the craft is still worth improving, and if it is still worth improving, let's do it and see what we discover!
Disclaimer:
(If nothing about the above offends you, feel free to stop here. The main article is finished.)
I love the art of Japanese sword making. I have studied it in some depth. The techniques involved are ingenious. Yes, we have known about them for a long time, but the original inventors of the techniques deserve recognition for their invaluable contributions to our current level of technology. I am very glad to see that the traditional methods have been preserved, and I would like to gain some experience in them. I plan to eventually forge my own katana, as close to the traditional methods as possible. In other words, I have great respect for this ancient art that produces one of the highest quality products mankind has ever made. Still, I am almost certain that there is room for improvement, because there is always room for improvement. It is a shame that we are hiding this with the claim that the art has already been perfected.
17 April 2016
Do Machines Make Us Less Human?
"Machines are dehumanizing." This is an often quoted phrase referring to the fact that machines are being used to replace human labor. The implication is that when machines do things that humans could be doing, it makes people less human. This is part of a claim that machines make humans less valuable. So, do machines really make us less human?
The first thing to keep in mind is that people make and use machines. When a machine takes over the work of several people, it is because some human somewhere decided it should. From the perspective of the worker, the machine is replacing them. From the other side, however, the machine is an extension of the boss, who is now able to do more work with fewer workers. If a machine makes some workers less human, it makes the boss more human. This is a zero sum game. Looking at it this way, the most anyone could say is maybe that the machine is taking humanity from the workers and giving it to the boss.
The second thing, which is the most important thing, in my opinion, is that this entire idea is based on a flawed definition of humanity. If the most important thing in a person's life is that they are working a job, then yes, a machine that does that person's work could be said to reduce that person's humanity. The definition of "human" has nothing to do with work though. The fact is that when a machine takes over the work of a human, the human does not magically become less human, nor does the machine suddenly become more human (the machine is already partially human in the sense that it was created by a human mind). A human without a job is just as human as a human with a job. A homeless man is no less human than a CEO. This idea that machines are dehumanizing is built on the false idea that everyone should have to work for a living. It is based on the concept that a person's employment defines their value as a person, and this claim that "machines are dehumanizing" perpetuates the idea that fairness dictates that every person should have to work for their living or starve to death. In other words, it is based on a lie.
Here is the truth about machines: Machines are an extension of human creativity and the human will. The machine that replaced 100 workers is an extension of the will of some boss somewhere. That cell phone that allows you to call anyone from nearly anywhere is an extension of your will. A car that allows you to easily and quickly travel long distances is another extension of your will. Machines empower humans. An essential part of human nature is adaptation. Machines help us to adapt and they often make us more adaptable. Machines amplify human ability and will. In other words, machines actually make people more human. Machines are an extension of human creativity. There are very few species on Earth that even use tools. Humanity is the only one that builds automated tools.
Machines are even more than this though. Humans create machines as an alternative route to evolution. Evolution's exclusive goal is survival. Evolution does not ask us what we want. It gives us what makes us more likely to survive, or it kills us off to make way for someone more fit. If evolution had its say, a vast majority of living humans would be dead, because most of us have deficiencies that would make it difficult or impossible to survive without human innovation. Machines, however, give us another route to improvement. The difference is that with machines, we can become what we want to become, instead of what nature thinks will work best. Side-by-side, these two tracks of progression give humans a major advantage over any other form of live found on Earth. If we don't embrace machines, then we are dehumanizing ourselves. Without machines, humans are just another species of animal that happens to be smarter than others. With machines though, humans are a higher form of life.
It is still important to realize that this does not mean we do not have to use machines responsibly. If we don't curb our desires and do things in the right order, we could paint ourselves into a corner. For example, if we strip mine all valuable materials out of the Earth before we have someplace else to go and the means to relocate, we will destroy ourselves. Nuclear war is another example that we hovered on the brink of for almost half a century. If we are wise though, we can create machines that will add so much to our humanity that we can become super humans! (In fact, I would argue that we are already at some stage of super humanity right now, and we are continuing to progress at a rapid rate.)
Machines are not dehumanizing. Machines are the pivotal factor in our humanity, and without machines, we are mere animals. Machines increase our humanity. If they are causing us problems, it is not because the machines or our reliance on machines make us less human. It is because we are choosing to hold on to ideals that are holding us back. If we let go of these dehumanizing ideals and embrace machines, we can be far more human than humanity has ever been.
The first thing to keep in mind is that people make and use machines. When a machine takes over the work of several people, it is because some human somewhere decided it should. From the perspective of the worker, the machine is replacing them. From the other side, however, the machine is an extension of the boss, who is now able to do more work with fewer workers. If a machine makes some workers less human, it makes the boss more human. This is a zero sum game. Looking at it this way, the most anyone could say is maybe that the machine is taking humanity from the workers and giving it to the boss.
The second thing, which is the most important thing, in my opinion, is that this entire idea is based on a flawed definition of humanity. If the most important thing in a person's life is that they are working a job, then yes, a machine that does that person's work could be said to reduce that person's humanity. The definition of "human" has nothing to do with work though. The fact is that when a machine takes over the work of a human, the human does not magically become less human, nor does the machine suddenly become more human (the machine is already partially human in the sense that it was created by a human mind). A human without a job is just as human as a human with a job. A homeless man is no less human than a CEO. This idea that machines are dehumanizing is built on the false idea that everyone should have to work for a living. It is based on the concept that a person's employment defines their value as a person, and this claim that "machines are dehumanizing" perpetuates the idea that fairness dictates that every person should have to work for their living or starve to death. In other words, it is based on a lie.
Here is the truth about machines: Machines are an extension of human creativity and the human will. The machine that replaced 100 workers is an extension of the will of some boss somewhere. That cell phone that allows you to call anyone from nearly anywhere is an extension of your will. A car that allows you to easily and quickly travel long distances is another extension of your will. Machines empower humans. An essential part of human nature is adaptation. Machines help us to adapt and they often make us more adaptable. Machines amplify human ability and will. In other words, machines actually make people more human. Machines are an extension of human creativity. There are very few species on Earth that even use tools. Humanity is the only one that builds automated tools.
Machines are even more than this though. Humans create machines as an alternative route to evolution. Evolution's exclusive goal is survival. Evolution does not ask us what we want. It gives us what makes us more likely to survive, or it kills us off to make way for someone more fit. If evolution had its say, a vast majority of living humans would be dead, because most of us have deficiencies that would make it difficult or impossible to survive without human innovation. Machines, however, give us another route to improvement. The difference is that with machines, we can become what we want to become, instead of what nature thinks will work best. Side-by-side, these two tracks of progression give humans a major advantage over any other form of live found on Earth. If we don't embrace machines, then we are dehumanizing ourselves. Without machines, humans are just another species of animal that happens to be smarter than others. With machines though, humans are a higher form of life.
It is still important to realize that this does not mean we do not have to use machines responsibly. If we don't curb our desires and do things in the right order, we could paint ourselves into a corner. For example, if we strip mine all valuable materials out of the Earth before we have someplace else to go and the means to relocate, we will destroy ourselves. Nuclear war is another example that we hovered on the brink of for almost half a century. If we are wise though, we can create machines that will add so much to our humanity that we can become super humans! (In fact, I would argue that we are already at some stage of super humanity right now, and we are continuing to progress at a rapid rate.)
Machines are not dehumanizing. Machines are the pivotal factor in our humanity, and without machines, we are mere animals. Machines increase our humanity. If they are causing us problems, it is not because the machines or our reliance on machines make us less human. It is because we are choosing to hold on to ideals that are holding us back. If we let go of these dehumanizing ideals and embrace machines, we can be far more human than humanity has ever been.
02 April 2016
America is Already Socialist
America is already socialist, and it has nothing to do with welfare. Socialism as a style of government is based on the fact that civilization is a social construct. It is essentially the idea that everyone in a formal society (like a nation with its own government) has implicitly agreed to a social contract to support and conform to that society. The other side of the social contract is that society makes it possible for all members to survive reasonably comfortably within society. From a socialist perspective, this is where welfare comes from, however, the U.S. welfare system does not come from socialism. It comes from Christianity, where welfare is a charitable, love-based thing. Of course, most of this love-based charity seems to come from non-Christians, at least in the U.S.
I don't want to talk about actual Socialism though. Most Americans, especially conservative Americans, believe that Socialism is defined as a system of government where all the means of production are controlled by the government. This may be one way, and admittedly the most popular way, of enforcing the social contract of Socialism, it is not the only way. It is, however, the way that most conservative Americans fear, and probably with just cause. This brand of Socialism has been tried before, with mixed results. The USSR spent most of its existence on a downhill slope, as its toxic mix of Socialism and Communism discouraged a good work ethic and marginalized the masses. Ultimately, it fell apart. The People's Republic of China has fared much better. Aside from poor representation of the people and mass murder of its own citizens, China has managed to avoid the steady drop in productivity that the USSR saw. In the end though, China is still finding that even the government itself fares better when some businesses are privatized.
In U.S. has largely feared this brand of Socialism since the beginning. The very idea of government owned or controlled monopolies was derided by many of this nation's founders. During certain periods of our history, merely discussing the merits of Socialism could result in imprisonment, despite the laws that supposedly protect American citizens from government discrimination based on religious and political opinion. The fear of this kind of Socialism is still strong among conservatives. The fact, however, is that it has existed since the very beginning. The United States of America has already embraced what is widely considered the most toxic form of Socialism, though, on a very small scale, and this Socialism exists as a power, granted to the Federal government, by The Constitution of the United States of America.
The common definition of Socialism is a system of government where the government controls the means of production. The government does not strictly have to own the means of production. In practice, what this means, is that the government says who can and cannot produce things. The government may or may not control distribution (controlling distribution is closer to Communism, though this depends on the specifics). Merely regulating production does not qualify. The government can impose regulations without explicitly saying who can and cannot produce a product. Requiring a license for producing a product could qualify, but it is a bit of a stretch if anyone can qualify for a license by meeting some general guidelines. U.S. Socialism limits production to specific individuals or sometimes small groups, who may extend that permission to a third party (technically this permission can be granted to any number of third parties, at the discretion of the individual or group, but it is far more common, now and historically, for exclusive production rights to be granted to a single third party).
Why has this not been realized and rectified? Ironically, the most vocally anti-Socialist political party has put a great deal of effort and money into ensuring that this Socialist system is maintained and even significantly strengthened. The Republican Party has worked tirelessly to further extend the duration and scope of government granted rights to production. They call it "fair," despite the fact that those who have been granted these production rights often end up with profit margins far over 100% and have potentially unlimited profit margins. Violation of these production rights once was only a civil offense that could only be punished with a moderate fine based on the profits lost by the controller of the production rights. Over the last several decades, however, the violation of this Socialist system has become a very serious criminal offense. The penalties have been extended to include jail time and exorbitant fines based on the amount of profits that the production rights owner could have or might have lost, without any burden of proof that any profits were actually lost. It turns out that the most vocal opponent of Socialism is actually the driving force behind the most Socialist practice allows by the U.S. government.
What, exactly, is this Socialism? Simple, intellectual property law. The U.S. Constitution grants the Federal government the power to grant temporary monopolies over production of patented and copyrighted material. Our modern law actually goes beyond what is allowed by The Constitution to include copyright for things that have not explicitly been copyrighted. This system is Socialist, because the government controls the means of production by dictating who can and cannot produce patented or copyrighted works. It is worse than this though. The government does not actually directly control production. It delegates the control of production to someone with a vested interest in the profitability of the product. When pure Socialism puts the production in the control of the government, it does so with the intent to avoid conflicts of interest and maintain fairness for everyone. The U.S. brand of Socialism does the exact opposite. Ironically, the U.S. Constitution seems to predict this, as the stated purpose of this Socialist power is to stimulate progress in the arts and sciences. Unfortunately, the government does not care about this anymore, the Supreme Court makes decisions based on personal opinion instead of Constitutional law, and the biggest sponsor of this Socialist system, the Republican party, is more interested in profits than doing what is right or fair. This may be one of the biggest conflicts of interest in the history of the U.S., but the people are blind to fact that their biggest fear has been realized.
The real facts are these: "Intellectual property" laws are more Socialist than any amount of government welfare. The enormous costs associated with patent wars are ultimately paid by the general public, so this Socialism is actually far more toxic than directly government ownership of production. The stifling of innovation is also bad for society, and it directly violates the Constitutional purpose of patents and copyrights. The evidence provided by the media piracy "epidemic" proves that oppressive intellectual property laws are unnecessary to ensure that content creators receive fair compensation for their work (in fact, the evidence seems to indicate that weaker "protection" would actually help a majority of content creators).
When The Constitution was drafted, Thomas Jefferson, among others, expressed concern with the idea of giving the government control over any level of production. He recognized the toxic Socialist influence it could have, and he has turned out to be right. It is a crying shame that it has taken over 200 years for anyone to notice this, and it is especially concerning that a major political party that claims to oppose this kind of oppression is the biggest supporter of it.
I don't want to talk about actual Socialism though. Most Americans, especially conservative Americans, believe that Socialism is defined as a system of government where all the means of production are controlled by the government. This may be one way, and admittedly the most popular way, of enforcing the social contract of Socialism, it is not the only way. It is, however, the way that most conservative Americans fear, and probably with just cause. This brand of Socialism has been tried before, with mixed results. The USSR spent most of its existence on a downhill slope, as its toxic mix of Socialism and Communism discouraged a good work ethic and marginalized the masses. Ultimately, it fell apart. The People's Republic of China has fared much better. Aside from poor representation of the people and mass murder of its own citizens, China has managed to avoid the steady drop in productivity that the USSR saw. In the end though, China is still finding that even the government itself fares better when some businesses are privatized.
In U.S. has largely feared this brand of Socialism since the beginning. The very idea of government owned or controlled monopolies was derided by many of this nation's founders. During certain periods of our history, merely discussing the merits of Socialism could result in imprisonment, despite the laws that supposedly protect American citizens from government discrimination based on religious and political opinion. The fear of this kind of Socialism is still strong among conservatives. The fact, however, is that it has existed since the very beginning. The United States of America has already embraced what is widely considered the most toxic form of Socialism, though, on a very small scale, and this Socialism exists as a power, granted to the Federal government, by The Constitution of the United States of America.
The common definition of Socialism is a system of government where the government controls the means of production. The government does not strictly have to own the means of production. In practice, what this means, is that the government says who can and cannot produce things. The government may or may not control distribution (controlling distribution is closer to Communism, though this depends on the specifics). Merely regulating production does not qualify. The government can impose regulations without explicitly saying who can and cannot produce a product. Requiring a license for producing a product could qualify, but it is a bit of a stretch if anyone can qualify for a license by meeting some general guidelines. U.S. Socialism limits production to specific individuals or sometimes small groups, who may extend that permission to a third party (technically this permission can be granted to any number of third parties, at the discretion of the individual or group, but it is far more common, now and historically, for exclusive production rights to be granted to a single third party).
Why has this not been realized and rectified? Ironically, the most vocally anti-Socialist political party has put a great deal of effort and money into ensuring that this Socialist system is maintained and even significantly strengthened. The Republican Party has worked tirelessly to further extend the duration and scope of government granted rights to production. They call it "fair," despite the fact that those who have been granted these production rights often end up with profit margins far over 100% and have potentially unlimited profit margins. Violation of these production rights once was only a civil offense that could only be punished with a moderate fine based on the profits lost by the controller of the production rights. Over the last several decades, however, the violation of this Socialist system has become a very serious criminal offense. The penalties have been extended to include jail time and exorbitant fines based on the amount of profits that the production rights owner could have or might have lost, without any burden of proof that any profits were actually lost. It turns out that the most vocal opponent of Socialism is actually the driving force behind the most Socialist practice allows by the U.S. government.
What, exactly, is this Socialism? Simple, intellectual property law. The U.S. Constitution grants the Federal government the power to grant temporary monopolies over production of patented and copyrighted material. Our modern law actually goes beyond what is allowed by The Constitution to include copyright for things that have not explicitly been copyrighted. This system is Socialist, because the government controls the means of production by dictating who can and cannot produce patented or copyrighted works. It is worse than this though. The government does not actually directly control production. It delegates the control of production to someone with a vested interest in the profitability of the product. When pure Socialism puts the production in the control of the government, it does so with the intent to avoid conflicts of interest and maintain fairness for everyone. The U.S. brand of Socialism does the exact opposite. Ironically, the U.S. Constitution seems to predict this, as the stated purpose of this Socialist power is to stimulate progress in the arts and sciences. Unfortunately, the government does not care about this anymore, the Supreme Court makes decisions based on personal opinion instead of Constitutional law, and the biggest sponsor of this Socialist system, the Republican party, is more interested in profits than doing what is right or fair. This may be one of the biggest conflicts of interest in the history of the U.S., but the people are blind to fact that their biggest fear has been realized.
The real facts are these: "Intellectual property" laws are more Socialist than any amount of government welfare. The enormous costs associated with patent wars are ultimately paid by the general public, so this Socialism is actually far more toxic than directly government ownership of production. The stifling of innovation is also bad for society, and it directly violates the Constitutional purpose of patents and copyrights. The evidence provided by the media piracy "epidemic" proves that oppressive intellectual property laws are unnecessary to ensure that content creators receive fair compensation for their work (in fact, the evidence seems to indicate that weaker "protection" would actually help a majority of content creators).
When The Constitution was drafted, Thomas Jefferson, among others, expressed concern with the idea of giving the government control over any level of production. He recognized the toxic Socialist influence it could have, and he has turned out to be right. It is a crying shame that it has taken over 200 years for anyone to notice this, and it is especially concerning that a major political party that claims to oppose this kind of oppression is the biggest supporter of it.
30 March 2016
Why Base 10 is Not Natural
This article may be confusing to those who are not familiar with different number bases, so I will give a brief explanation. A number base is generally defined by the number of digits used in that base. The most commonly used base is base 10 or decimal, which has the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Notice that there are 10 digits. The base of a number system also defines what the difference places mean. In all bases, the first place is always 1s. The next place is the the base itself. For base ten, the second place is the 10s place. The third place is the base squared (100 in base 10), the fourth is the based cubed (1000, in base 10) and so on. Another common base is base 2 or binary. Base 2 has 2 digits, 0 and 1, and the places are powers of 2. The first place is 1s, the second is 2s, the third is 4s, and so on. Some bases have more than 10 digits. Base 16 or hexadecimal has 16 digits. It uses 0 through 9, like base 10, but it runs out of traditional digits there, so it adds A, B, C, D, E, and F for the 10, 11, 12, 13, 14, and 15 digits. Other systems (like base 12) have been invented that reuse other symbols or have unique symbols for those past 9. Math in different bases works very much like base 10, except that you carry and borrow differently, based on the number of digits available.
There have been numerous discussions about numerical bases. Base 10 is rather inconvenient in many aspects, and bases like 12 have some significant benefits. Base 12 is especially useful, because it makes common fractional math extremely easy. Base 12 makes division by 2, 3, 4, 6, and 12 trivial. In base 10, 1/3 = 0.333... This makes any math involving division by 3 complicated and difficult. Even division by 4 is a bit hairy in base 10, where 1/4 = 0.25. The problem with this is that the most frequent division we do is division by small numbers. We might divide a restaurant bill between 2, 3, or 4 people. If there are more people than that, they are generally in groups, where 2, 3, or 4 people end up paying. A great example of why base 12 works so well is time. Seconds and minutes are counted in base 60, but hours are counted in base 24 (in this case, base 24 is just double base 12, so it works the same way). If we need to break up the time for some task between several people (work shifts, for example), base 24 makes it easy. An 8 hour shift is 1/3rd of a day. If you have 4 people, you have 6 hour shifts. It does not work so well with 5 people, but with 6 people, you have 4 hour shifts. With 8 people, it is 3 hour shifts. The fractions involved here, 1/2, 1/3, 1/4, and 1/6, are not just found in time math though. They are found all over the place. The argument for switching to base 12 is quite strong, but there are some problems with it.
The biggest problem with base 12 is that it is not a natural base for humans. We don't have enough fingers to count in base 12 on our hands. This is actually the only logical argument against using base 12. The other problems all stem from the fact that nearly all historical math uses base 10, and while teaching base 12 to children should not really be any more difficult than teaching base 10, it would not be sufficient. Children would have to learn both base 10 and base 12, because there is so much work done in base 10. They would also have to learn to convert between them. Besides that, a lot of practical stuff would have to be transitioned, at great cost. This would include speed limit signs, prices, a huge number of computer programs, measurement systems (though some, like the Imperial System, are already partway there), and the entire world would have to change at the same time to avoid international confusion. It is just not practical. There are certainly major benefits, but they are not worth the cost.
So, why do we use base 10 in the first place? Supposedly it is because it is the most natural way to count for a species with 10 fingers. If humans had 6 fingers and each hand, we would probably count in base 12 instead of base 10. The problem is that this is not actually true. Base 10 is not the most natural way to count for a species with 10 fingers. We actually use base 10 because of a mistake. That mistake is caused by the fact that humanity learned to count before the number 0 was discovered.
The real natural way to count with 10 fingers is base 11. Because humans had not discovered 0 though, only the 10 positive digits that can be counted on hands were considered. In fact, looking at ancient writing systems, we will find that many don't use base 10. Many also have a single glyph (or digit) for the number 10 (instead of combining 1 and 0). Many civilizations that learned to count from fingers had difficulty counting higher than 10, because the lack of a 0 made the place value system currently used almost impossible to discover. A few civilizations did create a placeholder digit for this, but it had no meaning by itself. At least one just left a blank space for empty places, which often made the numbers difficult to interpret. There was clearly a lot of confusion over this, but ultimately, base 10 came to the forefront. Our current base 10 system seems to come from Arabic, which retained the 10 digits idea, but shifted it down one to include 0 and exclude 10. The fact, however, is that on 10 fingers, you can represent digits from 0 to 10, which is actually 11 digits, not 10. Counting on 10 fingers, if you realize that 0 is a number, naturally leads to a base 11 system, not a base 10 system. (Be glad we did not get stuck with base 11 though. As a prime number, 11 is not divisible by anything but 1 and itself, which puts it in the category of the worst possible bases for practical use. In base 11, even division by 2 is difficult!) If you dig a bit deeper though, you might find something else that is interesting.
Base 10 is not the only common number system used anciently. Aside from some very unusual systems, like Roman Numerals that do not have a clear base, there are some that use smaller bases very effectively. The Mayan system (which did include 0) was written in base 5, presumably originating from the fact that humans have 5 fingers. The Mayans are not the only example of a civilization that used base 5. Base 10 systems seem to be the most common, historically, but base 5 systems are actually quite common as well. Even modern tally marks use base 5. The interesting thing with base 5 with fingers though, is that when you include 0 and get base 6, you get a base that is actually quite useful!
Like base 10, base 5 is not natural, because 5 fingers offer 6 digits, if 0 is not forgotten. Base 6 is the natural base for counting with 5 fingers. Including 0 through 5, you can represent a single base 6 digit on one hand. Unlike 11 or even 10, base 6 is quite flexible. It is not as flexible as base 12, but it is, perhaps, close enough. Base 6 fixes the division by 3 problem just as well as base 12. In base 6, 1/3 = 0.2. Base 6 does not fix division by 4, but it does not make it any worse: 1/4 = 0.15 in base 6. It still manages division by 2 as gracefully as base 10 or 12: 1/2 = 0.3 in base 6. The only thing lost that base 10 provides is division by 5, which is only important because we use base 10 everywhere: 1/5 = 0.12 (though, this is no worse than 1/4 in base 10). The advantage base 6 has over base 12 is that you can count in base 6 on your hands. Base 6 has another significant advantage over base 12 and base 10 in hand counting though: Since you only need 6 digits, and these can be supplied with only one hand, the second hand can be used for a second place, which in base 6 is the 6s place. In other words, you can count to 35 on your hands in base 6! (In base 6, 35 is written 55, which is 5 fingers on each hand.)
It turns out that there are two natural ways for humans to count using their fingers. The most obvious one is base 11, and the less obvious one is base 6. Base 11 is completely unsuitable for practical math, but base 6 is surprisingly good. Not only that, but base 6 allows counting to 35 using two hands.
There have been numerous discussions about numerical bases. Base 10 is rather inconvenient in many aspects, and bases like 12 have some significant benefits. Base 12 is especially useful, because it makes common fractional math extremely easy. Base 12 makes division by 2, 3, 4, 6, and 12 trivial. In base 10, 1/3 = 0.333... This makes any math involving division by 3 complicated and difficult. Even division by 4 is a bit hairy in base 10, where 1/4 = 0.25. The problem with this is that the most frequent division we do is division by small numbers. We might divide a restaurant bill between 2, 3, or 4 people. If there are more people than that, they are generally in groups, where 2, 3, or 4 people end up paying. A great example of why base 12 works so well is time. Seconds and minutes are counted in base 60, but hours are counted in base 24 (in this case, base 24 is just double base 12, so it works the same way). If we need to break up the time for some task between several people (work shifts, for example), base 24 makes it easy. An 8 hour shift is 1/3rd of a day. If you have 4 people, you have 6 hour shifts. It does not work so well with 5 people, but with 6 people, you have 4 hour shifts. With 8 people, it is 3 hour shifts. The fractions involved here, 1/2, 1/3, 1/4, and 1/6, are not just found in time math though. They are found all over the place. The argument for switching to base 12 is quite strong, but there are some problems with it.
The biggest problem with base 12 is that it is not a natural base for humans. We don't have enough fingers to count in base 12 on our hands. This is actually the only logical argument against using base 12. The other problems all stem from the fact that nearly all historical math uses base 10, and while teaching base 12 to children should not really be any more difficult than teaching base 10, it would not be sufficient. Children would have to learn both base 10 and base 12, because there is so much work done in base 10. They would also have to learn to convert between them. Besides that, a lot of practical stuff would have to be transitioned, at great cost. This would include speed limit signs, prices, a huge number of computer programs, measurement systems (though some, like the Imperial System, are already partway there), and the entire world would have to change at the same time to avoid international confusion. It is just not practical. There are certainly major benefits, but they are not worth the cost.
So, why do we use base 10 in the first place? Supposedly it is because it is the most natural way to count for a species with 10 fingers. If humans had 6 fingers and each hand, we would probably count in base 12 instead of base 10. The problem is that this is not actually true. Base 10 is not the most natural way to count for a species with 10 fingers. We actually use base 10 because of a mistake. That mistake is caused by the fact that humanity learned to count before the number 0 was discovered.
The real natural way to count with 10 fingers is base 11. Because humans had not discovered 0 though, only the 10 positive digits that can be counted on hands were considered. In fact, looking at ancient writing systems, we will find that many don't use base 10. Many also have a single glyph (or digit) for the number 10 (instead of combining 1 and 0). Many civilizations that learned to count from fingers had difficulty counting higher than 10, because the lack of a 0 made the place value system currently used almost impossible to discover. A few civilizations did create a placeholder digit for this, but it had no meaning by itself. At least one just left a blank space for empty places, which often made the numbers difficult to interpret. There was clearly a lot of confusion over this, but ultimately, base 10 came to the forefront. Our current base 10 system seems to come from Arabic, which retained the 10 digits idea, but shifted it down one to include 0 and exclude 10. The fact, however, is that on 10 fingers, you can represent digits from 0 to 10, which is actually 11 digits, not 10. Counting on 10 fingers, if you realize that 0 is a number, naturally leads to a base 11 system, not a base 10 system. (Be glad we did not get stuck with base 11 though. As a prime number, 11 is not divisible by anything but 1 and itself, which puts it in the category of the worst possible bases for practical use. In base 11, even division by 2 is difficult!) If you dig a bit deeper though, you might find something else that is interesting.
Base 10 is not the only common number system used anciently. Aside from some very unusual systems, like Roman Numerals that do not have a clear base, there are some that use smaller bases very effectively. The Mayan system (which did include 0) was written in base 5, presumably originating from the fact that humans have 5 fingers. The Mayans are not the only example of a civilization that used base 5. Base 10 systems seem to be the most common, historically, but base 5 systems are actually quite common as well. Even modern tally marks use base 5. The interesting thing with base 5 with fingers though, is that when you include 0 and get base 6, you get a base that is actually quite useful!
Like base 10, base 5 is not natural, because 5 fingers offer 6 digits, if 0 is not forgotten. Base 6 is the natural base for counting with 5 fingers. Including 0 through 5, you can represent a single base 6 digit on one hand. Unlike 11 or even 10, base 6 is quite flexible. It is not as flexible as base 12, but it is, perhaps, close enough. Base 6 fixes the division by 3 problem just as well as base 12. In base 6, 1/3 = 0.2. Base 6 does not fix division by 4, but it does not make it any worse: 1/4 = 0.15 in base 6. It still manages division by 2 as gracefully as base 10 or 12: 1/2 = 0.3 in base 6. The only thing lost that base 10 provides is division by 5, which is only important because we use base 10 everywhere: 1/5 = 0.12 (though, this is no worse than 1/4 in base 10). The advantage base 6 has over base 12 is that you can count in base 6 on your hands. Base 6 has another significant advantage over base 12 and base 10 in hand counting though: Since you only need 6 digits, and these can be supplied with only one hand, the second hand can be used for a second place, which in base 6 is the 6s place. In other words, you can count to 35 on your hands in base 6! (In base 6, 35 is written 55, which is 5 fingers on each hand.)
It turns out that there are two natural ways for humans to count using their fingers. The most obvious one is base 11, and the less obvious one is base 6. Base 11 is completely unsuitable for practical math, but base 6 is surprisingly good. Not only that, but base 6 allows counting to 35 using two hands.
14 March 2016
Pi Day 2016
I recently wrote an article on the subject of whether we should use π (pi) or τ (tau) in circle related math. As a refresher, π is the ratio of the circumference of a circle to its diameter. It turns out that in a majority of equations that use π, it is multiplied by 2. A growing group of mathematicians and scientists is pushing to replace π with τ, which is just 2π. They argue that this would simplify a lot of math and make geometry and trig significantly easier to learn. This is probably true, but it addresses the problem from the wrong side. I argue that π is not the problem. The problem is that we have this unreasonable attachment to radius. The reason for having to apply a multiple of 2 everywhere is not that π is the wrong value. The reason is that π is a ratio of the diameter of a circle, but we always pair π with the radius, which requires a multiple of 2 to correct this.
There are a lot of different arguments for why we should use τ instead of π, but in the end, they are based on the idea that the radius is the natural way to measure a circle. This comes from the idea that a circle is composed of an infinite number of infinitely small triangles, but while that is a valid representation, it is not actually true. A circle is composed of a continuous, regular curve, with no straight lines anywhere. Just as we would not try to define any other shape as the distance from the center to any point along its perimeter, radius is not the natural way to measure a circle. Outside of mathematics and science, where it has become tradition to use radius, measuring merely half the width of an object is not something that is often useful.
The answer is not to switch from π to τ. The answer is to use the natural measure of the size of a circle: diameter. Some "tauists" claim that the decision of ancient civilizations to use diameter instead of radius was arbitrary. If that is true though, then why did every civilization that set out to measure the ratio of the circumference of a circle to its size choose to use diameter instead of radius? The answer is not chance. The answer is that the choice was not arbitrary. Diameter is the natural way to measure a circle. To someone that has not been taught to measure a circle by radius, diameter is the obvious measure of size.
The fact is, replacing radius with diameter in circle equations simplifies them just as much as replacing π with τ, with the added benefit that new students will not be confused as to why we suddenly only care about half of the size of the circle. Besides that, how does the average person measure the radius of a circle? They measure the diameter and divide by two, because half a width is not a natural measurement to try to take!
In celebration of Pi Day, I bring you the following:
This is the real unit circle. You will notice that one full turn is not equal to 2π. This is because we are measuring in diameters instead of radians. There is no need to redefine the circle constant when using diameter, because diameter is what it was made from! Unfortunately, "diameterians" does not sound as good as "radians," so I propose just calling them "diameters." That works just fine, since the circumference of a circle is, by definition, π diameters. Besides that, I think "diameters" would be far less confusing to new students, as it does not sound like some kind of new unit like "radians" does. (Be honest, how many of you struggled with radians, because it was not initially clear that radians are literally just the distance around the circle measured in radii? Now, think about π diameters. Without the fancy sounding name, it is much more clear what it means.)
Now, with my nice new diameter based unit circle in mind, here are some basic circle and sphere equations using diameter instead of radius:
Circumference: πd
Area: 1⁄4πd2
Surface Area: πd2
Volume: 1⁄6πd3
I considered adding some trig to this, but there is so much, and most of it is already so complex, that it would have taken a lot of algebra to reduce things down. In short, I gave up. This is a good taste though.
Here are some things I notice with the above. First, in the circle equations, you can replace π with diameters (see the unit circle above) to find the values for partial circles. For example, π⁄2d will give you the circumference of half a circle (π⁄2 diameters is halfway around the circle). You can do something similar using τ with radius, but I just wanted to point out τ does not have an advantage here. Now take a look at the circle circumference equation and the sphere surface area equation. Notice the logical step from the first to the second? Merely squaring the diameter promotes the equation to the analogous equation of the equivalent shape one dimension higher.Area to volume is not so pretty, but sphere volume is simpler than its radius based version, and the additional factor of 4 on the circle area equation adds trivial complexity. (I made an algebra mistake in circle area. It is fixed now.) I also notice a similar progression with circle area to sphere volume, where the multiplier is 1/(2 * dimensions), and like circumference to surface area, the exponent is the number of dimensions of what we are measuring. The sphere volume is simpler with diameter, and the circle area is only trivially more complex. In fact, the only places that complexity is increased noticeably are the two standard form equations that are typically used as the definitions for circles and spheres, and outside of education, more general forms are typically used for these, which are so much more complex that the extra factor of 4 would not make any difference.
The big advantage τ has is that replacing a bunch of "2π"s in textbooks is much easier than doing the algebra required to simplify the equations when you swap r for d⁄2. If you aren't going to do it right though, what is the point of doing it at all? It is true that teaching τ with radius will be easier than what we are doing now, but many students will still start off confused that we are measuring only half of the circle (and isn't one of the big "tauist" arguments that it is absurd that 1 π only gets us halfway around the traditional unit circle?). Sticking with π, but using diameters instead of radians, means that we don't have to overthrow a constant that has been ingrained in mathematics over the course of many millenia. We don't have to deal with teaching two constants just so students will be able to understand even recently written papers, not to mention all of the classical mathematics treatises. It is a lot easier to teach students that r = d/2 than it is to get them to memorize two circle constants out to n digits just so they can work with math from different eras. We also don't have to try to explain to students why we only care about half the width of a circle. The only advantage τ has is convenience in fixing textbooks. Using π with diameters just makes sense, even to those without a heavy mathematical background.
I hope you like my Pi Day celebration! Give a few minutes to celebrate diameter today as well.
There are a lot of different arguments for why we should use τ instead of π, but in the end, they are based on the idea that the radius is the natural way to measure a circle. This comes from the idea that a circle is composed of an infinite number of infinitely small triangles, but while that is a valid representation, it is not actually true. A circle is composed of a continuous, regular curve, with no straight lines anywhere. Just as we would not try to define any other shape as the distance from the center to any point along its perimeter, radius is not the natural way to measure a circle. Outside of mathematics and science, where it has become tradition to use radius, measuring merely half the width of an object is not something that is often useful.
The answer is not to switch from π to τ. The answer is to use the natural measure of the size of a circle: diameter. Some "tauists" claim that the decision of ancient civilizations to use diameter instead of radius was arbitrary. If that is true though, then why did every civilization that set out to measure the ratio of the circumference of a circle to its size choose to use diameter instead of radius? The answer is not chance. The answer is that the choice was not arbitrary. Diameter is the natural way to measure a circle. To someone that has not been taught to measure a circle by radius, diameter is the obvious measure of size.
The fact is, replacing radius with diameter in circle equations simplifies them just as much as replacing π with τ, with the added benefit that new students will not be confused as to why we suddenly only care about half of the size of the circle. Besides that, how does the average person measure the radius of a circle? They measure the diameter and divide by two, because half a width is not a natural measurement to try to take!
In celebration of Pi Day, I bring you the following:
This is the real unit circle. You will notice that one full turn is not equal to 2π. This is because we are measuring in diameters instead of radians. There is no need to redefine the circle constant when using diameter, because diameter is what it was made from! Unfortunately, "diameterians" does not sound as good as "radians," so I propose just calling them "diameters." That works just fine, since the circumference of a circle is, by definition, π diameters. Besides that, I think "diameters" would be far less confusing to new students, as it does not sound like some kind of new unit like "radians" does. (Be honest, how many of you struggled with radians, because it was not initially clear that radians are literally just the distance around the circle measured in radii? Now, think about π diameters. Without the fancy sounding name, it is much more clear what it means.)
Now, with my nice new diameter based unit circle in mind, here are some basic circle and sphere equations using diameter instead of radius:
Circle
Definition: d2 = 4(x2 + y2)Circumference: πd
Area: 1⁄4πd2
Sphere
Definition: d2 = 4(x2 + y2 + z2)Surface Area: πd2
Volume: 1⁄6πd3
I considered adding some trig to this, but there is so much, and most of it is already so complex, that it would have taken a lot of algebra to reduce things down. In short, I gave up. This is a good taste though.
Here are some things I notice with the above. First, in the circle equations, you can replace π with diameters (see the unit circle above) to find the values for partial circles. For example, π⁄2d will give you the circumference of half a circle (π⁄2 diameters is halfway around the circle). You can do something similar using τ with radius, but I just wanted to point out τ does not have an advantage here. Now take a look at the circle circumference equation and the sphere surface area equation. Notice the logical step from the first to the second? Merely squaring the diameter promotes the equation to the analogous equation of the equivalent shape one dimension higher.
The big advantage τ has is that replacing a bunch of "2π"s in textbooks is much easier than doing the algebra required to simplify the equations when you swap r for d⁄2. If you aren't going to do it right though, what is the point of doing it at all? It is true that teaching τ with radius will be easier than what we are doing now, but many students will still start off confused that we are measuring only half of the circle (and isn't one of the big "tauist" arguments that it is absurd that 1 π only gets us halfway around the traditional unit circle?). Sticking with π, but using diameters instead of radians, means that we don't have to overthrow a constant that has been ingrained in mathematics over the course of many millenia. We don't have to deal with teaching two constants just so students will be able to understand even recently written papers, not to mention all of the classical mathematics treatises. It is a lot easier to teach students that r = d/2 than it is to get them to memorize two circle constants out to n digits just so they can work with math from different eras. We also don't have to try to explain to students why we only care about half the width of a circle. The only advantage τ has is convenience in fixing textbooks. Using π with diameters just makes sense, even to those without a heavy mathematical background.
I hope you like my Pi Day celebration! Give a few minutes to celebrate diameter today as well.
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