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In reality, one would seldom multiply bananas by bananas. I brought that up to help you understand the point. If you want to multiply a quantity of something - you multiply by a pure number, not by a number of items.

You have to consider
1) what each term means (what does multiplication *mean*)? and
2) what are the applicable rules (properties that apply)


Paul wrote, regarding bananas^2: "is wrong."

No. It's not wrong. You think it's wrong, because you haven't made any effort to understand it. Have you EVER driven a car? Have you EVER taken a plane or a train or a ship? Anyone who built any of those devices use the same math - and always have.


Paul: 4*4=16
Correct ... however, you continue ...

Paul: ... of course = 4(units)^2 = 4bananas^2
nope. 4*4 <> 4(units)^2


Paul: and 4(units)^2 = 16 (units)
again. nope.

Paul, What harm is there in learning the rules, BEFORE you write them off? They exist for a reason. Humanity has thought about this for thousands of years. Learn them. Practice them. It's NOT beyond your intelligence; but it IS currently beyond your ego and beyond your patience.

If you learn the rules and practice them, you begin to understand HOW it all fits together and WHY the rules are what they are. You get a remarkable simplicity - and more than that, you get a beautiful consistency.

.
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I understand that you don't agree with any of this.

Do you at least accept that the entire technical world agrees with what kallog and I have said - or do you think we're just making stuff up? (If someone strongly disagreed about basic math with the creator of Mathematica, you would think it would be big news.)

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paul Offline OP
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I could be discussing this with TFF but its like algebra
its a total waste of time and effort.
having a discussion with TFF serves no usefull purpose.
I once wrote to him and said.

Quote:
I believe this concludes my discussion with you.


and what I said was what I meant.


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Originally Posted By: paul
I could be discussing this with TFF but its like algebra
its a total waste of time and effort.
having a discussion with TFF serves no usefull purpose.
I once wrote to him and said.

Quote:
I believe this concludes my discussion with you.


and what I said was what I meant.



Did actually think algebra itself is a total waste of time and effort?

Do you accept at least that I'm using the same math that every other technical person on the planet is using?

Do you understand that you're not just disagreeing with kallog and me? That you are actually disagreeing with EVERY scientist, mathematician, and engineer on the planet?

That is, do you understand that the scientists and mathematicians that you applaud use math the same way that kallog and I do?

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paul Offline OP
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somewhere I heard that there was another website that you can use to perform calculations at.

it is

http://web2.0calc.com/

I entered (2) then pressed the (x)2 button then pressed the (multiply) button
then entered (2) and pressed the (x2) button then pressed the (equals) button.

here is the order of buttons I pressed

2
x2
x
2
x2
=

this calculator performs correct math

it returns 16

which is the correct number that you get when you multiply
2^2 * 2^2 = 16

because 2^2 = 4

so 4*4=16

I looked in the help section to see if the calculator would perform calculations that included ft I couldnt find ft in the help section so I tried the following equations.
and below are the sickening results.

4ft^4*4ft^4=0.00119189962736[m^8]

however when I didnt use units it delivers correct answers

2*2=4
and
2^2*2^2=16

so It looks as if the calculator can do simple math as long as you dont enter units.

you should already know what the units are anyway.

and units shouldnt be multiplied in the first place
the program is programed to deliver a correct answer
only when a correct equation is entered into it.

to test this I typed in

2 bananas * 2 bananas =

and it couldnt supply a result

then I typed in

2*2=

and it responded with

2*2=4

which is correct

I noticed that it didnt say

2*2=4^2

because it would have given a wrong result if it had and
it hasnt taken algebra because it cant so it still has enough brains to figure that simple equation out and deliver a correct result.

unlike many people today who think they can , but in reality only issue garbage out when they do calculations.




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I mentioned that site in a previous email. It may not have a symbol for "ft", but you can just type in the ft. IIRC, the problem is that it will automatically convert to meters which will confuse matters.

Cut n paste the following into it: 2m^2 * 2m^2

The "m" means meters. It returns the correct result.

The cut n paste the following: (2m)^2 * (2m)^2

Should be a different answer. The CONVENTION is that the square only applies to the next nearest thing to the left - no matter what that thing (variable, constant, unit, function) UNLESS the order is altered by parentheses.

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I'm not asking you to believe anything.

I'm not asking you to accept anything that doesn't make any sense to you.

I'm not even asking you to admit you're wrong - or even that you MIGHT BE wrong.

I'm asking you for simple, yes/no answers to these questions.

A) Do you actually think algebra itself is a total waste of time and effort?

B) Do you accept at least that I'm using the same math that every other technical person on the planet is using?

C) Do you understand that you're not just disagreeing with kallog and me - that you are actually disagreeing with EVERY scientist, mathematician, and engineer on the planet?

D) That is, do you understand that even the scientists and mathematicians that you applaud use math the same way that kallog and I do?

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someone requested that I type in
2m^2*2m^2

so I did and the result was
4m^4

what a ridiculous result!!

2 meters squared = 4 square meters
if I multiply 4 sq meters * 4 sq meters my result that
I get using logical calculations equals 16 sq meters.

4*4=16

but logic might not be in play anymore
when simple multiplication is required.

I expect to see more and more structural failure in the near future.


because idiots seem to be overtaking more than just politics.

http://en.wikipedia.org/wiki/List_of_structural_failures_and_collapses

from the looks of it , Im right

we build less and less structures and more fall down.

IDIOTS

it might be that people who are forced to take subjects like algebra in order to take other subjects that are beneficial to their future actually end up thinking that algebra actually has something to do with reality.

so they apply the crap results of the example above when designing structures and of course the structures fall down.

they needed 16 square meters of steel plate but they only used 4m^4

whatever that is.

what does 4m^4 mean in the real world?
and explain how you determined what it means.
quantify it.

what does the stupid 4m^4 represent?

Quote:
However, in algebra the variables stand for a number that gets multiplied by the number attached to it (no signs between letters and numbers means multiply).


Quote:
2bananas * 2bananas = 4bananas^2 ( Four Bananas Squared )


(2*bananas)*(2*bananas)=4bananas^2

(no signs between letters and numbers means multiply)
so your answer is wrong by definition

according to the above by definition in algebra it would be

(2*bananas)*(2*bananas) = 4*bananas^2( Four Times Bananas Squared )

so in essence the above has no value at all!!
it was a waste of time talking about algebra.

Quote:
in algebra the variables stand for a number that gets multiplied by the number attached to it


because bananas is not a number that has a value
it must be a variable
and because bananas has no value.
and 2 is attached to bananas so 2*bananas = 0
and because no information was given for the
ananas variables the ananas variable has no value either.

therefore

(2*b*ananas)*(2*b*ananas) = 4*b*ananas^2( Four Times B Times ananas Squared )

(2*0*0)*(2*0*0) = 0

there is no reason to square your result so the equation becomes

(2*b*ananas)*(2*b*ananas) = 4*b*ananas( Four Times b Times ananas )
the equation is now

(0)*(0)= 0

because 2*0=0
and 2*0*0 = 0
and 4*0*0 = 0
so (0)*(0)= 0

which is ridiculous by definition.
or basically its just ridiculous definition or not.

most people who have even the least amount of cognitive powers dont need such stupid crap as the above to make a large portion of their day seem as if a day isnt really worth much .

especially when that large portion of their years of studying for a worthwhile career could have allowed them to study courses that actually have value.


Quote:
A) Do you actually think algebra itself is a total waste of time and effort?


YES I DO!!!
Absolutely




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There have been structural failures. There's no evidence that these were caused by using standard algebra. If standard algebra were the cause, you would expect a lot more failures than that, because it is used hundreds of times a day by the engineers who are making new products, building bridges, cars, etc. We should expect THOUSANDS of failures every day from all over the world.

Without even hinting that you might be wrong, can you please answer the following questions clearly with a "yes" or "no"?

A) Do you actually think algebra itself is a total waste of time and effort?

B) Do you accept at least that I'm using the same math that every other technical person on the planet is using?

C) Do you understand that you're not just disagreeing with kallog and me - that you are actually disagreeing with EVERY scientist, mathematician, and engineer on the planet?

D) That is, do you understand that even the scientists and mathematicians that you applaud use math the same way that kallog and I do?


Last edited by TheFallibleFiend; 10/05/11 08:45 PM.
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Originally Posted By: paul
Quote:
Are you sure?

I suppose I should rephrase that.
2 anythings * 2 anything = 4 anythings
as long as the anything are the same units.
the answer would also be delivered in anything units.


Only with units?
2x * 2x <> 4x
2m * 2m = 4m

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Originally Posted By: paul
soaccording to the above by definition in algebra it would be

(2*bananas)*(2*bananas) = 4*bananas^2( Four Times Bananas Squared )


YES!

Quote:

so in essence the above has no value at all!!


Huh? It's a perfectly useful answer, just like
3m * 4m = 12m^2 (12 square meters)
which tells us the area of a 2m*4m rectangle.

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paul Offline OP
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Quote:
3m * 4m = 12m^2 (12 square meters)
which tells us the area of a 3m*4m rectangle.


YES

EXACTLY

12m^2 (12 square meters)

not

12m^2 (12 meters squared)

(four bananas squared)

a simple typo that turned into a long argument that could
have been solved simply by admitting his typo.










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It's not a typo. They mean the same thing.

1 meter^2 = 1 meter squared = 1 square meter

Often (not always) engineers will refer to meter-squared.
Usually (not always) lay people refer to square meters.

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Originally Posted By: TheFallibleFiend
1 meter^2 = 1 meter squared = 1 square meter


Hmm I thought I replied before but it seems to have vanished.

We can at least agree on something:

3m * 4m = 12 square meters
3ft * 4ft = 12 sq ft


But then we still can't solve the problem which kicked this off:

80N * 50s = 4000N ??

Paul's way doesn't tell us how to decide what units the answer should have. So we're helpless when faced with:

80 bananas * 50 apples = 4000 bananas ??

80 m/s/s * 50 s = 4000 m/s/s ??

80 kg.m/s/s * 50 s = 4000 kg.m/s/s ??

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Originally Posted By: kallog

80N * 50s = 4000N ??



Paul says: 80N * 50s = 4000N

As you have pointed out previously, this equality can't be an equality, because it has different units on each side. That is, it fails the test of dimensional analysis.

No amount of feet, nor any amount of pounds can equal 10 seconds. On the left we have some # of N times some # of s, but on the right we only have some number of N. This is the problem with Paul's system: the equal sign doesn't actually mean "equal" the way he's using it.

Once again, he disagrees with every technical person on the planet. We cut-n-paste "80N * 50s" into http://www.wolframalpha.com/ and the result comes up: 4000 N s (newton seconds)

Wolfram says you're right. Every other scientist, engineer, and mathematician on the planet says you're right.

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Originally Posted By: TheFallibleFiend
As you have pointed out previously, this equality can't be an equality, because it has different units on each side. That is, it fails the test
...
Wolfram says you're right. Every other scientist, engineer, and mathematician on the planet says you're right.


Yea trouble is those arguments are too easy to persuade Paul! And in fact they don't necessarily apply if he has a consistent system. Our way of using units happens to be all nice and beautiful and works perfectly, but that doesn't mean some other system (Paul's) won't work.

I just don't quite understand the rules. If they were clearer then it would be easy to look for internal inconsistencies to disprove it without invoking "the way everybody else does it". The "equals sign means equal" doesn't really work unless you already assume a meaning for "Ns" It doesn't mean "newtons times seconds" in Paul's system because you're don't multiply units there.

There are other systems in common use. For example this formula for hull speed of a boat:

velocity in knots=1.35 x sqrt(waterline length)

That clearly fails dimensional analysis, but it will still be correct using a different convention.

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I don't have an issue with Paul disagreeing - only with his being disagreeable - insisting that everyone else is an idiot.

The thing is he hasn't learned the "correct" way sufficiently to criticize it.

He also hasn't thought through the implications of what he is saying; namely, that even the scientists whose work he finds acceptable use the same math that everyone else uses.

If equal doesn't mean "equal" then you eventually end up with inconsistencies.

I'm not familiar with the formula you give, but it can easily be made dimensionally consistent by putting the correct units as part of the constant. Technically, the formula is incorrect - even if it works.

For example, there are people who will say that you can multiply the number of feet by 12 to give you inches. This also works, but is incorrect. It doesn't matter in the simplest cases, but losing the units on more complicated problems is a recipe for disaster.

1) Using his method, we lose one of the most basic checks - dimensional consistency.

2) Using his method, we are at a fundamental inconsistency:
1m * 1m = 1m^2, BUT
m^2 * m^2 <> m^4

3) Using his method, we lose the ability to communicate with the rest of the technical people.

4) If the standard way of addressing this were as far off as Paul insists, then we should literally be having 1000s of colossal engineering failures every day.

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http://simple.wikipedia.org/wiki/Square_metre

Quote:
A square metre is not the same as a meter square, an area 2 metres wide by 5 metres long would be 10 square metres, in contrast 10 metres squared means an area 10 metres by 10 metres. So 10 metres squared = 100 Square meteres.



Quote:
(four bananas squared)


is 4 * 4 = 16

believe it or not.

I knew it wasnt a typo , I was just giving you a face out.
that you didnt take.

Quote:
I don't have an issue with Paul disagreeing - only with his being disagreeable - insisting that everyone else is an idiot.


you were wrong and you are also stupid enough to not admit it.

http://en.wikipedia.org/wiki/Idiot

even though we have tried to explain to you the difference between square and squared you insist that square and squared have the same meaning , therefore my usage of the term idiot.








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Quote:
But then we still can't solve the problem which kicked this off:

80N * 50s = 4000N ??


I suppose I should have used

4000N/50 seconds


I just thought that it was clear because the 80N was being applied for 50 seconds.

because the time is inside the Newton already !!!

1N = 1kg * 1m/s^2

so if I apply a force of 1N to a 1kg mass for 50 seconds
the mass will accelerate at a rate of 1m/s/s for 50 seconds
the total amount of force that was applied to the 1kg mass was 1N times 50 seconds which equals 50N

1N * 50 seconds = 50N

like if I use 1000 watts * 50 hours = 50,000 watts or 50kwh.

you wouldnt write the above like

1000 watts * 50 hours = 50,000 watts / 50 hours !!!

and TFF were not doing or trying to do algebra so dont even
attempt to to inject that stupid crap anymore , I will not even consider
that the information is comming from a reliable source.











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The words are ambiguous. The notation is not.

Wiki is not the most reliable source, however, it does give good links usually - and that's true in this case. Their reference is Dr. Math and I find him usually dependable.

Wolfram gives a result I expect:
http://www.wolframalpha.com/input/?i=10+meters+squared

However, unlike you I

1) can admit that I might possibly be wrong, and
2) am not afraid to consult someone who knows more than I do,

so I will send an email to Dr. Weisstein at Mathworld to ask for clarification.

If there is an inconsistency here, it's only in the words which are ambiguous and not in the notation.

---
Here's the message I just sent to Mathworld.

Inconsistency.

According to http://mathforum.org/dr.math/
10 meter squared <> 10 square meters

However, Wolfram Alpha provides a different result:
http://www.wolframalpha.com/input/?i=10+meters+squared

Could this be the result of an inconsistency between British and American usage?

It seems clear that using standard notation eliminates the inconsistency: 2m * 2m = 4m^2 (regardless of whether one calls it four meters squared or 4 square meters)

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