statistics problems

[PG1995]

Hi

While discussing the topics of continuous data and discrete data it was told that time is not continuous. I don't agree with this. In my opinion it is continuous for sure. In the context of statistics, growth of a human being is an example of continuous data. So, why can't time being an example of continuous data? I can see my question is somewhat vague but I hope you can get what I'm trying to say. These definitions (definition #1 and definition #2) might be of some help to understand my query. Please don't forget this was discussed in statistics class. Thank you.

Helpful links:
1: https://www.linkedin.com/groups/Is-time-continuus-is-time-56601.S.191776324

Regards
PG

 

[steveB]

It's hard to comment without knowing the full context of the discussion, the framework of the subject and the source of the information.

In this forum we certainly consider time to represent a continuous variable in the context of physics and control theory. But, perhaps your discussion was related to something other that what we typically deal with. Or, perhaps the source of the information is in error.

If you provide more details, we might be able to make some progress into discovering which of these might be the case.

 

[JimB]

PG

Looking at the definitions which you have provided I would agree that time is continuous.

However from the point of view of someone who can only think of time in integer numbers of hours/minutes/seconds, then time would appear to be discrete.

But as us technical types know, time can be divided into mS, μS, nS, pS and whatever comes next, femto seconds? (that is a bit fast for any of my kit!)

JimB

 

[jpanhalt]

The question of whether time is quantized has been studied. Here is an answer: https://www.scientificamerican.com/article.cfm?id=is-time-quantized-in-othe

If it is quantized, then the unit is very small, e.g., on the order of 10E-44 second.

I am more bothered by the example given in your links that GPA's are a continuous variable. If one considers a grade as a type of ranking (i.e., ordinal values), then one should use different statistical tools than one would use with a continuous variable: https://en.wikipedia.org/wiki/Ranking

Albeit, GPA's and results from opinion surveys are often and incorrectly treated as continuous variables.

John

 

[MrAl]

Hello there,


The question can have two different answers for two different applications, but in general time would appear discrete because we can't measure time down to an infinitesimally small interval, as it is always broken up into pieces. There's no timepiece that can measure non discrete units of time (a motor clock would seem to be continuous, but then we see the magnetic field changing polarity from plus to minus which is still discrete). We can go down into the nanoseconds, picoseconds, etc., but never down to the point where there is no jump to the next interval. The catch however is in the application, where we might go down low enough to consider it continuous, but if we dont go down low enough we might consider it to be discrete.

Consider a voltage meter, analog movement. In classical mechanics the needle has the ability to be positioned at any place on the dial, and that means that we can not find an interval that it is forced to move to after it has reached a different place, but can move between any two intervals we can find on the face. So if we divide down to 0.1 inches, the needle can move between 0.2 and 0.3 inches for example, and if we choose 0.02 and 0.03 inches, the needle can still move between those two places. And if we choose 0.000002 and 0.000003 inches the needle can still rest between those two, and so on and so forth We can never find two places that are different where the needle can not rest in between. And note that we are making a measurement here.
Quantum mechanics would differ a little, but you'd have to go to great lengths to show that there are still discrete steps because the data becomes random to some extent and so we end up with a needle placement that depends on a changing quantity where the average gives us our reading, so this would probably be ignored in all but quantum mechanics itself.

Now back to the timepiece. The gears turn in jumps as the special gear limits the movement to discrete increments (unfortunately i cant remember the name of this special mechanism in mechanical clocks). In the atomic clock the oscillations of a particular kind of atom are counted, so it's a count after all.

I guess we could get radical here and use a volt meter to measure time, using a capacitor that charges up to generate the voltage. But that's more of a cheat than anything else as it has very limited scope so we would only be measuring over a discrete time period anyway.

The more application specific view is noted by their own use of the word continuous when they describe grade point average as being continuous. I've never seen one like 3.2876475892837432324 have you

 

[jpanhalt]

I don't buy those arguments comparing time keeping to voltmeters at all. Either measure can provide whatever degree of resolution the user wants within the limits of technology. And of course in practice, time can be measured with much higher accuracy and precision than voltage. Most important, the definition of volt includes time as a variable. So, if time is not continuous, then volts are not either.

John

 

[MrAl]

Hello,


Well clocks all have a counting mechanism and a volt meter (analog movement) has a continuous range that does not work in discrete steps.
And as i said, if to the given application we can consider the time increment very very small then we might want to call it continuous. That is obvious from continuous time systems, but then again that's theory not measurement.

This is all about measurement and measurement involves a practical real life aspect rather than simple manipulation of numbers using mathematical concepts. This is not about theory.

 

[jpanhalt]

I disagree that analog voltmeters do not have discrete steps in a micro sense. Friction will cause a grab and release action in any real voltmeter. Thus, there will be an increment of voltage that does not produce any movement. In a practical sense, voltage and time are both continuous variables.

As for the watch mechanism that you describe, it is called an "escapement." Not all time keeping devices have escapements.

Back to the OP, the description and examples given to illustrate continuous and non-continuous variable are very poor.

John

 

[MrAl]

I disagree that analog voltmeters do not have discrete steps in a micro sense. Friction will cause a grab and release action in any real voltmeter. Thus, there will be an increment of voltage that does not produce any movement. In a practical sense, voltage and time are both continuous variables.

As for the watch mechanism that you describe, it is called an "escapement." Not all time keeping devices have escapements.

Back to the OP, the description and examples given to illustrate continuous and non-continuous variable are very poor.

John

Hello again,


Well there are arguments on both sides of this topic so it's not really correct to say that the descriptions and examples are poor. That's your opinion.

I also argued the same you thing you are arguing about the voltmeter, but it's nonetheless true because we dont look at defective devices and argue "if it's defective then it has to be discrete". For a smooth operating analog movement it would be considered continuous. But for a smooth working mechanical clock it would be very very clear (dont have to hunt for exceptions) that it is discrete.

The argument i posed was that if we use quantum mechanics instead of classical mechanics then everything is discrete, but it's said that quantum levels can still produce a continuous range of levels because of the way the quantum particles act when they appear in groups rather than one alone. Ultimately though i believe if we looked hard enough we would see noise in that range of levels, rather than discrete steps. So we'd see an average that is the combination of the particles themselves and the positions of each particle, and there could be billions to consider at any given time. So thinking of it as continuous makes sense.

But to recap, a perfectly working volt meter analog movement is definitely continuous, while a perfectly working mechanical clock is clearly discrete.

Another point we havent considered yet is that this 'course' may require adapting to a given definition whether any of us agree with it or not.

 

[PG1995]

Thank you very much, everyone, for your input.

As far as I can get it now, the instructor had it wrong but he won't accept it!

Regards
PG

 

[jpanhalt]

@PG

That is an important lesson to learn -- probably more important than the stated intent of the lesson. In real life, you will find mean and standard deviation used all the time for nonparametric data.

John

 

[MrAl]

Hello again,


I thought we had established that time in actual measurement for mankind is discrete, but in problems it can be either continuous or discrete.

Continuous: time it takes to run the 100 yard dash.
Discrete: your age in years.

 

[jpanhalt]

Hello again,


I thought we had established that time in actual measurement for mankind is discrete, but in problems it can be either continuous or discrete.

Continuous: time it takes to run the 100 yard dash.
Discrete: your age in years.

I don't recall doing that. You simply presented a straw-man example of an escapement-based clock.

Time is continuous. If it is not, then neither are volts or amperes. That is simple physics.

John

 

[MrAl]

Hello again John,


Well i know someone who is 45 years old, and i even could know someone who is 45.284756391 years old, but i dont know anyone who is
45.2847563911837342398237423984723432948724326131890534587353287624312751231289332597825234121232
years old, do you?
If so, then maybe you also know someone who is:
45.2847563911837342398237423984723432948724326131890534587353287624312751231289332597825234121233
years old too.