...

Just for giggles I will do my next calcbook unitless and will see what sort of feedback I will get. ... Assume a spherical cow in a vacuum... Wait! its a coccus with horns and a tail!!!

Jean, you concept of unitless math is very true; however, math applied usually asks for a some sort of a frame of reference, which is given to us by the units.

Alex, what's good about units: they are democratic. Very useful up to college level.
m*m*m*m = m^3 and similar stuff. Entering avdvanced maths, symbolic engines reply
in red [Mathcad 11] or a full page in blue [Mathematica 4.0].

Try this: push the greasy round cow in the square hole ... corned beef for Easternes.

Jean

Wrote

By the way, your Reynolds formula, being physically incorrect, also doesn't compensate for using centipoises.

Wrote

So you are reasoning, that engineers should:

1. substitute their understanding of a physics of what they work with, with some authorized magic formulas,
   
2. blindly believe that those formulas are correct?

Let me link here an example article that discusses one Russian standard where gas hydraulic formulas are given. Unfortunately, it's in Russian. It discusses the incorrectness of that formulas, and the causes that had lead to that incorrectness. Among them are using "magic coefficients" that stem from using values in specific nonstandard units (like your cp, or t/hr), "masking" real physic laws with "convenient" formulas (they are "convenient" only when you need to use paper for calculations), and arbitrary rounding of those coefficients. Contemporary software is capable of taking your favorite units, and do robust translation to standard units so that you only have to know physics, without having to remember useless coefficients.

Having those magic formulas in standards is simply remnants of the era when you had not softwares that allow you to express physical laws in their natural ways, when you had to use such "convenience" formulas just to be able to do maths in a timely fashion. And they do have errors in them, because of that. Reasoning like yours would just prevent fixing those standards to contain pure physics instead of that crap.

I know many engineers that don't understand the underlying physics and just use those formulas as "black boxes" to get answers. That leads to improper use of the formulas, just because they cannot see the range of applicatibility of them! And it's difficult to catch errors in their complex calculations, because of those cryptic formulas.

Wrote

Actually, your point here eludes from my understanding. From what I see, it looks exactly analogous to this reasoning:
"Let's take some common words: "Number of minutes". Now, let's "multiply" (mix) them by some other word: "min". Let's see result: "Nmuimnbmeirn moifn mmiinnmuitnemsi". Utter garbage! Never use units!"

Using units properly in math software isn't taking a number that you made unitless explicitly, and trying to see its absent units.

Wrote

So what? You have a job that requires you to do dimensionless maths. Does that mean that each must do same regardless of their circumstances?

Wrote

Alex, what's good about units: they are democratic. Very useful up to college level.
m*m*m*m = m^3 and similar stuff. Entering avdvanced maths, symbolic engines reply
in red [Mathcad 11] or a full page in blue [Mathematica 4.0].

Prof. V. F. Ochkov of Moscow Power Engineering Institute, an expert in Mathcad and other math packages, one of the authors of IAPWS standards and their software implementation, has a number of articles in Russian and in English, where he goes in depths discussing units in maths. I could't do better.

I just want to emphasize the difference of "pure" math and applied computations.
Sometimes, people do pure math. And yes, it is unitless.
But math is just the language of science, so it's science that uses math to express its relations. The science fills maths with meaning, and that meaning may be expressed with units. Proper use of units may help understanding the relations, or see new relations, or discover shortcomings of a theory, or allow catching logical errors in input data.

Having a tool that allows you to quickly catch errors is golden in any work. However pedantic you are, you aren't bullet-proof from errors. Even though you may "dismiss" some errors as "irrelevant", they are inevitable. And being able to catch x% of them almost for no price (modulo some short training) is precious! Yes, you having very trained brain, may make less errors, but your price is more attention to details that could be spend better doing useful work, if you allow software do some muscle job for you. And if some software gives you errors when you use units, this may indicate that either you use improper math (go fix it!), or you're dealing with some empirical formulas, or maybe some problem in software that should be fixed, instead of calling this proper software behaviour.

Let's look at an analogous case. In recent decades, software programming languages have evolved immensely. And they started without type check. When the type checking appeared, it quickly became great tool allowing to catch errors easier. It has its rough edges, but it continue to evolve and it gets better each iteration. And they don't argue that "type checking is for kiddies"! Because keeping 1 hr a day from dumb work allows me to do more work in that hour, instead of being proud of being "true hacker" accomplishing less.

Units aren't silver bullet. They must be used wisely; you need some training to do that. Their systems evolve, aren't something established for ages. There are times when you need some extra effort (esp. when dealing with empirical formulas). There are tasks that are better done without them. There are people that dislike them. But it's plain wrong to blindly call them useless, and ask everyone to abandon this tool!

0.3537 is like a universal constant in the SI t/hr in Process control fluid mechanics.
The all matter is if unit system is proftable use it and abuse reading as you wish.
Don't fill air plane in lbs instead of kg as it happened [miracle, nobody got killed].
Just make your client happy unit/unitless. Wise to know both routes.

Don't forget that most decision makers are old timers like myself, using references
[books, standards ...] that use unitless maths. All your blue stuff would make many
laugh, wondering about the burden to cross check results.

Cheers, Jean. No point to read more on that.

Many of us, adept or not of units, we will suck the roots beore seing
a unified system work for all users and all systems. Units won't make
the maths work, rather the vice versa. One I forgot: the quadratic
meter [m^4 => quadratic moment]. The sole reference to keep track of
the SI in evolution is the BIMP as new sientific units appear evry
moment, vg: the unit of the strength of the peper sauce "scott", no
recollection of the orthograph.

Behind the scene, the unit system is an adjoined processing system
that will require error mesages and which one will be guilty ?
That puzzles me a lot. Good thing: it will keep Smath teams
[Designers/Collabs] in fruitful conversation.

As a byside comment: the Maple blue, Smath blue is the worst color
choice, why ? Not ergonomic, why ? blue is the least abondant color
in nature. It keeps the Fourier part of the brain pedalling and
obstructing the mind. The true vision of the human eye is jut a little
circle, the remaining is visual extrapolation. What other color ?
Green, the most abundant color in nature ? Worst choice again, why?
Mot abundant color in nature,,, not green again my little brain says.
My choice is red [pure or denatured] ... I have voted.

Jean

Wrote

...

Stream of consciousness.
At least when talking to someone who describes himself engineer, I hoped to see clear and precise definitions and arguments.

You right Mike: we are saying the same thing, in different words.
Not a joke, the day I received a 48" butterfly valve to be installed in a 4" pipe:
all the monkeys went down the three to admire the new born "Strümpfchen" .

Jean