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

 

[Hap]

It didn't copy over correctly. Yes, there should be a "^"

 

[mortgageman]

<SNIP> If a formula contains operators with the same precedence - for example, if a formula contains both a multiplication and division operator - Excel evaluates the operators from left to right

The declared functionality is not a bug.
Excel follows the declared rules therefore it’s not a bug.

<SNIP>

I won't argue semantics here. If you want to mantain that since Excel is following its **own rules** correctly, then it is not a bug - Mazel Tov.
Like I said earlier, I have my answer - the _______ (fill in the blank) is known but uncared about I guess.

I guess I have a broader defintion of bug - or perhaps I am willing to let the defintion fo down futher then just one level! The reason that we write (or type) into Excel 2^3^2 instead of "stacked symbols" is simply because most keyboards do not have that capability. I do not know anyone who would seriously argue that the caret is not a clear translation from stacked symbols. Put another way: Imagine that I verbally ask the following question in my math class: "Class please tell me what is 2 raised to the power 3 raised to the power 2. You may use whatever resources you like - just tell me the answer tomorow morning." The student who uses pencil and paper - AND WHO KNOWS THE CORRECT ORDER OF OPERATIONS - will come back and answer 512. The student who decides to use Excel - typing in 2^3^2, because that is the only symbology allowed by the keyboard - will get the wrong answer. According to you, this is not a bug, this would be a user error since the user should know that Excel's design incorporates a flaw in Arithmetic. Pity - since in any math class, that student gets a zero on her hw.

Gene Klein

 

[xenou]

The student who decides to use Excel - typing in 2^3^2, because that is the only symbology allowed by the keyboard

A positive outcome will be that the student has now learned how to use Excel (and many hundreds of other computer packages that act similarly). This will be greatly to his/her advantage. Indeed, being knowledgeable in how to use their computer application of choice and aware of its rules of operation -- such being absolutely essential for the use of Excel for mathematics -- the student might well enter 2^(3^2) right off and not get the answer wrong at all.

 

[FastExcel]

"The student who decides to use Excel - typing in 2^3^2, because that is the only symbology allowed by the keyboard - will get the wrong answer" to your question, and will therefore hopefully learn how to use Excel properly.

Of course it isn't the only symbology allowed by the keyboard: 2^(3^2) is also valid and gives the correct answer to your question.

 

[mortgageman]

"The student who decides to use Excel - typing in 2^3^2, because that is the only symbology allowed by the keyboard - will get the wrong answer" to your question, and will therefore hopefully learn how to use Excel properly.

Of course it isn't the only symbology allowed by the keyboard: 2^(3^2) is also valid and gives the correct answer to your question.

Naturally - and once the student is aware of Excel's "mnmn mnmn" (<= fill in whatever word you like, but I'm not allowed to say bug here) he or she will do so. There is no disagreement that the student (or anyone) would NEED to use parenthesis. My only point is that the parenthesis are mathematically NOT REQUIRED. Just like they are not required in 2+3x4. Nobody (or at least nobody who knows the rules of math) would think to type in 2+(3x4). In fact imagine if you were using a version of Excel that required you to type in 2+(3x4) to get the right answer. And when you complained, the response was "Excel was designed to operate Left to Right - without regard to the rules of Math. So stop complaining because there is no bug". I suspect you would insist that the design flaw (is that better?) be corrected. Since a power to power comes up far less frequently, most of you are less concerned. I think the principle is the same though.

Gene Klein

 

[xenou]

Well, 2+3x4 is not the best comparison because as we have noted powers to powers involve vertical (up/down) positioning which is not normally how we input this on the keyboard. By contrast, 2 + 3 x 4 is exactly the same on paper and in an Excel formula - and the rules operate the same. If a power to a power is the only example to be found then I think that we can assume that pioneering computer scientists made a since effort to transpose the conventions of mathematics from a pre-computer age into the world of bits and bytes where almost everything is flattened out in a line of text - a job which surely was a difficult one. My impression of the history of computing is that many of these unsung heroes were scientists and mathematicians of a very high caliber - a story that I hope continues as the science develops.

Be that as it may - if you feel a better way exists, then there's room for all opinions. I think I prefer the rule as it is since its consistent with all the rules of operation and this is how most computing packages work. I understand and expect that there are separate conventions in the world of computing and the world of written formulas - in the future we'll probably be able to write/type the superscripts easily and the rules will once again be the same (or perhaps some new, as still unknown notation will replace both of these ... ).

ξ

 

[xenou]

Just as a note - look how much interest this topic generates! Computer scientists, programmers, power users - all of this ilk are nothing if not passionate about mathematics. You could hardly argue that there is indifference. It is even possible that just such a passionate discussion once occurred in the bowels of some early Microsoft office. And then a decision had to be made ...

 

[mikerickson]

Mike. How would you know this sematically without encapsulating the "-" or assigning the negative to the 2 prior to the exponential operation?

I'm not sure what you mean. "negative two" is the (additive) inverse of "two"

Ala the Peano axioms "two" is the successor of the successor of zero.

If the question is "what do we mean by negative two" the answer is "the additive inverse of the second successor of zero", its represented by the symbol "-2".

If the question is "what does Excel do when with a "-" in a formula", or "how does Excel parse a formula" (e.g. where does Excel put the parenthesis before evaluating a formula".

If I were writing a compiler/interpreter, one of the first things that I would do would be to identify all the negative atomic numbers. (find all "-###" and replace it with "(-###)".

By training I'm a mathematician.
I recall that in my senior year Algebra class, the text treated A*B as "A then B". My first year graduate text in Algebra treated A*B as "B then A".

There is no conflict, no theorems became False (heck, most of them didn't even change form). Its all notational conventions. The key is not in finding the "correct" convention. The key is in knowing what convention the text book (or the software) is using, so that you can communicated effectively with that book or software.

The discussion of what 2^3^2 should mean is similar to the discussion of whether 3/5/2011 is in March or May.

 

[Hap]

I agree that its not false any more than French is false because it's not english. However, since it is often considered that math is the universal language maybe there needs to be a concrete answer to the order even if it is driven by computer science. Reading it for understanding is not difficult for most with a reasonable level of math. Clearly the difficulty is in identifying the "dialect". I like the input!!!

 

[mikerickson]

That's (perhaps) a misconception about mathematics.

Math is not about whether the symbols "2^3^2" mean (2^3)^2 or 2^(3^2).

Math is the realization that in either system (2^a)*(2^b) = 2^(a+b).