# Semantic difficulty

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1373968.  Mon Feb 08, 2021 4:46 pm

 barbados wrote: Surely if a hat trick was involved, then one of the animals would have been a rabbit? Who ever heard of someone pulling a dog or a cat out of a hat!

But what about Dr Seuss? And suppose the cat in the hat is sat on a mat?

1373979.  Mon Feb 08, 2021 11:51 pm

 Brock wrote: But, to be honest, I don't expect simple puzzles like that one to be written in programming language syntax. I expect them to use everyday language and symbols that the majority of the general public would understand. The only place you'll see "=" used as an assignment symbol is in a computer program.

But in post 1373750 it didn't seem to bother you:

Brock wrote:
Numerophile wrote:
 Brock wrote: But that's nonsense. You can't multiply one bird plus one cat by a dog.

Oh for heaven's sake! If it had been expressed as

3a = 30
3b = 9
3c = 3

would you say it was 'nonsense' to multiply (a+b) by c?

No, of course not, because a, b and c are algebraic symbols that represent numerical values.

In that post the statements:

 Quote: 3a = 30 3b = 9 3c = 3

Are just assigning values to symbols using the "=" operator. If one were to be pedantic it should have been preceded with a "Let" director, but that didn't bother you then so you can't really complain about it now.

So we have our hat trick. And as the saying goes, if you have three untrue things before breakfast why not round it off with breakfast as Milliways...

PDR

1373980.  Mon Feb 08, 2021 11:54 pm

crissdee wrote:
 barbados wrote: Surely if a hat trick was involved, then one of the animals would have been a rabbit? Who ever heard of someone pulling a dog or a cat out of a hat!

But what about Dr Seuss? And suppose the cat in the hat is sat on a mat?

Be careful invoking him - his publishers are notoriously litigious where they suspect plagiarism. Their corporate motto could have been:

Could you, would you
With a writ
Would you, could you
Sue the git!

PDR

 1374002.  Tue Feb 09, 2021 6:30 am Suppose Pat, the cat in the hat, was sat on a flat mat, with Nat the bat, and Matt, the fat rat, with a vat of tat? What about that? I'll stop now....

1374007.  Tue Feb 09, 2021 7:25 am

PDR wrote:
In that post the statements:

 Quote: 3a = 30 3b = 9 3c = 3

Are just assigning values to symbols using the "=" operator. If one were to be pedantic it should have been preceded with a "Let" director,

No, not really. Don’t be misled by the simplicity of the example.

With due respect to ali, all this talk about assignments is a complete red herring, arising from the fact that some unimaginative programming language designers used the “=” symbol as an assignment operator. That is not what’s going on here.

You can only assign values to variables, not to expressions. An equation is not an assignment. When you write

(expression involving variables)=(other expression involving variables)

you are not assigning (the value of) the second expression to the first, and neither does the situation change if you rearrange terms so that all the variables appear on the left hand side. For example, if you write “x²=2x-5” you are not assigning the value 2x-5 to x². Nor are you assigning the value -5 to x²-2x, let alone assigning either of the values 1±2i to x. The process of solving equations is one of deducing values for the variables, not assigning values to them.

In mathematics, “Let” is generally used to define, not to assign (e.g. “Let a and b be constants...”). When it is (mis)used as PDR suggests, it is equivalent to a “Suppose that”, not to an assignment, and an equation (or system of equations) is never standalone; it is always accompanied by the question “What value(s) of the variables would make this a true statement?”, or “If this equation is a true statement, what would be the value of (some other expression involving the variables)?”

“3a = 30” is not an assignment, and neither, of course, is it a statement about the real world; it is an abstract statement, which is true when a is replaced by the appropriate value. The same applies to “Three birds = 30”. If “Three feathered animals = 30” doesn’t make sense, you need to look for an alternative interpretation that does. Since the right hand side is a number, the left hand side also needs to be a number, and when “bird” is replaced by “ten” it makes perfect sense; i.e. you solve the equation that results when you treat "bird" as an unknown variable.

A word means what Humpty Dumpty uses it to mean, not what Alice understands by it.

(Edited to improve legibility, once I'd discovered how to enter superscripts!)

Last edited by Numerophile on Tue Feb 09, 2021 9:43 am; edited 1 time in total

 1374009.  Tue Feb 09, 2021 8:25 am Back to what seems to have set this off, if someone puts as a puzzle: 3 birds = 30 What is it that anyone does not understand about that? What was the original puzzle this was part of that made it so complicated?

 1374010.  Tue Feb 09, 2021 8:32 am See post 1373733. But please don't let's start going round in circles again...

 1374011.  Tue Feb 09, 2021 8:33 am Only one person had a problem understanding the question, then after who knows how many times he was told what it meant, it finally clicked. Everyone else was fully aware of the meaning from the first time it was asked

 1374016.  Tue Feb 09, 2021 8:52 am https://youtu.be/q5mLjKI968g

1374020.  Tue Feb 09, 2021 9:52 am

PDR wrote:

In that post the statements:

 Quote: 3a = 30 3b = 9 3c = 3

Are just assigning values to symbols using the "=" operator.

No, I'm afraid they're not. They are algebraic equations, using "=" as the equality operator. "3a = 30" is a statement saying that three times the value of a is equal to the value of 30. There is no such thing as an "assignment operator" in mathematics.

That's why it's possible to do things like divide both sides of the equation by 3, and get "a = 10". You started off with two things that were equal, and then performed the same operation on each of them. If "3a = 30" were an assignment statement, it would be impossible to do that.

 Quote: If one were to be pedantic it should have been preceded with a "Let" director, but that didn't bother you then so you can't really complain about it now.

No, that's not correct. "3a = 30" is an equation telling you something about the properties of a. It doesn't assign a value to a; the value of a is assumed as fixed through the problem.

That's the difference between algebraic variables and variables in a computer language. The fact that we call them both "variables" is unfortunate; an algebraic variable can't change its value. It represents a fixed, unknown value.

 Quote: So we have our hat trick. And as the saying goes, if you have three untrue things before breakfast why not round it off with breakfast as Milliways...

I make it 1-1 (the second goal was disallowed).

1374021.  Tue Feb 09, 2021 10:12 am

 CB27 wrote: Back to what seems to have set this off, if someone puts as a puzzle: 3 birds = 30 What is it that anyone does not understand about that? What was the original puzzle this was part of that made it so complicated?

OK, I'll try to explain better.

The puzzle said "three birds = 30, three cats = 9, three dogs = 3. What is the value of one bird plus one cat, multiplied by a dog?" (The wording may not be exactly right.)

Now, what you were presumably meant to do was to reason "one bird = 10, one cat = 3, one dog = 1, so the answer is (10 + 3) x 1 = 13".

But what does that mean? What do the values actually represent?

As I said in the other thread, suppose it had been "three birds cost £30, three cats cost £9, three dogs cost £3". You'd have ended up with (£10 + £3) x £1 = £13 x £1, which is meaningless.

Or suppose it had been "three birds weigh 30kg, three cats weigh 9kg, three dogs weigh 3kg". Again you get 13kg x 1kg, which is meaningless.

There doesn't seem to be any way of assigning a meaning to the puzzle that makes it coherent. And I'm saying that that's a semantic difficulty; three birds can't be equal to a number. They can have a value; but that's not the same thing.

The absurdity of "three birds = 30" can easily be demonstrated. If two things are genuinely equal, you ought to be able to substitute one for the other without any change in meaning (in some contexts at least). So try it:

"There are three birds in this tree" -> "There are 30 in this tree"

Or the other way round:

"My son is 30 years old" -> "My son is three birds years old"

You simply get nonsense, whatever you try to do. That would suggest to me that they can't be genuinely "equal".

1374025.  Tue Feb 09, 2021 10:27 am

 Numerophile wrote: “3a = 30” is not an assignment, and neither, of course, is it a statement about the real world; it is an abstract statement, which is true when a is replaced by the appropriate value.

Yes, agreed (and the rest of your post up to there).

 Quote: The same applies to “Three birds = 30”. If “Three feathered animals = 30” doesn’t make sense, you need to look for an alternative interpretation that does. Since the right hand side is a number, the left hand side also needs to be a number, and when “bird” is replaced by “ten” it makes perfect sense; i.e. you solve the equation that results when you treat "bird" as an unknown variable.

OK, so you're saying that in the puzzle, the noun "bird" is being used as a synonym for the noun "ten" (i.e. a group of ten).

So a bird is a group of ten, a cat is a group of three, and a dog is a group of one. A group of ten plus a group of three can form a group of thirteen; but what is a group of thirteen times a group of one? Nothing that I can make any sense of.

It's the same difficulty as before.

1374028.  Tue Feb 09, 2021 10:33 am

I had no problem understanding the question, barbados. I made it quite clear at the top of the thread that this is an issue about formal semantics, and that alone. If you're not interested in technical stuff about formal semantics, it's probably not the right thread for you.

1374033.  Tue Feb 09, 2021 10:51 am

 Brock wrote: But what does that mean? What do the values actually represent?

No more and no less than a statement "3x=10".

For some reason you have decided to dictate to the rest of the world that only the specific things that you approve of can be used as symbols.

You are fine with saying a letter can be a symbol, but if it's a word you go off on some puritanical rant about the word only being ALLOWED to be used in its literal sense.

Well sorry, pal. You don't get to invent rules and impose them on the rest of the world. There is no reason other than your pseudo-religious dogma why the word "dog" cannot be used as a symbol in precisely the same way that the letter "x" can.

PDR

1374038.  Tue Feb 09, 2021 10:57 am

 Brock wrote: I don't think that most people, seeing "three birds = 30", would take it to mean "three birds are assigned the value 30". I certainly didn't. I took it to mean "three birds are equal to thirty", which is incoherent. And I've studied both maths and computer programming.

I am not, of course, most people, and I have not studied either maths beyond O level or computer programming at all. Nonetheless, when I saw a problem of this nature on Facebook, I immediately understood that three birds had been assigned the value 30, which meant to me that one bird had the value 10. It seemed neither difficult nor complex to me.

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