# If everyone in the world disappeared except 35 random people, how long would it take for one of them to realize they're not alone?

Everyone suddenly disappears from earth except 35 people randomly scattered wherever they were before everyone disappeared. How long would it take on average for 2 or more people to meet? What other factors would indicate to a person that they're not the only person who didn't disappear?

• I don't have the maths for this, but could the ideal gas law could be used to answer this question ? 35 molecules of gas, in a container that represents the land area of earth ? Aug 22 '18 at 19:37
• A few key questions: 1. Do the people know that there are 34 others on the earth? 2. Do they all have the goal of finding another person? If so, what is their motivation? 3. Are all the people involved guaranteed to be rational adults, or is it possible that they may be children, or mentally disabled? Aug 22 '18 at 22:41
• There is a xkcd What If? on this : Lost Immortals. Unfortunately, only available in the book. But it asks "If two immortal people were placed on opposite sides of an uninhabited Earthlike planet, how long would it take them to find each other?" The easiest solution proposed that doesn't involve leaving a trail of markers (but does rely on both people being on the same continent and using the same strategy) is to walk the coast line until you encounter each other. If you make a full circle without seeing someone, flip a coin to decide whether to change direction. Aug 22 '18 at 22:42
• @Legisey That question has 75,000 survivors, this question has 35. That's a very important difference. With 75,000 survivors, people would find each other rather quickly. Aug 23 '18 at 17:08
• @Criggie - That assumes that they're just wandering around aimlessly rather than a) Heading for major landmarks and cities and b) Using radio signals to spread the word of their location to others who might be listening Aug 23 '18 at 21:12

Assuming that it's purely random, let's consider where these people would probably be. Taking the percentage of the population each country represents, we get:

• China: 18.2% = 6.37 people
• India: 17.5% = 6.125 people
• America: 4.29% = 1.5 people
• Indonesia: 3.43% = 1.2 people
• Pakistan: 2.78% = 0.93 people

...etc. The percentage keeps going down. This means that roughly 6 people will be in China and India, each, and then the next 7 countries or so will probably have 1 survivor each (maybe 2 for America). The other 15-16 survivors would probably be found somewhere in the next 25-30 countries (as the probability of having any survivors approaches 50% or less).

So really, our most likely candidates for people meeting each other are China, India, and Europe (9.83% of the population as a whole for probably 3, maybe 4 survivors).

For India, 72.2% of the population lives in 641,000 rural villages, and this population is pretty evenly distributed, meaning 4-5 of our 6 survivors are probably located on a unique patch of 650-820 thousand square kilometers (3.2 million square kilometers divided by 4-5 people). This means they could walk for 800 kilometers in any direction, and never see each other.

The only real chance that they'd ever find each other would be if they all decided to go to the same major city. But which one to choose? There are 53 cities in India with over 1 million people, and at least 8 with more than 5 million. Would someone in the populous region of Bihar go the 1300 km to Mumbai, the biggest city, or the 800 km to the capital of New Delhi? If you go to the wrong city, will you travel another several hundred km to a different city and hope your luck gets better? Most people are more likely to go to ground, either before any travel, or after failing to find someone after travelling once.

And even if two people, by chance, happen to go to the same city, it would be rather unlikely that they'd run into each other. Let's take Mumbai, for example. It has an area of 603 square km, which increases to almost 4400 square km including the metropolitan area. This means that two people would have to run into each other in an area that is roughly 25-70 km across and deep.

Chinese survivors have the advantage in that their population is concentrated in cities, but with a maximum metropolitan area holding only about 3% of the population, the survivors are still likely to be scattered all across China, or at least the eastern half, which still has an area of about 4 million square kilometers (greater than that of the entirety of India). The issues with choosing a city are also present for survivors looking to migrate, as Shanghai, Nanjing, Beijing, Hong Kong, Guongzhou, etc. are all major cities.

For Europe, this only gets worse. The area expands to 10 million square kilometers, and unlike India or China, which have their own capitals that could act as a rallying point, each country in Europe (which would probably have at most one survivor) would probably attract survivors to their own capitals. A single German survivor, for example, would likely head to Berlin rather than Paris.

So in summary: most survivors would probably be scattered over an incredibly vast area (hundreds of thousands to millions of square kilometers for a single person); if they decided to go to a big city to intentionally look for other survivors, there's a good chance they'd go to different cities than each other; and even if two survivors both decided to go to the same city, finding another person in even the same city is rather unlikely.

• Interestingly, as a European, I'd probably head south in such a situation. With no other survivor in sight, I would be very wary of electricity/fuel running out, and aim for a warm winter: South of Portugal/Spain/Italy would be easier to survive than freezing Berlin. Aug 23 '18 at 9:31
• In short, leaving technology aside, they would probably all be dead before that happens. Aug 23 '18 at 11:18
• Several of the 35 would likely be in transport during the disappearance (a passenger in a car, train, aircraft etc.) and so would almost certainly die within a few minutes. Then take away the elderly, children, disabled and pregnant people and you might end up with less than half of the initial 35 people to even make a start. Aug 23 '18 at 11:35
• And while you didn't attempt to offer and explicit calculation of probability, it's probably worth considering that in this scenario, once any of these people manage to find a decent stockpile of resources, they are then highly disincentivized to travel from then on. As your take assumes they are even actively looking, but there's a good chance they'd all very quickly come to the conclusion that they are alone, and give up looking. Aug 23 '18 at 14:36
• Random distribution doesn't imply uniform distribution: I think you're ignoring the birthday paradox. Quite apart from that fact that it's highly unlikely such a destructive event would be truly random in the first place. You would end up with clusters of survivors. Aug 23 '18 at 16:10

## It's HF radio, or nothing

The odds of anyone meeting again are almost exactly equal to the odds of at least two being either radio hams, or able to learn the skills from books.

The population density of 35 people worldwide is so extremely low that the odds of finding someone without the benefit of global communications is practically zero.

Strategies like finding a printing press and posting thousands of fliers in different cities are a bold try, but they are hopeless: they fail to grasp the massive scale of the task. You could distribute 100,000 fliers in each of a hundred cities: and your odds of finding someone are still very, very long.

So it's global comms, or nothing.

Internet comms could work, but you have a matter of at most a few days to sort yourself out before the system fails. Act quick: find someone, somewhere, amidst all the autogenerated cacophony and BS, in the next three days. Time's up.

HF radio, on the other hand, is highly resilient, extraordinarily efficient global communication system. It can remain operational until you run out of spare parts -- the power requirements for QRP operations can be met by solar, batteries, or even pedal generators. There are standard hailing frequencies, standard protocols. Including standard protocols for global catastrophes. You might not make contact the first time you try, but if you keep trying, it approaches certainty.

Yes, HF radio is a skill. But you have the rest of your life to learn it, or die alone.

• Totally agree with this. I'd say it is pretty common sense to learn HF radio, and with 35 people, at least several will realize its importance. I think there is at least one other approach though, probably to use in addition to radio... Learn to fly a plane and start dragging advertising banners over all the population centers you can get to. Anyone looking for other survivors will almost certainly be heading towards the big population centers. Aug 22 '18 at 17:09
• HF radio gives 2-way communication; but one-way communication can be done through many methods. As an example, cross the country lengthwise with a fuel truck and bulldozer and fuel pumping gear, clearing a highway: takes (say) 10 years, but (A) you just made a lot of noise (which could be heard over a long distance), and (B) you left a really obvious trail. Leave HF radio instructions along the path of destruction. Now anyone crossing the country/continent gets a 1-way message from you.
– Yakk
Aug 22 '18 at 17:13
• @BlackThorn Learning to fly a plane without an instructor is difficult and dangerous. We want our survivors to survive. Aug 22 '18 at 17:29
• It's worth noting, though, that you'd need to even know where an HF radio is and/or be able to recognize it when you see it. Plus you'd need to power it (does it have a battery? Has the battery corroded before you get to it?). I doubt most people would have any idea what they'd be looking for. Most would probably try to go to a TV station or something, and try to use the equipment that requires a power grid and an active network. Aug 23 '18 at 3:25
• Maybe the people find each other because #StillAlive becomes the only trending hashtag on Twitter? ;) Aug 24 '18 at 1:23

This is an interesting question.

Obviously, just walking about and hoping to meet someone is fruitless, the chances are just ridiculous. What you would want to do is communicate. Now we know how many people survived and what the likely distribution is, but they do not.

From the perspective of a survivor, everyone around is suddenly dead or disappeared. Unless you are criminally stupid, your first thought will be about survival. Short-term that is not a problem, go into an empty shop and take what you want. Mid-term you are down to canned food. Long-term, you are going to have a serious problem.

So you want to get to a city edge and set yourself up there - with both farmland and supply depots (aka supermarkets and other shops) within reach. That also means that - at least at first - the city center is just a quick drive away, provided that whatever catastrophe took everyone else left the roads useable. Since you don't know if there are other survivors and how many, you would pick a landmark site, something others would think about as well, and post a written notice there. This is easy, low-cost and thus something that makes sense to do "just in case", even if it is fruitless you didn't invest much.

You would also post on FB, Twitter or whatever websites your frequent, just out of habit "hey guys, what is going on?" and for the same reason - it is easy.

Most of the answers so far assume too much knowledge and thus targeted activity on the side of the survivors.

The Internet would probably be down by the time you start any targeted activities, as pointed out in other answers.

Your billboard notice is a gamble, but you don't know the odds. It is, however, the most likely thing to work, as it is intuitive and doesn't require to people to be in the same place at the same time. Especially if people go roaming, there is actually a reasonable chance that they would meet. Let me explain:

Once you got the survival thing down, you are left in a world with plenty of cars and practically unlimited fuel - for a time. Current fuel goes bad in about a year, and the cooling etc. required to keep it longer will fail together with the electricity. Once you realize that a) there are very few other survivors, if any and b) survival alone is much more difficult than in a group, the logical next step is a game of "what would the others do?"

And I believe it is trivially obvious that everyone would head to the nearest largest city. The capital. Leave a message there, in a central place. In Europe, you would take a car and drive to Paris, post your notice at the Eiffel Tower. Then drive to Berlin, post at the Brandenburger Tor, and so on. Invite others to leave their messages so you know someone else is alive and then POST YOUR ROUTE. Make it a circle through the 5-6 major cities in the area and drive it two or three times. You can easily cover the distances (again assuming roads are free) in 1-2 days. You can do this early when supplies are not yet an issue.

If after 3 or so rounds you see no notices and nobody waiting for you at the next stop, assume the entire area is empty and go elsewhere. If you start out in the Americas, good luck. If you start out on an island, go farming and enjoy the rest of your life.

• If the internet is still working, so will twitter bots, so seeing "hey, someone is still posting on twitter, there is life!" will not work. Aug 22 '18 at 10:35
• +1 for the "communication" option - but you don't seem to have taken into account Radio. Most cities have a Radio station that can broadcast on standard frequencies (AM or FM), but you also often have Amateur Radio gear in city halls or council buildings (for example, in England, most Council buildings will have a room with emergency gear for Raynet use) - and, with the right setup you can get a signal to pretty much the other side of the world. Of course, this assumes any of the other 34 bother tuning in... Aug 22 '18 at 11:03
• Yes, I am ignoring radio. It requires that the recipient is listening to the right station at the right time in the right area. Unlikely.
– Tom
Aug 22 '18 at 11:25
• Not to mention the vast majority of people probably wouldn't know where to go, or how to use the equipment, and without the power grid, you'd need to use some kind of portable generator that would likely burn through increasingly valuable fuel supplies. Aug 22 '18 at 11:27
• @Tom: I disagree. It is a long way from certain, but the odds are far better than any other method proposed. Basically the question comes down to "do at at least 2 of the survivors understand radio communication?" If they do, then eventually finding each other approaches certainty: there are only a limited number of "hailing frequencies", and many systems have the ability to "beacon" continuously. For example, a standard hailing frequency, broadcasts once per minute "Listen here at 0:00 GMT to contact another survivor. Current time is 03:24 GMT." Aug 22 '18 at 12:31

(This answer supposes that electricity and the internet survives for a day or two)

Either a couple of days, or many months, if ever.

## Hello!

Everybody in the world has disappeared. Considering that you are reading this, electricity, the internet, a search engine, and Stack Exchange must still be working, and you had the state of mind to search for "why has everybody in the world disappeared". Congratulations, there is hope to reach other survivors. The fact that you can read this means that The Event must have happened very recently. Once it's down, everything will be so much harder.

#anybodyoutthere
#有别的人吗
#क्यावहाँबाहरकोईहै
#alguienporahí
#هلمناحدفيالخارج
#ilyaquelquun


(Please edit my question before The Event happens to correct the hashtags, in particular for Chinese, Hindi, and Arabic, and replace them with a more colloquial phrase)

And describe where you are. Please confirm that you have read this message. Translate your message and the hashtag with Google Translate in the most common languages. Continuously check Twitter to see if anybody follows suit.

Learn how to produce electricity with solar panels, and how to operate radio, if you don't already know how to. Initially you may be able to use the internet for this, but seen you'll have to raid a library for this. See Securigers answer for more on radio.

If you manage to reach people this way, discuss together what to do.

If you don't, it's time to start travelling. Try to drive a car, even if you don't know how to. I don't know if the roads are accessible, but there should be plenty of cars with fuel available. If you can't refuel, switch cars whenever you run out of fuel.

If you are in Eurasia or Africa, please all head to the Eiffel Tower, Paris, France Baiyun Mountain, Guangzhou, China. Probably half of survivors live within this circle and Guangzhou is right in the middle of it. From Western Europe you should be able to drive there in around 3 weeks.

If you are in North or Central America (anywhere north of the Darien Gap), please all head to Boulder, Colorado, United States.

If you are in South America, please all head to Christ the Redeemer in Rio de Janeiro, Brazil.

If you are anywhere else, I hope you'll be able to navigate a boat to any of those continents.

During your travels, please pass by as many major urban landmarks as you can, and leave many traces. This is not the time for practising wilderness ethics!

I hope there are fellow survivors. If there are, they may also find this message. I hope you will reach each other.

If you find each other before the internet goes, you might know about each others survival in days. Otherwise, it may be many months, or you might never realise.

Good luck. I don't envy you.

• Comments are not for extended discussion; this conversation has been moved to chat.
– L.Dutch
Aug 23 '18 at 18:27
• This is assuming the distribution of who magically get to stay is uniform. I don't see any reason why it should be. Aug 23 '18 at 19:56
• @mathreadler There is no such assumption in my answer. What makes you think there is? Aug 23 '18 at 20:20
• "Probably half of survivors live within this circle and Guangzhou is right in the middle of it.". You are assuming total randomness is per person and not for example per area of the globe or whatever other distribution it may be. Aug 24 '18 at 0:54
• @mathreadler The question says "randomly scattered". Unless otherwise stated, a uniform distribution is the most generic and therefore the default assumption. Aug 24 '18 at 8:55

I figured, since a lot of people are bringing up the Birthday Problem, I'd add a separate answer just for discussing it. Simply put for those not familiar with it, the idea is that based on probability the actual number of individuals needed within a sample before overlapping becomes nearly certain is far less than the actual number of possibilities.

The original problem discusses how many people you need in a group before you are almost certain to have two people with the same birthday. Obviously 366 people means that it's 100% certain (discounting leap years), but 70 people gives a 99.9% certainty of at least two people having the same birthday, and even just 23 people gives roughly a 50% chance.

So let's apply this to the current problem. The first question, though, is how we should divide the world to check it. The most logical way to do this is via population samples, since geographical area obviously won't have equal weight due to variable population density. Let's use 40 million, as that's around the size of most of the largest metropolitan areas of the world (Tokyo, NYC, etc.). Given 7.6 billion people, this would give us 190.

Using a calculator, this would give us a surprisingly high 96% probability of at least two of our 35 people sharing the same population segment. Now, this may seem impressive, but one must consider that 40 million people is the population of many Indian states, or any 2-30 American states (with a few exceptions such as New York or California). "There might be two people who are both in California" isn't too helpful, "There might be two people somewhere in the American Midwest (sans Illinois/Michigan)" is less helpful, and "There might be two people in all of Canada" is even less so.

So let's reduce our search to within a unit of 10 million people. That's about the same as Tokyo proper or all of the country of Greece. Now it's a little more specific. Reducing our population by a factor of 4 increases our number of sections by the same. So now we have 760 possibilities. This brings our odds to about 55%. Still larger than might be expected, but it's now a coin flip as to whether anyone is in the same city proper, or section of a populous state.

Now, that's not to say that it's a coin flip whether someone is in the same population sample as any other given person. If you were a survivor, it would not be a coin flip that a second person in 10 million also survived in your area, but rather a coin flip that there is a second person anywhere. There's a 16% chance that a second person is in the same 40 million original population section as you (1-(189/190)^34), and 4% chance that there's another person in your own sample of 10 million.

Now, though, let's consider this by area. For example, if by "randomly scattered" the OP means "picked up and dropped in random locations". (The Birthday Problem requires equal probability, so this approach isn't really applicable to realistic distributions.) Given roads and long views in rural areas, let's consider the world to be one fifth as large as it is. This helps reduce the effect of deserts, mountains, and other boundaries, as well as the effects of people travelling on roads. (Let's call this our "scaling factor")

So we have a land area of around 150 million square kilometers, reduced to 30 million square kilometers from our scaling factor. Let's say that you can find someone within 30 kilometers, about the size of a large city, when they fire a gun, honk a car horn, etc. This gives us an area of 900 square kilometers to locate someone within. Let's call it 1000 to make things nice and even.

30 million over 1000 gives us 30,000 land units. The odds of two people both "spawning" in any single land unit of 1000 square kilometers would be about 2%. This is actually surprisingly high, but still means that it is unlikely that anyone would start within 30 kilometers of each other. Though the odds of two people "spawning" within 100 kilometers of each other (about 10 times more area) is actually only about 18%, which is amusingly high. Though again, this is anyone, period, not the odds of a you having a partner in your 100x100 km area (which would be around 1%).

• Well, interesting but let me challenge your answer a bit. If you split the population by areas of the same population will be in a single city in one are and in a vast area in other.What composes of a singly city can become Shara, Siberia or tundra in Canada. Now you suggest that being in the same population cluster makes yourself physically close - well not necessarily and the probability that the cluster in which there is more than one person is a dense one is again just few percent. Regardless of that it's a nice answer ;-) Aug 22 '18 at 10:22
• I didn't say that it would make people physically close. Actually, I said just the opposite. I pointed out specifically that 2 people both ending up in Canada would likely be hopelessly far apart. That's the reason why, in the second example, I reduced it to 10 million to at least somewhat reduce the problem. Aug 22 '18 at 11:10
• Yeah, just it doesn't reduce the problem a bit ;-) Looking at the second part of your answer, there is just 2% chance that there are two people who are no more than 30 km apart. They may or may not seek each other and they may or may not seek in the same direction/manner. So I would say it's much more up to the strategy taken during the search than the position of specific people. We can safely assume that only if the search strategy taken by let's say 10 people will allow them to have at least overlapping 20 visited places then they are likely to meet or at least find out about each other Aug 22 '18 at 13:11
• "... randomly scattered wherever they were before everyone disappeared." The analysis in your first answer is more apropos than randomly placing people around the entire world's land masses. Aug 22 '18 at 21:20
• @Drazex yep, understand that :-) But all the consequences of your calculation might not be clear to someone who is not that familiar with math (especially probabilistic). One might think - oh, there are cities that are 10 mln large and there is 55% chance there will be two people in that city(). Wow, they *will find each other. (*)Only they may be in a different 10-mln cluster that spans thousands of kilometers. You may consider making that more clear ;-) Aug 23 '18 at 7:23

With only 35 people left, nobody is left to monitor the electricity powerplants and perform the recurrent operations (like refueling or manual checks) that are part of any plant, so most plants will automatically shutdown within hours, and with them all modern communication means. So here is an answer that assumes there is no phone/Internet/etc.

A common survival technique is to find a river and go downstream, until you find either someone or the ocean:

If you can't make out any signs of civilization, look out for rivers or streams. Head for those streams and follow them downwards. It is highly likely that you will find civilization downstream.

Among 35 people, many (A) will come up with that idea after a few hours or after a few years, and at least try once after finding nobody in their nearby cities and in their country's capital city. I am not saying everybody would immediately do it, but many would certainly try it. Even with GPS not working, following rivers is relatively easy. Most inhabited regions have roads along rivers.

There are many rivers that throw their waters directly into the ocean, but the great thing is that some rivers have huge drainage basins:

There is a reasonable probability (B) that two people are in the same drainage basin, for instance in the Ganges (India/Bangladesh). If these two people go downstream and leave messages once in a while, they have a non-negligible chance (C) of walking through a place where the other has or will walk.

Most the people will intentionally or not leave hints after their passage, for instance if I went along this river I would try to write a message on that tree or on the white wall of the riverside building in the background:

Via these messages the two people have a small probability (D) of eventually finding each other.

My estimate:

• A: 50%
• B: 30%, math pending
• C: 30%, rather low because: 1) Rivers have two sides 2) Some rivers have complex estuaries 3) Detours for food/etc
• D: 20%

Result: 1% chance. Which is not that bad.

Note:

• How will people be able to walk long distances? No planes nor trains, of course, but we have to remember that these people have the remainder of their lonely lives in front them, so they have time plenty of time to find a house left open (people have disappeared, including those who were at home, and a large fraction of them probably did not lock all doors), and borrow the car keys hung on the keys rack behind the door, check how much gas is in the car, and find another car this way when fuel is low. Nearly each petrol station has fully-fueled vehicles with its keys on the floor near the cash register. The smart ones will find a good bicycle and put it in the car, or even figure out how to get jerrycans and how to use them. Unfortunately, gasoline goes bad after half a year, so after that people who have not figured out anything smarter will have to rely on bicycles again.
• Not bad, but I'd look for more sources to aid your numbers. Most of them just kind of come out of thin air. For example: (A) I'd say that far more people would look for landmarks rather than following rivers, especially going to their nearest big city. Rivers don't have a huge impact on most people these days. Additionally, those are the major rivers. What about minor rivers? I live right next to a river. I might follow that down to the ocean, and then wait for anyone of the <1 million people near that river to come. The next river a few kilometers over would have the same problem. Aug 22 '18 at 9:18
• Nice answer, but let me challenge it. This is a survival technique but used to find a civilization. The problem is once you reach it it no longer brings value. If you're in a city an there is no one why other city should give you more opportunities? Then you look for a strategy to pick the best city and you don't need to follow a river anymore to do that. Aug 22 '18 at 10:37
• @Drazex That's what classification is for. Don't kids learn that in school anymore these days? Drop me in a good library and I'll find some relevant books within hours. With those as a starting point, I think I would eventually find the relevant hardware, too. Aug 23 '18 at 11:19
• @Drazex I very strongly suspect that a good library will have books with very practical information on operating radios, a technology that long predates the internet, a 40 year old guidebook is still useful. They might also have archives of amateur radio magazines, might find names of prominent members, I'd break into their homes to search for more clues. It will take perseverance, of course, but I think it's entirely doable. Aug 23 '18 at 11:39
• Gasoline may deteriorate in quality but it definitely doesn't become useless in just "a few months". You'd be able to drive for at least a couple of years. Aug 27 '18 at 16:14

Given the scale of the Earth, and a purely random distribution, the odds are negligible that they would ever meet. Each person would have 4.2 million square kilometers of land to themselves, on average.

• Uniform population density isn’t a reasonable assumption to make, I don’t think. I agree with your answer: even if you assume the whole world population is only concentrated in cities the chance of two people sharing the same city and then meeting somehow is very small. Aug 22 '18 at 5:52
• Agreed, based on population distribution, other than China, India, and maybe America, it's unlikely that anyone would be in the same country, let alone the same city. Aug 22 '18 at 6:11
• @JoeBloggs time for a monte carlo simulation. Aug 22 '18 at 16:48
• Well based on this answer, what if we scale the problem down to a small-ish area. What are the odds 35 people would find each other if they were the only ones left on Earth and they were all located in Manhattan? Or if they were all located in Los Angeles county? Aug 22 '18 at 19:40
• @Drazex Agreed. I get a 44% chance that 2 or more people would remain in the US, a 35% chance for Indonesia, 25% for Brazil, 23% for Pakistan, and so on. China and India are ~ 99%. Aug 23 '18 at 14:44

To realize they are not alone will depend on the people, the technology available to them and the knowledge of the internet or communications. Assuming they are distributed across the world and no one is physically close to each other, they will still be able to contact each other online. Websites or online forums like Reddit, Stack overflow might be easier, since you can directly post and you will be the newest thing, while other social media websites like Instagram or Facebook will be a bit more difficult, as they show things you are interested in or related to and hence you may never meet online. There are also other options like forcing your search to be number 1 on google trends, which wouldn't be too hard or looking to see if there are any new articles or information out after the date (you will have to be careful of bots, but there are plenty and you will probably think they are real people anyway). (Several hours to several days).

Depending on their knowledge, they may also try and find and use/modify communication devices to broadcast to everyone they can. Things like Radio, TV or Satellite can allow them to send out a signal and hopefully someone else is listening in on them. Maybe they are a journalist for a newspaper and publish an online article. There would be lots of options. (Hours, to weeks).

Finally, you might get a couple of wanderers who will travel across the country and continents looking for anyone else. You would leave signs behind to signal that you exist and where you are heading while you travel. (Months, to years).

So down to your question, how long will it take for 2 people to meet? Well it depends on how far away from each other they are. They need to be able to travel to each other so your time frame starts at instantly (the person happens to be in the same room), to several months (Via ship over the open sea, but only if they know how), to several years/never (aka time to learn how to fly/sail and try it out). Of course this all starts from after they discover each other and confirm they are actual people and not hot singles in your area.

So if you wanted an average time, I would say around 5-7 days. If you think about it, over 30% of the worlds population is in china and india and over 50% in asia. There is a very high chance that 2 or more people will be in the same country and once they link up they should be able to get to each other fairly quickly by driving (You can cover several 100Km's a day by driving and there will be no one to enforce speed limits or stop you from stealing a fancy car and fuel).

• This would require these things to still be running. A post on straight dope suggests that the power grid would fail within a week. Further, what website do you use? A relatively small fraction of the population uses any single website, and many of the widest used ones (such as Facebook) are network-based. Something like Reddit would be more likely to reach others, certainly, but not guaranteed, especially with language differences. Aug 22 '18 at 6:06
• Further, how many people do you know that could use a radio to contact someone else? How many people even know how to get a radio that can broadcast to others? The average person is likely to be entirely separated from communications technology, and given an average of hundreds of kilometers apart (at least), a lot of short-range devices probably couldn't reach. Aug 22 '18 at 6:08
• While internet is still running, people may go on a mission to visit every popular website which allows comments or contributions from public, and do two things: check for newest postings and live own message. Aug 22 '18 at 7:35
• Even assuming that most of the few dozen survivors find a way to communicate with one another, most will be in asia, some will not speak a language the others can understand, some will be trapped alone on an entire continent to themselves while others could make a road-trip to meet up. Imagine being the one person stuck in australia and nobody has a boat or the skills to sail it there, let alone fly a plane safely. Even in the best-case that everyone quickly establishes communications with one another and can talk, there are going to be people trapped alone. Aug 22 '18 at 8:17
• The top search idea is really interesting. It suggests that Google is inherently designed to react to a natural disaster. If there were a massive flooding, anyone going to Google to seek out information on the flood would see that other people are also searching for information about the flood, since it with be the thing most people are searching for. So if only 30 people are left, searches for "where did everyone go?" and "am I the only one left" would quickly be the top search (assuming Google's algorithm gives significantly more weight to recent searches over volume of searches, etc). Aug 22 '18 at 19:35

The Earth has a surface area of 196.9 million mi² (510.1 million km²) (land mass only). On average, that means each person will have 4.8 million mi² (14.6 million km²), which is equivalent to a square 2203 mi (3818 km) on each side. That's roughly the distance from New York City to Los Angeles.

It is enormously unlikely that anyone will ever meet another soul before they die if they were uniformly distributed.

The best hope for this argument is that people are not uniformly distributed. 55% of people live in urban areas. These urban areas cover 3.5 million square kilometers. This means that 19 of your 35 people will likely be from these urban areas, with only 184,000 square km to each -- a square 429km in length. That's a bit more than the distance from New York City to Washington DC. Now we're getting somewhere. Still a terribly long distance.

However, there's one more trick up our sleeve. This is a birthday problem, because any two of the individuals being close together will do. I'd need more accurate demographics to see how much this affects things, but it makes it more likely that at least one of the pairs is within roughly 20km!

Of course, there is a huge catch here. Those who are in urban environments are far less likely to have the survival skills required to live for a very long time and execute such a search. While those who lived in rural environments will likely live out their lives without too much additional difficulty, urban survival will call for a new set of skills. It is unclear how much this will affect things.

• Using square kilometers is extremely misleading. A straight line distance would be far more accurate. 400Km is going to cost you either 3-8 hours of driving. Easily achievable in a single day. Aug 22 '18 at 5:06
• At a moderate walking pace of 4 km/h and by walking 8 hours/day, 429 km is easily traversable in 2 weeks. Even a completely unfit person should be able to manage half of that, which means that you'll cover that distance within a month. Of course, that doesn't help if you don't know where to go and the other person either goes to where you're going, or stays put! If everyone is wandering around looking, that alone would be a serious obstacle for anyone to find anyone else. I would guesstimate that most people can spot another person 1 km away in open terrain, but probably not 10-100 km away.
– user
Aug 22 '18 at 5:50
• Yawn at your survival skills caveat. Some Bushmen with mad survival skills might be able to field dress a deer and make fire from their ass or whatever, but that doesn't make them any more skilled at finding one person that's likely 1000km or more away. Humans are clever and social. We are designed to survive novel situations. A "spoiled urbanite" may not be able to track a wildebeest by scent, but no one is so helpless they would starve as soon as the lights went out or would walk off a cliff without GPS. Aug 22 '18 at 19:54
• @Anthony The point of that caveat was that we can reasonably expect a bushman to live out their life in this case, at their full life expectancy. I think that we have to limit our assumptions of life expectancy for the urbanite, because their environment is radically changed by this shift. This affects how far they can walk. Aug 22 '18 at 22:13
• I think that there is going to a huge ceiling on anyone's survival if they don't find other people within a certain period of time. Determining what that amount of time is is an interesting question in and of itself. I suppose I see your point that someone in an urban area has to migrate farther to reach an area of sustainable resources (regardless of any presumed skill sets), but I think this would be offset by the vast availability of non sustainable resources within their urban area, eg canned foods that will take a lifetime to go through. Aug 22 '18 at 22:17

A thing that seems not to have been addressed yet is the age and survival chance of the 35 non-vanishing persons. Depending on the mode by which the rest of humanity vanishes, many of the chosen ones might just die in minutes or days

Reasons would include among other things:

• having been in the car/ship/train/airplane where the driver/captain/pilot vanishes, resulting in an accident
• being to old or too young to care for oneself like a baby
• being incarcerated at the moment or being otherwise stuck
• going insane and commiting suicide shortly after the event

The already small chance of ever finding someone else diminishes further, if you simply die. Even if the other person is "close" (i.e. a few kilometers away).

However, when you know where the other person is, the meeting probably can be done in a few weeks. So the initial communication infrastructure would be most important. If the Internet stays active long enough, people could get in touch quite fast - just post and visit pages on popular sites, where actively viewed content is featured. Again, this depends on the age/culture of the persons in question - a senior in a rural area might not even think of this. Similarly, the already mentioned option of radio communications requires some expertise which could be missing among the surviving portion of the 35..

If they are going to meet, retain more people than 1 per 200 million. (of which probably half would be dead in a week)

Of your 35 survivors, it is likely that 7-8 of them are Muslims. I imagine that at least a few of those might decide that now is a particularly good time to undertake Hajj, a pilgrimage to Mecca. Particularly as such a pilgrimages are organised to arrive on the same day, then it is quite likely that they would meet each other there.

• A pilgrimage to Mecca, which is in the middle of a huge desert, may be particularly difficult to organise when civilisation is gone. It's one of the most inhospitable places on the planet. Aug 24 '18 at 17:16
• It wouldn't be that hard. If people is gone but machines and roads remain, it isn't hard to pick a truck (and a boat) and go anywhere. Even if you need to live in the ground (without a truck) it isn't so hard to hunt in semidesertic lands if you are the only hunters. Hunter gatherers have been living quite well in the Kalahary desert until recently.
– Pere
Aug 27 '18 at 20:37
• @gerrit - what makes crossing a desert difficult is the fact that doing so takes you a long way away from support, so you have to take everything you're going to need with you. Other than the fact that you can't expect any kind of assistance if something does go wrong, it won't be any harder. Take a reliable vehicle, fill it with supplies, and you should get there. Or go traditional: take a camel train. You could expect one or two camels to not make it, but if you take four you should still have enough supplies to make the journey even if the worst happens. Aug 29 '18 at 19:12

Was going to do this as a comment, but decided to write it up:

Total landmass on earth: 148.94 million km^2 (148940000km^2) - approximates to a square ~12300km on a side (Might be entering spherical cow territory here, but bear with me)

Randomly distribute 35 people within that square and calculate the minimum distance between any two of them

Repeat*100

Sum up all of our minimum distances and divide by 100 to get the average - ~70km or less! This is due to the what @Cort Ammon mentioned - the birthday problem - as the number of people goes up, the chances of any two of the being close rises exponentially

This of course assumes that people are evenly distributed, which they aren't, It also ignores the shape of continents, oceans, and travel difficulties

My incredibly rough calculations in a python script: NB: please forgive my horrible code, it's just meant to give an idea of my thought process and maybe act as a jumping off point

Factors which will affect the time it takes for two of them to meet:

• Radio contact - two of them getting a ham radio set
• One of them being in a position to spread news effectively - i.e. online news, emergency broadcast
• How long infrastructure stays operational
• If one has access to information that can track survivors; emergency services, mobile phone network, reddit?
• How easy it would be for a single person to stand out amongst the noise generated by automatic processes such as bots, queues of updates for websites etc
• Based on a post on straight dope, the answer to your infrastructure question, at least for power generation, is probably "less than a week". Internet and power would probably be down before the dust settled, so anything that relies on news broadcasts or internet would most likely be inconsequential, especially because you'd have to deal with the language barrier in the vast majority of cases. Aug 22 '18 at 7:33
• Good points! OP stated everyone else "suddenly disappeared", so I"m not sure how that would affect the infrastructure time. Language barrier can be overcome with a certain amount of thinking - display a map with a little flag and they have a general idea of your location Aug 22 '18 at 8:39
• True. The post suggests that some areas might even start failing without oversight within hours, though, with a week being the absolute limit in many cases. I think a lot of people would be too deep in their own networks to realize the problem until the internet suddenly cuts out. This is especially true given it's unlikely that more than a few people would remain who spoke the same language, which can affect which sites you visit as much as your ability to communicate with others once there. Aug 22 '18 at 8:44

Foreword: This may duck the spirit of the question for the literalist interpretation.

Thinking Outside The Box

If I was a '35er, the very first thing I would do is hop on my smartphone and start hailing the ISS in every way I can manage. At their twitter, at their Insta, if I can find a HAM radio I'll darn well hit em there. I'll try the astronauts personal twitter, email, linkedIn, whatever I can possibly find.

I believe this will be a doable effort. Even if there are bots creating bogons, I believe the only person tweeting, emailing, DMing, Hamming, about how they've lost contact with Houston will eventually make contact. The ISS has (very slow) internet access and I believe it is a much better option than HAM for making and maintaining the contact we will need for this next step.

Even if you can't maintain contact over the short longer term, you have made contact with a very important asset. The astronauts on the ISS are the only humans guaranteed to be alive at this juncture. Any attempt to quickly (day of, day after, while internet survives) pick out and contact another survivor seems doomed to fail in my opinion.

The Plan

The Astronauts are an incredible asset in your plan to save the human race (lets face it, without your action, there ain't no chance of more babies). They will allow you to greatly increase your communication output in the crucial period before the global communication network shatters. You email every person in your email contact list. You message everyone you have on facebook or any other social network.

MAJOR KEY ALERT: you try to find the address of your closest HAM radio club or organization. Dig for details of either the first member you can find (time-sensitive internet access) or the closest member to your location (transit time contingent). Download a copy of the two most popular Ham radio operation manuals you can find on E-Book (you can always get one at a library later, believe me you'll have the time for it).

Meanwhile, have the ISS do their part. They will have a more traditional array of communications tools alongside their slow internet. They are all exceptional people and bring a set of skills, knowledge, experience, and raw brainpower that you alone could never match. Follow their instructions if they seem reasonable and try to avoid wasting time communicating about their unavoidable long-term death.

Short Term Contingencies

Now, this first stage of the plan is contingent on a few things, luck first among them. Depending on the circumstances of the disappearance and your own personal situation, a car could crash, take down a line or generator or other sundry key part of the communication network linking you to the ISS. This is too terrible to contemplate so I'll not bother. Answers to this question seem to think otherwise have a set of 2-5 (ok maybe not five) days before the internet is pining for the fjords.

Back to the Plan

The time between when you make contact with your team and when you lose them over the internet is precious beyond simple explanation. I personally cannot imagine what brilliant things you could come up with, under extreme "motivation", with decades of their experience as soldiers, academics, or whatever. 232 extraordinary global citizens have spent time ex-terra at the ISS Hilton, so you could have more or less any combined skill set up there. What I suggest seems reasonable to me under these bounds.

You take control of the ISS personal astronaut social media accounts, the ISS social media accounts, the NASA social media accounts, and/or any other email-linkedin-weichat-VKontakte accounts you can. If anyone has the talent to hack or learn to hack quickly, take control of any and all social media, news, or simply popular webpages you can. Take into hand any further ISS-based communication equipment, and broadcast a looping screed of "Are you out there? We are still alive! us at !". If you can take control of printers, print your the address of your nearest town hall (to be left with a briefing cache) along with the above message.

You have cast the widest net possible in the shortest time possible. Await responses while brainstorming your next step over email with the spacers. Download a translation program and a set of dictionaries to a flash drive and use google translate while you still can.

If you get any responses, generically tell them to acquire a ham radio and a generator before proceeding. See if you can get them hooked up with the ISS if you can, to facilitate communication. If you can figure out a potential halfway-point for future meeting, hash that out.

My guess is that you don't see any response (you can cast a big net but earth is large as hell with balkanized communication for the most part), but you've given it your best. Either way, form a plan for continued (personal and species-level) survival. At some point you'll have to switch to a Ham Radio for (much reduced) ISS communication (which will end one day) and a library for research and planning purposes.

Going Forward

1. Survive! If your person doesn't survive, nothing else matters (to you).
2. Help others survive! Even if you can't reach them, assist them in any way you can. Keep in HM radio contact as often as possible, and pool your (foodgathering, medical, transportation) information, and socialize. It would be very easy to get discouraged or suffer from mental health issues in this scenario.
3. Form a community of survivors. Travel to a centralized site with access to food, resources, and information. Choose a language (please god no English or Chinese), form a society, have kids. Choose a leader and stick to it because god knows you can't afford a civil war.
4. Make your community safe. You'll have a Mayflower's worth of people, with no guarantee of carpenters nor doctors. Based on this chart and your ability to contact, preserve, and gather your fellow humans, you will have a very limited workforce with limited skills. Choose a safe (good weather and limited natural disasters) location and exploit existing structures and resources, like farms, orchards, quarries, etc.
5. Preserve Knowledge and Progress. Form a religion to preserve knowledge, human rights, and provide for the people. To what extent you can, mold your society around reclaiming the mantle of humanity, reclaiming progress, and preserving the environment. This is your chance to change the course of human history. Even if in the future, regionalism and person ambition breaks your community into different groups, you can hope your church will tie them together culturally and diplomatically. I'm aiming for a mix between the state-within-all-states Early-Middle-Ages Catholic Church and Star Trek's Federation.

Acknowledgements

What I detailed above is by no means the most likely scenario. It is simply one scenario, and one far more positive than most of the answers so far in my opinion.

• I like how your literal interpretation of "people on Earth have disappeared" to not include people in LEO. Aug 24 '18 at 17:15
• The ISS always has one Soyuz docked to it, so the crew can leave in an emergency. You might even be able to convince them to land near you. Aug 28 '18 at 19:55

The headline and the detailed question are not equivalent.

If everyone in the world disappeared except 35 random people, how long would it take for one of them to realize they're not alone?

is not the same as

Everyone suddenly disappears from earth except 35 people randomly scattered wherever they were before everyone disappeared. How long would it take on average for 2 or more people to meet?

It depends on what you mean by the word "realize." That's not the same as "prove." How long did it take the human species to "realize" that there were not alone (or better, in a vast if not infinite universe or multiverse, extraordinarily unlikely to be alone) as a self-conscious species, even though none had ever been encountered?

So what is required is for one of the thirty five to "realize" that if s/he survived then there are two possibilities. Either out of 7.4 billion people s/he is the only one, or there are others. If one person survived then that is proof that it was possible to survive. Given that the thirty five were taken at random, it is reasonable to assume that there were no special circumstances relating to the survival of that individual, indicating that there were 7.4 billion chances for at least one other to survive. As with the case of intelligent life on planets other than the earth, the huge number of other possibilities for life, i.e. survival, would lead me (if I was lucky or unlucky enough to be one of the survivors) to almost immediately "realize" that there were overwhelmingly likely to be others, even though it might be very unlikely that I would ever meet one. What is the chance that of thirty five random individuals one would think the same way as me - pretty good, I'd say.

• It is tautological that there were "special circumstances relating to the survival of that individual"; after all, millions of people around them just disappeared and they didn't. While most people would consider it a possibility that the probability of survival is between 3e-10 and 3e-4, I can't see anyone considering it a certainty. Aug 22 '18 at 9:23
• Welcome to Stack Exchange. While the wording of the question title may say "realise", it is clear from the main body that the OP is asking how long it would take for two of the 35 people to meet. As a result, your post fails to answer the question since you are just addressing the technicalities of the question's wording. Please take the tour and visit the help centre for more information about this site.
– Aric
Aug 22 '18 at 9:33
• I think you're also making errors of probability here, RevLS. There's very little we can induce from a sample of one. We have have no evidence that we can extrapolate from to guess the likelihood that living creatures exist on other planets, and your survivor has no evidence to extrapolate from to guess the likelihood that other people survived. If the survivor knows how or why he was spared (just like if we knew how life came to exist on Earth), then he could form some theory about whether it was likely to happen to others. Aug 23 '18 at 17:28

Get something like

and hope that someone manages to hack into the data center and receive your message. Combine with other methods such as HF radio.

• How about fireworks? It might not be a bad idea for a survivor to set off a few bottle rockets every clear night he's near a major city center. Aug 23 '18 at 18:14

This is another Birthday Problem answer. It seems likely that two people could find each other (if that was their goal) if they were in the same city, as cities have centralized layouts and are small compared to countries. So one way of addressing this question is to ask: how likely is it that two people would remain in a single city?

I chose simulation, finding a list of about 50,000 cities and their populations. The total population was about 2.2 billion out of an assumed population (US census bureau) of 7,494,217,000; I assumed that anyone not falling in one of those cities would have 0 chance of finding any others. In 7 out of 100 simulation there was at least one city with two or more people remaining, suggesting that the probability is between 5.5% to 8.5% with ~95% confidence.

• You can directly calculate the odds based on the Birthday problem. Using a calculator for simplicity, using 35 people in 50,000 cities gives only a 1.18% chance have two being in the same city. You yourself pointed out that only 29.7% of people are included. That means we're actually only looking at about 10 people. This gives only a 0.08% (8/10,000) chance of anyone being in the same city as anyone else. Aug 23 '18 at 3:51
• @Drazex That's not a reasonable calculation, since some cities have tens of millions of people and other cities have fewer than a thousand. You must take the sizes into account, which is why I used simulation rather than an exact calculation. Aug 23 '18 at 12:02
• Fair enough, but without more information about your simulation, it's impossible to tell what assumptions you're making to get that number. I made the assumption of equal probability because that's what it sounded like you were doing. Aug 23 '18 at 12:22
• @Drazex The intent is to use the actual populations of the largest cities on Earth today. Of course there are different definitions of what the city is (city proper, urban area, etc.), different census results in different years, and various other reasons to get different numbers, but in practice I just went with whatever numbers I found. I encourage you to find your own list and run your own simulation as a double-check -- if your numbers differ substantially from mine, either more than 8.5% or less than 5.5%, let me know. Aug 23 '18 at 14:24
• @Drazex I ended up using this list: kaggle.com/max-mind/world-cities-database (just the cities with listed populations) Aug 23 '18 at 14:27

In order to realize you are not the only one, you have to meet another. That in itself is a major challenge even if you use one of the more sensible strategies suggested in other answers. The success of the strategy also depends on someone else using a strategy compatible with the one you chose.

So, what is the probability that two or more of 35 people who see no evidence that anyone else exists will think that there might be someone else? Then, what are the chances that those two or more but less than 35 will think that it is worthwhile to try to find each other, and then that the ones that think so will design methods that have a chance of working?

On the other hand, if two of them happen to be fans or followers of a popular page/account on a social media site, and keep looking at it in spite of it having no activity after they notice that apparently they are alone, one of them might post “WTF happened?” and the other see it. Once they realize there is one other, they may be motivated to collaborate on a search for others.

Finally, are those 35 truly random? Or is there something they have in common that exempted them from the disappearance? If so, is that something that will increase the probability of some of them knowing or suspecting there are others?

• In order to realize you are not the only one, you have to meet another — not necessarily. One might leave an obvious trace, and the other might find it, even years later. Aug 23 '18 at 9:26

It depends on whether Facebook is still working. Of the 35 survivors, about 10 of them are on FB. The first thing they will do after the event is go online to find out what happened. Assuming that FB has a facility to allow active users to find each other, and that the algorithms scale downward to 10 users, they will start interacting in about 10 minutes.

Of course this is problematic. None of the 35 are keeping the power grid up, or the networks up, or the servers running. So this all has to be done by bots using AI. Provided the bots survived the event.

• I thought of this, but spambots will make this very hard. And what facility to find each other would Facebook have? I don't think there is any. Aug 22 '18 at 11:23
• Well, disappearing of people doesn't mean their account disappear from social network as well. So I'm afraid it will not get you anywhere. What could work though is creating for a group like "Everyone disappeared, what now" and then search for similar groups in a hope that there was someone who had similar idea. The drawback is that relying on computers gives just few days to contact as stated by others. Then the entire power network goes down. Aug 22 '18 at 12:24
• Facebook has facilties to suggest new friends to you. Those algorithms are well suited to a user community o a billion. Adapting to a user community of 10 might be a real challenge. But maybe not. Aug 22 '18 at 13:11
• If any of the 35 is a Facebook sysop, they might have ways to find out any others left alive. If not, good luck. Aug 22 '18 at 13:15
• Livestream yourself publicly on facebook, maybe? Aug 22 '18 at 16:56

Since all kinds of modern transportation and communication and food production will break down without people operating and the world is as large as it is, they would most probably die before they found anyone.

• That's just silly. Dry and canned food in the supermarkets could supply a single person for a decade before they all go bad, more than enough time for even a city slicker to figure out how to grow a garden. Ordinary cars less than 10 years old will certainly be reliable enough for a year or two, and anyway, long-distance transportation isn't a necessity for life any more than long-distance communication is. Since food, water, shelter, and transportation are going to be ridiculously easy in this scenario, your post seems to suggest one would die from lack of TV and internet. Aug 24 '18 at 19:11
• I can't imagine where you must live, to ask such questions. The answers to your questions are (1) very, very much, certainly tens of thousands of cans between the three or four major grocery stores in my small city, millions of cans in any major city (2) wood (3) river or spring (4) in the woods, until I can build an outhouse Aug 24 '18 at 19:53
• For cooking, I think we could find a BBQ grill even in a city, and I doubt the sewage or trash produced by one person is going to make a significant impact anywhere. We're talking about a scenario in which there are only 35 people in the world, remember? Aug 24 '18 at 20:43
• With an axe and/or saw and wooden houses all over the place, you have a massive supply of dry wood to burn. Also, a commercial kitchen in a restaurant might have a large supply of propane on site. Aug 25 '18 at 17:06
• @mathreadler you don't seem to have any idea how most people in the first world used to live, only 50 years ago. And some of the 35 survivors will probably either remember first hand experience of that, or at least have heard stories from their parents and grandparents. Aug 25 '18 at 17:09

With radios yes, without technology .... no

Does it have to be 35 people? Why not 356, 1 for everyday of the year. Then you can at least have a few people setting up radios in different citys they visit and maybe leaving repeating messages. And eventually, after maybe a 3-5 years maybe even a decade if 200 or more are still alive, someone would find someone.

35 Is just way to low, unless you're planning on inventing ways for them to have electricity and communication methods for at least a week but even then a month would do much better, but that would be impossible as much power grids would fail in 12 to 48 hours for major areas maybe in a week depending on if it is solar or renewable, or nuclear. But even then, would things like the internet and google or facebook or other online things still work correctly. Would international phonecalls work? What citys and systems would stay online long enough to help.

Again, maybe even increase the number to 3,560, 10 people for each day of the year, although 356 would sound more world ending or godly fashioned, 3 thousand or 10 thousand would be more doomsday or planned by a person instead of a god.

Even 100 or 1000, and have 1 to 10 people of each year and age, although the kids or elderly would lower the population without help.

Honestly, it would just really help if you explained why 35 is a part of your story and what kind of story your trying to tell with this. Like what is your world, and what time or year is it is also very helpful.

If the power grid failing sounds far fetched, then read this other thread. https://www.quora.com/If-everyone-in-the-world-died-at-once-how-long-would-electricity-and-the-Internet-continue-to-function

• Why does everyone say power grid will fail in a few days? Is it really that fragile? I thought that the 1965 New England disaster had prompted huge improvements in reliability. Aug 23 '18 at 22:08
• I did the math in my answer, and it turns out that with 365 people there's a 99% or higher chance two are in the same city. Aug 30 '18 at 18:13

Where do you find a decent Starfish Prime when you need one.

I could see the results of this one for 1 week plus from 4000 miles away.

How to find, access and 'utilise' such a device is left as an exercise for the student.

From here - many more on web.

You're the "last person on Earth", pick a communication method

which may be as simple as physically talking with someone.

1. It has a noise-to-signal ratio for people to detect if you're alive, talking and flying a plane are near 100% (weather and person's hearing permitting add those in if you can :3). Radio transmission probably less (There could be raw signal issues.) Call this $Signal\Delta$
2. It also has an observable area for the communication method (can only shout so far). Call this $CommArea$
3. Assume either you or someone else was constantly moving so that the entirety of Earth was covered... You would need to move because other person is not guaranteed to be moving (if other person's existence of movement is random you're further reducing chances by 50% if you're not moving, if they're doing same strategy as you then reducing proportional to communication area). Thinking Cap time: If you consider same-speed movement between a pair of people, parallel movement results in maintaining separation. Non-parallel motion results in separation or closing. If you consider only your angle relative to their parallel motion you can see that the range of angles you can take that close the distance is determined by a) your movement speed relative to the distance and b) the angle that the lines between their previous position and next position make with you (if you're right behind this line of travel no angles result in closing, only the parallel maintains distance). We can probably neglect speed entirely because sensing distance is much larger than movement speed. And if we consider a random walk then Closing is random but reduces to a neat percentage. Because every motion situation has an exact opposite combination that can occur. And the other person can't know your motion without knowing you're alive, then:

$Closing\% \approx .50$

(Also consider the case of everyone chasing each other in a single line across the globe. They'd never catch each other. While random deviations can lead to a new situation)

Only problem is a random walk has a Gaussian probability of distance from start:

$\mathcal{N}(\mu,\sigma^2)$

$\mu = Mean = 0, \sigma = spread = travel speed*time*other$ ...idk remember the other part that allows you to calculate sigma over time...However I do know the following:

Out of all the areas we can possibly travel:

• 68.27% of them are within 1 $\sigma$ of the start.
• 95.45% of them are within 2 $\sigma$
• 99.73% of them are within 3 $\sigma$

Conversely one can say there is a lower chance of ending up outside of 2 $\sigma$ from the start. There's only a 4.55% chance of this happening. As well as the fact that if we can possibly travel $D$ distance in the time already passed then 3$\sigma$<$D$

1. Population density effects starting positions which effects chance of finding each other because of the Gaussian distribution of your position relative to your start. So what are the odds of two people starting close to each other? Well all people within a circle around you of radius $R$ contribute to the people that would be considered at least as close as $R$. So the population in that circle compared to the whole world's is the $Density\%$ and is the odds that someone starts within $R$ from you.

These probabilities are then affected by the same statistics behind the insight in the Birthday Paradox. It's not "What is the probability that someone has my B-Day?" it's "What are the odds that nobody has any other person's B-Day?" You have one instance of the probability happening for each person.

So what are the odds all these factors line up?:

Well it's a rough estimate because some communications are global in nature and don't change location necessarily just because you move (internet is one for example). However we can get a pretty good estimate.

Person1:

Individual Probability of Communication First Pass after time t:

$P_I(t,n) = Signal\Delta_n*Closing\%_n*\mathcal{N}(\mu,\sigma_n^2)*Density\%_n$

$\sigma_n \approx R_n(t)/3$

$Density\%_n = PeopleWithinDist_n(R_n(t))/EarthPopulation$

Max. Communication distance over time (radius of CommArea+Distance):

$R_n(t) = \sqrt{CommArea_n/\pi}+Speed_n*t$

$CommDistArea_n = R_n(t)*\sqrt{CommArea_n/\pi}$

Odds of being outside of all $CommDistArea_n$ OR being inside but missing the communication:

$CommArea\%_n = CommDistArea_n / EarthArea$

$P_T()= 1 - (1-CommArea\%_1*P_I(t,1))*(1-CommArea\%_2*P_I(t,2))\ldots*(1-CommArea\%_{35}*P_I(t,35))$

EX: Airplane travel with clear visual of 35 people taken from high population density landmass throughout expansion (ie population density remains at a consistently high level as one walks in a single direction.)

Assuming: 80km is visual distance, 885 km/h is airplane speed, 25,709 km² is population density.

$EarthArea =$ 510.1 million km² (Although there's only about 40 million higher density we're using entire surface)

$EarthPopulation =$ 7.5 billion

We're gonna get a quick and dirty number of about .00000171393 after one hour minimum. (Ie odds of a single person being next to another person is 1 in a million after first hour). A key observation is our potential area traveled increases with the square of the potential distance. So after about a day our area encompasses a large portion of Earth's Area and most definitely drags our number up to .02

2% success rate is actually all we need. Birthday Paradox effect takes care of the rest. Resulting in 51% chance of someone "meeting" another individual within 180km. Which for a 885km/h plane is no time at all. If you want 98% success rate....Then actually doubling the time from 2% is actually enough.

TL;DR predicated mostly on all candidates being dropped in the centers of high population areas... There's a significantly high chance of finding another candidate before death.

What other factors would indicate to a person that they're not the only person who didn't disappear? Fresh destruction could be an indicator of life. Much like tracking in the wild. Finding a new nuclear crater would tell you something happened. If it was improbable to accidentally happen, then you could guess at someone else being alive.

• Some logic with dirty napkin math. Probably could be improved greatly, I'm sure I missed more than what I know I missed. Use grains of salt... Aug 29 '18 at 14:34

Here is a full simulation for whether two people out of N survivors given a list of the largest cities and a population of 7 billion people will find each other. The simplifying assumption is that two people will find each other if they are in the same city. In any case, here is the code for a Monte Carlo simulation:

def main():

population_file = sys.argv[1]
people = sys.argv[2]

global_population = 7 * 1000 * 1000 * 1000
successes = 0

data = [int(s) for s in data]
# the rest of the world
blackhole = global_population - sum(data)

aug = data + [blackhole]
aug = [ (1.0 * a) / global_population for a in aug]
cumu = [sum(aug[0:idx]) for idx in range(len(aug))]
top = cumu[len(cumu) - 1]

people = 2000

def draw():
r = random.uniform(0, 1)
if r > top:
return -1
# Replace with binary search if many cities
return next(i for i in range(len(cumu)) if cumu[i+1] > r)

trials = 10000
for t in range(trials):
locations = [draw() for _ in range(people)]
locations = [loc for loc in locations if loc > 0]
successes += len(set(locations)) < len(locations)

print '%d people, %.2f%% chance' % (people, (100.0 * successes) / trials)

main()


Here are some results:

python monte.py summe 35
35 people, 4.61% chance
...
100 people, 30.82% chance
120 people, 42.06% chance
140 people, 52.86% chance
200 people, 76.73% chance
365 people, 99.02% chance
500 people, 99.94% chance
1000 people, 100.00% chance


As you can see the breakeven for two people being in the same city limited to the 1000 most populous cities, which is about 12% of the global population, is around 140 people. Even with 35 people, there is a respectable chance of about 5% two people will be in the same city.

If you repeat my experiment with more cities the chance will go up slightly, because I assume two people who are not in the top 1000 cities will not meet. You may want to extend the experiment to 2000 or 10000 cities. But this is a lower bound then.

My answer takes into account the birthday paradox which a lot of the othe answers do not. For instance, the accepted answer makes the simplifying assumption that you should only consider the top 3 most populous countries, which is exactly the simplifying assumption you do not want to take. The birthday paradox is the mathematical result that 23 people probably share the same birthday out of 365 days. But you do not only limit your search to the 31 day months: of course the two people may share a birthday in February, April, June, September or November. And any 2 people of the 23 may collide, so intuitively it's less of a 23/365 chance and more of a 23*23 = 529/365 chance (there may be multiple collisions and this intuition does happen to overestimate).

Therefore, this proves, mathematically, that: There is at least a 4.6% chance that 2 of the 35 people will live in the same geographically defined city. With 140 people, there is at least a 50% chance. With 500 people, it is a near certainty.

I would bet more that two urbanites have a better chance of covering Shanghai or Chicago than two rural people have a chance of covering Oklahoma or the Yukon.

• But the majority of people do not live in the world's largest 850 cities. Aug 29 '18 at 17:38
• @forest I ran a full simulation for you, here are the results. Taking into account past the 1000 cities only makes the occurrence more likely. Aug 30 '18 at 18:05
• Oh interesting. Thanks for the analysis! Aug 31 '18 at 21:34