Dimensions and units.
In dimensionality, what do we mean when we say "properties of a variable" in terms of dimensions?
Can we use the same bracket notation for a different dimensionality?
How have early mathematicians and scientists develop dimensional analysis to convert quantities of one
dimension into another
What exactly is the purpose of dimensionality and bracket notation?
That entire last section lost me.
Can you explain how you went from [x] = L to Dim(x) = [L]?
What happens if there are two dimensions that start with the same letter (not like Length and L the
dimension but like two dimensions that both started with L) - how do you know which one takes
precedence over the other?
Why is one able to "choose" c=1 and why are there no units associated with the speed of light?
Are we required to use bracket notation on our exams? Also, can you clarify what dimensionality is
supposed to mean (I am slightly confused)?
Im not grasping the point of dimensionality. Whats its purpose and whats the difference between a
variable and dimensionality or does every variable have certain dimensionality?
Can a period of time be measured in length, e.g. define a meter as the equivalent of 3 nanoseconds?
Why do x, delta x, and y not have the same value? If you're comparing their dimensionality (which I'm still
not entirely clear on), why is the equal sign used if they don't have the same value?
Referring to being able to compare values as long as they are obtained by the same kind of
measurement, what is an example of a situation where this is done?
Are only dimensions arbitrary and not units, and if so, why
Are there any other notations we need to become familiar with in terms of indicating peculiarities (i.e.,
Dim(x) = L rather than [x] = L)?
x] = [?x] = [y] = L, In this model, how can they have different values but the same demensionality?
How do you choose which units of length/time/mass etc. to use when equating dimensions to each other?
Do the brackets in bracket notation signify anything (such as the absolute value of the measurement)?
In this equation, [x] = [?x] = [y] = L, how are we supposed to know that the symbol, =, doesn't mean
equals to but rather it means the same dimension?
How are dimensions incorporated into models of physics scenarios?
Would phases of molecules (gas, liquid, solid) be considered dimensions since it is representing the
physical quality, although not arbitrarily? Also, what would you consider a measurement which is
quantifying the likelihood of something happening? such as reduction potential?
What is the purpose of using a bracket? Is it to indicate what the letter stands for? I don't really
understand the use of the bracket for dimensionality.
How will we be able to tell whether "L" stands for a dimensionality or a variable? Will it be stated in the
question or will we be assigning it ourselves based off of a question?
Can you only equate quantities that have the same dimension because if they have the same dimension,
they must have the same units?
How would a consensus be reached to determine a standard unit for new dimension?
Just to clarify, does saying that different lengths have the same dimensionality mean the same thing as
saying they can be measured in the same units?
The article stresses that a dimension is an arbitrary assignment to a physical quantity. However the term
"arbitrary" has different denotations. How is arbitrary defined in this context, with regard to a dimension?
How can we correctly assume a letter, such as "L", stands for dimensionality or is a variable? a
I am having some trouble distinguishing between measurements and dimensions. Are measurements
used to determine dimensions?
Are our dimensions focused on the metric system
In this article it states, "The arbitrariness of the standard unit is the key for the implications of dimensions."
How does the chosen unit affect these implications? What do dimensions implicate about the physical
system?
I've read the article over a few times, and I'm having some trouble grasping the concept of dimensionality.
For example, it says in the last lines "...it says they all have the same dimensionality (are obtained by the
same kind of measurement)..." What exactly does that mean when it says "the same kind of
measurement" ?
Could the choice of unit of measurement of dimension subconsciously skew a reader's understanding of
the measurement itself?
Does C, the speed of light always equal 1?
What is the relationship between units and dimensions because it seems as thought a dimension can
encompasses many units and at the same time some units encompass multiple dimensions? For
example the dimension of length can be measured in units of centimeters, meters, inches, etc but then
units such as joules can measured using units from multiple dimensions.
If, for example, meters and seconds are both dimensions and thus an arbitrary form of measurement, why
can you not just set these units equal to each other? In other words, although they are considered
different dimensions, if arbitrary, why can they not be equal?
The reading concludes that "We can only equate quantities that have the same dimensions and we can
only expect the numbers of both sides if we use the same units". Are there cases where this is not true?
For example, "cm" as a unit is commonly used to measure length, however this may be manipulated in
order to change it to a volume measurement unit (cm^3). Essentially 1 cm^3 = 1 ml follows the given rule
that only quantities with similar dimensions (both volume measurements) may be equated, but does not
follow the second part of the statement stating that we can only expect the numbers on both sides of the
equation to be the same if we use the same unit. In this case, we have the same number (1) but different
units (cm^3 and ml). My question concerns whether there are exceptions to the provided statement such
as the one example I had provided.
I've come across several instances (mostly in chemistry) where an equation uses unitless values. It
seems to me that there are two types, values resulting from cancellation of units and values arbitrarily
assigned. Is this a correct assumption? Do two unitless values ever appear in the same calculation, and
are they able to be added together?
Is there any dimension/physical quantity in the universe (that you know of) that scientists are aware of but
do not yet have any way to measure it by? So, in other words, a dimension that is unitless?
Over time, how did scientists even begin to describe dimensions, and how do the dimensions on earth
differ to the ones in space?
In past classes we have used the gas constant R, which can be represented in many units but uses a
combination, such as [(L)(atm)]/[(mol)(K)]. Does this mean that this constant has a single or multiple
dimensions, and what is/are they? If it has multiple dimensions how would this be notated?
Is the dimensionality equation written alongside exam problems or is it an expression to demonstrate an
idea?
The notation for dimensionality is confusing; what does the bracket represent?
Will dimensionality have a unit associated with is it even expressed in numbers?
I don't quite understand the significance of brackets.
Other than length, time, mass, charge, and temperature, what are some other major dimensions used in
advanced physics?
If choosing dimensions and units is arbitrary, then how do scientists reach unanimous decision?
What are some examples when we need to use the bracket notation?
In the explanation of how [X] =[Change in X] = [Y] = L does not indicate the same value but shows the
same dimensionality, what does it mean to be obtained by the same measurement?
As long as the bracket notation is fixed on variables, this means we can equate different quantities by
their unit of measurement?
how is dimensions related to measurement?
How do we know how to compare the dimensionality between quantities?
Using the equation, [x] = [dx] = [y] = L, we are assuming that x, dx, and y have the same dimensionality.
Why can we set these variables equal to each other even though they are not actually equal? Is there
another method to compare these variables?
When writing out an equation in attempt to equate quantities, is it possible that different units could be
used on the opposing sides or do they always have to be the same? For example L1=L2 are just
dimensions but both equate to each other. Can we have the same dimensions in an equation but instead
use different units such as feet and inches which are both units of the dimension of length?
In what context would we use the bracket notation, like an example of a type of problem?
How was the speed of light measured and how do we know it is the same for all observers?
In the given L1 = L2 equation, how exactly would we equate a length and a time, if something like "1
meter = 1 second" is obviously incorrect?
Do scaling/exponential relationships between different dimensions stay the same across their
corresponding units equally (is the length:mass ratio the same when units are changed)?
In the web page, it is said that speed is invariant and therefore can be set to c=1 without any units. What
is an exact definition when something is invariant and how does this lead to unitless variables?
When one converts to a micro measurement, as in the case of Planck length which is
1.616199(97)×10?35 meters can one use mathematical conversion from a meter, or do other factors
become apparent that inhibit conversion?
Since units are so arbitrary is there a method in which units are derived from each other, for example how
kelvins are converted to degrees celsius and so forth?
What is the benefit to using bracket dimensionality notation, shown in the article, rather than just simply
stating the units and doing conversations as needed?
For example - "12 ft + 3 yards" Why write: dim(ft) = dim(yd) = [length]; when one could write 3ft = 1yd,
hence 12 ft = 4 yds so 4 yards + 3 yards = 7 yards or 21 feet?
How would two variables with different dimensionality be written? Or would it simply not be corresponded
with a specific symbol (ie. a bracket notation or other possible symbol)?
I am still confused as to which notation is really "standard," the second notation written in this article is
less confusing than [x] = L, so why is it not considered the "standard" for our class?
In this class will the dimensions be defined in a problem such as instead of writing "x, y are lengths and s
and z represent time it would be given as [x] and [y] = L and [s] and [z] = T?" Is the purpose of this
bracket notation a shorthand for representing that "these are dimensions?"
"We can only equate quantities that have the same dimension and we can only expect the numbers of
both sides to be the same if we use the same units."
What if the units are equivalent to each other? Then wouldn't the numbers, dimensions, and units would
be the same?
What is the purpose of using " Dim(x) = [L]" ?
To me it seems to have an opposite meaning of [x] = L. [x] = L. means that dimension x is specified by L.
When using "Dim(x) = [L]" it seems like we are saying dimension L is specified by x. I am confused about
how the two equations mean the same thing.
Statement: "This would indicate that we are taking some information from x and setting it equal to a new
and peculiar kind of quantity -- a dimension. This would prevent lots of confusion. With the other notation,
we write "L" to stand for dimensionality, but in the same problem we might be using as a variable, "L", for
a particular length. Unfortunately, the notation above is standard so we will stick with it. You will just have
to use your sensitivity for contexts to decide whether "L" stands for a dimensionality or a variable.
Question: When it says "we will just have to use your sensitivity for contexts to decided whether "L"
stands for dimensionality or variable" what does that exactly refer to? In what ways do we use our
"sensitivity" to decipher what L may or may not stand for? Would we have to write this statement '[x] = [?x]
= [y] = L' every time we would like to say three quantities have the same dimensionality? I'm slightly
confused for how to use this equation using the three quantities.
Can you explain the significance of the bracket notation in terms of dimensionality?
Is it possible for a variable to be described in more than more dimensionality and if so, how would that be
shown using the proper notation?
In the discussion of the arbitrariness of dimension, in the example explaining how time can be used to
measure distance, I do not understand why we are assigning a value of c=1, when c, actually has a value.
What is the significance of equaling to c to 1, in this example? Really confused.
Since one can convert from unit to unit with a conversion factor is it not true to say that all measurements
are comparable? IE Liquid to length or liquid to mass even though they aren't the same dimensionality.
In this reading it mentions that we can't equate two quantities that have different dimensions. In my
experience in chemistry I thought that you can equate two different things if you have a conversion factor.
Is it the same in physics?
Do all quantities with the same dimensionality have the same units?
In the "Note" portion on the variable/dimension L, the text stated that we would have to use some
judgement in deciding when to use L, or other letters, to represent certain ideas. Will there ever be any
ambiguity when we are reading a certain equation, or will the problem state exactly what the letter is
representing
For notating dimension, is [x] suppose to represent a numerical value with units?
Can different dimensions be expressed using different units?
When using dimensional analysis, do we usually just use the dimensionality, or do we sometimes also
use the specific units for that dimension? For example, if we wanted to say x is a length, would we only
ever say x = [L], or would we sometimes say x = [meters] as well?
If we are only able to relate quantities with the same dimensionality, what do we do when we encounter
multiple dimensions that need to be equated?
What is the physical equivalent of a conversion constant? Many equations use constants whose
dimensions are the inverses of the dimensions of the other quantities they are being multiplied with. Are
these quantities just correction factors or do they actually represent something else in the physical
relationship between two quantities with different dimensions?
In the example given referring to dimensionality and notating dimension that
[x] = [?x] = [y] = L
is the reason that they can be equated because they are all measurements of length and have the same
units even though they might be different lengths?
Does the dimensionality notation ever incorporate numerical values, or is it only used to represent the
variable as a dimension?
In the last section "Noting Dimension," how is it that the equal sign in the example does not mean that the
x, deltax, y and L are equal to each other? I don't understand what it means to be equal in dimension but
not value.
Can you model systems with infinite dimensions?
In what problem circumstance would we need to use bracket notation? Can we not just assign unknowns
with the same dimensionality L1, L2, L3, etc?
Why is the speed of light the fundamental speed associated with the universe?
Does the bracket notation mean that by putting [x], it indicates that "x" was measured by a specific
dimension, with the other side of the equation being the specific dimension? Or does the other side of the
equation not matter as much because the letter "L" could be taken as a variable or as a dimension?
what is the difference between "dimensions" and 'units"?
What does this statement mean "The length we are measuring can be fit with a reasonable number of
pieces of our measuring stick?" Does it mean that the length of our object can't be too small like smaller
than an atom because that's too hard to measure accurately?
In this article it is stated that the dimensions is assigning a number to a physical quantity. How would
these dimensions affect the way we measure it compared to those dimensionless number?
Why is it important to know the difference between dimension and units?
So does a dimension refer to the particular characteristic you are examining? For example, could speed
be a dimension?
When working problems do quantities with the same dimensionality always have the same units?
Just so I understand correctly, if box A is 3x4x2cm and box B is 6x8x4cm, can you say that [A]=[B]?
How would you notate it if you had Dim(x)=L and Dix(y)=T and you wanted to have a variable that
multiplied/divided/or added to two dimensions?
Seeing as the choice of dimension depends on our current state of knowledge, what is an example (if
any) of dimensions used in the past that are now obsolete? How did they become obsolete? What is the
most updated dimension used in its place?
In physics, are the units and dimensional analysis similar to chemistry? I know that between biologists
and chemists there are preferred variables and units used. Where does physics stand on this spectrum?
Why is it that we can use an equal sign for example "[x] = [?x] = [y] = L" even if the values are not equal?
Because in "The idea of algebra: unknowns and relationships (2013)" it was stated that never write an
equal sign between 2 quantities that are not equal.
In what context is bracket notation used and can the dimensionality for a particular variable change?
Under Notating Dimension, for bracket notation, how do you differentiate between T for temperature and
T for time?
My question is towards the third paragraph where is starts with "it is amusing to realize...."
why c = 1 doesn't have unit? and how from this they figured 1 meters correspond to about 3
nanoseconds?
because from the rest of the article, we understand that we can only put two things equal to one another
as long as they have same units but here we have second and meter.
I'm confused with what the purpose of using brackets is, is it used to show that to different variables have
the same units or the same dimension?
Why, in physics, do we usually set two values equal to each other, as this article mentions when it says
that the two quantities must be in the same dimensions? What end point do we get to when we set two
quantities equal to each other
Can you use the same bracket variable to describe two different dimensions of an object such as its
length and volume?
What is the difference between dimension and measurement? Is measurement more specific to
dimension?
If we can only equate quantities with the same dimension, how can we use equations to model systems
with more than one variable or dimensionality?
What is charge (Q) and its units?
Could you use different notations to characterize the same dimension just by giving it a different variable
In the "Notating Dimension" section, [x]=L is said to mean that "x" has the dimensionality of length.
However, the note section states the "x" is being set to a new type of quantity--a dimension. Does this
mean that "L" is arbitrary and stands for any dimension? Or does "L" mean the dimension of length?
Since the dimension that we can identify is based on current information, which produces arbitrary values,
does that mean that there exists possibility that other forms of dimensions can exist? If there are, would
the reason why we can't identify them be because they overlap some of the current dimensions, which
creates a relation, similar to the other ones, but that we can still use to find a value?
What is an example of when using the [ ] notation in biological sciences?
Can an equation only measure one type of dimensionality at a time, or can more than one dimension be
calculated?
Is the symbol for both length and distance (L) ?
If I understand correctly, m/s is a form of unit and the dimension used to measure the speed is distance
and time?
When using bracket notation does [x]=L mean that x is equal to L or the dimensionality of x is equal to L?
Can we please go over an example of dimensionality?
What exactly is dimensionality useful for, and why/when do we use it in physics? It is briefly mentioned in
the article but could you elaborate on this a little more?