order of operations in a straight equation

[JEL]

Wouldn't it actually be more prudent to do away with the fixed order of precedence, and simplify the understanding of math by having precedence just take place based on order of appearance? Basically apply the KISS-rule here
And then only use brackets whenever deviations from the straight-forward are needed.

It seems to me that this obscure rule isn't doing math-ubergeeks any favors among the more simple-minded lower-class populace. You facepalm them, they facepalm you, no one gets any smarter

 

[agentgonzo]

Wouldn't it actually be more prudent to do away with the fixed order of precedence, and simplify the understanding of math by having precedence just take place based on order of appearance? Basically apply the KISS-rule here
And then only use brackets whenever deviations from the straight-forward are needed.

Unfortunately, no it wouldn't. Unless you have a strict order of precedence, things can be open to interpretation and misunderstood leading to confusion. Mathematics is based on strict rules and it needs to be defined by them, otherwise the whole field falls down around itself. 'Order of appearance' is subjective and whilst it makes sense with 10 + 10 * 0 it gets entirely confusing with more complicated equations. Spraying brackets around just makes everything hard to read. In a way, the KISS rule here is to do exactly NOT what you are saying - ie stick to one simple order of preference EVERYWHERE. It's far simpler than trying to figure out which one gets performed first for each equation.

It seems to me that this obscure rule isn't doing math-ubergeeks any favors among the more simple-minded lower-class populace. You facepalm them, they facepalm you, no one gets any smarter

To be fair, math uber-geeks don't really care that the thickos don't understand their language in the same way that Guatamalan people don't care that the ancient Aztecs couldn't understand their language. They're not going to communicate with them so what does it matter?

Mathematicians have an entirely coherent and logical language with which they can express their ideas to other people who understand the language. That is the only factor in it. If people don't understand the language, they can either learn it or sit there whining about it being too complicated whilst they sit there flipping burgers for a living.

 

[Artlav]

this obscure rule

But the problem is that this rule is far from obscure, it's one of the basic ones.

Disambiguation is paramount in a precise language like mathematics.
Imagine the english language without order of words.
Nous what verbs and adjectives not apparent that reference is it.

There is a way to do away with order and make it as simple as possible - reverse polish notation.

10+10*0 will be 10 10 0 *+
2048-128*(10+6) will be 2048 128 10 6 +*-

Straight, no obscure rules, nothing to worry about, not human readable.
That is what the expressions is often translated to by computers before evaluating.

 

[agentgonzo]

reverse polish notation.

My directory of studies at uni had a reverse polish calculator. Most confusing calculator I've ever used. Ended up having to use a normal one to check that I was doing the input correctly! Fun though

 

[Artlav]

Human-readable and computer-readable are two completely distinct things, and even experts sometimes fail to understand that.
Just look at the big-endian vs little-endian discussions.

 

[GoForPDI]

Well.. I was always taught to Divide first, then Multiply, then Add, then Subtract.

And there are clear differences between (10 + 10) x 0 and 10 + (10 x 0)

This is just some smart arse on Facebook giving a trick question.

 

[C3PO]

My directory of studies at uni had a reverse polish calculator. Most confusing calculator I've ever used. Ended up having to use a normal one to check that I was doing the input correctly! Fun though

The engineering school I graduated from encouraged everyone to use RPN, and I still use my good old HP 48GX. I even have the calculator in my smartphone in RPN mode.

 

[JEL]

Mathematics is based on strict rules and it needs to be defined by them, otherwise the whole field falls down around itself.

I fully agree with you. A language without pre-defined rules is chaotic.
But that doesn't mean we shouldn't try to improve on the rules, making them simpler, easier and more straight-forward to understand for a wider range of people, thus including more people in the club of those who understand it and can use it. There's no reason to make it harder than it has to be

'Order of appearance' is subjective and whilst it makes sense with 10 + 10 * 0 it gets entirely confusing with more complicated equations.

Could you give me an example-equation?
An equation that would be more difficult to write if using only a left-to-right order of precedence for the operators (you're still allowed the use of brackets)

I was just thinking that since western standard is to read from left to right, it would make more sense to students (and non-mathematicians in general) if math followed that same standard (reduce and simplify... I believe that's a golden rule of math )

Is there ever a time where an educated mathematician would need to write 10 + 10 * 0 rather than 0 * 10 + 10 ?

As a fun experiment; try opening your windows calculator.
Enter 10 + 10 * 0 in both standard view and scientific view... you get 2 different results based on which view you're in. That's not good.
Now enter 0 * 10 + 10 in both standard view and scientific view... you get the same result in both views. That's much better. More consistent, more rigid, more stable = less confusion, less prone to errors, closer to the goal of a universal language.
KISS: when using a left-to-right order of precedence your calculator doesn't need to be clever to give the correct answer = everybody wins

 

[Artlav]

Is there ever a time where an educated mathematician would need to write 10 + 10 * 0 rather than 0 * 10 + 10 ?

Electrons have negative charge despite of having a charge, did you know that?
Makes no sense, all because some scientist who made the notation guessed wrong.
Why is the notation still there?

The computer you're staring at is running on x86 architecture (unless it's a phone or some geeky thing), which is a clusterfoock of crutches and compatibility hacks.
Why is this architecture still there?

Same about mathematical language - with billions of texts written in regular notation an billion people knowing how to speak it, changes would only make untold confusion.

It's not always worth dumbing things down to common denominator.

 

[agentgonzo]

Could you give me an example-equation?
An equation that would be more difficult to write if using only a left-to-right order of precedence for the operators (you're still allowed the use of brackets)

Starting simply, what is ¼ + ¾?
Under the conventional system, it's 1:
Under LtoR it's 13/16. You'd have to write (¼) + (¾) to make it what was intended, adding parentheses which just bloat out the equation.

As for confusing, what about:
[math]\frac{1+2}{3+4}[/math]What does this equate to? ((1 + 2) / 3) + 4. That's misleading as the division bar encompasses all of 1+2 and 3+4, but under LtoR rules it wouldn't.

You can even have simple things that become confusing.
What is [math]4x^2[/math]? Under your method, it's actually [math](4x)^2 = 4x \times 4x = 16 \times (x^2)[/math]
Extending this, what about [math]a^2b^2[/math]? Under your method, it's different to [math]b^2a^2[/math] because
[math]a^2b^2 = ((a^2)b)^2 = (a^4) \times (b^2)[/math]

---------- Post added at 15:46 ---------- Previous post was at 15:43 ----------

The computer you're staring at is running on x86 architecture (unless it's a phone or some geeky thing)

Actually, it's more likely to be running x64 or IA-64 nowadays.

 

[Artlav]

x64 or IA-64 nowadays.

IA-64 is marginally forgotten server architecture, and never appeared on desktops.

x64 is x86-64, which is an extension of x86 to 64 bit, i.e. another layer of crutches.

Neither would have been a choice for any rational programmer, except for the fact that it owns the market due to overwhelming backlog of programs made for it.

 

[jthill]

Do away with operator precedence you'll be writing so many parentheses around terms you'll get sick of it and propose operator precedence.

 

[Artlav]

Actually, isn't there an "operator precedence" in spoken language as well?

Put together ten apples and ten oranges=10*a+10*b.

It arises naturally from spoken language, since you won't say you'll end up with 20 apples of oranges, you'll end up with 10 apples and 10 oranges.

Multiplication is number of objects, counted before the summation of all objects.
What can be simpler than that?

 

[Ross]

Do away with operator precedence you'll be writing so many parentheses around terms you'll get sick of it and propose operator precedence.

:rofl:

Although, being a math tutor, I find that when students are learning algebra, it is helpful to put in many parentheses and grouping symbols so they realize which operations come first. But they have to be taught which operations come first.

When I saw the screenshot of the argument, I was appalled! It just shows how people's convictions and perceptions are stronger than their logical reasoning (at least in this case).

No brackets = no bedmas????? come on!!!! We still have exponents, multiplication/division, and addition/subtraction. Wow. I'm glad I chose to be a math major If anything, I understand the order of operations!

-------

Artlav: Nice way of explaining it

 

[JEL]

Starting simply, what is ¼ + ¾?
Under the conventional system, it's 1:
Under LtoR it's 13/16. You'd have to write (¼) + (¾) to make it what was intended, adding parentheses which just bloat out the equation.

As for confusing, what about:
[math]\frac{1+2}{3+4}[/math]What does this equate to? ((1 + 2) / 3) + 4. That's misleading as the division bar encompasses all of 1+2 and 3+4, but under LtoR rules it wouldn't.

You can even have simple things that become confusing.
What is [math]4x^2[/math]? Under your method, it's actually [math](4x)^2 = 4x \times 4x = 16 \times (x^2)[/math]
Extending this, what about [math]a^2b^2[/math]? Under your method, it's different to [math]b^2a^2[/math] because
[math]a^2b^2 = ((a^2)b)^2 = (a^4) \times (b^2)[/math]

I stand down . Good points and examples. Excellent in fact
Thanks

 

[fireballs619]

Actually, isn't there an "operator precedence" in spoken language as well?

Put together ten apples and ten oranges=10*a+10*b.

It arises naturally from spoken language, since you won't say you'll end up with 20 apples of oranges, you'll end up with 10 apples and 10 oranges.

Multiplication is number of objects, counted before the summation of all objects.
What can be simpler than that?

Along these lines, we can see how ambiguous statements exist in language, similar to how 10 + 10 x 0 is quite ambiguous in mathematics. Consider the statement "I would like a Coke or water with ice.". What exactly does this statement request? Does the person want a (Coke) (or Water with ice), or do they want (Coke or Water) (with Ice)? Ambiguous statements like these should be avoided while writing or speaking, just as ambiguous expressions like 10 + 10 x 0 should be avoided. In other words, if one is careful with his or hers work, this whole predicament can be avoided.

 

[agentgonzo]

just as ambiguous expressions like 10 + 10 x 0 should be avoided. In other words, if one is careful with his or hers work, this whole predicament can be avoided.

Yes. And the ambiguity in the statement 10 + 10 x 0 is neatly avoided by having rigourous mathematical rules to expressly state what this means, ie 10 + (10 x 0)

 

[fireballs619]

Yes. And the ambiguity in the statement 10 + 10 x 0 is neatly avoided by having rigourous mathematical rules to expressly state what this means, ie 10 + (10 x 0)

Exactly! Unfortunately however, some people don't realize the parenthesis are implied there, and there for go left to right. I bet if the original question was formed in the way you have just presented it [ such as 10 + (10 x 0) ], there would be many less errors on the Facebook poll.

 

[JEL]

Any thoughts on the windows calculator giving different results based on whether or not you use it in standard versus scientific view?

With personal laptops (running windows) being used more and more in school it seems to me that this behavior could lead to more confusion rather than better education. Some students maybe run the calculator in standard view while others (the geeks perhaps) run it in scientific view. Mayhem in class.

Heard in class:
"But the calculator on my computer says it's zero!?!"
"Yeah really!? On mine it says it's 10!?"
"Your computer sucks! It's Vista, I have win7!"
"You're stupid! Mine is x64, yours is only x86"
Meanwhile the teacher is pulling his or her hair out while fearing the parents raising a complaint about bad teaching and maybe even a law-suit against the school...

I think I would prefer if Microsoft got their calculator set up so it always gave the results the math-rules prescribe, regardless of which view it's used with.
Their default Works spreadsheet gets it right though. Atleast on my computer (knock on wood)


I wonder how many other pocket-calculators will have "10 + 10 x 0" be zero?

I just tried my iPhone calculator, it gives 10 as the result.
Maybe my next computer should be an Apple... :hmm:

 

[HarvesteR]

I've tried it here too... very misleading indeed.

But it should be common sense that pocket calculators will only do one operation at a time. You can't chain operations as you would with a scientific calculator.

So a pocket calculator expects you to know that limitation, and calculate one term at a time, knowing the rules of precedence... that's why it has those memory functions no one uses.

Sadly, it appears a lot of people just don't

Cheers