1. ## Re: spark's dimension thread

I'm not quite sure why I am doing this but...

In a previous thread, spark said:
Now could you be so kind and make a post and recap all relevant criticism?
Rather than recap all the criticism, I think it would be more sensible to try and take things one step at a time. We still seem to have a fundamental misunderstanding/disagreement about your very first point.

There are five children, ten sweets each, let's multiply...

You have five children, i.e. the dimensions are child.

Q1. Do you agree with this? If not, why not?

You have ten sweets each, i.e. each child has ten sweets or 10 sweets per child, i.e. the dimensions are sweet/child. (As many people have pointed out.)

Q2. Do you agree with this? If not, why not?

Let's multiply...

(5 child) * (10 sweet/child) = 50 child*sweet/child = 50 child*sweet/child = 50 sweet.

Q3. Do you agree with this? If not, why not?

Before we go any further can you simply and clearly explain what you object to in this response, because so far you have just ignored or dismissed it.

After that, it may be possible to go on and discuss some of the other points...

[For the record, I created this thread because I was under the impression that spark wanted to continue discussion of his idea. It turns out that he was expecting me to make his case for him. That isn't going to happen, obviously, as everything I have seen from him so far is either incomprehensible or wrong.]
Last edited by Strange; 2011-Aug-26 at 08:36 AM. Reason: [footnote]

2. Originally Posted by Strange
I'm not quite sure why I am doing this but...

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## OP: proposition " momentum p = m * v " is logical ?

a [fs] formal statement [c^2=a^2+b^2] is a theorem [fs]!, a proven hypoyhesis [fs]?: [fs true?] => proof => [fs]!
------

OP is a [fs € DA]? : [0] [ p = m x v] true ?
it is a synthetical way of saying: "I'd like to discuss the logical foundations of DA, have taken an example of statement [0] from DA, can we discuss it?, [0] can be considered a theorem?, a hypothesis that has been/ can be proven?, would you bring a logical argument showing the validity of theorem, that hypothesis is true/ logical?"

subject, the only issue is [Q x Q =>] D x D => 1) QC, quantity calculus, that is

2) x [multiplication] => ST, [set theory]
3) Q [physical quantity] and
4) D [dimension] => DA

(def. of n = n°; QC° = 1°) 1°: QC " ...is...analogous to a system of [A] algebra". [=> Q(c)A]
..................after 200 years.. b)............"axiomatization has yet to be completed"

1°b proves question [0]? legitimate, grounded: if axiomatization has been impossible, there might be serious logical problems.

Now, if no demonstration is available
a) quote and ,( mainstream def. of Q and D *[as related to Q]), and if you think QA not = A
b) explain the rules of this calculus (requisites, properties, restrictions...) that allow one to perform operations and create (new) derived Q 's
put your previous statements (degree of freedom, multiplical properties...) in meaningful contest.

(note *) wiki: "physical quantity" quotes VIM3 as formal def. of Q (3°). Although it is fuzzy, messy, we are able to recognize Q [time, space, motion..] as a Category [=> Ontology]. I couldn't find any def. of D, and most of all, how you get from Q [time] to => D [time]

--------------------
2°: x " is repetition of addition...of n *(sub)sets of m elements"
example [1) child x sweet each, 2) child x sweet, 3) crate x box,.] was not provocative, it was only an eye-catching ad; but it stole the show and now is the issue,
method sweet/child is off-topic, because (if it is valid) applies only to 1 , which is a trivial problem any child can solve,
logical key is identification of *( subset)

4. (And no, "sweet/child" is NOT off topic, because it was integral to your claims. You were setting up a situation with "children" and "sweets per child", then later using "children" and "sweets per child" and claiming some issue. That is, your set-up in post #1 of your other thread was directly contradicted by your later claims. You need to be consistent.

It was as if you were suddenly dropping the "per second" off velocity to try to show momentum is badly calculated.)
Last edited by pzkpfw; 2011-Aug-29 at 08:37 PM. Reason: Add last line.

5. Originally Posted by spark
(def. of n = n°; QC° = 1°) 1°: QC " ...is...analogous to a system of [A] algebra". [=> Q(c)A]
..................after 200 years.. b)............"axiomatization has yet to be completed"
I must say, it seems like you are being intentional obfuscatory... or unnecessarily complicated and obscure, and I have a degree in mathematics with some specialization in abstract algebra. I have no idea what your point is....

6. A minor point: it's valid to multiply or divide values of any dimensions. The result doesn't necessarily represent any sensible physical quantity, but it's valid, the dimensionality of the result is completely defined. You can multiply apples and koalas as an intermediate step and get a quantity with units of apple-koalas, but you'd better divide one of them out further down the line if you want a meaningful answer.

This isn't so for addition/subtraction...you can never subtract kilograms from meters. The dimensions must be identical.

That aside...spark, I also have no idea what your issue is. You set up a situation where you clearly have values with units of "children" and "sweets/child", and then insist for no apparent reason that the latter is just "sweets". The only thing illogical is your assignment of units.

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Originally Posted by spark
a [fs] formal statement [c^2=a^2+b^2] is a theorem [fs]!, a proven hypoyhesis [fs]?: [fs true?] => proof => [fs]!
------

OP is a [fs € DA]? : [0] [ p = m x v] true ?
it is a synthetical way of saying: "I'd like to discuss the logical foundations of DA, have taken an example of statement [0] from DA, can we discuss it?, [0] can be considered a theorem?, a hypothesis that has been/ can be proven?, would you bring a logical argument showing the validity of theorem, that hypothesis is true/ logical?"

subject, the only issue is [Q x Q =>] D x D => 1) QC, quantity calculus, that is

2) x [multiplication] => ST, [set theory]
3) Q [physical quantity] and
4) D [dimension] => DA

(def. of n = n°; QC° = 1°) 1°: QC " ...is...analogous to a system of [A] algebra". [=> Q(c)A]
..................after 200 years.. b)............"axiomatization has yet to be completed"

1°b proves question [0]? legitimate, grounded: if axiomatization has been impossible, there might be serious logical problems.

Now, if no demonstration is available
a) quote and ,( mainstream def. of Q and D *[as related to Q]), and if you think QA not = A
b) explain the rules of this calculus (requisites, properties, restrictions...) that allow one to perform operations and create (new) derived Q 's
put your previous statements (degree of freedom, multiplical properties...) in meaningful contest.

(note *) wiki: "physical quantity" quotes VIM3 as formal def. of Q (3°). Although it is fuzzy, messy, we are able to recognize Q [time, space, motion..] as a Category [=> Ontology]. I couldn't find any def. of D, and most of all, how you get from Q [time] to => D [time]

--------------------
2°: x " is repetition of addition...of n *(sub)sets of m elements"
example [1) child x sweet each, 2) child x sweet, 3) crate x box,.] was not provocative, it was only an eye-catching ad; but it stole the show and now is the issue,
method sweet/child is off-topic, because (if it is valid) applies only to 1 , which is a trivial problem any child can solve,
logical key is identification of *( subset)

Your last couple lines sum up the whole problem. This is a trivial problem that a child can solve. That is what you have been told again and again.

The only way p=mv is in the slightest incorrect is that it should be three bars in the equal sign cause it is a DEFINITION.

There is an experimentally confirmed quantity that behaves as the product of mass and velocity. This quantity is defined as momentum

This is all there is too it. You have made olympus mons out of a mole hill.

8. Originally Posted by spark
I'd like to discuss the logical foundations of DA
I have no idea what the rest of that means but ... are you looking for a formal proof that dimensional analysis is valid/meaningful/correct? Something like the Buckingham pi theorem?

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Originally Posted by spark
VIM3 = ?, let's take it as a working hypothesis.
Explain(?'s) how it applies to Q = time (X= does not apply here), and if it can apply to sight or taste...
physical (?) quantity (?) time is: property (?) of a phenomenon (?), body (X) or substance (X) where the property has a magnitude (?)....
Originally Posted by Strange
I have no idea what the rest of that means but ... are you looking for a formal proof that dimensional analysis is valid/meaningful/correct? Something like the Buckingham pi theorem?
no proofs, clear definitions:
1) VIM3 is the official definition of Q?, if it is not, could you give a better one?
2 ) how this definition applies to time: Q (time) is the property of a phenomenon ...that has..magnitude, is time a phenomenon? , what is magnitude? it is analogous to dimension?

3) what is this particular definition of D,( in English): what is a dimension in DA, is it different from the normal meaning of this word? is it " an amount of something" or " a degree of freedom" or what?
are these definitions correct? are they obscure?

4) how D time is related to Q time?, if Qtime (is: the property of the phenomenon) what is the dimension of a property of a phenomenon?

5) what are the rules of quantity calculus, if it is analogous to (not the same as) algebra

is this obscure?
I have only quoted
I am obscure and cannot speak English? or definitions are obscure?
I am just asking you to define your terms, as they are used in DA (and you are using them) in an unusual way

10. Originally Posted by spark
no proofs, clear definitions:
OK, proof is not the right word; but you are looking for a formalization/axiomatization?

You might find what you are looking for in:
* Rayleigh's method of dimensional analysis
* Quantity_calculus
There are plenty of references there to follow up. Although that latter page says "a full axiomatization has yet to be completed" so you may not get all that you want.

ETA: I see you have that very phrase in one of your earlier posts so I assume you have read those pages. Once again, it would be helpful if you provide references for your sources.

Originally Posted by spark
if axiomatization has been impossible, there might be serious logical problems.
There might be or there might not. It certainly doesn't imply there are any "logical problems". Do you have any evidence that there are?

You keep repeating this. Do you accept that this is definition is only appropriate for trivial arithmetic on the natural numbers? It doesn't apply to complex numbers (how do you repeat addition i times?); it doesn't apply to vector/matrix arithmetic; it doesn't even apply to the reals (how do repeat something -0.618 times?) It also isn't a formal definition, which seems to be what you are looking for. And anyway, how is it relevant to your point?
Last edited by Strange; 2011-Sep-03 at 10:41 AM. Reason: expanded on axiomatization after rereading post

11. Originally Posted by spark
is this obscure?
Just to indicate the sort of thing that makes it hard for me to understand what you are saying; from your first post in this thread:
a [fs] formal statement [c^2=a^2+b^2] is a theorem [fs]!, a proven hypoyhesis [fs]?: [fs true?] => proof => [fs]!
I struggle to make any sense of this. I'm not sure if there is insufficient or too much punctuation. Is it all one sentence? Do you mean:
"A formal statement, such as c^2=a^2+b^2, is a theorem; is this a proven hypothesis?" (I may have got this wrong, I'm not sure what all the "[]!:?" notation means).

If so, then I would say no. The relationship between hypothesis and theorem in mathematics is somewhat different than that between hypothesis and theory in science. As I understand it, a hypothesis is closer to a logical antecedent of a theorem (rather than a theorem that is yet to be proved).

I have only quoted
Also, you never clearly state where you are quoting from.

12. Taking p=mv ...

m is mass, for example in units of kg

v is velocity, for example in units of m/s (metres per second)

so

p is momentum, for example in units of kg m/s (kilogram metres per second)

That (kg m/s) is actually the SI unit for momentum.

I still don't understand what your issue really is, other than that it seems you are claiming that "because some things can't be multiplied, nothing can be multiplied".

That is, you seem (to me) to think that because we can't multiply apples by koalas, we can't multiply mass by velocity.

If my understanding of your issue is correct, then what I think you are missing is that the units are not being magiced away.

We learn in math that we can't multiply dissimilar things.

e.g. 3A x 4B = 12AB

We can't take the A and B any further because we don't know what they are.

That's what we are doing in p=mv too!

We may say mass x velocity = momentum; but by calling it "momentum" we are not introducing some new thing out of nowhere.

kg x m/s = kg m/s

We still have that "kg", we still have that "m/s". Together, like that, we call them momentum.

What's the problem?
Last edited by pzkpfw; 2011-Aug-29 at 08:38 PM. Reason: Fix italics

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Originally Posted by pzkpfw
Taking p=mv ...

m is mass, for example in units of kg

v is velocity, for example in units of m/s (metres per second)

so

p is momentum, for example in units of kg m/s (kilogram metres per second)

That (kg m/s) is actually the SI unit for momentum.

I still don't understand what your issue really is, other than that it seems you are claiming that "because some things can't be multiplied, nothing can be multiplied".

That is, you seem (to me) to think that because we can't multiply apples by koalas, we can't multiply mass by velocity.

If my understanding of your issue is correct, then what I think you are missing is that the units are not being magiced away.

We learn in math that we can't multiply dissimilar things.

e.g. 3A x 4B = 12AB

We can't take the A and B any further because we don't know what they are.

That's what we are doing in p=mv too!

We may say mass x velocity = momentum; but by calling it "momentum" we are not introducing some new thing out of nowhere.

kg x m/s = kg m/s

We still have that "kg", we still have that "m/s". Together, like that, we call them momentum.

What's the problem?
I could swear someone has pointed that out before. I wonder who....

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Many of you keep asking what is my issue, some think they know better then myself.
I stated it in my OP and repeated it here. This is a new thread, I replied because it wanted to follow one step at a time. Please set aside, for the time being, what was said in old thread. Once settled the main issue, if someone is interested we can discuss details.
If you think something is confused, quote only the words or sentence, or put a mark in the quote and precise what is not clear.
I'll try to respond to every post, but now I am very busy, I can barely stick to the main issue.
Please do not make any more false assumptions or argumenta ad hominem
This is my issue:
Originally Posted by spark
: "I'd like to discuss the logical foundations of DA,
the only issue is Q x Q => D x D => QC,
I'm glad you are experts of abstract algebra, logic and computer programming. As you know, =>, is a disconnect, if you do not justify it. I asked you to do that, you did not, if you don't, that alone is a fatal error.
I do understand, as you say, that DA works in praxis and you are shocked that someone dares challenge it, I really do!.
But it is also possible you are not aware because you make double wrong and that seems to make a right. I repeat, before you are annoyed, that, only if you do not define your terms.
You define Q, then multiply D and then get back to (a derived) Q (momentum). This is perfectly legitimate when you have demonstrated the logical step.
Is the issue clear now? I am not thinking, saying, hinting that 0 is F.alse.
I am just asking you to give logical arguments. Full stop. Why don't you just give me the def. of D and the other details I need to gladly declare:
0 logical ? T.rue!., thank you, sirs, for your kind help!
____

Thanks, pzkw, for sending your argument a0.
the problem (s)?
I've already mentioned () straw man and lack of premises, (def. of terms, axioms, rules..), it is pointless to get into details
Originally Posted by pzkpfw
Taking p=mv ...so p is momentum ?,
(.
.. what your issue really is,....you are claiming that..., you ... think that because we *can't multiply apples by koalas,....I think you are missing is that the units are not being magiced *away.).[B]
(just: ? (begging the question), * F, * into (=>) (it's a nice phrasal verb!) )

flowchart is simple, one diamond:
definitions:
(1° 3° 4° 5°= U°nit) => DA
system of axioms:
2°: x (AR.ithmetics) => ST
is QA = A ? Yes => a1 T !
No => Go to b)
b) rules of QA => a2 T, a1 F !

As you know an argument can be true or false, it depends on the premises.
So a0 can be true If and only if it is deduced from the right premises

__
As nobody answered question VIM3 = ?, let's take it as a working hypothesis. Explain(?'s) how it applies to Q = time (X= does not apply here), and if it can apply to sight or taste...
physical (?) quantity (?) time is: property (?) of a phenomenon (?), body (X) or substance (X) where the property has a magnitude (?)....
Last edited by spark; 2011-Sep-01 at 01:22 PM.

15. Originally Posted by spark
... You define Q, then multiply D and then get back to (a derived) Q (momentum). This is perfectly legitimate when you have demonstrated the logical step. ...
You seem to be trying hard to be obscure.

Akg x Bm/s = ABkg m/s

Simple. The quantities and dimensions both multiply.

(It's even verified by experiment. (i.e. devise a way to measure momentum. Alter the weight and velocity of the thing being measured, and see the effects. The relationship holds).)

In your "Q" and "D" statements you appear to be trying to separate and mis-apply the values.

16. Originally Posted by spark
Many of you keep asking what is my issue, some think they know better then myself.
I stated it in my OP and repeated it here. This is a new thread, I replied because it wanted to follow one step at a time. Please set aside, for the time being, what was said in old thread. Once settled the main issue, if someone is interested we can discuss details.
If you think something is confused, quote only the words or sentence, or put a mark in the quote and precise what is not clear.
I'll try to respond to every post, but now I am very busy, I can barely stick to the main issue.
Please do not make any more false assumptions or argumenta ad hominem
sparks,

Stop telling other people how to reply to this (or any thread). One of our rules (rule 16) says that only moderators can act as moderators on BAUT. If you think someone else has posted something inappropriate, then you use the Report function (black triangle in the lower left corner of every post) to report that post and let us deal with it. But you don't get to set the rules around here.

Second, your posts are very hard to understand. If English is not your native language, than we can understand the problem and will try to be patient. But you need to try to explain more clearly, and you need to use standard terminology. And if you are using an abbreviation, you need to explain what the abbreviation means.

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Originally Posted by pzkpfw
... we can't multiply apples by koalas ...
Three apples times five koalas taste-testing apples
is fifteen tastes.

Three apples times five koalas polishing apples is
fifteen times that a koala polishes an apple.

-- Jeff, in Minneapolis

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I'm repeating my post from the other thread because it
wasn't replied to, and I think it gets at the fundamental
problem, even if it is very simple.

Originally Posted by spark
There are 10 sweets, 5 children, let's multiply...
There are five children, ten sweets each, let's multiply...
In the first case, with ten sweets, the result of multiplying
the ten sweets by five childeren is fifty of something, but you
didn't specify fifty of what. Fifty times that the ten sweets
are taste-tested by the five children in a product comparison
study? Fifty times that the ten sweets are individually sent
through the mail to the next child on the list? Fifty missed
opportunities to steal candy? Fifty counts of petty theft
against the five children for stealing the ten sweets?

The possibilities should be constrained to have something
to do with those ten sweets and five children, but that still
leaves an awful lot of possibilities. We know, however, that
the result of the multiplication is neither sweets nor children--
it is only something *involving* the sweets and the children.

In the second case, with ten sweets per child, the immediate
result of multiplying ten sweets per child by five children is
fifty sweets. Notice, however, that you are not multiplying
sweets times children-- you are multiplying sweets per child
times children.

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
... I think it gets at the fundamental problem, even if it is very simple. *( ... Fifty times that the ten sweets are taste-tested by the five children.....are individually sent....)
Hi Jeff,
I decided to answer your nice post as it would be unpolite to ignore it a second time. But you (in general) are ignoring for the umpteen time what I wrote.
the fundamental problem is to define the premises of your argument. If you define the axioms of your system * in a coherent, logical fashion, you can develop any theory, even the most absurd and far-fetched: non Euclidean geometry, multi dimensional universe, general relativity, superstring ...Such theory is scientific, logical, possible in theory, because it has no internal contradiction. But it has to be tested, to see if it is really possible in this world. I am not able to tell you what axioms you need to support your arguments, you may give it a try!

Here we are discussing math, mainstream current math: The only valid axioms are the ones of set theory, arithmetics : addition, subtraction, multiplication...
We all MUST follow those rules when we perform any operation. Nobody has authority to break the rules, never.
I considered it improper, diminishing to remind scientists what they are, but , if it is necessary, here we are:
you can not add apples and bananas, apples and koalas
you can multiply apples by koalas, crates by boxes in certain circumstances, but not forgetting multiplication is a shorthand form of addition
When you cannot, you just don't, you stop.
Now, you (mainstream) have sometime developped a theory, a system of calculus: DA, QC
I am only asking you to tell me what are the logical premises and the axioms and the rules of this Calculus, because I couldn't find a def. of Dimension, Which is the pillar of DA. The only def. I read (here) sounded like " a degree of freedom".
If you, too, cannot find one it means there is a black hole in the theory.( Just simply and honestly say so, and we move to next point, later on, I might help you make one). If you can, if you know one, it is really preposterous that you haven't presented it, yet !

says :" QC analogous to A, because ..."
does that mean that it has different rules ?, you know math and physics, you are scientists, it's up to you to answer that question.
You have AR, A and QA, once Q and D are defined , you must specify which system is valid. Then it is easy to say : 0 = False/ True !.

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Originally Posted by spark
Hi Jeff,
I decided to answer your nice post as it would be unpolite to ignore it a second time. But you (in general) are ignoring for the umpteen time what I wrote.
the fundamental problem is to define the premises of your argument. If you define the axioms of your system * in a coherent, logical fashion, you can develop any theory, even the most absurd and far-fetched: non Euclidean geometry, multi dimensional universe, general relativity, superstring ...Such theory is scientific, logical, possible in theory, because it has no internal contradiction. But it has to be tested, to see if it is really possible in this world. I am not able to tell you what axioms you need to support your arguments, you may give it a try!

Here we are discussing math, mainstream current math: The only valid axioms are the ones of set theory, arithmetics : addition, subtraction, multiplication...
We all MUST follow those rules when we perform any operation. Nobody has authority to break the rules, never.
I considered it improper, diminishing to remind scientists what they are, but , if it is necessary, here we are:
you can not add apples and bananas, apples and koalas
you can multiply apples by koalas, crates by boxes in certain circumstances, but not forgetting multiplication is a shorthand form of addition
When you cannot, you just don't, you stop.
Now, you (mainstream) have sometime developped a theory, a system of calculus: DA, QC
I am only asking you to tell me what are the logical premises and the axioms and the rules of this Calculus, because I couldn't find a def. of Dimension, Which is the pillar of DA. The only def. I read (here) sounded like " a degree of freedom".
If you, too, cannot find one it means there is a black hole in the theory.( Just simply and honestly say so, and we move to next point, later on, I might help you make one). If you can, you know it, it is really preposterous that you haven' present it, yet!

says :" QC analogous to A, because ..."
does that mean that it has different rules ?, you know math and physics, you are scientists, it's up to you to anwer that question.
You have AR, A and QA, after you have defined Q and D you must specify what system is. Then it is easy to say : 0 = False/ True !.

if you want the mathmatical definition of a dimension or a unit, you are going to need an advanced linear algebra course/text. Even then, it boils down to 'an amount of something'.

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spark,

You replied to me but you didn't reply to anything in my post.
Instead you restated what you are after and several opinions

I'll do exactly the same. I replied to part of your original post,
pointing out a couple of problems with the example you gave.
I believe that the problems with the example are to the point.
They are not merely problems with the example involving
multiplication of children and sweets, they are problems
which explain the apparent (to you) ambiguity of p=m*v.
I'm saying that your example was a good one, and studying
is why you set out the example in the first place, isn't it?

Originally Posted by spark
There are 10 sweets, 5 children, let's multiply...
There are five children, ten sweets each, let's multiply...
In the first, short line of your "example", you presented one
scenario, but in the very next, also short line, you presented
a different scenario. At no time did you say or acknowledge
that you presented two different scenarios.

In the first scenario there are ten sweets. In the second
scenario there are ten sweets per child, or fifty sweets.

Do you agree?

If not, why not?

I will also give my opinion on something: Everything we
know is based on experience. We can use logic, such as
the logic of mathematics, to deduce what seems must be
from what we experience, but fundamentally, everything
we know is based on experience. All definitions are based
on experience. Terms must be used in any definition.
You only understand the meanings of those terms through
experience. You must begin with experience, and you can
build your definitions on that experience. You can't begin
with definitions. That just isn't possible. You need the
experience for the definitions to have any meaning.

In my opinion, you are trying to define things which
must be learned through experience.

-- Jeff, in Minneapolis

22. For those who are wondering about the "VIM3", that is the "International Vocabulary of Metrology, 3rd edition", see wikipedia here

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I didn't realize other people were confused by his use of "x", too!

He uses bits of English and bits of math, but the resulting mix is
a language I don't recognize and can't read.

Can you do something to fix that, spark?

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
I didn't realize other people were confused by his use of "x", too!

He uses bits of English and bits of math, but the resulting mix is
a language I don't recognize and can't read.

Can you do something to fix that, spark?

-- Jeff, in Minneapolis
sure, jeff, x is the math symbol of multiplication.
you can substitute it in all instances.
I use it just as a strong reminder that the issue here is D x D = Q

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