Why do calculations need to be balanced anyone?

[Iwonderaboutthings]

Why do calculations need to be balanced anyone?

 

Yes I understand how a check book needs to be balanced otherwise you get over-drawn.

However that is a man made system of monetary.

 

How does that apply to chemistry, nuclear engineering, and even in Wall Street IE Stock Market?

I don't get it nor fully understood this for many years.

 

For instance, how can something be balanced using pure math and numbers?

 

To me this sounds impossible especially when this is linked to chemistry and other physical natural laws of the universe, unless their are constants of some kind?

 

IE : percent used for money, pi ratio, the speed of light, g for science?

 

This being the case then maybe this gives me some insight.

 

 

I assume it is a harmony of some kind that is needed to balance out equations, but how can harmony be applied to a man made concept of balance when all we have are numbers?

 

Thanks in advance

Edited July 12, 2013 by Iwonderaboutthings

[Ophiolite]

I'm not entirely sure what you are asking, as I suspect there are different answers depending upon what field you are looking at. Let's consider chemistry and let's take a simple chemical reaction. Let's add an acid to a base, the product of which should be a salt, plus water.

 

NaOH + HCL = NaCl + H₂O

 

That is a balanced equation. Why can't I write it this way?

 

NaOH + HCL = 2NaCl + H₂O

 

Because that would mean that in mixing sodium hydroxide with hydrocholric acid I create, from nowhere, an additional sodium atom for everyone in the original mixture. That is in violation of the conservation of mass. The two sides of the equation must be balanced. What do you find troublesome about that?

 

 

[swansont]

There are situations where some quantity is conserved, be it atoms, energy, momentum or something else. If it's conserved then the equation describing it must balance

[Delta1212]

A balanced equation looks like this:

 

1+1=2

 

An unbalanced equation looks like this:

 

1+1=3

 

or

 

1+1=1

 

If your equation doesn't balance, something is appearing from nowhere or disappearing without a trace. Any equation describing a situation where it has been proven to be impossible for this to happen must balance.

[timo]

Is it universally agreed upon that a "balanced calculation" means that two sides of an equation are equal? Just asking because I have no idea what a "balanced calculation" is supposed to be (Swansont's reply gives a hint, but I think it was merely an attempt to make sense of the OP).

[J.C.MacSwell]

Is it universally agreed upon that a "balanced calculation" means that two sides of an equation are equal? Just asking because I have no idea what a "balanced calculation" is supposed to be (Swansont's reply gives a hint, but I think it was merely an attempt to make sense of the OP).

This. Because the = sign is logical shorthand meaning that the equation will balance.

 

The equations need to be balanced to be true, Otherwise they are false.

[Iwonderaboutthings]

I'm not entirely sure what you are asking, as I suspect there are different answers depending upon what field you are looking at. Let's consider chemistry and let's take a simple chemical reaction. Let's add an acid to a base, the product of which should be a salt, plus water.

 

NaOH + HCL = NaCl + H₂O

 

That is a balanced equation. Why can't I write it this way?

 

NaOH + HCL = 2NaCl + H₂O

 

Because that would mean that in mixing sodium hydroxide with hydrocholric acid I create, from nowhere, an additional sodium atom for everyone in the original mixture. That is in violation of the conservation of mass. The two sides of the equation must be balanced. What do you find troublesome about that?

 

 

What I find very very hard to grasp is this part "additional sodium atom for everyone in the original mixture"

So what you are saying is that it "is" possible that from "out of no where" multiple sodium atoms can be created???

I'm not sure if I understand this correctly sorry, however, I am grateful you have responded...

 

When I read out of no where, I am thinking exactly that. If this is the case then how on earth can that be??

 

Conservation of mass? As in energy neither creates nor destroys?? Like E=mc sqrd??

 

 

Thanks

A balanced equation looks like this:

 

1+1=2

 

An unbalanced equation looks like this:

 

1+1=3

 

or

 

1+1=1

 

If your equation doesn't balance, something is appearing from nowhere or disappearing without a trace. Any equation describing a situation where it has been proven to be impossible for this to happen must balance.

YIKES! That sounds very true. But does this balance = proportionality, inverse of something, is it a product??

You see what I really have issues with is visualization, you see now we have " numbers" and variables ds dx and so on..

 

Its as if though we have several things to balance here:

 

My #1 round off errors, bases of ten, h, c, pi ratio, the numbers, and SI units all together.

 

These then are attached to:

 

Units

Velocities

Stock Market

Genetics

 

And so fourth..

 

Its the numbers I have problems understanding and they these somehow balances other things in science.

Edited July 13, 2013 by Iwonderaboutthings

[timo]

This. Because the = sign is logical shorthand meaning that the equation will balance.

 

The equations need to be balanced to be true, Otherwise they are false.

For me, the "=" means "equal" in the sense of "identical" or "the same", not "balanced". Additionally, I wouldn't equate the term "calculation" with "equation", either. You are certainly right that equal things must be equal for an equality statement to be true. My questions was if "balanced" really is common/proper/correct terminology to use in this case.

[studiot]

Hello Iwonderaboutthings,

 

I'm glad you said

 

"why do calculations need to be balanced"

not

"why do equations need to be balanced"

 

You clearly appreciated the difference.

 

Calculations refer to a process. Often you start with one (or more) things and end up with something else, as you examples ably showed.

 

So for instance % - You start with two things profit and principal and as a result of the process end up with %Profit.

 

There is nothing balanced about this.

 

So the simple answer is calculations do not need to 'balance'.

 

On the other hand, when referring to equations, swansont gave a hint when noting that something may be preserved in an equation.

 

This something may be the subject itself of the equation or it may be a property of the the subjects. That depends upon the nature of the equation.

 

We should also note some things about equations.

Chemical equations may have a preserved property (eg number of atoms) as Oophiolite was saying - or they may not.

 

For instance the general chemical equation

 

Acid plus base = salt plus water

 

need not 'balance' ie the subject of balance need not be considered for the equation to make sense. This equation refers to a process as I noted above.

Chemists often recognise this by using an arrow symbol in place of the = sign we read the word 'makes' instead of equals.

 

However timo is not quite correct in stating that an equality is the same as an identity.

 

Consider the two equations

 

3x²+8x+6 = 2x²+5x+4

 

3x²+8x+6 = (x²+4x+1) + (2x²+4x+5)

 

The first is only true for certain values of x - This is an equation.

 

The second is true whatever the value of x - This is an identity.

 

The first equation does not 'balance' there are not the same number of x squareds, x's and constants on each side (I mean the coefficients are not the same).

Or as swansont says nothing is preserved.

We can execute a process on this equation to 'solve' it for the particular values of x for which it is true.

 

The second equation does balance since the collected coefficients are the same on both sides.

However we cannot now apply our solution process to this expression. You cannot 'solve' an identity.

 

In physics consider the forces acting on a body. There is no requirement for them to be in balance.

 

If they are in balance there is no resultant and the body is in equilibrium.

So we apply the laws of equilibrium or statics.

 

If there is a resultant this is a condition that the body is not in equilibrium ie it is accelerating.

Then we apply the laws of dynamics.

 

So in the physics case balance is used as a test of equilibrium.

Edited July 13, 2013 by studiot

[Iwonderaboutthings]

Hello Iwonderaboutthings,

 

I'm glad you said

 

"why do calculations need to be balanced"

not

"why do equations need to be balanced"

 

You clearly appreciated the difference.

 

Calculations refer to a process. Often you start with one (or more) things and end up with something else, as you examples ably showed.

 

So for instance % - You start with two things profit and principal and as a result of the process end up with %Profit.

 

There is nothing balanced about this.

 

So the simple answer is calculations do not need to 'balance'.

 

On the other hand, when referring to equations, swansont gave a hint when noting that something may be preserved in an equation.

 

This something may be the subject itself of the equation or it may be a property of the the subjects. That depends upon the nature of the equation.

 

We should also note some things about equations.

Chemical equations may have a preserved property (eg number of atoms) as Oophiolite was saying - or they may not.

 

For instance the general chemical equation

 

Acid plus base = salt plus water

 

need not 'balance' ie the subject of balance need not be considered for the equation to make sense. This equation refers to a process as I noted above.

Chemists often recognise this by using an arrow symbol in place of the = sign we read the word 'makes' instead of equals.

 

However timo is not quite correct in stating that an equality is the same as an identity.

 

Consider the two equations

 

3x²+8x+6 = 2x²+5x+4

 

3x²+8x+6 = (x²+4x+1) + (2x²+4x+5)

 

The first is only true for certain values of x - This is an equation.

 

The second is true whatever the value of x - This is an identity.

 

The first equation does not 'balance' there are not the same number of x squareds, x's and constants on each side (I mean the coefficients are not the same).

Or as swansont says nothing is preserved.

We can execute a process on this equation to 'solve' it for the particular values of x for which it is true.

 

The second equation does balance since the collected coefficients are the same on both sides.

However we cannot now apply our solution process to this expression. You cannot 'solve' an identity.

 

In physics consider the forces acting on a body. There is no requirement for them to be in balance.

 

If they are in balance there is no resultant and the body is in equilibrium.

So we apply the laws of equilibrium or statics.

 

If there is a resultant this is a condition that the body is not in equilibrium ie it is accelerating.

Then we apply the laws of dynamics.

 

So in the physics case balance is used as a test of equilibrium.

Equilibrium yes! now it is more clearer to me and now things make more sense, thank you so much your time is appreciated and I will get further skilled with this.