What's the answer to this very basic maths problem?

I think Wolfram Alpha does it the way it does only because the tools to enter the sum properly do not exist online in a convenient way. Touch devices are new and hand-writing recognition inconsistent. They HAVE to deal with calculator style single-line entry.

I think you're both right really, in that you both recognize you're arguing within a framework that is artificially constraining. You both recognise that if you broke out of this framework to real mathematical notation, you would be in agreement. One of you even said that past primary school, the operator symbols should be abandoned. They create a false idea of chained operations whereas real maths isn't like sequential programming, but like functional programming (for those who are familiar with that).
 
danlightbulb said:
I get what you are saying.

What I would like to do is find a known formula that describes something. Then demonstrate that only one convention works, otherwise you end up with a nonsense formula. I stand to be corrected that it lands the opposite way to what I think lol.
Click to expand...

I'm not really sure what you mean? What do you stand to be corrected on? I'm not sure what finding a known formula written in a way which already assumes one convention is going to show as of course then using the other will make no sense or at least be confusing. Though then again I'm not sure why anyone would need to write out a formula using either these days anyway as division can be made much more explicit. I suspect that anything in say old physics journals/books (as mentioned by the wikipedia article) where stuff is written on one line probably would give higher precedence to implicit multiplication.

h4rm0ny said:
I think Wolfram Alpha does it the way it does only because the tools to enter the sum properly do not exist online in a convenient way. Touch devices are new and hand-writing recognition inconsistent. They HAVE to deal with calculator style single-line entry.
Click to expand...

they could just as easily chose to interpret 1/2x as 1/(2x) and therefore give implicit multiplication a higher priority - the constraints of entering a formula in a single line apply either way
 
@dowie I get you. It's the ÷ symbol that is the issue.

We are agreed that in correct mathematical notation there is no issue. We are also agreed that formulas written in this way would need further grouping () added to guarantee correct interpretation. Exactly what we have to do when inputting formulas into excel.

I maintain though, that the only logical way to interpret a poorly written formula using that notation is to do implicit operators first. This ensures the correct grouping of terms. This is perhaps not as a result of the maths but as a result of good English comprehension.

Essentially BODMAS doesn't apply when formulas are written that way because the English comprehension overrides it.

Out of interest are the ones advocating the alternative American?
 
danlightbulb said:
I maintain though, that the only logical way to interpret a poorly written formula using that notation is to do implicit operators first. This ensures the correct grouping of terms. This is perhaps not as a result of the maths but as a result of good English comprehension.

Essentially BODMAS doesn't apply when formulas are written that way because the English comprehension overrides it.
Click to expand...

I'm a tad confused now - what do you mean by 'English comprehension' in this context?

I think you can merely argue that it is desirable (or at least would have been if constrained to writing formula on a single line) that you adopt a convention giving higher precedence to implicit multiplication - I don't think that you can argue that this is the 'only logical way' etc.. clearly either convention can be used/implemented.

And yes I'm pretty sure we do agree that in using correct mathematic notation the basic rules of arithmetic still apply - I don't think that was even up for debate! :)

(Excel avoids the issue entirely by not allowing for implied multiplication)
 
Ok so I mean this.

A = 1/2x

You would read this aloud as "a equals one, divided by 2 times x" which implies immediately a logical grouping and convention. This punctuation naturally happens due to the location of the break symbol in this case the slash. Or you might say "a equals one over 2x". Again your speech is naturally grouping 2x together.

You add a space and this changes the natural break position so this happens:

A = 1/2 x

"a equals one divided by two, times x"

It becomes a matter of English comprehension not maths as such. The space changes the way you say it.

I think you would be hard pressed to find anyone who naturally said "a equals one over two, times x" in reading the first formula. Even someone who didn't know the purpose of this or even recognise it as maths would likely say "one slash 2x".
 
Last edited:
Sorry but I'm not sure that some subjective view on how you'd like to read it out loud really makes any difference. But yes I can see the argument that you could perhaps use a space to distinguish between (1/2)x and 1/(2x) (I did mention this earlier in the thread too as I thought this was what ubersonic was originally getting at).
 
I think it's very relevant. This whole issue occurs because we have formulas written in single line text. Therefore how you say them, in your head, is very relevant.

It then follows that the maths convention you use should mirror how you say it, because this is likely to lead to less interpretation errors.
 
not really as there is an element of subjectivity in how you'd read 1/2x in your head based on your preconception of what you think the convention should be
 
dowie said:
they could just as easily chose to interpret 1/2x as 1/(2x) and therefore give implicit multiplication a higher priority - the constraints of entering a formula in a single line apply either way
Click to expand...

My point is that they would avoid the situation altogether if the Web had an easy way to enter mathematical formula into search strings.
 
@dowie Hmm I don't think so. I think if you presented that to 100 non informed people most if not all would say "one slash 2x"

Don't you think so?

They would naturally group 2x together in their pronunciation.



And amongst informed people then yes I think they would naturally group 2x because we are used to seeing that terminology in other places. I.e in algebra we see a coefficient grouped with a variable. It is the natural way of things.
 
Last edited:
dowie said:
Sorry but I'm not sure that some subjective view on how you'd like to read it out loud really makes any difference.
Click to expand...

It's the crux of the issue. This whole debacle is because rather than using proper mathematical notation, we are treating it as we would when teaching a child - which is read aloud each step as you go and solve it.

You might as well be trying to discuss political history whilst using the terms Good Guys and Bad Guys. So long as you do not use proper notation, this will inevitably come down to "how you'd like to read it".
 
h4rm0ny said:
My point is that they would avoid the situation altogether if the Web had an easy way to enter mathematical formula into search strings.
Click to expand...

I think they need to account for a variety of different ways people would notate this stuff regardless and therefore would need to chose a convention even if they did allow for entry of fractions using a fraction bar.

I used them as an example simply to demonstrate that people clearly do use different conventions that don't give precedence to implicit multiplication as dan was arguing it was the only logical way

wolfram and google don't appear to agree and will interpret say 1/2x as (1/2)x

h4rm0ny said:
It's the crux of the issue. This whole debacle is because rather than using proper mathematical notation, we are treating it as we would when teaching a child - which is read aloud each step as you go and solve it.
Click to expand...

the issue just comes down to convention re: whether implicit multiplication is given a higher precedence or not - that's the main source of confusion/argument. The question does use proper notation, just in a way that is confusing. AFAIK it stems from someone posting their kids homework on an online forum ergo I think in context implicit multiplication isn't the convention used and the 'correct' answer they were looking for is 9.
 
h4rm0ny said:
It's the crux of the issue. This whole debacle is because rather than using proper mathematical notation, we are treating it as we would when teaching a child - which is read aloud each step as you go and solve it.

You might as well be trying to discuss political history whilst using the terms Good Guys and Bad Guys. So long as you do not use proper notation, this will inevitably come down to "how you'd like to read it".
Click to expand...

Sure I agree. But if 99% of the population naturally read it a certain way, then it makes sense to adopt that as the convention. People who try to do it different are just being awkward.

In this case the natural reaction is to group 2x together not least because the slash acts as a natural separator whereas the 2x has none.

Therefore the convention is set. Therefore the answer to the formula 6÷2(3) AS WRITTEN is 1.

I'll concede if you write the formula differently the answer changes, because the comprehension changes.

6÷2*3 = 9 (comprehension and BODMAS gives same answer)
6÷2a where a=3, is 1 (comprehension sets the convention)
3*6÷2 = 9. This one is interesting because comprehension and BODMAS are opposing each other if you read it out. But this one:
3*6/2 is fine because you tend to naturally group "6 over 2" as one term.

Google and the other site are probably interpreting left to right. It's not intelligent enough to make the perceptional groups that a human would.
 
Last edited:
danlightbulb said:
Google and the other site are probably interpreting left to right. It's not intelligent enough to make the perceptional groups that a human would.
Click to expand...

a human (or rather humans) have made the decision at google and at Wolfram re: whether they're going adopt a convention that gives precedence to implicit multiplication or not

either convention could have been chosen

it has got nothing to do with google not being "intelligent enough to make the perceptional groups that a human would" ???

I showed an example earlier of two different Casio calculators each using a different convention for implicit multiplication
 
dowie said:
a human (or rather humans) have made the decision at google and at Wolfram re: whether they're going adopt a convention that gives precedence to implicit multiplication or not

either convention could have been chosen

it has got nothing to do with google not being "intelligent enough to make the perceptional groups that a human would" ???

I showed an example earlier of two different Casio calculators each using a different convention for implicit multiplication
Click to expand...

Fair enough yes you did. Could there be cases where the approach I'm advocating caused issues and that's why they chose the one they've landed on?

Or it could have been not even considered and whatever programming language they used defaults to it.
 
Here's a question for you. If I was schooled in the 90s why am i still doing this the old fashioned way?

Could it be that I have naturally landed on it as the most logical approach rather than being taught it?

Or could it be the inherent links I make in my mind to proper notation forms which are more clear cut. So for example if I see a÷bc I read a/(bc).

If I was taught to interpret a÷bc as c(a/b) that would be quite a difference wouldn't it.
 
danlightbulb said:
Fair enough yes you did. Could there be cases where the approach I'm advocating caused issues and that's why they chose the one they've landed on?
Click to expand...

I'm not sure what you mean? What sort of issues?

Either convention could be used... I've got two calculators, they both work, they use different conventions.

Or it could have been not even considered and whatever programming language they used defaults to it.
Click to expand...

very unlikely - especially in the case of wolfram, this would almost certainly have been a conscious decision

danlightbulb said:
Here's a question for you. If I was schooled in the 90s why am i still doing this the old fashioned way?

Could it be that I have naturally landed on it as the most logical approach rather than being taught it?
Click to expand...

I'm not sure what you mean by the 'old fashioned' way?

Are you saying that choosing to give precedence to implicit multiplication is 'old fashioned'?
 
dowie said:
I'm not sure what you mean by the 'old fashioned' way?

Are you saying that choosing to give precedence to implicit multiplication is 'old fashioned'?
Click to expand...

Seems to be yeah. Because it stems from the use of the ÷ notation in older texts. I think that has been already said in the thread somewhere. But it goes way way back so it doesn't make sense why I would been taught it. I am actually coming around to not putting implicit operators first now, the more I look into it.
 
You must log in or register to reply here.
Back
Top Bottom