yes
constraint = bottleneck = limiting factor
For bottlenecks, it can help to consider just pouring in a huge amount of water (or trying to produce a huge amount of products from a factory). If you pour way more water in the top than will flow through anytime soon, then you can figure out which part is limiting the rate the water flows through.
Ok, but I answered kinda to that question.
Conflict Resolution:
z or āthe goalā: know why TOC focusing steps are called āfocusing steps.ā
x: I thought because TOC is about working on the 1% of key issues and that focusing steps is about making improvements, I thought we were focusing on important issues
y: I thought āfocusing stepsā means weāre focusing on the right thing. Like, weāre focusing on key issues.
w: I thought āfocusing stepsā was just about making improvements, so weāre focusing on making improvements
u: I thought that āfocusing stepsā wasnāt related to the important issues cuz it wasnāt brought up. If itās not brought up then itās a reach to think that. Why? I donāt know. Iām not used to making long connections like that
v: I thought that āfocusing stepsā was talking about the actual steps and nothing else. I didnāt want to jump ahead and bring up the 1 percent of key issues. Why? Cuz itās hard to know if Iām hard with stuff like that.
ok for limiting factor, Iām thinking itās equal to limiting part of the system. Iām gonna look again at a past post about factors in a system to be more familiar with them.
Ok, in the Marris Consulting example the spouts are parts of the system, they let water through. The system is somethingā¦ I forgot. I want to say a part of the system is synonymous to a factor in a system. I think I need more practice with these words and expressing them.
Things to practice:
Below is what I wrote in a hurry so sorry for mistakes:
First sentence of your quote talks about how to think about bottleknecks to understand them. It talks about what example to think of that will help. The part in parantheses is another example to think of. Theyāre very similar. Youāre moving resources to a goal at the end.
The first clause of the second sentence talks about something to look out for. Itās also what to think of when considering pouring a huge amount of water. Thereās also measurements involved I think. At least numbers, cuz how would you know that thereās more water from the top coming in than coming out of the bottom. Something important tho I think is the part of the first clause that talks about water flowing through. Like, you initially pour a lot of water and thereās way more there than will flow through the system. That will help you find the bottkneck or think about finding the bottlekneck I think.
The second clause of the last sentence looks like youāre looking at parts of the system. One of those parts has got to be the limiting factor. The clause also talks about you looking at the rate of the water flowing through. I think if you know what the rate the water flows through is and what parts of a system is and that a part is limiting that rate then you can find the bottlekneck.
Edit: in the conflict resolution i made, on letter v the last sentence, I meant to say: itās hard to know if im right. I was thinking too much about difficulty and wrote the sentence wrong. Mb
My following reply is me writing it with low energy, but I will follow up with what I think I could work on after writing a section:
Optimizing seems like it means make the constraint better or make things better for it. I donāt see that happen that much but I notice it when I play Marvel Rivals. It happened yesterday where I was messing up the enemy team as a dps hero and then the enemy diver changed up his strat kind of and it started working out for his team. I wonder what he optimize to win them the game or if I even have to think about that to win.
Stay focused sounds intersting. I bet itās talking about staying focused on the key issues donāt focus on working on stuff that has excess capacity. The same sentence about staying focused also says donāt optimize other parts that donāt need it i think. That right there is improving stuff that already is probably enough. Itās like you already found your constraint why are you focusing away from it?
That seems like taking the whole system into account. Like, youāre looking at the bigger picture i think. If a certain part of the system makes stuff at a certain rate when will the constraint receive that? when can the constraint start working? It all makes me think of the Marris Consulting example and being advised to not look at stuff individually.
Also, I see the first clause say if you need futher improvment. That means that you can improve your system and maybe not get all the desired results that you wanted? I wonder if itās bad that you need further improvement after you already tried to improve stuff.
Itās hard to visualize this. I want to relate this to the marris consulting example cuz I like that example. How would other parts make it hard for the constraint in that example? I was thinking that it would have to interfere with the middle spout passing water. Idk
Thatās interesting. Even tho we found the constraint that doesnāt mean itās all on it. Like, a part of the system can give the constraint a lot of work to do. If the constraint works at a certain rate and has a lot to do then it has a big burden I think. I think another way is to not give the constraint enough to do maybe?? I donāt thatās right. Maybe the constraint is only working a few hours a day but can work at other hours too.
work on using references more intuitively like keep track of a reference when I use it. If i use more than once just use the actual word instead.
work on making sure I write verbs for every sentence like on the second to last I forgot to write āthinkā
You say improve further and need further improvement in above quoted paragraph and the one before. Whatās the first way to optimize the constraint then? In the second paragraph of the Focusing Steps section it says to then optimize the constraint. i probably have to watch the video to get more info. If I remember correctly, you wanna make stuff for the constraint easier first before increasing its capacity.
In the Marris Consulting example increasing the capacity of the constraint would be to increase the size of the middle faucet. Maybe thereās other ways.
I wonder why itās more efficient to make other changes first. When I play Marvel Rivals, I focus on increasing the capacity to find my target or understand their strafing pattern first. I think I always focus on increasing the capacity first. Maybe itāll be easier for me to make things more efficient for the constraint. I gotta find the constraint reliably first tho.
I wonder what are the other changes you want to do first. Also, I wonder why making things for the constraint is more efficient. āEfficientā has to do with saving time or energy I think.
I think adding resources to the constraint means to have stuff go through the system? Like, just use the system and check on the constraint. That or it means increasing the capacity of the constraint.
You can repeat these steps cuz there will always be a constraint and part of the steps is to find the constraint first.
Is there any literature or discussion tht says this? Ot says something similar?
I dont think i know wat a constraint is, like i think im using the word just to use it in a sentence and move on. Why not think of examples of constraints and start optimizing them? Thtll let u know what optimizing a constraint means.
Seems like i have some idea about what optimizing a constraint means. Why not try identifying the constraint then name some examples of optimizing them?
What strat did he change? How was i messing up the enemy team? Tht sounds like a system with good enough parts.
I seem to not understand the system the enemy and their team used. I think finding tht out can let me lay out all the parts of the system and find the constraint.
say the constraint is AI tokens. then itād be efficient to carefully spend a lot of time figuring out the best prompts to give the AI. your time has excess capacity.
if AI tokens are cheap and your time is the constraint, then instead you should give the AI prompts a lot more casually, experimentally and repetitively (try multiple similar prompts) and let it do more work instead of you.
if the constraint is a big oven that can only 3 8-hour batches per day, then you could do quality control before the oven so fewer broken parts go through the oven, so the oven is used more efficiently.
the idea is the constraint is hard/expensive to improve/increase or else it wouldnāt be the constraint (you would have already improved it). this doesnāt apply in very early stages of things before the system is stabilized and the constraint stops changing much.
ātarget the enemy carryā is a common strategy which can turn games around.
I just looked up AI tokens via gemini. I havenāt heard of those before. They seem to be information that AI uses to predict what a text is saying(??) It seems to be what the AI uses to talk to others.
I think i donāt know what the word āpromptsā means, but Iām guessing that itās to have AI understand more. Oh, wait i kinda looked up āpromptsā and Iām thinking the prompts are to have the AI do something for you. Something like, āGemini can you please make an essay about Karl Popperās epistemology?ā
I wanna try showing my understanding by predicting what you could say next. First tho, Im gonna analyze the first two AI token examples to help me:
In your previous two examples, what Iām seeing is that you found your constraint and youāre using something that has excess capacity to do something(?). Iām not understanding what that something is. Well, the goal of the first two examples is maybe having the AI help you with a task or do a task for you. I think it helps to know that a system has parts or factors.
In the first example, the systemās AI tokens may not understand a whole lot from an average prompt. Is using your time to make the best prompts a part of the system? I think yeah, if you didnāt use any of your time then you wouldnāt be able to make any prompts. Thatās with exception of maybe making an automated system to do it for you.
In the second example, u may not have a lot of time to get a good response from the AI without trying a bunch of prompts. Since the AI can pick up a prompt and respond fast, u can use it efficiently to get wat u want.
Now im thinking tht time is a raw resource and ure turning it into stuff for the goal.
My prediction:
Idk how to think about this actually. Every time I think of the constraint, I think of something that works slowly, but that doesnāt necessarily seem true. Like, Iām trying to think of what other parts of the system can take the load for the oven. But then Iām thinking how will they even do that? I know thereās time, like maybe u can make a good enough batch that u only need one 8 hour batch instead of three.
I read the rest of the quoted paragraph and I was kind of on the right track. I guess I shouldāve given myself more context. Idk
Ok, I had a feeling tht was kind of what u were talking about. Like, Iām thinking when I try to improve my aim, I sometimes work on stuff that has very low accuracy like 1%-20%. I often think if I even have a functional system there. I think, how does this stuff relate to TOC? Like, can I apply focusing steps to a barely functional system? I think u can
Kind of. Hereās how Iād explain it:
LLMs need an āalphabetā to take in information. English isnāt very good because it has so few symbols, which are inefficient to run an LLM on. Instead, we could create an alphabet with like 200,000 characters which is much more efficient. Each one of those characters is a ātokenā. Practically, this (very roughly) equates to 4/3 tokens per word. Some words are one token, other words are made up of multiple tokens.
LLMs have something called a context window which is the most amount of information they can āseeā at once. You canāt fit more data in, but you can summarize data to ācompressā it. This context window is measured in tokens ā the largest context windows today are about 1M tokens (so about 750k words). For comparison, all 3 LOTR books together are about 470k words.
Different LLM models can use different token alphabets, but often related models (in the same family) use the same token alphabet. If you want to see what it looks like, check out https://platform.openai.com/tokenizer (paste in any text)
Yes, prompt(s) are what you send to LLMs. The prompt probably refers to the first message you send to an LLM most of the time.
Technically, each time you send a message to an LLM you are sending the entire chat history with your most recent message at the end. So in a sense you can think of the whole chat history as āthe promptā that the AI completes.
I see alphabet is in single quotes so Iām thinking uāre using that word as a metaphor? Or as a lack of better words.
We use alphabets to build words that we can talk/write with. AI maybe does the same with the tokens.
Ok, mb I didnāt read the rest of the quote above after the word alphabet. To take information in sounds interesting. When i give the AI a prompt Iām thinking it takes information in via the tokens. Like, maybe when I tell it to make up a short paragraph of a short story, it uses AI tokens to take information from my prompt? Like, maybe because I said paragraph it can do something related to a paragraph? Depends on the tokens. Iām not sure.
I think youāre talking about the alphabet? Those symbols? Imma look it up
I saw maybe u mean stuff like, ā#$%^.ā There doesnāt seem to be a lot of those symbols. I wonder how many symbols an LLM needs and why. I also see that u actually say that itās inefficient to run an LLM on English. I bet it takes so long to run it on English.
I bet the LLM can access those 200,000 characters quickly cuz thatās a lot of characters. I wonder why itās more efficient.
So maybe thereās tokens with parts of words. Maybe it could be āantiā and āthesisā from the word antithesis.
Maybe the word(if weāre talking about English words) paragraph is made the tokens, āparaā and āgraphā. Maybe the tokens are unrelated to the actual words? Like, maybe the āmanyā token and āsentencesā token can express the word paragraph? Idk
I wonder if information can be measured. Like is it quantitative? If weāre talking about bits from a computer then maybe yeah?
I looked up the question via gemini, āwhatās the most information in can a context window have?ā and I got this:
It seems information is measured in tokens.
I wonder if u can be creative to compress the data.
Mb maybe i should read everything first quickly then do a careful reading?
Seems like u can convert tokens to words. Theyāre both information. Itās like converting miles to kilometers maybe?
more than half a million tokens i think.
ty ill take a look. Maybe it all this will help with the AI token constraint examples(unburden the constraint).
I tried a word and look at that. It takes three tokens not two:
I was wondering how the AI tracks the convo. Thatās if it takes the whole convo history as a prompt. Im wondering if u keep messaging it and add to the prompt, does the AI change its answer? Like, would it respond differently to something u said before? Like, it changed its āopinionā along the way.
Kind of. I put it in quotes because it is an alphabet in a sense, but itās unlike human alphabets. Itās not strictly a metaphor. Iām trying to indicate that it is a similar concept but not exactly the same as what people usually think of as an āalphabetā. Particularly, tokens are the atomic units that LLMs can āreadā. Just like english character symbols + punctuation are the atomic units that we use to construct words, sentences, etc.
The conversion from text-based data to token-based data is deterministic and works forward and backward, so you can think of it like a way of encoding normal human-readable data as LLM readable data.
Yes, it converts the prompt from text-based to token-based. LLMs at the mathematical level only understand tokens.
If LLMs only understood english symbols, then we could create a mapping like this: a = 1, b = 2, ā¦, z = 26, A = 27, ā¦, Z = 52, [space] = 53, . = 54, , = 55, ? = 56, etc. Then, any word could be encoded as a list like "any" = [1, 14, 25]. We would feed that list into the LLM for processing. Since LLMs process things one character (token) at a time, itās not efficient to have so few characters. But if we could pick an alphabet with hundreds of thousands of characters (tokens), then we could have something like "any" = [33814]. So itās like a single ācharacterā for an entire word.
I mean any symbols. a is a symbol, A is another different symbol. ? is also a symbol (though not technically part of the english alphabet, it is an english writing symbol ā another reason that I put āalphabetā in quotes).
We tend to think of these as different kinds of symbols (which is fine for human reading/writing/etc), but with LLMs we need to think a bit more generally and abstractly.
Yes ā though as you saw later, where and how words are broken up isnāt always intuitive. Thatās because the tokenization method is itself something learned via machine learning. Itās based on frequency of appearance and other things.
Sure, though even asking it the same question later in the chat isnāt the same thing. Like I could ask āX?ā and it says yes, then I point out some things and ask āX?ā again and it says no. The second time Iām not just asking X, Iām sending it the whole chat log including reasoning about why X might be no, and then asking X.
What I think Elliot means here is that you might be constrained by how much you can afford (longer prompts ā higher cost), or maybe also things like how much fit in the input prompt.
LLM usage is billed per million tokens in and per million tokens out. GPT-5.4 is something like $1 / Mtok in and $14 / Mtok out. If you were using it for coding, you could send the whole codebase + some instructions as input, and get the LLM to produce a particular file with changes as output. This is about the most expensive way to do it. Instead, you could send a few specific relevant files as input, and have the LLM output just the changes rather than the whole file. This would consume fewer input tokens and require fewer output tokens, too, reducing overall cost.
Assuming you were implementing this LLM-coding system by hand, the first method is simpler and takes less time to implement. The second method is more complex and takes more time to implement, but has lower LLM costs. Which approach makes sense? It depends on how much time and money you have (ie, where the constraint is).
Oh I think I kind of see what youāre saying. I use question marks and periods and letters to make words and sentences.
I wanna look up atomic to get more of what youāre saying. I found oxford languages define atomic like this:
Does that mean that english character symbols and punctuation are irreducible? Itd be nice to know what irreducible means, but in a way I donāt see why I would need to break down a period or english letter to make a sentence or paragraph. Like, I can access those symbols and punctuation to make up any word, sentence, or paragraph.
So if we look at LLMās making sentences(particularly Tokenizer OpenAI):
So the atomic units I as human would use to make the sentence in the photo above are things like ākā, ātā āeā, ā.ā OpenAI would use atomic units such as āIā(i), ā likeā(space before like), and ā.ā It would use those units to read or form words, sentences, etc.
This is what I think Iām missing from trying to understand all this:
A note on terminology: I use āatomic componentsā and āatomsā to mean the same thing as āatomic unitsā. They all mean the same thing in this case when speaking abstractly. Iāll avoid using them ambiguously.
Yes, characters are irreducible if we are talking about spelling, punctuation, etc. You canāt use half an a to spell something. You also canāt decompose w into uu or m into nn etc.
Aside: we can change to a different abstraction / frame of reference to reduce characters, but then weāre not talking about english and spelling anymore. For example, looking at characters as glyphs (as in a specific font), we can see they are made up of straight lines, curvy bits, wide bits, thin bits, serifs, etc. Or, if we consider letters as patterns on a seven segment display, then itās obvious that we have 7 parts that are either on or off.
Edit: oops, forgot a 7 segment display couldnāt show all characters ā it can show all digits. There are displays with more segments (9, 14, 16 according to wiki)
Aside: DNA is another example: the DNA itself is made up of irreducible base pairs (A, T, G, C), but as molecules those base pairs are composed of chemically bonded elements (carbon, oxygen, hydrogen, nitrogen, phosphorus).
Yes.
Pedantic aside: Technically āOpenAIā isnāt the right noun here, but I know what you mean. OpenAIās models use those atomic units. (A model is the specific collection of neural nets and related structures (like embeddings) and how theyāre all connected that makes the complete LLM.)
Yes but the question isnāt very specific. Almost every system has atomic units/components.
So usually youād ask like āWhat are the [atomic] components of X?ā and the exact answer depends on context. eg programming languages have primitive types (integer numbers, floating point numbers, strings, etc) which are a similar idea. Everything[1] we build is built up from those. (Though we usually have access to lower level stuff too like bitwise operations, so whether primitives are atomic or not is moot. For computation more generally, one set of atomic components are bits and transistors.)
Depends what you mean by ālike humans doā ā for most contexts iād say ānoā. Putting that aside, I think itās self-evident that LLMs construct words and sentences.
Iām not quite sure how to help you here with grokking them abstractly. Maybe think about examples and answer those questions for the examples. So consider things made of other things. Like lego ā what are the atoms of lego and what do they do? What are the atoms of numbers? (And what about modern arabic numbers, roman numerals, numbers in different bases?) What about mathematical notation like algebra? Mathematical constructions like functions? If you were building a traffic simulation, what would the irreducible elements be? What about music? Do pictures have atomic components? What about in specific contexts? (a digital image, an oil painting, a drawing, a mosaic, etc) What about prepared meals?
If you get stuck on any of them, try other ones first and come back to the oneās youāre stuck on. There arenāt necessarily clear exact answers to some of those questions, but I think there are reasonable answers to all of them (and maybe more than one set of reasonable answers, too).
In the right context, sure. But youād confuse people if you just changed on a whim. Youād need a shared theory of how to break those things down with whomever youāre communicating.
Well not exactlyā¦ All data structures at least. ā©ļø
