# data[].attributes.body
(We can focus on a few important ones)

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Can be interpreted as a metaphor for online dating

The “swipe right, swipe left” mechanism of dating apps (e.g. Tinder) is reflected through the husbands descending and ascending the ladder —> ("Swipe right" means to like or accept someone, while "swipe left" means to reject them)

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Lauren sends her husbands back into the attic whenever a slight inconvenience arises in hopes that the next one will be better

She relies on the attic to ESCAPE from her marital problems instead of working with her partner to fix them.

“And thanks to the attic… she can send him away without even having an awkward conversation about it.“

(P. 61)

“She wanted to know that if something went wrong her first thought would be How can I fix this? and not Should I leave?”

(P. 98)

Coco

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“Back on the landing, the attic hangs above her like a threat.” (P. 29)

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Lauren investigates the attic for the 1st time…

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Lauren investigates the attic for the 1st time…

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“In the murk there is only furniture, and boxes, and a dark shape that she flinches from before realizing it’s a half- disassembled Christmas tree.”

“Only the attic, and the light bulb, which is, admittedly, starting to glow just a little.”

(P. 29)

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Lauren’s fear and hesitancy of CHOOSING and COMMITTING to a partner for eternity

“It must be nice to be that sure of anything, to risk the mistake, to have the big party.“ - Lauren about Elena’s wedding

(P. 99)

Coco

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What Causes People To Have Commitment Issues? A Couples’ Therapist Explains (Coco)

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What Causes People To Have Commitment Issues? A Couples’ Therapist Explains

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What it *really* means to have commitment issues.

# data[].attributes.body
A historical game of French origins to determine whether a person’s love interest returns their affections, often using the repetitive phrases, “he loves me, he loves me not…”

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Lauren finds it harder to make a decision as she’s presented with an INFINITE number of husbands

She gets caught up in an endless cycle of generating and sending away husbands without making a deep connection with any of them (except for Carter and Bohai)

Coco

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Option paralysis is a real phenomenon in the online dating world. Option paralysis is the feeling of being overwhelmed by too many choices. So, it occurs when someone has too many options to choose from and ends up not choosing any of them.

It's easy to fall into the trap of option paralysis when you're online dating. There are so many potential matches out there, and it can be overwhelming trying to figure out who is right for you.

Where Did the Term 'Option Paralysis' Come From?

Option paralysis is a phenomenon discussed by psychologist Barry Schwartz in his 2004 book, "The Paradox of Choice: Why More Is Less."

Dating Apps Provide Too Many Choices

With so many dating apps and sites to choose from, it's easy to get caught up in an endless cycle of swiping and scrolling without ever making a real connection. And even when you do match with someone, there's no guarantee that things will go anywhere, given the number of potential options that are just a message away.

People who are presented with too many choices are more likely to experience negative feelings, such as being overwhelmed.So, if you feel down about your dating prospects, it could be due to an overload of choices.

Why Too Many Dating Choices Can Be an Issue

With the advent of online dating, people now have more dating options than ever before. In theory, this should be a good thing, as it gives people more opportunities to find a partner with whom they are compatible.

You Might End Up Never Making a Decision

However, research suggests that too much choice might actually be a bad thing when it comes to online dating. One of the reasons why online dating can be so difficult is that there are just too many options to choose from. A 2011 study published in Biology Letters found that people who were presented with many potential partners were less likely to make any decisions at all.

In fact, the participants in the study became so overwhelmed by the sheer number of choices that they found it difficult even to narrow down their options.

Examples of Option Paralysis in Online Dating

Option paralysis can be frustrating and overwhelming, but it's important to remember that it's normal to feel this way when presented with too many choices.

Option paralysis can manifest itself in several ways in the online dating world. Here are some examples:

1. You spend hours scrolling through dating apps without ever connecting with anyone.

2. You match with someone on a dating app but don't message them because you're not sure they are the right person for you.

3. You go on first dates with multiple people but never follow up with any of them because you can't decide who you want to pursue.

4. You keep your dating options open and never commit to one person because you're afraid of missing out on someone better.

If any of these sound familiar, you may suffer from option paralysis in your dating life.

How to Overcome Option Paralysis in Online Dating

If you find yourself experiencing choice paralysis in your online dating life, there are some things you can do to overcome it.

Marisa Cohen, PhD, relationship expert and licensed marriage and family therapist notes, "it's important to practice mindfulness and be fully engaged and present with the person you are with. In fact, you may not be a match, but if you aren't able to fully invest in the person you are spending time with, you aren't giving them a fair shot."

A Word From Verywell

If you find that you're struggling with option paralysis in your online dating life, remember that you're not alone. It's a common problem that can be overcome with a little effort and mindfulness. Try to be more selective in who you talk to, set aside a specific amount of time for online dating each day, and don't forget that there are other ways to meet people as well. With a little effort, you can break out of the cycle of option paralysis and succeed in online dating.

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If you've ever been paralyzed by too many choices, you're not alone. Here's how to deal with option paralysis when dating online.

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Symbolises a VICIOUS CYCLE —> the only way to stop the attic from regenerating husbands is to destroy it 🔥

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A LIMINAL SPACE —> a place of transition, waiting (for the next husband) and not knowing (what kind of person he is and whether Lauren likes him)

The “in-between” of Lauren’s current universe and infinite possibilities of husbands in other alternate universes

Invokes feelings of discomfort

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Plot: cyclical nature with different husbands

Movement of husbands ascending and descending the ladder into/ from Lauren’s attic

Some husband’s repeated appearances as different roles in her life (e.g. Jason is her gardener when she is Felix’s wife)

Lauren’s stuck in a vicious cycle of choice paralysis

Coco

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Domesticity is reflected through simple and direct language

The coziness of her apartment is juxtaposed by the attic’s mysterious powers, and the unpredictable and unsettling changes in her apartment, interpersonal relationships and even her appearance based on the new husband

Coco

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Flow-chart style quizzes to help people narrow down their options to make a decision —> similar to Lauren’s thought process in choosing a husband

Coco

# data[].attributes.body
mechanism similar to a game

# data[].attributes.body
movement like repetitive manufacturing in factories

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process/ technique: printing? —> repetitive but also unpredictable

# data[].attributes.body
“Golconda” (oil painting by Belgian surrealist René Magritte)

Visual language is similar to Lauren’s attic that is “generating an endless supply of husbands”

# data[].attributes.body
merges domestic scenes with striking natural landscapes to form environments that are surreal, yet always tinged with familiarity

https://www.alfiecaine.com/biography

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She's been too vague in her search, too unclear about that she wants from a husband. (p.83)

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They step through to a wide alcove, and beyond that to a tilted entrance hall the size of her living room with a staircase looping the edges. (p.117)

House description (Chapter 15)

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you've got a load of interviews lined up. And each time one of the candidates comes in, at the end of the interview you decide if you want to hire her. But you have to decide right there. If you say no you can't go back to her later. And if you don't hire anyone you're stuck with whoever's last, even if she's terrible. Mathematically, you should say no to the first thirty-seven per cent of candidates, then yes to the first person you see who's better than any of them. (p.193)

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Graphs of probabilities of getting the best candidate (red circles) from n applications, and k/n (blue crosses) where k is the sample size

The secretary problem demonstrates a scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also known as the 37% rule.

The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy ( stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.

The shortest rigorous proof known so far is provided by the odds algorithm. It implies that the optimal win probability is always at least (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality. The optimal stopping rule prescribes always rejecting the first applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the stopping rule, because the probability of stopping at the best applicant with this strategy is about already for moderate values of . One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.

Although there are many variations, the basic problem can be stated as follows:

There is a single position to fill.

There are n applicants for the position, and the value of n is known.

The applicants, if all seen together, can be ranked from best to worst unambiguously.

The applicants are interviewed sequentially in random order, with each order being equally likely.

Immediately after an interview, the interviewed applicant is either accepted or rejected, and the decision is irrevocable.

The decision to accept or reject an applicant can be based only on the relative ranks of the applicants interviewed so far.

The objective of the general solution is to have the highest probability of selecting the best applicant of the whole group. This is the same as maximizing the expected payoff, with payoff defined to be one for the best applicant and zero otherwise.

A candidate is defined as an applicant who, when interviewed, is better than all the applicants interviewed previously. Skip is used to mean "reject immediately after the interview". Since the objective in the problem is to select the single best applicant, only candidates will be considered for acceptance. The "candidate" in this context corresponds to the concept of record in permutation.

The optimal policy for the problem is a stopping rule. Under it, the interviewer rejects the first r − 1 applicants (let applicant M be the best applicant among these r − 1 applicants), and then selects the first subsequent applicant that is better than applicant M. It can be shown that the optimal strategy lies in this class of strategies.[citation needed ] (Note that we should never choose an applicant who is not the best we have seen so far, since they cannot be the best overall applicant.) For an arbitrary cutoff r, the probability that the best applicant is selected is

The sum is not defined for r = 1, but in this case the only feasible policy is to select the first applicant, and hence P(1) = 1/ n. This sum is obtained by noting that if applicant i is the best applicant, then it is selected if and only if the best applicant among the first i − 1 applicants is among the first r − 1 applicants that were rejected. Letting n tend to infinity, writing as the limit of (r−1)/ n, using t for (i−1)/ n and dt for 1/ n, the sum can be approximated by the integral

Taking the derivative of P( x) with respect to , setting it to 0, and solving for x, we find that the optimal x is equal to 1/ e. Thus, the optimal cutoff tends to n/ e as n increases, and the best applicant is selected with probability 1/ e.

For small values of n, the optimal r can also be obtained by standard dynamic programming methods. The optimal thresholds r and probability of selecting the best alternative P for several values of n are shown in the following table.

1

2

3

4

5

6

7

8

9

10

1

1

2

2

3

3

3

4

4

4

1.000

0.500

0.500

0.458

0.433

0.428

0.414

0.410

0.406

0.399

The probability of selecting the best applicant in the classical secretary problem converges toward .

This problem and several modifications can be solved (including the proof of optimality) in a straightforward manner by the odds algorithm, which also has other applications. Modifications for the secretary problem that can be solved by this algorithm include random availabilities of applicants, more general hypotheses for applicants to be of interest to the decision maker, group interviews for applicants, as well as certain models for a random number of applicants.[citation needed ]

The solution of the secretary problem is only meaningful if it is justified to assume that the applicants have no knowledge of the decision strategy employed, because early applicants have no chance at all and may not show up otherwise.

One important drawback for applications of the solution of the classical secretary problem is that the number of applicants must be known in advance, which is rarely the case. One way to overcome this problem is to suppose that the number of applicants is a random variable with a known distribution of (Presman and Sonin, 1972). For this model, the optimal solution is in general much harder, however. Moreover, the optimal success probability is now no longer around 1/ e but typically lower. This can be understood in the context of having a "price" to pay for not knowing the number of applicants. However, in this model the price is high. Depending on the choice of the distribution of , the optimal win probability can approach zero. Looking for ways to cope with this new problem led to a new model yielding the so-called 1/e-law of best choice.

1/e-law of best choice

The essence of the model is based on the idea that life is sequential and that real-world problems pose themselves in real time. Also, it is easier to estimate times in which specific events (arrivals of applicants) should occur more frequently (if they do) than to estimate the distribution of the number of specific events which will occur. This idea led to the following approach, the so-called unified approach (1984):

The model is defined as follows: An applicant must be selected on some time interval from an unknown number of rankable applicants. The goal is to maximize the probability of selecting only the best under the hypothesis that all arrival orders of different ranks are equally likely. Suppose that all applicants have the same, but independent to each other, arrival time density on and let denote the corresponding arrival time distribution function, that is

, .

Let be such that Consider the strategy to wait and observe all applicants up to time and then to select, if possible, the first candidate after time which is better than all preceding ones. Then this strategy, called 1/e-strategy, has the following properties:

The 1/e-strategy

(iii) selects, if there is at least one applicant, none at all with probability exactly 1/e.

The 1/e-law, proved in 1984 by F. Thomas Bruss, came as a surprise. The reason was that a value of about 1/e had been considered before as being out of reach in a model for unknown , whereas this value 1/e was now achieved as a lower bound for the success probability, and this in a model with arguably much weaker hypotheses (see e.g. Math. Reviews 85:m).

However, there are many other strategies that achieve (i) and (ii) and, moreover, perform strictly better than the 1/e-strategy simultaneously for all >2. A simple example is the strategy which selects (if possible) the first relatively best candidate after time provided that at least one applicant arrived before this time, and otherwise selects (if possible) the second relatively best candidate after time .

The 1/e-law is sometimes confused with the solution for the classical secretary problem described above because of the similar role of the number 1/e. However, in the 1/e-law, this role is more general. The result is also stronger, since it holds for an unknown number of applicants and since the model based on an arrival time distribution F is more tractable for applications.

In the article "Who solved the Secretary problem?" ( Ferguson, 1989), it's claimed the secretary problem first appeared in print in Martin Gardner's February 1960 Mathematical Games column in Scientific American:

Ask someone to take as many slips of paper as he pleases, and on each slip write a different positive number. The numbers may range from small fractions of 1 to a number the size of a googol (1 followed by a hundred zeroes) or even larger. These slips are turned face down and shuffled over the top of a table. One at a time you turn the slips face up. The aim is to stop turning when you come to the number that you guess to be the largest of the series. You cannot go back and pick a previously turned slip. If you turn over all the slips, then of course you must pick the last one turned.

Ferguson pointed out that the secretary game remained unsolved, as a zero-sum game with two antagonistic players. In this game:

Alice, the informed player, writes secretly distinct numbers on cards.

Bob, the stopping player, observes the actual values and can stop turning cards whenever he wants, winning if the last card turned has the overall maximal number.

Bob wants to guess the maximal number with the highest possible probability, while Alice's goal is to keep this probability as low as possible.

The difference with the basic secretary problem are two:

Alice does not have to write numbers uniformly at random. She may write them according to any joint probability distribution to trick Bob.

Bob observes the actual values written on the cards, which he can use in his decision procedures.

Strategic analysis

Alice first writes down n numbers, which are then shuffled. So, their ordering does not matter, meaning that Alice's numbers must be an exchangeable random variable sequence . Alice's strategy is then just picking the trickiest exchangeable random variable sequence.

Bob's strategy is formalizable as a stopping rule for the sequence .

We say that a stopping rule for Bob is a relative rank stopping strategy iff it depends on only the relative ranks of , and not on their numerical values. In other words, it is as if someone secretly intervened after Alice picked her numbers, and changed each number in into its relative rank (breaking ties randomly). For example, is changed to or with equal probability. This makes it as if Alice played an exchangeable random permutation on . Now, since the only exchangeable random permutation on is just the uniform distribution over all permutations on , the optimal relative rank stopping strategy is the optimal stopping rule for the secretary problem, given above, with a winning probability

Alice's goal then is to make sure Bob cannot do better than the relative-rank stopping strategy.

By the rules of the game, Alice's sequence must be exchangeable, but to do well in the game, Alice should not pick it to be independent. If Alice samples the numbers independently from some fixed distribution, it would allow Bob to do better. To see this intuitively, imagine if , and Alice is to pick both numbers from the normal distribution , independently. Then if Bob turns over one number and sees , then he can quite confidently turn over the second number, and if Bob turns over one number and sees , then he can quite confidently pick the first number. Alice can do better by picking that are positively correlated.

So the fully formal statement is as below:

Does there exist an exchangeable sequence of random variables , such that for any stopping rule ,

?

For , if Bob plays the optimal relative-rank stoppings strategy, then Bob has winning probability 1/2. Surprisingly, Alice has no minimax strategy, which is closely related to a paradox of T. Cover[7] and the two envelopes paradox. Concretely, Bob can play this strategy: sample a random number . If , then pick , else pick . Now, Bob can win with probability strictly greater than 1/2. Suppose Alice's numbers are different, then conditional on , Bob wins with probability 1/2, but conditional on , Bob wins with probability 1.

Note that the random number can be sampled from any random distribution, as long as has nonzero probability.

However, for any , Alice can construct an exchangeable sequence such that Bob's winning probability is at most .[1]

But for , the answer is yes: Alice can choose random numbers (which are dependent random variables) in such a way that Bob cannot play better than using the classical stopping strategy based on the relative ranks.

The remainder of the article deals again with the secretary problem for a known number of applicants.

Expected success probabilities for three heuristics

Stein, Seale & Rapoport 2003 derived the expected success probabilities for several psychologically plausible heuristics that might be employed in the secretary problem. The heuristics they examined were:

The cutoff rule (CR): Do not accept any of the first y applicants; thereafter, select the first encountered candidate (i.e., an applicant with relative rank 1). This rule has as a special case the optimal policy for the classical secretary problem for which y = r.

Candidate count rule (CCR): Select the y-th encountered candidate. Note, that this rule does not necessarily skip any applicants; it only considers how many candidates have been observed, not how deep the decision maker is in the applicant sequence.

Successive non-candidate rule (SNCR): Select the first encountered candidate after observing y non-candidates (i.e., applicants with relative rank > 1).

Each heuristic has a single parameter y. The figure (shown on right) displays the expected success probabilities for each heuristic as a function of y for problems with n = 80.

Finding the single best applicant might seem like a rather strict objective. One can imagine that the interviewer would rather hire a higher-valued applicant than a lower-valued one, and not only be concerned with getting the best. That is, the interviewer will derive some value from selecting an applicant that is not necessarily the best, and the derived value increases with the value of the one selected.

To model this problem, suppose that the applicants have "true" values that are random variables X drawn i.i.d. from a uniform distribution on [0, 1]. Similar to the classical problem described above, the interviewer only observes whether each applicant is the best so far (a candidate), must accept or reject each on the spot, and must accept the last one if he/she is reached. (To be clear, the interviewer does not learn the actual relative rank of each applicant. He/she learns only whether the applicant has relative rank 1.) However, in this version the payoff is given by the true value of the selected applicant. For example, if he/she selects an applicant whose true value is 0.8, then he/she will earn 0.8. The interviewer's objective is to maximize the expected value of the selected applicant.

Since the applicant's values are i.i.d. draws from a uniform distribution on [0, 1], the expected value of the tth applicant given that is given by

As in the classical problem, the optimal policy is given by a threshold, which for this problem we will denote by , at which the interviewer should begin accepting candidates. Bearden showed that c is either or . (In fact, whichever is closest to .) This follows from the fact that given a problem with applicants, the expected payoff for some arbitrary threshold is

Differentiating with respect to c, one gets

Learning in the partial-information sequential search paradigm. The numbers display the expected values of applicants based on their relative rank (out of m total applicants seen so far) at various points in the search. Expectations are calculated based on the case when their values are uniformly distributed between 0 and 1. Relative rank information allows the interviewer to more finely evaluate applicants as they accumulate more data points to compare them to.

Since for all permissible values of , we find that is maximized at . Since V is convex in , the optimal integer-valued threshold must be either or . Thus, for most values of the interviewer will begin accepting applicants sooner in the cardinal payoff version than in the classical version where the objective is to select the single best applicant. Note that this is not an asymptotic result: It holds for all . However, this is not the optimal policy to maximize expected value from a known distribution. In the case of a known distribution, optimal play can be calculated via dynamic programming.

A more general form of this problem introduced by Palley and Kremer (2014) assumes that as each new applicant arrives, the interviewer observes their rank relative to all of the applicants that have been observed previously. This model is consistent with the notion of an interviewer learning as they continue the search process by accumulating a set of past data points that they can use to evaluate new candidates as they arrive. A benefit of this so-called partial-information model is that decisions and outcomes achieved given the relative rank information can be directly compared to the corresponding optimal decisions and outcomes if the interviewer had been given full information about the value of each applicant. This full-information problem, in which applicants are drawn independently from a known distribution and the interviewer seeks to maximize the expected value of the applicant selected, was originally solved by Moser (1956), Sakaguchi (1961), and Karlin (1962).

There are several variants of the secretary problem that also have simple and elegant solutions.

Pick the second-best, using one try

One variant replaces the desire to pick the best with the desire to pick the second-best.[13][14][15] Robert J. Vanderbei calls this the "postdoc" problem arguing that the "best" will go to Harvard. For this problem, the probability of success for an even number of applicants is exactly . This probability tends to 1/4 as n tends to infinity illustrating the fact that it is easier to pick the best than the second-best.

Pick the top-k ones, using k tries

Consider the problem of picking the k best secretaries out of n candidates, using k tries.

In general, the optimal decision method starts by observing candidates without picking any one of them, then pick every candidate that is better than those first candidates until we run out of candidates or picks. If is held constant while , then the probability of success converges to . By Vanderbei 1980, if , then the probability of success is .

Pick the best, using multiple tries

In this variant, a player is allowed choices and wins if any choice is the best. An optimal strategy for this problem belongs to the class of strategies defined by a set of threshold numbers , where .

Specifically, imagine that you have letters of acceptance labelled from to . You would have application officers, each holding one letter. You keep interviewing the candidates and rank them on a chart that every application officer can see. Now officer would send their letter of acceptance to the first candidate that is better than all candidates to . (Unsent letters of acceptance are by default given to the last applicants, the same as in the standard secretary problem.)

At limit, each , for some rational number .

Probability of winning

When , the probability of winning converges to . More generally, for positive integers , the probability of winning converges to , where .

computed up to , with .

Matsui & Ano 2016 gave a general algorithm. For example, .

Experimental psychologists and economists have studied the decision behavior of actual people in secretary problem situations. In large part, this work has shown that people tend to stop searching too soon. This may be explained, at least in part, by the cost of evaluating candidates. In real world settings, this might suggest that people do not search enough whenever they are faced with problems where the decision alternatives are encountered sequentially. For example, when trying to decide at which gas station along a highway to stop for gas, people might not search enough before stopping. If true, then they would tend to pay more for gas than if they had searched longer. The same may be true when people search online for airline tickets. Experimental research on problems such as the secretary problem is sometimes referred to as behavioral operations research.

While there is a substantial body of neuroscience research on information integration, or the representation of belief, in perceptual decision-making tasks using both animal and human subjects, there is relatively little known about how the decision to stop gathering information is arrived at.

Researchers have studied the neural bases of solving the secretary problem in healthy volunteers using functional MRI. A Markov decision process (MDP) was used to quantify the value of continuing to search versus committing to the current option. Decisions to take versus decline an option engaged parietal and dorsolateral prefrontal cortices, as well ventral striatum, anterior insula, and anterior cingulate. Therefore, brain regions previously implicated in evidence integration and reward representation encode threshold crossings that trigger decisions to commit to a choice.

The secretary problem was apparently introduced in 1949 by Merrill M. Flood, who called it the fiancée problem in a lecture he gave that year. He referred to it several times during the 1950s, for example, in a conference talk at Purdue on 9 May 1958, and it eventually became widely known in the folklore although nothing was published at the time. In 1958 he sent a letter to Leonard Gillman, with copies to a dozen friends including Samuel Karlin and J. Robbins, outlining a proof of the optimum strategy, with an appendix by R. Palermo who proved that all strategies are dominated by a strategy of the form "reject the first p unconditionally, then accept the next candidate who is better".

The first publication was apparently by Martin Gardner in Scientific American, February 1960. He had heard about it from John H. Fox Jr., and L. Gerald Marnie, who had independently come up with an equivalent problem in 1958; they called it the "game of googol". Fox and Marnie did not know the optimum solution; Gardner asked for advice from Leo Moser, who (together with J. R. Pounder) provided a correct analysis for publication in the magazine. Soon afterwards, several mathematicians wrote to Gardner to tell him about the equivalent problem they had heard via the grapevine, all of which can most likely be traced to Flood's original work.

The 1/ e-law of best choice is due to F. Thomas Bruss.

Ferguson has an extensive bibliography and points out that a similar (but different) problem had been considered by Arthur Cayley in 1875 and even by Johannes Kepler long before that, who spent 2 years investigating 11 candidates for marriage during 1611 -- 1613 after the death of his first wife.

The secretary problem can be generalized to the case where there are multiple different jobs. Again, there are applicants coming in random order. When a candidate arrives, she reveals a set of nonnegative numbers. Each value specifies her qualification for one of the jobs. The administrator not only has to decide whether or not to take the applicant but, if so, also has to assign her permanently to one of the jobs. The objective is to find an assignment where the sum of qualifications is as big as possible. This problem is identical to finding a maximum-weight matching in an edge-weighted bipartite graph where the nodes of one side arrive online in random order. Thus, it is a special case of the online bipartite matching problem.

By a generalization of the classic algorithm for the secretary problem, it is possible to obtain an assignment where the expected sum of qualifications is only a factor of less than an optimal (offline) assignment.[28]

1. ^ Ferguson, Thomas S. (August 1989). "Who Solved the Secretary Problem?". Statistical Science. 4 (3): 282-289. doi:10.1214/ss/1177012493.

2. ^ Hill, Theodore P. (2009). "Knowing When to Stop". American Scientist. 97 (2): 126-133. doi:10.1511/2009.77.126. ISSN 1545-2786. S2CID 124798270. For French translation, see cover story in the July issue of Pour la Science (2009).

3. ^ Cover, Thomas M. (1987), Cover, Thomas M.; Gopinath, B. (eds.), "Pick the Largest Number", Open Problems in Communication and Computation, New York, NY: Springer, pp. 152-152, doi:10.1007/978-1-4612-4808-8_43, ISBN 978-1-4612-4808-8

4. ^ Palley, Asa B.; Kremer, Mirko (8 July 2014). "Sequential Search and Learning from Rank Feedback: Theory and Experimental Evidence". Management Science. 60 (10): 2525-2542. doi:10.1287/mnsc.2014.1902. ISSN 0025-1909.

5. ^ Sakaguchi, Minoru (1 June 1961). "Dynamic programming of some sequential sampling design". Journal of Mathematical Analysis and Applications. 2 (3): 446-466. doi:10.1016/0022-247X(61)90023-3. ISSN 0022-247X.

6. ^ Rose, John S. (1982). "Selection of nonextremal candidates from a random sequence". J. Optim. Theory Appl. 38 (2): 207-219. doi:10.1007/BF00934083. ISSN 0022-3239. S2CID 121339045.

7. ^ Szajowski, Krzysztof (1982). "Optimal choice of an object with ath rank". Matematyka Stosowana. Annales Societatis Mathematicae Polonae, Series III. 10 (19): 51-65. doi:10.14708/ma.v10i19.1533. ISSN 0137-2890.

8. ^ Vanderbei, Robert J. (21 June 2021). "The postdoc variant of the secretary problem". Mathematica Applicanda. Annales Societatis Mathematicae Polonae, Series III. 49 (1): 3-13. doi:10.14708/ma.v49i1.7076. ISSN 2299-4009.

9. ^ Roitman, Jamie D.; Shadlen, Michael N. (1 November 2002). "Response of Neurons in the Lateral Intraparietal Area during a Combined Visual Discrimination Reaction Time Task". The Journal of Neuroscience. 22 (21): 9475-9489. doi:10.1523/JNEUROSCI.22-21-09475.2002. PMC . PMID 12417672.

10. ^ Heekeren, Hauke R.; Marrett, Sean; Ungerleider, Leslie G. (9 May 2008). "The neural systems that mediate human perceptual decision making". Nature Reviews Neuroscience. 9 (6): 467-479. doi:10.1038/nrn2374. PMID 18464792. S2CID 7416645.

11. ^ Costa, V. D.; Averbeck, B. B. (18 October 2013). "Frontal-Parietal and Limbic-Striatal Activity Underlies Information Sampling in the Best Choice Problem". Cerebral Cortex. 25 (4): 972-982. doi:10.1093/cercor/bht286. PMC . PMID 24142842.

12. ^ Kesselheim, Thomas; Radke, Klaus; Tönnis, Andreas; Vöcking, Berthold (2013). "An Optimal Online Algorithm for Weighted Bipartite Matching and Extensions to Combinatorial Auctions". Algorithms - ESA 2013. Lecture Notes in Computer Science. Vol. 8125. pp. 589-600. doi:10.1007/978-3-642-40450-4_50. ISBN 978-3-642-40449-8.

Bearden, J.N. (2006). "A new secretary problem with rank-based selection and cardinal payoffs". Journal of Mathematical Psychology. 50: 58-9. doi:10.1016/j.jmp.2005.11.003.

Bearden, J.N.; Murphy, R.O.; Rapoport, A. (2005). "A multi-attribute extension of the secretary problem: Theory and experiments". Journal of Mathematical Psychology. 49 (5): 410-425. CiteSeerX 10.1.1.497.6468. doi:10.1016/j.jmp.2005.08.002. S2CID 9186039.

Bearden, J. Neil; Rapoport, Amnon; Murphy, Ryan O. (September 2006). "Sequential Observation and Selection with Rank-Dependent Payoffs: An Experimental Study". Management Science. 52 (9): 1437-1449. doi:10.1287/mnsc.1060.0535.

Bruss, F. Thomas (June 2000). "Sum the odds to one and stop". The Annals of Probability. 28 (3): 1384-1391. doi:10.1214/aop/1019160340.

Bruss, F. Thomas (October 2003). "A note on bounds for the odds theorem of optimal stopping". The Annals of Probability. 31 (4): 1859-1961. doi:10.1214/aop/1068646368.

Bruss, F. Thomas (August 1984). "A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options". The Annals of Probability. 12 (3): 882-889. doi:10.1214/aop/1176993237.

Flood, Merrill R. (1958). "Proof of the optimum strategy". Letter to Martin Gardner. Martin Gardner papers series 1, box 5, folder 19: Stanford University Archives.

Gardner, Martin (1966). "3". New Mathematical Diversions from Scientific American. Simon and Schuster. [reprints his original column published in February 1960 with additional comments]

Girdhar, Yogesh; Dudek, Gregory (2009). "Optimal Online Data Sampling or How to Hire the Best Secretaries". 2009 Canadian Conference on Computer and Robot Vision. pp. 292-298. CiteSeerX . doi:10.1109/CRV.2009.30. ISBN 978-1-4244-4211-9. S2CID 2742443.

Gnedin, A. (1994). "A solution to the game of Googol". Annals of Probability. 22 (3): 1588-1595. doi:10.1214/aop/1176988613.

Hill, T.P. "Knowing When to Stop". American Scientist, Vol. 97, 126-133 (2009). (For French translation, see cover story in the July issue of Pour la Science (2009))

Ketelaar, Timothy; Todd, Peter M. (2001). "Framing Our Thoughts: Ecological Rationality as Evolutionary Psychology's Answer to the Frame Problem". Conceptual Challenges in Evolutionary Psychology. Studies in Cognitive Systems. Vol. 27. pp. 179-211. doi:10.1007/978-94-010-0618-7_7. ISBN 978-94-010-3890-4.

Matsui, T; Ano, K (2016). "Lower bounds for Bruss' odds problem with multiple stoppings". Mathematics of Operations Research. 41 (2): 700-714. arXiv:. doi:10.1287/moor.2015.0748. S2CID 31778896.

Miller, Geoffrey F. (2001). The mating mind: how sexual choice shaped the evolution of human nature. Anchor Books. ISBN 978-0-385-49517-2.

Seale, D.A.; Rapoport, A. (1997). "Sequential decision making with relative ranks: An experimental investigation of the 'secretary problem'". Organizational Behavior and Human Decision Processes. 69 (3): 221-236. doi:10.1006/obhd.1997.2683.

Stein, W.E.; Seale, D.A.; Rapoport, A. (2003). "Analysis of heuristic solutions to the best choice problem". European Journal of Operational Research. 151: 140-152. doi:10.1016/S0377-2217(02)00601-X.

Vanderbei, R. J. (November 1980). "The Optimal Choice of a Subset of a Population". Mathematics of Operations Research. 5 (4): 481-486. doi:10.1287/moor.5.4.481.

Vanderbei, Robert J. (2012). The postdoc variant of the secretary problem (PDF) (Report). CiteSeerX 10.1.1.366.1718.

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The secretary problem demonstrates a scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.

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Symbolize:

Magic, mystery, unknown.

----switching from darkness (unseen, unknown) to lightness

implies its supernatural power and the uncertainty of possibilities

Rain:

It reminds me of the movie 'Coherence', in which darkness also represents uncertainty and the house at the end of the road represents one of the possibilities.

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Yayoi Kusama’s infinity mirror installations

Intense repetition echoes mechanism of the attic

Claustrophobic atmosphere reflects Lauren’s overwhelmed feelings when choosing a husband

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Lauren is going through a NON-PHYSICAL LIMINAL SPACE

31 years old: a “big milestone” in a woman’s life where she’s expected to have a stable career, husband and even children —> Lauren feels lost about what she wants in life

Lauren just broke up with her ex, Amos and still has not gotten over him (transitional period between an old and new relationship)

Watching her friends get married and “settle down” and feeling unfulfilled

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Panels from the webcomic “Sandra and Woo,” where the protagonist’s friend chastises her for “cheating” when plucking the petals

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“You know you should always start with the answer you want, right?” -Jason

(P. 136)

—> a flawed method to make decisions as most flowers have odd numbered petals and humans are inclined to start with an affirmative —> they always end up with the answer they want

—> Near the end of the book, Lauren plucks petals to choose whether she wants to continue generating more husbands or stop entirely

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I interviewed my dad after reading the book.

Rain: What do you think of this story? husband can be changed at any time.

Him: After marriage, the problems that didn't appear before will appear to surface. Many people I know aren't satisfied with their spouse, they presume what would happen if they were married to a different person. But can anybody perfectly fit for anyone, to find 'the right one' out of 7000 billion people? the possibility would be very very low. the point is, that people tend to fantasise about a perfect partner, someone would meet all their requirements instead of spending time being with their partner, to understand your partner, learn to compromise, and to face the problems in marriage, to solve problems.

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Rain

Lauren changes husbands very quickly ----- showing unwillingness to stay longer to learn what these husbands are like ------ to dive deeper into their 'relationship'

Use sticking notes to write a 'criteria' to assess coming husbands, keep them if they meet her standard ------- want the husbands to align with her standard, instead of communicating, making compromises and solving problems with the husbands.

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Rain

People in modern times pursue productiveness and efficiency. It spoiled many aspects of human life; environment (non-degradable materials), industrial food (leads to disease), amusement culture, and relationships (快餐式恋爱/婚姻）.

Lack of attitude to dive deeper to explore self, other people and the environment.

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Lauren’s original apartment

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Lauren’s NEW apartment with Michael

He’s wearing a “grey T-shirt and soft tartan trousers.”

“the big grey landing… is, somehow, blue. And it has a rug. It never had a rug before.”

“The sofa is dark brown… when she left this morning it was green. The clock on the wall has Roman numerals instead of normal numbers.”

“Her old vase on the shelf has tulips in it, her wonky lino print of an owl is gone. The books are wrong or in the wrong place, the curtains have been replaced with shutters.”

“Most of the pictures are wrong… One of them is of a wedding.” (p. 4)

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Lauren’s garden with Jason

“an arch of maybe-roses” (p.34)

“Flowers and grass and a wooden table. A dozen little brown birds that take off as she approaches.” (p. 34)

“In the back corner, a big netted box with mazy branches inside and a blackbird outside, gripping on and pecking through the holes.” (p. 34)

“a wooden lattice, taller and growing all over with vines, some of them green and some with clusters of tiny white flowers and some pouring with long purple strands… a gate in the middle of it, connecting the two halves.“ (p.35)

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“She’s still theoretically assessing newcomers by her old Post-it criteria, although they’re not always reliable.” (P. 299)

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Flashing lights in my dorm laundry room (can be used as animation reference)

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Five fictional (and factual) attics | The Simple Things (Coco)

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Attics are often used as sources of mystery/ secrets/ the unknown in fiction

“The attic is a metaphor for the brain - a space right at the top of the house, where all manner of creative and imaginative happenings might occur, a place where memories are stored, and made.”

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We're all predisposed to love an attic aren't we? The chance of finding a long lost treasure, the secrecy of a huge room, hidden at the top of a house, the thrilling idea that it could be a private space just for us?

It's little wonder they feature in so many books, both fiction and factual. The attic is a metaphor for the brain - a space right at the top of the house, where all manner of creative and imaginative happenings might occur, a place where memories are stored, and made. How many writers scribbled in garrets, locked away in a dusty loft, after all? You don't hear of many writers furiously penning novels in sparkling open-plan kitchens, do you? They're a space to get away, feel 'above' mere mortals bumbling about in living rooms and bedrooms. Here we celebrate five literary attics:

1. Thornfield Hall's attic in Jane Eyre

The first Mrs Rochester is the inhabitant of the attic in Charlotte Bronte's best-known novel. Jane hears various crashes, moans and the like and it transpires that the source of them all is Bertha Rochester, one-time beauty and now 'demon' in the attic who starts fires, bites visitors and chews up Jane's wedding veil. Since we know Rochester is about to marry Jane bigamously, frankly we're with the first Mrs R on this one and think the veil-shredding (and probably some of the biting) is fair enough. (Also, Mr Rochester is pretty irritating. We might have bitten him too.) Poor Mrs R jumps to her death during a fire at Thornfield but holds a special place in our hearts as the first and our favourite 'mad woman in the attic'.

2. Jo March's attic in Little Women

Like many women writing in attics, Jo is a bit of a bluestocking, who wished to be a boy and found her skirts cumbersome. She writes her way out of her femininity, wearing a 'scribbling suit' of a black pinafore to soak up the ink and a feathered cap, like a master craftsman, and into a comfortable inhabitation of confident womanhood. Again, the attic is both an escape and a sign of Jo's superior intellect. And we loved her for her inky hands and the rats that nibbled her pencils.

3. Anne Frank's attic in the secret annex

Never could an attic be more thrilling than the real attic in Amsterdam in which Anne Frank enjoyed some fresh air, away from the stuffiness of the rest of the annex each morning. Anne wrote her famous diary in the secret annex in which she was hiding and the rat-infested attic, which was mostly used for storage was her escape, with one little window that it was possible to look out of without fear of being seen.

4. The attic in Flowers in the Attic

Much though we love a creepy Gothic tale in autumn, we might not linger too long on this very disturbing tale by VC Andrews of incest and abuse that haunted many of our teenaged years. Suffice to say, the attic here holds many a secret and spawns many more secrets of its own. <Shudder>

5. The attic in The Yellow Wallpaper

It's the decor that's the real star of this novel by Charlotte Perkins Gilman. When a young woman is sent to spend a period of rest in a colonial mansion at the turn of the last century, she's shut up in the old nursery on the top floor of the house. Far from resting her mind, the room itself turns her imagination inside out as she endlessly describes the wallpaper, comes to believe there is a woman trapped inside it and then becomes that woman herself. A beautiful feminist novel that's deliciously creepy, too. You aren't sure whether you want to never go upstairs again or disappear to the top of the house forever.

In our September issue our My Place feature is all about (much less creepy and much more beautiful) attic rooms like this one above by @finlay_fox. Buy this month's The Simple Things - buy, download or subscribe

More from our September issue...

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Five fictional (and factual) attics | The Simple Things

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We're all predisposed to love an attic aren't we? The chance of finding a long lost treasure, the secrecy of a huge room, hidden at the top of a house, the thrilling idea that it could be a private space just for us?

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—> slice of life, an exaggerated reflection on real issues that single people face in contemporary society

Coco

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—> what if your home generates an infinite supply of husbands? —> how will readers make a choice?

Coco

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Switch between darkness and light, to indicate the process from unknown to one of the possibilities.

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Rain

Magical moments happen throughout the book, while Lauran looks for a practical solution to stop magic from continuing. She wants her life to be on the ground once again, instead of changing and flowing all the time.

------- Perhaps using colour (high-resolution colour vs. black and white. Detail vs. simple. Textured vs. Smooth. Surrealism vs. reality....)

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https://i.pinimg.com/originals/db/26/5e/db265e9fcccf0a66b33db149908ca838.gif

👆more references

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https://www.vogue.com/article/searching-for-each-other-in-a-sea-of-words?epik=dj0yJnU9bHowaTBMU05vTkd0TU43bl9GbjR2Tng2ZlA5SFZ3YW8mcD0wJm49elFlM2VySUJMVkpHcXF6bUE3TTdZdyZ0PUFBQUFBR1dabUxZ

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My first impression of the cycle regarding Lauren and her husbands and stairs

1. A lot of the interactions in between appearing and disappearing of husbands revolves around the stairs

2. Opposite to the attic, the stairs more or less symbolises the relationship/ dynamics in a marriage

3. Where the attic is about come and go, stairs is about ups and downs

4. The loops follows Lauren whenever she decides the husband have qualities which she is into -> deciding to let that husband stay -> discovering the flaws -> letting them go

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Different aspects in marriage represented in husbands

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Different aspects in marriage represented in husbands

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Genre: Slice of life, comedy drama, romance(?)

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Genre: Slice of life, comedy drama, romance(?)

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Communication

Despite Lauren’s hostile reaction in the beginning of the book, he stayed calm and concerns over her well being

When discovers Lauren’s lies about her whereabouts and suspected infidelity in the second appearance, Michael appears upset and disappointed, remained calm and checked the attic when asked to

Michael values communication -> “But maybe I should also tell you that I looked through your phone a while back. Which I shouldn’t have done, obviously... I’m sorry, I should have just talked to you about it at the time, but I looked through your messages and that one wasn’t there any more. Obviously it could have been from a spammer.” -> “He wants so badly for her to be able to explain everything.”

Discipline

Michael being described as “he sounds very industrious”

Is said to be training for a marathon

Mochi

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The constancy of plant motifs symbolise Lauren’s stagnant character development throughout the novel

symbolic of Lauren’s passive attitude towards dating? -> doesn’t want to put in effort in compromising, communicating and understanding her husband’s shortcomings

Lauren waters the umbrella plant with “a half-used bottle of beach- waves sea-salt crunchy hair spray, which is both expired and out of fashion” and hopes for it to flourish -> does the bare minimum and expects a relationship to work out

Coco

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https://laundryday.itch.io/attic

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https://www.instagram.com/hollywarbs/?img_index=1

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art by 切尸红人魔

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【【高布兰毕业作品】迷幻忧伤的天堂寻妻记

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【【高布兰毕业作品】迷幻忧伤的天堂寻妻记 | 再见，杰罗姆！AU REVOIR JÉRÔME !(2021)-哔哩哔哩】 https://b23.tv/nu6UFqC

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https://www.itsnicethat.com/features/jackson-joyce-illustration-the-graduates-2018-130818

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First time sees a husband at her flat. It's raining outside. (chap 1)

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Trying to lock the door with chair (pg 7)

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Route to Felix’s House/ rough house interior

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Route to Felix’s House/ rough house interior

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Felix: materialism, control and surveillance 

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Felix: materialism, control and surveillance 

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Materialism

Detailed descriptions of the house and surrounding sceneries

Includes a lot of extravagant deco on the house

Suggested that Lauren might have been the second or third wife-> trophy wife(?), might have not been a marriage entirely out of love

Control and surveillance

The CCTV room next to alcove

“she can see herself standing, looking at the screen, her stiffening back, movement as she turns to look up. Above the cabinets, a squat grey cylinder is nestled discreetly. She has to force herself to turn away from it and look through the rest of the screens” -> a bit of an allegory of the marriage itself

Hanging birds (similar concept to above)

‘I don’t know the gym code, I’m not allowed in case I drown. Look on your phone.’ A bit controlling regarding the son’s saftey

There isn’t a lot of trust within their supposed marriage: codes to access doors, suggested alert system, Lauren avoiding cameras, Lauren sneaking in later in the story.

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Dancing with Michael during their wedding (pg 14)

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husbands...TOO MANY husbands

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hugging Bohai. Lauren cried and smiled in relief. (pg 174)

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talking to Bohai, exchanging experiences. (chap 23)

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【这种流动效果的转场是怎么做的？【mg动

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【这种流动效果的转场是怎么做的？【mg动画】Drab™ Fibertel Attributes-哔哩哔哩】 https://b23.tv/tADOr3m