| Topic: |
Science > Physics |
| User: |
"Peter Christensen" |
| Date: |
20 May 2006 04:20:57 AM |
| Object: |
The 'FOFX-Paradox' (Math or Physics?) |
With 'f-of-x' I mean f(x). From math we could have a function f(x)=sin(x),
and from physics we could have a 'function' E(p) = p*c. There is something
with the way the concept 'function' is used in physics. For example, I can
not determine E(v) simply by using E(p=v) in the expression for E. This
would give E(v) = c*v, which is not correct. I'm just trying to describe
this problem, or 'paradox', in a funny way...
For example, if you see the expressions:
1) f(x) = cos(x)
2) f(y) = sin(y)
Should you understand it like in mathematics, and conclude that the two
different definitions of the function f does not match? -Or should you think
like in physics. As the quantity f is known, both from x and from y, then we
have the relation between x and y:
cos(x) = sin(y)
==========
-And if we know E(v), then is it possible to determine E(p) just by using
p=v? (Never!) -These problems with functions can give errors as bad as "2
and 2 is 22". (*)
There is really a difference between f{x} ('expressed from') in physics and
f[x] ('function of') as f(x) in math. I'm trying to describe this problem in
a funny way on this page:
www.peterchristensen.eu/math/fofx
The physicist is not trying to define a function E, when he writes E(v). And
the mathematician does not like expressions like u(r,phi) for u(x,y) in
other coordinates. (Because another function should not be called by the
same label.)
Hope you see what I mean...
PC
______________________
(*) Add 2 and we get 222 :-)
.
|
|
| User: "Dirk Van de Androcles" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
21 May 2006 03:04:32 PM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:446edf75$0$15794$14726298@news.sunsite.dk...
| With 'f-of-x' I mean f(x). From math we could have a function f(x)=sin(x),
| and from physics we could have a 'function' E(p) = p*c. There is something
| with the way the concept 'function' is used in physics. For example, I can
| not determine E(v) simply by using E(p=v) in the expression for E. This
| would give E(v) = c*v, which is not correct. I'm just trying to describe
| this problem, or 'paradox', in a funny way...
|
| For example, if you see the expressions:
|
| 1) f(x) = cos(x)
| 2) f(y) = sin(y)
|
| Should you understand it like in mathematics, and conclude that the two
| different definitions of the function f does not match? -Or should you
think
| like in physics. As the quantity f is known, both from x and from y, then
we
| have the relation between x and y:
|
| cos(x) = sin(y)
| ==========
Err... the argument to the cosine and sine functions is an angle.
cos(x) = sin(y) when y = 90 degrees - x degrees.
f(x) as you've described it is sqrt(2)/2.
Perhaps this may help:
http://www.androcles01.pwp.blueyonder.co.uk/sincos.PNG
The circle is of radius 1.
| -And if we know E(v), then is it possible to determine E(p) just by using
| p=v? (Never!) -These problems with functions can give errors as bad as "2
| and 2 is 22". (*)
p = mv. Why would you say p = v unless m = 1?
|
| There is really a difference between f{x} ('expressed from') in physics
and
| f[x] ('function of') as f(x) in math. I'm trying to describe this problem
in
| a funny way on this page:
|
| www.peterchristensen.eu/math/fofx
|
| The physicist is not trying to define a function E, when he writes E(v).
E(v) = 1/2 mv^2.
E(m) = 1/2 mv^2.
E(m,v) = 1/2 mv^2.
E(m, v, banana, liverwort, cocacola, birthdaysuit + bikini - Boeing747,
elephant) = 1/2 mv^2.
m(elephant) < m(Boeing747).
The function m (for mass) is such that m(elephant) means "mass of elephant."
We can't add apple to orange but we can add m(apple) to m(orange), and we
can add priceonion(mass(onion*4)) + pricepotato(mass(potato*6)), which is
exactly what the grocery store clerk does when the she runs up your bill.
| And
| the mathematician does not like expressions like u(r,phi) for u(x,y) in
| other coordinates. (Because another function should not be called by the
| same label.)
|
| Hope you see what I mean...
Nope.
Mathematicians don't care so long as you are consistent and they are
indifferent to likes and dislikes. priceonion() is a different function
to pricepotato(), even if 4 onions cost the same as 6 potatoes.
Dirk Van de Androcles.
.
|
|
|
|
| User: "Chip Eastham" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
20 May 2006 09:05:21 AM |
|
|
Peter Christensen wrote:
With 'f-of-x' I mean f(x). From math we could have a function f(x)=sin(x),
and from physics we could have a 'function' E(p) = p*c. There is something
with the way the concept 'function' is used in physics. For example, I can
not determine E(v) simply by using E(p=v) in the expression for E. This
would give E(v) = c*v, which is not correct. I'm just trying to describe
this problem, or 'paradox', in a funny way...
For example, if you see the expressions:
1) f(x) = cos(x)
2) f(y) = sin(y)
Should you understand it like in mathematics, and conclude that the two
different definitions of the function f does not match? -Or should you think
like in physics. As the quantity f is known, both from x and from y, then we
have the relation between x and y:
cos(x) = sin(y)
==========
-And if we know E(v), then is it possible to determine E(p) just by using
p=v? (Never!) -These problems with functions can give errors as bad as "2
and 2 is 22". (*)
There is really a difference between f{x} ('expressed from') in physics and
f[x] ('function of') as f(x) in math. I'm trying to describe this problem in
a funny way on this page:
www.peterchristensen.eu/math/fofx
The physicist is not trying to define a function E, when he writes E(v). And
the mathematician does not like expressions like u(r,phi) for u(x,y) in
other coordinates. (Because another function should not be called by the
same label.)
Hope you see what I mean...
Hi, Peter:
I would describe your examples as unexcused abuses of notation.
There can be occasions in which using the same notation or label
to refer to two different things can be excused, because the reader
has sufficient knowledge to discern from context between the two
meanings. Your "physics" example, of E(p) versus E(v) may be
of this kind, although I'm missing the context. A mathematician
may switch from Cartesian to polar coordinates, with some
explanation of this fact, and begin working with function u(r,phi)
rather than u(x,y) if it seems more convenient to retain the same
label u for the function as a reminder of the change-of-variable
relationship, rather than introduce an arbitrarily distinct label. A
"middle way" to promote clarity might be to define, given u(x,y):
U(r,phi) = u(r cos(phi), r sin(phi))
Mathematical exposition is a more challenging art than may
appear at first glance, for one is addressing human beings
and not automatons. Therefore the motivation and direction
of attention of the "audience" is a crucial author's burden.
Note that in your example:
f(x) = cos(x)
f(y) = sin(y)
the inference cos(x) = sin(y) is not valid unless you also
assert/assume x = y.
regards, chip
.
|
|
|
| User: "Peter Christensen" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
20 May 2006 01:07:53 PM |
|
|
"Chip Eastham" <hardmath@gmail.com> skrev i en meddelelse
news:1148133921.021881.25630@y43g2000cwc.googlegroups.com...
Peter Christensen wrote:
With 'f-of-x' I mean f(x). From math we could have a function
f(x)=sin(x),
and from physics we could have a 'function' E(p) = p*c. There is
something
with the way the concept 'function' is used in physics. For example, I
can
not determine E(v) simply by using E(p=v) in the expression for E. This
would give E(v) = c*v, which is not correct. I'm just trying to describe
this problem, or 'paradox', in a funny way...
For example, if you see the expressions:
1) f(x) = cos(x)
2) f(y) = sin(y)
Should you understand it like in mathematics, and conclude that the two
different definitions of the function f does not match? -Or should you
think
like in physics. As the quantity f is known, both from x and from y, then
we
have the relation between x and y:
cos(x) = sin(y)
==========
-And if we know E(v), then is it possible to determine E(p) just by using
p=v? (Never!) -These problems with functions can give errors as bad as "2
and 2 is 22". (*)
There is really a difference between f{x} ('expressed from') in physics
and
f[x] ('function of') as f(x) in math. I'm trying to describe this problem
in
a funny way on this page:
www.peterchristensen.eu/math/fofx
The physicist is not trying to define a function E, when he writes E(v).
And
the mathematician does not like expressions like u(r,phi) for u(x,y) in
other coordinates. (Because another function should not be called by the
same label.)
Hope you see what I mean...
Hi, Peter:
I would describe your examples as unexcused abuses of notation.
I try to take the different definitions, and then to show what can happen,
if they are mixed together in a wrong way. My eksamples are not something,
that I would like to argue for. They are ment as examples of errors, that
one should not do.
There can be occasions in which using the same notation or label
to refer to two different things can be excused, because the reader
has sufficient knowledge to discern from context between the two
meanings. Your "physics" example, of E(p) versus E(v) may be
of this kind, although I'm missing the context. A mathematician
may switch from Cartesian to polar coordinates, with some
explanation of this fact, and begin working with function u(r,phi)
rather than u(x,y) if it seems more convenient to retain the same
label u for the function as a reminder of the change-of-variable
relationship, rather than introduce an arbitrarily distinct label. A
"middle way" to promote clarity might be to define, given u(x,y):
U(r,phi) = u(r cos(phi), r sin(phi))
When U(r,phi) is used, there wouldn't be any problems with the other
function u(x,y).
Mathematical exposition is a more challenging art than may
appear at first glance, for one is addressing human beings
and not automatons. Therefore the motivation and direction
of attention of the "audience" is a crucial author's burden.
I agree, and please don't misunderstand me. I was thinking about this with
functions in physics and functions in mathematics more than 10 years ago.
(When I had my introductory physics courses) I do not have problems
understanding the difference. I just thought that this subject could be
interesting to discuss.
But often things could have been specified or defined much better. That's
what I thought then, and that's what I'm still thinking about...
Note that in your example:
f(x) = cos(x)
f(y) = sin(y)
I still think about this one with E(p)=p^/(2*m) = E(v)=1/2*m*v^2. E is
known, so p^/(2*m) =
1/2*m*v^2, which again gives p=m*v. I think, that I've seen this specific
notation in my old physics book. Just using E instead of E(p) and E(v) would
solve the problems.
the inference cos(x) = sin(y) is not valid unless you also
assert/assume x = y.
Rgds,
PC
.
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|
| User: "Paul Cardinale" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
20 May 2006 07:10:20 AM |
|
|
The problem is not with physics, nor with the way math is used in
physics. The problem is that when you misapply mathematics, you get
nonsense. If you have a function in physics that gives energy as a
function of speed, and you write this as E(v), the reason that you
can't simply stick in momentum into the formula is because the formula
is meant to take speed. If you plug the wrong quantity into a formula,
you get a bogus result. Misapplying math yields wrong answers. This
isn't news.
.
|
|
|
| User: "Peter Christensen" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
21 May 2006 02:42:32 AM |
|
|
I expected, that my posting would be misunderstood. The examples i gave was
not the result of stupidity, but it was meant as examples on the ways that
one should not do. I gave examples with 'and' and 'add', and the way they
could possibly be misunderstood, because of their different meanings in
ordinary language. The same with 'f-of-x'.
The problem with the functions in physics is similar: Physicists are
sometimes thinking different than mathematicians, and for those who have
read my posting and the HTML-page that I added, it should be clear, that the
discussion concerning the difference between f(x) seen as f[x] or f{x}
should have meaning.
Sometimes physics need to focus on a quantity, rather than a function. If we
focus on the quantity energy (E), then it can be needed to express the
quantity E by for example the momentum p or the velocity v. (Very easy
example from introductory mechanics). We would like to express 'E(p)' and
also 'E(v)'. But while using this notation, we get in trouble with the
function concept from mathematics, there can't be two definitions for the
function E(). So there is a question, do we use functions or quantities, I
call this using f[x] or using f{x}. With the latter I mean 'quantity
expressed from' and several different are here possible. Both u{x,y} and
u{r,phi} could be stated, because we focus on u as a quantity, and not as a
function of the parameters.
I do not complain about these different ways of seeing f(x), because both
these two ways, as a function and as a quantity expressed of something, are
needed in practice. I have no problems seeing if a case with f(x) should be
seen like one or another. I just wonder why the same symbols are used, and
sometimes, I just have the impression that the problem is a sloppy notation
sometimes used in physics.
Trying to write something with humour, always have problems. And maybe I
shouldn't have used the word 'paradox' (not even in '').
PC
"Paul Cardinale" <pcardinale@volcanomail.com> skrev i en meddelelse
news:1148127020.190694.324250@j33g2000cwa.googlegroups.com...
The problem is not with physics, nor with the way math is used in
physics. The problem is that when you misapply mathematics, you get
nonsense. If you have a function in physics that gives energy as a
function of speed, and you write this as E(v), the reason that you
can't simply stick in momentum into the formula is because the formula
is meant to take speed. If you plug the wrong quantity into a formula,
you get a bogus result. Misapplying math yields wrong answers. This
isn't news.
.
|
|
|
| User: "Paul Cardinale" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
23 May 2006 09:01:56 PM |
|
|
Peter Christensen wrote:
[snip]
Sometimes physics need to focus on a quantity, rather than a function. If we
focus on the quantity energy (E), then it can be needed to express the
quantity E by for example the momentum p or the velocity v. (Very easy
example from introductory mechanics). We would like to express 'E(p)' and
also 'E(v)'. But while using this notation, we get in trouble with the
function concept from mathematics, there can't be two definitions for the
function E().
Sure there can. You can have any number of definitions for E(); it
just depends upon context.
There are a gazzillion things whose meaning is context dependent.
Paul Cardinale
.
|
|
|
| User: "The Sorcerer" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
24 May 2006 04:38:30 AM |
|
|
"Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
news:1148436116.095765.41000@j73g2000cwa.googlegroups.com...
|
| Peter Christensen wrote:
|
| [snip]
|
No he didn't. You wrote it, liar.
Androcles.
.
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|
| User: "Paul Cardinale" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
29 May 2006 10:18:36 AM |
|
|
The Sorcerer wrote:
"Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
news:1148436116.095765.41000@j73g2000cwa.googlegroups.com...
|
| Peter Christensen wrote:
|
| [snip]
|
No he didn't. You wrote it, liar.
Androcles.
So, your brutally intense stupidtude has risen to the point where you
can't even comprehend the context of a reply.
.
|
|
|
| User: "The Sorcerer" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
29 May 2006 12:01:03 PM |
|
|
"Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
news:1148915916.033019.213960@i40g2000cwc.googlegroups.com...
|
| The Sorcerer wrote:
| > "Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
| > news:1148436116.095765.41000@j73g2000cwa.googlegroups.com...
| > |
| > | Peter Christensen wrote:
| > |
| > | [snip]
| > |
| > No he didn't. You wrote it, liar.
| > Androcles.
|
| So, your brutally intense stupidtude has risen to the point where you
| can't even comprehend the context of a reply.
*****, snipping, lying *****. Nobody is interested in what you have to say
except you.
Androcles.
|
.
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|
|
| User: "Paul Cardinale" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
02 Jun 2006 03:02:56 PM |
|
|
The Sorcerer wrote:
"Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
news:1148915916.033019.213960@i40g2000cwc.googlegroups.com...
|
| The Sorcerer wrote:
| > "Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
| > news:1148436116.095765.41000@j73g2000cwa.googlegroups.com...
| > |
| > | Peter Christensen wrote:
| > |
| > | [snip]
| > |
| > No he didn't. You wrote it, liar.
| > Androcles.
|
| So, your brutally intense stupidtude has risen to the point where you
| can't even comprehend the context of a reply.
*****, snipping, lying *****. Nobody is interested in what you have to say
except you.
Androcles.
Now, now. You're just upset because you don't know how to read a post,
and everyone else does. You'll be much less angry if you stop denying
what everyone knows; just admit to yourself that you're an imbecile.
Paul Cardinale
.
|
|
|
| User: "The Sorcerer" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
02 Jun 2006 07:45:08 PM |
|
|
"Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
news:1149278576.599943.90410@c74g2000cwc.googlegroups.com...
|
| The Sorcerer wrote:
| > "Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
| > news:1148915916.033019.213960@i40g2000cwc.googlegroups.com...
| > |
| > | The Sorcerer wrote:
| > | > "Paul Cardinale" <pcardinale@volcanomail.com> wrote in message
| > | > news:1148436116.095765.41000@j73g2000cwa.googlegroups.com...
| > | > |
| > | > | Peter Christensen wrote:
| > | > |
| > | > | [snip]
| > | > |
| > | > No he didn't. You wrote it, liar.
| > | > Androcles.
| > |
| > | So, your brutally intense stupidtude has risen to the point where you
| > | can't even comprehend the context of a reply.
| >
| > *****, snipping, lying *****. Nobody is interested in what you have to
say
| > except you.
| > Androcles.
| >
|
| Now, now. You're just upset because you don't know how to read a post,
| and everyone else does. You'll be much less angry if you stop denying
| what everyone knows; just admit to yourself that you're an imbecile.
|
| Paul Cardinale
I'm not upset, *****.
Anyone sane knows what a constant velocity is, only you insane
shitheads think it is a reversal of direction.
http://www.androcles01.pwp.blueyonder.co.uk/DominoEffect.GIF
Now be a good little troll and *****.
Androcles.
.
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| User: "tadchem" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
20 May 2006 09:20:29 AM |
|
|
Your problem seems to reduce to one of equivocation.
Mathematics is one context; physics is another. Ther terms you are
using are context-dependent - as are all terms.
The word "function" has a slightly different meaning in mathematics
from its meaning in physics, and it has yet a different meaning in
mechanics, sociology, psychology, and almost any other field.
Any time you trasfer a term from one context to another without paying
careful attention to the changes in meaning (however subtle) you run
the risk of creating errors of equivocating. In logic 'equivocation' is
considered one of the classical fallacies of informal logic.
To highlight the point, in physics the word 'variable' nearly always
refers to a quantity which comes bundles with 'units'. The letter v
usually represents velocity - distance per unit time with a direction -
while the letter p represents momentum - mass times velocity. In
mathematics where quantities are dimensionless, v and p may be
interchangeable, but they are not so in physics.
Try to keep your areguments within one context. When it is necessary
to change contexts in the middle of an argument you need to be aware of
what *else* changes when you cross the boundary.
Tom Davidson
Richmond, VA
.
|
|
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| User: "Peter Christensen" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
20 May 2006 11:10:29 AM |
|
|
"tadchem" <tadchem@comcast.net> skrev i en meddelelse
news:1148134829.831466.209820@j55g2000cwa.googlegroups.com...
Your problem seems to reduce to one of equivocation.
Mathematics is one context; physics is another. Ther terms you are
using are context-dependent - as are all terms.
I agree. But the difference is interesting to study a little.
The word "function" has a slightly different meaning in mathematics
from its meaning in physics, and it has yet a different meaning in
mechanics, sociology, psychology, and almost any other field.
Exactly, I just wanted to make some examples, so this slight difference can
be seen.
Any time you trasfer a term from one context to another without paying
careful attention to the changes in meaning (however subtle) you run
the risk of creating errors of equivocating. In logic 'equivocation' is
considered one of the classical fallacies of informal logic.
I didn't make these 'errors' by mistake, just to give some illustrations,
about what could go wrong. Often these subtle differences are not pointed
out good enough, I think. For example I don't like when a book is using
u(x,y) and then later u(r,phi), without any comment about this choice.
Unless otherwise is specified, I would use u_1(x,y) and u_2(r,phi).
To highlight the point, in physics the word 'variable' nearly always
refers to a quantity which comes bundles with 'units'. The letter v
usually represents velocity - distance per unit time with a direction -
while the letter p represents momentum - mass times velocity. In
mathematics where quantities are dimensionless, v and p may be
interchangeable, but they are not so in physics.
That's exactely the difference, which I was thinking about.
Try to keep your areguments within one context. When it is necessary
to change contexts in the middle of an argument you need to be aware of
what *else* changes when you cross the boundary.
The one with E(p) and E(v) was an example of an error, which should not be
made. I wrote never to do this mistake of just putting in another physical
quantity in for example E(v). (Never!)
I think, that you basically see the difference between functions in math and
physics the same way as I do. In physics we have quantities with units,
while we have usually variables without units in mathematics. That's a very
important difference.
PC
.
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| User: "tadchem" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
20 May 2006 03:04:37 PM |
|
|
Peter Christensen wrote:
I didn't make these 'errors' by mistake, just to give some illustrations,
about what could go wrong. Often these subtle differences are not pointed
out good enough, I think. For example I don't like when a book is using
u(x,y) and then later u(r,phi), without any comment about this choice.
Unless otherwise is specified, I would use u_1(x,y) and u_2(r,phi).
Personal story: When I was about 8 years old and first opened up an
algebra book I found the mathematics almost trivial, but I was confused
when I found in the first problem set that x was one thing in one
problem, then a couple of problems later x was something else.
Mentally I was trying to carry the context of the individual equations
too far - far enough to include the whole set of problems rather than
the individual equation.
Only when I got over that mental block and realized that the context of
a problem was far more limited than I was assuming did I progress and
start focussing on developing my algebra skills.
Tom Davidson
Richmond, VA
.
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| User: "Peter Christensen" |
|
| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
21 May 2006 04:55:43 AM |
|
|
"tadchem" <tadchem@comcast.net> skrev i en meddelelse
news:1148155477.232263.213160@j55g2000cwa.googlegroups.com...
Personal story: When I was about 8 years old and first opened up an
algebra book I found the mathematics almost trivial, but I was confused
when I found in the first problem set that x was one thing in one
problem, then a couple of problems later x was something else.
Mentally I was trying to carry the context of the individual equations
too far - far enough to include the whole set of problems rather than
the individual equation.
Only when I got over that mental block and realized that the context of
a problem was far more limited than I was assuming did I progress and
start focussing on developing my algebra skills.
Thanks. That's why it is always nice to have a teacher to ask. Then you
would
probably not have spend more than 5 minutes on this problem. But that's how
it is. I also spend quite some time on my function-problem. (I don't know
why I didn't just talked to the teacher about it.) But I found out, a long
time ago, that there was a difference from mathematics, in the sciences
where quantites and units are applied instead of just abstract functions. I
sorted things in cases of f[x] and f{x} (ny own notation), until I thought
that things were clear once again, and then I just continued to use f(x)
again. (10 years ago now)
But recently I got into this problem with u(x,y) and u(r,phi). I just
decided, that I would write a posting about it, and I tried to write it in
what I would like to call 'a funny way'. That's why I also introduced it as
a 'paradox'.
That's just my problem with trying to write 'funny postings' once again: On
Fools Day 2006 (April 1st), I decided to write a joke-posting for
sci.phys/sci.math and a few other groups. Just really nothing, I just made
op a story, that the mass of the photon should be undefined. I said that the
mass (rest-mass) of it can be measured, because the photon doesn't exist at
rest. Then I took an undefined symbol from math, here 0^0, and used this as
a symbol from mathematics of 'undefined'. This means, that I claimed that
m_photon (the mass of the photon) should best be given with m_photon = 0^0.
(Actually it's known to be zero and not 0^0). This was just meant as a sort
of a joke.
This little joke wasn't understood as a joke, and I ended up with a thread
with 417 articles. (Link:
http://groups.google.com/group/sci.physics.relativity/tree/browse_frm/thread/a588600b78c54da4/65c3f960dd1ee657?rnum=1&hl=en&q=pech%40mailaps.org&_done=%2Fgroup%2Fsci.physics.relativity%2Fbrowse_frm%2Fthread%2Fa588600b78c54da4%2F22535d3586b44eb0%3Flnk%3Dst%26q%3Dpech%40mailaps.org%26rnum%3D1%26hl%3Den%26#doc_65c3f960dd1ee657
on Google.groups) A lot of people tried to correct me, and there was quite a
discussion going on. -When I try to post a serious thread, usually the
average number of articles is only between 5 and 10 or even less.
That's a little about me and my silly humour..
Rgds,
Peter Christensen
(Denmark)
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| User: "tadchem" |
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| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
27 May 2006 04:00:25 AM |
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Peter Christensen wrote:
This little joke wasn't understood as a joke, and I ended up with a thread
with 417 articles. (Link:
http://groups.google.com/group/sci.physics.relativity/tree/browse_frm/thread/a588600b78c54da4/65c3f960dd1ee657?rnum=1&hl=en&q=pech%40mailaps.org&_done=%2Fgroup%2Fsci.physics.relativity%2Fbrowse_frm%2Fthread%2Fa588600b78c54da4%2F22535d3586b44eb0%3Flnk%3Dst%26q%3Dpech%40mailaps.org%26rnum%3D1%26hl%3Den%26#doc_65c3f960dd1ee657
on Google.groups) A lot of people tried to correct me, and there was quite a
discussion going on. -When I try to post a serious thread, usually the
average number of articles is only between 5 and 10 or even less.
To quote an old philosopher/comedian: "Humor is a funny thing."
Jonathan Swift, the famous English satirist and author of the satirical
classic "Gulliver's Travels", was nearly lynched over his essay "A
Modest Proposal" by people with no tolerance for satire.
Since 9/11 this has become an even less humor-tolerant world. It seems
it has always been easier to go to war with people than to understand
them.
Tom Davidson
Richmond, VA
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| User: "Dirk Van de moortel" |
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| Title: Re: The 'FOFX-Paradox' (Math or Physics?) |
20 May 2006 04:11:19 PM |
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"tadchem" <tadchem@comcast.net> wrote in message news:1148155477.232263.213160@j55g2000cwa.googlegroups.com...
Peter Christensen wrote:
I didn't make these 'errors' by mistake, just to give some illustrations,
about what could go wrong. Often these subtle differences are not pointed
out good enough, I think. For example I don't like when a book is using
u(x,y) and then later u(r,phi), without any comment about this choice.
Unless otherwise is specified, I would use u_1(x,y) and u_2(r,phi).
Personal story: When I was about 8 years old and first opened up an
algebra book I found the mathematics almost trivial, but I was confused
when I found in the first problem set that x was one thing in one
problem, then a couple of problems later x was something else.
You mean like this:
http://users.telenet.be/vdmoortel/dirk/Stuff/WebsterAtSchool.gif
Mentally I was trying to carry the context of the individual equations
too far - far enough to include the whole set of problems rather than
the individual equation.
Only when I got over that mental block and realized that the context of
a problem was far more limited than I was assuming did I progress and
start focussing on developing my algebra skills.
Many crackpots here are still severely struggling with this:
Eleaticus:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/Crimes.html
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ImbecilePhysics.html
Androcles:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/Mutual.html
Marcel Lutgens:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/SRSymbols.html
Thomas Smid:
http://groups.google.co.uk/group/sci.physics.relativity/msg/c692727b3dbba929
Daryl McCullough:
| > Wait a minute. Are you now in agreement that you
| > were wrong about your *original* reason for saying
| > that Einstein's derivation is inconsistent? You
| > seem to be moving onto a completely different
| > argument.
| >
| > We've discovered algebraic mistakes that you've
| > made, and algebraic mistakes that I've made, but
| > we have not yet found an algebraic mistake that
| > Einstein made.
|
Smid:
| I have never claimed that Einstein made an algebraic
| mistake but that his equations are mathematically
| inconsistent as he worked from the equations
| x-ct=0
| x+ct=0
| which is inconsistent unless everything is identically
| zero. If I had to review a paper containing these
| equations, I would reject it out of hand (whether it
| was written by Einstein or anybody else).
Dirk Vdm
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