Revisions to Is it mathematically wrong to use units instead of words/parameters/names in equations?

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edited Jul 29, 2020 at 14:14

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A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energyKinetic energy is

$$\begin{align} K&=\frac{1}{2} mv^2 \\ \text{Joules}&=\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2 \end{align}$$$$\begin{align} K&=\frac{1}{2} mv^2 \\ [\text{Joules}]&=\frac{1}{2}[ \text{kilograms}\times\text{meters}^2/\text{seconds}^2] \end{align}$$

We also have gravitational potential energygravitational potential energy:

$$\begin{align}U&=mgh \\ \text{Joules} &= \text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}\\ &= \text{kilograms} \times \text{meters}^2 / \text{seconds}^2 \end{align}$$$$\begin{align}U&=mgh \\ [\text{Joules}] &= [\text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}]\\ &= [\text{kilograms} \times \text{meters}^2 / \text{seconds}^2] \end{align}$$

So, is JoulesJoules both $\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ and $ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

You could start from any of these unit-formulations, and you would get difference answers for the number of kilograms. The answer is not unique seen from the units since the original formula could have contained unit-less parameters.

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$\begin{align} K&=\frac{1}{2} mv^2 \\ \text{Joules}&=\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2 \end{align}$$

We also have gravitational potential energy:

$$\begin{align}U&=mgh \\ \text{Joules} &= \text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}\\ &= \text{kilograms} \times \text{meters}^2 / \text{seconds}^2 \end{align}$$

So, is Joules both $\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ and $ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

You could start from any of these unit-formulations, and you would get difference answers for the number of kilograms. The answer is not unique seen from the units since the original formula could have contained unit-less parameters.

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$\begin{align} K&=\frac{1}{2} mv^2 \\ [\text{Joules}]&=\frac{1}{2}[ \text{kilograms}\times\text{meters}^2/\text{seconds}^2] \end{align}$$

We also have gravitational potential energy:

$$\begin{align}U&=mgh \\ [\text{Joules}] &= [\text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}]\\ &= [\text{kilograms} \times \text{meters}^2 / \text{seconds}^2] \end{align}$$

So, is Joules both $\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ and $ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

You could start from any of these unit-formulations, and you would get difference answers for the number of kilograms. The answer is not unique seen from the units since the original formula could have contained unit-less parameters.

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

added 240 characters in body

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edited Mar 18, 2017 at 9:32

Steeven

52.3k
15
105
199

A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$\begin{align} K&=\frac{1}{2} mv^2 \\ \text{Joules}&=\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2 \end{align}$$

We also have gravitational potential energy:

$$\begin{align}U&=mgh \\ \text{Joules} &= \text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}\\ &= \text{kilograms} \times \text{meters}^2 / \text{seconds}^2 \end{align}$$

So, is Joules both $\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ and $ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

You could start from any of these unit-formulations, and you would get difference answers for the number of kilograms. The answer is not unique seen from the units since the original formula could have contained unit-less parameters.

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$\begin{align} K&=\frac{1}{2} mv^2 \\ \text{Joules}&=\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2 \end{align}$$

We also have gravitational potential energy:

$$\begin{align}U&=mgh \\ \text{Joules} &= \text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}\\ &= \text{kilograms} \times \text{meters}^2 / \text{seconds}^2 \end{align}$$

So, is Joules both $\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ and $ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$\begin{align} K&=\frac{1}{2} mv^2 \\ \text{Joules}&=\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2 \end{align}$$

We also have gravitational potential energy:

$$\begin{align}U&=mgh \\ \text{Joules} &= \text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}\\ &= \text{kilograms} \times \text{meters}^2 / \text{seconds}^2 \end{align}$$

So, is Joules both $\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ and $ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

You could start from any of these unit-formulations, and you would get difference answers for the number of kilograms. The answer is not unique seen from the units since the original formula could have contained unit-less parameters.

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

Improved math formatting and other formatting.

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edited Jul 8, 2016 at 6:59

David Z

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A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$K=\frac{1}{2} mv^2$$ $$\mathrm{Joules}=\frac{1}{2} \mathrm{kilograms}*\mathrm{meters}^2/\mathrm{seconds}^2$$$$\begin{align} K&=\frac{1}{2} mv^2 \\ \text{Joules}&=\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2 \end{align}$$

We also have gravitational potential energy:

$$U=mgh$$ $$ \mathrm{Joules} = \mathrm{kilograms} *(\mathrm{meters} / \mathrm{seconds}^2) * \mathrm{meters}\\ = \mathrm{kilograms} * \mathrm{meters}^2 / \mathrm{seconds}^2 $$$$\begin{align}U&=mgh \\ \text{Joules} &= \text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}\\ &= \text{kilograms} \times \text{meters}^2 / \text{seconds}^2 \end{align}$$

So, is Joules both $\frac{1}{2} \mathrm{kilograms}*\mathrm{meters}^2/\mathrm{seconds}^2$$\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ andand $ \mathrm{kilograms}*\mathrm{meters}^2/\mathrm{seconds}^2$$ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$K=\frac{1}{2} mv^2$$ $$\mathrm{Joules}=\frac{1}{2} \mathrm{kilograms}*\mathrm{meters}^2/\mathrm{seconds}^2$$

We also have gravitational potential energy:

$$U=mgh$$ $$ \mathrm{Joules} = \mathrm{kilograms} *(\mathrm{meters} / \mathrm{seconds}^2) * \mathrm{meters}\\ = \mathrm{kilograms} * \mathrm{meters}^2 / \mathrm{seconds}^2 $$

So, is Joules both $\frac{1}{2} \mathrm{kilograms}*\mathrm{meters}^2/\mathrm{seconds}^2$ and $ \mathrm{kilograms}*\mathrm{meters}^2/\mathrm{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.

A specific parameter might correspond to a specific (SI) unit, but not all units correspond to a specific parameter!

Kinetic energy is

$$\begin{align} K&=\frac{1}{2} mv^2 \\ \text{Joules}&=\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2 \end{align}$$

We also have gravitational potential energy:

$$\begin{align}U&=mgh \\ \text{Joules} &= \text{kilograms} \times(\text{meters} / \text{seconds}^2) \times \text{meters}\\ &= \text{kilograms} \times \text{meters}^2 / \text{seconds}^2 \end{align}$$

So, is Joules both $\frac{1}{2} \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ and $ \text{kilograms}\times\text{meters}^2/\text{seconds}^2$ at the same time? If you have a value in Joules and you need to find the number of kilograms, then how would you go backwards? How would you do the algebra?

The problem is that there are many kinds of energy with the same unit. In general, parameters have unique units, but units don't belong to unique parameters. You cannot go "backwards" from the unit formulation of a formula.