Title says it all.
At a physics conference is a physicist saying they get a negative result the same as same that result should be subtracted from something else? Minused? (is that even a word?)
Missed the edit:
*…same as saying that result…
Need more context. A “negative result” could mean that a hypothesis was tested and found to be false.
I would also say that if “negative result” means a result that is a negative number, that may mean it can be subtracted from something else but doesn’t necessarily mean it should be.
Otherwise, a positive number plus a negative number is the same as the positive number minus a positive number.
2 + (-1) is the same as 2 - 1
In that sense, negative, subtract, and minus are interchangeable.
Something like this (I queued it up to what made me wonder about this):
That appears to be two different meaning of the word “negative.”
With respect to an experiment, or for looking for evidence of something, a “negative result” simply means the hypothesis to be tested was not proven, or no evidence was found. This has nothing to do with subtraction.
There is also a mathematical use: negative numbers are less than zero. Adding a negative number to a positive number is equivalent to subtracting a positive number of the same magnitude.
In your video, he’s talking about the value of the part of the equation that he’s referencing being negative, i.e. a number less than zero.
(And part of your OP is a bit odd - describing something as negative never implies that it should be subtracted from something else.)
I concur with what the others (Richard_Pearse, Colibri, Riemann) have said.
And see the thread Crafter_Man linked to if you really want to dig into “negative” vs “minus.”
First off, I would always take “negative result” in an experimental context to mean that the experiment failed to do something. Sometimes that means it failed to refute a hypothesis, so it might even be confirmatory.
But it might also mean that a computation was carried out and the answer was a negative number. That gets us into the mathematical use of the term. Until sometime around 1980 or 90, you would read -7 as minus seven and that was the only way anyone ever read it. At some point, some pointy-headed educators decided that the word minus meant two things: the name of the subtraction operator and the name of a negative number and this would confuse students. Did they have any evidence that this confused students? Damfino. I never saw any such evidence. Nor do I ever remember anyone, even the poor students in my math courses, ever express confusion on this point.
At any rate, they had all the school textbooks rewritten so that suddenly -7 became negative seven. They never told us college professors about the change. The way I found out about it was that the students started using that language. Of course, I didn’t. Among other things, I didn’t realize how widespread it had become. At first I thought it was just a peculiarity involving just some students. Oddly, no student seemed the least confused when I said minus seven.
They just knew you were an old fuddy duddy & didn’t want to hurt your feelings.
Like when my parents back in the 1960s would read “5 - 3 = 2” as “3 from 5 gives 2” whereas 7 year old me would say “5 minus 3 equals 2”.
Of course, the experimenters should be reporting explicit confidence intervals or likelihood intervals or similar, and the statistical methods used to derive them, so that there can be no question what are the results of the experiment.
@Hari_Seldon, did you also use “minus” as the name of the subtraction operator? That is, would you have read “5 – 3 = 2” as “five minus three equals two”? Or if not, what wording would you have used?
What I have seen students get confused about (and even slipped up myself once or twice) is, when using a calculator, pressing the “subtract” button when they should have pressed the “minus sign” or “negation” button. Many modern calculators have these two separate buttons, and they (at least in some contexts) do different things: If I punch in –3 using the unary-negative-sign button, the calculator interprets this as me entering the negative number –3. If I punch in –3 using the subtraction button, the calcator subtracts 3 from the result of the previous calculation.
I was in school during the 1970s and 80s, and I honestly can’t remember whether -7 was referred to as “minus seven” or “negative seven” or both; but both wordings sound natural to me and are something I might say myself. (I would say “negative seven” if I thought it needed to be made clear that I was referring to a negative number and not to subtracting 7 from something.)
Yes, of course that’s what I would have said. But the two uses of minus just never caused confusion. And 5 - 3 = 2 could be any of five minus two equals/gives/makes two are all the same.
I’ve really only used RPN calculators where no confusion is possible.
My RPN calculator (an HP 48) has separate buttons for “minus” and “negative”, which don’t work the same way. “Minus” is a binary operator, which will consume two elements from the stack and put their difference onto the stack. “Negative” is a unary operator, which will consume one element from the stack, and put its additive inverse onto the stack.
additive inverse. That was the phrase we got beaten into our heads in 9th grade Algebra I, circa 1965. -7 is the additive inverse of 7. 7 in the additive inverse of -7.
Here is the definition our textbook had, as best I remember the wording (which I think is substantially correct):
I always thought that sounded like it was written by a lawyer. The way they taught “New Math”, I always thought, sounded like the whole thing was written by lawyers.
Consider that this was addressed to beginning algebra students, with no assumption (AFAIK) that they had any prior knowledge of negative numbers. If you had no prior knowledge of negative numbers, would you have been able to make head or tail of the above definition?
There is a third use of the - symbol having to do with negativity. These two have been mentioned:
- A unary operator, taking a single operand and producing its “additive inverse”.
- A binary operator, indicating subtraction.
There is a third interpretation that occurs with a symbol like, e.g., -7.
Consider, to start with, that we have only symbols to write positive numbers. Then we “discover” negative numbers, which we can create by taking a positive number, like 7, and applying the negation operator to create the expression -7.
Here, -7 is an expression, indicating an operand to be operated upon and the operation to be performed. But wouldn’t it be helpful if we then had a symbol by which to write the resulting number?
So we decided to adopt -7 as a single symbol to represent the number that results from the expression -7. (Got that distinction?)
It would be useful for students to see the use of -7 as an expression as well as -7 to represent the result of that expression, because we adopt the same trick in several other cases too.
Suppose we begin with just integers, and develop the concept of fractions as a ratio of integers. Along with this, we develop the idea of division as the inverse of multiplication. Thus, 7/2 is an expression telling us to divide 7 by 2, resulting in some non-integer number.
Now, how shall we write that number? Well, we decided to adopt the notation 7/2 (meaning, the usual vertical arrangement of 7 with a horizontal bar below it and 2 below that) as a single symbol to represent the number that results from doing the arithmetic 7/2.
There’s more: Eventually we hit upon the idea of square roots, and develop the notation of √2 to mean: Find the number whose square is 2. That is, √ is a unary operator defined to be the principal inverse of the x2 function. Now, how shall we write the resulting number? Again, we adopt √2 as the single symbol to represent the number that results from computing the expression √2.
Is it really described in the manual as a “negative” button, and not a “change sign” button? Similarly, is the “−” button ever given an explicit name like “minus”?
Great post. Thank you.
I’d add that along the way the limitations of computer displays & keyboards have raised their ugly heads and further muddied the waters.
In traditional typography, the negative / negation symbol was a horizontal line drawn high up to the left of the leftmost digit. Whereas the subtraction operator symbol was drawn at middle height also to the left of the leftmost digit of the right operand.
Most keyboards don’t have both symbols. And early printers and CRT displays couldn’t display both symbols either. So they folded the two meanings into the single symbol available.
Division and fraction is similar with slash versus horizontal bar.
In non-math punctuation there’s a similar bicker that hyphen, em-dash, and en-dash carry 3 very different meanings but are all rolled into the same single character in casual typography, and soon enough become a single blur in ordinary people’s folk knowledge of correct punctuation. I know I can’t keep the distinctions straight even though I know how modern word processors & output devices can be goaded into entering & rendering all 3 symbols.
High precision and low ambiguity of expression is a good trait in any orthography, but especially so in mathematics (or computer programming). But that impulse can be carried to anal-retentive extremes, where any context-sensitive nuance demands a separate symbol and name.
As you and Hari have said, that’s not correctness, that’s hyper-correctness.
While I do still have the manuals for the HP 48 (a pair of inch-thick books, so I’m sure the answer is in there somewhere), they’re currently deeply boxed away, so I don’t know what the technical name is for either of those buttons.
The waters were muddied right from the get-go.
This was certainly a far worse problem in the earlier days of computers. Older computers typically had only 6-bit characters, thus a maximum of 64 symbols in their character set and no such thing as multi-byte characters. The world in those days standardized on a basic set of 48 characters: A-Z, 0-9, + - * / = ( ) $ period comma and blank space and one other oddball character that I forget. Programming languages of the day (FORTRAN and COBOL, always written with all-capital letters) limited themselves to those. Various manufacturers of computers added miscellaneous other characters to fill out a 63-character set (leaving one character to mean “end-of-line”).
(ETA: And since computers were heavily used in business and commerce since very early-on, I always wondered why they included $ in the character set yet generally did not include % @ and # )
Thus, FORTRAN used ** to mean “raised to the power” as in X ** 3, and combinations like .EQ. .NE. .LT. .GT. .LE. .GE. .AND. .OR. and .NOT. for relational and logical operators. This also got us into the habit of using nested parentheses like (A * ((B - C) / D)) instead of {A * [(B - C) / D]} like we learned in Algebra I (at least that’s how I learned it).
Whereas Algol chose to unhitch itself from any real-life character sets of the time and use an arbitrarily complete character set for everything, and also keywords like if, then, else, begin, end, and many others, which were defined as single atomic terminal characters. This led to everyone writing different compilers for different computers to actually implement Algol, adapting as best they could to the 48-character set, so it ended up that Algol, designed to be completely specific-computer independent, ended up being so dependent that you could never easily port a program written for one computer to another.
And the mathematical subtraction symbol was yet another symbol distince from all the above (generally printed in math books looking something like an en-dash). I was never aware that the unary minus had a representation separate from the binary minus, except as a pedagogical device to help beginning students keep track of what they were doing.