Known bug in Excel????

[mortgageman]

According to math rules 2^3^2 should equal 2^9 (you go right to left in this case). Excel gives 64. Is this a known bug?

Gene Klein

 

[mikerickson]

(addendum to above)

What makes math the universal language is that the notation doesn't matter.

One of the biggest notational conflicts is how the polar angle is measured in spherical polar coordinates.
Physicists use a system where the polar angle is measured from the zenith (North pole at 0)
Mathematicians use a system where the polar angle is measured as elevation from the reference plane (North Pole at pi/2).

That mathematicians and physicists can use such different systems (the fall-out of this difference are much greater than the "A then B" vs. "B then A") and still understand each other is because mathematics is the language where the notation doesn't matter. Math can be applied to any (consistant) notation. And any sufficiently rich notation can be used to express math.

To say that mathematic is the universal language is the same as saying that it doesn't matter if 2^3^2 is (2^3)^2 or 2^(3^2), just as long as one doesn't change systems mid-problem.

 

[mortgageman]

(addendum to above)

What makes math the universal language is that the notation doesn't matter.

One of the biggest notational conflicts is how the polar angle is measured in spherical polar coordinates.
Physicists use a system where the polar angle is measured from the zenith (North pole at 0)
Mathematicians use a system where the polar angle is measured as elevation from the reference plane (North Pole at pi/2).

That mathematicians and physicists can use such different systems (the fall-out of this difference are much greater than the "A then B" vs. "B then A") and still understand each other is because mathematics is the language where the notation doesn't matter. Math can be applied to any (consistant) notation. And any sufficiently rich notation can be used to express math.

To say that mathematic is the universal language is the same as saying that it doesn't matter if 2^3^2 is (2^3)^2 or 2^(3^2), just as long as one doesn't change systems mid-problem.

Mike, I'm not sure what your last sentence is intended to mean. Let me try a comparison to a math class again, hopefully in try and clarify. If I gave a test and one question was what is 2^3^2.
choice a is (2^3)^2
choice b is 2^(3^2)

The students who picked choice b would be marked correct.
The students who picked choice a - regardless of any explanation about systems and changing and whatnot - would be marked wrong.

Gene Klein

 

[shg]

I agree wholeheartedly with Mike.

There is no utility is arguing that Excel is wrong; it simply does what it does, and does it (meaning expression evaluation) in completely self-consistent fashion. Help explains clearly the precedence of its 17 operators.

EDIT:

The students who picked choice b would be marked correct.

Not if it were an Excel class.

 

[mortgageman]

I agree wholeheartedly with Mike.

There is no utility is arguing that Excel is wrong; it simply does what it does, and does it (meaning expression evaluation) in completely self-consistent fashion. Help explains clearly the precedence of its 17 operators.

EDIT:


Not if it were an Excel class.

There is no utility is arguing that Excel is wrong <= Agree
it simply does what it does, and does it (meaning expression evaluation) in completely self-consistent fashion <= Agree

However, the fact that there is no utility in my argument doesn't make Excel actually correct. Excel and other caclulators serve Math - NOT the other way around.

Gene Klein

 

[xenou]

Mike, I'm not sure what your last sentence is intended to mean. Let me try a comparison to a math class again, hopefully in try and clarify. If I gave a test and one question was what is 2^3^2.
choice a is (2^3)^2
choice b is 2^(3^2)

The students who picked choice b would be marked correct.
The students who picked choice a - regardless of any explanation about systems and changing and whatnot - would be marked wrong.

A student will give you an answer, not a notational system. The answer is 512. The reason you know this is "Math". The notation is Excel/google/Ti-84 and what have you. I think that's more or less Mike's point.

As for me, I think it's ridiculous to ask a question like what is 2^3^2 without context. You should ask what is 2^3^2 in excel or in my class. I've said repeatedly there's no up/down or vertical orientation on a flat line of text. You must give a rule.

What most of us are saying is that if you want the rule to be right to left then fine - the rule is right to left. For goodness sakes, no problem! But if you are using Excel and you want the right answer then follow its conventions. As long as you are clear about your conventions, everyone gets the same answer. Mike brought up the topic of polar angle is measured in spherical polar coordinates (which I've never heard of). Though in the world of computers it makes me think of big-endian vs. little-endian:

Two binary numbers:
10000000
00000001

Both equal 1, if properly communicated.

 

[mikerickson]

If I gave a test and one question was what is 2^3^2.
choice a is (2^3)^2
choice b is 2^(3^2)

One would have to attend class, or at least read the pre-chapter "Notational Conventions" in the text book to answer correctly.

 

[shg]

However, the fact that there is no utility in my argument doesn't make Excel actually correct.

There may be a point hiding in there, but I can't find it.

You could use a surfeit of parens so that Excel's evaluations agree with your idea of 'correct,' or, if its behavior offends you at an existential level, select a different spreadsheet or math package.

This much is certain: Excel's expression evaluator will never change.

 

[Jonmo1]

Perhaps math isn't such a uneversal language after all.

Hello new alien species, welcome to Earth.
I'm so glad we have this universal language called math so we can communicate with each other.
Here's a copy of the book that describes all the rules we earthlings have applied to it.
Wait, you can't read English can you..
That's OK, we have it in Spanish too, or French or German..
You don't speak any of those languages?
What language Do you speak...Martian you say..
Hey Steve, go down to the Library and see if they have a copy of that book in Martian.
Mr Alien, you'll also need to know left from right so you can read our math correctly..
Huh, you don't know left or right?
Hmm, You'll have to go take Ms. Smith's Remedial Life Skills class at the
Adult Education Building down on 5th Street.

Hey Steve, How do you say "Inter-Planetary Incedent" in Math?

So glad we can communicate so well.

Which is the correct spelling
Color or Colour ??

Both are correct, In US it's Color, In UK it's Colour.


Math may be the Language...
But Excel is the person speaking it.
And Math CLASS is a different person speaking it.

 

[RoryA]

I think you mean maths is the universal language...

 

[Hap]

Maybe that is the perfect question to test for understanding. You're not looking for one answer or you would clarify the question. Maybe the better student is the one who "got it wrong"!!!