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Semantic difficulty

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barbados
1374360.  Fri Feb 12, 2021 2:40 pm Reply with quote

What are you actually struggling with here?
The initial post was explained - the term "bird", "cat" & "dog" are variables they are not the animals - and that is perfectly clear.
When you reworded to include terms like "cheese" that was also explained to you relates to the variable you have decided to name "cheese", it could easily be anything - pick any word from the OED, or actually any dictionary you choose, and if you word the question in the way that you posed the question, the descriptor used is a variable, not a cat, not a dog, not cheese, not a year - they are simply variables.
As I pointed out earlier, you are either struggling with KS1 arithmetic, or you are trolling, trying to act all smart. Which is it?

 
Brock
1374361.  Fri Feb 12, 2021 2:48 pm Reply with quote

barbados wrote:
What are you actually struggling with here?


Nothing. I've told you several times that it's just a technical discussion about semantics, and that I'm just having the discussion because I enjoy having these sorts of discussions.

If you don't enjoy them, you really don't have to take part.

I don't know what else to say.

 
barbados
1374362.  Fri Feb 12, 2021 3:03 pm Reply with quote

How is it a question of semantics.
You are clearly using the terms as a variable, there is no doubt and no other way you can interpret the terms in the question you are asking.

If you are looking at this as a matter of semantics you are wrong, because the overwhelming factor - the one that removes any doubt over the meaning of the expressions removes that doubt, is the context. In the context of the statements provided there is zero doubt that the terms are nothing more than variables in an equation that could easily be solved by a 7 year old - in fact, it is the way they teach 7 year old children how to work out these simple arithmetic problems, because they can visualise 3 birds easier that raw number.

 
Numerophile
1374369.  Fri Feb 12, 2021 3:58 pm Reply with quote

barbados wrote:
It is exactly the same question n variable = nn the value of the variable is always n/nn basic KS1 arithmetic

Somebody needs to revise his basic KS1 arithmetic! ;-)

Brock wrote:
Now you seem to be saying that the fact that "year" and "month" also have meanings that are periods of time is relevant. In other words, the usual meanings of the words in the problem do have some bearing on how it's interpreted.

No, I'm not. It's not relevant to the interpretation of the problem, but it may make it more likely that the problem will be misinterpreted, leading to the head-scratching you referred to above. You asked why one formulation was more confusing than the other (for which you didn't have an answer); I've explained it.

 
barbados
1374370.  Fri Feb 12, 2021 4:01 pm Reply with quote

I did the Australian variant ;-P

 
Leith
1374379.  Fri Feb 12, 2021 6:32 pm Reply with quote

An example of the original sort of puzzle that Awitt mentioned, for reference:



The icons are readily identifiable as abstractions because that's what we're used to icons being - a symbol representing an emotion, function or artifact.

Convert the above to words and it starts to look less algebraic, more like natural language. Perhaps at that point we start to lose the intuitive distinction between the symbol and what it represents.

 
barbados
1374388.  Sat Feb 13, 2021 4:20 am Reply with quote

We don’t lose anything though do we, because we use context to remove any doubt.
If you remove the icons and replace them with words we still know that the hotel, in the example given is not a hotel at all, it is merely a variable with the value of 4. Four what is immaterial - you don’t need to know “four whats” just that it is 4.

 
Numerophile
1374394.  Sat Feb 13, 2021 6:15 am Reply with quote

@Leith: As a matter of interest (going back to the point at which this discussion sprouted off), are they expecting the answer 64 (left to right) or 34 (operator precedence)?

 
Leith
1374397.  Sat Feb 13, 2021 6:39 am Reply with quote

Not all doubt I would say. The worded example is easy enough to understand, and not difficult for anyone with some exposure to algebra, but I would expect the seven year olds that puzzle is targeted at to not necessarily make sense of a worded version immediately. The icons are more immediately intuitively recognisable as symbolic, I think.

In a pure arithmetic puzzle like the one above, we want the symbols to behave as complete abstractions. Hence arithmetic algebra is traditionally taught using simple letters, shorn of all additional meaning that might imply properties other than those of the real number they represent.

In software engineering we use words in variable names precisely because we want the model elements they represent to be intuitively relatable to the real world entities whose properties and behaviours they embody.

Programs that analyse, or interact with, some real world entity using variable names that don't mean anything are difficult to intuitively understand and maintain. Using variable names evoking entities whose behaviour is different, or even opposite to that of the program's subject renders them actively misleading.

If a program is rendering different portions of a national flag, then naming the portions as:
A
B
C
is not particularly helpful.

Naming them:
blue
green
red
is guaranteed to lead readers astray.

The first set of variable names don't relate to the colour of their flag section, so aren't helpful in determining which is which. The second set intuitively look like they represent the colours of the flag, but misleadingly evoke the wrong colours.

The above example worded as "house", "tenement", "factory" could briefly lead one to consider whether they might be intended to represent some numerical property associated with actual buildings, but not for long, and the presence of multiplication in the puzzle renders that sort of real world reference unlikely (heterogeneous sets of houses, tenements and factories lack an obvious distributive property).

Replacing with the words "year", "month", "day" is more misleading because these words represent non-numerically abstract entities with specific numeric relationships between them.

The puzzle might intend us to associate "year" with 4 and "month" with 10, but we will be intuitively aware that a real year is bigger than a month, and in fact represents a very specific number of months. The words strongly remind us of numbers, but the wrong numbers.

 
Brock
1374398.  Sat Feb 13, 2021 6:50 am Reply with quote

barbados wrote:
How is it a question of semantics.
You are clearly using the terms as a variable, there is no doubt and no other way you can interpret the terms in the question you are asking.


And that's a question of semantics. Semantics, according to the COED, is "the branch of linguistics and logic concerned with meaning", and that's precisely what we're looking at.

Quote:
If you are looking at this as a matter of semantics you are wrong


Of course I'm not wrong. That's the whole premise of the thread. That's why the thread is called "Semantic difficulty", and why I started the thread by saying "This is a post about semantics. If you're not particularly interested in semantics, or language, or philosophy, then I suggest you skip it, because it's likely to seem a bit technical". I reiterated that point in several other posts as well. Dr. bob put it very neatly, I thought:

dr. bob wrote:
To be fair to Brock, he's repeatedly stated that he understands the puzzle as written, he's simply indulging in nerdy over-examination of the semantics surrounding it. If we're going to ban nerdy over-examination from these forums, I'm really not sure what will be left to talk about.


If you've managed to get through five pages of this discussion without realizing it's a discussion about semantics, then you must be like Moliere's Bourgeois Gentilhomme, who was surprised to learn that he'd been speaking prose all his life without realizing it.


Last edited by Brock on Sat Feb 13, 2021 7:27 am; edited 1 time in total

 
Dix
1374399.  Sat Feb 13, 2021 6:56 am Reply with quote

Numerophile wrote:
@Leith: As a matter of interest (going back to the point at which this discussion sprouted off), are they expecting the answer 64 (left to right) or 34 (operator precedence)?

STOP IT RIGHT THERE!

Please, can we have the operator precedence / left-to-right discussion in a different thread? It could go on for pages and pages... :-)

(but if you really do want to know: since I'm maths literate and have a background in computing and engineering, the answer you'll get from me is operator precedence)

Barbados wrote:
We don’t lose anything though do we, because we use context to remove any doubt.
If you remove the icons and replace them with words we still know that the hotel, in the example given is not a hotel at all, it is merely a variable with the value of 4. Four what is immaterial - you don’t need to know “four whats” just that it is 4.

Erm... unfortunately that is not always enough.
Some of the more devious ones will alter the pictograms in the last line.
For example:
You work out that "bunch of bananas" represents 4 from the first lines(s).
In the last line there will be a slightly different pictogram that does not have the same number of bananas. The "bunch of bananas" that represents 4 shows four bananas, the one used in the last line will look very similar but actually show five bananas, not four. And you're meant to realize that the "bunch of bananas" isn't to be read as one symbol but rather as (banana banana banana banana) represents 4, so in the last line (banana banana banana banana banana) must represent 5.

With that hotel/house example that trick might have been done with for example the number of windows, but it hasn't.
Oh, hang on..... look closely at the "little house in garden" pictogram. The one in the last line is different.
It looks to be just a rendering problem (accidental), but it might not be. It's too small for me to work out if the number little coloured dots etc adds up to anything meaningful.

 
Brock
1374400.  Sat Feb 13, 2021 7:04 am Reply with quote

Leith wrote:
An example of the original sort of puzzle that Awitt mentioned, for reference:



The icons are readily identifiable as abstractions because that's what we're used to icons being - a symbol representing an emotion, function or artifact.

Convert the above to words and it starts to look less algebraic, more like natural language. Perhaps at that point we start to lose the intuitive distinction between the symbol and what it represents.


Thanks for that. First of all, I apologize for not having understood the nature of the original problem - I had assumed that it was written in words rather than being graphical. (Obviously Awitt had to use words rather than symbols to represent it in this medium.)

However, if I were to attempt to represent the above puzzle in words, I'd probably write:

hotel + hotel + hotel = 12

rather than

three hotels = 12

which is a rather different concept in my view.

 
Dix
1374401.  Sat Feb 13, 2021 7:12 am Reply with quote

It was an informal description, so I wouldn't think accuracy was intended. It conveyed to me that the maths teacher in question was using puzzles of roughly the type Leith has helpfully posted. Not a particular version of such a puzzle.

 
Dix
1374402.  Sat Feb 13, 2021 7:17 am Reply with quote

(and by the way, if describing a maths puzzle "three hotels" to me would be either 3 x hotel or hotel + hotel + hotel, but as I should hope we all know, the multiplication operation is really just a handy shorthand for performing multiple additions.
3 x hotel = hotel + hotel + hotel)

 
Brock
1374403.  Sat Feb 13, 2021 7:20 am Reply with quote

Dix wrote:
(and by the way, if describing a maths puzzle "three hotels" to me would be either 3 x hotel or hotel + hotel + hotel, but as I should hope we all know, the multiplication operation is really just a handy shorthand for performing multiple additions.
3 x hotel = hotel + hotel + hotel)


"Three hotels" would be neither of those to me. It would simply be a picture of three hotels next to each other, with no other symbols.

"3 x hotel" would be the symbols "3 x " followed by a picture of a hotel.

 

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