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Inspired by this other question: Suppose you did had "infinite" money, which is more than "all" the money, how fast could you build some impossible construction. For this question, let's assume a 100km tall pyramid on the south pole.

Disregard the usual economics of you having infinite money instantly deflating the money of others. In real life, with today's technology, is it possible to pay off every single person on the planet to come together to build it? The only motivation is monetary; the pyramid is definitely not to stop the summoning of Cthulhu or anything.

Notes:

  • The pyramid can be made of anything, from diamonds to carbon nanotubes.
  • Spare no expenses.
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    $\begingroup$ An "impossible construction" cannot, by definition, be built, no matter how much money you have. $\endgroup$ – KSmarts Apr 13 '15 at 19:35
  • $\begingroup$ I think such a thing could probably be built if it was just a steel skeleton, from progressively thicker to lighter layers.. $\endgroup$ – GrandmasterB Apr 13 '15 at 21:44
  • $\begingroup$ If you cut out money, You will still be limited by available resources, Time, Space, and limits of technology (need to know how and have precise enough tools to build something). $\endgroup$ – Tezra Oct 13 '16 at 15:40
  • $\begingroup$ Others have already elaborated on how you are still limited in resources, labor, laws of physics etc. I just want to point out that you cannot "disregard the usual economics of deflating the money of others". The limitation on resources and labor is the same as deflation, just not expressed in monetary terms. Your infinite amount of money just gives you access to a larger share of the still-limited resources, leaving less (or nothing) for others. BTW, it's inflation, not deflation. $\endgroup$ – Kevin Keane Jan 5 '17 at 8:26
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A little digression on money and what it represents
First of all, money itself has little value. We value money because our society has established it as an abstract representation for labor + materials.

Thus projects requiring expensive materials or lots of labor cost more money.

So how does this affect your question?

Assume Project X might be humanity's #1 goal and we might throw all sorts of labor at it.

  1. We have to understand that many many ordinary activities must continue (farming, water workers, road construction, etc.).
  2. Plus, we may want to transport unlimited materials for a project, but we have limited ability to transport materials.
  3. The project may require special materials (e.g. Platinum as a catalyst) and it will compete with other necessary activities that we are still doing.

During special times, governments have severely limited "normal" activities to devote more effort towards the "special" activities (think rationing during WWII).

So you saying assume infinite money, is the equivalent of saying assume infinite labor and resources. Which limits us only to what our current state of science says is practical.

The case of the Pyramid 100 km tall
Lets look at your case, a pyramid 100 km tall. Our materials and structural knowledge are immensely greater than ancient Egypt's. But I don't need to know the materials that we'd use in such a pyramid because I can look at the Earth for equivalent natural formations and find none.

Why is this?

Because under immense pressure, the Earth's materials flow like plastic. If you built a big enough structure, you'd cause the crustal plate it had been built on to begin sinking into the Earth (the concept is called Isostacy). As a very rough approximation, I'd look at the tallest natural structures and use that as the order of magnitude guess maximum size of man-made structures.

So perhaps 10km is doable given infinite man-power and resources but it couldn't get much taller.

Other Candidate Projects
I've also thought that megastructures on Earth weren't all that interesting, so I included some other projects that I'd expend our infinite labor and resources upon:

  1. National Aerospace Plane
  2. Cheap Space Launch Infrastructure
  3. Fusion Power Plants
  4. Interplanetary Spacecraft
  5. Space Colonies
  6. Space Elevator
  7. Interstellar Spacecraft
  8. Terraform Mars
  9. Terraform Mercury
  10. Terraform Venus

1. National Aerospace Plane
In the late 1980s I worked on the National Aerospace Plane. At the start, of the project, I felt that we could not such a thing. By the end, I had come to the conclusion that we could build it, if we sunk enough resources into it.

Estimated time to complete 5-10 years.

2. Cheap Space Launch Infrastructure
R&D and construction for Light Craft / laser launcher, Ram Accelerator, Light Gas Gun, or Coil Gun to launch objects into space cheaply.

Estimated time to R&D 5-15 years.
Estimated time to construct 5-10 years.

3. Fusion Power Plants
We still don't understand everything that we need to build viable fusion power plants but after 60 years of trying we are finally at least in the ballpark. At current project funding, such a plant won't reach scientific break-even for a decade or so. Within 5-10 years after that we might achieve engineering break-even. Economic break-even will follow sometime after that.

Unlimited resourced would speed this up significantly, perhaps halving the time it takes to finish.

Estimated time to complete 10-20 years.

4. Interplanetary Craft
Using current state of the art nuclear power and propellants, we could build space craft that would scoot to Saturn within months rather than 6 or more years.

Estimated time to complete: 10-20 years

5. Space Colony
Using the craft mentioned above, there are no theoretical reasons that we could not build, populate, and maintain colonies on many bodies of the solar system.

Estimated time to complete 20-30 years.

6. Space Elevator
Until about 15 years ago, space elevators weren't even deemed scientifically feasible. Oh sure, the required materials strength was within the theoretical maximum chemical bond strength of materials we knew (e.g. single crystal iron could do it), however, we didn't know of any bulk materials with the sort of tensile strength required for the project.

Then we discovered how to make nanotubes. Single nanotubes have the desired strength and light weight properties for a project like this. However, we still don't know how to make single tubes with a length of 48,000+ km long.

But imagine that we develop a method to grow the nanotubes in-situ microgravity. The main problem facing a project after resolving that issue would be the politics :(

Estimated time to complete R&D 20+ years
Estimated time to complete construction 10-20 years

7. Interstellar Craft
Some of the most advance propulsion schemes current known (e.g. Nuclear Pulse Propulsion [aka the old BOOM - BOOM], Fission Fragment Rocket, & Fusion Fragment Propulsion) to be possible would make manned interstellar flights possible. However, it would take most of the industrial output of the entire Earth for many decades to put it together.

Estimated time to complete 50-100 years to build
Estimated trip time 150+ years

8. Terraform Mars
Why stop with basic outposts when physics tells us what we need to do to make Mars a "shirt sleeve" environment. Use our interplanetary craft and begin playing Solar System billiards.

Shove smallish ice blocks from Saturn's rings so that they impact at Mars' poles. We bombard the poles for two reasons,

  1. We don't want to significantly alter Mars' rotation and
  2. Mars already has significant quantities of volatiles locked in its polar caps and any volatiles we liberate from the poles will reduce the quantities we need to move around.

While we're at it, ring it with solar reflectors to warm the planet up. It is the safe movement of the blocks of ice from Saturn's rings that takes all the time but we know of no reason that this can't be done now.

Needs to be warmed, $ H_2O $, $ N_2 $, and $ O_2 $.

After taking care of those physical and chemical needs, we need to inoculate Mars with biota that will create a biosphere we can live in.

Estimated time to complete 500+ years (but more likely 1000+ years).

9. Terraform Mercury
A more difficult project but one we could complete given enough resources and time. Move Mercury out to the current orbit of Mars. It is necessary to put Mars and Mercury in a cooler region so their atmospheres don't blow off too fast. Also, set up Mercury and Mars to orbit each other as the solar system's first true double planet (and it'll provide an amazing view!).

Moving Mars is done indirectly by means of a "gravity tractor". It takes a very long time to set up this infrastructure. Start by putting engines on a small sized asteroid (probably more than one) in one of Jupiter's Trojan points. Shove that asteroid on a course that slingshots it past Jupiter onto a course that takes it by a mid to large sized main Asteroid Belt asteroid (say Vesta). Use trajectories to alter Vesta's orbit so that it intersects Jupiter's. Ultimately, we want Vesta to perform repeated gravity assist flybys between Mercury and Jupiter. Mercury flybys will increase Mercury's momentum by robbing it from Vesta. Jupiter flybys will increase Vesta's momentum by robbing it from Jupiter. We'll use our small Trojan Asteroids as sheepdogs to make course corrections to Vesta.

Begin bombard it with ice from Saturn's rings as with Mars after cooling the surface. If you are skillful, the bombardment can also serve to spin the planet faster. Increasing Mercury's rotation (for the correct day/night cycle) may also significantly strengthen Mercury's magnetic field. Mercury already has a "strong" magnetic field (about 1% of Earth's) so its atmosphere will be somewhat protected from the solar wind.

Since at the beginning of the effort Mercury is too hot, and bombarding it with ice will add energy, it might be smart to provide it with a Sunshade to cool it off. If you are done with the Solar reflectors at Mars, just move them over and reuse them as umbrellas. If not, move them anyway but reflect light away from Mercury and towards Mars.

Needs to be moved, cooled, spun-up to a 24 hours day, $ H_2O $, $ N_2 $, and $ O_2 $.

After taking care of those physical and chemical needs, we need to inoculate Mercury with biota that will create a biosphere we can live in. Also by this time Mars' terraforming should be significantly ahead of Mercury's. It might provide a convenient base of operations for the Mercury effort.

This might allow us, in time, to have 3 inhabitable planets (Earth + Mars + Mercury).

Estimated time to complete 750+ years. I used approximately the same time to move as Mars, but I added some time to adjust the planet's rotation and volatiles - more likely 1250+ years).

10. Terraform Venus
A much more difficult project but one we could complete given enough resources and time. Since at the beginning of the effort Venus is way too hot and bombarding it with ice will add even more energy (and we won't be moving it away from the Sun), we must provide it with a Sunshade to cool it off. Assume you are done with the Solar reflectors for Mars (or Mercury) and just move them over and reuse them as umbrellas.

If we cool Venus low enough, it's $ CO_2 $ will freeze into convenient to handle blocks of dry ice. This makes ridding Venus of its excess $CO_2 $ "easy", just cut it up, load it onto a rocket, and launch it into space on something like the giant sized Orion which can launch 8,000,000 tons per launch. You could send some of it to Mercury and Mars to supplement those planets volatile inventory. I'm not sure what to do with the rest.

Bombard with water ice from Saturn's rings as with Mars. But like the terraforming of Mercury, use that bombardment to spin the planet up to a decent day / night cycle. I guess this means you bombard the equator with ice while you mine the poles for $ CO_2 $ and launch from there.

Needs to be cooled, spun-up to a 24 hours day, $ H_2O $, $ O_2 $, and $ CO_2 $ removal.

After taking care of those physical and chemical needs, we need to inoculate Venus with biota that will create a biosphere we can live in.

This might allow us, in time, to have 4 inhabitable planets (Earth + Mars + Mercury + Venus).

Estimated time to complete 1000+ years (approximately the same time to move as Mars, but longer to adjust the planet's climate - more likely 1500+ years).

What to do with Vesta when you're done? If you plan to do more Solar System billiards (e.g. Moving Io or Europa), then park it at one of the Jupiter Trojan points. If you're done with the Solar System billiards, then put it at a convenient point for Solar System infrastructure (that sucker is probably loaded with useful metals).

NOTE: I ordered these project based upon the time to complete the project. It will take longer to terraform planets than to build an interstellar spacecraft. However, I'm pretty sure the construction of an interstellar spacecraft would require more labor and resources - as in the entire world's industrial output for 50 or more years.

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Is it possible to pay off every single person on the planet to come together to build it?

Alas, not even close. Let's say you did manage it. How would you get them to the Antarctica? There simply isn't enough shipping to manage it. Furthermore, you'd need to devote a lot of what there is to provide support for those who do go. Food, water, shelter, etc. The South Pole is not noted for its temperate climate, and not many workers will accept a job which will kill them.

Furthermore, assuming the job will take more than a fairly short time, you have to leave a great many people behind to continue providing support. Somebody has to pump the oil and run the pipelines and run the refineries to provide the heating oil to keep the workers from freezing. And somebody has to run the farms to grow more food, and ship the food to the processing plants, and run the plants, and ship the processed food to the ships to send to Antarctica to feed the workers. And on and on.

There's an old saying:

Amateurs study tactics. Dilettantes study strategy. Professionals study logistics.

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  • $\begingroup$ I like that old saying, it seems like many things should be possible until you realize that there are other normal constraints, like food, water and fuel $\endgroup$ – grimmsdottir Apr 13 '15 at 4:48
  • $\begingroup$ You don't meed many workers though. Only a few hundred thousand. And if we're sparing no expense, chances are most anyone will take a 5 year contract if they get to walk away with $10,000,000 at the end. We know they'll be safe because we're spending a lot of money to make them safe. $\endgroup$ – corsiKa Apr 13 '15 at 14:48
  • $\begingroup$ As you say, we can't assume infinite money because that implies infinite labor and materials. We can't even assume all human labor can be used because we still need to feed, house, water, and medicate all of humanity. What we're really saying is something like careful rationing to ensure nearly all human labor other than simple sustenance is consume by the project. Who knows what that number is?! $\endgroup$ – Jim2B Apr 15 '15 at 0:24
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Interesting question. I gotta agree with WhatRoughBeast, in the sense that it's still going to be a logistical nightmare, but....

Did you say 100 km tall pyramid?

What is this pyramid made of? Just rocks like one of the original (edited) pyramids? Or more modern construction material?

Just for the sake of argument, lets say you wanted to create 100 km tall replica of the Great Pyramid of Giza. What would you need?

Architects and a realistic plan for scaling up at that level

Infinite money? Boom, done. Best architects in the world instantly hired.

Construction material

The pyramid of Giza had 210 layers of stones, with 2.5 Million cube shaped stones in total. Its only 146 m tall. I say only because 100 KM PYRAMID.

Just extrapolating height and number of layers, our replica will have 143,836 layers. Now to understand how many stones you'll need, we can't simply extrapolate. This is more of a volume issue. Enter hyperpyramid.

Sparing you the boring (and definitely ballpark) math, the number of cube shaped stones you'll need will be 803,306,796,361,084 or 803 trillion approximately.

That may take some time. Even if you want something simple like cubes of stone, where will you get that many? We're in the south pole right?

Giant Ice cubes? Ok. That might work. 803 trillion? Will take some doing.

Who will do it?

Laser cutters (as many as you can afford) to cut ice in comparable dimensions at high speed. I'd recommend predominant automation with oversight by human operators. Drones is the way to go for speed and precision.

Drones for cutting. Drones for carrying. Drones for installation. Humans for controlling drones. I reckon the number of drones will be under a billion (I know its ludicrous but stick with me for a bit). Can't be more drones because after a point you'd be spending more time making drones than making the pyramid if you just keep making drones. And even if you have unlimited money, you don't have unlimited manpower and natural resources. So a billion drones at peak operations seems to be a decent middle ground between batshit ridiculous and just plain ridiculous with unlimited money.

But drones bring another issue.

Power

You'll need extensive power generation and supply for this scale. I don't nearly have the expertise to imagine even loose ball park figures for the power requirements. I'm thinking at least a few dozen nuclear power plants, but feel free to correct me. But you'll be looking at a billion drones at peak operations with at least a billion personnel to provide for in terms of heat, lodging etc. You'd practically be building a country and an economy larger than - oh right infinite money.

Also:

People

At the center of your plan, will be people and concerns thereof. Engineers to maintain drones and ensure construction is in order. Architects for architect stuff. Medical facilities, food provisions, provisions for amenities like fresh water and cable tv. Internet. General communication issues in the freakin south pole.

Could you pay everyone to do it?

You could but what's the point? A lot of people would agree to come together do build it, but when you can build robots to lift heavy ice and place it perfectly, why hire people for it? Get specialist engineers and architects (with support systems) on site. Everyone else operates from the edge of Antarctica at drone factories. And by everyone I don't mean everyone because after a point it'll become counterproductive.

You need people to maintain supply chains (material has to reach Antarctica in the first place!). People who maintain supply chains obviously need people who supply goods that are to be transported, who in turn need food, lodging, utilities, medical facilities. This is a generational project, with requirements of specialized personnel (over a billion people on site remember?) Let the world be as it is, just re-focus everyone to chip in. A farmer continuing to farm is still critical for your goal. Let him be.

How long will it take?

At best? A few centuries. You'd initially build basic requirements at the site, drone factories, streamline supply routes, reorganize raw material procurement, food distribution etc. You'd design, test and build specialized drones for cutting ice and carrying it, installing it etc. If all goes smoothly my best guess is that you'd be starting construction with a few hundred drones by the fifth or sixth year.

By the seventeenth or eighteenth year I reckon you'd have a few hundred thousand drones at least, better models more efficient etc and most importantly, drones to build drones (remember all your energies are dedicated to this). Things should speed up around the nine to ten million drones mark, around the 35th year (there is no basis for that estimate, I must confess, but hey, drones making drones).

803 Trillion cubes. Ten million drones. If a drone can cut, carry and install a hundred cubes a day, you're looking at a billion cubes every day. You know how many years it'll take to build the pyramid at this rate? 22,000. So, more drones please.

Around the 50th year, you'll probably be looking at over a hundred million drones, with about 780 trillion cubes to go. At the hundred and fiftieth year, I hope you'll have half a billion drones, each capable of carrying and installing 400 cubes a day. Now you're talking.

600 Trillion cubes to go. Half a billion drones who are super efficient (best case secnario). That's 40 billion cubes a day. For 600 trillion cubes, that'll take 110 years. And as you make more drones it'll only get quicker. At my most optimistic I'd say you're done polishing and painting by the 250th year mark.

Congratulations. And this was with the most readily available resource at hand - ice. Imagine if you wanted to try diamonds. I don't think our planet has that much.

Any Alternatives?

Well, you could try just a fiber glass rip-off with only outer walls to make a hollow pyramid. But then that's not a real replica. And it'll still take you a few decades because the surface area of such a beast will still be insane. You'll probably need - Yeah. Drones.

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  • $\begingroup$ I think the last (as in previous) pyramid is of modern materials, not rocks. It's in Las Vegas. $\endgroup$ – JDługosz Apr 13 '15 at 12:11
  • $\begingroup$ @JDlugosz - Fair enough. But in my experience hypothetical scenarios work best with limited variables. The Vegas pyramid has glass (of various types I presume), steel, concrete, internal plans, ventilation, water supply and god knows what not. And that awesome light thing on top. The Giza pyramid utilized literally two variables - people and stone. I wanted to go for simpler extrapolation, and it still turned out to be a pretty complex estimate. Not sure how I'd even go about trying to extrapolate the Vegas pyramid. $\endgroup$ – Ambarish Sathianathan Apr 13 '15 at 12:18
  • $\begingroup$ Fine, but you meant "the original" not "the last". $\endgroup$ – JDługosz Apr 13 '15 at 12:20
  • $\begingroup$ @JDlugosz, yep. Editing now to reflect correction. Thanks! $\endgroup$ – Ambarish Sathianathan Apr 13 '15 at 12:31
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Logistics aside (It's only money...) is it even possible? It is only to be seen (presumably from space) so the material does not matter. Could it support its own weight? The shape works to our advantage, but even so any material will flow, shatter, or change phase with that much weight piled on it.

But, like the Roman Coloseum, it does not have to be the same material all the way up!

The top can be aerogel. Even with skeletal construction to just support a façade, the bottom will be in trouble. Go with the third option, change phase. Under the weight, the whatever-it-is will esist in a high pressure phase, and is chosen to be something that will support it, albeit in a plastic flowing consistency. Even without the toothpaste effect, the high-pressure material needs to be contained at the edges or it would explode outward by changing phase. The pressure must be contained on all sides.

So imagine a (substantial) thickness of wall material to, hold a pool of mantle. The weight of the structure above is placed only over the mantle pool, not on the walls. The woukd entail a cantilever truss as a lid for that bottom layer. (The weight over the extended part is low since the pyramid is sloping inward, and is designed to isolate the weight of that skin apart from the core).


Another idea: a tent. The central pole is 100km tall, and is the only part with a compressive load. The sides are framed out with wires that act as guy wires, and are in tension. Articles about space elevators indicate that carbon nanotube continuous filliment could handle that. The sides could be all wires close spaced to look solid enough, or it can be covered with a sheeting.

Now for the pole: it can be mase from non-physical material, like a fountain of magnets. Again, look up space elevators for a description of that. It offers the feature that the tent can be raised vertically after attaching all the lines, while on the ground. In fact, the lines can be extruded as it is raised!

So it is indeed possible, and much cheaper than you thought. Oh, and it will keep the Cthulhu away from The Mountains of Madness at the south pole, too.

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This is a pyramid scheme within a pyramid scheme

I'll take this to be the main question: "how fast could you build some impossible construction.", not this "a 100km tall pyramid on the south pole.", as it appears arbitrary and unnecessarily difficult.

The main limitations on the question are then: "is it possible to pay off every single person on the planet to come together to build it?" and "The only motivation is monetary"

So the question becomes: "Is monetary compensation enough incentive for all (or close enough to all) humans to be motivated to build something that is possible to build only with the cooperation of (effectively) all of humanity, but is otherwise impossible to build?"

The answer, I believe, is "Probably".

As other questions have pointed out, Logistics will still be key, workers at all levels of the actual construction of the [whatever it is, regardless of size] will need to be clothed, housed, fed, provided with materials, etc. So even if all of humanity is contributing, they cannot all be construction workers on the project, they'll have to contribute in other ways.

Now, as for 'monetary compensation', the issue with inflation is caused by everyone having a lot of something (in this case money), so no-one wants that something that others have, because they already have their own. If everyone has hundreds or thousands of pieces of paper that have the number 100 and the word Dollars on them, why would they want more of those same pieces of paper from someone else? The reason anyone might want those pieces of paper now, is because they believe they can trade them for something that will improve their quality of life. So as long as the compensation comes in a form that improves the quality of life for everyone involved, there should be no reason it wouldn't be enough of an incentive. In other words, if their life is made significantly better by participating in this project, and to a degree that cannot be matched through any other career option, through the compensation provided, why would anyone refuse? In this sense, the term "monetary" might be stretched to resemble something closer to a barter system, but I think it still fits within the realm covered by the question. Payment would be made in the form of whatever the receiver most needed or desired, and obtained from whoever had more than they needed/wanted of whatever it was.

Basically, it's a utopia. Providing better quality of life for everyone becomes part of the logistics of supporting the actual workers on the construction, while simultaneously serving as payment to all of humanity involved.

To address how fast it could be accomplished, I'd say "VERY VERY FAST". Here are some examples of just how fast humans can already build big stuff. Granted, it's nothing like the scale this question is talking about, but assuming everyone on the planet was motivated to this project, I see no reason why the worlds best project coordinators wouldn't quickly identify the worlds best construction and planning and design experts both for speed and quality, who would then quickly identify the equipment needed, where it could be obtained, and so on. With the best of the best at the top levels of every aspect of the project, and hoping to complete it as soon as possible to start actually living their 'improved quality of life' by avoiding conflict among themselves, I see no reason why a project like this should take more than 'few' years (exactly how long is not something I know enough about logistics to estimate, but I'd be surprised if it reached a decade).

Now the problem is convincing everyone that you can actually provide them that payment, in order to get the project started, is another question ...

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