[HN Gopher] O(n) vs. O(n^2) Startups
       ___________________________________________________________________
        
       O(n) vs. O(n^2) Startups
        
       Author : ocean_moist
       Score  : 66 points
       Date   : 2025-05-15 04:54 UTC (3 days ago)
        
 (HTM) web link (rohan.ga)
 (TXT) w3m dump (rohan.ga)
        
       | brudgers wrote:
       | _An O(n) startup grows_
       | 
       | If it grows at O(n) it is not a startup in the way "startup" is
       | used in Silicon Valley. It is just an ordinary new business.
       | 
       | It's worth noting that starting an ordinary new business is hard.
       | Probably as hard as starting a startup for anyone who has not
       | started a new business a few times before. And maybe harder
       | because most new businesses are undercapitalized and therefore
       | likely to suck up personal capital while startups get to use
       | other people's money.
        
         | ocean_moist wrote:
         | I use business, startup, and company interchangeably. Generally
         | I tried to use business for O(n), startup for O(n^2), but I
         | guess I wasn't strict with my usage...
         | 
         | Perhaps they are harder to start, but they are also vastly more
         | likely to succeed to their O(n^2), and this is not only due to
         | the increased barrier to entry.
         | 
         | That's what I mean when I say, founders are more likely to
         | succeed at O(n) companies.
        
           | brudgers wrote:
           | Most businesses are playing pinball...success this month/year
           | means you can play again next month/year.
           | 
           | Very few have successful exits where the owner walks away
           | with life changing money and no obligation.
        
             | kylecordes wrote:
             | Unfortunately, many businesses are arguably a bit worse
             | than that: success this year means you put even more at
             | risk next year.
             | 
             | (For example, you get successful enough that you need a bit
             | of office space. Well, your little business is not going to
             | persuade anyone with nice office space to lease to it
             | alone... Landlords will instead demand the owners
             | personally guarantee the lease, i.e. commit to paying it or
             | go bankrupt trying, even if the business shrinks and no
             | longer needs or can afford the space. So you thought,
             | great, we had a couple years of strong growth. Now you get
             | to commit personally to five years of a huge expense.
             | Congratulations.)
        
               | Aurornis wrote:
               | Where are you seeing commercial office space require 5
               | year personal guarantees from the founders? Terms like
               | that would have everyone laughing as they hung up the
               | phone around here.
        
               | brudgers wrote:
               | In the US, that sounds rather normal for normal triple-
               | net commercial space for a normal new business run by
               | people without established commercial relationships.
               | 
               | Typically, new businesses don't get very much credit on
               | favorable terms without established commercial
               | relationships.
               | 
               | Dealing with failing or failed businesses is just not
               | worth the hassle for most established businesses working
               | in the established business market segment.
               | 
               | Silicon Valley is probably different because the business
               | relationships are different. And of course month to month
               | and short lease real estate are an entirely different
               | market segment than triple-net.
        
               | SoftTalker wrote:
               | You need to look for hungrier landlords.
        
       | chubot wrote:
       | Related: _Black Swan Farming (2012)_
       | 
       | https://news.ycombinator.com/item?id=4497461
       | 
       | https://paulgraham.com/swan.html
       | 
       | It is interesting that YC started as being more Founder friendly
       | ... and I guess "Founder's Fund" did too
       | 
       | But there is still some divergence in interests ... i.e. if you
       | have to make a choice between a safer O(n) path and a riskier
       | O(n^2) path, then the investor prefers the riskier path
       | 
       | Or I'd be very interested in an argument that they don't
        
       | mperham wrote:
       | Don't forget about us O(1) solo entrepreneurs!
        
         | smahs wrote:
         | Still O(n).
        
         | wavemode wrote:
         | N is customers not employees
        
           | mitthrowaway2 wrote:
           | In the article it's apparently "time since launch".
           | 
           | Kind of like how an O(n^2) sorting algorithm sorts n^2
           | elements in time n. Right?
        
             | wavemode wrote:
             | No, it's the opposite. An O(n^2) algorithm sorts n items in
             | n^2 time. So O(n^2) is worse than O(n).
             | 
             | (should really be th rather than O but you get my point)
        
       | danjl wrote:
       | > O(n) companies can't afford to hire the absolute best talent.
       | 
       | O(n) companies tend to have more experienced founders and
       | engineers in my experience. This is partly why they have "nice
       | deadlines, clear SoW" and "understand their customers" enough to
       | have PMF. The strength of their talent, experience and job
       | networks often greatly outweighs the cash incentives, allowing
       | them to hire top candidates. They do not just hire "to fit a job
       | description" because, since money was tighter, they are super
       | conservative about hiring, have always done the job they are
       | hiring for themselves for a long time, and know exactly what they
       | need. It is the O(n^2) companies that hire for job descriptions
       | that fit the positions the VCs tell them they need. I think your
       | experiential datapoints may be too sparse.
        
         | jbmsf wrote:
         | And also, engineers who are sick of the stupidity that comes
         | from having too much VC money and not enough wisdom to use it.
        
         | Aurornis wrote:
         | In my experience the heavily VC funded companies have a lot of
         | very talented and experienced people, too.
         | 
         | But they have so much money and pressure to hire that they
         | start dipping deeper and deeper into their candidate pipeline.
         | They start lowering their standards to keep the employee count
         | growing. This results in a mix of talented people trying to get
         | work done and a lot of people who are good at interviewing and
         | stretching the truth about their experience.
         | 
         | Every time I've been at a company like this, they tell
         | themselves they'll hire fast and fire fast to compensate. Then
         | they never fire fast or at all, because nobody wants their
         | little empire to shrink.
        
         | ryandrake wrote:
         | The vast, vast majority of companies don't need "the absolute
         | best talent." Their product is a JSON interface to someone
         | else's service. You don't need John Carmack to write that.
         | Companies comically overestimate the level of talent they
         | actually need, and let positions stay open for months,
         | sometimes years, looking for that unicorn programmer they don't
         | actually need, and passing up hundreds of candidates who would
         | work out fine.
        
         | ocean_moist wrote:
         | Experience != talent. Perhaps a better way to phrase it is that
         | they hire the minimum needing to succeed in a well defined
         | role. Startups aren't afforded this comfort as the roles are
         | not well defined.
        
       | bee_rider wrote:
       | Huh.
       | 
       | Not working in the field, I assumed startups went like sigmoids
       | (everything is a sigmoid after all).
       | 
       | Exponential at first as word of mouth spreads, then linear as
       | your users start bumping into each other and word of mouth stops
       | working, and then you eventually start leveling off near carrying
       | capacity (you've hit your addressable market).
       | 
       | I thought the game was to try to get bought by some massive
       | company while you are in the linear phase (where you are big
       | enough to be treated seriously but your growth rate still looks
       | absurdly high).
        
         | withinboredom wrote:
         | This is actually a better model and one that more closely
         | reflects reality. You can see it on revenue as well, since even
         | if growth is exponential, churn is a percentage of your total
         | paying users. Thus, it produces a sigmoid curve unless you can
         | get churn to 0% (pro-tip: you can't).
         | 
         | But, these are the two basic levers for a SaaS: growth and
         | churn.
        
           | jvanderbot wrote:
           | The first thing I learned when I joined my first business was
           | covered in orientation with leadership: every product or
           | business unit is a sigmoid, and to maintain growth you must
           | add new products or business units without spending too much
           | to do so. Then the overall company profit can grow linearly
           | or whatever by being a sum of sigmoid functions that spawn
           | over time.
           | 
           | Good leadership knows when the flattening will happen and
           | pivots.
           | 
           | This is called "innovation". That really stuck with me as a
           | mental model.
        
           | thaumasiotes wrote:
           | > You can see it on revenue as well, since even if growth is
           | exponential, churn is a percentage of your total paying
           | users. Thus, it produces a sigmoid curve unless you can get
           | churn to 0% (pro-tip: you can't).
           | 
           | Exponential growth means that additional users are a
           | percentage of your total users.
           | 
           | It is trivial to see that adding a source of exponential
           | decay will give you another exponential function. All churn
           | (as you've defined it) does is lower the exponent. It will
           | never take you from exponential to sigmoid.
        
             | nis251413 wrote:
             | Sigmoid (or the logistic function specifically rather) _is_
             | exponential until you get close to the  "turning point" (or
             | rather, its growth bounded from below by an exponential).
             | It's as you approach that point that it becomes linear, and
             | after that its growth decays.
             | 
             | However you are sort of right that "churn" does not
             | necessarily have to do with it being sigmoid because it
             | will be anyway. It may be bring it earlier if the churn
             | rate surpasses the user growth, but that's probably not
             | important here.
        
               | thaumasiotes wrote:
               | If the churn rate surpasses user growth, you won't go
               | sigmoid, you'll stay exponential. You'll just be
               | shrinking instead of growing. To be sigmoid, you need the
               | growth rate to vary.
        
             | withinboredom wrote:
             | Growth is not a function of users, though, it is a function
             | of something else that *may* be exponential, for a time.
             | Users don't beget users (word-of-mouth doesn't last
             | forever; ad money has diminishing returns), and eventually
             | your market will be saturated, so you can't grow
             | exponentially forever.
        
         | ocean_moist wrote:
         | Yeah sigmoid is good. I kind of hint at this when I mention
         | "saturate their TAM at some rate".
         | 
         | You can think about it like we are looking at the concave up
         | portion of the sigmoid only. The early growth phase.
        
         | mgraczyk wrote:
         | They are sigmoids, but for some the plateau is 30 years in the
         | future with a 5T market cap.
         | 
         | For example Facebook's revenue is still increasing at an
         | increasing rate, 21 years later
        
           | alangibson wrote:
           | This is an incredibly important thing to understand. Buffet
           | himself said it's better to be an average business in a great
           | market that to be a great business in an average market.
        
             | ptero wrote:
             | Interesting. Not doubting this, but one of his sayings I
             | saw many times is that "it is better to buy a great company
             | at a good price than a good company at a great price",
             | implying that great companies are worth significant
             | premiums.
        
         | godelski wrote:
         | I took the author's use of O(n) vs O(n^2) as a framing point
         | rather than a literal model. It just seems to be missing the
         | forest for the trees. Besides, we can approximate sigmoids with
         | linear or quadratic functions when windowing them. Considering
         | startup as context I think we know what part of the graph we're
         | talking about... Do we see that exponential explosion or is the
         | sigmoid much more flat. Replace the x in your sigmoid with (ax)
         | and is a <1 or >=1?
        
           | nis251413 wrote:
           | Big-O notation is about asymptotics. You have to approach
           | something, and typically there is some infinity involved
           | because if it is not, then you can just compute things
           | instead of giving asymptotic approximations, or else you have
           | 10^10*n and 0.001*n^2-10^20*n and the big-O asymptotics at
           | infinity are useless for smaller numbers. I understand what
           | OP tries to say but that's not really a good framing point
           | for many reasons. If you want to talk about a finite period
           | of time, use a regression model, not asymptotics. But that's
           | probably also a more personal preference around using
           | mathematics colloquially but also in a manner that is not a
           | good metaphor and does not correspond with what the
           | mathematical theory is referring to. And I am not sure at all
           | whether it is very well understood "what part of the graph
           | we're talking about", in the sense that the modern
           | organization of economy is far from acknowledging the fact
           | that resources on earth are actually finite. Talking about
           | O(n) and O(n^2) or O(exp(n)) as if growth can be indefinite
           | comes with a specific kind of mindset, and the frame used
           | reflects this type of mindset.
        
             | godelski wrote:
             | > Big-O notation is about asymptotics.
             | 
             | Excuse me, but what made you believe I do not understand
             | this? I'm not sure what comment you're responding to, but
             | it sure isn't mine.                 >> I took the author's
             | use of O(n) vs O(n^2) as a framing point rather than a
             | literal model.
             | 
             | Honestly, the reason I said this is because from the
             | article                 | The reason I borrow the
             | asymptotic notation is because it implies the growth rate
             | is an upper bound (best case scenario) and generalizes away
             | specific constant factors and sums. The analogy breaks down
             | when you force n or n^2 imply something numerically
             | specific about your growth rate, or introduce functions
             | with different growth rates like logs or exponentials. For
             | now we will (somewhat unprincipledly) stick with two sole
             | classes: O(n) and O(n^2).
             | 
             | Along with their emphasis on "vaguely". I can forgive the
             | author for bad verbage. It is a personal blog where they're
             | not trying to sell anyone on a fully fledged out idea and
             | appear to be trying to spur conversations. Especially
             | considering it looks like they are an undergrad. Frankly, I
             | can understand them despite the wrong words. Given this, it
             | would require me to operate in bad faith by rejecting the
             | main thing they are attempting to communicate by focusing
             | on the details that ultimately don't matter to their claim.
             | > If you want to talk about a finite period of time, use a
             | regression model, not asymptotics
             | 
             | They did. They said "startup". The whole time they bound
             | the conversation to early businesses. I even directly
             | stated this                 >> Considering startup as
             | context I think we know what part of the graph we're
             | talking about...
             | 
             | Maybe you're referring to the preceding line
             | >> Besides, we can approximate sigmoids with linear or
             | quadratic functions when windowing them.
             | 
             | Which again, same thing.
             | 
             | My point is: you're derailing the conversation
             | 
             | You are technically right, but you're derailing the
             | conversation in an effort to prove your intellectual
             | capabilities to a person who were not questioning them in
             | the first place. You're flexing to the wrong group. You
             | just responded to something my comment was never about.
             | >  I understand what OP tries to say but that's not really
             | a good framing point for many reasons.
             | 
             | So address what the OP tries to say, * _and while doing
             | so*_ you can add additional technical correctness. * _This
             | does not derail the conversation.*_ It _continues_ the
             | conversation _and_ enhances it! You can do both! But as
             | your comment stands (and bee_rider 's), you just are moving
             | the conversation away from what OP wanted to discuss and
             | instead hyper-fixating on what they themselves said is not
             | the best language.
        
         | danjl wrote:
         | If only it was exponential in the beginning, as word-of-mouth
         | spreads. Sigh. The reality is that you need to claw and scrape
         | your way to your first customers. The numbers vary depending on
         | whether your product is b2b, consumer, or more niche, but the
         | first customers are the hardest. You rarely get word-of-mouth
         | in the beginning. Instead, it comes much later, typically after
         | a long period of slow growth as you learn more about your
         | customer's workflows and problems and adjust the product to get
         | closer to PMF.
        
       | sshine wrote:
       | Since O(n^2) is used as a proxy for "something superlinear, but
       | don't get hung up on how much", you might also choose O(n^(1+e)),
       | an upper bound characterised by some arbitrarily superlinear
       | function.
        
         | brap wrote:
         | Why not O(nlog*(n)) startups
        
           | sfpotter wrote:
           | Not that it matters, but O(n log n) is often referred to as
           | "quasilinear", but O(n^(1+eps)) is regarded as "superlinear"
           | (and in fact grows faster than O(n log n) for any eps > 0).
        
           | sshine wrote:
           | Because, as the article states,
           | 
           | > _The analogy [between asymptotic growth and company
           | economic growth] breaks down when you force or imply
           | something numerically specific about your growth rate, or
           | introduce functions with different growth rates like logs or
           | exponentials. For now we will (somewhat unprincipledly) stick
           | with two sole classes: O(n) and O(n^2). Perhaps choosing a
           | better two functions could more closely explain the growth
           | dynamics of network effects, which could be more exponential.
           | I think the analogy diminishes in value if you try to
           | directly numerically match it to some growth metric._
           | 
           | So the article specifically tries to be unspecific about
           | _what_ superlinearity we 're talking about, and also calls it
           | _vaguely superlinear_. Since O(n^(1+e)) is _arbitrarily
           | superlinear_ (O(n^1) = O(n), and e is some arbitrary small
           | amount, making it superlinear by definition, and practically
           | nothing else), it is a good choice when that is all you wish
           | to say.
           | 
           | If you went with O(n log n), you'd get the same questions as
           | with O(n^2): Why not O(...something else...): That's not the
           | point! :-D
        
         | ocean_moist wrote:
         | Sure makes sense.
        
       | SoftTalker wrote:
       | Story applies to most people in regular life: the average return
       | of working a regular job is far higher than playing the lottery.
       | But for a rare few, playing the lottery works out.
        
       | wavemode wrote:
       | > An O(n) startup grows its key metric (revenue, users, etc.)
       | roughly linearly with time--double the time, double the metric.
       | An O(n^2) startup accelerates, with growth compounding super-
       | linearly over time.
       | 
       | Kind of a strange formulation to have n represent the key metric.
       | In algorithm analysis, we would typically have n represent time
       | (or some other cost). So we would say that the startup whose key
       | metrics accelerate exponentially with time is actually an O(log
       | n) startup - they only have to spend (log n) time to get n
       | results.
        
         | thaumasiotes wrote:
         | >> An O(n) startup grows its key metric (revenue, users, etc.)
         | roughly linearly with time--double the time, double the metric.
         | An O(n^2) startup accelerates, with growth compounding super-
         | linearly over time.
         | 
         | > Kind of a strange formulation to have n represent the key
         | metric. In algorithm analysis, we would typically have n
         | represent time
         | 
         | In the quote you pulled, n _is_ time. If n were the key metric,
         | everything would be [?](n).
         | 
         | > So we would say that the startup whose key metrics accelerate
         | exponentially with time is actually an O(log n) startup - they
         | only have to spend (log n) time to get n results.
         | 
         | No, you don't know how the notation is used.
        
           | wavemode wrote:
           | > In the quote you pulled, n _is_ time.
           | 
           | It's definitely not. If their usage of O(n) has n as time,
           | then they wouldn't say an O(n^2) startup has accelerated
           | growth of the key metric. You'd be squaring the time, which
           | means _slowing down_ growth of the key metric.
           | 
           | When they say O(n^2) startup they clearly mean a startup
           | which achieves n^2 results in n time. Which is the opposite
           | of how the notation would typically be used.
           | 
           | > No, you don't know how the notation is used.
           | 
           | No, you're confidently wrong.
        
         | danjl wrote:
         | Normally, with big-O notation, the goal is to _reduce_
         | complexity. The author 's wording kinda reverses that
         | assumption only to "surprise" you in the end? A somewhat forced
         | irony.
        
           | Maxatar wrote:
           | Big-O notation does not have a goal, it's a description not a
           | strategy.
        
           | nis251413 wrote:
           | Well, you may want to increase complexity in some contexts,
           | eg in cryptography.
        
           | ocean_moist wrote:
           | Only in algorithmic analysis. Big-O generally is used to
           | describe and classify any arbitrary function.
        
         | Maxatar wrote:
         | > In algorithm analysis, we would typically have n represent
         | time (or some other cost).
         | 
         | No, n is never time in any kind of algorithmic analysis. n is a
         | function of the size of the input and the output is some
         | measure of the cost related to the input.
         | 
         | In O(n^2), the size of the input is n and the amount of time,
         | or space, or some measure of the cost has an upper bound that
         | is proportional to n^2.
        
           | wavemode wrote:
           | > In O(n^2), the size of the input is n and the amount of
           | time, or space, or some measure of the cost has an upper
           | bound that is proportional to n^2.
           | 
           | Yes, this is my point. In the article, they classify an
           | O(n^2) startup as one which achieves n^2 results in n time,
           | which is the opposite of how the notation is typically used.
        
       | ridiculous_leke wrote:
       | I wonder what's optimal for me as an employee. I am working in a
       | _O(n)_ startup where colleagues are nice, work is streamlined yet
       | challenging, and I do see growth potential in the long term.
       | Several _O(n^2)_ founders have reached out recently and the pay
       | is attractive(even after accounting for a move to an HCOL area).
        
         | danjl wrote:
         | Or, really, to say the unsaid bit out loud: there are lots of
         | important considerations when taking a job. The author seems to
         | assume that money is the only driver, when, for many top
         | candidates, money is not their primary motivation. The ability
         | to plan well and thereby reduce stress is a good measure of the
         | management experience. Other non-cash incentives tend to be
         | given out more readily at well-run non-enterprise companies,
         | including remote work, longer vacations, and more strategic
         | control, to name just a few.
        
         | robocat wrote:
         | Modern society tends to severely overemphasize money as the
         | optimisation goal. This is an emergent behaviour of our good
         | capitalist system.
         | 
         | Your time is precious. You spend it once and you can't
         | predictably get any more of it.
         | 
         | I suggest you choose your optimisation goal function very very
         | carefully to suit the outcomes you want (money is only an
         | intermediate step). It's hard to decide what we really want.
         | Money is the default game that we see our peers playing (and
         | it's easy to gain moderate success at the money game). It
         | requires more attention to find and learn from people that have
         | had success playing less common games.
         | 
         | Cynically (or even conspiratorially) investigate the suggested
         | life defaults for you by your society as though they were dark
         | patterns designed to mislead you.
         | 
         | I like what Naval wrote about status games (money is only one
         | aspect of status). Paraphrased:                 Status is a
         | zero-sum game, not a positive-sum game. There's always a subtle
         | competition going on between status and wealth. For example,
         | when journalists attack rich people or the tech industry,
         | they're really bidding for status. The problem is, to win at a
         | status game you have to put somebody else down. That's why you
         | should avoid status games in your life - because they make you
         | into an angry combative person. You're always fighting to put
         | other people down and elevate yourself and the people you like.
         | Status games are always going to exist; there's no way around
         | it. Realize when you're getting attacked by someone else and
         | they're trying to look like a goody-two shoes. They're trying
         | to up their own status at your expense. They're playing a
         | different game. And it's a worse game.
         | 
         | Disclaimer: I've had moderate success at chasing money. I've
         | had less success at optimizing for other goals (work in
         | progress in my 50s).
         | 
         | Money has no maximum so it's a weird goal to try and reach. I
         | wonder why Warren Buffett waited until 95 to decide to retire?
         | He would easily be the richest man in the world if he hadn't
         | charitably given so much away.
         | 
         | Another relevant paraphrased snippet from an interview about
         | better lives for the elite: https://archive.ph/kF0YR
         | There's this study called the American Freshman Survey
         | [edit:snip] In the 1960s, 50% of students said making as much
         | money as possible was a really important goal. Today, that's
         | 80% to 90%. That change shows that this is not human nature. It
         | is culture.
        
       | curiousgibbon wrote:
       | This is one of the myriad situations where Omega should have been
       | be used, not O. What are they teaching in schools these days?
        
         | ccppurcell wrote:
         | Should be O(n) vs Omega(n^2)
        
           | curiousgibbon wrote:
           | Yep
        
         | TypingOutBugs wrote:
         | The author is an early CS bachelors student so... they might
         | still learn this in school
        
         | ocean_moist wrote:
         | I actually passed my discrete math class and final a few days
         | ago and got the big O vs Theta vs Omega question right.
         | 
         | The reality is that companies often _underperform_ their best
         | case possible growth rate. O(n) and O(n^2) are meant to
         | represent the _best possible growth rate_ which may be
         | practically be underperformed.
         | 
         | You may be thinking about algorithmic analysis where the term
         | "worst case" is used for the upper bound, but here, the upper
         | bound represents the _best case_. Sort of counter-intuitive but
         | the underlying mathematical notation is properly defined.
        
           | curiousgibbon wrote:
           | It's entirely nonsensical to use O as a lower bound though.
           | You could have two companies no growth whatsoever in value
           | and correctly state that one has O(n) growth rate and the
           | other has O(n^2) because a constant is both O(n) and O(n^2)
           | (and O(n!) and O(exp(n^n)) ...). The author is trying to
           | argue that there's some separation between two hypothetical
           | startups' growth rates and as such an upper bound on one, say
           | O(n), and a lower bound on the other, say Omega(n^2), is
           | warranted. It sounds like you're not entirely an expert
           | despite your recently-passed final. Strange concept, eh?
        
             | ocean_moist wrote:
             | I am actually the author.
             | 
             | You're right that mathematically, a function with constant
             | (or no) growth _is_ O(n)and also O(n^2), and
             | O(anything_that_grows_faster).
             | 
             | My use of "O(n) startup" and "O(n^2) startup" is intended
             | to classify the _type_ of business based on its *inherent
             | best-case growth potential or ceiling*.
             | 
             | An O(n) startup in my framework is one whose fundamental
             | business model, market, or structure means its growth,
             | _even in its best-case scenario_ , is capped at roughly
             | linear. It _cannot_ achieve sustained super-linear growth;
             | its upper bound _is_ linear.
             | 
             | An O(n^2) startup is one whose model (e.g., strong network
             | effects) has the _potential_ for super-linear (which I 've
             | simplified to n^2) growth as its best-case scenario. It
             | might be underperforming (even flat, and thus also
             | technically O(n) in that moment), but its _design_ allows
             | for a fundamentally different, higher growth ceiling. The
             | whole point is illustrate potential withholding
             | implications or conclusions from its current growth rate,
             | which is necessary at a companies inception.
             | 
             | So, yes, a flat-lining "O(n^2) type" startup would
             | currently show growth that is O(c) (and thus also O(n)).
             | But the point of my labels is to say that an "O(n) type"
             | startup, by its very nature, _cannot_ achieve the n^2 best-
             | case that the other type _can_ , even if both are
             | struggling.
             | 
             | The labels describe the _class_ they have, dictating their
             | _asymptotic best-case limit_ , not just any loose upper
             | bound on current, possibly sub-optimal, performance. The
             | separation I'm arguing for is based on that fundamental
             | difference in their _potential trajectory's ceiling_.
             | 
             | If I used Omega this would imply _the actual_ growth rate
             | of the startup would have to strictly be better n or n^2.
        
       | neilv wrote:
       | > _O(n) companies can 't afford to hire the absolute best talent.
       | [...]_
       | 
       | > _O(n^2) companies hire high agency people. [...] People are
       | generally given a lot of equity to join and as a reward._
       | 
       | O(n^2) is often a matter of ZIRP-VC-powered artificial-growth
       | (e.g., their example of Uber). That also includes hiring a large
       | _quantity_ of people.
       | 
       | For factors in _genuine_ O(n^2) growth, you might be onto
       | something: with structuring culture to leverage employee agency,
       | and for using meaningful equity to help align employees with
       | business success.
        
         | danjl wrote:
         | Or, O(n^2) companies are founded and run by people motivated
         | solely by making lots of money, while O(n) companies are there
         | for multiple reasons: passion for the topic, making employee's
         | lives better, and helping their customers solve problems.
         | Though those motivations exist at O(n^2) companies too, they
         | are in the shadow of making money. While, at O(n) companies,
         | money is also essential, but it exists to support the other
         | goals. A slight shift in priorities can make all the
         | difference.
        
       | avereveard wrote:
       | Counter hypothesis: fast but linearly growing early stage startup
       | acquire good early funding and enter into a growth loop dominated
       | by the ability to invest these fund in marketing, which increase
       | valuation and allow for further funding, fueling more growth etc.
       | 
       | After all cost of customer acquisition is largely dominated by
       | external factors and cost per user mostly linear until close to
       | market saturation.
       | 
       | Now there might be economy of scale intervening at some point
       | increasing the margin per user, which feed back into growth, but
       | on average fast growing startup are cash negative until much
       | later in life.
       | 
       | TLDR I think the implications in the article is inverting cause
       | and effect
        
       | kristopolous wrote:
       | When I saw the headline I thought it was referring to complexity,
       | legacy and stagnation of tech debt
        
       | vessenes wrote:
       | To quote a private equity investor friend: "I've known startup
       | CEOs of billion-dollar companies that are flat broke. Meanwhile
       | people with $50mm/ARR dating sites from Europe live like kings."
       | 
       | A good reminder that it's worth deeply understanding venture
       | portfolio economics before you get on the ride. Not that it's a
       | bad ride. But it's a ride.
        
       | xyst wrote:
       | What ever happened to providing a good service? Why does
       | everything have to be a "unicorn"? You greedy capitalists, and
       | billionaires have sucked out the life of everything -- tech,
       | food, airlines.
       | 
       | VC culture, private equity, and "hyper-growth" mentality has
       | screwed over many good companies that once provided good services
       | to the community. Good paying jobs with excellent benefits and
       | providing upward mobility.
       | 
       | Now the labor benefits are shrinking, company loyalty is gone,
       | customers screwed over, labor exploited with minimal in return,
       | rising cost of living, increasing wage disparity, abuse of
       | powers.
       | 
       | One can argue the neoclassical/neoliberal economic theory and
       | "Reagan-omics" that birthed PE/VC culture gave power to the
       | idiocracy we see today.
        
         | Snawoot wrote:
         | > What ever happened to providing a good service?
         | 
         | I'm getting an impression it's just not profitable enough. For
         | many years I get a feeling that business is considered sound
         | only if it is superprofitable (not exactly the right term, but
         | still) in order to cover all losses.
         | 
         | Probably it's because of market competition required to be at
         | least noticed. Some companies' spendings for marketing are
         | greater than for R&D, production and operations combined. Maybe
         | we got ourselves into a situation where everywhere competing
         | for low-hanging fruits or trying to make customer believe it's
         | the service they need while all of it doesn't really overlap
         | with real society needs.
        
       | ark296 wrote:
       | VC-land is a strange place with strange laws. If you stay in it
       | for too long, you forget that most of the world doesn't follow
       | the power law, and that most of the VC-reasoning just does not
       | help.
        
       | dvt wrote:
       | > I think many prospective founders, if their goal is money,
       | should optimize for O(n) businesses from day 1.
       | 
       | Honestly, I don't think anyone "picks" the kind of business they
       | want to run. You just kind of go with the flow. If you raise VC
       | money, you follow their lead, if you're running a small bakery,
       | you'll do whatever makes sense there.
       | 
       | So while this is a fun intellectual exercise, it's an exercise in
       | hindsight. In the moment, you're really just trying to survive
       | the day-to-day and not really "optimizing" for a specific growth
       | pattern.
        
         | ocean_moist wrote:
         | I think any prospecting founder should be able to answer the
         | question "will it always take a fixed amount of work to get
         | each new customer?".
         | 
         | Generally if you have some sort of idea of what you want to do,
         | you'll be more successful at it.
        
           | scarface_74 wrote:
           | Most founders - especially vc backed founders - only care
           | about whether the optics look good enough for an acquisition
           | or an IPO. They could care less if it fails after that.
           | 
           | YC backed companies are no exception
           | 
           | https://medium.com/@kazeemibrahim18/the-post-ipo-
           | performance...
        
       | fooker wrote:
       | There's an interesting misunderstanding in this article.
       | 
       | The argument for O(n) is well formed here.
       | 
       | O(n^2) is not, the core argument is that these grow faster
       | because of compounding. Compounding is fundamentally an
       | exponential process, far larger asymptotically than a quadratic.
        
         | nine_k wrote:
         | True exponential growth is possible, but I suspect is rare,
         | because the expenses can also compound, so a polynomial growth
         | may be an acceptable approximation. It's also important to
         | remember that "every exponential growth curve is a sigmoid in
         | real life" (can't remember the source of the quotation).
        
           | jxjnskkzxxhx wrote:
           | > True exponential growth is possible, but I suspect is rare,
           | because the expenses can also compound
           | 
           | If you have an exponential (revenues) and another exponential
           | of smaller rate (expenses; assume you have profit) then the
           | difference is still an exponential.
        
         | robocat wrote:
         | The article clearly isn't meant to be mathematically correct:
         | you are being over-rigorous in your criticism. From the
         | article:                 Businesses generally grow following a
         | few patterns. They generally have some TAM to saturate and
         | saturate the TAM at some rate. This rate can be vaguely linear,
         | what I call O(n), or vaguely superlinear, what I call O(n2).
         | The reason I borrow the asymptotic notation is because it
         | implies the growth rate is an upper bound (best case scenario)
         | and generalizes away specific constant factors and sums. The
         | analogy breaks down when you force n or n2 imply something
         | numerically specific about your growth rate, or introduce
         | functions with different growth rates like logs or
         | exponentials. For now we will (somewhat unprincipledly) stick
         | with two sole classes.
         | 
         | Article would be better using something like O(linear) and
         | O([?]linear). The big O notation is a useful and memorable
         | metaphor, but the n squared is really confusing. The article
         | also doesn't use Unicode for the notation - which fucks
         | usability (e.g. I used screenshot OCR and reedited).
        
         | ocean_moist wrote:
         | Addressed in the footnotes:
         | 
         | > [2] Perhaps choosing a better two functions could more
         | closely explain the growth dynamics of network effects, which
         | could be more exponential. I think the analogy diminishes in
         | value if you try to directly numerically match it to some
         | growth metric.
        
       | nine_k wrote:
       | > _[The conclusion is that] O(n) companies are higher EV than
       | O(n^2) companies. I mean that, on average, a founder will make
       | more money pursuing an O(n) company than an O(n^2) company. And
       | not an insignificant amount, the amount of liquidity and networth
       | a 20m ARR O(n) company is extremely hard to match by a
       | traditional VC backed O(n^2) company._
       | 
       | It's a bit like getting a regular job vs playing a lottery: the
       | former gives you better financial results on average, while the
       | latter gives you a chance to make it really big.
       | 
       | (I also wish it were "linear companies" and "quadratic /
       | exponential companies", or maybe "snooker-cue companies" vs
       | "hockey-stick companies".)
        
       | gmuslera wrote:
       | I wonder about the cultural effects at large getting the O(n2)
       | most of the funding. That expansive, aggressive and not always
       | safe behavior is promoted, while the slow but solid approach is
       | not. That shapes the ecosystem and the people in it, in and out
       | those companies.
       | 
       | Maybe it is a good way for short term profits, but that is just
       | one metric. That kind of dynamic may be harmful in the long term,
       | and in a really big scale.
        
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