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3.14 = 3 = 1 = 0 all numbers are zero unless ''activated'' by a something to give the number a meaning. 0 objects, 0 mph etc.
Methinks Mr Box is confused by the concept of dimensionless numbers. Fortunately for the existence of the universe, such dimensionless constants as e, π, and α are not zero. And annoyingly for philosophers, numerologists and mystics in general, they are not rational either!
Excellent. Then you might be interested in Boolean algebra and vector operations, which may clarify some of your statements by the use of operators that most of us understand.
Vector operations you mean like x,y,z, and time?
velocity and magnitude.
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!
Quote from: Thebox on 21/04/2015 18:16:09Vector 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.Quote from: Thebox on 21/04/2015 18:16:09velocity 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?
Quote from: Thebox on 22/04/2015 00:16:10x,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.
Quote from: Thebox on 22/04/2015 16:53:34I 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 []Quote from: Thebox on 22/04/2015 16:53:34 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?
''there are also component and computation vectors which we construct to help with calculations and understanding.''can you please expand this?
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.
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.
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.
,,,,,, I would personally generalise this to mostly being products of speed and forces and direction, does not sound to difficult.
Quote from: Thebox on 23/04/2015 00:14:24,,,,,, 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.
isn't a vector an imaginary line from A-B?
Technically the wind does not really blow.