Building the Great Pyramid of Giza with Lyres of Building - some math

Pathfinder RPG General Discussion

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I originally posted this on Dicefreaks.

I did a case study a while back to figure out how long it would take to build the Great Pyramid of Giza using a Lyre (or lyres) of Building. I share it in case anyone is interested. The estimate involves a number of estimates and assumptions, some of which are fairly arbitrary.

1. Work requirements of the real pyramid, in Ancient Egyptian man-days:

14,500 men x ten years, to go with one scholarly estimate. We'll round up some for conservatism and round numbers.

Rounded 15,000 labor force x 4,000 days = 60 million ancient Egyptian man-days to assemble the pyramid.

2. Conversion to Pathfinder man-days

The ancient Egyptian man-day is very low-tech and thus relatively less productive.

The lyre produces man-days of labor measured according to the output of a generic Pathfinder work crew, which is working with late Renaissance technology, which in construction includes cranes, windlasses, etc. Not to mention more ancient (but post-Egyptian) innovations such as iron and steel tools.

We’ll estimate, somewhat arbitrarily, that due to technological deficiencies the ancient Egyptian man-day was only half as productive as a Pathfinder man-day. Great Pyramid = 30 million Pathfinder man-days.

3. Lyre of Building base productivity

The Lyre of Building does the work of 100 Pathfinder men working for three days in a half-hour of playing. It requires a DC 18 skill check to keep playing for any length of time, but we’ll assume that if you are the type of person who can contemplate building a gigantic stone pyramid for yourself you can afford someone who can't fail the check. The lyre therefore performs 600 Pathfinder man-days worth of labor per hour that it is played, which is 4800 man-days of labor per 8-hr playing day.

4. Other considerations applied or not applied, and calculation of required time.

Since our lyrist has the rest of the week off, we’ll assume that given enough motivation he can play for 16 hrs on his one work day before fatigue intervenes. 9600 man-days per lyre session.

We’re going to neglect the effects of recurring time slippage (i.e., having to start playing 16 hrs later each week because that’s when you stopped using the item before). That makes the math irritating. We’ll assume our lyrist plays once a week with no time slippage.

The lyre work force requires no logistical support – no butchers, bakers, or candlestick makers. Part of the labor cost of the Great Pyramid, on the other hand, is to see to the needs of the workers. We’ll apply a factor of 1/2 to our 30 million man-days target to represent the fact that the lyre’s output is pure labor whereas part of the 30 million man-days represents logistical support. The adjusted target is 15 million man-days at a rate of 9600 man-days a week. We’re looking at 1562.5 weeks of playing, or roughly thirty years. Our estimated ancient workforce of about 15,000 Egyptian workers (=7,500 PF workers) is ultimately about three times faster than our bard.

5. Maximum lyrism

If we pull out all the stops we can go faster. Let’s assume that instead of a mortal lyrist our player is a lyre-obsessed bard lich who plays 24/7 and can’t fail the skill check. In fact, so obsessed is he that he never has to wait to use the lyre again, because he never stops voluntarily and is never forced to. This pushes his output up from 9600 man-days a week to 100,800 man-days a week. 139 weeks or about two years eight months.

6. Rejected factors and unconfirmed assumptions

I included no factor to account for production bottlenecks, when some workers are left idle because they are waiting on others to finish. One could argue that the lyre would be less constrained by such bottlenecks than mortal workers. I have assumed (and would rule) that the lyre’s production matches that of 100 mortal workers including those workers’ bottlenecks, and that no additional factor is necessary.

Besides the fact that the factors I applied are arbitrary estimates - I don't know whether a Pathfinder is really exactly twice as productive as an Egyptian work day, and in fact I pulled the specific factors out of a warm and dark place - another source of a potentially large error right now is that I am not certain that the scholarly estimate for the workforce really did include logistical support people. I have assumed that it did because it seems most likely, but I got the estimate from Wikipedia, and the link to the original had gone bad, so I did not verify. It is possible that they meant for their number to only include those directly engaged in construction, in which case our man-day requirement would double and so would our time to completion.

7. Cost of lyring compared to manual labor

Pathfinder unskilled labor is 1 sp a day. We’ll also estimate that skilled labor is 5 sp a day, average, and estimate that these average costs are similar for direct labor and for overhead. With our required 7500-person workforce of more productive Pathfinder workers needed to complete the pyramid on schedule, we’ll make a final fairly arbitrary estimate that this involves 6,000 unskilled and 1,500 skilled workers and thus that labor costs come to 600+750=1,350 gp/day over the course of 4,000 days, for a project total of 5.4 million gp in labor costs.

The lyre costs 13,000 gp up front, and let’s assume for the sake of argument that retaining a bard skilled enough to fulfil our requirements costs 100 gp/week, which I think is quite conservative (A bard with a +17 Perform modifier working for himself could make about 25 gp/week if he worked seven days; or if he's above minimum skill, with +20, he could make about 75 gp working seven days a week for himself). At our calculated 1562.5 (1563) weeks, this will cost 156,300 gp. Total costs for the mortal bard are therefore 169,300 gp. If we needed to match the Giza construction schedule, we might invest in three bards, resulting in 195,300 gp of labor-related costs to complete the project on the same schedule [1] [2] [3].

Potentially one could recoup half of the cost of the lyres after finishing construction, or alternatively one could build up a stock of a number of lyres and use them on many different projects while only paying the price once, but for the sake of conservatism I assume that the sticker price of each lyre is a fully sunk cost. Similarly, theoretically one could make use of various forms of compulsory or unpaid labor to avoid some labor costs of manual labor (since such huge work-forces are likely out of the reach of anyone but the government), but I assume that the labor cost is met fully.

8. Generalizing to generic structures

300 man-days per half-hour of labor, at the mortal bard’s rate of work (16 hrs) per week, means that the mortal bard constructs any given structure at about the same weekly rate as a team of 2,000 (1,920) dedicated Pathfinder construction workers working five-day weeks.

Our lich bard, or any other lyrist who can play without breaking, constructs any given structure at about the rate of 20,000 (20,160) dedicated construction workers, which, considering premodern logistics, might involve a total workforce substantially larger than 20,000.

Notes:

[1] It is worth noting that in our model labor costs do not rise from adding more bards, because two bards complete the work in half the time as one bard and thus each gets paid half. Costs rise linearly at a rate of 13,000 (one lyre) per bard, while the 156,300 is fixed (C = 156,300 + (13,000B) where B=number of lyre-equipped bards and C=cost).

[2] On the other hand, we can calculate how quickly we could build the Pyramid for the same 5.4 million gp in labor costs. As noted by Kain over on Dicefreaks, you can get 403 lyre-equipped bards for the same gp cost as it would take to hire a Pathfinder conventional labor force, resulting in a total assembly time of 1,563 bard-weeks / 403 bards = 3.87 weeks, or four weeks rounded up. Of course you may start to run into musician shortages at some point.

[3] Note that the costs of the construction workforce =/= total costs. You're likely on the hook for some architectural/engineering services at the very least. Your lyre may be able to assemble simple building materials that are locally available without further costs, but it's not clear on the subject, and even if so you'd have to cover material costs for fancier buildings, like an opulent palace of opulence.

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I think it may be time for my group to encounter their second lich bard.

In 3.5 Lesser Restoration's curing fatigue (which you get if you don't sleep) explicitly removed the need to sleep (some clerics in a module have devoted their second level spell slot to this so they can remain awake for a ritual). If this is the same in PF (no reason it shouldn't be) you don't even need the bard to be a lich if they are good enough to keep playing while fatigued for a bit.

Unless you are quarrying your stone from your pyramid, it's not happening.

You can only be in one place at a time, and your AoE won't even cover half of the construction site, much less the quarrying and transportation of the stone.

You're Lyre of Building won't avoid bottlenecks, it is a massive bottleneck that the Egyption's never had to deal with.

Wall of Stone!

Alternatively: Why not build your base at the quarry itself? Not like "middle of a desert" is that great a strategic position (I hope you're not using all that effort to build yourself a grave).

deuxhero wrote:
Wall of Stone!

You're going to cast <100 5th level spells/day to create blocks that are only 5" thick?

Quote:
Alternatively: Why not build your base at the quarry itself? Not like "middle of a desert" is that great a strategic position (I hope you're not using all that effort to build yourself a grave).

You're AoE is less than 1/2 the base of the pyramid (~740'x~740'x~418'). You are either quarrying the stone, following the group transporting the stone to the specific point of the pyramid under construction, or sitting withing reach of the area under construction.

Even if you build your pyramid literally on the edge of the quarry (not a good idea) you still don't have a large enough AoE to manage all of the above simultaneously. FYI - the limestone for the Great Pyramid had to be transported several hundred meters from the quarry. The Granite beams had to be transported over 900 km.

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I think with some planning, we can overcome the limitations on area of effect, but a wizard and an ape can take care of much of the labor given the right equipment.

Divide the 8 or 16 hour work day by how long it takes to assemble the individual pieces but subtract the time to quarry and transport the raw materials, and after a few days, I feel confident that a bard of even 12 intelligence or wisdom would know how to best spend his time (so that does eliminate some potential bards).

I also think the companion pieces from 2ndE would speed up the lyre of building. For example, the mattock of the Titans allows a huge creature to move 10 cu ft of stone per hour.

Let's find a huge bipedal creature with hands and have our bard charm monster it. Alternatively, let's play a wizard with level dips or feats enough to permanently cast enlarge person on his animal companion ape (who may or may not be awakened enough to use the mattock).

In one hour, he could quarry out a total of 10 cu ft of stone, but this does not have to be just one block of stone. Let's say he doesn't quarry out a 10 cu ft block, but quarries out 10 cu ft worth of stone around an even larger block.

With 1ft of stone removed on 5 sides of this block (this is assuming our quarry has one open face that is already removed, and not two, which would be more realistic), we could loosen up two separate blocks which are 10' by 10' by 10' in one hour.

But once we remove one block from its position, we now have another block which has two sides exposed, then each block after that would have three sides already carved out (one from below where we started, one from the side of where we started, and the original open face of the quarry). By adjusting the space between blocks slightly, we can remove four blocks per hour.

So let's talk about moving these blocks. They weigh 75 tons each (which is about 30 times the weight of the stones used at Giza) (figured at 150lbs per cu ft which is the medium density of limestone multiplied by our 1000 cu ft inside our blocks). Now our ape has 26 str (lvl 9 AnC, with both ability boosts in str), to which we adjust from large to huge, then add muleback cords, ant haul, and a masterwork backpack.

This nets (thank you Rimzy.net carry capacity calculator) a maximum load of 38,400 lbs, or 19.2 tons). So our ape will need some mechanical assistance moving the block. Enter favorable conditions from the carry capacity section:

"A character can generally push or drag along the ground as much as five times his maximum load. Favorable conditions can double these numbers, and bad circumstances can reduce them by half or more."

Now our ape can push or pull up to 192 tons worth of blocks (let's look to the Egyptians on how they gained their advantage by mounting the blocks on skis and scooting them across the desert sand). Moving two blocks at a time, the ape could reasonably move his one hour of digging in less than one additional hour, so one Ape-hour worth or manpower yields let's say roughly 200 tons of granite.

If the pyramid weighs 5.75 million tons (thanks Sciencing.com!), it would take 28,750 hours or 3595 8 hour work days, or 719 forty-hour work weeks, or 14 years (assuming a two week vacation) for the ape to move the needed materials.

This I think works well with the hours of labor that a skilled bard with the lyre can produce, cutting down on time wasted on the heavy labor, and freeing him up to walk around and play around the actual construction. But let's seriously give him a headband of intelligence +2 or +4 with ranks in knowledge engineering.

What's really terrifying looking at the numbers now is how this setup scales to power levels between roleplaying games and the actual power commanded by the Pharaohs who built the pyramids. Four dynasties and close to a millennia of territorial expansion and unspeakable human cruelty yields similar results to a 9th lvl party of a wizard, bard, and ape.

Let's hope their alignment is lawful good, or at least good, or at least not evil.

Yay math!
Oli

Oli Ironbar wrote:

I think with some planning, we can overcome the limitations on area of effect, but a wizard and an ape can take care of much of the labor given the right equipment.

Divide the 8 or 16 hour work day by how long it takes to assemble the individual pieces but subtract the time to quarry and transport the raw materials, and after a few days, I feel confident that a bard of even 12 intelligence or wisdom would know how to best spend his time (so that does eliminate some potential bards).

The point is, the Egyptians did not have to divide time, quarrying and transportation were ongoing during the entire construction time.

Even if you quarried all your stone in advance, which means zero labor being spent on the pyramid, you have to expend labor nearly equal to that required to construct the pyramid to store the cut stone in a meaningful fashion, which you cannot do at the same time the stone is being cut and transported.

You would need a dozen lyres + players just to manage the logistics side of the project. Logistics is where the limited AoE of the lyre completely fails.

In ten minutes, for one burn, a level 18 kineticist can create 18 10'x10'x10' cubes, using a crafting or knowledge engineering check to make it detailed, out of pure aether. Assuming you can make extremely detailed things with 18 ranks of craft: pyramid, this could be a really nice toy.

Assuming you can get to an easy 24 con after overflow bonuses by level 18 (34 is probably more likely, but let's play with low numbers), given that you probably have nothing else to put effort towards as a kineticist besides a little dex and a touch of int to use it all well, you can take 10 points of burn per day.

With 10 burn per day, this is now 1800 cubic feet of material to build with, on spot, permanent and free, and you can probably fly around with your telekinesis to see what you're doing easily. It takes you less than two hours of easy work, though it doesn't feel good thanks to the burn, every day.

I apologise, being at work on my phone with a headache I'm having difficulty following the post from Oli Ironbar regarding how many 10' cubes of matter we need to create this semi-visible, scintillating pyramid of force. If someone would like to dissect my little drop-off here, to determine efficiency? I believe at the lowest level of comparison, this certainly alleviates any questions of logistics from the event, given that he can still work his normal Profession: Rules Lawyer job 8 hours a day while undertaking this task, and it costs him nothing but the land to put the pyramid on. He needs no supply chain, outside aid, or equipment of any kind.

As one final note, the largest pyramid a quick Google search pulled up was 86,700,000 cubic feet. This did not account for any air/passages/rooms, it was a basic measurement of occupied volume. Divided by my 1800 cubic feet per day, 48,166.6r days of work. This now makes almost 132 years of effort, before any attempt to reduce the volume based on used space. If your pyramid is loosely half tunnels and rooms, half full stone, the level 18 not particularly optimized Aetherkineticist can pull off this crafting project in a surprisingly reasonable 66 years.

If you pushed for a more con-focused build, starting with an 18 built, and gaining +4 from levels, +6 from belt, +4 from wishes, up to 32 now, and getting a +6 size bonus to con from overflow. Now we're very respectable at 38 con. On top of that, let's be a Vanara, who have FCB: +1/3 extra burn per day over your normal limit. We now get 3+14+6, 23 burn per day. Actually... We might need to scale back that Vanara, I think we probably just passed out at some point. We'd have needed to average above a 6 on all our HP rolls, not impossible but let's back our daily down to 21. If we take toughness this is now great, we have about 18 hp to spare per day if we're rolling average. Talk about killing yourself for your art.

This is now 3,780 cubic feet of material in just at 3.5 hours, without being horribly unreasonable about how we choose to build the character (So far we've invested race, FCB, one feat, and chosen con as our best stat in a con based class. We also got a standard edition belt of con.).

22,936 days of work for the full volume, that's 63 years give or take.

So now it's very reasonable to accommodate a pyramid the size of the great pyramid of Khufu and just over half empty space from hallways and rooms in about 30 years as a level 18 kineticist, with nothing more than a plot of land and the will to accomplish it.

I object to the initial plan: You definitely want to give him an extra lyre. It's going to cost less than paying him to sit there waiting on the first one. A third will speed things up but not save you money. (This, of course, assuming the bard has to rest.)

Shiroi wrote:
With 10 burn per day, this is now 1800 cubic feet of material to build with, on spot, permanent and free, and you can probably fly around with your telekinesis to see what you're doing easily. It takes you less than two hours of easy work, though it doesn't feel good thanks to the burn, every day.

18 10'x10'x10' cubes, times 10, is actually 180 000 cubic feet. You just cheated yourself by a factor of 100.

avr wrote:
Shiroi wrote:
With 10 burn per day, this is now 1800 cubic feet of material to build with, on spot, permanent and free, and you can probably fly around with your telekinesis to see what you're doing easily. It takes you less than two hours of easy work, though it doesn't feel good thanks to the burn, every day.
18 10'x10'x10' cubes, times 10, is actually 180 000 cubic feet. You just cheated yourself by a factor of 100.

... Meet you in the middle, calculator says 10x10x10x18 is 18000, I missed one zero not two. That's what I get for doing quick maths while burned out tired. Since most other calculations were based on this, everything time-wise past that point goes up or down a zero. It's now very each to do this in less than five years, with breaks and not pushing so hard.

I guess that leaves you a lot of spare time to paint it dirt colored so it's not see-through...

You're still missing the fact that 10 burn gives you 18 x 10 = 180 of those 10x10x10 cubes. I meant what I said about cheating yourself by a factor of 100...

avr wrote:
You're still missing the fact that 10 burn gives you 18 x 10 = 180 of those 10x10x10 cubes. I meant what I said about cheating yourself by a factor of 100...

Wow I have got to get out of my slump. Okay, so in a horrific 6 months or so you can just build whatever you want, and in a single lifetime a half elven Aetherkineticist can probably manufacture a semi-clear New York. :/

deuxhero wrote:

Wall of Stone!

Alternatively: Why not build your base at the quarry itself? Not like "middle of a desert" is that great a strategic position (I hope you're not using all that effort to build yourself a grave).

That's what they did at the actual pyramid (and as alluded to in my note [3], the numbers in my OP are for locally available building materials). The limestone (the main building material) was quarried at Giza.

Volkard Abendroth wrote:
You're AoE is less than 1/2 the base of the pyramid (~740'x~740'x~418').

The lyre of building text is below, and you will note that the 300 ft radius effect of the lyre applies to the structure-protecting effect. The construction effect does not have an area of effect but instead limits its effect according according to units of construction labor. We're not interested in the protection effect here, so its radius is unimportant.

Even if you decided to houserule otherwise, the numbers in the OP are just ballpark numbers, and having to walk around while playing is not the type of constraint that would throw the numbers into a different ballpark.

(It's not an order-of-magnitude problem.)

Lyre of Building:
This magical instrument is usually made of gold and inlaid with numerous gems. If the proper chords are struck, a single use of this lyre negates any attacks made against inanimate construction (walls, roof, floor, and so on) within 300 feet. This includes the effects of a horn of blasting, a disintegrate spell, or an attack from a ram or similar siege weapon. The lyre can be used in this way once per day, with the protection lasting for 30 minutes.

The lyre is also useful with respect to building. Once a week, its strings can be strummed so as to produce chords that magically construct buildings, mines, tunnels, ditches, etc. The effect produced in 30 minutes of playing is equal to the work of 100 humans laboring for 3 days. Each hour after the first, a character playing the lyre must make a DC 18 Perform (string instruments) check. If it fails, she must stop and cannot play the lyre again for this purpose until a week has passed.

Quote:
You're Lyre of Building won't avoid bottlenecks, it is a massive bottleneck that the Egyption's never had to deal with.

Bottlenecks at a construction site occur when one portion of the work force is waiting on another part to finish its work before the first part's work can proceed. E.g., stone-cutters fall behind, so stone-raisers are left idle, waiting on the stone-cutters to dress more stones before they can raise them into final position. Or they have both gotten ahead of the quarriers. Whatever.

You implied that your criticism applies to the solo lyrist (because you suggest that using a dozen lyrists might solve the problem), but if we're considering a solo lyrist, I'm not really clear about who ends up waiting on the lyrist to do something and when.

I do agree, however, that if you are contemplating a project using special materials imported over a large distance, you will have to consider how you obtain those materials and likely make some special provisions for doing so, outside of the basic lyre stuff I have here, similar to what I say in note [3].

This isn't relevant to my numbers for the Great Pyramid because the granite that you note was transported over a great distance was used in a ratio of about 1:1000 compared to local limestone. It's just a specialty material used for the interior chambers and such, very minor compared to the overall pyramid. As such it's below the radar of my numbers, which aren't accurate to 0.1% and don't claim to be (if you're guessing I estimated ancient Egyptian productivity to within 0.1% or even 1%, go read section 6 of my OP and then guess again).

If a character were to embark on this in a game world they'd have to find a way to cover .1% stuff like this, but it's not going to double my bard's lyre time or anything so I'm comfortable neglecting it.

Ending with:

a) My note [3] in the OP is about building materials.
b) It's cool to read about magic-ape-based or kineticist-based alternatives to improve the specific logistics of material supply.
c) As noted under section 6 in my OP, I considered bottlenecks as a factor, and decided not to use it. Still, as above, I think that if I did use it it would cut in favor of the lyre and not against.

deuxhero wrote:
In 3.5 Lesser Restoration's curing fatigue (which you get if you don't sleep) explicitly removed the need to sleep (some clerics in a module have devoted their second level spell slot to this so they can remain awake for a ritual). If this is the same in PF (no reason it shouldn't be) you don't even need the bard to be a lich if they are good enough to keep playing while fatigued for a bit.

Yeah, it doesn't have to be a lyre-obsessed lich specifically. :)

Just thinking of a regular bard, I figure he won't really want to play a lyre 24/7 whether or not he's getting restoration shots to keep his body going, at least not if it's just work for hire. 16 hours at a time might be a conservative cutoff - a really motivated bard probably could do better and thus build faster, especially with magical help - but I don't mind being conservative.

It's certainly not a hard ceiling though, and the lich is only one example of a creature that might max out the lyre.