A misunderstanding about multiplication

[Deepak Kapur]

I have a small room. 6m by 5m.

I want to get it carpeted so I compute its area.

Area= 6m × 5m = 30m2 ( metre square).

 

But....

 

Muliplication is also repeated addition..

so, I add 6m + 6m + 6m + 6m + 6m..... but I get the answer 30m and not 30m2.

 

My point is...

 

Irrespective of how we do multiplication the answer (including the units) should be same....

 

but by repeated addition I get the same numerical value but not the same units.

 

1. Either mathematics does not depict nature/reality properly.

Or

2. I am insane.

Edited June 7, 2015 by Deepak Kapur

[Delta1212]

6m + 6m + 6m + 6m + 6m is not 6m * 5m. It is 6m * 5, which is 30m.

 

You are actually adding 5 6m by 1m rectangles, so it's (6m * 1m) + (6m * 1m) + (6m * 1m) + (6m * 1m) + (6m * 1m) or 30 square meters.

[Deepak Kapur]

6m + 6m + 6m + 6m + 6m is not 6m * 5m. It is 6m * 5, which is 30m.

You are actually adding 5 6m by 1m rectangles, so it's (6m * 1m) + (6m * 1m) + (6m * 1m) + (6m * 1m) + (6m * 1m) or 30 square meters.

A great reply, Thanks

 

...however....I will think over this..

[studiot]

Good snappy response deta1212.

 

+

[Sensei]

2. I am insane.

3. You don't know how to multiply units.

 

You have line with length a=3 m (in axis x)

it's straight line.

 

You have another line with length b=2 m (in axis z)

it's also straight line, perpendicular to first line.

 

m*m=m^2

Meter * meter (distance unit) = meter square (area unit)

 

3m * 2m = 6m^2

 

Then if you add yet another dimension, c=4m, axis in y:

m*m*m=m^3

Meter * meter * meter (distance unit) = meter cubic (volume unit)

 

3m * 2m * 4m = 6m^2 * 4m = 24m^3

 

Actually your room has 3rd dimension- height.

So you can actually calculate volume of your room. And also tell us how much air is there.

From it you can calculate amount of Nitrogen, amount of Oxygen, amount of CO₂, Krypton, Neon, etc.

Edited June 8, 2015 by Sensei

[Deepak Kapur]

3. You don't know how to multiply units.

You have line with length a=3 m (in axis x)

it's straight line.

You have another line with length b=2 m (in axis z)

it's also straight line, perpendicular to first line.

m*m=m^2

Meter * meter (distance unit) = meter square (area unit)

3m * 2m = 6m^2

Then if you add yet another dimension, c=4m, axis in y:

m*m*m=m^3

Meter * meter * meter (distance unit) = meter cubic (volume unit)

3m * 2m * 4m = 6m^2 * 4m = 24m^3

Actually your room has 3rd dimension- height.

So you can actually calculate volume of your room. And also tell us how much air is there.

From it you can calculate amount of Nitrogen, amount of Oxygen, amount of CO₂, Krypton, Neon, etc.

I know all of this...anyway thanks....

 

My point was about repeated addition of dimensions/units...It has been explained nicely already...

[conway]

see "relative mathematics" in speculation thread.

[swansont]

see "relative mathematics" in speculation thread.

 

 

!

Moderator Note

 

Or not

 

Rule 2.5

Stay on topic. Posts should be relevant to the discussion at hand. This means that you shouldn't use scientific threads to advertise your own personal theory

 

[michel123456]

I have a small room. 6m by 5m.

I want to get it carpeted so I compute its area.

Area= 6m × 5m = 30m2 ( metre square).

 

But....

 

Muliplication is also repeated addition..

so, I add 6m + 6m + 6m + 6m + 6m..... but I get the answer 30m and not 30m2.

 

My point is...

 

Irrespective of how we do multiplication the answer (including the units) should be same....

 

but by repeated addition I get the same numerical value but not the same units.

 

1. Either mathematics does not depict nature/reality properly.

Or

2. I am insane.

While Delta1212 was exactly to the point, the bizarre thing is indeed that when you multiply units by units you get "another unit".

I like especially this below from prof. E. Laithwaite

http://www.gyroscopes.org/papers/The%20multiplication%20of%20bananas%20by%20umbrellas.pdf

 

For example the well known c^2 is the result of the multiplication of velocity by velocity, which is (should be) something else than velocity, but who cares.

[Strange]

For example the well known c^2 is the result of the multiplication of velocity by velocity, which is (should be) something else than velocity

 

It obviously IS something other than velocity. What is your point?

[michel123456]

 

It obviously IS something other than velocity. What is your point?

Name it.

What is c^2?

[studiot]

Actually since c is a constant c² is also a constant with dimensions L²T^-2

Edited June 16, 2015 by studiot

[Strange]

Name it.

What is c^2?

 

What do you mean "name it"?

 

I choose to call it Fred.

[studiot]

 

I choose to call it Fred.

 

 

Surely an 'Albert' would be more appropriate?

 

[overtone]

If you describe multiplication as a scaling process, rather than a repeated addition, you can save yourself a lot of headaches.

[imatfaal]

!

Moderator Note

conway I have hidden your two latests posts - you were specifically told not to bring your speculation into a mainstream thread. Do not do so again - do not further derail this discussion by responding to this modnote.

 

!

Moderator Note

 

 

Michel

 

While Delta1212 was exactly to the point, the bizarre thing is indeed that when you multiply units by units you get "another unit".

I like especially this below from prof. E. Laithwaite

http://www.gyroscopes.org/papers/The%20multiplication%20of%20bananas%20by%20umbrellas.pdf

 

For example the well known c^2 is the result of the multiplication of velocity by velocity, which is (should be) something else than velocity, but who cares.

 

Whilst Professor Laithwaite's work on maglevs and other heavy duty electrical engineering was groundbreaking and highly regarded his work on gyroscopes was wrong. Even Homer nods and in this case the well-esteemed academic was captivated by gyroscopic motion and made some sweeping and not entirely correct claims. Here is a link to Doctor Hugh Hunt's page on Gyroscopes and Boomerangs which contains discussion of Professor Laithewaite's ideas. If you wish to discuss gyroscopes then I would suggest a new thread and keep this thread about units and multiplication.

 

 

[conway]

You got to be kidding me! I didn't hi jack anything. I keep both statements short. Does this mean I can't talk about multiplication at all? Just because I mentioned it in my thread. Screw this site im done dancing with these bs moderators.

[michel123456]

When you multiply units, the standard geometric representations is an orthogonal set.

For example square meters from meters:

 

_put one meter on the X axis

_put one meter on the orthogonal Y axis.

 

By multiplying the one with the other you obtain a square meter and that makes sense.

 

For other units it is not always that evident.

 

For C squared

 

_put c on the X axis

_put c on the Y axis

 

Multiplying the one with the other you obtain c squared and I am asking what sense does that make? What is the physical meaning of a velocity perpendicular to another velocity (or the same velocity) ?

 

Then you multiply this "physical meaning" with Mass and you obtain Energy.

IOW Energy can be geometricaly represented by a cube with vertices Mass, Velocity and Velocity (where Velocity=c).

And as a side note: this "physical meaning" c^2 has no name.

[Strange]

And as a side note: this "physical meaning" c^2 has no name.

 

Why do you assume that c² has a "physical meaning" or should have a name.

 

If you measure the fuel efficiency of your car in litres per kilometre, then that efficiency measure has the units of area. Does that area have any physical meaning? I don't think so.

[studiot]

 

If you measure the fuel efficiency of your car in litres per kilometre, then that efficiency measure has the units of area. Does that area have any physical meaning? I don't think so.

 

 

I've not come across that one before. +1

 

[John Cuthber]

 

Why do you assume that c² has a "physical meaning" or should have a name.

 

If you measure the fuel efficiency of your car in litres per kilometre, then that efficiency measure has the units of area. Does that area have any physical meaning? I don't think so.

Yes it does.

It's the area of the "thread" of fuel that you would have to leave on the ground if, rather than having a tank, the vehicle picked up its fuel from the floor as it went along.

 

It's a physical meaning, but not very useful.

[Myuncle]

I have a small room. 6m by 5m.

I want to get it carpeted so I compute its area.

Area= 6m × 5m = 30m2 ( metre square).

 

But....

 

Muliplication is also repeated addition..

so, I add 6m + 6m + 6m + 6m + 6m..... but I get the answer 30m and not 30m2.

 

My point is...

 

Irrespective of how we do multiplication the answer (including the units) should be same....

 

but by repeated addition I get the same numerical value but not the same units.

 

1. Either mathematics does not depict nature/reality properly.

Or

2. I am insane.

 

That's interesting. When we say 6m, we never specify 6m of what, is it 6m of tape? 6m of chalk? 6m of atoms? 6m of air? 6m of nothingness? If it's 6m of atoms, then it is not just 6m, because atoms have a thickness....

[Endy0816]

Distance or more properly length.

if you want the exact definition:

"The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second."

http://physics.nist.gov/cuu/Units/meter.html

[Epicurus]

You are correct ONLY if you count along one side of the room, instead of two. If, however, you did that same equation (6+6+6+6+6=30) twice, you get you square. I used to be a Carpenter, so I handled this type of equation constantly. While 6*5=30, the actual equation you are performing is 6x5, meaning that each side of the square (assuming the room is square) must be multiplied by it perpendicular (X*Y)tthat's why the answer for area will always contain a power (squared, cubed, fouth, fifth, etc).