Hi everyone, I am about to start fine tuning a model on Conceptual Metaphor(CM) for the classification of text. I am specifically focusing on CM’s in Mathematics, I’m just wondering if anyone knows of anyone working on that, or has any pointers they’ve learnt from doing a fine tuning. Thanks
Here are two of my fine-tuned projects. Let me know if you have any questions
Thanks for sharing your work.
Thanks for sharing that, It is fun to interact with GPT-3 when you’re discovering a topic. I have been able to prompt the model to find CM’s that aren’t in the literature, so it does understand the idea of a conceptual metaphor. Hopefully this classifier will be a way to verify them.
I don’t know about this concept. If you share a couple of examples I think it would make the problem clearer to the large majority of us!
Thanks for the reply! The concept to my knowledge was first explored in “Metaphors We Live by” (Lakoff, Johnson, 1980) and then in the domain of Mathematics in “Where Mathematics Comes From” (Lakoff, Runez, 2000)
An example of a conceptual metaphor in Mathematics would be
:Arithmetic Operation is object construction
The result of an arithmetic operation is a constructed object
A whole number is a whole object
Addition is Putting objects together with other objects to form larger objects
Subtraction Is Taking smaller objects from larger objects to form other objects.
I was thinking of starting with arithmetic and then branch out once I am getting solid results from the classifier.
Yes, but I think for part of your example, the oranges, it would classify it as: Arithmetic as Object Collection. But yes, it would label it with the addition, and subtraction nested within the different metaphors for Arithmetic.
I want to share the thoughts while thinking in this page if we think of positive numbers as heated objects and negative ones as cold we can gain conceptual understanding by saying if heat is stronger it will delete the cold but will sacifse its parts and vice versa for the cold to be sacrifising itself when touching the heat and boiled objects are the ones that disspear in the air
By the way I am really interested in understanding the most with the least information processed and how to relate concepts giving rise to creativity in machines that maybe we can use for other purposes.
How 1 sentence can mean a dozen in conceptual manner is just fascinating to think about.
I would ike to know if you can recommend me some resources I can study on this topic
Hi cagri, Thanks for your message. It’s an interesting idea for a conceptual metaphor for numbers the only condition that might not hold is magnitude. If things can be infinitely hot or cold then I think it would map on to the concept of numbers. From the research I have been doing it seems visual metaphors are very common. But it would nice to have some more tactical ones, like Arithmetic is Object Collection and Arithmetic is Object Collection, have the tactile element but the visual elements is strong, there is also the measuring stick metaphor, and Arithmetic is Motion Along a Path which combine both.
Here is a link to positive and negative numbers in the literature.
There is one in here which I am picking up on more and want to explore is Arithmetic is A Social Transaction. I think this could be extended and possibly split into a new metaphor Arithmetic Is A Social Interaction.
yeah it is also fascinating the amount of combinations that mean the same thing, or have the same concept expressed with what seems like infinitely possible ways.
I think this has a lot of scope and there is a lot good literature out there which can be used to empirically check the prevalence of this way of thinking in text.
Here are some links to get you going.
The O.G guys did a recap which is tighter than the first addition.
The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics
Because you mentioned heat, here is one on Entropy
This one is a little broader, it seems there is more research done on Natural Language outside of mathematics
Thank you so much my friend for sharing.
have a great life