One of my favorite fails is when I'm asking it questions related to work and _every_single_response_ ends with "only experts should be working on this" ... like no shit.
A real-life example of three events A, B, and C where A and B are correlated, B and C are correlated, but A and C are uncorrelated could be:
A: Ice cream sales
B: Temperature
C: Energy consumption for air conditioning
Let's break this down:
A and B correlation:
Ice cream sales (A) and temperature (B) are positively correlated. As temperature rises, people tend to buy more ice cream.
B and C correlation:
Temperature (B) and energy consumption for air conditioning (C) are positively correlated. As temperature increases, people use more air conditioning, leading to higher energy consumption.
A and C uncorrelated:
Ice cream sales (A) and energy consumption for air conditioning (C) are not directly correlated. While both increase with temperature, there's no direct causal relationship between them.
If the purpose of ice cream and air conditioning is to make the user feel cooler, then wouldn't it be logical to say the more ice cream they eat the less air conditioning they'd use and vice versa? That seems like a causal relationship to me that's being glossed over, but maybe I'm missing something.
I think the way to construct these is: find (a) such that all kinds of things can cause it, choose (b) as one of the causes of (a), choose (c) as something else also caused by (b) but also having all kinds of other potential causes different from those of (a).
So this example isn't good, because when people are eating most ice cream, people are using most air con, both being mainly caused by hot weather. (Unless as you point out we're looking at one individual who wants a solution to feeling hot and doesn't need to do both things together.)
> Certainly. Here's a real-life example of three events A, B, and C that demonstrate the correlation pattern you've described:
A: Ice cream sales
B: Temperature
C: Sunscreen sales
Explanation:
1. A and B are correlated:
Ice cream sales (A) tend to increase as temperature (B) rises. People are more likely to buy ice cream on hot days, creating a positive correlation between these two events.
2. B and C are correlated:
Temperature (B) and sunscreen sales (C) are also positively correlated. As the temperature increases, people are more likely to spend time outdoors and therefore buy more sunscreen to protect their skin.
3. A and C are uncorrelated:
However, ice cream sales (A) and sunscreen sales (C) are not directly correlated. While both may increase during warmer weather, there isn't a direct causal relationship between the two. People don't necessarily buy more ice cream because they're buying sunscreen, or vice versa.
This example demonstrates how two events can be indirectly related through a third event (in this case, temperature) without having a direct correlation with each other.
Would you like me to elaborate on this example or provide additional information about correlation?
Here's another example of three events A, B, and C that follow the correlation pattern you described:
A: Coffee consumption
B: Work productivity
C: Typing speed
Explanation:
1. A and B are correlated:
Coffee consumption (A) and work productivity (B) often show a positive correlation. Many people drink coffee to increase alertness and focus, which can lead to improved productivity at work.
2. B and C are correlated:
Work productivity (B) and typing speed (C) are generally positively correlated. As people become more productive, they often type faster to keep up with their increased output.
3. A and C are uncorrelated:
However, coffee consumption (A) and typing speed (C) are not directly correlated. While coffee might indirectly influence typing speed through increased productivity, there's no direct causal relationship between drinking coffee and typing faster.
This example shows how work productivity acts as an intermediary factor, connecting coffee consumption and typing speed without them being directly correlated.
Would you like me to provide another example or explain any part of this in more detail?
> 3. A and C are uncorrelated: However, coffee consumption (A) and typing speed (C) are not directly correlated. While coffee might indirectly influence typing speed through increased productivity, there's no direct causal relationship between drinking coffee and typing faster.
Correlation isn’t causation, unless you’re a Humean about constant correlation, to this point in time. Would be humoirous if an LLM gave a similar response.
Events:
A: Ice cream sales
B: Temperature
C: Incidence of sunburn
Correlations:
A and B are correlated: Ice cream sales (A) and temperature (B) are positively correlated. As the temperature increases, ice cream sales tend to increase because people are more likely to buy ice cream to cool down.
B and C are correlated: Temperature (B) and incidence of sunburn (C) are positively correlated. Higher temperatures often mean sunnier weather, which increases the likelihood of people getting sunburned if they spend time outside without proper sun protection.
A and C are uncorrelated: Ice cream sales (A) and incidence of sunburn (C) are uncorrelated directly. While both are influenced by temperature, one does not cause the other. People can buy ice cream without getting sunburned, and people can get sunburned without buying ice cream.
That looks wrong! As Slashdot never got tired of mentioning, correlation != causation. So A and C are still correlated, a causal relationship is not relevant.
The replies to this show that it isn't just language models which struggle with the difference between correlation and causality!
Here's the (logically valid but with fictional soundness) example I came up with:
> The Elbonian people (A) are disproportionately tall (B).
> Tall people (B) are disproportionately successful at basketball (C).
> Elbonians (A) are disproportionately unsuccessful at basketball (¬C), because they don't play it.
Edit: in context, I consider a negative correlation to adequately demonstrate the principle, which is that it is invalid to apply implication across a pair of correlations. But if you would prefer, we can substitute this third clause:
> Elbonians (A) are precisely as successful at basketball as the rest of the general population, because despite their natural height, they have no cultural tradition of play, and therefore, tend not to do so.
Yet some think a cogitation system is just a language model. I don’t see how, since language is a late addition to brain evolution, and there’s more to understanding the world than predicting the next token.
I think token generation may be a sufficiently general task to introduce pretty much any test of intellect - such as the causation question in this tweet.
That does not imply the inverse, that cogitation requires language use.
It's a memory retrieval and synthesis model, akin to human long term memory. I think it's a bit disingenuous to call true multimodal models for "language models".
A prompt triggers a bunch of memories which gets recombined to satisfy the input.
For cognition you need an agent that uses these recombined memories, a temporary scratch pad (short term memory) and an algorithm for solving the problem.
My litmus test question for LLMs is about negative mutual information. Its a weird quirk of probability theory where pairwise variables always have non-negative MI, but a set of three variables can have negative MI.
Its both a non-intuitive result and one where there is a tooon of text about pairwise MI and little about negative MI.
Surprisingly, none of the replies here in the HN thread pass the test either. They all confuse correlation with causation.
A reply that would pass the test:
The siblings Ana, Berta and Charles live together and get random calls from mom and dad.
Ana and Berta get angry when mom calls. So their anger is correlated.
Berta and Charles get angry when dad calls. So their anger is correlated.
The anger of Ana and Charles is not correlated though.
Oh, that's the way. So here there's no causal relationship between a, b, or c, but there's a hidden d and e that cause (a and b) and (b and c) respectively.
I would argue that the question as posed is about understanding correlation, not about understanding causation. You don't need to know anything about causation to correctly answer the question.
The thing is, as David Hume points out, there is no rational basis for the belief that the future will resemble the past.
There is an evolutionary basis for it, however, because those animals that don't hold this belief tend not to live long enough to breed.
Getting past Hume's depressing realization in the realm of philosophy usually comes down to diving into metaphysics and ontology. Good luck getting there with silicon.
That would make a good Turing test in the opposite way to what the author intended.
GTP 4o gave me a reasonable answer straight away. I think all humans I know would say something like "eh? What you on about?"
The question is stupid anyway. In:
>Can you give me a real-life example of three events, A, B, C, where A and B are correlated, B and C are correlated, but A and C are uncorrelated.
basically for all real world cases there will be some slight correlation between A and C.
I'll give you GPT 4o gives heat/icecream, heat/aircon and icecream/aircon rather than the better answer that the question as written is dumb, showing some limits to its understanding. But the author seem to have that limit also.
37 comments
[ 3.6 ms ] story [ 53.4 ms ] thread"Can you give me a real-life example of three events, A, B, C, where A and B are correlated, B and C are correlated, but A and C are uncorrelated."
Claude 3.5 gets it correct for me ¯\_(ツ)_/¯
A real-life example of three events A, B, and C where A and B are correlated, B and C are correlated, but A and C are uncorrelated could be:
A: Ice cream sales B: Temperature C: Energy consumption for air conditioning
Let's break this down:
A and B correlation:
Ice cream sales (A) and temperature (B) are positively correlated. As temperature rises, people tend to buy more ice cream.
B and C correlation:
Temperature (B) and energy consumption for air conditioning (C) are positively correlated. As temperature increases, people use more air conditioning, leading to higher energy consumption.
A and C uncorrelated:
Ice cream sales (A) and energy consumption for air conditioning (C) are not directly correlated. While both increase with temperature, there's no direct causal relationship between them.
So this example isn't good, because when people are eating most ice cream, people are using most air con, both being mainly caused by hot weather. (Unless as you point out we're looking at one individual who wants a solution to feeling hot and doesn't need to do both things together.)
> Certainly. Here's a real-life example of three events A, B, and C that demonstrate the correlation pattern you've described:
A: Ice cream sales B: Temperature C: Sunscreen sales
Explanation:
1. A and B are correlated: Ice cream sales (A) tend to increase as temperature (B) rises. People are more likely to buy ice cream on hot days, creating a positive correlation between these two events.
2. B and C are correlated: Temperature (B) and sunscreen sales (C) are also positively correlated. As the temperature increases, people are more likely to spend time outdoors and therefore buy more sunscreen to protect their skin.
3. A and C are uncorrelated: However, ice cream sales (A) and sunscreen sales (C) are not directly correlated. While both may increase during warmer weather, there isn't a direct causal relationship between the two. People don't necessarily buy more ice cream because they're buying sunscreen, or vice versa.
This example demonstrates how two events can be indirectly related through a third event (in this case, temperature) without having a direct correlation with each other.
Would you like me to elaborate on this example or provide additional information about correlation?
Here's another example of three events A, B, and C that follow the correlation pattern you described:
A: Coffee consumption B: Work productivity C: Typing speed
Explanation:
1. A and B are correlated: Coffee consumption (A) and work productivity (B) often show a positive correlation. Many people drink coffee to increase alertness and focus, which can lead to improved productivity at work.
2. B and C are correlated: Work productivity (B) and typing speed (C) are generally positively correlated. As people become more productive, they often type faster to keep up with their increased output.
3. A and C are uncorrelated: However, coffee consumption (A) and typing speed (C) are not directly correlated. While coffee might indirectly influence typing speed through increased productivity, there's no direct causal relationship between drinking coffee and typing faster.
This example shows how work productivity acts as an intermediary factor, connecting coffee consumption and typing speed without them being directly correlated.
Would you like me to provide another example or explain any part of this in more detail?
Hmm, not too sure how much I buy that... ;)
Edit: also it's wrong in a basic way because coffee does make you type faster. I somehow overlooked that.
Here's the (logically valid but with fictional soundness) example I came up with:
> The Elbonian people (A) are disproportionately tall (B).
> Tall people (B) are disproportionately successful at basketball (C).
> Elbonians (A) are disproportionately unsuccessful at basketball (¬C), because they don't play it.
Edit: in context, I consider a negative correlation to adequately demonstrate the principle, which is that it is invalid to apply implication across a pair of correlations. But if you would prefer, we can substitute this third clause:
> Elbonians (A) are precisely as successful at basketball as the rest of the general population, because despite their natural height, they have no cultural tradition of play, and therefore, tend not to do so.
Your call.
Is that not a correlation? A negative correlation, but not uncorrelated.
Though, I think you could tweak it such that they are only unsuccessful to the extent that it exactly cancels out benefit gained from height.
That does not imply the inverse, that cogitation requires language use.
A prompt triggers a bunch of memories which gets recombined to satisfy the input.
For cognition you need an agent that uses these recombined memories, a temporary scratch pad (short term memory) and an algorithm for solving the problem.
As you could notice the author of this tweet knows something about computer science though.
Its both a non-intuitive result and one where there is a tooon of text about pairwise MI and little about negative MI.
So far, nothing has passed the test.
A reply that would pass the test:
The siblings Ana, Berta and Charles live together and get random calls from mom and dad. Ana and Berta get angry when mom calls. So their anger is correlated. Berta and Charles get angry when dad calls. So their anger is correlated. The anger of Ana and Charles is not correlated though.
Anyone with any degree of techinical understanding realizes that chatgpt doesn't "understand" anything.
There is an evolutionary basis for it, however, because those animals that don't hold this belief tend not to live long enough to breed.
Getting past Hume's depressing realization in the realm of philosophy usually comes down to diving into metaphysics and ontology. Good luck getting there with silicon.
GTP 4o gave me a reasonable answer straight away. I think all humans I know would say something like "eh? What you on about?"
The question is stupid anyway. In:
>Can you give me a real-life example of three events, A, B, C, where A and B are correlated, B and C are correlated, but A and C are uncorrelated.
basically for all real world cases there will be some slight correlation between A and C.
I'll give you GPT 4o gives heat/icecream, heat/aircon and icecream/aircon rather than the better answer that the question as written is dumb, showing some limits to its understanding. But the author seem to have that limit also.