I really enjoy immersive thinking in science or math worlds (described in more detail here). I’ve been reflecting recently on how much I miss this kind of thinking - I’m doing a lot more subconscious-style non-immersive thinking recently, and don’t really ‘have’ to travel to other thought worlds. I just want to. So, sketched some notes below to remind myself what the typical steps are for ‘getting into the right state’ to have thoughts, and wrote notes from a recent session below. I’ll often while in a science world refer to a plasmid or a bacteria or <insert your favorite object here> as ‘me’, or write other things that don’t make a lot of sense, because I’m just in the mindstate of ‘being a plasmid and writing down what that would feel like’, so to the extent these notes are correspondingly incoherent - well, if you closed your eyes and tried to imagine yourself as a plasmid I’m curious what you would write down.

Also remembering I wrote a comic about this way back when.

Notes on getting into a science world:

are you in a state of distress (anxiety or depression)

- if outside range addressable through thought (physiological), give yourself what you need physiologically (prob several hours min)

- water

- lie down

- grounding exercise

- if thoughts, write down, see internal, meditation, talk to others - work through

are you curious about something

- if not, ask yourself gently, what might I be curious about

- hold a state of open awareness, looking around - usually there is something there glimmering

sit in a room with enough space to move around in (1m x 1m) and NO DISTRACTIONS, no possibility of interruption

- you need sound isolation

- put in headphones with music with a beat that moves forward

- close your eyes and believe, ask to enter the world of the problem

when you are in the world

- accept you may only have an hour

- sugar helps - physiological checkin on whether need to eat to have enough energy to complete, often if I don’t will take a few hours to focus enough to do

- the more you can dance with the concepts, the more the world might unfold

if the above is hard, try doing in nature, or going on a retreat to your favorite place just focused on this

if nothing comes to mind, study enough that something will come to mind. but practice doing this a bit with whatever comes to mind.

'what's important to think about in your life right now' is not the same as what you might want to think about, accept that in this space

added: accept maybe a ~2 hour lag time, to come back to ‘remembering what your priorities are’ afterward, that’s about the (proper) tail of ‘but the concepts are the most important feeling’ at minimum, important to remember to plan around work

Example notes from a ~30 min world to remind myself what it feels like, things I liked from it in bold (not edited and apologies to any readers for the swearing):

- how do concepts in math map to geometric representations that we explore visuaslly

- I can see my brain trying ot generate them

- how math is sucha vast and infinite world

- the strangeness of the concepts there, unlike anything I"ve ever seen or felt before

- to anthropamporphize them?

- if humans had more senses, would we interact with math in more ways?

- looking at a set (points in a circle)

- why is a set points in a circle? that implies distance between the points, orientation in relation to each other

- in partciular, when I look at a bunch of points in a circle visually, the points are literally unique or different, but in a set they should all be indistiguishable (but they are distiguisnable by position in the visual I'm looking at)

- waht does indistiguishable mean then? I'm presented with a point, and I dion't know 'which one' it is or not? or the set simply has a number associated with it, not pionts? but you have to keep track ofthem somehow for mapping - hmmmm, confusing

- does a set have a notion of order in it? or no - imposed on it? how do you map between sets if points are indisituguishable? oh, so the must be distiguishable somehow, so a set is like an ordered list? each poitn has some identifier?

- what's up with exponentials, why do they go up so fast? or the inverse square law - why is it so striking / counter intuitive when things accelerate as tey get closer to. you? how would we feel if that was our life?

- why do I have like zero experiences of bieng so densely surrounded as I would be in a cell?

- what does anentituy look like when it is receiving or giving information? how does that feel? how to think about that? is it changing the entity, internally?

- looking at bacteria floating around me trying to talk to each other but it feels kind of forced - why?

- they don't want ot be there, that'snot their purpose - what the hell are they doing when they are talkign to each tother

- oh, they are in a biofilm now - that's a bit better, why are they in a biofilm?

- they want to...share roesources, worko together

- they want something they can't get by themselves

- how does the biofilm work, what does it loook like?

- there are channels..I don't really know, how stuff goes in and out is really important, if it's too big then ethey can't get what they need - yeah you kind of **have to re-solve the diffusion problem ina biofilm**, that's a way to think about vascuature like it's res-olving the diffusion problem from when things were fre floating

- why are biofilms a certain size - **are there scaling laws, could they be infinitely big**

- does it matter where you are in it, like is it good to be closer to the outside - I'm curious , are there any advantages to being on the **very most inside of the biofilm**, I feel like that would be kind of a dependent place ot be, you would really be screwed if the other bacteria didn't help you out = what kind of abcteria would end up there? really trusting ones? Idk - that's not quite it - you're saying, maybe you want to be **doing stuff for the biofilm** so the bacteria on the outside ned you too

- are nutrieints the main thing - what about genetics, what are your genetics *fuck this is the part I never understand how does evolution think about this* - like it's so confusing to me that they say evolution is about making copies of yourself, but if you do that without changing who you are you won't evolve to get better and so you want to change. who you are but be similar (?) or preserve some property (?) or just you want to be part of a lineage that produced the lineage that is there today but it's not about siilarity to hte previousgeneration? so evolution is **all just about being part of a lineage** < why the fuck do I not understand this yet this is literally the most confusing thing I have ever thoughta bout

- okay, what do the bacteria want

- there are a certain number of bacteria in the biofilm

- they are happy or not

- they are giving each toher stuff and interacting with each other

- also exchanging DNA which fundamentally changes who they are *??????????* idk how to thikn about this at all what the hell is going on there

- why is the DNA so confusing - because it changes who you are, why would i want to do that? to keep going, but what if I liked who I am? so all the bacteria are kind iof like - they're not even entities, they're just part of one big process? bu tthen why have many of them, why not just one thing - I never understand this, replication?

- god, it's so confusing

- if I were surrounded by bacteria, as I was by stars, flying thorugh the universe, what woudl I feel?

- I would feel more seen and understood - they're talkign to each other, they're trying to do something

- they kow the others exist - do they all?

- why the hell are multi-agent systems so prevalent

- what bothers me about this?

- what do they want?

- it's the connection between them that matters - a web, slowly growing more aware of itself

- how do you visualize multi-agent systems? what's the right perspective? as a bacteria trying to figure out hwere it is? or as the information itslef - let's say you're a plasmid, what would your life feel like? it all depends on how you were made, how far you go

- you're trying to get to everyone

- time constraints around copying and distributing the message - are the thhose the fundamental constraits on communication as a group scales?

- all I see is how far I go, not what happens outside

- I can only go as far as there are things to carry me

- I might meet and co-travel with other plasmids

- it's kind of a boring life, I don't really change?

- do I change though? do bacteria edit plasmids as they move through circulation?

- communication systems can change the dynamics

- previously we just had passive diffusion

- **the move from passive diffusion to direct communication as one of the most important jumps in biology?** < huh think more about this

- direct communication = you can specify a rceipient *you didn't used to be able to do this* or could you?

- what does the informaiton want?

- the information wants to figure something out

- to express the world in a compressed way

- what would help me see this wiorld better? help me, please

- just looking at a 2d plane of abacteria

- it's not their size it's - ***how the communication works, how fast it can happen, if I knew more about that, it might be helpful?***

- ^ coming back to this as a motivation for information gathering

- how does the 'ability' to compute or produce emergent properties change as function of communication, what is this communication doing in unicellular populations and multicellular systems

- ^ okay, back to this as a motivation, feeling curious

- how do we know two things are communicating? what does that mean vs just 'sensing the environment'?

- how much does the communication system vary across the whole population? *if that stays the same, can it tell you something about the whole population dynamics to just know about the communication system? do you need to know something else about the technology, etc?*

- what would a good toy problem here look like - like, what's the most complex thing a group of bacteria could do (but they're not really trying to do it) **I wonder if you could try to evolve a group of bacteria to do something that only a group could do (?) - like, a process that would involve the whole group heterogenously coordinating within itself to achieve the behavior***

- renewed motivation to get numbers on / color on / understand communication in unicellular populations and between cells in a multicellular context

- who understands this best in the world, who would *just know* this? what framework would they use?

- bits exchanged?

- capability...somehow?

- the level or type of complex, emergent behavior?

- look for papers that have tried to evolve groups of bacteria to do (complex?) tasks that require heterogenous coordination within the group (what types of bacteria do well here, what types of bacteria would do best here, how do communication systems constrain this - how, actually, do the capabilities of the individual bacteria constrain this?)

- how many groups can do something like this?

- what is everything we know about biofilms? what are other contexts where groups of bacteria work heterogenously together?

combine single cell perspective (bionumbers) with inferring properties of the group from intuitions from there (are there other ways to look at this - the genome content across a population? what would one analyze there?)

what if they were all just one thing, what would that look or feel like? I'd primarily notice the differences, all the ways I didn't fit with myself

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Random other notes, generally, on the state of immersive thinking

• curious if it has any relation to ‘see-in’ / ‘feel-in’

• curious what’s the difference between a session with dancing vs one without (the former is almost always better? but might require more ‘belief’ in the world?) might require ‘committing’ to a world for a longer session + a more tangible link between some physical principle or movement and moving through the world

• I still have no idea why a certain kind of music is so important to this, why a few songs so consistently matter so much to exploring this state

• is feeling ‘free’ important for the most immersive experience of this state (corollary - is it ever possible to experience the most immersive version of this state in a cafe vs in a field w/ no one around?)

  • I’m curious how to explore / expand this feeling of being ‘free’ - or is that just, like, it will just be the number of people within sensory distance, that is an absolute limit on how immersed you can get

___

I’m just gonna keep updating this with my daily thinking notes b/c I feel like it, whenever the state triggers (and I feel like updating this)

2024-11-16 - overall theme, was in a cell / got to the point of genuine curiosity about how quickly or efficiently one could build a mitochondria which felt like a really fun thought experiment prompt, and then thought about groups for a while, mostly trying to load back to the point where I could see them as simple objects. slight immersion, not super deep, but state present. 501 / 101, woohoo!

I'm in a cell

what is the point/purpose?

where is the mitochondrion?

someting is turning - what is it?

ah, I see in front of me some kind of pump - what is that, ATPase?

How fast is it turning?

- look up a picture of atpase to check the visual

- GPT claimes 130 revs/sec

- ^ is this fast? compared to what? how fast could ATPase go at the max?

I feel a desire to know how the mitochondrion works

why do I care about how fast ATP turns? just for the isual?

What timescales is ATPase rotation relevant to?

I see - it could be relevant to ion flow across the channel, that + the total amount of ATPase would then constrain (?) the rate of ATP production - so, that's interseting, what is the bottleneck for speed of ATP prorduction? could I make a much faster ATPase - like 10-100x?

**how fast can a mitochondrion go? can I build a faster mitochondrion go? how does efficiency work - how efficient are mitochondria? - how much of our energy do mitochondria make?**

so, I could do this, thank you

'see the thing actually happening vs infer'

connection to reality (re models)

- alphafold to see protein structures

interim notes

having a 'place to stand' and enough that you can load information - 'don't know what you don't know' - giving tools to play instead of a pre-loaded structure

to merge - to see from their eyes

nature is there, and she wants to be seen

an emotion of 'back of the head opening' - music, nature 'she wants to be seen'

feeling of privacy / safety - can move around freely, no one will hurt or interfere (might be hard in cafe)

a set of concepts that are close at hand, there must be enough there to enter the world

- how to slip back into that world for math

- how to load back to see the objects - ways to remember

- Anki could help? store interim states?

https://www.youtube.com/watch?v=yc47a7OHETA

thinking about groups

group - the world

waht was the object I glimpsed?

waht thought experiment helped see it?

I feel disconnected from the world of the group

waht do groups want to say?

well, them being closed is an important property - tha tmust cause all osrts of interseting things to happen

you can always go back, and you can stay where you are

what do groups *do* - what is structure, in a group?

which moves are connected to / map to which other moves?

what are some fun groups to play with - ah, I'm missing that

is the identity element a group?

I see - I could hold some group objects steady in my mind, but what would be beautiful about that?

it's the structure behind the structure - the structure implied by the moves, and the symmetry

If I were a group, what would I feel?

what is the ultimate form of a group - I see a red and a blue dot exchanging places, but what is really the structure behind that? the simplest version of it?

what are all the different ways you could represent a group? hmm, I remember something about permutations?

what is not a group, that I think might be?

I see - to map a group, I map between states, the movements are the maps between states

what if I just saw groups as Cayley diagrams?

I want to cry, it's so pretty, I can see the edges of it - or, feel its existence, without seeing it

In a group, does every arrow in a Cayley diagram have a return arrow?

if a group were a space, and each move was an orthogonal axis, you would need to be able to move anywhere in space (?)

I see - simplest nontrivail group two states linked you can go back and forth

do moves map from a particular state? or can you always do a move no matter what state you are in? or is that not the right question

I see, in all Cayley diagrams each node has to be mapped by/to every generator? is that right? what about every action? what distinguishes actions - do actions ever map from particular states?

if actions map from any state then...groups are state invariant? or is that true? in what ways do groups not have symmetry?

**Cayley diagrams and multiplication tables as core diagrams in group theory**

^ can I think of new types of Cayley diagrams to generate, that help see a particular kind of insight?

what if you eliminated the nodes in the group graph and just had the arrows?

what if you can't tell, from the arrows, where you start out

ah - you could tell where you start out if you're manipulating a many-sided shape and you color the sides different colors, but without that, just from flipping it in a particular way, you wouldn't tell the difference between the sides from the structure

to really love the objects, themselves

In a Cayley diagram, an arrow does not have to be its own inverse

but every move can be reversed by a member of the group

I see a pendulum swinging back and forth, as I'm thinking about the group with a move, its inverse and the identity

if I were that group, what would I see

ah - the object isn't moving, it's above movement

ug I feel an overwhelming feeling of wanting to expand into and become the universe

if these structures are so beautiful, and I can conceptualize them, what does that mean about my relationship to the universe in this moment?

I see, this feels closer and more when I think about the group with an acction, its inverse (what is the difference between the group where there is an action and it is its own inverse and the group where there are two actions, each eachothers inverse)

I have no way of telling the difference between the two right now, they feel the same to me?

I want to make friends with more groups, I want to feel (or see?) the beauty in them

I want to play with them, watch them move

what would they want to do if they were playing together?

how does mathematics want to work, in my mind?

it feels like a bunch of objects, so beautifully foreign - what do they want to do? how strange!

and I still don't understand how proofs work - I haven't the faintest idea, how wonderful, what a wonderful thing that one day I will know

20

what does a group view of an object look like?

OH MY GOD

what does a group view of an object look like

if I look at an object abstracting away the groups there what do I see?

a triangle pillow different from a square pillow, for example - well, first I would see all the ways the object could turn and look the same and then what would I do - I would move into group land and create a representation of the object symmetries that then was its own object?

so ‘very symmetric’ objects would immediately look simpler

but how is a group different from symmetry in this case?

I see - I would almost want to see the cycle view, and then maybe even that collapsed down?

for groups - every node looks the same, so you could permute the nodes for all n nodes and - well the view from each node would look the same but the relationship between the nodes would not

so I could just see what it looked like from one node in the group, but would that really tell me everything I needed to know?

I see a world with permutations on one side and the group on the other - by Cayley’s theorem every group of order n maps to a subgroup of S_n, so a set of permutations - do permutations feel natural? is it possible to break the problem of visualizing or seeing a group down recursively, into smaller and smaller permutations that I understand?

how should I see a group?

oh - underlies everything

what do groups for a circle look like? what’s up with Lie stuff

a group is a weirdly closed space - every node looks the same, reminds me a bit of the basketball scene in a wrinkle through time (houses on the street all look the same) - and no matter where you go you stay in the group

would it be incredibly… to be in a group universe?

would look the same everywhere, and everywhere you go you are always in the same place

that’s what it means to ‘see things from a group view’ in one way - what about colorings though, but the structure is the same

what things are not groups? the number line feels not this way but it actually is this way becuase it’s infinitem you can never ‘tell where you are’?

is that the deal with being in a group - when you’re in a given node, you can never ‘tell where you are’, there is in fact no concept of ‘being in a particular place’ - unless you color the object the group is acting on which would break symmetry but you could do that I guess?

so groups as things like the basketball scene in ‘a wrinkle in time’ - everywhere you go looks exactly the same, there’s really no concept of being in a different place

but you can move between places and there’s some structure there? is there any higher-order group structure that isn’t directly inferrable from the view from one node (I think there is, like which actions combine to form which other actions, but is there actually?)

why is permuting things interesting, ever?

2025-01-06

feel too tired to get into state - drained, lights super bright

what am I curious about?

what does a group feel like? as the object?

I don’t think I have the computational power for it today

where does my mind go when I think of a group?

there’s a difference between being immersed and flickers of images - like I remember a cache of ‘a group is the dual of the states’ but it’s like looking at a flat picture, without ‘feeling’ it

what does feeling it entail? it means I have the object loaded enough that I can move it around and see what happens, and that I have some sense of a narrative generating ‘something next’, and some directions to walk in for the world to unfold

what does the world of groups look like? just…a bunch of different groups? or one group in particular? when you’re in one group, what hpapens? well, you might have a feeling-hint of all the different symmetries that are adjacent. like, it expands into the world (the portals it has to the world) are all the ways in which symmetries related to it show up in the world

but is this…true? how is this true for a simple group, like swapping two objects next to each other? how do I give a fuck about that, at all? like I literally could not care less - or could I? it just seems like - how does knowing that is a group help me literally at all. well, I guess - could I build other groups from it? there’s a sense of the infinite, in that two swaps gets you back to the original. if it wasn’t a group, what would be true about it? well, what are the group principles - binary operation, could violate one of 1) it operating multiple times gives you a member of the group 2) it has a reciprocal (identity implied by this?) 3) associativity - so, for the case of swapping two objects, it would be different (less round / closed?) if you could make a thing by swapping that was a new state - more like going infinitely in one direction or something, kind of off in the wilderness. what about reciprocal - like once you’d swapped, that was it you were done. you couldn’t always go back to where you started. so groups are kind of special, like a slippery fish, you can always get back to where you started. associativity - not really sure how to visualize this one here. well there are also only one element if it’s a swap where the swap operates on itself - how is that different from a swap where the other operation is something different? when will groups ever be fully loaded ughhh what problems are good to do with them. my brain keeps wanting to make them a world. in a group, you can always go back, you can stay, compressing a path starting from etiehr end leads to teh same result (what is a good way to talk about associativity)? yeah it feels like the right question isn’t so much what’s the smallest group as what’s the smallest element to be in to be in that world - maybe a node of a group, where any node looks the same? that feels like such a fundamental place to sit. I remember thinking about and not resolving - from one node, can you figure out where any other group is