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

 

[shg]

Going way back to Kenneth's post, I used to love RPN on HP calculators (and did they have nice calculators -- I just went looking for, and found, my HP11C; the batteries are still good!)

2, 3, y^x, 2, y^x

You still need to know that x is the number at the bottom of the stack (considering it to build upward), y is above it, and a binary operation collapses two values to one.

 

[mortgageman]

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"!!!

I (or any other math teacher) would be looking for one answer; if a student asked for clarification, any math teacher would say none is needed. Your "better" student would not get hired - since s/he would not pass the class.

I'm sure you have a point

Gene Klein

 

[n0gel]

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

I believe the correct term is "design feature".

 

[mortgageman]

I believe the correct term is "design feature".

You must work for IBM

Gene Klein

 

[FastExcel]

I think programmers and spreadsheet users find it nearly inconceivable that Excel should interpret 2^3^2 as a power of a power.
Mathematicians may think differently, particularly if they (mistakenly in my view) see Excel as designed for doing Math.
Maple (which is a serious Math program IMHO) shows you the equation in stacked superscript format, so there is no doubt about what its going to do.
Mathematica (also a serious Math program) prefers using a POWER() function where the third and subsequent arguments are treated unambiguously as stacked superscripts, but does also allow a^b^c^d to be translated into its POWER(function).
Most hand calculators apart from top-end scientific ones seem to follow the left-to-right unstacked rules.
Personally speaking, since I have been more of a programmer than a mathematician for the last xx years I am firmly in the LTR unstacked camp, but I can accept that some would regard me as belonging to the ignorant majority!

 

[mortgageman]

I think programmers and spreadsheet users find it nearly inconceivable that Excel should interpret 2^3^2 as a power of a power.
Mathematicians may think differently, particularly if they (mistakenly in my view) see Excel as designed for doing Math.
Maple (which is a serious Math program IMHO) shows you the equation in stacked superscript format, so there is no doubt about what its going to do.
Mathematica (also a serious Math program) prefers using a POWER() function where the third and subsequent arguments are treated unambiguously as stacked superscripts, but does also allow a^b^c^d to be translated into its POWER(function).
Most hand calculators apart from top-end scientific ones seem to follow the left-to-right unstacked rules.
Personally speaking, since I have been more of a programmer than a mathematician for the last xx years I am firmly in the LTR unstacked camp, but I can accept that some would regard me as belonging to the ignorant majority!

I have been considering what you ("you" here is collective - meaning everyone who does not agree with me ) have said, and I must say, it is not compelling. If I am understanding you all, your point is that Excel has an operator, known as the caret and which looks like this: "^". This operator follows the built in precedence for which it was designed - Left to Right. Since the caret is doing what it is supposed to do, what is the problem? (say you). Well the problem is (says me), is that the caret - IN EVERY OTHER REGARD THEN THIS LEFT TO RIGHT PRECEDENCE - acts exactly like the exponent with which the rest of the world is familiar. You are in the position of maintaining that the caret is accordingly not the exponent, since it is written using a different notation! There is a famous story
http://dig.csail.mit.edu/2005/09/6.898/ of what Gauss had to say about notation.

What about multiplication? It is written with a "*" not the traditional "x" or "." or even "()". Is Excel free to change the Order Of Operations wrt the "star operation"? Or is it just luck that the * acts just like the more familiar notation?

Gene Klein

 

[shg]

What is your objective -- to get everyone to agree that it's wrong?

And if everyone did, what would it accomplish in terms of your practice in using Excel?

The serenity prayer seems relevant here, mm.

 

[mortgageman]

What is your objective -- to get everyone to agree that it's wrong?

And if everyone did, what would it accomplish in terms of your practice in using Excel?

The serenity prayer seems relevant here, mm.

Way earlier in this thread I said my original question was answered. At this point, I am simply giving a reasoned argument in the face of what seems to be universal disagreement. I might ask you what was the point of asking me what my objective is. What exactly does it contribute - to your point or to this thread?

Actually, if your only retort to my argument is the equivalent of "Stop pointing out all these anoying facts", then I guess I have my answer - don't I?

Gene Klein

 

[shg]

It was an honest question, mm; what responses could you receive that would give you the closure you clearly seek?

For Excel, I would argue that fixed (and documented) operator precedence, followed by (documented) left-to-right evaluation, is simple and easy to understand, and therefore serves users well. I cater willingly to the methods of a variety of tools if they serve the purpose at hand.

 

[xenou]

I don't think its a bug and personally I prefer the left-to-right rule being consistently applied for otherwise identical operators. It is well known and consistent - therefore there is no problem that I can see. I don't expect the syntax of computers to be the same as written mathematics - hence, I don't see parentheses as multiplication symbols in Excel, and I do know what 2^3^2 is. Your Gaussian quote strikes me the opposite way (I guess) that you intend - if the notion is clear, I won't stumble on notation.

I think therefore I am not simply saying "stop pointing out all these anoying facts". If you will, I am saying that Excel's rules make sense to me and are appropriate in a computing environment. Since I can't write superscripts to superscripts (easily, if at all) in Excel, I think the Excel notation and its rules are appropriate at the keyboard when the traditional notation cannot be used.

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