scrape_r_rational/data/cache/2fmgpn.md

[MK] The Two Year Emperor, Chapter 60: Industriously Revolutionary

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• u/GeneralSCPatton:

  Just for funsies, because of that bit about atoms. Each size category is a factor of 2 along each dimension and confers a + or - 4 on Hide checks. Iron atoms have a diameter of 252 picometers. Dividing the average human height by the diameter and taking the log base 2 reveals that iron atoms are about 33 size categories smaller than humans. If someone manages to temporarily get about +132 to Spot checks, they'll be able to see atoms. I don't know if you can come up with a plausible excuse for this to happen, but it would be hilarious. I'm sure one of those threads on optimizing for epic skill checks would help. Fortunately, at such high levels they can get almost halfway there just on skill ranks alone. Also, freaking out about being made of cells. "I can see my own eyeballs! And they're made of little things! Oh Gods, they're moving!"
  

  • u/alexanderwales:

    Given that most people seem to have at least 60 levels now, anyone who has specialized in Spot should have +60 to it at a bare minimum (ranks only, no special feats, items, or weird stuff). While that's not enough to see atoms, the smallest bacteria is about 200 nanometers across, which is 800 times larger than an iron atom - or about 10 size categories. So to see a single cell, you only need to have a spot check of +92 - which is fairly easily achievable for any of the newly hyperleveled characters.
    
    Incidentally, such high Spot checks allow you to see invisible creatures without really trying:
    
    > A creature can generally notice the presence of an active invisible creature within 30 feet with a DC 20 Spot check. The observer gains a hunch that “something’s there” but can’t see it or target it accurately with an attack. A creature who is holding still is very hard to notice (DC 30). An inanimate object, an unliving creature holding still, or a completely immobile creature is even harder to spot (DC 40). It’s practically impossible (+20 DC) to pinpoint an invisible creature’s location with a Spot check, and even if a character succeeds on such a check, the invisible creature still benefits from total concealment (50% miss chance).
    
    But if we were *really* following the D&D Spot rules, you wouldn't be able to see much beyond a few hundred yards (or something like that), which makes almost no sense.
    
    Edit: +15 to Wisdom from 60 levels and +5 to Wisdom from the POPE gives you +70 without much optimization. That's enough to see things on the micrometer scale when you take 10. Of course, it's sort of questionable whether things in Stupidworld are even made up of cells or atoms in the first place, but I guess given the matter-antimatter reaction they must be. If you take 20 you can see cells, and that's without a microscope.
    

• u/fortycakes:

  How come Isaac didn't have to pay Graham's number of experience to create the Earring? Wish doesn't remove the experience point cost of creating items, so unless the XP cost for the Earring is somehow (vastly) less than the XP stored within it, it should have used more XP to cast that Wish than Isaac could have possibly had.
  

  • u/eaglejarl:

    You might want to re-read that section.  Reload the page and search for "explode".
    
    You might also note a namedrop in that vicinity.  :)
    

  • u/eaglejarl:

    Interesting question.  What's your guess?
    

    • u/Zephyr1011:

      Assuming that it isn't some random rule like "When creating an item with XP, you need not pay the XP ", it could have been a god intervening? Loki already did that with the cannons, so there is a precedent. And I'm sure this trick would amuse some of them. Besides, if it failed because Isaac lacked XP, they could have just used another candle of invocation to make it
      

      • u/eaglejarl:

        Repeating what I posted to fortycakes so that you see it too:
        
        You might want to re-read that section.  Reload the page and search for "explode".
        
        You might also note a namedrop in that vicinity.  :)
        

        • u/Zephyr1011:

          Why thank you. I'm flattered. 
          
          Also, I will now in future assume that all innocuous seeming questions from you to readers are plot hole damage control
          
          Why do they give my alter-ego 2 wishes though? Surely one wish would be sufficient for not-me to fulfill the deal in good faith. And then they'd have gotten a free wish. Likewise for when Jake did it a while ago
          

          • u/eaglejarl:

            > Also, I will now in future assume that all innocuous seeming questions from you to readers are plot hole damage control
            
            Heh.  Actually, I think this is the first time that's happened.  Usually when I ask innocuous seeming questions it's because I've got something up my sleeve and I don't want to spoil it but I can't resist hinting a little bit.
            
            [giving 2 wishes vs 1]
            
            In both cases, it's because the extra Wish didn't matter and there's a question of perception.  If the person you're doing the deal with is getting more out of it than you are, there's a small sense of irritation.  If you're getting more out of it, you feel all magnanimous and DEFINITELY don't want to screw around.
            
            And the second Wish really didn't matter -- in the first case, one Ring was enough to get infinite Wishes.  In the second, Wishes were easily available and XP was the limiting factor, which the Earring solved.
            

    • u/Chronophilia:

      The gods object to Wishing for items without paying the XP costs, because that limitation prevents infinite wish loops with the Ring of Three Wishes or similar.
      
      Jake had to ask for specific permission from Arros to make the Earring. He doesn't need special permission to make the Bedroll Gnome Gnome Gnome Gnomes, just a general "I'm OK with spell engines".
      

      • u/eaglejarl:

        Indeed.
        
        The gods would have gone ballistic if Jake had created the Earring without permission, thereby meaning that he never had to pay XP for anything ever again.
        
        Of course, fortycakes is also correct -- a vanilla Wish couldn't create the Earring.  Hence why it is no longer a vanilla Wish that does.
        
        retcon, retcon, lovely lovely retcon.
        

• u/Zephyr1011:

  This was wonderful. Jake has gotten so much better now he's not a PTSD suffering alcoholic. I presume that they were automating the production of useful things like HoOA? And that the Landguard made ice Assassins off screen? 
  
  If they're forbidden from turning Neklos' servants against him, shouldn't the gods be annoyed by their treatment of Colborn and plans for Hammond? 
  
  Also, would any kind of limited time Grey Goo be useful? Eg. Something which converts an area of matter in front of itself into a copy of itself until arbitrary time. Or, say, a spell engine which cast Sunburst, or one which created such engines, dropped onto a field of undead?
  

  • u/eaglejarl:

    > This was wonderful. Jake has gotten so much better now he's not a PTSD suffering alcoholic. 
    
    Heh.  Thanks, glad you think so.  To be honest, I was just as tired of writing him that way as everyone seems to have been of reading him that way.  When Icefi showed up, his primary mission was to get the humans onside, but his secondary mission was to steal Jake's brain and get the information out.  It was a perfect opportunity to fix the bad parts en passant.
    
    > I presume that they were automating the production of useful things like HoOA? And that the Landguard made ice Assassins off screen?
    
    Yes and yes.
    
    > 
    > If they're forbidden from turning Neklos' servants against him, shouldn't the gods be annoyed by their treatment of Colborn and plans for Hammond?
    
    It was more "you can't do that en masse".  Converting individual worshippers of a god is an acceptable and time-honored tactic in divine warfare.  Stealing entire swaths of them in one go is not cricket, however.  Anything that violates the divine equivalent of the Geneva Conventions gets all the gods uniting to spank you with an axe.
    
    > 
    > Also, would any kind of limited time Grey Goo be useful? Eg. Something which converts an area of matter in front of itself into a copy of itself until arbitrary time. Or, say, a spell engine which cast Sunburst, or one which created such engines, dropped onto a field of undead? 
    
    As to the Sunburst -- it would be useful, yes, but it's approximately the same thing that Fragment already kiboshed.  They might try asking about it separately, though.
    
    Grey Goo...might be useful, although the only thing I can think of that you'd use it for would be utterly destroying an area of ground and everything on it, and there's already plenty of ways to do that.  It's pretty much the same problem as the AM explosions -- chewing up lots of landscape tends to piss off the mountain / earth / river / etc gods.
    

  • u/tilkau:

    The distinguishing characteristic of all Jake's rejected plans in this chapter is that they are *en masse*, and generally stupidly OP exploits -- 'kill/turn all the undead' definitely fits in that category. 
    
    Using a Helm of Opposite Alignment opportunistically on significant *individuals* is positively mundane -- highly effective, but nothing jawdropping -- as war strategy goes. I would call the gods seriously OCD if they were bothered by that.
    

• u/eaglejarl:

  Incidentally, if anyone can come up with a Wolfram-Alpha-able equation that graphs the production capacity of the 3-tier production lines, I'd love to see it.  I wrote out the first few levels of it longhand to make sure it had the production I wanted.  Later on I tried to actually write down the equations, but my brain kept breaking when I did.
  
  You can safely assume that all GGGs fire before all GGs before all Gs.
  

  • u/Zephyr1011:

    Ignoring the volume constraints, the problem is just a simple polynomial. If then cannot spread the things out fast enough, this just remains an upper bound. 
    
    Assuming that it starts at round 0 with 1 GGG and nothing else, that each round the total number of GGs is the sum of the previous number of GGs and GGGs and likewise for Gs and FBRs, you get:
    
    0: (1, 0, 0, 0)  
    1: (1, 1, 1, 1)  
    2: (1, 2, 3, 4)  
    3: (1, 3, 6, 10)  
    4: (1, 4, 10, 20)  
    5: (1, 5, 15, 35)  
    ...
    
    This generalises to (1, n, n(n+1)/2, n(n+1)(n+2)/6), or (1, nC1, (n+1)C2, (n+2)C3).
    
    If you started with a G^r, rather than a G^3, it would be (G^r, ..., G, FBR)=(1, nC1, ..., (n+r-2)C(r-1), (n+r-1)Cr)
    
    So, after 1 minute you would have 220, 5 minutes would give you 22100, half an hour would give you 4545100,  and an hour would give you 36180200, enough for all of Grofhamr and Flobovia's population. If you're willing to wait a day, every person in Grofhamr and Flobovia can make 13500 Ice Assassins and give them all a Fortifying Bedroll, with a few left over for all the trees and animals in Flobovia.
    
    EDIT: Gnomes are apparently able to cast Wish the same round that they are created. My solution has been amended accordingly
    

  • u/tilkau:

    I think triangular numbers may be relevant here. 
    I don't know much about Wolfram Alpha, but here it is in Python, in the most simple, easy to understand way I could write it:
    
        ggg = 1
        gg = 0
        g = 0
        fbr = 0
        maxturns = 100
        graph = []
        for turn in range(maxturns):
            for i3 in range(ggg):
                gg += 1
            for i2 in range(gg):
                g += 1
            for i1 in range(g):
                fbr += 1
            graph.append(fbr)
    
    Obviously, this only runs for 100 turns (ending in 171700 FBRs on the final turn).
    If I were making a larger graph I would probably use something more efficient, like this:
    
        ggg = 1
        gg = 0
        g = 0
        fbr = 0
        maxturns = 10000
        graph = []
        for turn in range(maxturns):
            gg += ggg
            g += gg
            fbr += g
            graph.append(fbr)
    
    After 10000 rounds, 166716670000 FBRs have been produced; in the 10000th round alone, 50005000 FBRs have been produced (naturally, the number of G's is the same as this.. The number of GG's is 10000; the reason for this should also be obvious.)
    
    
    Very quick graph of FBR production, turns is X axis:
    
    http://i.imgur.com/I9prTfQ.png
    
    It looks like you could fit this to a polynomial and be able to put it into WA that way.
    
    I ignored the googolplex limit because I calculated that I couldn't possibly run into it until I'd run my algorithm for a googolplex rounds.
    
    
    Soooo... maybe those GGGs are a tad overspecced.
    

    • u/JT_Macguffin:

      Indeed, the number of Gs exactly follows the [triangular number sequence](http://en.wikipedia.org/wiki/Triangular_number), which can be calculated with the polynomial 1/2x^2 + x/2. Since the rate FBR increases per round is just the number of Gs, we now know the derivative. 
      
      Simply take the integral and you get 1/6x^3 + 1/4x^2, where x is the number of FBRs. (Of course, this assumes infinite space, which constrains the actual numbers of a bit. Stupid reality screwing up math.)
      
      Anyway, here's the [Wolfman Alpha graph](http://www.wolframalpha.com/input/?i=%28x^3%29%2F6+%2B+%28x^2%29%2F2+at+x+%3D+100), at x = 100. It matches your calculation.
      

      • u/Zephyr1011:

        Your figure for the FBRs is a bit off. You are using calculus, which assumes that the production is continuous, when it is discrete. The actual formula is n(n-1)(n-2)/6 at round n, assuming that it starts with 1 GGG at round 0 and nothing else
        

        • u/JT_Macguffin:

          Oh, shoot. You're correct. I was wondering why I was getting decimal results. I suppose it's just a good approximation if you're in a hurry.
          

• u/None:

  [deleted]
  

  • u/None:

    [deleted]
    

    • u/eaglejarl:

      That's...quite sick.  Slick.  I meant slick.
      
      Vicious, but slick.
      

• u/bbrazil:

  [Derivative Clicker](http://gzgreg.github.io/DerivativeClicker/), now in D&D form!
  

  • u/eaglejarl:

    Thanks *ever* so much for posting this.  My entire morning just got shot to hell.  *grumble*
    

• u/TimeLoopedPowerGamer:

  I love this story. One of my favorites.
  
  But for some reason, every time I see it in my alerts I instantly think:
  http://i.imgur.com/yVzjYyv.jpg
  
  ANYWAY, thanks for the update.
  

  • u/eaglejarl:

    ?
    
    What is that from?
    
    (Also, glad you like it. :) )
    

    • u/TimeLoopedPowerGamer:

      http://en.wikipedia.org/wiki/Adventure_Time
      
      Ostensibly, a very popular kids/stoners cartoon. *Also*, a sometimes dark and adult story about a violent, post-apocalyptic world, with lots of fantasy and sci-fi trappings built into the absurdist presentation. It *quite often* meets rational fiction story requirements, with serious consequences and logical plot outcomes.
      
      The characters are kids, but they still use the world as well as they can. Rules exist for a reason, if it is a fantasy trope, and are consistent. Things that happened earlier that no one noticed often come back as highly significant in later plot lines, often for perfectly logical reasons. It does world-building and plot advancement in almost every episode, even if that isn't always apparent. Virtually no take-backsie one-shots that don't change anything.
      
      Usually rather funny, but also really sad sometimes with some serious moments. Like the ongoing storyline with a character who continually loses their memories, having lived centuries with a cursed magical artifact that they had originally used to survive the apocalypse. Their also-immortal friend has to deal with the situation of knowing someone who only sort-of remembers them and their long history together. It is maturely handled and emotionally moving. Some other downright futurist concepts get snuck in there sometimes, as well.
      
      The creators are genuinely intelligent in their writing, and it is never dumbed down for its supposed younger audience. Instead, the metaphor and heavy significances are simply silently left in for the more adult topics and never explained. It isn't done like a Pixar movie, with the wink and a nudge for the parents. But instead, it is simply told mostly from a younger perspective, and the dialog reflects that. The world is still fully formed and deep, though, and that comes through all the time. Especially in the wreckage of civilization and the world itself, which is literally shattered.
      
      Also, a stretchy dog creature farts. So. Yeah.
      
      Won't make any sense at all unless one invests serious time reading up wikis and such, or watching a hundred or so episodes in some sort of order.
      
      Which is one reason a lot of people dismiss it as merely banana-monkey-dishwasher wackiness when they drop in half-way through a single episode in, say, the last few episodes in the third season.
      
      These people are shallow and dismissive of something genuinely good on TV. I like to laugh in their faces when those same people complain that English language TV doesn't have anything as deep and artistically significant as Japanese anime. Which I also like to watch quality examples of, of course, because *I'm* not a shallow, dismissive idiot myself. At least, not about that.
      
      In conclusion, if you have the means, I highly recommend picking it up.
      
      That was from *Ferris Bueller's Day Off* (1986), BTW.
      
      Oh yeah. The dog is named "Jake". Huh.
      

• u/themenniss:

  <3 Graham's number. For the mathematics nerds, you may want to check out the [my number is bigger](http://forums.xkcd.com/viewtopic.php?t=7469) thread on the xkcd forums. g64 is suitably overkill (its already large enough that doubling it doesn't make much difference), but Ack(Ack(g64, g64), Ack(g64, g64))...
  
  Or y'know, 
  
      define h(1) = g64  [Ack(Ack(g64, g64), Ack(g64, g64)) up arrows] g64;
      h(n) = h(n-1) [Ack(Ack(h(n-1), h(n-1)), Ack(h(n-1), h(n-1))) up arrows] h(n-1);
      earring.setExperience(h(g64));
  

  • u/None:

    I think [this /r/math thread](http://www.reddit.com/r/math/comments/283298/how_to_compute_a_very_large_number/) is very related, and a great read on top of that. Check it out!
    

• u/Laborbuch:

  I have to wonder how the various stat blessings will affect people (especially Jake as the viewpoint character). 
  
  I mean, if I get that right, the POPE will grant +5 to the various stats, respectively, right? And given the exponentially growing blessing capability soon enough everyone will have arbitrarily high stats, with the only distinguishing difference being what the characters started with and selected for when they gained character levels. My assumption is, soon enough either everyone will have a POPE and can increase all their stats +5 every… day or so.
  
  Since all stats are similarly increased, there shouldn't even be a period of acclimatization to the increased stats be necessary. Sure, everyone is suddenly stronger, but their **wisdom** and thus perceptional and intuitive faculties ought to be increased as well, so no accidental dislocating door handles and other mishaps, right? 
  
  But what are the limitations? Will soon enough everyone be strong enough to 
  
  * jump hundreds of meters high (based on **strength**), 
  * put eyes out with paper air planes consistently (hand-eye coordination based on **dexterity**), 
  * have astronomical hit points (are there even hit points?), 
  * disable everything (based on **intelligence**), 
  * be living lie detectors (Sense Motive, Listen, Spot all based on **wisdom**), 
  * and be insanely appealing to everyone not *blessed*?
  
  Also, if I got your chapter right, Jake now has +25 INT to whatever his natural score was due to each "I wish to be smarter" granting him +5 INT; the parenthesis pandemonium that followed was due to (a) the sudden increase and (b) Jake not having the appropriate increase in WIS that would have the willpower and intuition to deal with this. 
  
  (I never played D&D, but due to popcultural osmosis am aware of enough tidbits to reason a lot of stuff out, yet do not know the rules and, more relevant, tripfalls of the system.)
  

  • u/Zephyr1011:

    There is a cap of +5 to any stat from inherent bonuses like Wish. You can only use a POPE once for each stat. When Jake wished 5 times to be smarter, he only got +1 INT per wish, for a total of +5. And the author has said that there are to-be-revealed reasons why Jake can't get extra CHA and WIS, as if he does he would utterly break the story, as his major weaknesses would eb removed
    

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