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Author Topic: Numbers 1*1=2  (Read 8184 times)

Offline alancalverd

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Re: Numbers 1*1=2
« Reply #25 on: 21/04/2015 23:49:16 »
There is a more general definition of vectors, which can have any number of dimensions, but the interesting aspect of simple vector arithmetic is the difference between the vector product ("cross product", AxB) and the scalar product ("dot product", A.B) of two vectors. A great deal of physics comes down to the sums and products of vectors!
 

Offline Colin2B

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Re: Numbers 1*1=2
« Reply #26 on: 21/04/2015 23:59:40 »
Vector operations you mean like x,y,z, and time?   

No, used in this way x,y,z and t are coordinates that can define a vector.

velocity and magnitude.
Velocity is a vector quantity, magnitude is scalar.
A vector has magnitude and direction, scalar quantity only has a magnitude.
By vector operations Alan means addition, subtraction, scalar multiplication, dot product, cross product, triple product, etc.

Edit: sorry Alan, hadn't noticed you post before I replied.
« Last Edit: 22/04/2015 00:10:14 by Colin2B »
 

Offline Thebox

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Re: Numbers 1*1=2
« Reply #27 on: 22/04/2015 00:15:05 »
There is a more general definition of vectors, which can have any number of dimensions, but the interesting aspect of simple vector arithmetic is the difference between the vector product ("cross product", AxB) and the scalar product ("dot product", A.B) of two vectors. A great deal of physics comes down to the sums and products of vectors!

isn't a vector an imaginary line from A-B?
 

Offline Thebox

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Re: Numbers 1*1=2
« Reply #28 on: 22/04/2015 00:16:10 »
Vector operations you mean like x,y,z, and time?   

No, used in this way x,y,z and t are coordinates that can define a vector.

velocity and magnitude.
Velocity is a vector quantity, magnitude is scalar.
A vector has magnitude and direction, scalar quantity only has a magnitude.
By vector operations Alan means addition, subtraction, scalar multiplication, dot product, cross product, triple product, etc.

Edit: sorry Alan, hadn't noticed you post before I replied.

x,y,z are imaginary lines also?
 

Offline Colin2B

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Re: Numbers 1*1=2
« Reply #29 on: 22/04/2015 08:25:31 »
x,y,z are imaginary lines also?
If you imagine them, they are imaginary  :)

Seriously, with coordinates it's usually accepted that they are a construct we use for convenience. Usually, as you are aware, we draw them on paper to help our calculations, but often we don't need to - that's the value of having operators.

If you are going to look at vectors, start with breaking into components then combining vectors (vector addition). Those two along with constructing them will take you a long way. You'll find you are already familiar with most of it.

If you look at Boolean algebra it's also worth looking at sets and Venn diagrams. Again you'll recognise a lot of it, particularly as you have worked with computers, because truth tables and gate logic are in there and (along with Venn diagrams) can help people to visualise what is happening with the operators.

Have fun, that's what it's all about.





 

Offline Thebox

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Re: Numbers 1*1=2
« Reply #30 on: 22/04/2015 16:53:34 »
x,y,z are imaginary lines also?
If you imagine them, they are imaginary  :)

Seriously, with coordinates it's usually accepted that they are a construct we use for convenience. Usually, as you are aware, we draw them on paper to help our calculations, but often we don't need to - that's the value of having operators.

If you are going to look at vectors, start with breaking into components then combining vectors (vector addition). Those two along with constructing them will take you a long way. You'll find you are already familiar with most of it.

If you look at Boolean algebra it's also worth looking at sets and Venn diagrams. Again you'll recognise a lot of it, particularly as you have worked with computers, because truth tables and gate logic are in there and (along with Venn diagrams) can help people to visualise what is happening with the operators.

Have fun, that's what it's all about.

I always have fun, it is often other members who try to stop me enjoying and having fun whilst learning.   I see vectors as trajectory path, I do not really see any problems in calculating a trajectory as long as there is some form of semi fixed point.
« Last Edit: 22/04/2015 16:55:14 by Thebox »
 

Offline Colin2B

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Re: Numbers 1*1=2
« Reply #31 on: 22/04/2015 19:45:04 »
I always have fun, it is often other members who try to stop me enjoying and having fun whilst learning. 
Ahh, shame on them, spoiling your fun ;D


I see vectors as trajectory path, I do not really see any problems in calculating a trajectory as long as there is some form of semi fixed point.
That's ok, but some of the vectors might be transitory.
Take the trajectory of a ball thrown in a g field. At any point in it's trajectory there will be a vector tangential to it's curve describing it's instantaneous speed and direction. Each point on the curve could be considered your semi fixed point.  If your cool with that, then we're on a similar wavelength.

There are other vectors which describe not a trajectory, but the forces acting on an object.

Some vectors, position vectors, just describe the relationship between points or vectors.

There are also component and computation vectors which we construct to help with calculations and understanding.

(And more!)

I assume you are ok with those?
« Last Edit: 22/04/2015 20:08:41 by Colin2B »
 

Offline Thebox

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Re: Numbers 1*1=2
« Reply #32 on: 22/04/2015 20:39:17 »
I always have fun, it is often other members who try to stop me enjoying and having fun whilst learning. 
Ahh, shame on them, spoiling your fun ;D


I see vectors as trajectory path, I do not really see any problems in calculating a trajectory as long as there is some form of semi fixed point.
That's ok, but some of the vectors might be transitory.
Take the trajectory of a ball thrown in a g field. At any point in it's trajectory there will be a vector tangential to it's curve describing it's instantaneous speed and direction. Each point on the curve could be considered your semi fixed point.  If your cool with that, then we're on a similar wavelength.

There are other vectors which describe not a trajectory, but the forces acting on an object.

Some vectors, position vectors, just describe the relationship between points or vectors.

There are also component and computation vectors which we construct to help with calculations and understanding.

(And more!)

I assume you are ok with those?

I had to look up transitory, the thing is with all vectors in my opinion, they are never really there and it is a bit like dot to dot, i.e a cannon balls curvature path. 

we can plot a curve from a-b, and calculate speed over distance etc, we can use the ground to define a plane, and place points at different heights to represent the curve.


''there are also component and computation vectors which we construct to help with calculations and understanding.''

can you please expand this?
 

Offline Colin2B

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Re: Numbers 1*1=2
« Reply #33 on: 22/04/2015 22:30:17 »
''there are also component and computation vectors which we construct to help with calculations and understanding.''

can you please expand this?

Let's take your example:

we can plot a curve from a-b, and calculate speed over distance etc, we can use the ground to define a plane, and place points at different heights to represent the curve.

You are using the ground as a reference plane and perpendicular to that a line representing height.
Let's say at a particular point your ball has a velocity of 14 units, 45 upwards.
We can imagine that this velocity vector is composed of 2 vectors (component vectors) one parallel to the ground plane and one upwards. If you use right angled triangles you can work out that each has a magnitude of almost 10 units. So this tells us how fast your ball is rising vertically and how fast it is travelling horizontally (at that point in time).
You can do the same with forces, even though the forces are stationary eg reaction forces, and don't represent any trajectory.
Useful?


I had to look up transitory, the thing is with all vectors in my opinion, they are never really there and it is a bit like dot to dot, i.e a cannon balls curvature path. 


But the movement, velocity and forces are real. We are only using numbers, lines, angles, coordinates as a way of describing what is happening.
Some of the vectors have a very real effect.
Let's say you are in a boat with no wind, if the boat moves forward you will feel a wind in your face, but there is no wind blowing! We can describe that apparent wind with a vector of equal magnitude to the boat speed but in the opposite direction to that of travel.
Now let's add a real wind blowing at 90 over the side of the boat, let's say for convenience that the wind is equal to the boat speed. You don't feel 2 winds blowing, one from the side and one from the front, you feel a single wind blowing from 45 between ahead and the side. This wind is very real even though it is termed the apparent wind, and it is the resultant of the 2 wind vectors, one from ahead the other from the side.
« Last Edit: 22/04/2015 22:58:10 by Colin2B »
 

Offline Thebox

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Re: Numbers 1*1=2
« Reply #34 on: 23/04/2015 00:14:24 »




You are using the ground as a reference plane and perpendicular to that a line representing height.
Let's say at a particular point your ball has a velocity of 14 units, 45 upwards.
We can imagine that this velocity vector is composed of 2 vectors (component vectors) one parallel to the ground plane and one upwards. If you use right angled triangles you can work out that each has a magnitude of almost 10 units. So this tells us how fast your ball is rising vertically and how fast it is travelling horizontally (at that point in time).
You can do the same with forces, even though the forces are stationary eg reaction forces, and don't represent any trajectory.
Useful?




But the movement, velocity and forces are real. We are only using numbers, lines, angles, coordinates as a way of describing what is happening.
Some of the vectors have a very real effect.
Let's say you are in a boat with no wind, if the boat moves forward you will feel a wind in your face, but there is no wind blowing! We can describe that apparent wind with a vector of equal magnitude to the boat speed but in the opposite direction to that of travel.
Now let's add a real wind blowing at 90 over the side of the boat, let's say for convenience that the wind is equal to the boat speed. You don't feel 2 winds blowing, one from the side and one from the front, you feel a single wind blowing from 45 between ahead and the side. This wind is very real even though it is termed the apparent wind, and it is the resultant of the 2 wind vectors, one from ahead the other from the side.


Ok, I think I understand what you are saying, I would personally generalise this to mostly being products of speed and forces and direction, does not sound to difficult.


 

Offline PmbPhy

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Re: Numbers 1*1=2
« Reply #35 on: 23/04/2015 04:51:19 »
Quote from: Thebox
I always have fun, it is often other members who try to stop me enjoying and having fun whilst learning.
What total nonsense that is. Nobody is trying to stop you from having fun. What a silly paranoid claim. What people are doing are explaining your mistakes to you when you post the nonsense that you're widely known for in this forum.
 

Offline Colin2B

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Re: Numbers 1*1=2
« Reply #36 on: 23/04/2015 09:39:44 »
,,,,,, I would personally generalise this to mostly being products of speed and forces and direction, does not sound to difficult.
No, it's not too difficult, and you are right about the products (resultants) of speed and direction. That is using a scientific method. But note that none of the vectors are related to a point!

But let me ask you a question, which way is the wind blowing?
There are many ways to measure wind direction. We can turn so the wind blows in our face, we can look at a flag, watch smoke, even use a wind vane. All point 45.
So our senses and instruments all show 45.
But as you often tell us, your senses tell the real truth, what you see is reality.
So this must be more than the products of speed and direction, it must be reality, and in the middle of an ocean at night it would be hard to tell different.
When considering science, we are often in this position where our senses fool us and we don't see the full picture.
In this case it is easy to use relativity and say from the point of view of the boat the wind is 45, but from an observer on the shore it is blowing across the boat side, but in many situations we have to look beyond the seemingly obvious.
 

Offline Thebox

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Re: Numbers 1*1=2
« Reply #37 on: 23/04/2015 12:59:21 »
,,,,,, I would personally generalise this to mostly being products of speed and forces and direction, does not sound to difficult.
No, it's not too difficult, and you are right about the products (resultants) of speed and direction. That is using a scientific method. But note that none of the vectors are related to a point!

But let me ask you a question, which way is the wind blowing?
There are many ways to measure wind direction. We can turn so the wind blows in our face, we can look at a flag, watch smoke, even use a wind vane. All point 45.
So our senses and instruments all show 45.
But as you often tell us, your senses tell the real truth, what you see is reality.
So this must be more than the products of speed and direction, it must be reality, and in the middle of an ocean at night it would be hard to tell different.
When considering science, we are often in this position where our senses fool us and we don't see the full picture.
In this case it is easy to use relativity and say from the point of view of the boat the wind is 45, but from an observer on the shore it is blowing across the boat side, but in many situations we have to look beyond the seemingly obvious.

An honest answer to which way the wind blows , would be no direction, direction at the moment is figurative to speech and pointing at nothing.

A arbitrary answer would relate to the dynamics of any spinning object and aerodynamic displacement of air.

Technically the wind does not really blow.
« Last Edit: 23/04/2015 13:01:30 by Thebox »
 

Offline alancalverd

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Re: Numbers 1*1=2
« Reply #38 on: 23/04/2015 19:50:04 »

isn't a vector an imaginary line from A-B?

You can often represent a vector with a line, but it's rather more general than that,
 

Offline alancalverd

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Re: Numbers 1*1=2
« Reply #39 on: 23/04/2015 19:54:42 »

Technically the wind does not really blow.

I thank the powers that be, that you weren't flying in my vicinity today. According to all the instruments on all the aeroplanes and airports, the wind was indeed blowing, in all sorts of directions and at all sorts of speeds. Indeed there were quite a few wind vectors about. If any one of us had taken you at your word, several of us would be dead.

If you want to consider the dynamics of spinning objects, you would do well to read up on the hairy ball theorem and absorb the concept of a spin vector.
 

Offline Aemilius

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Re: Numbers 1*1=2
« Reply #40 on: 23/04/2015 22:46:56 »
an empty 1 can only equal zero or nothing.

Exactly.... one can never be greater than none! I, for one, have always thought it was a singular mistake for any one to think one could be greater than none no matter what one thinks one is, even if it's an empty one one is considering, nor could any one say that a full one, or even a half empty/full one is equal to none either because, as every one knows, if we go by the letter of the law....

One none can only equal one none....


....and one one can only equal one one....


....but one one is only seventy-five percent of one none....


....even though one none is one hundred and thirty-three point three three etc. percent of one one....


Very simple when one thinks about it.
« Last Edit: 24/04/2015 02:01:40 by Aemilius »
 

Offline Colin2B

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Re: Numbers 1*1=2
« Reply #41 on: 23/04/2015 23:55:25 »
An honest answer to which way the wind blows , would be no direction, direction at the moment is figurative to speech and pointing at nothing.

A arbitrary answer would relate to the dynamics of any spinning object and aerodynamic displacement of air.

Technically the wind does not really blow.

Whatever!

I'm off to look at the weather forecast, find out what the wind speed and direction is predicted for tomorrow.
 

Offline Aemilius

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Re: Numbers 1*1=2
« Reply #42 on: 24/04/2015 00:41:13 »
I'm off to look at the weather forecast, find out what the wind speed and direction is predicted for tomorrow.

Me too, maybe go sailing. Puget Sound and Lake Washington here in the Northwest is perfect for it.... and the non-blowing wind is surprisingly forceful!
 

Offline yor_on

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Re: Numbers 1*1=2
« Reply #43 on: 25/04/2015 18:38:57 »
You should be pleased Box, there are some people of good imagination answering you here. Then there are logic naturally. Logic is defined by your limits. When you set natural numbers as something complementary to your definitions of 'nothing' you make it more complicated than it needs to be. On the other tentacle you make it new :) and make people consider what you might mean by it. That's one of the things that makes TNS a place to have fun on.
 

Offline EEK

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Re: Numbers 1*1=2
« Reply #44 on: 04/05/2015 00:28:32 »
1 x 1 = 1 ; means, Go 1 unit on x-axis and then 1 units on y-axis, we get 1 unit square
0 x 0 = 0 means, Go 0 units on x-axis and then 0 units on y-axis, we get 0 unit square

Although we write sometimes for simplicity 3 x 2 = 2 + 2 + 2 but technically this wrong as per dimensional analyses. Reasons:

On LHS, we get 6 unit square which is dimension of AREA while
On RHS we simply get 6 unit which is the dimension of LINE
 

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Re: Numbers 1*1=2
« Reply #45 on: 04/05/2015 03:05:07 »
1 something*1 nothing = 1

1 nothing * 1 nothing = 0


an empty 1 can only equal zero or nothing.

Brilliant! You just figured out the hidden logic early mathematicians left for us. I remember using 'empty' numbers yesterday. How did I use them? Well, I just thought of numbers and I multiplied them and so on. There was no point really. People use empty numbers ALL THE TIME. This post of yours could help those people by assigning those numbers to something (How productive would that be!!). How could we have ever thought of that. Alas, now we know that the early mathematicians used numbers to count or... Or add something which they could visually see. Pure genius of you!
Now let me get back to my 'non-sarcasm' mode. HOW ON THE EARTH did you manage to not educate yourself with the fact that numbers were made for calculating things we could visually see or in nature, to know a particle's behavior so on. What.. WHAT in the world were you trying to imply by 'empty' numbers?
 

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Re: Numbers 1*1=2
« Reply #46 on: 04/05/2015 03:17:52 »
You should be pleased Box, there are some people of good imagination answering you here. Then there are logic naturally. Logic is defined by your limits. When you set natural numbers as something complementary to your definitions of 'nothing' you make it more complicated than it needs to be. On the other tentacle you make it new :) and make people consider what you might mean by it. That's one of the things that makes TNS a place to have fun on.

Aw... Come on, Yor_on! I respect you but please don't motivate Mr.Box. This topic he posted is... In simple terms, sh1t! Complete utter sh1t!
Logic is defined by your limits? What is that supposed to mean?
'He (The Box) makes it new?' seriously? How... By defining the purpose of why maths was essentially made, on a forum meant for adults?
« Last Edit: 04/05/2015 03:20:13 by Jasper Hayden »
 

Offline Colin2B

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Re: Numbers 1*1=2
« Reply #47 on: 04/05/2015 07:24:05 »
On RHS we simply get 6 unit which is the dimension of LINE
But you could consider 6 children's building blocks arranged in a 2x3 rectangle?
 

Offline Thebox

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Re: Numbers 1*1=2
« Reply #48 on: 04/05/2015 09:00:29 »
1 something*1 nothing = 1

1 nothing * 1 nothing = 0


an empty 1 can only equal zero or nothing.

Brilliant! You just figured out the hidden logic early mathematicians left for us. I remember using 'empty' numbers yesterday. How did I use them? Well, I just thought of numbers and I multiplied them and so on. There was no point really. People use empty numbers ALL THE TIME. This post of yours could help those people by assigning those numbers to something (How productive would that be!!). How could we have ever thought of that. Alas, now we know that the early mathematicians used numbers to count or... Or add something which they could visually see. Pure genius of you!
Now let me get back to my 'non-sarcasm' mode. HOW ON THE EARTH did you manage to not educate yourself with the fact that numbers were made for calculating things we could visually see or in nature, to know a particle's behavior so on. What.. WHAT in the world were you trying to imply by 'empty' numbers?

I am not implying anything, I am simply stating zero point space and the fact that numbers are pretty meaningless and made to fit a process.   Science always argues with me to produce the maths, because apparently maths is the god of science, except this sis not really true.  Every famous equation there ever was is not really special in any way, it is only arbitrary to our use and not relative to the universe.

 
 

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Re: Numbers 1*1=2
« Reply #48 on: 04/05/2015 09:00:29 »

 

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