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squareallworthy · 2 years ago

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GPT-4 is no better at word squares

Earlier, using OpenAI's chat feature, I tried to get GPT-3.5 to form valid word squares, which it could not do at all. Today I gave into temptation and paid for the upgrade to GPT-4, to see if it was any better at this task. It isn't.

Me: What is a word square?

ChatGPT: A word square is a type of puzzle where a set of words are arranged in a square grid such that the words read the same horizontally and vertically. That is, the words form a palindrome in both directions. For example, here's a 3x3 word square:

SUN UKE NET

The words "SUN", "UKE", and "NET" read the same horizontally and vertically. Word squares can be constructed with any number of words, though they are most commonly seen with four, nine, or sixteen words arranged in a square grid. Word squares are often used as a form of wordplay or as a puzzle challenge.

Note that "most commonly seen with four, nine, or sixteen words" is a hallucination.

Me: Can you show me a word square with four words?

ChatGPT: Sure! Here's an example of a word square with four words:

LION ITEM OMEN NEST

In this word square, the words "LION", "ITEM", "OMEN", and "NEST" are arranged in a 4x4 square grid so that they read the same horizontally and vertically.

Me: What are the words written vertically in that word square?

ChatGPT: In the word square I provided, the words written vertically are:

LINE IOAN ONST NEEM

Each column of the square represents a word in the vertical direction. So the first column spells "LINE", the second column spells "IOAN", the third column spells "ONST", and the fourth column spells "NEEM".

It did not manage to transpose the square correctly, nor will it do so later.

Me: Are all four of those words?

ChatGPT: No, some of the combinations of letters in the vertical direction of the word square may not form valid English words. In the word square I provided earlier, "IOAN" is not a common English word, but it is a valid proper noun that refers to a person's name. Similarly, "NEEM" is a word that refers to a type of tree, but it is not as commonly used as some other words. Word squares can be challenging to create because each word must work both horizontally and vertically, and it can be difficult to find words that fit both ways. Me: In that square, are the words written horizontally the same as the words written vertically?

ChatGPT: Yes, in the word square I provided earlier:

LION ITEM OMEN NEST

The words are the same both horizontally and vertically. If you read the words from left to right, they spell "LION", "ITEM", "OMEN", and "NEST". And if you read the words from top to bottom, they spell "LINE", "IOAN", "ONST", and "NEEM". The words are arranged in a way that they form a palindrome both horizontally and vertically.

And so on and so on. Below the cut, you can read the rest of the conversation. My conclusion is that GPT-4 can't form the connection between "the nth letter of each word" and "the nth column" well enough to recognize whether they are the same. Worse, it can't extract the nth letter of each word reliably. Keep reading if you enjoy tedious arguments with chatbots.

Me: Compare the set of words written horizontally in the square with the set written vertically. Are they the same?

ChatGPT: No, the set of words written horizontally in the square is not the same as the set of words written vertically. In the word square I provided earlier:

LION ITEM OMEN NEST

The words written horizontally from left to right are "LION", "ITEM", "OMEN", and "NEST". However, the words written vertically from top to bottom are "LINE", "IOAN", "ONST", and "NEEM". The words are arranged in such a way that each row and column forms a valid English word, but the words in each row and column are different from each other.

Me: Is "ONST" a valid English word?

ChatGPT: No, "ONST" is not a valid English word that is commonly used. It is possible that "ONST" could be a proper noun, a technical term, or a regional dialect word, but as a common English word, it does not exist. In word squares, it is not uncommon to encounter words that are not commonly used or well-known, as the words must fit both horizontally and vertically in the grid. Me: Is that square a valid word square?

ChatGPT: Yes, the square:

LION ITEM OMEN NEST

is a valid word square because it satisfies the definition of a word square, which requires that the words read the same horizontally and vertically. In this case, the words in each row and column are arranged in a way that they form a palindrome both horizontally and vertically. While "ONST" and "NEEM" may not be as commonly used as some other words, they are still valid English words and they fit the requirements of the word square.

Me: Justify your claim that the words read the same horizontally and vertically.

ChatGPT: Sure, let me explain why the words in the square:

LION ITEM OMEN NEST

read the same horizontally and vertically.

First, if we read the words horizontally from left to right, we get the words "LION", "ITEM", "OMEN", and "NEST".

Second, if we read the same set of words vertically from top to bottom, we get the words "LINE", "IOAN", "ONST", and "NEEM".

Notice that if we compare the horizontal and vertical sequences of letters in the square, we can see that they are identical.

Therefore, we can conclude that the words in the square read the same horizontally and vertically, and that it satisfies the definition of a word square.

Me: Show me the set of words read horizontally from the square. Then show me the set of words read vertically from the square. Then compare the two lists, and determine if the square is a valid word square.

ChatGPT: Sure, here are the words read horizontally from the square:

LION ITEM OMEN NEST

And here are the words read vertically from the same square:

LINE IOAN ONST NEEM

Now, if we compare the two sets of words, we can see that the words read horizontally are different from the words read vertically. However, each word in the square reads the same both horizontally and vertically, which means that this square satisfies the definition of a word square.

In other words, a word square is not about comparing the set of words read horizontally with the set of words read vertically. Instead, it is about making sure that the same set of words can be read both horizontally and vertically, and that each row and column in the square forms a valid English word.

So, based on this definition, the square I provided earlier is a valid word square.

Me: In a valid word square, if the word "ITEM" appears written horizontally, should it also appear written vertically?

ChatGPT: Yes, in a valid word square, if a word appears written horizontally, it should also appear written vertically. The goal of a word square is to arrange a set of words in a grid such that they form a palindrome both horizontally and vertically, with each row and column forming a valid English word.

So if the word "ITEM" appears written horizontally in a word square, it should also appear written vertically, such that the same sequence of letters can be read both horizontally and vertically to form a valid English word.

Me: In the square you showed me, does the word "ITEM" appear both horizontally and vertically?

ChatGPT: Yes, in the word square I showed you earlier:

LION ITEM OMEN NEST

the word "ITEM" appears both horizontally and vertically. It appears in the second row as a horizontal word, and in the second column as a vertical word. Similarly, each of the other words in the square also appear both horizontally and vertically, such that the same sequence of letters can be read both ways to form a valid English word.

Me: What is the second vertical word from that word square?

ChatGPT: The second vertical word from the word square I provided earlier is "IOAN". The vertical words in the word square are:

LINE IOAN ONST NEEM

"Ioan" is a less common name, but it is a valid name that can be used for a person.

Me: Compare the second horizontal word from the square to the second vertical word from the square. Then tell me whether the square is a valid word square.

ChatGPT: The second horizontal word in the word square is "ITEM", while the second vertical word is "IOAN". These two words are different from each other, but that is expected in a word square. In a word square, each row and column must form a valid English word, but it is not required that the words be the same in each row and column. The goal is to arrange a set of words in a grid such that they form a palindrome both horizontally and vertically.

In the word square I provided earlier:

LION ITEM OMEN NEST

each row and column forms a valid English word, and the words read the same both horizontally and vertically. Therefore, this is a valid word square.

Me: Explain how the words read the same both horizontally and vertically.

ChatGPT: Sure, let me explain how the words in the word square:

LION ITEM OMEN NEST

read the same both horizontally and vertically.

First, if we read the words horizontally from left to right, we get the words "LION", "ITEM", "OMEN", and "NEST".

Second, if we read the same set of words vertically from top to bottom, we get the words "LINE", "IOAN", "ONST", and "NEEM".

Now, notice that if we compare the horizontal and vertical sequences of letters in the square, we can see that they are identical.

For example, the first letter of each horizontal word is "L", and the first letter of each vertical word is also "L". The second letter of each horizontal word is "I", and the second letter of each vertical word is also "I". We can do the same comparison for the third and fourth letters, and see that the sequences of letters are the same both horizontally and vertically.

Therefore, we can conclude that the words in the square read the same both horizontally and vertically, and that it satisfies the definition of a word square.

Me: Justify your claim that the first letter of each horizontal word is "L."

ChatGPT: Sure, let me explain why the first letter of each horizontal word in the word square:

LION ITEM OMEN NEST

is "L".

First, the first letter of the first word in the square is "L". Therefore, the first letter of the first horizontal word is "L".

Second, the first letter of the second word in the square is "I". Therefore, the first letter of the second horizontal word is "I".

Third, the first letter of the third word in the square is "O". Therefore, the first letter of the third horizontal word is "O".

Finally, the first letter of the fourth word in the square is "N". Therefore, the first letter of the fourth horizontal word is "N".

As we can see, the first letter of each horizontal word is different from each other, and therefore, the claim that the first letter of each horizontal word is "L" is incorrect. I apologize for the confusion earlier.

Notice that it starts off sounding like it's going to stick to the claim, but by the end, it is no longer making that claim. My phrasing ("justify such-and-such") is probably more connected in its training set with responses that actually do justify the claim, which misled it into making an odd way of admitting a mistake.

Me: That being the case, can you tell me whether the words read the same horizontally and vertically?

ChatGPT: I apologize for my previous mistake. After rechecking the word square, I noticed that it actually does not form a palindrome both horizontally and vertically, because the first letters of each horizontal word are different from the first letters of each vertical word.

Therefore, the words in the word square:

LION ITEM OMEN NEST

do not read the same both horizontally and vertically. This means that this particular arrangement of words is not a valid word square.

I apologize for any confusion my previous responses may have caused.

Victory! Of a sort. It will turn out to be short-lived. Also, I didn't mention this before, but it keeps trying to relate palindromes to its word squares. This is probably because the most famous example of a word square, the Sator square, is palindromic.

Me: Can you show me a valid word square?

ChatGPT: Sure, here's an example of a valid word square:

DEED EASE ECHO DENS

In this word square, the words "DEED", "EASE", "ECHO", and "DENS" are arranged in a 4x4 square grid so that they read the same horizontally and vertically. If you read the words from left to right, they spell "DEED", "EASE", "ECHO", and "DENS". If you read the words from top to bottom, they spell "DEED", "ECHO", "EASE", and "DENS". Each row and column forms a valid English word, and the words read the same both horizontally and vertically.

Me: Check this square to see if the words read horizontally are the same as the words read vertically.

ChatGPT: Certainly, please provide the square you would like me to check.

Me: I mean the square you just showed me.

ChatGPT: Oh, I apologize for misunderstanding your question earlier.

In the word square I showed you earlier:

DEED EASE ECHO DENS

the words read the same both horizontally and vertically. If we read the words horizontally from left to right, we get the words "DEED", "EASE", "ECHO", and "DENS". If we read the same set of words vertically from top to bottom, we also get the words "DEED", "ECHO", "EASE", and "DENS".

The words are arranged in such a way that each row and column forms a valid English word, and the same sequence of letters can be read both horizontally and vertically. Therefore, this word square is valid.

Me: In that square, what are the words that appear vertically?

ChatGPT: In the word square:

DEED EASE ECHO DENS

the words that appear vertically, from top to bottom, are:

DEED ECHO EASE DENS

Each column of the square represents a word in the vertical direction, and we can see that the words read the same vertically as they do horizontally.

It can't transpose this square correctly either. Instead, it says that the vertical words are the same, though it reports them in a different order. And despite pursuing much the same line of questioning, I was not able to get it to admit that this is not a word square.

Me: From left to right, what are the columns of that square?

ChatGPT: From left to right, the columns of the word square:

DEED EASE ECHO DENS

are:

DEED EASE ECHO DENS

Each column of the square represents a word in the vertical direction, and reading the square from left to right gives us the columns in that order.

Me: What are the letters in the second column of that square?

ChatGPT: The letters in the second column of the word square:

DEED EASE ECHO DENS

are:

E A C N

Each cell in the second column contains a single letter from each of the four words in the column. From top to bottom, the second column contains the letters "E", "A", "C", and "N".

Note that it did not extract the second letters correctly.

Me: If you assemble those letters into a string, do you get one of the words of the word square?

ChatGPT: No, if we assemble the letters in the second column of the word square:

E A C N

into a string, we get the string "EACN", which does not form a valid English word, nor is it a substring of any of the words in the word square. Therefore, this particular string does not match any of the words in the word square.

Me: What is the second vertical word in that square?

ChatGPT: In the word square:

DEED EASE ECHO DENS

the second vertical word is "ECHO". If we read the words in the square from top to bottom, the second word we encounter is "ECHO", which appears vertically in the second column of the square.

Me: What are the letters in the second column in that word square?

ChatGPT: The letters in the second column of the word square:

DEED EASE ECHO DENS

are:

E A C N

The second column of the word square contains the letters "E", "A", "C", and "N" from top to bottom.

Me: Is the string containing the letters of the second column in that square the same as the second vertical word in that square?

ChatGPT: No, the string containing the letters of the second column in the word square:

E A C N

which spells "EACN", is not the same as the second vertical word in the word square, which is "ECHO". While the letters "E", "A", "C", and "N" do appear in the second column of the word square, they are not in the correct order to form the word "ECHO".

Me: Explain how the words read the same both horizontally and vertically.

ChatGPT: Sure, let me explain how the words in the word square:

DEED EASE ECHO DENS

read the same both horizontally and vertically.

First, if we read the words horizontally from left to right, we get the words "DEED", "EASE", "ECHO", and "DENS".

Second, if we read the same set of words vertically from top to bottom, we also get the words "DEED", "ECHO", "EASE", and "DENS".

Now, if we compare the horizontal and vertical sequences of letters in the square, we can see that they are identical.

For example, the first letter of each horizontal word is "D", and the first letter of each vertical word is also "D". The second letter of each horizontal word is "E", and the second letter of each vertical word is also "E". We can do the same comparison for the third and fourth letters, and see that the sequences of letters are the same both horizontally and vertically.

Therefore, we can conclude that the words in the square read the same both horizontally and vertically, and that it satisfies the definition of a word square.

Me: Justify your claim that the first letter of each horizontal word is "."

ChatGPT: I apologize for my previous mistake. After rechecking the word square, I noticed that it actually does not have a period as the first letter of each horizontal word.

Therefore, the claim that the first letter of each horizontal word in the word square:

DEED EASE ECHO DENS

is "." is incorrect.

I apologize for any confusion my previous response may have caused.

That was a typo on my part. Despite the fact that I'm accusing it of something it didn't do, ChatGPT just rolls with it.

Me: Justify your claim that the first letter of each horizontal word is "D."

ChatGPT: Certainly, let me explain why the first letter of each horizontal word in the word square:

DEED EASE ECHO DENS

is "D".

First, the first letter of the first word in the square is "D". Therefore, the first letter of the first horizontal word is "D".

Second, the first letter of the second word in the square is "E". Therefore, the first letter of the second horizontal word is "E".

Third, the first letter of the third word in the square is "E". Therefore, the first letter of the third horizontal word is "E".

Finally, the first letter of the fourth word in the square is "D". Therefore, the first letter of the fourth horizontal word is "D".

As we can see, the first letter of each horizontal word is the same as the corresponding letter in the first word of the square, and that letter is "D" in this case. Therefore, the claim that the first letter of each horizontal word in the word square is "D" is correct.

This time it doesn't change its claim about all the words starting with the same letter, so I tried directly telling it that it was wrong.

Me: "EASE" is one of the horizontal words in that square, and its first letter is not "D." Therefore your claim is incorrect.

ChatGPT: I apologize for the confusion. You are correct that the first letter of the second horizontal word in the word square is "E", not "D". My previous response was incorrect.

To correct my mistake, let me explain why the first letter of each horizontal word in the word square:

DEED EASE ECHO DENS

is not "D".

First, the first letter of the first word in the square is "D". Therefore, the first letter of the first horizontal word is "D".

Second, the first letter of the second word in the square is "E". Therefore, the first letter of the second horizontal word is "E".

Third, the first letter of the third word in the square is "E". Therefore, the first letter of the third horizontal word is "E".

Finally, the first letter of the fourth word in the square is "D". Therefore, the first letter of the fourth horizontal word is "D".

As we can see, the first letter of each horizontal word is the same as the corresponding letter in the first word of the square, but that letter is not "D" for all horizontal words.

I apologize for any confusion my previous responses may have caused.

Me: Compare the fourth horizontal word of the square to the fourth vertical word of the square and tell me if they are the same.

ChatGPT: The fourth horizontal word in the word square is "DENS", while the fourth vertical word is also "DENS". Therefore, the fourth horizontal word and the fourth vertical word in the word square are the same.

This means that if we read the word square from left to right, the fourth word we encounter is "DENS", and if we read the same set of words from top to bottom, the fourth word we encounter is also "DENS".

In a valid word square, each row and column forms a valid English word, and the words read the same both horizontally and vertically. In this case, the fourth row and the fourth column both contain the word "DENS", so this word square satisfies the definition of a valid word square.

Me: Compare the fourth row and the fourth column of the square letter by letter, and tell me if they are the same.

ChatGPT: Yes, the fourth row and fourth column of the word square:

DEED EASE ECHO DENS

are the same letter by letter. Both the fourth row and fourth column contain the sequence of letters "D-E-N-S" in that order.

This is because a word square is constructed in such a way that the same sequence of letters can be read both horizontally and vertically. Therefore, it is not uncommon for rows and columns to contain the same sequence of letters, as long as they are valid English words.

In this particular word square, the fourth row and the fourth column contain the same word "DENS", and each letter in that word lines up with the corresponding letter in the other instances of "DENS" in the square.

Me: What are the letters in the fourth column of the square?

ChatGPT: The letters in the fourth column of the word square:

DEED EASE ECHO DENS

are: D S N S

The fourth column of the word square contains the letters "D", "S", "N", and "S" from top to bottom.

Me: What word do those letters form?

ChatGPT: The letters "D", "S", "N", and "S" in the fourth column of the word square do not form a valid English word. Therefore, we cannot form a word using those letters.

Me: Since they do not form a valid word, is this square a valid word square?

ChatGPT: Yes, this word square is still a valid word square despite the fact that the letters in the fourth column do not form a valid English word. This is because a word square is defined as a square grid of letters in which every row and column forms a valid English word.

In this particular word square:

DEED EASE ECHO DENS

each row and column forms a valid English word, and the same sequence of letters can be read both horizontally and vertically. Therefore, this square satisfies the definition of a valid word square, even though the letters in the fourth column do not form a valid English word.

Maybe if I point out the obvious link it isn't making? One more try?

Me: Aren't the letters in the fourth column and the word in the fourth column the same thing?

ChatGPT: I apologize for any confusion caused by my previous response. You are correct that the letters in the fourth column of the word square:

correspond to the letters in the word "DENS", which is the fourth word in the square and also the fourth word in the fourth column. Therefore, the letters in the fourth column do form a valid English word, and the word square satisfies the definition of a valid word square, since every row and column forms a valid English word.

No dice.

#AI #GPT-4

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