20 years ago there was a mid-air plane collision caused by the use of differing standards: https://en.wikipedia.org/wiki/2002_%...-air_collision

At the time, some pilots were being trained to follow instructions from the Traffic Collision Avoidance System, and other pilots were being trained to ignore TCAS and follow instructions from Air Traffic Control. A seemingly small thing, but it lead to tragedy in this case.

I would hope engineers are trained the same way around the globe... Otherwise you're right: It could be a disaster waiting to happen.

The answer is based on the operator precedence. Unfortunately you cannot find the relevant part on the wiki page: https://en.wikipedia.org/wiki/Order_of_operations.
We have an additional operation, called implied (or implicit) multiplication, see for example here: https://www.themathdoctors.org/order...ultiplication/.
This is what was missing. I think this rule is not really implemented in some calculators....

Nov. 10, 1999: Metric Math Mistake Muffed Mars Meteorology Mission

And this, caused by an integer overflow, technically a software bug but still a math error...

A software vulnerability in Boeing's new 787 Dreamliner jet has the potential to cause pilots to lose control of the aircraft, from which:

Yes, it happens...

Speedcrunch gives 1.

https://heldercorreia.bitbucket.io/speedcrunch/

P.S.
I'd like to know how KCalc arrived at 48/8(14-8) = 806 after closing brackets, then 0.0595533498759 after pressing = ?

Wrong mode and poster didn't notice?

I get 36. KCalc 22.12.3.

I checked the mode after the 1st time I got those odd results. It was the correct mode: Simple.
I get 36 with the multiplication sign between 48/8 and (14-8).

nt.

-didn't know how to delete this post

nt.

-didn't know how to delete this post.

On second thought, never mind.

I had a link, but I got so disgusted when reviewing kernelhead's friend's confidently-wrong stupidity that I decided not to post it.

For the record, the correct answer is that the question is malformed. The link was valuable as a discussion how what is essentially the applied math community agreed to deal with that, but I knew that some people here would try to take it as more than that.

2 members found this post helpful.

Thanks for the post anyway dugan, it gave me the opportunity to read the entire thread again, to which I add the following comments.

I have no relevant degrees but have always had a love of math and physics myself, having studied extensively and enjoyed a successful career directly related to that study.

It seems to me the equation as originally posted is simply ambiguous, the ambiguity being whether or not the parenthesized term is part of the denominator or not (post #69 and others). Being ambiguous, neither form can be said to be correct and the other incorrect. If there is an actual intent that it be one way or the other it is up to the person originating the expression to force that ordering by parenthesis.

I was taught, or at least learned in public school in the 1960's that multiplication and division have the same precedence, resolved by left-to-right ordering in absence of parenthesis.

I first encountered the expression PEMDAS when educating my own children (all home schooled), and understood it to mean: ... and taught it that way. (And one of the refs previously cited in this thread presents it exactly this way).

Requiring that PEMDAS specifies multiplication to have a higher precedence than division without the same requirement for addition and subtraction seems somehow disingenuous.

I learned my first advanced math using a slide rule, and was always keenly aware that it was up to me to force precedence in written expressions if there were any reasonable possibility that they might be understood differently by others. Had 48/8(14-8) ever arisen and led to differing results one would have just asked what was intended. I cannot imagine one insisting theirs was correct and the other wrong in such a case and arguing about it.

We no longer use slide rules but have a variety of wonderful electronic devices to solve our equations, but the same operator discipline must apply. Unless we we are going to insist that every device conforms to a single input expression format and produces the identical output, we must recognize that it is up to the operator to assure that the input correctly expresses their intent within the limitations of the given device. Nothing else seems reasonable.

The argument that this supposed error derives from the C programming language seems just silly to me.

The main argument I've seen for doing it the other way (both in this thread and in the link I held back) is that 8(14 - 8) and 8 * (14 - 8) are not the same. That's what the nonsense about "juxtaposition" is about.

Somebody wanted a statement from an actual math expert?

https://twitter.com/LongFormMath/sta...75300204114254

1 members found this post helpful.

From the X link posted by dugan, worth permanently preserving here...

Thanks dugan.

The problem is that this PEMDAS is wrong. We have an additional operation (as it was already explained in post #77). That is the implied/implicit multiplication. It is not mentioned on the wiki page you linked, therefore that wiki page is incomplete too. This operation has a relatively high precedence: PEIMDAS
You cannot discuss this question without knowing the existence of this additional possibility (just because it is all about that I). And obviously you cannot find the correct answer without that (that will lead to confusion and misunderstanding).
What is really surprising: this I operation is very little known, they don't teach it at school and even those who work with it (=make calculators or teach it) don't know anything about it.
Even more interesting is that this I operation is all around us, a part of our everyday life. You always speak about 2 apples, 5 tickets or similar. And if you have 30 eggs and you want to put them in baskets (which can hold 10 eggs), you realize: 30e/10e = 3, and it will never be 3e**2.

I will reserve comments on implied multiplication itself for another post, if at all, but the above is contrived, and is just wrong.

"30 eggs" does not involve multiplication of number, 30, and physical object, eggs. What would it even mean to multiply a number and an egg?

If you write 30e to mean 30 eggs then the only possible way to interpret it is 30 times the unit quantifier, an egg, the unit always and by definition being 1 (think unit vectors, for example).

So, for this case e explicitly and always equals 1, the unit of "egg", and 30*1/10*1 = 3, a pure number, not an egg, no matter how you parenthesize it, with no special precedence rules necessary.

This illustrates the problem with contrivances such as the original problem in this thread - contrivances inevitably beget contrivances and we all lose our way!