John II, the king, set an objective for his admirals to find a route to India that bypassed the usual middlemen for the spice trade (the Mamluks & Venetians). 16 years later, Vasco da Gama did it. Nice example of “goals and plans can work”.
https://en.m.wikipedia.org/wiki/Matchlock there seems to be an unfortunate definitional overload where “handgun” in the early modern period refers to a gun held by a human as opposed to a cannon? but in the late 15th century all “handguns” were long guns, it seems.
this means verifying multiple things. the compiler, the parser, the debugger, etc. all relative to a formal specification of what they’re supposed to do.
do you write a different specification for each thing you’re checking? this introduces lots of wasted/duplicated/inconsistent work. maybe you should just have a single specification for the language.
this is what K is: a framework for writing language specifications.
symbolic execution—don’t plug in values, map out branches of how the program behaves with any possible input. good for testing and verification.
biology is multiscale and multimodal. genes! proteins! cells! tissues!
in particular we have dynamical spatial systems that govern developmental processes:
cell division & microtubules
neurite branching
mitochondrial fission & fusion
plant organogenesis in shoot & root growth
neural tube closure.
what happens (over time) is a function of what’s going on nearby in space;
macro geometry (the shapes of organs, bodies, etc) is a consequence of micro, local dynamics
declarative modeling:
one example of a bio dynamical system is differential equations defined by diffusion operators on the concentrations of chemical species (as functions of spatial position and time).
an abstract syntax tree (AST) is a way of representing the symbols of a mathematical expression (tree depth corresponds to order of operations, nested functions, that thing)
you could define a declarative modeling language as a space of ASTs that define models, a mapping between ASTs and dynamical systems (the mathematical objects that correspond to the symbolic objects) and transformations between ASTs.
for example one transformation is: you start with a chemical reaction; you reverse the arrow to get the reverse reaction; or, you change the rate constant to get a different reaction rate.
now, when do these manipulations commute? there is a quantum-inspired “operator algebra” for chemistry
each chemical species is a “state”; there are transition probabilities between them
mass action laws define relationships between the equilibrium concentrations of each species (as a function of the chemical reaction & the reaction constant)
“operators” for each species destroy or create particles of that species; what happens if you hit the system with an “operator”? add these up and you get the “chemical master equation” that defines the dynamical system and the enforced probability preservation (probabilities must sum to 1)...(again i don’t totally get it)
now we can also add parameters to these models. for instance a model governing cell division might depend on the size of the cell.
now we can start talking about cell division as a function of things like position, cell type, concentrations of signaling molecules, and so on, with invariants (like “1d growth”)
and we can do similar operator stuff based on probability distributions of what values parameters can take...
ok so what’s the point of all this?
normally in mathematical modeling of biological processes, you pick out a priori which variables to care about.
but alternatively, you could start with a finer model that throws in everything and the kitchen sink, and automatically discern which variables don’t really affect the result much no matter what values you plug in, and then “reduce” to a coarser model.
...but you could also do that statistically? i hate to be the “but how is this practical” guy but this literally is applied mathematics...
it’s pretty though. wish i had time to go through more carefully.
https://qntm.org/devphilo i love his short stories; his “developer philosophy” also seems sensible, though might be hard to make work in a real business with customer/deadline pressure?
if some governmental policy seems Not Fair, to people like you and me, we don’t actually have much of a (perceived) affordance to change it through collective civic action.
conventional political activism is more like a zero-sum negotiation between interest groups.
“it’s not fair” doesn’t move the needle by itself, even if everybody you tell can see it’s true.
organized political violence to achieve goals isn’t much of a thing these days either; the closest thing is disorganized violence (rioting, lone shooters)
the courts sort of are an avenue to push back against unfair policies, but civil courts are declining drastically in use.
links 2/4/25: https://roamresearch.com/#/app/srcpublic/page/02-04-2025
https://www.nature.com/immersive/d41586-025-00269-y/index.htmlmitochondria are thread-shaped not bean-shaped. I truly do not understand these critters.
things i learned while reading about Venice:
https://en.m.wikipedia.org/wiki/Benedetto_Pesaro brutal, successful admiral who held off the Turks for a bit
https://en.m.wikipedia.org/wiki/Vasco_da_Gama
John II, the king, set an objective for his admirals to find a route to India that bypassed the usual middlemen for the spice trade (the Mamluks & Venetians). 16 years later, Vasco da Gama did it. Nice example of “goals and plans can work”.
https://en.m.wikipedia.org/wiki/Matchlock there seems to be an unfortunate definitional overload where “handgun” in the early modern period refers to a gun held by a human as opposed to a cannon? but in the late 15th century all “handguns” were long guns, it seems.
https://www.thetimes.com/us/news-today/article/new-york-finally-claims-a-small-victory-in-forever-war-on-rats-m7x230sg8
https://drive.google.com/file/d/1iXda2NyGzKVWxkd02IlXj5Tq5cOM_gNd/view
a “verified” programming language would be cool!
this means verifying multiple things. the compiler, the parser, the debugger, etc. all relative to a formal specification of what they’re supposed to do.
do you write a different specification for each thing you’re checking? this introduces lots of wasted/duplicated/inconsistent work. maybe you should just have a single specification for the language.
this is what K is: a framework for writing language specifications.
symbolic execution—don’t plug in values, map out branches of how the program behaves with any possible input. good for testing and verification.
K does this. (I don’t understand details)
https://arxiv.org/pdf/1804.11044 very interesting and ambitious concept!
biology is multiscale and multimodal. genes! proteins! cells! tissues!
in particular we have dynamical spatial systems that govern developmental processes:
cell division & microtubules
neurite branching
mitochondrial fission & fusion
plant organogenesis in shoot & root growth
neural tube closure.
what happens (over time) is a function of what’s going on nearby in space;
macro geometry (the shapes of organs, bodies, etc) is a consequence of micro, local dynamics
declarative modeling:
one example of a bio dynamical system is differential equations defined by diffusion operators on the concentrations of chemical species (as functions of spatial position and time).
an abstract syntax tree (AST) is a way of representing the symbols of a mathematical expression (tree depth corresponds to order of operations, nested functions, that thing)
you could define a declarative modeling language as a space of ASTs that define models, a mapping between ASTs and dynamical systems (the mathematical objects that correspond to the symbolic objects) and transformations between ASTs.
for example one transformation is: you start with a chemical reaction; you reverse the arrow to get the reverse reaction; or, you change the rate constant to get a different reaction rate.
now, when do these manipulations commute? there is a quantum-inspired “operator algebra” for chemistry
each chemical species is a “state”; there are transition probabilities between them
mass action laws define relationships between the equilibrium concentrations of each species (as a function of the chemical reaction & the reaction constant)
“operators” for each species destroy or create particles of that species; what happens if you hit the system with an “operator”? add these up and you get the “chemical master equation” that defines the dynamical system and the enforced probability preservation (probabilities must sum to 1)...(again i don’t totally get it)
now we can also add parameters to these models. for instance a model governing cell division might depend on the size of the cell.
now we can start talking about cell division as a function of things like position, cell type, concentrations of signaling molecules, and so on, with invariants (like “1d growth”)
and we can do similar operator stuff based on probability distributions of what values parameters can take...
ok so what’s the point of all this?
normally in mathematical modeling of biological processes, you pick out a priori which variables to care about.
but alternatively, you could start with a finer model that throws in everything and the kitchen sink, and automatically discern which variables don’t really affect the result much no matter what values you plug in, and then “reduce” to a coarser model.
...but you could also do that statistically? i hate to be the “but how is this practical” guy but this literally is applied mathematics...
it’s pretty though. wish i had time to go through more carefully.
https://openai.com/index/introducing-deep-research/ I don’t seem to have access yet but this is intriguing
https://qntm.org/devphilo i love his short stories; his “developer philosophy” also seems sensible, though might be hard to make work in a real business with customer/deadline pressure?
https://alicemaz.substack.com/p/commentary-on-xunzis-enriching-the Alice Maz on Xunzi. insightful political philosophy.
https://benjaminrosshoffman.com/si-no-se-puede/ Ben Hoffman seems straightforwardly correct here.
if some governmental policy seems Not Fair, to people like you and me, we don’t actually have much of a (perceived) affordance to change it through collective civic action.
conventional political activism is more like a zero-sum negotiation between interest groups.
“it’s not fair” doesn’t move the needle by itself, even if everybody you tell can see it’s true.
organized political violence to achieve goals isn’t much of a thing these days either; the closest thing is disorganized violence (rioting, lone shooters)
the courts sort of are an avenue to push back against unfair policies, but civil courts are declining drastically in use.