# Is it necessary for scientific equations to be dimensionally consistent?

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33 minutes ago, Strange said:

I have lost track of the point of the thread. The answer to the original question is, obviously, "yes". Everyone, including you seems to agree with that. You haven't produced any counter-examples. But you have taken it off in various random tangents for no apparent purpose. (Apart, I suppose, from the fun of a free ranging discussion.)

Then I'm sorry, but you haven't been listening and only seem to see what you want to see.

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10 minutes ago, studiot said:

Then I'm sorry, but you haven't been listening and only seem to see what you want to see.

Then could you clarify what I am missing, please.

Are you saying there are (valid, complete) equations which are not dimensionally consistent? If so can you provide a clear example?

Or are you saying that your various digressions are not random and have a clear purpose? In which case, could make that purpose clearer?

You have made a few posts along the line of "what about this ..." Where the only response is "what about it". But then you don't explain what you were thinking of. For example, you posted an assignment statement from a programming language. This is syntactically similar to an equation but isn't one. What was the point to be made there? (But, of course, it was dimensionally consistent anyway. Many languages include type checking to ensure this is the case.)

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7 hours ago, studiot said:

i = i + 1

You missed out the bit that makes it clear that  you are talking about an instruction rather than an equation

LET I=I+1

Granted, most languages permit that bit of sloppiness, in much the same way that chemical equations have energy changes bolted on with no regard for decorum.

21 hours ago, ydoaPs said:

7 apples = 3 bananas

Especially if a banana costs 7 cents, and an apple costs 3.

Or if a apple weighs three ounces, and a a banana weighs 7

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1 hour ago, studiot said:

The ratio of energy to moment in say a static lever is meaningless since they are different things even though they have the same dimensions.

But for a moving lever, the ratio is the number of radians turned; not exactly meaningless.

Radians is an interesting cause of screw-ups in dimensional analysis. The confusion with rotations has lead to countless errors.

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3 hours ago, Bender said:

But for a moving lever, the ratio is the number of radians turned; not exactly meaningless.

Radians is an interesting cause of screw-ups in dimensional analysis. The confusion with rotations has lead to countless errors.

Once again, thank you for a productive discussion, rather than just heckling.

Yes you are correct

work done  = moment x angle turned

and since the dimensions of moment are the same as those of work/energy  angle is regarded as dimensionless.

Good point +1

However energy involved in a static lever is zero, but the moment may not be.

What say you ?

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So can we assume you have moved on from the original question? Do you consider that answered?

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6 hours ago, studiot said:

However energy involved in a static lever is zero, but the moment may not be.

What say you ?

1) it is not because you found a meaningless example that the ratio is meaningless in general. I could divide the length of my shoe laces by the time I brush my teeth, but that does not make length over time a meaningless ratio.

2) if someone is controlling a load with an actuator, the ratio of stationary energy consumption could be useful to determine whether it is cost effective to install a break instead of using the actuator to keep the load stationary. I admit that the power over torque ratio is probably more useful, and most likely not constant enough to be used at all. However, it is not because I cannot give a convincing example off the top of my head, that it can never have a meaning.

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10 hours ago, Strange said:

So can we assume you have moved on from the original question? Do you consider that answered?

No, Bender is providing an example of the original question working out in practice towards a better conclusion than the original statement.

Cooperation is better than confrontation.

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21 minutes ago, studiot said:

Cooperation is better than confrontation.

I’m sorry if you find my questions confrontational. I can’t help that though.

I still haven’t seen an example of a (valid) equation that is not dimensionally consistent. Are there any?

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8 hours ago, Strange said:

I still haven’t seen an example of a (valid) equation that is not dimensionally consistent. Are there any?

This is in danger of becoming a "no true Scotsman" argument.

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11 hours ago, John Cuthber said:

This is in danger of becoming a "no true Scotsman" argument.

I don't think so. The equality sign in a "proper" equation has specific meaning. It eg shouldn't matter if you switch right and left (= is commutative ). This property is violated by both the chemical reaction and the computer language assignment.

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Posted (edited)
On 23/02/2018 at 10:22 AM, Strange said:

I still haven’t seen an example of a (valid) equation that is not dimensionally consistent. Are there any?

I think that John Cuthber's posts show that he is well aware that Chemists have a more relaxed attitude towards dimensions, than Physicists.

eg

Acid + Base = Salt + Water.

Perhaps you could tell me the dimensions of the solubility products, Ksp for silver chloride and lead chloride respectively and explain why they are different?

Then perhaps you could look at this chemistry problem that is posted on some other science websites at this moment.

Quote
 Calculate the ksp value and the mass of precipitated Agcl when 10 mL of 0.01 Μ AgNO3 and 10 mL of 0.0001 Μ NaCl solutions are mixed? Please explain step by step

What reaction equation would you propose?

Edited by studiot

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5 minutes ago, studiot said:

I think that John Cuthber's posts show that he is well aware that Chemists have a more relaxed attitude towards dimensions, than Physicists.

I would say they have a more relaxed attitude towards the completeness of the equations (and, as a consequence, they may not be consistent).

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Posted (edited)

38 minutes ago, Strange said:

and, as a consequence, they may not be consistent).

So you agree that not all equations used scientifically are 'consistent' (dimensionally I presume you mean) ?

Talking of facts,

In fact most of the reactions here have assumed that Physicists have taken a perfectly good Mathematical process and usurped it for purposes of their own, declaring a sort of UDI that they and they alone have the right to decide how equations are used.

Equations are of Mathematics, not of Physics ( though I grant they are vey very useful).

In Mathematics 5 x 3 = 3 x 5 = 15 period.

But in Physics, 5 metes times 3 metres make 15 square metre which are not the same as 5 Newtons times 3 metres for instance.

Mathematics does not distinguish.

The chemical equation you declined to offer has a combination of units of concentration and units of mass.

The solubility constant is dimensionaly consistent in any one equation (including the one required here), but its units differs from reaction to reaction.

Edited by studiot

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Posted (edited)
5 minutes ago, studiot said:

But in Physics, 5 metes times 3 metres make 15 square metre which are not the same as 5 Newtons times 3 metres for instance.

That is also mathematics.

Edited by Strange

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No, that is the difference between Mathematics and other Sciences (if you conssider Mathematics a Science).

Mathematics deals only with the numbers. (Note I did not say Mathematics only deals with numbers and nothing else - that is a different proposition that is not true)

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Posted (edited)
23 minutes ago, studiot said:

But in Physics, 5 metes times 3 metres make 15 square metre which are not the same as 5 Newtons times 3 metres for instance.

Mathematics does not distinguish.

Off course mathematics distinguishes.

$5 m \cdot 3 m= 15 m^2$

While

$5 N \cdot 3 m= 15 Nm$

If $N \neq m$ ,

$5 Nm \neq 15 m^2$

I can't comment on the chemistry part, since it has been too long, and never in English.

Edited by Bender

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So are you saying that physics does not use mathematics?

5 minutes ago, studiot said:

Mathematics deals only with the numbers. (Note I did not say Mathematics only deals with numbers and nothing else - that is a different proposition that is not true)

Huh?

It only deals with numbers, but it doesn't deal only with numbers? Riiiight...

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Ok, I finally managed to get my math typesetting right. Apparently needs refreshing.

Anyway, in mathematics m is usually not equal to N (even if it can sometimes be)

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Gentlemen, you are just repeating yourselves, without any supporting reasoning or evidence.

If gamma had a value of 1 then the laws of Physics would be different, but 5 x 1.4 would still be 7,, which is the mathematics.

Any first year mathematician will be exposed to countless analysis texts and lectures that stress the mathematics of 5 is extracting ( and dealing with the theory of) the 'fiveness' of 5 from the application.

Conversely, any first year Physicist is likely to come across the solution to the wave equation which discards half the mathematics under the phrase we only want the real part of the solution. The imaginary part has no meaning.

Science gives meaning to the mathematics

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1 hour ago, studiot said:

Science gives meaning to the mathematics

Ok. Now what does this have to do with the discussion so far?

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1 hour ago, studiot said:

Gentlemen, you are just repeating yourselves, without any supporting reasoning or evidence.

Back at ya.

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53 minutes ago, Bender said:

Ok. Now what does this have to do with the discussion so far?

It was asserted (not by me) that dimensions are part of Mathematics.

I am suggesting (and backing it up properly) that dimensions are what differentiates Mathematics from other Sciences.

(This is not the place to argue whether Maths is a science or not - I don't care)

Dimensions are what give meaning (in the physical world) to mathematical statements such as 5 x 3 = 15.

Mathematicians don't care if there are any objects or groups of objects with the properties '5' & '3'

They just deduce that if there were then the result would be 15.

Nor do they care what particular value a numerical constant used in other sciences such as gamma might have.

But that value may matter vey much in the other science.

All I am trying to do is hold an open discussion about these things without the other person starting with a closed mind and just automatically and unthinkingly  rejecting everything.

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Mathematics may not care whether m equals 1 meter or 5 apples or i £, but it can handle dimensional analysis pretty well and does not allow dimensional inconsistency.

Some sciences, such as chemistry might be less strict in using the mathematical formalisms, such as the use of the equality sign.

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1 hour ago, Bender said:

Some sciences, such as chemistry might be less strict in using the mathematical formalisms, such as the use of the equality sign.

Less strict than what?

Mathematics itself employs the equality sign for more than one meaning.

1 hour ago, Bender said:

Mathematics may not care whether m equals 1 meter or 5 apples or i £, but it can handle dimensional analysis pretty well and does not allow dimensional inconsistency.

An assertion without proof.

I do agree that much of dimensional analysis can be put into mathematical form, just as can much of other aspects of Science.

But how is Science able to throw away part of the consistent maths in my example of selecting only the real part of a complete solution.

In other words what are 5 i metres, or what is the arcsin of 3 ?