*sigh* You do not understand what I am saying. We are not in agreement and are saying opposite things. You wrote: "this kind of touching is not defined in physical world. where matter is concerned, as you said there is no touching at all, what we call matter is mostly empty space"
I say there is touching in both cases. Not only that, but this view of matter being "mostly empty space" is outdated by about 50 years; your so-called 'empty space' is full of virtual particles, which are the carriers of force between particles.
You also wrote: "i said 'two objects are touching if the contact area between them is > 0.' " . I wrote that this is mathematically incorrect, and gave 5 quotes references which disagreed with you. Not only that, but the the general population also disagrees with you, in that most people say that Utah and New Mexico "touch", even though they don't share a border.
"The answer does not have real scientific value." The things is, it does have value. Thought-experiements like this help identify and resolve ambiguous definitions. The underlying resolution to this sort of problem was figured out in the 1800s when limit theory was used to put a sound underpinning to calculus.
Lycantrophe: the problem is that you haven't defined what "touch" means. In physics, "touch" means the electron surfaces of two atoms/molecules is close enough that the repulsion forces dominate. (There's of course the question of when two neutrons "touch." I'm not going there.)
In geometry, "touch" means that there's an intersection. In this case, the plane touches the sphere at a point. For examples:
2) ".. and considers the point F at which the sphere touches the plane" (Encyclopédia of mathematics, By James Stuart Tanton; in Google Books)
3) "Let O (fig 146) be the center of a sphere; C the point in which the sphere touches the plane of projection ..." ( A treatise on crystallography By William Hallowes Miller; also at Google Books.)
5) (From 1840!) "... the line drawn from the centre to the point where the sphere touches the plane will be the shortest line which can be drawn from the centre of the sphere to the plane." (A treatise on geometry and its application in the arts By Dionysius Lardner; Google Books)
Quite obviously a number of people with math training disagree with your statement that "A perfect sphere and a perfect plane can never touch each other."
If you want to be more mathematical, and move from the ancient Greeks to the 1800s, the definition of "touch" corresponds to the idea of a limit. It's adversarial in nature. You pick a finite distance 'd'. Two objects touch if there are parts of the objects which are closer together than 'd', I just have to find examples. You are free to specify any finite value of 'd' you want, all I have to do is beat it. This definition neatly avoids the complex issues of infinities that you're having troubles with.
With that definition it's trivial to see that a sphere and a plane touch. If you pick "12 inches" then I just need to show a place where the sphere is within 12 inches of the plane. If you choose 5Å then I just need to show a place which is smaller than that. It should be obvious that no matter what finite size you pick, I can find a point on the sphere and a point on the plane which is closer. (After all, the distance between them is 0.) Hence, the sphere touches the plane.
But moreover, the generally accepting meaning of "touch" says that New Mexico "touches" Utah, even though the borders meet at a perfect geometrical point. This agrees with the limit-based mathematical definition, but by the definition you want to use, you say that those two states don't touch.
The issue here is you're trying to apply loose principles which work on a human scale to something beyond your everyday experiences. You need to define your terms in a way that's applicable to what you're trying to analyze.
Lycantrophe is absolutely correct. You can't talk about a perfect sphere or a perfectly flat plan which are composed of atoms/molecules. Zoom in close enough and you'll see that the surfaces are bumpy. This isn't just theoretical - we have images from x-ray, scanning tunneling microscopes, and other sources which show just how bumpy it is.
So you either have to talk about abstract math, or you have to talk about the real world. If you talk about abstract math, then the contact area is 0. If you talk about the real world - where your intuition comes from - then things deforms and you have a non-zero contact area.
Deformation doesn't even require atoms. The same thing would occur (as Philip Howie pointed out) in anything which is not perfectly stiff. "Stiffness", after all, being defined as "resistance to deformation."
This is not a perplexing question.
There's no reason to even make the statement: 'if we cannot calculate the value of pi to an absolute, then can we even create an accurate formula for a “perfectly spherical ball”?' -- a "perfectly spherical ball" is defined as the volume at or within distance 'radius' from a point. Pi isn't even involved in that statement. In any case, nothing in the math requires knowing an exact value of pi; we know the value exists, so we're free to use the symbol ? instead.
Alan Fray commented "in reality there is no contact point as the molecules do not actually touch." This is a somewhat useless comment. I think it's meant to point out that "touch" is not a well-defined topic. Molecules don't have a real surface, so don't "touch" in the common sense. Instead, there are the electrons around a molecule, and these electrons interact with other molecules. At a far distance there's the electrostatic force, when a charged ballon causes long hair to rise up, we don't say that those are touching.
When two molecules get closer, there's an attractive force. Geckos use this to cling to walls. But even closer there's a repulsive force when the electrons are so close that they are trying to occupy the same volume at the same time. The Pauli exclusion principle describes this effect. The effect is that the two molecules start to repel each other.
This repulsion is very much like a hard wall (see the Lennard-Jones potential for a picture). And this repulsive force is what we generally talk about when we say that two things are touching.
Using that understanding, two things touch when their electron shells are close enough that their repulsive terms are a significant component of their force interactions.
"what is the size of the contact area?" 0 "Would it not be infinitely small?" Yes.
But of course this is a non-physical world. If you worked out the force on that point it would be infinite, so something would need to give. The ball would become non-spherical, or the surface non-flat (and more likely, both), until the force in the contact patch - that's the area where the two surfaces touch - is no longer strong enough to continue to deform the objects. Either that, or one of them breaks.
A "villavagn" is a trailer-syle mobile home. I haven't seen a double wide, in Sweden and looking now I can't find a way to distinguish between that and a single wide, so you'll have to leave it at that.
However, the right translation for this house style is "modulhus" - a module house.
"Me gusta" is "gilla", as in "IKEAs modulhus? Gilla!" It's pronounced "Yee-la", with the emphasis on the first syllable.
"In Biblical times, for example, people used sheep and cattle as currency"
While this line was meant for grins, the Bible uses a weight of silver as a currency. Genesis 23:15 says ""Listen to me, my lord; the land is worth four hundred shekels of silver, but what is that between me and you? Bury your dead."
Here shekel is a unit of weight, and not coinage, but it's still currency.
Bill, the Wikipedia page about the dam, and the restoration project, says that there was debate about gradual vs. quick draining, and the conclusion was that quick draining would have less overall impact.
As you rethinking that, bear in mind that car drivers are less cautious near cyclists with a helmet than those without. That research was mentioned in the article.
From when I researched it a few years ago, helmets were effective for racers, but not for slower cyclers. Also, something like 90% of helmets are worn incorrectly.
ted: No one has explained how this is better than roll call, other than that it places less work on the teachers. My analysis suggests it doesn't save much, if any time or money. It seems as well to place more responsibility on the students to be early enough to go through scans, but you (incorrectly, in my opinion) seem to say students cannot handle responsibility.
Most of the schools mentioned in this article are elementary schools, and the core classes by Florida's constitution must have no more than 25 students in them. If the teacher can't tell who the fake student is during a test then there's a much more serious problem.
This situation therefore has nothing to do with the types of exam taking you are talking about, with photo ID and fraudulent test writing, and those points are clearly irrelevant.
I've been in a number of malls which don't have cameras - your point is ... ? And in my high school I held it all day rather than use the open door toilets.
In any case, this isn't fully an issue of privacy. This is a question of benefits and costs. What does the school system gain with this, and what does it lose? Are there alternatives which are more beneficial? How do you judge the overall success? How does one judge if this is more an issue of "ooh, flashy new thing!" than good education?
Since you have thoughts on this topic: how is a biometric system better than the current manual system?
Vmax: "the student scans their finger or swipes their card when entering the building"
I'm trying to understand the setup. A school with 3000-4000 students (where you say this is being used) must surely have multiple entrances. My high school was that size and had at least 8 doorways.
That said, Chipley, FL is a rural county and not one of the large schools you're talking about. The entire district of 8 schools plus the Department of Juvenile Justice school has 3,400 students.
Assuming each scan takes 1 second, which isn't possible, then 3000 students takes 50 minutes to process. Since each station "has a staff member to monitoring the process", that's at least one staff hour spent on monitoring, and more likely two. You'll want students processed within a few minutes of arrival, so you'll need multiple scanners going.
With a manual system, teachers take attendance. Figuring 25 students in a "core" class (which is what Florida law requires) and two minutes per class, that's about 5 hours of staff time. (Four for in-class counting and one for accumulating the results).
That's a savings of three staff hours per day, or about a 0.5 staff role, or about $15,000 per year per large school of about 3,000 students. That's the best case scenario: you also need to factor in training, backup plans in case the hardware is broken, power is out, how to handle kids with a bandaged finger, etc. Overall I just don't see much savings for the school.
Do you have numbers otherwise? Is my analysis wrong?
When you argue "unfortunately as the school enrollment goes up, school staff does not", then you don't know that the Florida Constitution sets "limits on the number of students in core classes (Math, English, Science, etc.) in the state's public schools" between 18 and 25, depending on the grade. Staff must go up as enrollment goes beyond a certain point.
I say there is touching in both cases. Not only that, but this view of matter being "mostly empty space" is outdated by about 50 years; your so-called 'empty space' is full of virtual particles, which are the carriers of force between particles.
You also wrote: "i said 'two objects are touching if the contact area between them is > 0.' " . I wrote that this is mathematically incorrect, and gave 5 quotes references which disagreed with you. Not only that, but the the general population also disagrees with you, in that most people say that Utah and New Mexico "touch", even though they don't share a border.
"The answer does not have real scientific value." The things is, it does have value. Thought-experiements like this help identify and resolve ambiguous definitions. The underlying resolution to this sort of problem was figured out in the 1800s when limit theory was used to put a sound underpinning to calculus.
In geometry, "touch" means that there's an intersection. In this case, the plane touches the sphere at a point. For examples:
1) "Take a sphere and place it on a plane. Let's call the exact point where the sphere touches the plane the south pole. The plane is tangent to this point." http://www.learner.org/courses/mathilluminated/units/8/textbook/05.php
2) ".. and considers the point F at which the sphere touches the plane" (Encyclopédia of mathematics, By James Stuart Tanton; in Google Books)
3) "Let O (fig 146) be the center of a sphere; C the point in which the sphere touches the plane of projection ..." ( A treatise on crystallography By William Hallowes Miller; also at Google Books.)
4) "The point at which the sphere touches the plane is a focus of the conic section", http://www.chemistrydaily.com/chemistry/Dandelin's_theorem
5) (From 1840!) "... the line drawn from the centre to the point where the sphere touches the plane will be the shortest line which can be drawn from the centre of the sphere to the plane." (A treatise on geometry and its application in the arts By Dionysius Lardner; Google Books)
Quite obviously a number of people with math training disagree with your statement that "A perfect sphere and a perfect plane can never touch each other."
If you want to be more mathematical, and move from the ancient Greeks to the 1800s, the definition of "touch" corresponds to the idea of a limit. It's adversarial in nature. You pick a finite distance 'd'. Two objects touch if there are parts of the objects which are closer together than 'd', I just have to find examples. You are free to specify any finite value of 'd' you want, all I have to do is beat it. This definition neatly avoids the complex issues of infinities that you're having troubles with.
With that definition it's trivial to see that a sphere and a plane touch. If you pick "12 inches" then I just need to show a place where the sphere is within 12 inches of the plane. If you choose 5Å then I just need to show a place which is smaller than that. It should be obvious that no matter what finite size you pick, I can find a point on the sphere and a point on the plane which is closer. (After all, the distance between them is 0.) Hence, the sphere touches the plane.
But moreover, the generally accepting meaning of "touch" says that New Mexico "touches" Utah, even though the borders meet at a perfect geometrical point. This agrees with the limit-based mathematical definition, but by the definition you want to use, you say that those two states don't touch.
The issue here is you're trying to apply loose principles which work on a human scale to something beyond your everyday experiences. You need to define your terms in a way that's applicable to what you're trying to analyze.
So you either have to talk about abstract math, or you have to talk about the real world. If you talk about abstract math, then the contact area is 0. If you talk about the real world - where your intuition comes from - then things deforms and you have a non-zero contact area.
Deformation doesn't even require atoms. The same thing would occur (as Philip Howie pointed out) in anything which is not perfectly stiff. "Stiffness", after all, being defined as "resistance to deformation."
This is not a perplexing question.
There's no reason to even make the statement: 'if we cannot calculate the value of pi to an absolute, then can we even create an accurate formula for a “perfectly spherical ball”?' -- a "perfectly spherical ball" is defined as the volume at or within distance 'radius' from a point. Pi isn't even involved in that statement. In any case, nothing in the math requires knowing an exact value of pi; we know the value exists, so we're free to use the symbol ? instead.
Alan Fray commented "in reality there is no contact point as the molecules do not actually touch." This is a somewhat useless comment. I think it's meant to point out that "touch" is not a well-defined topic. Molecules don't have a real surface, so don't "touch" in the common sense. Instead, there are the electrons around a molecule, and these electrons interact with other molecules. At a far distance there's the electrostatic force, when a charged ballon causes long hair to rise up, we don't say that those are touching.
When two molecules get closer, there's an attractive force. Geckos use this to cling to walls. But even closer there's a repulsive force when the electrons are so close that they are trying to occupy the same volume at the same time. The Pauli exclusion principle describes this effect. The effect is that the two molecules start to repel each other.
This repulsion is very much like a hard wall (see the Lennard-Jones potential for a picture). And this repulsive force is what we generally talk about when we say that two things are touching.
Using that understanding, two things touch when their electron shells are close enough that their repulsive terms are a significant component of their force interactions.
But of course this is a non-physical world. If you worked out the force on that point it would be infinite, so something would need to give. The ball would become non-spherical, or the surface non-flat (and more likely, both), until the force in the contact patch - that's the area where the two surfaces touch - is no longer strong enough to continue to deform the objects. Either that, or one of them breaks.
However, the right translation for this house style is "modulhus" - a module house.
"Me gusta" is "gilla", as in "IKEAs modulhus? Gilla!" It's pronounced "Yee-la", with the emphasis on the first syllable.
While this line was meant for grins, the Bible uses a weight of silver as a currency. Genesis 23:15 says ""Listen to me, my lord; the land is worth four hundred shekels of silver, but what is that between me and you? Bury your dead."
Here shekel is a unit of weight, and not coinage, but it's still currency.
As you rethinking that, bear in mind that car drivers are less cautious near cyclists with a helmet than those without. That research was mentioned in the article.
Basically this whole debate is detailed in http://en.wikipedia.org/wiki/Bicycle_helmet#Science:_testing_the_hypothesis_that_helmets_are_effective and there's scant evidence that cyclists with helmets are any safer overall than those without.
Most of the schools mentioned in this article are elementary schools, and the core classes by Florida's constitution must have no more than 25 students in them. If the teacher can't tell who the fake student is during a test then there's a much more serious problem.
This situation therefore has nothing to do with the types of exam taking you are talking about, with photo ID and fraudulent test writing, and those points are clearly irrelevant.
I've been in a number of malls which don't have cameras - your point is ... ? And in my high school I held it all day rather than use the open door toilets.
In any case, this isn't fully an issue of privacy. This is a question of benefits and costs. What does the school system gain with this, and what does it lose? Are there alternatives which are more beneficial? How do you judge the overall success? How does one judge if this is more an issue of "ooh, flashy new thing!" than good education?
Since you have thoughts on this topic: how is a biometric system better than the current manual system?
I'm trying to understand the setup. A school with 3000-4000 students (where you say this is being used) must surely have multiple entrances. My high school was that size and had at least 8 doorways.
That said, Chipley, FL is a rural county and not one of the large schools you're talking about. The entire district of 8 schools plus the Department of Juvenile Justice school has 3,400 students.
Assuming each scan takes 1 second, which isn't possible, then 3000 students takes 50 minutes to process. Since each station "has a staff member to monitoring the process", that's at least one staff hour spent on monitoring, and more likely two. You'll want students processed within a few minutes of arrival, so you'll need multiple scanners going.
With a manual system, teachers take attendance. Figuring 25 students in a "core" class (which is what Florida law requires) and two minutes per class, that's about 5 hours of staff time. (Four for in-class counting and one for accumulating the results).
That's a savings of three staff hours per day, or about a 0.5 staff role, or about $15,000 per year per large school of about 3,000 students. That's the best case scenario: you also need to factor in training, backup plans in case the hardware is broken, power is out, how to handle kids with a bandaged finger, etc. Overall I just don't see much savings for the school.
Do you have numbers otherwise? Is my analysis wrong?
When you argue "unfortunately as the school enrollment goes up, school staff does not", then you don't know that the Florida Constitution sets "limits on the number of students in core classes (Math, English, Science, etc.) in the state's public schools" between 18 and 25, depending on the grade. Staff must go up as enrollment goes beyond a certain point.