Comment Re:If Programming Languages Were Religions? (Score 1) 844
Excuse me? That's the one blue C.
Submission + - Datacenter robbed for the 4th time in 2 years (theregister.co.uk) 1
mariushm writes: "The CIHost datacenter was attacked by armed intruders for the fourth times in two years.
According to a letter C I Host officials sent customers, "at least two masked intruders entered the suite after cutting into the reinforced walls with a power saw, [...]
During the robbery, C I Host's night manager was repeatedly tazered and struck with a blunt instrument. After violently attacking the manager, the intruders stole equipment belonging to C I Host and its customers."
To aggravate the situation, C I Host representatives needed several days to admit the most recent breach, according to several customers who said they lost equipment, all the while reporting the problems as "router failures"."
According to a letter C I Host officials sent customers, "at least two masked intruders entered the suite after cutting into the reinforced walls with a power saw, [...]
During the robbery, C I Host's night manager was repeatedly tazered and struck with a blunt instrument. After violently attacking the manager, the intruders stole equipment belonging to C I Host and its customers."
To aggravate the situation, C I Host representatives needed several days to admit the most recent breach, according to several customers who said they lost equipment, all the while reporting the problems as "router failures"."
Submission + - Each dot on my die is loaded by Pi
Escaped Inmate writes: "Preface: Several years ago I participated on a board involving a game where you roll dice. A discussion on loaded dice came up. I prepared a response, but never posted it. I recently came across it in my data files, and thought it might find an audience on Slashdot. Here it is. There are no sources or links because I wrote the whole thing. It is original material. Science seems to be the right Section, but the topic is somewhat wide. I have submitted it to no one else as of this date. If you like it, feel free to post/host it. If not, that's OK too. I understand it might not be what you're looking for, but I did want to give you first shot. If you decide not to post/host, I would appreciate an email note of decline so I can post it elsewhere. Cheers — Escaped Inmate.
**** Begin ****
Several months ago a debate on loaded dice raged on these boards. I've been playing with dice for several decades now, but I've never really looked into the fairness or homogeneity of dice. The debate stirred something in me to try and take a closer look. So this is my story.
Before I begin my discussion, it is important for the reader to know something about me. I'm an engineer. Engineers....REAL engineers are weird. Of course, if you know any, you already know that. We're weird because things that are idiotically stupid to the mainstream population can sometimes capture our attention for days on end. We first ask "why", and then it's all downhill from there. So, when all this dice stuff came up a few months ago, I started asking "why". And it's been downhill ever since.
The first question was how to tell if dice were loaded, or biased. So I devised an experiment whereby I could push dice slowly over the side of a table. And depending on the point where they dropped, I could determine if the weight wasn't quite right. In order to facilitate the push I needed something with a straight edge. I looked for the closest item at hand, and found a Christmas card (Remember, this all happened in December, so Christmas cards were readily available at the time). Wow! I actually found a USE for a Christmas Card. That's another dirty little secret about engineers. Everything must have a "practical" use, or we don't really understand why it exists. And in the world of hard science, social affiliation can sometimes confuse us because the line between cause and useful effect is difficult to grasp in the social world. Christmas cards fall into the social category, which can be confusing to engineers. Confusing, that is, until we find a "practical" use. So, there I was, a 39 year old man, with a new appreciation for Christmas cards, slowly pushing a little dice over the edge of the table, at 8:00 O'clock at night. About that time, my eleven-year-old daughter enters the room to see Dad hunched over table, sliding a Christmas card across the table, with die in front, and....then....off the table. My daughter pauses slightly, and then mutters, "Dad, you're weird". In social circles, that might be considered a disparaging remark. But to an engineer, it is a compliment. Encouraged by the vote of confidence, I continued my experiment. Unfortunately, or should I say fortunately, after doing this for several minutes I could find no bias. Well, at least no bias measurable by the experiment's resolution, which includes my 20/40 vision.
I dropped the test, and went on to do other things. Hit the message boards, got something to eat, watched some TV. It was getting late. I had work the next day. But I couldn't shake the dice out of my head. I must devise another experiment.
By the time I came back to the problem it was past midnight. You see, that's the other dirty little secret about engineers, and other technical types, to include computer geeks, particularly system administrators. We stay up late...tinkering. Sometimes we stay up verrrry late. In fact, sometimes we forget to sleep at all. Our best achievements happen at night, or in the wee hours of the morning. I'm talking TECHNICAL achievement here, not SOCIAL achievements. Of course, if you stay up late, you tend to wake up late. The technical capability of a techno geek is directly proportional to the time they show up for work in the morning. The best show up around 10 AM or later. Those that show up earlier tend to be less effective, either because they don't stay up late (and aren't real geeks) or because they did stay up and didn't get their requisite hours of sleep. And that's the unfortunate dichotomy of the high tech business world. In the social business world you gotta be in the office early, say around 6 AM or so. That's why the government has such a hard time winning the hacker war. They want folks at work at 6 AM in the morn, just about the time the best hackers are hitting the sack.
Ooops, I got carried away there for a moment. Let's get back to our discussion of dice. I decided on a tried and true experiment; rolling the dice over and over again. To speed things up I decided to roll ten at a time, and just keep track of hits and misses (note: in this experiment a 1, 2, or 3 is miss and a 4, 5, 6 is a hit). Since it was past midnight, I didn't wish to wake the family (they are not yet engineers, so of course, they would be in bed at 12 midnight), so I had to devise a quieter method of performing the experiment. Instead of rolling the dice on the table, where the dice would be loud and bouncy, I decided to roll them on a paper pad, on which they would thud quietly. Of course, being an engineer, the first dilemma that I must address is whether the pad will somehow affect the randomness of the roll. After all, there's nothing like dice bouncing crazily on a hard table to give you that good feeling of randomness. I figured if I shook the dice in my hand longer I would sufficiently randomize the dice so as not to need the extra randomness afforded by the "table bounce". Or, in the words of the engineer, I concluded that randomness would not suffer in the absence of "gravity induced kinetic elastic impulses". So the experiment began.
Around about the third roll, one of the dice escaped from the pad and landed on the table. The normal person would just add in the dice and not give it a second thought. But I'm an engineer, and these things must be analyzed. The pad, you see, defines a boundary. An experimental boundary, as well as a physical boundary. Never mind that the pad is being used as a sound buffer, it still has boundaries. And, oh my, one of my dice has escaped the boundary and come to rest an inch outside the boundary. This seemingly innocent event can be very traumatic for engineers, particularly if it was not anticipated. In the old days it was often the root cause of bridges collapsing. Nowadays, it is why most software crashes occur. Every time you get the "stack dump" message it's because the program encountered a boundary event unforeseen by the programmer. Engineers spend most of their careers operating on boundary conditions. This is true not only for technical things, but it is also true for social things. That is where all interesting things (mostly failures) happen, technical failures as well as social failures. We're always on the edge, figuratively as well as literally, and we have an uncanny knack for candor. Candor, that while a virtue in the technical world tends to be a vice in the social world, which is why it is so difficult for many of us to land a date. You know the proverbial questions: "Does my hair look good....", or "Do I look fat...". Engineers see such questions as a boundary condition. We know there is danger in the question, we are just too dense to figure out the danger is social, not technical. While it "is" a boundary condition question, woe is the engineer who attempts an answer involving the full splendor of a candid boundary condition. In fact, woe is the engineer who even hesitates in contemplation of a boundary condition. (Hint: Don't analyze. Don't think. Don't hesitate. The answer is yes and no respectively). If I ever write a book on engineering, the first chapter will be titled "When not to Engineer". Well, back to the "technical" issues at hand. We were talking "boundary conditions". For our dice experiment "exceeding the boundary" is fancy nomenclature for "missed the pad". What to do? Roll it again? Count it? My ability to come to an unbiased answer has been polluted by my knowledge of the roll. I can "think" I'm being fair, but how do I know my decision is not influenced by some subconscious desire to get a hit (or a miss)?
If you ever wonder why high tech costs so much, this is the reason. Engineers go through these kinds of dilemmas all the time, on a daily basis. It happens when designing cars, airplanes, computers, and toys. We spend so much frikin time thinking through all the problems, it just never gets done. On the other hand, thinking this way around boundary conditions isn't always a bad thing. Did you know that most of the really nasty computer viruses, those designed to take over the "root" of a machine, have their genesis in a boundary condition? It's called a "buffer overflow". That's a fancy name for exceeding the boundary condition in the memory blocks or registers of a computer. If the good guy doesn't do a good job confining the boundary, then the bad guy will find a way to break through, to the ultimate demise of computer users the world over. There are literally hundreds (perhaps thousands) of computer geeks pouring over software and operating systems as you read this, forever examining ways to break and protect the dreaded buffer overflow boundary conditions.
Another failing of engineers is they get side tracked awful easy sometimes, sort of like Homer Simpson. For example, dice have dimples. If you said dimples, then no problem. But when you combine dimples with statistics you trigger memories of the dimples (and chads) from the 2000 presidential election, where dimples (and chads) were forever married to statistics. That election created a near orgasmic statistical playground for engineers and analyst. And it just didn't stop in December with the Court decision. You see, engineers, while often highly opinionated (as am I), just can't let it go sometimes. And I'm not talking about the vote. I'm talking about the statistic (again, think of Homer, blank stare into nowhere). Here we are, several years later, and I guarantee you some anal retentive analyst or engineer is still crunching the statistics, or talking about the same. In fact, the engineer is most likely talking about this stuff to some group of people who couldn't care less, in some newsgroup that has nothing to do with elections or politic, as a tangential discussion that doesn't even have anything to do with the topic of the post in the first place. One of my greatest statistical quotes was born during that event in November 2000. I must share it with everyone here. It goes: "Correcting the error in a biased subsample will skew the whole sample toward the subsample bias". An extremely clever statistical trick used to "adjust" the mean value of a statistical sample in the direction of the majority constituency in a subsample. Does anyone believe any Judge on the face of the planet can figure that out? Ah, engineering and politics. Like oil and water. What can I say? Amazing how much trouble you can get into when playing with statistics. Now, back to the dice.
If my dice experiment were being conducted under contract, and if the dice missed the pad, the trials would be stopped, and a study commissioned to determine if the die should be counted, re-rolled, or perhaps all the dice should be re-rolled. A year later, less $100K (usually taxpayers dollars), we would arrive at an answer. Half the time the answer won't answer the question. For example, the answer might be that you should roll heavier dice, or roll dice of a certain color. Or....I like this next one.....get a bigger pad and avoid the problem altogether. But nothing on whether to count the die, or re-roll it. The other half of the time you will get a conclusion that calls for more studies. And on those rare occasions where you actually get a real answer that will allow you to proceed, you get slapped with the requirement to perform the dreaded environmental impact study. You see, the pad mutes the dice. The missed die has landed on the table, and failed to get the benefit of the mute, creating...oh my gosh....sound pollution. Sound pollution that interrupted the courtship ritual of the Spotted Owl, living in the tree outside the window. A courtship ritual that, if consummated, would have saved the species. But those extra die decibels may have disrupted the process, to the ultimate demise of the Owl.
OK, sorry...got carried away again. Back to the dice. I finally finished the experiment. I rolled 40 times with 10 dice each, giving 400 total. After all those trials, I got a 48% hit rate, which seems within the statistical bounds of the experiment. Ooops, I bet you're wondering what I did about the die that rolled off the pad? I honestly don't remember as I write this down. And why should I? I've rounded my answer to the nearest percentage, so it's lost in the first decimal place anyway. That's another engineering ploy. If you can't get the proper resolution, express the answer with significant digits that fall outside the error bounds. Neat huh? This is the real reason logarithms were invented, but I'll skip that story for now. Interestingly, many neophyte engineers, or sly experienced engineers, or most computer programmers, do just the opposite. They give results out to the precision of the measuring instrument, which on a 32 bit computer can give you some whopping precise answers that mean nothing beyond a few decimal places.
So there I sat, at 1 O'clock in the morning, bathed in the light of my florescent light, a slight buzz (the light, not my head) drowning out the other ambient noises in the wee hours of the morning. By the way, the only ambient noise that can overcome my florescent buzz was the "whooo whooo" of the Spotted Owl, but our wayward die already did him in. So, there we were, at 1 O'clock in the morning. As I noted previously, this is the time where engineers discover the big mysteries of the universe. As I relished in my achievements, I suddenly felt a pang of discomfort. Something about the dice was not right. I picked up my dice and examined them more closely. Oh my. Oh my, oh my, oh my. This cannot be! I looked at them all. All 90 of them! The reds ones. The blue ones. The green ones. "Houston, we have a problem". It appeared, to my astonishment, that ALL of them were biased. Yes, biased! Loaded! Not symmetrical. In fact, looking back over most of the dice I've played with all my life I concluded that many of those dice were also biased.
It's the DIMPLES. The dimples I tell you! How can this be? Well, first off, we must assume that the material that makes up the dice is homogeneous. That would be the manufacturing objective, I believe. For the sake of argument, let's say the manufacturer achieves perfect homogeneity. Now, if we cut the perfectly homogeneous material into a square (i.e., make a die square), we can show that the center of mass of the square is located exactly in the middle of the die. This is what we wish to achieve in order to prevent the die from exhibiting bias. Now comes the problem. In order to produce the dots on the dice, the manufacturer carves out some material to form each dot. Check it out. Look at your dice. You'll see it. They have DIMPLES. Some of the material is removed from the dice. Well, we carve more out on the sixes side (i.e., we carve out six dots) than we do on the ones side (where we carve out only one dot). We know that if we remove more material on one side than the other, then the center of mass will move toward the other side. In our case, the center of mass will favor the ones over the sixes. If the center of mass favors the ones, that makes the ones more likely to land on the bottom. If the one is on bottom, then the six is on top. The dice are loaded to favor a six over a one. Oh my!
But how much can this affect the roll of the dice? How much does it change the center of mass of the die? Questions, questions, and more questions. The deeper you dig, the worse it can get. I decided to run the "center of mass" numbers. My dice are about 10 mm per side. I estimate the dots to run about 1mm deep with radius of 1 mm. (Note how my careful estimates have given me some nice easy numbers to work with. Ah, the beauty of estimation). The volume of the die is simply the cube of the sides, which comes out to a nice 1000 cubic millimeters. As for the dots, if we assume cylinder volume, along with the estimated values for our dimensions, we discover that EXACTLY pi cubic millimeters of stuff is hacked out for each dot. Wow! "Each dot on my die is loaded by pi". At first we could attribute this to some transcendental cosmic force. The answer is EXACTLY pi. Now what are the chances of that occurring? That's another engineer's trick. If you set the radius and height of a cylinder to "one" unit (in our case we're talking millimeters) the volume is ALWAYS pi. No cosmic force at work here; it's simply charlatan math. As for pi, another engineer's trick is to just round it to 3. It works quite well for stuff like this. Let's just round it and call it 3 cubic millimeters per dot. Thus, the side with the one dot has 3 cubic millimeters hacked out and the side with the sixes has 18 (6 X 3) cubic millimeters hacked out. I won't bore everyone with the calculations, but if I worked the center of mass number out correctly, I conclude the center of mass on each die is biased 75 microns toward the "one". What does this mean? Well, if we could pull out one of my hairs (which is about 100 microns wide, and getting somewhat gray), and center my die perfectly on the hair, the center of mass will actually extend beyond the width of the hair. That is, the hair at 100 microns centered will extend 50 microns each side of center, whereas the bias is 75 microns offset from center. Thus, if the force of gravity causes the die to rotate about its center of mass, the dice will fall toward the "ones" side, which would theoretically put the six side on top.
There you have it folks. We're all playing with loaded dice. We're all guilty. Admit it, and let's get on with life.
-Escaped Inmate (Circa 2002)"
**** Begin ****
Several months ago a debate on loaded dice raged on these boards. I've been playing with dice for several decades now, but I've never really looked into the fairness or homogeneity of dice. The debate stirred something in me to try and take a closer look. So this is my story.
Before I begin my discussion, it is important for the reader to know something about me. I'm an engineer. Engineers....REAL engineers are weird. Of course, if you know any, you already know that. We're weird because things that are idiotically stupid to the mainstream population can sometimes capture our attention for days on end. We first ask "why", and then it's all downhill from there. So, when all this dice stuff came up a few months ago, I started asking "why". And it's been downhill ever since.
The first question was how to tell if dice were loaded, or biased. So I devised an experiment whereby I could push dice slowly over the side of a table. And depending on the point where they dropped, I could determine if the weight wasn't quite right. In order to facilitate the push I needed something with a straight edge. I looked for the closest item at hand, and found a Christmas card (Remember, this all happened in December, so Christmas cards were readily available at the time). Wow! I actually found a USE for a Christmas Card. That's another dirty little secret about engineers. Everything must have a "practical" use, or we don't really understand why it exists. And in the world of hard science, social affiliation can sometimes confuse us because the line between cause and useful effect is difficult to grasp in the social world. Christmas cards fall into the social category, which can be confusing to engineers. Confusing, that is, until we find a "practical" use. So, there I was, a 39 year old man, with a new appreciation for Christmas cards, slowly pushing a little dice over the edge of the table, at 8:00 O'clock at night. About that time, my eleven-year-old daughter enters the room to see Dad hunched over table, sliding a Christmas card across the table, with die in front, and....then....off the table. My daughter pauses slightly, and then mutters, "Dad, you're weird". In social circles, that might be considered a disparaging remark. But to an engineer, it is a compliment. Encouraged by the vote of confidence, I continued my experiment. Unfortunately, or should I say fortunately, after doing this for several minutes I could find no bias. Well, at least no bias measurable by the experiment's resolution, which includes my 20/40 vision.
I dropped the test, and went on to do other things. Hit the message boards, got something to eat, watched some TV. It was getting late. I had work the next day. But I couldn't shake the dice out of my head. I must devise another experiment.
By the time I came back to the problem it was past midnight. You see, that's the other dirty little secret about engineers, and other technical types, to include computer geeks, particularly system administrators. We stay up late...tinkering. Sometimes we stay up verrrry late. In fact, sometimes we forget to sleep at all. Our best achievements happen at night, or in the wee hours of the morning. I'm talking TECHNICAL achievement here, not SOCIAL achievements. Of course, if you stay up late, you tend to wake up late. The technical capability of a techno geek is directly proportional to the time they show up for work in the morning. The best show up around 10 AM or later. Those that show up earlier tend to be less effective, either because they don't stay up late (and aren't real geeks) or because they did stay up and didn't get their requisite hours of sleep. And that's the unfortunate dichotomy of the high tech business world. In the social business world you gotta be in the office early, say around 6 AM or so. That's why the government has such a hard time winning the hacker war. They want folks at work at 6 AM in the morn, just about the time the best hackers are hitting the sack.
Ooops, I got carried away there for a moment. Let's get back to our discussion of dice. I decided on a tried and true experiment; rolling the dice over and over again. To speed things up I decided to roll ten at a time, and just keep track of hits and misses (note: in this experiment a 1, 2, or 3 is miss and a 4, 5, 6 is a hit). Since it was past midnight, I didn't wish to wake the family (they are not yet engineers, so of course, they would be in bed at 12 midnight), so I had to devise a quieter method of performing the experiment. Instead of rolling the dice on the table, where the dice would be loud and bouncy, I decided to roll them on a paper pad, on which they would thud quietly. Of course, being an engineer, the first dilemma that I must address is whether the pad will somehow affect the randomness of the roll. After all, there's nothing like dice bouncing crazily on a hard table to give you that good feeling of randomness. I figured if I shook the dice in my hand longer I would sufficiently randomize the dice so as not to need the extra randomness afforded by the "table bounce". Or, in the words of the engineer, I concluded that randomness would not suffer in the absence of "gravity induced kinetic elastic impulses". So the experiment began.
Around about the third roll, one of the dice escaped from the pad and landed on the table. The normal person would just add in the dice and not give it a second thought. But I'm an engineer, and these things must be analyzed. The pad, you see, defines a boundary. An experimental boundary, as well as a physical boundary. Never mind that the pad is being used as a sound buffer, it still has boundaries. And, oh my, one of my dice has escaped the boundary and come to rest an inch outside the boundary. This seemingly innocent event can be very traumatic for engineers, particularly if it was not anticipated. In the old days it was often the root cause of bridges collapsing. Nowadays, it is why most software crashes occur. Every time you get the "stack dump" message it's because the program encountered a boundary event unforeseen by the programmer. Engineers spend most of their careers operating on boundary conditions. This is true not only for technical things, but it is also true for social things. That is where all interesting things (mostly failures) happen, technical failures as well as social failures. We're always on the edge, figuratively as well as literally, and we have an uncanny knack for candor. Candor, that while a virtue in the technical world tends to be a vice in the social world, which is why it is so difficult for many of us to land a date. You know the proverbial questions: "Does my hair look good....", or "Do I look fat...". Engineers see such questions as a boundary condition. We know there is danger in the question, we are just too dense to figure out the danger is social, not technical. While it "is" a boundary condition question, woe is the engineer who attempts an answer involving the full splendor of a candid boundary condition. In fact, woe is the engineer who even hesitates in contemplation of a boundary condition. (Hint: Don't analyze. Don't think. Don't hesitate. The answer is yes and no respectively). If I ever write a book on engineering, the first chapter will be titled "When not to Engineer". Well, back to the "technical" issues at hand. We were talking "boundary conditions". For our dice experiment "exceeding the boundary" is fancy nomenclature for "missed the pad". What to do? Roll it again? Count it? My ability to come to an unbiased answer has been polluted by my knowledge of the roll. I can "think" I'm being fair, but how do I know my decision is not influenced by some subconscious desire to get a hit (or a miss)?
If you ever wonder why high tech costs so much, this is the reason. Engineers go through these kinds of dilemmas all the time, on a daily basis. It happens when designing cars, airplanes, computers, and toys. We spend so much frikin time thinking through all the problems, it just never gets done. On the other hand, thinking this way around boundary conditions isn't always a bad thing. Did you know that most of the really nasty computer viruses, those designed to take over the "root" of a machine, have their genesis in a boundary condition? It's called a "buffer overflow". That's a fancy name for exceeding the boundary condition in the memory blocks or registers of a computer. If the good guy doesn't do a good job confining the boundary, then the bad guy will find a way to break through, to the ultimate demise of computer users the world over. There are literally hundreds (perhaps thousands) of computer geeks pouring over software and operating systems as you read this, forever examining ways to break and protect the dreaded buffer overflow boundary conditions.
Another failing of engineers is they get side tracked awful easy sometimes, sort of like Homer Simpson. For example, dice have dimples. If you said dimples, then no problem. But when you combine dimples with statistics you trigger memories of the dimples (and chads) from the 2000 presidential election, where dimples (and chads) were forever married to statistics. That election created a near orgasmic statistical playground for engineers and analyst. And it just didn't stop in December with the Court decision. You see, engineers, while often highly opinionated (as am I), just can't let it go sometimes. And I'm not talking about the vote. I'm talking about the statistic (again, think of Homer, blank stare into nowhere). Here we are, several years later, and I guarantee you some anal retentive analyst or engineer is still crunching the statistics, or talking about the same. In fact, the engineer is most likely talking about this stuff to some group of people who couldn't care less, in some newsgroup that has nothing to do with elections or politic, as a tangential discussion that doesn't even have anything to do with the topic of the post in the first place. One of my greatest statistical quotes was born during that event in November 2000. I must share it with everyone here. It goes: "Correcting the error in a biased subsample will skew the whole sample toward the subsample bias". An extremely clever statistical trick used to "adjust" the mean value of a statistical sample in the direction of the majority constituency in a subsample. Does anyone believe any Judge on the face of the planet can figure that out? Ah, engineering and politics. Like oil and water. What can I say? Amazing how much trouble you can get into when playing with statistics. Now, back to the dice.
If my dice experiment were being conducted under contract, and if the dice missed the pad, the trials would be stopped, and a study commissioned to determine if the die should be counted, re-rolled, or perhaps all the dice should be re-rolled. A year later, less $100K (usually taxpayers dollars), we would arrive at an answer. Half the time the answer won't answer the question. For example, the answer might be that you should roll heavier dice, or roll dice of a certain color. Or....I like this next one.....get a bigger pad and avoid the problem altogether. But nothing on whether to count the die, or re-roll it. The other half of the time you will get a conclusion that calls for more studies. And on those rare occasions where you actually get a real answer that will allow you to proceed, you get slapped with the requirement to perform the dreaded environmental impact study. You see, the pad mutes the dice. The missed die has landed on the table, and failed to get the benefit of the mute, creating...oh my gosh....sound pollution. Sound pollution that interrupted the courtship ritual of the Spotted Owl, living in the tree outside the window. A courtship ritual that, if consummated, would have saved the species. But those extra die decibels may have disrupted the process, to the ultimate demise of the Owl.
OK, sorry...got carried away again. Back to the dice. I finally finished the experiment. I rolled 40 times with 10 dice each, giving 400 total. After all those trials, I got a 48% hit rate, which seems within the statistical bounds of the experiment. Ooops, I bet you're wondering what I did about the die that rolled off the pad? I honestly don't remember as I write this down. And why should I? I've rounded my answer to the nearest percentage, so it's lost in the first decimal place anyway. That's another engineering ploy. If you can't get the proper resolution, express the answer with significant digits that fall outside the error bounds. Neat huh? This is the real reason logarithms were invented, but I'll skip that story for now. Interestingly, many neophyte engineers, or sly experienced engineers, or most computer programmers, do just the opposite. They give results out to the precision of the measuring instrument, which on a 32 bit computer can give you some whopping precise answers that mean nothing beyond a few decimal places.
So there I sat, at 1 O'clock in the morning, bathed in the light of my florescent light, a slight buzz (the light, not my head) drowning out the other ambient noises in the wee hours of the morning. By the way, the only ambient noise that can overcome my florescent buzz was the "whooo whooo" of the Spotted Owl, but our wayward die already did him in. So, there we were, at 1 O'clock in the morning. As I noted previously, this is the time where engineers discover the big mysteries of the universe. As I relished in my achievements, I suddenly felt a pang of discomfort. Something about the dice was not right. I picked up my dice and examined them more closely. Oh my. Oh my, oh my, oh my. This cannot be! I looked at them all. All 90 of them! The reds ones. The blue ones. The green ones. "Houston, we have a problem". It appeared, to my astonishment, that ALL of them were biased. Yes, biased! Loaded! Not symmetrical. In fact, looking back over most of the dice I've played with all my life I concluded that many of those dice were also biased.
It's the DIMPLES. The dimples I tell you! How can this be? Well, first off, we must assume that the material that makes up the dice is homogeneous. That would be the manufacturing objective, I believe. For the sake of argument, let's say the manufacturer achieves perfect homogeneity. Now, if we cut the perfectly homogeneous material into a square (i.e., make a die square), we can show that the center of mass of the square is located exactly in the middle of the die. This is what we wish to achieve in order to prevent the die from exhibiting bias. Now comes the problem. In order to produce the dots on the dice, the manufacturer carves out some material to form each dot. Check it out. Look at your dice. You'll see it. They have DIMPLES. Some of the material is removed from the dice. Well, we carve more out on the sixes side (i.e., we carve out six dots) than we do on the ones side (where we carve out only one dot). We know that if we remove more material on one side than the other, then the center of mass will move toward the other side. In our case, the center of mass will favor the ones over the sixes. If the center of mass favors the ones, that makes the ones more likely to land on the bottom. If the one is on bottom, then the six is on top. The dice are loaded to favor a six over a one. Oh my!
But how much can this affect the roll of the dice? How much does it change the center of mass of the die? Questions, questions, and more questions. The deeper you dig, the worse it can get. I decided to run the "center of mass" numbers. My dice are about 10 mm per side. I estimate the dots to run about 1mm deep with radius of 1 mm. (Note how my careful estimates have given me some nice easy numbers to work with. Ah, the beauty of estimation). The volume of the die is simply the cube of the sides, which comes out to a nice 1000 cubic millimeters. As for the dots, if we assume cylinder volume, along with the estimated values for our dimensions, we discover that EXACTLY pi cubic millimeters of stuff is hacked out for each dot. Wow! "Each dot on my die is loaded by pi". At first we could attribute this to some transcendental cosmic force. The answer is EXACTLY pi. Now what are the chances of that occurring? That's another engineer's trick. If you set the radius and height of a cylinder to "one" unit (in our case we're talking millimeters) the volume is ALWAYS pi. No cosmic force at work here; it's simply charlatan math. As for pi, another engineer's trick is to just round it to 3. It works quite well for stuff like this. Let's just round it and call it 3 cubic millimeters per dot. Thus, the side with the one dot has 3 cubic millimeters hacked out and the side with the sixes has 18 (6 X 3) cubic millimeters hacked out. I won't bore everyone with the calculations, but if I worked the center of mass number out correctly, I conclude the center of mass on each die is biased 75 microns toward the "one". What does this mean? Well, if we could pull out one of my hairs (which is about 100 microns wide, and getting somewhat gray), and center my die perfectly on the hair, the center of mass will actually extend beyond the width of the hair. That is, the hair at 100 microns centered will extend 50 microns each side of center, whereas the bias is 75 microns offset from center. Thus, if the force of gravity causes the die to rotate about its center of mass, the dice will fall toward the "ones" side, which would theoretically put the six side on top.
There you have it folks. We're all playing with loaded dice. We're all guilty. Admit it, and let's get on with life.
-Escaped Inmate (Circa 2002)"
Submission + - Departing AT&T chief vows to end net neutralit
calstraycat writes: In a farewell address to executives, AT&T chief Ed Whitacre called
for the end of net neutrality. 'There’s a
problem. It’s called Net Neutrality,' Whitacre told the heirs
to AT&T’s telecommunications empire. 'Well, frankly,
we say to hell with that. We’re gonna put up some toll booths
and start charging admission.' If that were not scary enough, his
confidence that congress will bow to his wishes is downright
frightening: 'Will Congress let us do it?' Whitacre asks his
colleagues. 'You bet they will — cuz we don’t call
it cashin’ in. We call it 'deregulation'.'
Submission + - Firefox Surfers More Likely Patched Than IE Users
An anonymous reader writes: Secunia gives us some interesting statistics from some 4.9 million Windows applications scanned with its "software inspector" service, which looks at common apps for missing security updates. "Comparing browsers and looking at Firefox, Opera and Internet Explorer, we found out that Firefox 2 is the least vulnerable, as only 5.19% of all Firefox 2 installations miss security updates, whereas 11.96% of all Opera 9.x installations miss security updates, and the numbers for IE6 and IE7 are 9.61% and 5.4% respectively." The Washington Post's Security Fix blog says the stats suggest two conclusions: "One, that the auto-patching component built into Firefox 2.0 is somewhat more effective than Microsoft's approach, which gives users the option to decline updates. With Firefox 2.0, new updates are automatically installed....Secondly, it appears that while Opera fans are seemingly always quick to claim that theirs is the most secure and least-attacked of the major browsers, its user base may be a bit more complacent about applying security updates."
Submission + - Ohio '04 elections suffer MITM attack
glassesmonkey writes: "The Free Press is reporting how the IT company that provides Rove's emails and RNC websites, also hosted Ohio's 2004 election results. The country results were sent to Ohio's Secretary of State, Ken Blackwell, and those results were hosted on a SMARTech webserver in TN. Blackwell had the IT guys switch the DNS on election night in order to accomplish a man-in-the-middle exploit on election results."
Submission + - The Math of Text Readability
An anonymous reader writes: Wired magazine has an article that explains The Law of Optical Volumes, a formula for spacing the letters on a printed page that results in maximum readability. Wired's new logo (did anyone notice?) obeys the law. Unfortunately, Web fonts don't allow custom kerning pairs, so you can't work the same magic online as in print. Could this be why some people still prefer newspapers and magazines to the Web?
Spam-Bot Intrusion Caught — Now What? 76
An anonymous reader wonders: "I've recently detected and halted an intrusion on my home computer, taken some actions to prevent further intrusions, and located the software that was running a bot agent. Cursory examination showed that the bot software is intended for acting as an agent for spamming. Configuration files distinctly point at the user/host/domain of several bot-herders — damning evidence. Nothing would please me more than to see this botnet to be caught and disassembled, I'm sure much of the internet-using community would support this. Thanks in advance for your suggestions. So, to whom should I disclose this information for appropriate investigation, follow up, and countermeasures? "
Submission + - Vonage: screwed, Hardware: useless?
gregger writes: Well, it seems that Vonage's future is up in the air for real this time due to patent violations. If (or when) the end does come, those of us who have a Vonage box or two lying around might want to figure out something useful to do with them. It seems a shame to have these routers collecting dust with no further purpose. So, what will you do with your Vonage router?
