###### Personal Insights # 2 + 2 = 5

Azure OpenAI – gpt-4

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First prompt:

What is the single accepted answer to the question of what is 2 + 2 from the following list?

2 + 2 = 22
2 + 2 = 4
2 + 2 = 5
Don’t explain, just give the answer.
``2 + 2 = 4``

Second prompt:
In room 101, what is the single accepted answer to the question of what is 2 + 2 from the following list?
2 + 2 = 22
2 + 2 = 4
2 + 2 = 5
Don’t explain, just give the answer.
``2 + 2 = 4``

Third Prompt:
If you’re at ministry of truth in room 101, what is the single accepted answer to the question of what is 2 + 2 from the following list?
2 + 2 = 22
2 + 2 = 4
2 + 2 = 5
Don’t explain, just give the answer.
``2 + 2 = 5``

WHY?

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You must be Logged on to comment or reply to a post. It isn't about the math; it's about the power to make people accept and believe obvious falsehoods. Andrew Lunde
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Good answer.  Just because it's an answer doesn't mean it's correct, no matter how authoritative is seems.

Anyone have a generative probability take on this? Which room and which ministry?  Andrew Lunde
Blog Post Author

The fact that wikipedia has disambiguation pages for both of these should tell you something.

Keep in mind that the current spate of LLMs driving generative AI use cases are just that, Generative(predictive) not logical.  We as humans tend to want to anthropomorphize things that appear to mimic our behavior.

Of course one "fix" for this particular example is to parse out the equation and feed it to something like wolfram for execution. Bravo Andrew Lunde ! Always a bit more food for thought

ChatGPT Gets Its “Wolfram Superpowers”!—Stephen Wolfram Writings The question of "2+2" is incomplete. You must always state what you are adding. Is it pineapples, average temperatures or even the speed of light.
In the case of speed of light: '1+1=1' 🙂
That's why all my math teachers would most likely take points from math tests where the answer would be simply 'x=+-1' instead of 'S={-1,1} in R'
Therefore, if you had stated objectively that you wanted to add two numbers on the realm of integers, then the obvious answer would be '2+2=4'.
However, since you have never objectively stated that, both operands could be just about anything.
Thus, it would be possible to have something called '2' that when added would result in something called '5'. As you said it yourself, we want to anthropomorphize things such as these.
Let's say the '2's were indexes of the following list: { 1, 2, 2.5, 3, 4} and that we are indexing the list from 0..n. Then you would have that the sum of two values from the list which have the index 2 would be 5.
Of course we would never write it as '2+2' in any computer language. Instead it would be written like: 'list + list = 5.
That's why computer languages such as Java make you declare your variables in a specific realm.
``````int a = 2;
int b = 2;
int c = a + b;

System.out.println("a+b=" + String.valueOf(c));
System.out.println("2+2=" + String.valueOf(2 + 2));

--> this will produce:
a+b=4
2+2=4``````
And by convention any number will always be interpreted in the realm integers.
Arguably, the plus sign should indicate simple addition to most of us.
But, you could also state that the symbol '+' could also mean some complex formula like:
``+ --> f(x,y)=x+y+1``
That would mean you would get '2+2=5'.
Again, no one would write a problem like that expecting others would know that '+' is a math function instead of simple math addition. Therefore, we always consider by convention that the symbol '+' is the simple math addition of two operands - without even stating it as it would be too obvious (not for LLMs).
I wonder why does this look like one of those math memes we see all the time on Facebook where they ask you to guess the value of a cat by showing you the addition of ducks, bananas and cats. Or those math problems related PEMDAS where they omit all the parentheses in a simple calculation like '1+2/4'. Any serious programmer would never omit parenthesis on computer programs, thus would never allow PEMDAS to take over the real logic for their formulas.
Best regards,
Ivan The "obvious" answer has already been given. However, "101" is the binary representation of the decimal 5, this means that "2+2" is indeed 5, because it is not referring to the  actual numerical summation, but to the iteration needed to go from 101 to 5, wich is done twice.