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Old Nov 15th 2017, 11:00 AM   #1
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What is uncertainty?

Consider a cubical shaped object.

What is the uncertainty of position when I place it along a line?
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Old Nov 15th 2017, 11:11 AM   #2
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The answer depends on if you are a Physicist, an Engineer, a Philosopher, or ...

I would guess that the proponent of the original post that sparked this thread was speaking as an experimentalist,
which I think would place his interpretation alongside that of the Engineer,
i.e. how accurately can I reliably measure the position (with the tools I am using)?
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Old Nov 15th 2017, 11:18 AM   #3
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OK, thanks Woody you have offered an Engineer's view.

But you also mentioned others what do you think theirs might be and why do you think they are different?
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Old Nov 15th 2017, 12:22 PM   #4
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In order to determine the position of a cube of known size, you need 5 numbers. You could, for example, take the x, y, z coordinates of one corner in some coordinate system, and the x, y, z of, say, the diametrically opposite corner, in that same coordinate system. The fact that the distance between those two points is known gives one equation that reduces that to 5 numbers. There exist some uncertainty in all 5 of those numbers. If you are looking for one number to express the "uncertainty" of some generic position. You will first have to say how that position is defined.
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Old Nov 15th 2017, 12:38 PM   #5
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Thanks, HOI, this contains some of the essence of what I was thinking of, especially the last sentence.

I want to give everyone a chance before being more specific.

In order to give the Physicists (this is a Physics forum) a pointer I am thinking of perfectly homogeneous and isotropic cubes used to model common physical situations.

Last edited by studiot; Nov 15th 2017 at 12:43 PM.
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Old Nov 15th 2017, 01:33 PM   #6
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Originally Posted by studiot View Post
Consider a cubical shaped object.

What is the uncertainty of position when I place it along a line?
The term "position" as its used in physics refers only to a point object. As I said in another thread the term "uncertainty" is not defined in any other way in physics or math other than as the standard deviation of a set of quantities.

Thanks.

Last edited by topsquark; Nov 19th 2017 at 10:30 AM. Reason: Argumentative
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Old Nov 15th 2017, 02:13 PM   #7
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It is proven in any respectable mechanics textbook that you care to name that a rigid body or group of particles has a point, known as the centre of mass, which may be substituted for mechanical action of the whole body or group.

In simple terms the CofG is the point at which the weight appears to act.

There are other such centres in Science.

Talking of other sciences, the first of my statistics books I picked up lists three different sections on uncertainty in the index.

Introduction to operations research techniques

Daellenbach, George and McNickle

Last edited by topsquark; Nov 19th 2017 at 10:29 AM. Reason: Argumentative
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Old Nov 16th 2017, 02:55 AM   #8
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There is perhaps a semantic requirement to clarify the definition each of us is using.
<Dictionary Definition>
I would guess we are looking at point 3 in the dictionary definition list:
(3. unpredictability; indeterminacy; indefiniteness)

There is a connection between accuracy and uncertainty, but they are not the same.

In Engineering there is uncertainty in a measurement between one graduation of our measuring tool and the next.
In Physics, (Heisenberg) we can still be uncertain, even with the best possible accuracy of measurement.
In Philosophy, just about everything is uncertain...
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Old Nov 16th 2017, 04:37 AM   #9
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Thanks Woody, yes it is, in part a question of definition.

Surely discussion of that definition is one of the functions of such forums as this?



Uncertainty is definitely linked to probability.
Probability is a definite number (one numebr) between 0 and 1
So it is tempting to think that if the probability is p then the uncertainty can be defined as (1-p), but this doesn't really work.

To add more to my examples.

Let my cube be a model of my car and of side L.
Now the UK rules for parking said car state that if any part of the car is on a yellow line it is illegally parked and I could be subject to a fine (or worse).

So what is the allowable uncertainty in positioning my car when I park it?

Now let my cube be much smaller.
Let it be the rider on a beam balance.
What is the uncertainty in positioning this rider so that the balance operates correctly?

In both cases the uncertainty could be huge.
The car could be 100 miles form the nearest yellow line.
But there is a minimum distance for palcing the centre.

Which brings out another point.
Probability is just a number. It has no units or dimensions.

Uncertainty is usually expressed in the units of the measurand and generally has dimensions.
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