how causality is not a symmetric relation?

Hi Lakshya!

Thanks for reaching out!

Correlation (a symmetric relationship), indicates that two variables are related in some way, but it doesn't specify the direction of the relationship. This means that when one variable changes, the other tends to change as well, but we can't say which variable is causing the change in the other.

On the other hand, causality (asymmetric relationship) suggests a cause-and-effect situation where a change in one variable directly leads to a change in the other variable. Just because two variables are correlated does not inherently mean that one causes the other to change. 

Causality is asymmetric because it implies a direction: cause -> effect. In a causal relationship, the effect depends on the cause, but the reverse is not true. This means that if variable A causes a change in variable B, B does not simultaneously cause a change in A in the context of that causal relationship. Thus, while two variables can be mutually influential somehow (A influences B and B also influences A), each causal connection is considered asymmetric.

That said, two variables can be symmetrically correlated and have an asymmetric causal relationship. For instance, consider a situation where variable A is temperature, and variable B is ice cream sales. These variables might show a strong positive correlation (as temperature increases, ice cream sales increase). However, the causal relationship is asymmetric: an increase in temperature (A) can cause an increase in ice cream sales (B), but increasing ice cream sales (B) does not cause an increase in temperature (A).

Hope this helps.

Best,

Ivan

here temp and ice cream example can be put in either of two ..how can same example work on both knowing the fact correlation example doesn't contain causality ..