type class struggle tweets retweeted
the next big thing in PL theory is gonna be dynamic scoping. you heard it here first folks dynamic scoping is the future
me to a friend: "how could you reasonably define tea such that coffee isn't a type of tea"
their response: "coffee is kiki, tea is boba"
academia stackexchange is wild because you can ask "does anyone have advice on being trans in math academia" and someone will say "you should fly to colorado and go to this panel"
i dont want to sound like minimizing the danger of COVID. but its definitely true that that coronavirus is not really novel anymore
i will counter this bullshit invoking of the yoneda lemma with a bullshit invoking of Whitney's graph isomorphism theorem which shows that two things having the same "connectivity structure" does not imply they have the same "actual structure" (similarly vaguely)
Here's my heuristic case for optimism about being able to communicate with whales and dolphins.
Suppose we train an LLM on tokenized sperm whale clicks and can project out the latent space of whale concepts. Seems very doable, as their language clearly has a lot of structure. Yet without a Rosetta Stone, how do we then translate from whale to English?
It turns out LLMs are good at translation even when a given language is a tiny share of the training data, as different languages secretly map to concept embeddings with similar relational structure.
Take the classic word2vec example: king - man + woman = queen. In French, the words change but the vectors stay the same: roi - homme + femme = reine. Per Yoneda, concepts are uniquely determined by the totality of their relationships to other concepts, so language models can fill in the gaps of languages with sparse or unpaired data by aligning words to these shared embeddings.
What if whale and human languages have substantial conceptual overlap? It's not a crazy idea. We're both sexually dimorphic, highly social mammals that learn distinct cultures and dialects. We both organize into clans and hierarchies. Dolphins are cousins to sperm whales and can be trained to perform tricks that require complex vocal and gestural coordination with humans and other dolphins, etc.
Of course, sperm whales and dolphins likely have concepts with no parallel in human language, just as the vast majority of our concepts have no parallel in their languages. Nonetheless, at least in human languages, pretrained language models have been found to learn universal representations "without the requirement of any share vocabulary or domain similarity, and even when only a subset of the parameters in the joint encoder are shared."[1]
This is hugely promising, as it suggests human and whale languages, if they overlap at all, share enough representations to serve as fixed points for building up a richer whale-to-human dictionary.
For example, sperm whale vocalizations for "self," "family," and "extended clan" are apparently already known. Now suppose the word2vec in English for "extended clan - family" takes you to the concept "friend." You could then do the same operation in the whale2vec latent space and figure out which tokens correspond to whale-speak for "friend," and so on, steadily filling in the missing vocabulary.
Concepts that whales have that humans lack could then be built up from combinations of human concepts, similar to how many languages don't have the word "slush" but can still express the same idea by saying "wet snow" or "melted solid sky water" and so forth. Conversely, complex human concept could be communicated to whales by building them up from basic whale concepts. The abstract concept of "civilization," say, might translate to whale as the concepts "extended group" + "many" + "cooperation" + "long time."
In 2020, researchers built an autoencoder for dolphin audio communication, and found meaningful clustering within the embedding space.[2] More recently, researchers trained a language model on sperm whale clicks and confirmed outstanding hypotheses about which structures most likely encode meaning.[3]
The roadmap to building a human-whale Rosetta Stone seems clear from here, and well within the reach of current technology. Watch this space! π¬ (keke keke ke)
[1] arxiv.org/abs/1911.01464
[2] arxiv.org/abs/2005.07623
[3] arxiv.org/abs/2303.10931
call the inner circle's position (r,y) where r is also the radius
from the tangent w/ outer circle we get y^2 = 1-2r
letting (c^2, c) be the tangent point with the parabola, we can get an annoying quartic in y and c... at which point i gave up - i think there's no closed form
shell history is a form of configuration and should therefore be stored in the nixos config. in this essay i will
newton and leibniz never married?
shame, they'd be a good couple
Replying to @LongFormMath
Interesting. So, both Newton and Leibniz never married. The Calculus bachelors.














