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[Kirian]

One of the benefits of the metric system -- versus the imperial system -- is that you have fewer conversions.  Rather than having inches, feet, miles, furlongs, rods, hectares, acres, gallons, fluid ounces, teaspoons, and so forth you have meters.  Then you can have centimeters, kilometers, square meters, cubic centimeters etc., but you can convert amongst them trivially.

Well, YOU can, because you're very comfortable with using base 10. But the appendage comment enough points out this is a peculiarity to members of our species, rooted in cultures which use mathematical systems which eventually owe something back to the fact that a recessive trait is near-ubiquitous.

Yes, polydactylism is dominant.

I... I'm not sure how polydactyly being a dominant trait matters at all here.  Having ten digits may be recessive, but so is not being a dwarf.  Meanwhile, pentadactyly, despite being recessive, traces back to ancestral tetrapods.  Having ten fingers is the basal state.

The temperature scale didn't have that issue.  These days, the main advantage of the Celsius scale is its near universal ubiquity (which is a significant advantage, by the way!).

Well, except that your grams, metres, and litres aren't entirely arbitrary in their definitions. I mean, one of them is, but the others are based on having water having a density of 1 and handy conversions between the units (1 ml = 1 cm^3) under "standard atmospheric Earth conditions" (another way that the system is Earth-centric). Celsius scale has this advantage as well - 0 and 100 are special for water in such conditions. Actually, it's somewhat strange to my mind that the figures work out on round degrees in Fahrenheit. Probably if I looked a bit more into the history, I'd find that there is a reason for this (like it got rounded or changed at some point).

And yes, this is another thread ne-ne-ne-ne-necro.

Yes, obviously all of the original metric definitions are Earth-centric, which seems entirely reasonable given our lack of contact with extraterrestrial lifeforms.  It's not exactly a cultural ethnocentrism that causes systemic discrimination.

And none of the original metric units were arbitrary that I know of.  The kilometer was one ten-thousandth the distance from pole to equator; the kilogram was of course based on the mass of a liter of water, with liters derived from meters.  The second was based on its traditional definition, and you've already noted how the Celsius (and therefore Kelvin) scale was derived.  I suppose the ampere, candela, and mole are not Earth-centric, except insofar as the first two rely on the definitions of the meter.

[sudgy]

And none of the original metric units were arbitrary that I know of.  The kilometer was one ten-thousandth the distance from pole to equator; the kilogram was of course based on the mass of a liter of water, with liters derived from meters.  The second was based on its traditional definition, and you've already noted how the Celsius (and therefore Kelvin) scale was derived.  I suppose the ampere, candela, and mole are not Earth-centric, except insofar as the first two rely on the definitions of the meter.

The mole relies on the definition of the gram...

[Kirian]

And none of the original metric units were arbitrary that I know of.  The kilometer was one ten-thousandth the distance from pole to equator; the kilogram was of course based on the mass of a liter of water, with liters derived from meters.  The second was based on its traditional definition, and you've already noted how the Celsius (and therefore Kelvin) scale was derived.  I suppose the ampere, candela, and mole are not Earth-centric, except insofar as the first two rely on the definitions of the meter.

The mole relies on the definition of the gram...

Ah yes, good point.

Edit:  Have I mentioned anywhere that I simply cannot wait for the new SI definitions to be adopted?  It's like Christmas for people who are interested in metrology!

[sudgy]

And none of the original metric units were arbitrary that I know of.  The kilometer was one ten-thousandth the distance from pole to equator; the kilogram was of course based on the mass of a liter of water, with liters derived from meters.  The second was based on its traditional definition, and you've already noted how the Celsius (and therefore Kelvin) scale was derived.  I suppose the ampere, candela, and mole are not Earth-centric, except insofar as the first two rely on the definitions of the meter.

The mole relies on the definition of the gram...

Ah yes, good point.

Edit:  Have I mentioned anywhere that I simply cannot wait for the new SI definitions to be adopted?  It's like Christmas for people who are interested in metrology!

...There's new SI definitions?!?!?

EDIT: I just looked into it, I see now that they're redefining them without a change to their actual measurement.  That makes more sense.

[Kirian]

And none of the original metric units were arbitrary that I know of.  The kilometer was one ten-thousandth the distance from pole to equator; the kilogram was of course based on the mass of a liter of water, with liters derived from meters.  The second was based on its traditional definition, and you've already noted how the Celsius (and therefore Kelvin) scale was derived.  I suppose the ampere, candela, and mole are not Earth-centric, except insofar as the first two rely on the definitions of the meter.

The mole relies on the definition of the gram...

Ah yes, good point.

Edit:  Have I mentioned anywhere that I simply cannot wait for the new SI definitions to be adopted?  It's like Christmas for people who are interested in metrology!

...There's new SI definitions?!?!?

Yep.  Just like we have defined the speed of light as a specific nine digit number, and the value of the meter depends on that, the plan is to define, IIRC, Planck's constant for the kg, electron charge for the ampere, the Boltzmann constant for Kelvin, and the Avogadro constant for the mole.

[sudgy]

And none of the original metric units were arbitrary that I know of.  The kilometer was one ten-thousandth the distance from pole to equator; the kilogram was of course based on the mass of a liter of water, with liters derived from meters.  The second was based on its traditional definition, and you've already noted how the Celsius (and therefore Kelvin) scale was derived.  I suppose the ampere, candela, and mole are not Earth-centric, except insofar as the first two rely on the definitions of the meter.

The mole relies on the definition of the gram...

Ah yes, good point.

Edit:  Have I mentioned anywhere that I simply cannot wait for the new SI definitions to be adopted?  It's like Christmas for people who are interested in metrology!

...There's new SI definitions?!?!?

Yep.  Just like we have defined the speed of light as a specific nine digit number, and the value of the meter depends on that, the plan is to define, IIRC, Planck's constant for the kg, electron charge for the ampere, the Boltzmann constant for Kelvin, and the Avogadro constant for the mole.

Yeah, I was thinking that it was going to be things like the meter is now 50% larger (it would be something that makes more sense) or something like that.

[Ozle]

Edit:  Have I mentioned anywhere that I simply cannot wait for the new SI definitions to be adopted?  It's like Christmas for people who are interested in metrology!

What your going to sit around in your underpants eating cold turkey watching Home Alone when it happens?

[SirPeebles]

This topic is the 10th most viewed on the forums?  Really?

[jonts26]

This topic is the 10th most viewed on the forums?  Really?

Order of operations is serious business.

[SirPeebles]

This topic is the 10th most viewed on the forums?  Really?

Order of operations is serious business.

I'm currently grading quizzes for my differential equations class, and these students still make order of operations mistakes.

In the first homework assignment they had to check that y=e^-t/2 - e^-3t is a solution to y' + 3y = e^-t.  My office hour was full of one student after another who was stumped because they interpreted the solution as y=e^-t/(2 - 3e^-3t).

[Kirian]

This topic is the 10th most viewed on the forums?  Really?

Order of operations is serious business.

I'm currently grading quizzes for my differential equations class, and these students still make order of operations mistakes.

In the first homework assignment they had to check that y=e^-t/2 - e^-3t is a solution to y' + 3y = e^-t.  My office hour was full of one student after another who was stumped because they interpreted the solution as y=e^-t/(2 - 3e^-3t).

To be fair, if the problem was written like that, then it was poorly written; that first term can be unambiguously written with a standard division bar, or as 0.5e^-t

[jonts26]

I don't see any ambiguity there. Using / for inline equations is pretty standard. I guess you could have used 0.5 instead, but what if you wanted e^-t/x -e^-3t? That's the most compact way to do it, unless you want to argue for the always use x^-1 notation. Though if you're writing up homeworks it would be nicer to use an equation editor to make things look nicer.

[SirPeebles]

This topic is the 10th most viewed on the forums?  Really?

Order of operations is serious business.

I'm currently grading quizzes for my differential equations class, and these students still make order of operations mistakes.

In the first homework assignment they had to check that y=e^-t/2 - e^-3t is a solution to y' + 3y = e^-t.  My office hour was full of one student after another who was stumped because they interpreted the solution as y=e^-t/(2 - 3e^-3t).

To be fair, if the problem was written like that, then it was poorly written; that first term can be unambiguously written with a standard division bar, or as 0.5e^-t

The standard division bar would have taken up more space.  And eww, I really don't like to see decimals used for something like that.  My preference would have been (1/2)e^-3t.  But honestly, the textbook was fine here.  There shouldn't have been any confusion whatsoever.  Or at least, the students should have been able to notice the potential amibiguity and checked both solutions rather than come to my office hour just for this question.  Don't get me wrong, I like it when students come to my office hour.  But it tends to take a lot to get a student to go, so this must have genuinely stumped them.

jonts, it was in a textbook.

[Polk5440]

This topic is the 10th most viewed on the forums?  Really?

Order of operations is serious business.

I'm currently grading quizzes for my differential equations class, and these students still make order of operations mistakes.

In the first homework assignment they had to check that y=e^-t/2 - e^-3t is a solution to y' + 3y = e^-t.  My office hour was full of one student after another who was stumped because they interpreted the solution as y=e^-t/(2 - 3e^-3t).

To be fair, if the problem was written like that, then it was poorly written; that first term can be unambiguously written with a standard division bar, or as 0.5e^-t

You must disagree with the whole point of this thread, then. Order of operations exists SO THAT there is no ambiguity. There isn't a difference between Sir Peebles's example and the title of this thread.

[SirPeebles]

I don't have time for a full response.  As I see it, an ambiguity is a human thing.  It is when the audience sees multiple interpretations of a statement.  The order of operations present a framework for resolving certain ambiguities in mathematical exposition.  They do not prevent the ambiguities from manifesting for the audience unless the audience has fully internalized them.  It is the role of style to prevent ambiguities.  Of course, unambiguous writing can be at odds with clear writing, which is another reason conventions are set.

[Kirian]

This topic is the 10th most viewed on the forums?  Really?

Order of operations is serious business.

I'm currently grading quizzes for my differential equations class, and these students still make order of operations mistakes.

In the first homework assignment they had to check that y=e^-t/2 - e^-3t is a solution to y' + 3y = e^-t.  My office hour was full of one student after another who was stumped because they interpreted the solution as y=e^-t/(2 - 3e^-3t).

To be fair, if the problem was written like that, then it was poorly written; that first term can be unambiguously written with a standard division bar, or as 0.5e^-t

You must disagree with the whole point of this thread, then. Order of operations exists SO THAT there is no ambiguity. There isn't a difference between Sir Peebles's example and the title of this thread.

Well... in effect, yes.  Any mathematical expression can be written unambiguously without resorting to order of operations, via some combination of parens, fraction bars, and the like.  This is especially important in programming, where you're writing expressions on a single line and using functions like sqrt() for some expressions, and where you often have variables that aren't just single symbols.  I know some people think parens look ugly, but ambiguity is, in my opinion, worse.  So, for instance, to do an amortization:

$i = $yearly_rate/12;
$payment = ( $principal * $i * ( ( 1 + $i ) ^ $months ) ) ) / ( ( ( 1 + $i ) ^ $months ) ) - 1 );

The compiler can't misinterpret this because there is only one type of operation within each set of parentheses.

[jonts26]

The problem with your statement is that human brains don't work exactly like computers. Yeah, there's no ambiguity, but I, and most people, wouldn't be able to interpret that equation quickly. Huge amounts of nested parentheses become cumbersome and I end up having to translate into an easier form. When I'm coding longer equations, I have to pay really close attention because it's easy to make mistakes in translation to how I would write and be able to easily read an equation and how the computer must read it.

[Kirian]

The problem with your statement is that human brains don't work exactly like computers. Yeah, there's no ambiguity, but I, and most people, wouldn't be able to interpret that equation quickly. Huge amounts of nested parentheses become cumbersome and I end up having to translate into an easier form. When I'm coding longer equations, I have to pay really close attention because it's easy to make mistakes in translation to how I would write and be able to easily read an equation and how the computer must read it.

Certainly, but there are other ways to make it clearer to humans; lose the outermost parens on each side of the division, and replace the division with a fraction bar; then, because we can write the exponential in a clearer form when a human reads it, we can lose those parens; etc.  Similarly, polynomial terms can be written in specific ways that make them human-readable.  For the most part, the ambiguity only occurs when:

1. The operations are all on a single line;
2. Someone has intentionally tried to obfuscate the math.

Note that the original "problem" in the thread had both of those problems.

[StrongRhino]

I never learned the acronym for PEDMAS (or its variants), but I have seen how it's been misused. The problem with PEDMAS is that it can be interpreted to mean that you divide before you multiply and that you add before you subtract, when those operator pairs are equal in priority (and should therefore be done left to right).

For example, we have:
8-6+4=?

If you literally read PEDMAS as doing addition first, then you conclude the answer is -2. But since addition and subtraction have the same priority, you go from left to right, so the answer is actually 6.

Instead of learning PEDMAS, I just learned that the operators were grouped together, which makes sense, since subtraction is just addition and division is just multiplication. I just learned that multiplication happens before addition. Then we learned parentheses. Exponents would have come later. By the time I got to that point, we had known the order of operations.

I wouldn't teach PEDMAS if I were in a classroom. From what it sounds like, it's fairly ubiquitous, so I guess I'd be doing a disservice by ignoring the acronym. I would definitely teach it as PE(DM)(AS). Maybe use colors PEDMAS. It was actually one of those annoying trolling equations where I saw someone claim an entirely different answer because she used PEDMAS incorrectly, so now I'm wary of that tool.

PEDMAS? I've always heard it as PEMDAS.

[Awaclus]

[SirPeebles]

[eHalcyon]

Ugh, the comments on that video.

[SirPeebles]

Ugh, the comments on that video.

I have never in my life seen someone write 5.3 feet when they meant 5'3''.  And as a math professor, I have seen some absolutely horrendous crap from my students.

[Kuildeous]

Ugh, the comments on that video.

"You should do this about the metric system as well. Because that is incredibly more inconsistent."
"View all 62 Replies."

Oh, this is going to be good.

[theory]

I had a little argument with some others on this forum when I defended the use of Fahrenheit over Celsius.  In all other aspects, I think the metric system is generally preferable, but you will never convince me that Celsius is better for everyday use than Fahrenheit.