Brainteaser: Forehead Numbers

There are 3 people placed in a room.  They all have perfect logic.  The 3 people are told by a host that a number has been written on each of their foreheads.  Each of the 3 numbers are unique, they are all positive, and they relate to each other such that A + B = C (i.e. one is the sum of the other two).  In the room, each person can only see the other two people’s numbers, as they cannot see their own foreheads.

 

Suppose you are one of the 3 and you see one person with “20” on their forehead and the other person with “30.”  The host asks you, then the person with “20,” and then the person with “30” what number is on their heads and all 3 say that they don’t know.  The host then asks, again, you, then the person with “20,” and then the person with “30” what number is on their head, and all 3 answer correctly.  How does this happen?

 


 

Answer:

The key to this brainteaser is to calculate the logic of each person’s point of view, i.e. put yourself in each of their shoes.  The annoying part of solving this brainteaser, then, is having to keep track of 3 different points of view.

“First” person: If you see “20” and “30,” that means you are either 10 or 50.  So you don’t know what’s on your forehead among these two numbers.

The “20” person: You see either 1.) “30” and “10” or 2.) “30” and “50.”  In case 1.) you are either 20 or 40.  In case 2.) you are either 20 or 80.  So you don’t know.

 

The “30” person: You see either 1.) “20” and “10” or 2.) “20” and “50.”  In case 1.) you must be 30 because you cannot be 10 as well the “First” person.  So the key here is that if you see one person has number “x” and another has number “2x,” you know you cannot also have “x” on your forehead.  You must be “3x.”  So in this case, the “30” person would know the answer that he or she has 30 on his head.  In case 2.) the “30” person has either 30 or 70, and so he or she wouldn’t know.

 

Since after the first round, everyone answered that he or she did not know, that means that we cannot have the “30” person’s case 1.), which is that he sees “20” and “10.”  In other words, our “First” person cannot have 10.  He has 50 on his forehead.  So when the host asks the “First” person the second time, he or she will answer 50.

 

The most illuminating and clean part of the problem is just up to here, but in an attempt for completeness, I kept going.

 

From the “20” person’s point of view, we assume that he or she is able to figure out the above sort of logic on his or her own.  What the “20” person sees is “30” and “50,” which means that he or she is either 20 or 80.  Somehow, the “50” person figured out on his or her own on the second round of questioning that they have 50 on their head.  The logic is that in order to find out what your number is on the second round, you are using someone’s “I don’t know” answer in the first round of questioning.  So if the “20” person indeed has 20 on his or her head, they can deduce that the “50” person is able to figure out all the above and that his or her number is 50 on the second round.  If the “20” person has 80 instead, the “First” person sees “80” and “30” and is thus wondering if his or her number is 50 or 110 and the “30” person sees “80” and 50 and wondering if they’re 30 or 130.  In none of these cases is a person announcing that they are not seeing an “x” and “2x” situation (which is what the “First” person experiences: seeing a “2x” and “3x” situation, and then seeing that the “3x” person doesn’t immediately say that he or she knows that his or her number is “3x.”).  If the “20” person has 20, then, again, the “First” person sees that the “30” person is announcing that they aren’t seeing an “x” and “2x” situation, which means that the “First” person can’t have 10 and must have 50.  This causes the “20” person to know that his or her number is 20.

 

Similarly, the “30” person sees “50” and “20” initially doesn’t know if he or she is 30 or 70.  If it’s 70, the other people either see “70” and “50” or “70” and “20,” which doesn’t allow the situation described above of someone announcing that he or she doesn’t see an “x” and “2x” situation.  If it’s 30, then everything that’s been discussed happens, and so it must be 30.

 

The key basically is that if someone sees “x” and “2x,” they should know immediately that they are 3x.  If someone sees “2x” and “3x,” they are immediately on high alert to see if the “3x” person immediately knows that he or she is 3x.  If the “3x” person doesn’t know, that is an announcement that the “3x” person did not see an “x” and “2x” situation, which means that the person we started with must be “5x.”  So, in an “x” and “2x” situation, you know immediately that you are 3x.  In a “2x” and “3x” situation, if everyone says that he or she doesn’t know in the first round, that announces that no one saw (and the “3x” person in particular did not see) an “x” and “2x” situation, which means that you must be 5x.

Arendt, Action, and Psychological Stuff

I know next to nothing about Hannah Arendt except what I’ve read on Wikipedia and Reddit (archived).  Nevertheless, it sounds really cool.

She defined the three human activities as labor, work and action, with two mutually exclusive spheres: the political and everything else.

Arendt introduces the term “vita activa” (active life) by distinguishing it from “vita contemplativa” (contemplative life), which represents her understanding of Western society. There are only three human activities: labor, work and action. They correspond to the three basic conditions under which humans live. Action corresponds to the political actions of anyone…

What’s striking to me (and I agree with it) is the stark division between the active life and the contemplative life.  There’s action and there’s talk (so I’m already disregarding Arendt’s actual philosophical definition of “action,” but oh well.)

According to Arendt, modern life is divided between two realms: that of the public in which “action” is performed, and that of the private, site of family life where the father ruled. It is in the public realm where one distinguishes oneself through “great words and great deeds” in the same way as personal glory is attained on the battlefield.

Again, emphasizing how what you do matters.  Your private life is just for yourself.  Your public life affects you and can bring you things (reputation, resources, i.e. money, connections) that don’t really exist or have meaning with just yourself in your private, home life.

Arendt claims that her distinction is unusual and new as it has not been attempted previously by the thinkers who concerned themselves with the subject of ‘human activity’, e.g. Karl Marx. She goes on to explain that “labor” is one of the only three fundamental forms of activity that are the human condition. It is repetitive and only includes the activities that are necessary to mere living, such as the production of food and shelter as well as any material production, with nothing beyond that. The condition to which ‘labor’ corresponds is sheer biological life.

So “labor” is stuff like eating, bathing, cleaning and hygiene, and perhaps some other health and maintenance-related activities.

“Work”, on the other hand, has a clearly defined beginning and end. It leaves behind a durable object, such as a tool.

I don’t grasp the meaning of this.  I’d like to think it means the same as “work” in our normal sense, although that’s probably wrong.  But anyway, surely there’s something other than the “life maintenance” things we do (like eat, sleep, and bathe in private at home) and the political life, which I’d guess, is our normal definition of “work.”  And the point of “work” is basically accumulating resources that allow us to enrich our lives further than what bare life maintenance provides us.

 

On the other hand, exercise improves mood (archived), and not in a new age-y way but physiologically:

Looking deeper, Lehmann and his colleagues examined the mice’s brains. In the stimulated mice, they found evidence of increased activity in a region called the infralimbic cortex, part of the brain’s emotional processing circuit. Bullied mice that had been housed in spartan conditions had much less activity in that region. The infralimbic cortex appears to be a crucial component of the exercise effect. When Lehmann surgically cut off the region from the rest of the brain, the protective effects of exercise disappeared. Without a functioning infralimbic cortex, the environmentally enriched mice showed brain patterns and behavior similar to those of the mice who had been living in barebones cages.

Humans don’t have an infralimbic cortex, but we do have a homologous region, known as cingulate area 25 or Brodmann area 25. And in fact, this region has been previously implicated in depression. Helen Mayberg, MD, a neurologist at Emory University, and colleagues successfully alleviated depression in several treatment-resistant patients by using deep-brain stimulation to send steady, low-voltage current into their area 25 regions (Neuron, 2005). Lehmann’s studies hint that exercise may ease depression by acting on this same bit of brain.

I couldn’t find anything on the following from a bit of low-effort Googling, but I think there are some who say that action helps to alleviate depression or improve moods as well.  And when I say action, I don’t mean Arendt’s political action nor physical exercise, but just general action, like doing things, instead of sitting and contemplating about doing.

Walking helps with thinking (archived), especially creative thinking.  Dipping into fanciful evolutionary psychology headcanon (or I might’ve also read this somewhere else), if we were all persistence hunters once (or simply had to walk a lot to gather berries and water for our hunter-gatherer tribe), we walked a lot daily, and the body uses this time and monotonous activity to let the brain think.  Many people talk about their subconscious helping them figure out problems – problems that they couldn’t when they were face-to-face with it at a desk – while they were doing something completely unrelated, even really smart people (archived):

Poincaré deliberately cultivated a work habit that has been compared to a bee flying from flower to flower. He observed a strict work regime of 2 hours of work in the morning and two hours in the early evening, with the intervening time left for his subconscious to carry on working on the problem in the hope of a flash of inspiration. He was a great believer in intuition, and claimed that “it is by logic that we prove, but by intuition that we discover”.

Of course, I don’t know what exactly Poincare did during his off-hours and it may not have been persistence hunting.  But even if it wasn’t, as long as it’s something habitual (archived):

To illustrate the differing thoughts and emotions involved in guiding habitual and nonhabitual behavior, 2 diary studies were conducted in which participants provided hourly reports of their ongoing experiences. When  participants  were  engaged  in  habitual  behavior,  defined  as  behavior  that  had  been  performed almost  daily  in  stable  contexts,  they  were  likely  to  think  about  issues  unrelated  to  their  behavior, presumably because they did not have to consciously guide their actions. When engaged in nonhabitual behavior,  or  actions  performed  less  often  or  in  shifting  contexts,  participants’  thoughts  tended  to correspond to their behavior, suggesting that thought was necessary to guide action. Furthermore, the self-regulatory benefits of habits were apparent in the lesser feelings of stress associated with habitual than nonhabitual behavior.

 

It seems that action improves mood, and I assume an improved mood improves action.  But then if the opposite might be true, why does inaction worsen mood and a worsened mood worsen action?  Again into fanciful evolutionary psychology, perhaps it’s a survival mechanism.  When circumstances are bad, you want to conserve energy and action and stay away from possibly taxing or dangerous situations.  Basically, sit tight and wait out the night/rain/drought.  Of course, when this occurs not because of a lack of resources but some internal mental reason (which is much more likely in modern life), it’s much harder or at least more mentally complex to get out of that spiral.  A modern person’s way out of inaction or depression is not the same as a hunter-gatherer seeing food for the first time in a while (some external thing happening to him) that might quickly improve his mood, spur him into action, and so on and so forth.  The tricky thing is that while action may improve mood, if an internal mental reason is what caused mood to worsen to begin with, the action isn’t targeting the source of depression.  Action in this instance is a solution that’s unrelated to the source of depression/the bad mood.  Action and its positive effects on mood might still be good enough to overcome internally-caused depression.  But I imagine that the disconnect between action and source of depression is why modern depression isn’t easily solved by action and exercise even if it undoubtedly helps physiologically.  It’s interesting and crazy that we’re such contemplative beings with such big brains but we’re still meat and water bags that are heavily influenced by physical, biological, neurochemical existence.

The Theory of Interstellar Trade

The Theory of Interstellar Trade, by Paul Krugman (1978)

Archived

 

Assume we have two planets, Earth and Trantor, separated by a large distance, the traversal of which necessitates travel at velocities comparable to the speed of light.  Assume that Earth and Trantor are in the same inertial reference frame, i.e. they are not accelerating with respect to each other.

Assume that a spaceship traveling between the two planets travels at a constant v\ .

Let’s say that from the perspective of an observer on one of the planets, the time it takes for a spaceship to make the trip is n\ .

Then, the time it takes for a spaceship to make the trip from the perspective of someone on the spaceship is

\overline{n}=n\sqrt{1-\frac{v^2}{c^2}}

(which is shorter than n\ ).  The factor on the right is a well-known result from relativity, derived mathematically from the Lorentz transformation, that gives us “time dilation” from traveling at relativistic speeds.  Krugman demonstrates the above relation by representing the voyage in Minkowski space-time in a figure using imaginary axes.

 

Let

p_E\textup{, } p_T be the price of Earth goods and the price of Trantorian goods on Earth, respectively.

p_E^*\textup{, } p_T^* be the price of Earth goods and the price of Trantorian goods on Trantor, respectively.

r\textup{, }r^* be the interest rates on Earth and Trantor, respectively.

 

The first question Krugman asks is what is the correct interest rate on a planet with regard to interstellar trade, since depending on whether you’re on a planet or on a spaceship engaging in trade, the passage of time is different.  So putting ourselves on Trantor, we compare what happens to a Trantorian trader who can engage in investing in a Trantorian bond or engage in interstellar trade with Earth.

Interstellar trade with Earth would involve buying goods on Trantor, traveling to Earth, selling the Trantorian goods there and then buying Earth goods with those proceeds, and then traveling back to Trantor and selling the Earth goods there.  Let c\ be the cost of outfitting the spaceship.  The cost of buying goods on Trantor is q_T^* p_T^* where we define q_T^* as the quantity of Trantorian goods to be traded.  Thus, the initial expenditure of the Trantorian trader while still on Trantor is

c + q_T^* p_T^* .

The trader then travels to Earth and then sells its (not his or her) q_T^* goods at price p_T .  The trader now has money q_T^*p_T and will buy Earth goods with this money to bring back to Trantor.  Earth goods cost p_E so the quantity of Earth goods that can be bought is q_T^*p_T/p_E .  Let us call this quantity of Earth goods to be brought over to Trantor q_E^* .  So we have

q_E^* = \frac{q_T^*p_T}{p_E}

When the trader arrives back on Trantor, it will sell these Earth goods at price is p_E^* , resulting in a revenue of

\frac{q_T^* p_T p_E^*}{p_E}

But the Trantorian trader also had the choice of investing its money in a Trantorian bond before leaving for Earth.  The expenditure needed for the trading venture of c + q_T^* p_T^* invested into a Trantorian bond would:

after time 2n , which is the time it takes for a round trip from the point of view of a trader who decided to stay on Trantor for that duration of time instead of go to Earth and back, become

(c + q_T^* p_T^*)(1+r^*)^{2n}

or

after time 2\overline{n}=2n\sqrt{1-\frac{v^2}{c^2}}, which is the time it takes for a round trip from the point of view of a trader who decided to actually make the round trip and thus be on a spaceship for that duration of time (maybe he puts some money into a Trantorian bond and some money into the trading venture that he personally goes on), become

(c + q_T^* p_T^*)(1+r^*)^{2n\sqrt{1-\frac{v^2}{c^2}}}

So which perspective is right?  The perspective from Trantor or from the spaceship?  Krugman answers this by reminding us of the reasoning behind present value calculations, which is that of opportunity cost – any money that you choose not to possess today (by delay possessing it until the future for a larger amount) is money that you could have invested in a riskless bond today that would have also grown in value in the future.  And so the way I’ve framed it here sort of answers the question in advance, which is that the correct value of the bond is from investing it risklessly with some riskless bond issuer, like the Trantorian government.  The opportunity cost of spending money to outfit a trading venture to Earth is the lost opportunity of buying a Trantorian bond with that money and then receiving the proceeds by the time the trader would return from the venture, which according to the bond issuer, the Trantorian government, is 2n time.  Thus, we have Krugman’s First Fundamental Theorem of Interstellar Trade:

When trade takes place between two planets in a common inertial frame, the interest costs on goods in transit should be calculated using time measured by clocks in the common frame, and not in the frames of trading spacecraft.

Another way to think about it is that a bond earns interest because the bond issuer gets to possess cash now, invest it during some time, and afterwards will have more cash as a result.  The location that this is occurring is at the bond issuer’s location, which is Trantor.  The trader can always come back to Trantor and earn his bond interest and principal (assuming it’s a bond that automatically renews after maturing every time).  All this occurs on Trantor, and so the bond’s time progression is according to Trantor’s time progression.

 

Now, for simplification Krugman assumes that perfect competition reduces the profits of Earth-trading to 0.  In other words, we force the revenue earned from a trading venture to Earth that started with expenditure (c + q_T^* p_T^*) to equal the revenue earned from if we had invested that same expenditure into a Trantorian bond and waited the time that it takes to make a round trip to Earth and back:

\frac{q_T^* p_T p_E^*}{p_E} = (c + q_T^* p_T^*)(1+r^*)^{2n}

Also for simplification, Krugman assumes away c\ , the cost of outfitting a spaceship:

\frac{q_T^* p_T p_E^*}{p_E} = ( q_T^* p_T^*)(1+r^*)^{2n}

\frac{  p_E^*}{p_E} =  \frac{p_T^*}{p_T}(1+r^*)^{2n} \hfill \textup{(Relative goods prices)}

Krugman asks (or rather, asks what if someone asks) about a Trantorian trader who instead of going back to Trantor, decides to settle on Earth, thus making a one-way trading trip.  Krugman writes that the Trantorian trader has two options: either buy Trantorian goods, bring them to Earth, and sell them there, or buy Trantorian bonds, bring them to Earth, and sell them there.  While in a “realistic” situation, we would just need to assume that there is a liquid market for Trantorian bonds on Earth to make the second option possible, let us restrict our picture to just imagining one Trantorian in the whole universe who wants to migrate to Earth and then as many other traders as we want to imagine who all only intend to make round trips and live on their home planet and thus have no interest in the bonds of the other planet (thus, no Trantorian bond market on Earth).  In this case, Krugman assumes that we just have at least one Earthling who wants to migrate to Trantor and thus may be interested in buying a Trantorian bond before making his or her one-way trip.

So pursuing option 2, what price could this Trantorian bond fetch on Earth?  The Earthling has a choice of either buying and then bringing Earth goods to Trantor for sale or buying this Trantorian bond instead that can be redeemed when he or she arrives on Trantor.  The value of a one “T$ (Trantorian Dollar) bond on arrival at Trantor will be (1+r^*)^{2n} in Trantorian Dollars.  Thus, we want to know what value of Earth goods, when sold on Trantor, would net the same amount of Trantorian Dollars, for that is the Earth price of the Trantorian bond.

Suppose the Earthling buys q amount of goods on Earth to bring to Trantor.  The cost of that purchase is p_E q in Earth Dollars.  Once on Trantor, those q goods are sold for a total of p_E^* q Trantorian Dollars.   Let this equal the amount that would have been earned if a Trantorian bond was redeemed instead.  Thus, we have

p_E^* q = (1+r^*)^{2n}

q = \frac{1}{p_E^*}(1+r^*)^{2n}

The original Earth price for this transaction was

p_E q = \frac{p_E}{p_E^*}(1+r^*)^{2n}

Thus, \frac{p_E}{p_E^*}(1+r^*)^{2n} is the fair price in Earth Dollars for a Trantorian bond that can be redeemed in Trantor for (1+r^*)^{2n} .

If the Trantorian trader went with option 1, that means investing that one Trantorian Dollar in buying Trantorian goods to sell on Earth instead of buying a Trantorian bond and bringing it over.  One Trantorian Dollar buys \frac{1}{p_T^*} quantity of Trantorian goods, which on Earth will sell for a total of \frac{p_T}{p_T^*} Earth Dollars.  But from the “Relative goods prices” equation, we have that

\frac{p_T}{p_T^*} = \frac{p_E}{p_E^*}(1+r^*)^{2n}

Thus, one Trantorian Dollar invested in Trantorian goods and brought over to Earth can be sold for an amount of Earth Dollars that is the same as the fair price in Earth Dollars that a Trantorian bond will fetch on Earth.  So as long as there is at least one Earthling who also wants to make a one-way trip to Trantor and is open to buying a Trantorian bond instead of buying and bringing over Earth goods to sell, the Trantorian trader is indifferent between bringing over Trantorian goods to sell or bringing over Trantorian bonds to sell – both will earn the same profit.  This shows that the First Fundamental Theorem of Interstellar Trade holds as long as for one migrant going one way, we have another migrant going the other way.  What we seem to have is that as long as there is an “effective” round trip (either made by one Trantorian trader, or one Trantorian and one Earthling migrant) and the assumption of no arbitrage (so on each leg of the trip, the traveler is indifferent between carrying goods or bonds), we have a relation between the Trantorian interest rate and the prices of goods, and that none of this challenges the statement that the Trantorian bond’s interest gains run according to Trantorian time (the First Fundamental Theorem).  For Earth, we can construct the same scenarios except with the trip originating from Earth.  Krugman writes that he proves the theorem in the presence of transportation costs in a paper from the future.

Krugman then asks whether interest rates on Earth and Trantor will be the same or not.  The “Relative goods prices” equation (and its associated assumptions) are kept.  Even though transportation costs, as in c , the cost of outfitting a spaceship, was assumed away earlier, the “Relative goods prices” equation shows that there is an effective cost to transporting goods across stars that comes from the transportation time needed.  (If you are on Earth and you desire Trantorian goods, even if it costs no money for the Trantorian trader to outfit its spaceship to make the journey to Earth and sell its goods to you, the profit that the Trantorian trader makes by the time it returns to Trantor after its round trip needs to match the profit it would have made from just investing in Trantorian bonds and sitting at home for the same duration of time.  Thus, that gets built into the cost of Trantorian goods in planets that are interstellar distances away from Trantor.)  Could interstellar distances cause differences in the planets’ interest rates?

We imagine a scenario where a Trantorian trader buys Trantorian goods, travels to Earth, sells the goods there, invests the proceeds into Earth bonds, spends k time on Earth, redeems the bonds and buys Earth goods with that money, travels back to Trantor, and sells the goods there.  This scenario involves the prices of goods and Earth’s interest rate; and there is always another option: invest in Trantorian bonds at the beginning, sit at home for 2n+k time, and then redeem after that.  Then by forcing a no arbitrage condition, we are then able to obtain a relation between the prices of goods, Earth’s interest rate, and Trantor’s interest rate.

In the first option, the trader buys p_T^* q_T^* (where q_T^* is the quantity of Trantorian goods bought) worth of Trantorian goods, travels to Earth, sells these goods for p_T q_T^* , invests that in Earth bonds for k time, earns p_T q_T^* (1+r)^k $ after that, buys \frac{p_T q_T^* (1+r)^k}{ p_E} quantity of Earth goods, travels back to Trantor, and then sells these goods for a total value of \frac{p_E^* p_T q_T^*}{p_E}(1+r)^k Trantorian Dollars.  Forcing a no arbitrage condition, we require that this revenue equal the revenue from investing the initial expenditure in Trantorian bonds for the same amount of total time, giving us:

p_T^* q_T^* (1+r^*)^{2n+k} = \frac{p_E^* p_T q_T^*}{p_E}(1+r)^k

(1+r^*)^{2n+k} = \frac{p_E^*}{p_T^*}\frac{p_T}{p_E}(1+r)^k

From earlier, we had

\frac{p_E^*}{p_E} = \frac{p_T^*}{p_T}(1+r^*)^{2n} \hfill \textup{(Relative goods prices)}

Putting the two equations together gives us:

(1+r^*)^{2n+k} = (\frac{p_E}{p_T}(1+r^*)^{2n})\frac{p_T}{p_E}(1+r)^k = (1+r^*)^{2n}(1+r)^k

(1+r^*)^{k} = (1+r)^k

r = r^*

Thus, we have the Second Fundamental Theorem of Interstellar Trade:

If sentient beings may hold assets on two planets in the same inertial frame, competition will equalize the interest rates on the two planets.

In his conclusion, Krugman writes

I have not even touched on the fascinating possibilities of interstellar finance, where spot and forward exchange markets will have to be supplemented by conditional present markets.

I was thinking this was a light-hearted paper on a light-hearted topic but looks like there’s a lot more out there.  Thirty-five years later, Krugman gives a mention (archived) on the topic.

Hong Kong’s Infamous Kowloon Walled City Rebuilt as Amusement Park (Gizmodo)

Hong Kong’s Infamous Kowloon Walled City Rebuilt as Amusement Park (Gizmodo)

 

“The juxtaposition of a high-tech Japanese toilet in an authentically grimy bathroom has to be seen to be believed,” he writes.

I do have an objection to that, which is that you can find plenty of “authentic,” though perhaps not often grimy, Japanese toilets in modern Japan today.

“In r/badhistory, the view that technology is linear gets poked fun of every once in a while. Why is the view wrong?”

In r/badhistory, the view that technology is linear gets poked fun of every once in a while. Why is the view wrong?  Isn’t technology linear? Also, why is the west so dominant when compared to other once great civilizations?

 

Are you familar with the idea of local maximums? Imagine in a low spot between two hills. You can climb either hill. Regardless off what hill to climb, you are increasing your elevation. But one of the hills will not reach as high as the other.

In evolution, its called a fitness landscape. Paths of technological development can be similar.

A recent question on ask historians involved the development of iron weapons. The answer involved metallurgy – iron is frequently inferior to bronze, and it was only the development of consistant alloys and better techniques that gave iron an edge (a better edge in this case). Focusing on bronze is advantageous – until another civilization manages to be able to alloy a superior form of iron. Local maximums.

 

What I think is interesting is that once people discover that a new technique for metallurgy creates iron that is better than bronze, everyone starts to adopt it. This is some sort of direction to technology, is it not? One society goes in one direction and discovers a local maximum and another society goes in another direction and discovers a different local maximum. But if these two societies intermingle (whether it’s a peaceful or violent intermingling, take your pick), if the people in the two societies discover that one of the local maxima is higher than the other, then they’ve discovered a local maximum of a larger region and have made a step in the direction of the global maximum. Keep repeating this and as your map gets larger and more societies intermingle, your greatest local maximum gets higher and higher.

At the danger of summoning the hatred of Jared Diamond-critics, I think he mentioned in one of his works that one way he “measures” a civilization is its ability to dominate another civilization and avoid being dominated by other civilizations (whether it’s violent, peaceful, economic, diplomatic, or cultural domination). What I’m saying is, when two societies – each having discovered a different local maximum – intermingle, if one dominates another, they will have succeeded in that domination for some reason. That “some reason” is their local maximum. Once news of this knowledge spreads (if that “reason” can be identified and is made into knowledge), other societies will pursue that local maximum as well. As long as societies have enough knowledge of the past to pursue higher and higher maxima, they will be acquiring more and more things that enable them to “dominate other civilizations or avoid being dominated by other civilizations.” Could this suffice as a kind of definition for “technological progress?” If there is a “linear” component to it, it’s that as our “map” expands, our local maximum of that map increases or at least doesn’t decrease.

Of course, this assumes that knowledge of the past remains and there are no catastrophes that set back civilizations in general. But I think catastrophes setting back technologies isn’t something that goes against the belief of “linear technological progress.” I think even staunch “linear progress” believers allow for the fact that unseen catastrophes can cause set backs, or even that scientific knowledge is not a smooth process. I think the key question that both sides wrestle with is how progress seems to happen over generations, even if key inventions seem to happen by chance (like fermented foods or penicillin being discovered fortuitously by leaving things too long or less hygienic than intended). So could “societal domination leads to the adoption of more ‘dominating’ technologies” be a satisfactory explanation? This does mean that if societies that get dominated had wonderful, advanced technologies that get lost to time, it may be a long time until those technologies are rediscovered again, if at all. That’s just a matter of us not finding those directions in the map that could lead to undiscovered local maxima. The key is that as more people interact and more societies intermingle, as long as we would rather dominate than be dominated, “dominating” technologies are going to be adopted more and more. We could try to describe what exactly are more “dominating” technologies (e.g. faster, cheaper mobility for people, more crops per area of land produced that is sustainable, etc.), but I think it’s easier to fall into incorrect claims with details like that. The key is “What technologies help you dominate other societies (or people) or avoid being dominated by other societies (or people)?”

 

 

Variations of the Trolley Problem

Variations taken from this comment on Reddit.  I’d like to give my amateurish comments on each variation.

 

Trolley Problem, Fat Person

The Fat Person Variation

Note that in all of these variations, the six people at risk are tied down onto the tracks.  This is different from the example when it’s described that the six people are on the tracks of their own free will (perhaps workers, perhaps just taking a walk on the tracks) but simply cannot hear the trolley running towards them.  Thus, we can assume that the six people have been tied to the tracks against their will.

Most people would say not to push the fat person over the bridge to stop the trolley, betraying some sort of morality that is not strictly utilitarian.  In this variation, I think reciprocity (a very common theme in morality, I’m sure) gets highlighted.  Although the six people may be tied down against their will, the fact here is that you and the fat person, observing from the bridge, have more in common than with any of the people being tied down.  You would not want the fat person to be thinking of pushing you down the bridge (next time the situation occurs, perhaps the trolley is much smaller and lighter and so your body on the tracks would suffice, even if for this time, only the fat person’s body would be big enough).  Thus, you don’t push the fat person off because you don’t want to be pushed off next time.  However, I do think the assumption that “you and the fat person, observing from the bridge, have more in common than with any of the people being tied down” is needed.  If this wasn’t the case, it’s less clear.  In the extreme, say this is a war situation and you are in you base.  The six people tied down are your fellow soldiers (perhaps enemy spies came in the night and tied them down), and the fat man is an enemy prisoner-of-war (imprisoned in the base, perhaps under your guard, perhaps you captured him) that just happens to be beside you at this moment.  If you judge that you have more in common with the six tied down, pushing down the fat prisoner-of-war may be more likely since though you may be committing a war crime, you are saving six of your soldiers.  The theme is again reciprocity – you have more in common with your fighting mates than with an enemy.  If you’re in trouble next time, you’d want your fellow soldiers to sacrifice an enemy if it’ll save you.

Another aspect (still related to reciprocity) is that of shame or later social consequences.  If the situation happened in regular life (not war), pushing the fat man off the bridge would likely mean having to try to proclaim your innocence in trial or something.  I think there’s an assumption that it’s more likely that you’ll be tried for murder for pushing the fat man off than you’ll be tried for being a bad Samaritan for not doing anything on the bridge.  And even if you win your trial in the former case, no one would want to walk on a bridge with you ever again.  But if you were a king, or a god, or playing a computer game, and this situation happened to you, I think pushing the fat person off the bridge becomes more likely.  Or even simply if you’re a farmer and the fat person and the six people tied down instead are all livestock, like cattle or pigs.  So, in the end, it’s reciprocity, again.  Shame and social consequences occur because of reciprocity – people see that you won’t reciprocate, so they shame, ostracize, harass, or physically harm you.  But if you’re removed from that expectation and pressure of reciprocity, it is much less repugnant to be strictly utilitarian.  It seems that we’re first reciprocal, then utilitarian.

 

Trolley Problem, Tied Down

The Victim Variation

A different theme rears its head in this case, which is self-preservation.  If we allow the desire for self-preservation and the subsequent actions that that leads to (and it is likely that in a society where we reciprocate, if I want to preserve myself, I allow others to preserve themselves as long as it doesn’t endanger my self-preservation), then we allow the people that have been tied down to want the trolley to run over the people on the other side if it will save them.  But we can’t expect society to care for every person’s preservation – at some point, we leave people to self-preserve themselves.  We don’t hire security guards to guard every single street, intersection, door, hallway, and window in our society, or produce the best bear suit armors for everyone to wear.  Instead, we just hire enough police, and have enough laws regarding helmets for motorcycle riders, seat belts regarding car passengers, and airbags regarding car makers.  We don’t know what caused the six to get tied to the tracks.  Maybe it was purely chance – an act of god (the six truly don’t deserve it).  Or maybe it’s wartime and these are enemy spies or traitors from your side that have been captured are supposed to be humanely executed tomorrow but a renegade official particularly angry at them has decided to execute them more gruesomely a day before in secret.  In any case, if it isn’t an act of god, something caused them to be there.  Maybe they weren’t careful enough.  Maybe they couldn’t buy bear suits for their protection in time.  Anything could be the reason, but the people on the bridge were somehow able to self-preserve enough to not be tied down and the people tied down were not able to self-preserve enough to avoid being in their situation.  At some point, we ask people to self-preserve themselves.  A person tied to the tracks is allowed to wish for his or her self-preservation over others, and the people on the bridge are allowed to not have to risk their own self-preservation just because they’re on a bridge seeing the trolley bear down on those six.

 

Trolley Problem, Kantian

The “Kantian” Variation

If this is implying that the moral duty might be to pull the lever, it seems to be implying that if you are selfless enough, then the moral duty is the utilitarian answer of saving five people instead of saving one person (despite it being called the “Kantian” variation).  If we allow people to desire self-preservation, we allow the one person to let the trolley kill the other five people.  If not, it seems that (at least the author of the title of the graphic is saying that) we default to utilitarianism (a sort of “Kantian utilitarianism?  I have no idea).  So, first comes self-preservation, then comes reciprocity.  Then comes “default” utilitarianism.

 

The Veil of Ignorance Variation

The Veil of Ignorance Variation

If self-preservation comes first, then it is more likely that we’ll be one of the five tied down than the one tied down, so we’d pick for the trolley to run over the one person.  While we’re picking the same choice as the utilitarian choice, that’s not our reasoning – our reasoning is purely for self-preservation.

 

The "Hedonist" Variation

The “Hedonist” Variation

I think reciprocity is the name of the game here (and note how self-preservation is not, since if we’re standing at the lever, our self-preservation is not at danger).  If we feel something in common with the six people tied down, reciprocity makes us save them.  If we don’t feel the expectations and pressures of reciprocity – if we are a king, god, or we’re playing a computer game, then we may be the hedonist and let the six die for our amusement.

 

The Game of Chicken Variation

The Game of Chicken Variation

Allowing self-preservation allows us to not pull the lever.  If we were kings or gods or playing a computer game, we might command the two to pull the levers so that we get a utilitarian outcome.  If both the red-dotted person and black-dotted person were not standing on the tracks, it is possible for both to pull the level for the utilitarian outcome.

 

My amateurish analysis is that it’s likely that most people choose their actions according to self-preservation, some form of reciprocity (depending on who you feel in common with – who are your allies and who are not), and utilitarianism in that order.