The Opposing Law
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From: jdawe on 5 Jan 2010 01:20 On Jan 5, 3:30 am, jbriggs444 <jbriggs...(a)gmail.com> wrote: > On Jan 4, 4:42 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > > > > On 4 Jan, 01:58, "Inertial" <relativ...(a)rest.com> wrote: > > > > "jdawe" <mrjd...(a)gmail.com> wrote in message > > > >news:0be085c2-2b9c-4c3d-9377-286223e84994(a)b2g2000yqi.googlegroups.com.... > > > > > For each opposing operation are 2 opposing operands. > > > > That makes no sense > > > > > Increasing an operand brings a corresponding decrease in its opposing > > > > operand. > > > > > or > > > > > Decreasing an operand brings a corresponding increase in its opposing > > > > operand. > > > > That makes no sense > > > > > An operand can never be increased\decreased to the point where itself > > > > or its opposing operand becomes null. > > > > That makes no sense > > > > > An operand is never the same as its opposing operand it is always the > > > > complete inverse. > > > > That makes no sense > > > > All in all, yours was just another post completely devoid of sense > > > Then you're aren't very intelligent Inertial. Any fool can see that > > what he is describing is an inverse relationship between two > > quantities, and further stating that while the balance between these > > quantities can grow very large, it can never become such that any > > value is absolutely nothing. > > You can make sense out of pretty much anything if you squint hard > enough. The question is whether you're just making sense out of whole > cloth or actually distilling it from something that was originally > there. > > One problem with your reading of the posting is that it implies that > there's no such thing the square root of four. > > "an operand is never the same as its opposing operand" > > Apply this assertion to the equation: 4 = x * y. > > If we take your interpretation of OP's words then he's saying, plain > as day: > > "if we have a four sided rectangular with an area of four square > inches, the width and height of the window may never be two inches > each". > > > Off the top of my head, this accurately describes the way a weighing- > > scale works > > You're dangerously close to posting nonsense yourself. You haven't > identified a way in which a weighing scale demonstrates a > multiplicative inverse relationship. > > > - the only point at which one quantity can become zero, > > and the other infinite, is at the point where the weighting platforms > > are vertically separated, > > So what you're talking about is probably an [un-]equal arm pan > balance. The quantities you want to > talk about are the weights in the respective pans. But you haven't > thought the example through. Two mistakes: > > 1. You haven't paid attention to what invariant you're trying to > maintain. A equal arm pan balance has two free input variables. > Nothing says that there's ANY required relationship between them. > Normally we try to maintain the invariant: "the pans balance". That's > the bit that enforces a correlation on the two variables. > > I'm inclined to forgive this. It's implicit in the way we > normally use a pan balance. > > 2. For such a balance to balance it follows that the quantities in > the pans are directly proportional, not inversely proportional. > > Ooops! > > We can still make your example work. Put a fixed mass on a fixed > moment arm on the left side of the balance. Don't mess further with > that side. Put a rail on the right side of the balance extending out > horizontally. Optionally put indentations at fixed offsets on this > rail. Do not mess further with this rail. Hang a variable mass at a > variable distance on the right hand rail so that the scale balances. > Assume that the scale is left-heavy without such a mass. > > The _position_ of the mass is one operand. The _weight_ of the mass > is the other operand. For the scale to balance, these two operands > will have an inversely proportional relationship. > > fixed-torque[*k] = weight * distance > > That's the general form of an equation expressing an inverse > proportionality. Put your two correlated variables on one side and a > constant of proportionality on the other. The constant of > proportionality may have a > contribution based on your system of units if that system is not > appropriately coherent. > > > and that is the point at which the origin of > > the two quantities become indistinguishable from one another (i.e. one > > cannot tell merely from looking at the angle, on which side the weight > > was placed, and since the purpose of the scale is to compare the two > > quantities, the function of the scale breaks down because one cannot > > distinguish what was placed on the scale nor where it was placed). > > Given the error above, this part is empty babbling.- Hide quoted text - > > - Show quoted text - Remember, it is the Opposing Law for opposing operations therefore the operands are always the complete opposite. In other words think binary logic rather than algebra. Example: E = energy M = matter then you never have: E = M or M = E or in binary logic you never have: 1 = 0 or 0 = 1 -Josh.
From: Inertial on 5 Jan 2010 01:54 "jdawe" <mrjdawe(a)gmail.com> wrote in message news:394909e7-6b06-4cd8-a850-33acd017a6a1(a)m26g2000yqb.googlegroups.com... > On Jan 5, 3:30 am, jbriggs444 <jbriggs...(a)gmail.com> wrote: >> On Jan 4, 4:42 am, Ste <ste_ro...(a)hotmail.com> wrote: >> >> >> >> >> >> > On 4 Jan, 01:58, "Inertial" <relativ...(a)rest.com> wrote: >> >> > > "jdawe" <mrjd...(a)gmail.com> wrote in message >> >> > >news:0be085c2-2b9c-4c3d-9377-286223e84994(a)b2g2000yqi.googlegroups.com... >> >> > > > For each opposing operation are 2 opposing operands. >> >> > > That makes no sense >> >> > > > Increasing an operand brings a corresponding decrease in its >> > > > opposing >> > > > operand. >> >> > > > or >> >> > > > Decreasing an operand brings a corresponding increase in its >> > > > opposing >> > > > operand. >> >> > > That makes no sense >> >> > > > An operand can never be increased\decreased to the point where >> > > > itself >> > > > or its opposing operand becomes null. >> >> > > That makes no sense >> >> > > > An operand is never the same as its opposing operand it is always >> > > > the >> > > > complete inverse. >> >> > > That makes no sense >> >> > > All in all, yours was just another post completely devoid of sense >> >> > Then you're aren't very intelligent Inertial. Any fool can see that >> > what he is describing is an inverse relationship between two >> > quantities, and further stating that while the balance between these >> > quantities can grow very large, it can never become such that any >> > value is absolutely nothing. >> >> You can make sense out of pretty much anything if you squint hard >> enough. The question is whether you're just making sense out of whole >> cloth or actually distilling it from something that was originally >> there. >> >> One problem with your reading of the posting is that it implies that >> there's no such thing the square root of four. >> >> "an operand is never the same as its opposing operand" >> >> Apply this assertion to the equation: 4 = x * y. >> >> If we take your interpretation of OP's words then he's saying, plain >> as day: >> >> "if we have a four sided rectangular with an area of four square >> inches, the width and height of the window may never be two inches >> each". >> >> > Off the top of my head, this accurately describes the way a weighing- >> > scale works >> >> You're dangerously close to posting nonsense yourself. You haven't >> identified a way in which a weighing scale demonstrates a >> multiplicative inverse relationship. >> >> > - the only point at which one quantity can become zero, >> > and the other infinite, is at the point where the weighting platforms >> > are vertically separated, >> >> So what you're talking about is probably an [un-]equal arm pan >> balance. The quantities you want to >> talk about are the weights in the respective pans. But you haven't >> thought the example through. Two mistakes: >> >> 1. You haven't paid attention to what invariant you're trying to >> maintain. A equal arm pan balance has two free input variables. >> Nothing says that there's ANY required relationship between them. >> Normally we try to maintain the invariant: "the pans balance". That's >> the bit that enforces a correlation on the two variables. >> >> I'm inclined to forgive this. It's implicit in the way we >> normally use a pan balance. >> >> 2. For such a balance to balance it follows that the quantities in >> the pans are directly proportional, not inversely proportional. >> >> Ooops! >> >> We can still make your example work. Put a fixed mass on a fixed >> moment arm on the left side of the balance. Don't mess further with >> that side. Put a rail on the right side of the balance extending out >> horizontally. Optionally put indentations at fixed offsets on this >> rail. Do not mess further with this rail. Hang a variable mass at a >> variable distance on the right hand rail so that the scale balances. >> Assume that the scale is left-heavy without such a mass. >> >> The _position_ of the mass is one operand. The _weight_ of the mass >> is the other operand. For the scale to balance, these two operands >> will have an inversely proportional relationship. >> >> fixed-torque[*k] = weight * distance >> >> That's the general form of an equation expressing an inverse >> proportionality. Put your two correlated variables on one side and a >> constant of proportionality on the other. The constant of >> proportionality may have a >> contribution based on your system of units if that system is not >> appropriately coherent. >> >> > and that is the point at which the origin of >> > the two quantities become indistinguishable from one another (i.e. one >> > cannot tell merely from looking at the angle, on which side the weight >> > was placed, and since the purpose of the scale is to compare the two >> > quantities, the function of the scale breaks down because one cannot >> > distinguish what was placed on the scale nor where it was placed). >> >> Given the error above, this part is empty babbling.- Hide quoted text - >> >> - Show quoted text - > > Remember, it is the Opposing Law for opposing operations therefore the > operands are always the complete opposite. What would you define as an 'opposing operation'? Please give an example. What would you define as an 'opposing operatand'? Please give an example. > In other words think binary logic rather than algebra. I suggest you just try thinking before you post > Example: > > E = energy > > M = matter > > then you never have: > > E = M Yes .. you do .. in a natural unit system > > or > > M = E Yes .. you do .. in a natural unit system > or in binary logic you never have: > > 1 = 0 > > or > > 0 = 1 That's nothing to do with any reasonable notion of an 'opposing operation' .. '=' is an equality operator, so there is nothing 'opposing' there
From: jdawe on 5 Jan 2010 02:13 On Jan 5, 4:54 pm, "Inertial" <relativ...(a)rest.com> wrote: > "jdawe" <mrjd...(a)gmail.com> wrote in message > > news:394909e7-6b06-4cd8-a850-33acd017a6a1(a)m26g2000yqb.googlegroups.com.... > > > > > > > On Jan 5, 3:30 am, jbriggs444 <jbriggs...(a)gmail.com> wrote: > >> On Jan 4, 4:42 am, Ste <ste_ro...(a)hotmail.com> wrote: > > >> > On 4 Jan, 01:58, "Inertial" <relativ...(a)rest.com> wrote: > > >> > > "jdawe" <mrjd...(a)gmail.com> wrote in message > > >> > >news:0be085c2-2b9c-4c3d-9377-286223e84994(a)b2g2000yqi.googlegroups.com... > > >> > > > For each opposing operation are 2 opposing operands. > > >> > > That makes no sense > > >> > > > Increasing an operand brings a corresponding decrease in its > >> > > > opposing > >> > > > operand. > > >> > > > or > > >> > > > Decreasing an operand brings a corresponding increase in its > >> > > > opposing > >> > > > operand. > > >> > > That makes no sense > > >> > > > An operand can never be increased\decreased to the point where > >> > > > itself > >> > > > or its opposing operand becomes null. > > >> > > That makes no sense > > >> > > > An operand is never the same as its opposing operand it is always > >> > > > the > >> > > > complete inverse. > > >> > > That makes no sense > > >> > > All in all, yours was just another post completely devoid of sense > > >> > Then you're aren't very intelligent Inertial. Any fool can see that > >> > what he is describing is an inverse relationship between two > >> > quantities, and further stating that while the balance between these > >> > quantities can grow very large, it can never become such that any > >> > value is absolutely nothing. > > >> You can make sense out of pretty much anything if you squint hard > >> enough. The question is whether you're just making sense out of whole > >> cloth or actually distilling it from something that was originally > >> there. > > >> One problem with your reading of the posting is that it implies that > >> there's no such thing the square root of four. > > >> "an operand is never the same as its opposing operand" > > >> Apply this assertion to the equation: 4 = x * y. > > >> If we take your interpretation of OP's words then he's saying, plain > >> as day: > > >> "if we have a four sided rectangular with an area of four square > >> inches, the width and height of the window may never be two inches > >> each". > > >> > Off the top of my head, this accurately describes the way a weighing- > >> > scale works > > >> You're dangerously close to posting nonsense yourself. You haven't > >> identified a way in which a weighing scale demonstrates a > >> multiplicative inverse relationship. > > >> > - the only point at which one quantity can become zero, > >> > and the other infinite, is at the point where the weighting platforms > >> > are vertically separated, > > >> So what you're talking about is probably an [un-]equal arm pan > >> balance. The quantities you want to > >> talk about are the weights in the respective pans. But you haven't > >> thought the example through. Two mistakes: > > >> 1. You haven't paid attention to what invariant you're trying to > >> maintain. A equal arm pan balance has two free input variables. > >> Nothing says that there's ANY required relationship between them. > >> Normally we try to maintain the invariant: "the pans balance". That's > >> the bit that enforces a correlation on the two variables. > > >> I'm inclined to forgive this. It's implicit in the way we > >> normally use a pan balance. > > >> 2. For such a balance to balance it follows that the quantities in > >> the pans are directly proportional, not inversely proportional. > > >> Ooops! > > >> We can still make your example work. Put a fixed mass on a fixed > >> moment arm on the left side of the balance. Don't mess further with > >> that side. Put a rail on the right side of the balance extending out > >> horizontally. Optionally put indentations at fixed offsets on this > >> rail. Do not mess further with this rail. Hang a variable mass at a > >> variable distance on the right hand rail so that the scale balances. > >> Assume that the scale is left-heavy without such a mass. > > >> The _position_ of the mass is one operand. The _weight_ of the mass > >> is the other operand. For the scale to balance, these two operands > >> will have an inversely proportional relationship. > > >> fixed-torque[*k] = weight * distance > > >> That's the general form of an equation expressing an inverse > >> proportionality. Put your two correlated variables on one side and a > >> constant of proportionality on the other. The constant of > >> proportionality may have a > >> contribution based on your system of units if that system is not > >> appropriately coherent. > > >> > and that is the point at which the origin of > >> > the two quantities become indistinguishable from one another (i.e. one > >> > cannot tell merely from looking at the angle, on which side the weight > >> > was placed, and since the purpose of the scale is to compare the two > >> > quantities, the function of the scale breaks down because one cannot > >> > distinguish what was placed on the scale nor where it was placed). > > >> Given the error above, this part is empty babbling.- Hide quoted text - > > >> - Show quoted text - > > > Remember, it is the Opposing Law for opposing operations therefore the > > operands are always the complete opposite. > > What would you define as an 'opposing operation'? Please give an example. > What would you define as an 'opposing operatand'? Please give an example. > > > In other words think binary logic rather than algebra. > > I suggest you just try thinking before you post > > > Example: > > > E = energy > > > M = matter > > > then you never have: > > > E = M > > Yes .. you do .. in a natural unit system > > > > > or > > > M = E > > Yes .. you do .. in a natural unit system > > > or in binary logic you never have: > > > 1 = 0 > > > or > > > 0 = 1 > > That's nothing to do with any reasonable notion of an 'opposing operation' > .. '=' is an equality operator, so there is nothing 'opposing' there- Hide quoted text - > > - Show quoted text - I generally don't reply to aliasing ( juvenile ) posters. When you are able to invert from an immature state to a mature state and put your full name with what you say then I will be more than happy to help you out. -Josh.
From: Inertial on 5 Jan 2010 02:17 "jdawe" <mrjdawe(a)gmail.com> wrote in message news:1668c239-79ea-4803-bff0-316d25c30313(a)j24g2000yqa.googlegroups.com... > On Jan 5, 4:54 pm, "Inertial" <relativ...(a)rest.com> wrote: >> "jdawe" <mrjd...(a)gmail.com> wrote in message >> >> >> news:394909e7-6b06-4cd8-a850-33acd017a6a1(a)m26g2000yqb.googlegroups.com... >> >> >> >> >> >> > On Jan 5, 3:30 am, jbriggs444 <jbriggs...(a)gmail.com> wrote: >> >> On Jan 4, 4:42 am, Ste <ste_ro...(a)hotmail.com> wrote: >> >> >> > On 4 Jan, 01:58, "Inertial" <relativ...(a)rest.com> wrote: >> >> >> > > "jdawe" <mrjd...(a)gmail.com> wrote in message >> >> >> > >news:0be085c2-2b9c-4c3d-9377-286223e84994(a)b2g2000yqi.googlegroups.com... >> >> >> > > > For each opposing operation are 2 opposing operands. >> >> >> > > That makes no sense >> >> >> > > > Increasing an operand brings a corresponding decrease in its >> >> > > > opposing >> >> > > > operand. >> >> >> > > > or >> >> >> > > > Decreasing an operand brings a corresponding increase in its >> >> > > > opposing >> >> > > > operand. >> >> >> > > That makes no sense >> >> >> > > > An operand can never be increased\decreased to the point where >> >> > > > itself >> >> > > > or its opposing operand becomes null. >> >> >> > > That makes no sense >> >> >> > > > An operand is never the same as its opposing operand it is >> >> > > > always >> >> > > > the >> >> > > > complete inverse. >> >> >> > > That makes no sense >> >> >> > > All in all, yours was just another post completely devoid of sense >> >> >> > Then you're aren't very intelligent Inertial. Any fool can see that >> >> > what he is describing is an inverse relationship between two >> >> > quantities, and further stating that while the balance between these >> >> > quantities can grow very large, it can never become such that any >> >> > value is absolutely nothing. >> >> >> You can make sense out of pretty much anything if you squint hard >> >> enough. The question is whether you're just making sense out of whole >> >> cloth or actually distilling it from something that was originally >> >> there. >> >> >> One problem with your reading of the posting is that it implies that >> >> there's no such thing the square root of four. >> >> >> "an operand is never the same as its opposing operand" >> >> >> Apply this assertion to the equation: 4 = x * y. >> >> >> If we take your interpretation of OP's words then he's saying, plain >> >> as day: >> >> >> "if we have a four sided rectangular with an area of four square >> >> inches, the width and height of the window may never be two inches >> >> each". >> >> >> > Off the top of my head, this accurately describes the way a >> >> > weighing- >> >> > scale works >> >> >> You're dangerously close to posting nonsense yourself. You haven't >> >> identified a way in which a weighing scale demonstrates a >> >> multiplicative inverse relationship. >> >> >> > - the only point at which one quantity can become zero, >> >> > and the other infinite, is at the point where the weighting >> >> > platforms >> >> > are vertically separated, >> >> >> So what you're talking about is probably an [un-]equal arm pan >> >> balance. The quantities you want to >> >> talk about are the weights in the respective pans. But you haven't >> >> thought the example through. Two mistakes: >> >> >> 1. You haven't paid attention to what invariant you're trying to >> >> maintain. A equal arm pan balance has two free input variables. >> >> Nothing says that there's ANY required relationship between them. >> >> Normally we try to maintain the invariant: "the pans balance". That's >> >> the bit that enforces a correlation on the two variables. >> >> >> I'm inclined to forgive this. It's implicit in the way we >> >> normally use a pan balance. >> >> >> 2. For such a balance to balance it follows that the quantities in >> >> the pans are directly proportional, not inversely proportional. >> >> >> Ooops! >> >> >> We can still make your example work. Put a fixed mass on a fixed >> >> moment arm on the left side of the balance. Don't mess further with >> >> that side. Put a rail on the right side of the balance extending out >> >> horizontally. Optionally put indentations at fixed offsets on this >> >> rail. Do not mess further with this rail. Hang a variable mass at a >> >> variable distance on the right hand rail so that the scale balances. >> >> Assume that the scale is left-heavy without such a mass. >> >> >> The _position_ of the mass is one operand. The _weight_ of the mass >> >> is the other operand. For the scale to balance, these two operands >> >> will have an inversely proportional relationship. >> >> >> fixed-torque[*k] = weight * distance >> >> >> That's the general form of an equation expressing an inverse >> >> proportionality. Put your two correlated variables on one side and a >> >> constant of proportionality on the other. The constant of >> >> proportionality may have a >> >> contribution based on your system of units if that system is not >> >> appropriately coherent. >> >> >> > and that is the point at which the origin of >> >> > the two quantities become indistinguishable from one another (i.e. >> >> > one >> >> > cannot tell merely from looking at the angle, on which side the >> >> > weight >> >> > was placed, and since the purpose of the scale is to compare the two >> >> > quantities, the function of the scale breaks down because one cannot >> >> > distinguish what was placed on the scale nor where it was placed). >> >> >> Given the error above, this part is empty babbling.- Hide quoted >> >> text - >> >> >> - Show quoted text - >> >> > Remember, it is the Opposing Law for opposing operations therefore the >> > operands are always the complete opposite. >> >> What would you define as an 'opposing operation'? Please give an >> example. >> What would you define as an 'opposing operatand'? Please give an >> example. >> >> > In other words think binary logic rather than algebra. >> >> I suggest you just try thinking before you post >> >> > Example: >> >> > E = energy >> >> > M = matter >> >> > then you never have: >> >> > E = M >> >> Yes .. you do .. in a natural unit system >> >> >> >> > or >> >> > M = E >> >> Yes .. you do .. in a natural unit system >> >> > or in binary logic you never have: >> >> > 1 = 0 >> >> > or >> >> > 0 = 1 >> >> That's nothing to do with any reasonable notion of an 'opposing >> operation' >> .. '=' is an equality operator, so there is nothing 'opposing' there- >> Hide quoted text - >> >> - Show quoted text - > > I generally don't reply to aliasing ( juvenile ) posters. Nothing at all juvenile about keeping ones identity hidden and safe > When you are able to invert from an immature state to a mature state I'm already in a mature state, thanks. You ,however, are not .. neither in your behavior, nor in your manner of thinking. > and put your full name with what you say then I will be more than > happy to help you out. Then you are simply being childish and juvenile. Clearly you are unable to answer the question, and are simply avoiding the issues.
From: jbriggs444 on 5 Jan 2010 09:17
On Jan 4, 2:32 pm, Ste <ste_ro...(a)hotmail.com> wrote: > On 4 Jan, 17:30, jbriggs444 <jbriggs...(a)gmail.com> wrote: > > > > > > > On Jan 4, 4:42 am, Ste <ste_ro...(a)hotmail.com> wrote: > > > > On 4 Jan, 01:58, "Inertial" <relativ...(a)rest.com> wrote: > > > > > "jdawe" <mrjd...(a)gmail.com> wrote in message > > > > >news:0be085c2-2b9c-4c3d-9377-286223e84994(a)b2g2000yqi.googlegroups.com... > > > > > > For each opposing operation are 2 opposing operands. > > > > > That makes no sense > > > > > > Increasing an operand brings a corresponding decrease in its opposing > > > > > operand. > > > > > > or > > > > > > Decreasing an operand brings a corresponding increase in its opposing > > > > > operand. > > > > > That makes no sense > > > > > > An operand can never be increased\decreased to the point where itself > > > > > or its opposing operand becomes null. > > > > > That makes no sense > > > > > > An operand is never the same as its opposing operand it is always the > > > > > complete inverse. > > > > > That makes no sense > > > > > All in all, yours was just another post completely devoid of sense > > > > Then you're aren't very intelligent Inertial. Any fool can see that > > > what he is describing is an inverse relationship between two > > > quantities, and further stating that while the balance between these > > > quantities can grow very large, it can never become such that any > > > value is absolutely nothing. > > > You can make sense out of pretty much anything if you squint hard > > enough. The question is whether you're just making sense out of whole > > cloth or actually distilling it from something that was originally > > there. > > Indeed. But if someone's assertions are only partially or vaguely > correct, then it shouldn't be too hard to refute it, or re-state the > argument in more accurate terms, and that would be far more productive > than vindictive rants about posts being "completely devoid of sense". But the assertion in play (which jdawe's next post raises to the level of confirmed truth) is that jdawe's work product has zero sense content. It is easy to refute something that makes an unambiguous and incorrect prediction. It is difficult to refute something that cannot even be deciphered. > > > One problem with your reading of the posting is that it implies that > > there's no such thing the square root of four. > > I fail to see how that could be inferred from my post. Because you didn't define your terms either. You wrote "inverse relationship" and I read "inverse proportionality" on the assumption that you were smarter than jdawe. You might be. But not by much. > > > "an operand is never the same as its opposing operand" > > > Apply this assertion to the equation: 4 = x * y. > > > If we take your interpretation of OP's words then he's saying, plain > > as day: > > > "if we have a four sided rectangular with an area of four square > > inches, the width and height of the window may never be two inches > > each". > > I think a better re-statement would be to say that, if by definition a > rectangle (as distinct from a square) always has a longer side, then > area = longer side * shorter side. Longer side = area / shorter side. > Shorter side = area / longer side. You have a better eye then me if you can read the distinction between a rectangle and a sqare into jdawe's posting. > By this logic, if area is held constant, then an increase in the > longer side must necessarily mean a reduction in the shorter side. Yes! Inverse proportionality. > At > the point at which longer side = shorter side, the ability to > distinguish between the sides disappears, and the shape no longer > takes the form of a rectangle (and the formula becomes meaningless/ > useless). WRONG! You do not lose the ability to distinguish the sides. There is no singularity where the two sides become equal in length. The formula continues working just fine with width > height, width = height or with height > width. Your poor choice of parameter names is to blame for the poor behavior of the resulting formula. > > So yes, by that logic if area is held constant, then adjacent sides of > a rectangle may never be equal. The reason that the two adacent sides of a rectangle may never be equal is _your_ assertion that a square is not a special case of a rectangle. No matter. It's only a question of definition. Use different words if you like. There is a such a thing as a four sided regular polygon with sides of length 2 and an area of 4. > > > - the only point at which one quantity can become zero, > > > and the other infinite, is at the point where the weighting platforms > > > are vertically separated, > > > So what you're talking about is probably an [un-]equal arm pan > > balance. > > Clearly. If you had written clearly I wouldn't have to guess. > > > The quantities you want to > > talk about are the weights in the respective pans. But you haven't > > thought the example through. > > Nor did I pretend to have done so. > > > Two mistakes: > > > 1. You haven't paid attention to what invariant you're trying to > > maintain. A equal arm pan balance has two free input variables. > > Nothing says that there's ANY required relationship between them. > > Normally we try to maintain the invariant: "the pans balance". That's > > the bit that enforces a correlation on the two variables. > > The whole purpose of the scale is to express a relationship between > two weights. Write clearly. The purpose of a scale is to weigh things. A balance scale does this by determining which of two weights is greater. > The scale will determine whether the weights are unequal > and (to a very limited extent) the degree of inequality. It will also tell you which of the two is greater. Pay attention to the _direction_ the needle moves. > Obviously if > you know absolutely what weight is on one arm of the scale, then you > can determine absolutely what is on the other, Yes. This is the normal mode of operation. > and the inverse > relationship is used only to determine the arm to which/from which > weight should be added/removed. "Inverse relationship" doesn't tell you this. It doesn't tell you which side to add weight to. We can read into the term that there _is_ a side that will get you closer. But NOBODY has yet defined the term "inverse relationship". > > > I'm inclined to forgive this. It's implicit in the way we > > normally use a pan balance. > > > 2. For such a balance to balance it follows that the quantities in > > the pans are directly proportional, not inversely proportional. > > > Ooops! > > But a scale with 10 kilos on each arm cannot distinguish from a scale > with 1 kilo on each arm. Indeed, by the scale's measure, 10 kilos on > each arm is *equivalent* to 1 kilo on each arm. But that's because the > scale is designed to measure only relative weight - it performs its > function by reliance on the inverse relationship between the weight > placed on each side. Brilliant. I shall alert the Nobel prize team at once. As I understand your assertion now, it is that you can't put the reference mass and the test mass on the same side of a balance. [Actually most commercial scales normally operate in just such a configuration. Maybe that call to the Nobel committee is premature] Let me try to read as much sense as I can into your position: "In any otherwise isolated system where an equilibrium state is maintained in the face of two relevant inputs, those inputs must be (in some sense) equal and opposite". Unfortunately, it is easy to falsify that claim. |