# What is uncertainty ?

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I am promoting discussion about the question

What is a uncertainty in Science?

Uncertainty is definitely linked to probability.
Probability is a definite number (one number) 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.

Consider a cubical shaped object.

What is the uncertainty of position when I place it along a line?

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 placing the centre.

Which brings out two points.
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.

Uncertainty is usually expressed as a range with one end a maximum or minimum.

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It’s difficult to consider any type of exploration that does not include ample quantities of uncertainty, proportionally in most cases to whatever risks involved. Nothing ventured . . . . .

Edited by arc

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"What is certainty?"

Certainty is when everything goes the same way..

Universe that is repeated over and over again, exactly the same (boring) way..

Like in the movie.. When you watch it over and over again, it's still the same movie.. You can remember phrases said by actors before they even open mouth..

From time to time, "it's good to jump in and push some actors" to move differently..

LOL.

ps. Sorry for jumping in, and pushing you in this direction, the next time, I will jump in, and push you in different direction.. I promise..

Edited by Sensei

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My first thought was that we can consider the variance of a random variable to be a measure of its uncertainty: the higher it's variance the more uncertain we are of seeing a particular realisation, and with a variance of zero we are certain of the outcome of a variable.

Except...  variance is usually a theoretical property of a population, which we very rarely know and so have to estimate. This estimation itself contains variance - will have it's own distribution even.

But this latter fits better with uncertainty as related to science - we make a measurement which we assume to be some quantity. But the measurement, for various reasons, isn't precise - it will have some variance. We won't know exactly this variance, but we should be able to estimate it - by using our measuring instrument in very well controlled conditions and on quantities we know before hand.

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Thank you for your thoughts, Prometheus.

That is no criticism.

Any thoughts on my examples from synthesis, which all too often seems the poor relation in technical discussion?

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Not quite sure what you mean by synthesis in this context - probably why i didn't get what you were driving at with your examples.

I wouldn't have thought of uncertainty as being the min and max possible values - the range of a random variable is a metric of its distribution, but not necessarily a very useful one.

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23 minutes ago, Prometheus said:

Not quite sure what you mean by synthesis in this context - probably why i didn't get what you were driving at with your examples.

I wouldn't have thought of uncertainty as being the min and max possible values - the range of a random variable is a metric of its distribution, but not necessarily a very useful one.

Analysis is (passively) reporting on what is already there/happening.

Synthesis is actively creating something that is not (yet) there or moving something to be in a specific place.

My two examples for discussion involve the latter.

Note I didn't say that both max and min were necessarily involved.
But surely the great grandmaster of uncertainty - Heisenberg - has a greater than sign in his principle?
So any amount of uncertainty that is greater than the minimum value will conform to his principle.

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I'm still not sure i understand.

The uncertainty principle is a consequence of the nature of phenomena under study: it is inherent. Measurement error occurs due to some random imprecision: the thing we are measuring may not change but our measurements will to some extent.

By synthesis do you mean the former? If so i don't understand how it applies to a parked car.

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On 11/20/2017 at 1:57 PM, studiot said:

But surely the great grandmaster of uncertainty - Heisenberg - has a greater than sign in his principle?
So any amount of uncertainty that is greater than the minimum value will conform to his principle.

Everybody translates Heisenberg's principle as Uncertainty, but I have always thought that Indeterminacy is a better translation of his Unbestimmtheit. That way you avoid the association with probability. I remember decades ago reading that Heisenberg preferred that translation as being nearer what he meant, although I have no longer any faith in my memory, and I may well have imagined it.

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On 11/18/2017 at 3:15 PM, studiot said:

Which brings out two points.
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.

Absolute uncertainty has units, but you can also express relative uncertainty, which does not. e.g. ± 10%

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6 hours ago, Prometheus said:

I'm still not sure i understand.

The uncertainty principle is a consequence of the nature of phenomena under study: it is inherent. Measurement error occurs due to some random imprecision: the thing we are measuring may not change but our measurements will to some extent.

By synthesis do you mean the former? If so i don't understand how it applies to a parked car.

OK

The car is real and exists.
The road and yellow lines are real and exist.

What does not exist and has to be constructed is the gap between any poimt of the car and the end of the yellow lines.

I said take the car as a cube so we can easily determine its centroid.

Take the position line (x axis) as the line along the road and the 'position' of the car as the x value of its centroid.

So what is the minimum uncertainty you can accept in x to ensure that the car does not attract a fine when parked, given the x values of the extent of the yellow lines?

Still on a motoring note here is a more difficult one which bring out the difference further.

The Police speed check is 2% accurate.

The Police say "we clocked this car at 44 mph in a 30 mph zone"

Is the uncertainty sufficient to avoid a conviction?

Note the issue of the beam balance rider position has an additional twist because of the position of the fulcrum.

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3 hours ago, studiot said:

What does not exist and has to be constructed is the gap between any poimt of the car and the end of the yellow lines.

Constructed? Why constructed and not measured? I suspect this is the crux of my misunderstanding.

3 hours ago, studiot said:

So what is the minimum uncertainty you can accept in x to ensure that the car does not attract a fine when parked, given the x values of the extent of the yellow lines?

Wouldn't that depend on the precision of your measuring device?

3 hours ago, studiot said:

The Police say "we clocked this car at 44 mph in a 30 mph zone"

Is the uncertainty sufficient to avoid a conviction?

The accuracy of your speedometer is irrelevant here, it's the recording the police take that is taken as evidence, unless they take into account the objection 'i was only doing 30'. I must be missing your point...

In case you're wondering, i'm not deliberately being dense, it comes quite naturally. However, i am quite enjoying the irony of being so uncertain about a thread on uncertainty.

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Certainty is when a system acts according to a rule or a set of rules when time passes. Uncertainty is when a system does not act according to rules with time passing. Isn’t it that simple?

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Quote

The simplest form is the standard deviation of a repeated observation. In metereology, physics, and engineering, the uncertainty or margin of error of a measurement, when explicitly stated, is given by a range of values likely to enclose the true value.-  Wiki

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2 hours ago, koti said:

Certainty is when a system acts according to a rule or a set of rules when time passes. Uncertainty is when a system does not act according to rules with time passing. Isn’t it that simple?

No. There is noise in all systems, so there will be variation in any repeated measurement. There is no violation of any rule involved.

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5 minutes ago, swansont said:

No. There is noise in all systems, so there will be variation in any repeated measurement. There is no violation of any rule involved.

What if we exclude the „noise” which is always random anyway?

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On 11/18/2017 at 2:15 PM, studiot said:

I am promoting discussion about the question

What is a uncertainty in Science?

Uncertainty is definitely linked to probability.
Probability is a definite number (one number) 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.

Consider a cubical shaped object.

What is the uncertainty of position when I place it along a line?

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 placing the centre.

Which brings out two points.
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.

Uncertainty is usually expressed as a range with one end a maximum or minimum.

In one sense, a myth is an idea that, while widely believed, is false, failing to correspond with reality.

In a deeper sense, which is employed by students of religion, a myth serves as an orienting and mobilizing story for a people, a story that reminds them who they are and why they do what they do. When a story is called as a myth in this sense—which we can call Myth with a capital M—the focus is not on the story's relation to reality but on its function. This orienting and mobilizing function is possible, moreover, only because Myths with a capital M have religious overtones. Such a Myth is a Sacred Story.

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14 minutes ago, koti said:

What if we exclude the „noise” which is always random anyway?

The variation is the noise is, isn't it?

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19 minutes ago, koti said:

What if we exclude the „noise” which is always random anyway?

You can't

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!

Moderator Note

Off-topic QM rant and reply split to Trash.

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1 hour ago, swansont said:

You can't

ok I see the point but that just tells us that there is no certainty and everything is intrinsically uncertain from physics point of view. It doesn’t resolve the question what uncertainty is. Doesn’t my extremely simple definition from 4 post above still apply?

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1 hour ago, swansont said:

You can't

You can, actually.

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3 minutes ago, koti said:

ok I see the point but that just tells us that there is no certainty and everything is intrinsically uncertain from physics point of view. It doesn’t resolve the question what uncertainty is. Doesn’t my extremely simple definition from 4 post above still apply?

Everything being inherently uncertain is not saying there is no uncertainty. Quite the opposite. Everything has uncertainty.

There is also quantum uncertainty.

Are you referring to following a rule? That doesn't work. Getting a different answer with multiple measurements is the rule, not a violation of it. Physical systems do not violate the rules. If you think it did, you didn't really know what the rule was. Physical law is not like legal law.

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33 minutes ago, swansont said:

Everything being inherently uncertain is not saying there is no uncertainty. Quite the opposite. Everything has uncertainty.

There is also quantum uncertainty.

Are you referring to following a rule? That doesn't work. Getting a different answer with multiple measurements is the rule, not a violation of it. Physical systems do not violate the rules. If you think it did, you didn't really know what the rule was. Physical law is not like legal law.

Did you mean: "Everything being inherently uncertain is not saying there is no certainty" ? If yes, I don't understand, -can you use an example? QM works according to a set of rules and we'd need to break them in order to achieve certainty wouldn't we? If you mean what you wrote I'm even more lost.

The second part of your post is clear to me - I'm trying to think of a valid definition of uncertainty. Since this is in physics we can skip the philosophical aspect of "tomorrow is Wednesday" which seems exactly 100% certain to me.

Edit: I just read Mordred’s post above which seems atractive - „indetermined” is a much better term than „uncertain” in the context of QM. It still doesn’t explain what uncertainty is though.

BTW...Im sad to see SuperPolymath loosing his screws. If you are reading this Super, I hope you find them man. Stay cool.

Edited by koti

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13 minutes ago, koti said:

Did you mean: "Everything being inherently uncertain is not saying there is no certainty" ? If yes, I don't understand, -can you use an example? QM works according to a set of rules and we'd need to break them in order to achieve certainty wouldn't we? If you mean what you wrote I'm even more lost.

13 minutes ago, koti said:

The second part of your post is clear to me - I'm trying to think of a valid definition of uncertainty. Since this is in physics we can skip the philosophical aspect of "tomorrow is Wednesday" which seems exactly 100% certain to me.

Edit: I just read Mordred’s post above which seems atractive - „indetermined” is a much better term than „uncertain” in the context of QM. It still doesn’t explain what uncertainty is though.

It reflects that we can never measure with arbitrary precision. Measurement devices limit this, as does nature itself.