Saturday, May 11, 2013

Should it be legal?



Time for another episode of "should it be legal ?"

Think of it… we're in Philadelphia, no the movie, not the city. And Tom Hanks discovers that the corporate email server is very slow… too slow in fact to receive the document he is trying to emailed to his assistant before the end of statute of limitations was set to expire the next day. Would this count towards illegal discriminatory behavior based on race, age, sexual preference or country of origin?

Actually a more important question to ask is does anybody even care of fairness at work place? Are there any amongst you that would agree to racial discrimination just to receive some shares of stocks or to feed your family? In this time of terrible economic crisis, I think most people in America do not have the liberty to act on concerns of unfairness.

Why has there been more frequent economic crisis? I think I finally know why. It is not because corporate America cannot keep accounts straight or evaluate risk on mortgage loans! The crisis for all practical purposes legalizes discrimination. Everybody is holding their own mouths shut for fear of being seen as against the company.
Is it legal in America to restrict employee work-place internet connections and bandwidth based primarily on race, and place of origin?

Personally, having no law degree, I feel that it is race based preferential treatment and unfairly bias against a certain group based on racial characteristics and place of origin.

Oh, I mean, I know it can't be traced to the company… just like that fax was lost and recovered inexplicably in Philadelphia. But the mere fact of this capability should be announced publicly like when police decides to arrest people they have to say out loud what and why they are doing it. When the company inspects the employee's connections from work place computer and delay it or disrupt it, it must be done in an unbiased way.

Am I, like, the only one?


Dude, am I like the only one under the sun who don't know who or how emails are being "unsent" ?
The symptom is this: I type the email, hit send, it goes away. Next day (or several days later), I become aware that recipient did not receive the email. I look for the email and it is stored as an unsent "DRAFT" in gmail.
I did some quick search on google and didn't see anybody else talk about this. But my email (gmail) often become unsent after I hit the send button. I doubt it is a bug on google's side. I also doubt it is very wide spread, since I have neither seen or heard anybody mention this problem.
But it does happen often when the content of email is undesirable for the recipient. This happens both in google's free accounts and in a paid enterprise version of gmail. It happens both in work email and in personal email.
I mean, I guess I should admit, now that I'm at it, that I also have occasional ED… Because it is of similar level of embarrassment for a computer guy to not know this crucial skill is probably like ED to sexual ability of man--naturally occurring but failing. Oh, and!?, btw!? I also have urinary incontinence. Experiencing all three, I can tell you that they don't kill you, but all are very inconvenient and can be very very embarrassing.
Let's see, what have I tried:
* Tried google's 2-phase verification.
* Tried paying google for the gmail account.
* HTTPS always, man-in-the-middle due to invisible corporate proxy cannot be. And it happens at home too.
* And failing that, using a mobile device that goes through an entirely physically separate cellular network.
* Use chrome, which supposedly is more secure than other browsers.
* Bcc myself on all mail.
* porn, sex, not drinking water, and diapers.
Still, emails become unsent the next day. The problem with this is that if it is not a bug, then the people who cause this to happen is seriously detracting from my ability to work and live. I mean, I have thought about how it might be my boss who just want to delay a few projects so that he doesn't have to give me bonus, or my coworker who want to make me look bad so that he can get bonus, or the HR/legal of company who want to reduce liability of the company by making it look like I didn't communicate vital but damaging information.
But those are just suspicions of a really insane person. I mean, seriously, what are the chances that the silly secretary or office manager have more access to information and control my communications than I do? I mean, com'on I actually work and produce things that the company sell for money, it cannot possibly be that there is a person who sits there and reads every single email and evaluates them and selectively unsends them.
I don't have trouble believing that shrewd corporate competitors and business man and an occasional hacker have the means to do this, but the unsending of email happens at several companies, several accounts under management by different people. It happens enough to make me think that every company officially has the capability of unsending emails hosted by google?
Is this an attack by Microsoft? Part of the scroogle campaign? Some coworker do come from M$ family… Corporate conspiracy to defame google?
Despite these occasional intrusions, I have not been motivated to seek out a new email service provider (ESP) for my personal account, and certainly have no better alternative to recommend to work place.
Also, it could be that I just suffer from some kind of interruption in consciousness and somehow I have clicked on "INBOX" instead of "Send" on those occasions. But this is very unlikely as many of these emails contain important information. Also, there are occasions when I've checked that the email is in the "SENT" box before leaving work and then seeing the email in "DRAFT" folder several days later.
I know I won't be the first or last guy to complain about ED… But how come there isn't awareness campaigns and support groups for people who's email get unsent?
p.s.
Btw, if you ever get raging hemorrhoids that stay for months and months or anal fissure that reappear daily, try to use some baby diaper cream in addition to the fiber that the doctor prescribe. They cream help you heal just as much as they help baby. fyi I guess... At least I have found some solutions regarding this embarrassing matter.

Insurance, Universal Health, and BS (slight repeat)


I would not be the first one to point out that this is the way things are. Hospital bills are insanely high. The birthing of my child including the subsequent 11 days of hospital NICU (neonatal intensive care unit) stay at the Stanford Lucile Packard Children Hospital resulted in a combined bill for both mom and child of $157k. And let me say upfront the staff at LPCH worked very hard to make our stay comfortable. We learned a lot about taking care of the baby there from all the wonderful nurses and Dr.'s
$175k is a lot of money: With that money I could three(3) base Model S's. Or I could pay off of some of my mortgage. Or pay off my parent's mortgage. At my planned saving rate of about $20k a year, it would take me 8.5 years to accumulate that amount of money, just for a single incident of child-birth(not including continuing costs after the fact). Now, being an informed modern man, I appreciate the 99.99%(estimated) success rate of child-birth that this cost buys me. And indeed my child is healthy and alive, and she may very well not be if we had her in a wilder situation where the cost is less. The peace of mind that we have knowing that there is a machine and two nurses watching over the child during those tenuous times is very much worth it.
Now there are two issues of concern. One of them is that the entire process was not 100% pleasant, there were times when we wondered if the doctors/nurses/staff were picking on us because of our minority status or apparent lack of wealth or influence. Some staff were quite obnoxious, one even dropped his badge in an inconspicuous place in order to lift my wife's cover to search for it. what a pervert!
Anyway, that's not the problem. This $175k bill would have put me in debt for 8.5 years if I did not have an insurance. The insurance company negotiated a different price tier and then paid for about 95% of the negotiated fees to the LPCH. Without insurance company, I may have simply taken the child home after birth and watched her stop breathing and then eventually rush her body to the hospital. Without insurance, my wife would suffer from untreated back injury from the birthing process. Without insurance, I would not be able to take the baby to a dr. about the mucky eyes she has and eating/pooping/peeing issues and various growths and spots and all kinds of weird alien things baby produce. Life would not be life as I know it without the group comprehensive insurance provided by my employer.
Recalling just a mere 6 months prior to this, I was rejected for insurance by a large PPO because I checked a box that said I snored--due to a prior condition. I am a fairly healthy person in my mid 30's and being rejected for health insurance was the last thing I expected... it kind of ended my consulting career.
Let's think of health insurance in more detail. Insurance is a benefit, part of my compensation package, my employee give me for my service to the company. What this means is that I must work for an employee that provides group insurance in order to continue to receive this kind of benefit.
It would seem that the pressure and flow of money is as follows: medical cost is high, insanely high, to a point that it would appear an uninsured person cannot pay for basic care. Each individual is highly incentivized to work for large corporations that provide group health insurance, because if they don't they cannot get health coverage and because the cost of health care is high, they cannot get health care. (oh, and also in the same breath, only spouse of a heterosexual marriage can benefit under group health insurance)
I personally appreciate the role of doctors play in society. They use their life's time and energy to become good at treating people's illnesses so that other people can live long and happy lives. I think the medical-industrial-complex that power advanced research in science and technology that produce advanced diagnostic tools (xray,mri, etc.) and drugs, and genetic therapy, and stem cell research, all these things trying to make people's life better are great! It costs a lot of money and require a lot of resources: universities, hospitals, buildings, power/computing infrastructure, lots of smart people to achieve advancement. So an expensive drug, expensive test, if charged by original developer, is cost to pay for past and future research. Expensive doctor is to pay for his educational cost and to maintain his alertness, dedication to the unbiased professional medical treatment of his patients. I want them to make more money because I don't want to have to wonder if my Jewish doctor treat Jewish children better than my child or if my Russian doctor treat his Russian patients differently from my wife. I want to receive good treatment and I believe that most doctors are paid above other people not only because of their unique skill sets but also because they rise above all that, ethically, and heal their patients any human patients to health.
BUT, that fact is being exploited by large corporations. Only large corporations can afford group health insurance. Therefore only they have access to people who want health care. Fundamentally, there is nothing wrong with this. But practically it forces all health-conscious people to subscribe to corporate culture. We do not have a choice in how we contribute to society, but as long as we want to see a doctor when we need, we must be part of a large organization full-time.
Some additional aspects of this arrangement: If I had a serious prior condition that requires constant treatment, then I must be employed at a large company in order to survive with life. If there are any bias in corporate employment then the same bias would occur in availability of medical treatment. If I stop working or have never had insurance, I must work for a company because I will not be able to get insurance having a break in health coverage. I cannot leave the company for injustice or corruption immediately and in the duration of dispute, I may not be able to continue with insurance, and the interruption in coverage will result in the impossibility of my getting health insurance.
I have always been in favor of universal health care in America. This is not because I come from a faux-social/communist China. I am in favor of universal health care despite the fact that the medical super industry will not receive as much money from patients because the US government will surely negotiate an even better price than the private insurance companies. I am in favor of universal health care--for basic maintenance care--because health, along with wealth, is part of our pursuit of happiness. I do not believe one can be happy secured with his wealth but insecure with his health, and we should have the freedom to choose health independent of wealth. Health is life. Right of life means right of health, protection for right of life means protection for right of health--in fact protection to right of health should be on par with the right to secure one's wealth. Health is happiness. Pursuit of happiness requires health. This is why I think universal health care--to a certain level--is a must. Even if it detracts slightly from advanced medical research.
Okay, moving on. A thought occur to me the other day on the way home from my health-coverage earning job in corporate America. I thought of the transitive action space(TAS) more. The TAS encodes actions between people, therefore should be thought of as only encompassing all endeavors regarding acting morally. Again, I justify this because the original thread of thought came form the golden and silver rules of ethics both of which directs us in how to act.
But clearly they have said more than that, for instance it has been said that one should "love thy neighbor as thy self." Granted this a command in the TAS, but more action this is a feeling. Love is a feeling, is a state of mind that can occur without visible action in the TAS. Perhaps we should also mention the existence of transitive emotional space, TES. Subsets of TES instructs us about the moral ways to feel--whether we have control over feelings, and are they moral if we control the feeling rather than naturally feel, is an entirely different discussion. We can, in fact, specify the subspace of TES that is moral, the Bible sure does.
There are of course yet other instructions in morality that instructs us on how to "be". "Be one with God," "Be one with the universe," "Being a higher being," "Being enlightened"... and so on and so forth. Some argue that the being is creating an internal state, and therefore being moral is the moral motive force that enable us to act and feel morally. Some even stipulate that without a moral motive force a moral space in TAS is not moral. For instance, if I feed my baby with an intent driven by the perverted curiosity of seeing a grossly obese 1yr old, then the action of "feeding a baby" in TAS is entirely moral (possibly universally), but the being inside BS is immoral. Most would agree that the act is entirely immoral.
Therefore we should also seriously consider BS--Being Space that contain all the ways that we could be. The challenge of such a space is that BS is of much higher cardinality than TAS. In the real world, we can very likely specify countable discrete TAS for a certain self contained situation in which we have to make moral choices, where as I am not able to imagine the "enlightened" and "universe" beingness of BS--do they intersect? does one contain the other? What are the sets in TAS that corresponds to their intersections? Does intersection and containment make sense in the BS? How do I choice to be something BS? How do I be something in the BS?
Ultimately, the choice of TAS seem rightous at this stage of my investigation. And I beleive that even if BS is ultimately the only space where morality is true, that there is a TAS projection from BS that can be modeled. From time to time, we may need to point out the relation between a TAS set and BS but until I have the language to discuss it, BS shall remain mysterious and unexplained.

Code.org Advertisement and no-WFH


Recently code.org publicized a promotional video featuring ppl like Mark Zuckerberg of Facebook and Bill Gates of Micro$oft saying American schools should teach programming more.
I don't like it.
I don't think programming is for everyone and that more programming is for social good or scientific advancement. It lowers cost of labor for all those people in the Advertisement, but it isn't as good as it sounds.
As a person who completed a CS degree, I feel that computer language can be made much better so that there won't be a "computer programming"
The day that I tried to teach my dad to program a for-loop in C and he turned around and teased me about forgetting the closed form expression for arithmetic series was the first time that I thought about how stupid this stuff I do is. It was the expression on my dad's face... I remember it vividly... For it was then that I realize that I did not comprehend the sheer vulgarity of
for(int x=0;x<100;++x);
so primitive, so stupid.
The next time is when I read about Map-Reduce--sooo freaking cool. I think tomorrow I will find another way to think, another way to say, and another way to program.
I want to make a better programming language. a better computer. That would be better than community colleges teaching Fortran IMHO
Oh, and p.s.
I think Yahoo!'s new no-policy is nice. I think is real progress for protection of civil liberty in America. Technology companies insists on ownership and monitoring of its employees while working, and admittedly justified to do so. Therefore when Marissa Mayers decided to cancel all WFH, she made a call that will end monitoring of employees' home networks--because if you don't work from home, the company will have no cause to instrument any kind of monitoring of your home network.
I think this is a really forward thinking technology leader who care about her employees. I am buying myself some Yahoo! stocks in support of this bold move.

The Ethical Hiearchy III


Recall, from last time, this illustration of the Ethics Hierarchy overlaying capability sets in the space of all transitive actions:
gold versus silver 1
I should simplify terminology. The set labeled "Things I want" are "my desires", "things Jesus wants me to do" is the Jesus way, "Things Confucius wants me to do" the Confucian way, "Things I can do" are "my strengths" and "Things can be done to me" are "my weaknesses".
I should also like to begin referring to what I have been calling the Ethics Hierarchy as the Moral Hierarchy. My own postings exhibit cultural bias. I include more from eastern culture than western culture. Some comments I have received indicate that there are others out there who have looked at culture/art/literature comparisons with the opposite bias. The fact of matter is, this Moral Hierarchy itself does not imply absolute superiority of any kind. Relatively speaking, one is larger, contains more transitive actions, than the other, but bigger is not necessarily better. In fact, it is one of my hopes to understand how they are different. Reasonably speaking, I should not expect to find that one is superior to the other--quite the opposite, I feel that exhaustive investigation of this subject will reveal to us more about the way the world, humans, and our society are than about the rights and wrongs within their contexts. Because morals have cultural biases and ethics is the philosophical study of morals, I may switch back to Ethics Hierarchy when I wish to emphasize that I am trying to be objective.
Therefore, to continue, let us be fair, what is drawn are idealized sets and intersections. The Jesus way is actually one of many allowed sets of actions that has an inner-bound restriction of being bigger than the my desires. Under this prescription alone, one can do everything in the universe and still not violate the Golden rule. The Confucius set, similarly is one of many possible sets fully contained in my wants set. The Silver rule has a maximum outer bound, one can only do things within my wants. Under silver rule, one cannot do everything in the world.
Some extreme examples might be, for instance, a person that goes around slaughtering each person with a knife is allowed under one interpretation of the Jesus way, as long as he also does everything that he wants for that person. This can be quite arbitrary, say, the perpetrator wants to be fed carrot cake, then he feed everyone carrot cake and then knifes them. What's worse is if the person is masochist, then he is forced to act as sadomasochist. If he wants to be fed carrot cake and knifed, then Jesus way requires that he _must_ both feed everyone carrot cake and knife them.
On the other extreme, suppose one tries to follow Taoist suggestion to do nothing, it easily fall within Confucian way without regard to the size of my desires. While the only way for a person to do only nothing under the Jesus way is for him to want nothing. This is impossible because follower of the ways of Jesus at least want to enter heaven, so trivially Jesus way is never empty and prevents follower from doing nothing.
It's interesting to think of the possibilities. Let's look at just the Confucian way. Set D is outside of my strengths, and it is outside of my weaknesses, however, because I desire it, it is within the Confucian way. Set A are things I desire, within my strength to do and outside of my weakness to receive. These are the things that I can only give and will never receive in kind. On the opposite end, set C are within my desires and weaknesses but not within my strengths. O is the set of my opportunities--these are the things I want but am not yet capable of receiving. Set B is a sweet spot. Here, not only are we within the ways of both Confucius and Jesus, we also desire to do so. This is a region to maximize, if we had the choice to do so.
gold versus silver 3
It should be pointed out that zone B contains only actions that we can reciprocate when receiving and receive reciprocation when giving--in kind--in other words, an eye for an eye, a tooth for a tooth zone.
Zone U in this graph points out an area of the an-eye-for-an-eye-a-tooth-for-a-tooth zone that is outside of my own desire and therefore not recommended by either Confucius, but is allowable by the Jesus way.
Let's backtrack and admire the an-eye-for-an-eye-a-tooth-for-a-tooth zone T in its full glory
gold versus silver 2
Wow! It does exists!

With Higher Knowledge Come Higher Responsibility


The other day, at work, (and by now you know I work for a Japanese Automotive Electronics company), we talked about autonomous cars for consumes. Since everyone is either technology freak or car freak the discussion was pretty intense.
I explained to every one the ethical issue surrounding autonomous cars that may be not be completely resolved or resolvable by technology.
The matter is this: an autonomous car will with absolute certainty be faced with a situation where it has to choose between two actions each will be killing a different person. Suppose two person suddenly dash in front of the car to the left and to the right, and suppose that the car is moving too fast to stop. it can veer to avoid one person with certainty. But which will it choose?
Another scenario: the car can brake very hard and avoid killing a pedestrian, but in the process it will have killed the passenger because the car is mechanically able to endure much higher de-acceleration than its occupants.
The legal problem also, if I configure the car, or if some car company configure the car to always protect its owner (rational), that I the owner, the designer, the manufacturer is then liable to be sued for killing people?
"But your honor, the car swerved!! I had nothing to do with it"
Okay, so the people who want autonomous cars (myself partially included), will say that with better equipment, high-speed video/audio recording and black-boxes, there might be far fewer arguments about who was responsible for accidents. But there are some things in our current law that are absolute. If a car hits a person inside the cross walk, the car is always responsible. If the car is rear-ended the car in arrear will be responsible. What will happen to these absolute laws that are in many circumstances unreasonable but serve to protect the safety of the population?
And finally, even if, and I believe it will, autonomous vehicles reduce death to 1% or less of today's vehicle related death rate, that 1% where two person dash in front of the car, and the car has to choose, what then? Why is this so hard?
One of the big problems is informed decision is hard. The car, given today's technology, machine learning technology for object detection, vision algorithms, radar, laser range scanner, eeg/ekg, EMR technologies can pretty reliably detect with plenty of time to choose which one to save, that there are two person dashing infront of the car one to the left, one to the right, velocity, estimated trajectory, mass, the certainty of these estimate and the margins of error (where else could each person likely be by the time we collide, etc.)
The reason human get away with killing in this situation is that we do not have the speed and ability. It is beyond our control--until we programmed a computer to do it, and then we are suddenly faced with choice that we never had to make before: kill left, kill right or maim both? or risk killing both? or kill myself to completely avoid  their injury?
Hmm, let's see, What would Confucius allow? What would Jesus insist? Well, I don't want to be killed, so don't kill other people. I would want other people to save me so I would want to brake an save both crazy people. Hmm, I guess it really depends on the person's desire. One would say a more moral person may not wish for another moral entity to suffer in exchange for his own sake, as well to exchange another's life for his own. But by and large most people would ask the car to save himself no matter which place he is in.
The moral problem arise in that we are not in any of those three situations. We are in the autonomous car's designer's shoes. We are in Asimov's shoes. What should we write as the laws of autonomous vehicles? When we know that at some point, the car will know almost certainly that it must kill/damage/disrupt someone/thing, and knows exactly which wire to send electric signal down to to choose which person. What should we tell the car to do?
Because soon the car will be looking at that scenario in slow-mo... with 10ms to decide and then 250ms seconds to turn the steering wheel left or right and apply brakes.
So, as you can see, the mere knowledge of morality and capability to choose encumber us with the responsibility of behaving morally. Because I know it's wrong, I must not do wrong. Another person may think that the root of this evil is the fact that I know of this moral dilemma and that I have gained the speed to travel fast or gained the speed to determine people's fate.
I wonder if the are right that those things are works of devil and that the absolute best moral thing to do is just to stay away from them? I should consider this carefully. What if I find that it is wrong for me to live? or wrong for me to blog about morality? What if it is found that internet is not moral? or god forbid that it is immoral to have stereo audio in cars? Because I already of the ability to terminate any one of them--at least for myself.
*shiver*
p.s.
I can accept an argument that placing one's self into a situation where there is no moral choice is immoral. The autonomous car makers will insist that car drive carefully so that it will never be faced with 2 people in said situation. But somehow, science, technology--human inquiry--may find a way to inform us that that is just delusional, that it is provably impossible to avoid crazy human. ;) back to square-one I suppose.

The problem with Transitivity II--Unfixing Trivalency


Looking at my old blog entries, I think there is a problem with our earlier attempt at addressing tri-transitivity and higher order valences. The problem actually points to a larger issue. Let us try an extended example of trivalency
I am giving you a slave named Tom.
Subject: I
Object: you
Object being done with: A slave named Tom
Thinking of ethical issues: My giving a slave may be considered wrong and you allowing a slave to be given to you my be considered immoral. But ultimately, that Tom is a slave is perhaps something not ethical in and of himself. What about
I am giving you a slave named Tom to keep you alive from being quadriplegic and demented.
This seem to make me a good person and give you just cause to require full time service of a devoted person. Is this act allowable? I would if I followed Jesus's way, and I could if I followed Confucian way.
What about the veil of innocence, how come it isn't compatible here? at first glance, it seems that it should, what if you were Tom and you were being given. You would then choose not to give tom as slave right? But in Bi-transitive Action Space, let's call it BTAS for short, we have no way of evaluating that, you are either subject or object, there is no third position.
The reasoning here, therefore, must extend analysis of Tri-Transitive Action Space, TTAS, and other higher valencies, HTAS's,  to analyze the TAS itself for inclusion and usage of ethical entities that are considered of same importance as the subject and objects of TAS analysis.
* Giving a person as slave is unethical.
* Using a person as a slave is unethical.
* Being used as a slave is unethical.
The first two come from a traditional ethical systems. One cannot use another ethical entity in a subjugated manor, and one should not force an ethical entity into such a position. But what about the third, that seems a little stranger, allowing oneself to be enslaved is an unethical act. Certainly an ethical entity may be able to enslave another and should do that instead of being enslaved. Alas, these problems are indeed at the heart of concerns driving these current carpal tunnel stiffened hands into worse states than they are in already. At least, our action space needs to give us the ability to consider the third ethical entity.
Let us be more specific about BTAS as well, it is really very easy to include HTAS inside BTAS. So we need a class of TAS that include exclusively Bi-transitive verbs where the verb themselves do not use or influence any other entities affecting ethical value. This class of actions we shall refer to as Full-Bi-Transitive Action Space, or FBTAS(ef-bee-taz) for short. And similarly FTTAS for tri-transitive verbs with clearly distinguishable subject, object, and third thing which the action uses and affects evaluations of ethical nature.
I fear soon we will run out of letters and theory synonyms as we look into this matter deeply. I am driven to think of another way to think about this issue... Naming a new space for different situations is too troublesome and impractical.

IG and the Quantification of Privacy


A while back, I talked about computing IG--information gain--by clandestine methods via an otherwise secret(personal) email. I will point to some other prior blogs entries about what can we reasonably consider private and some reasons why I think it's bad (Because it removes competition....
The basic challenge is this: If your competitor can spy on what you do (unilaterally) then they will never be motivated to innovate. Their key strength will be their ability to hack your secrets and they will work hard on that, but not on how to build a better product or cure a disease or solve a new problem. If you can both spy on each other with perfect information then there is no need to innovate, just calculate the equilibrium and aim for that. If you can disinform your opponent then all your effort will go into disinformation instead of innovation. Basically it is much easier to do something sneaky and cheat than to do the right thing and innovate. This is why the government, a non-competing body whose interest is to make sure everyone compete (at least in America government this is the case), should provide for information security.
)
I realize in retrospect that IG may not make sense to most people based on the formulation I laid out. Let's review. IG is the change in entropy from a state without additional knowledge to a state with knowledge
IG = H(secret) - H(secret | private email)
This measurement seem to be of a quite abstract concept of entropy--a unitless measurement. Why would I think this useful for any reason other than that it is called "Information Gain?" Well truth be told, what I had in mind was more of the IG from machine learning literature: Class purity after conditioning on some private information. It is actually used more as a measurement of correctness of predicting discrete output than abstract change in entropy of distribution after conditioning. I will refer reader to these excellent introductory books regarding "classification" algorithms.
… Some days passes and the books will hopefully have arrived on your desks…
So the example is if my secret is the probability that I will have Chinese food tonight. Let's throw in several more classes, say Italian, Mexican cover 99.9% of all possibilities. This probability may be internal to me. Or it may be an externalizable model like I will toss a three-sided die and figure out what I will eat tonight.
Actually, this system forces us to think of a new class. I will call this new class the innovation class. It covers all cases where something new might happen, such as tonight when I went off on a tangent and forgot to eat dinner completely. Or I might be abducted by Aliens for demanding privacy, Japanese paramilitary for blogging, or God for thinking all these awful things. The fact is, I do not know what will happen, but what I do know is that things I don't know will happen. So the class is called IC, Innovation Class--now we have a 4 sided die: Chinese, Mexican, Italian, IC; Let's write naively that the probability for each class is:
ChineseMexicanItalianIC
33%33%33%1%
The formula for the entropy of these classes is written as:
-H(Dinner)= p(Chinese) * log(p(Chinese)) + p(Mexican) * log(p(Mexican)) + p(Italian) * log(p(Italian)) + p(IC)*log(p(IC))
the above evaluates to almost the maximum possible entropy in three-class situation: H(Dinner)= 1.6499060116098556
that's it. that's the formula for calculating entropy that we will use repeatedly. Now, suppose that you have read my email to my wife saying "oh man, look at this great deal on groupon, 50% off on Indian food right near our home" What is the right thing to think about the distribution of my dinner?
P(IC)=99%
Indian food is not Chinese or Mexican or Italian, but we have thought of that and put in IC to account for it.
ChineseMexicanItalianIC
10%10%10%70%
-H(Dinner|private email to wife) = p(Chinese|private email to wife) * log(p(Chinese|private email to wife)) + p(Mexican|private email to wife) * log(p(Mexican|private email to wife)) + p(Italian|private email to wife) * log(p(Italian|private email to wife)) + p(IC|private email to wife)*log(p(IC|private email to wife))
gives us the conditional entropy of probability of dinner after reading my private email. This entropy H(Dinner|private email to wife)=0.09596342477405478
IG(Dinner; private email to wife) = H(Dinner) - H(Dinner|private email to wife) = 1.6499060116098556-0.09596342477405478=1.5539425868358008. This corresponds to an IGR of 1619.31%, that is, 15X more information after you saw the email than before.
Great! so now we know how much information is gained by reading that one private email of mine. This number, I think quantifies my loss of privacy.
Btw, this innocent example contain some hand waving. H(Dinner) for example is something that we may or may not know. Most people have trouble writing down a distribution for dinner choices. also, P(Dinner|private email to wife) here written as a table contain assumed values. What if after reading my private email you feel that P(IC)=85%? Who is to say what the reality of this probability is? This is why I felt that this model will not make to main stream legal system because the link between private email and the actual secret itself is not so obvious. You might use naive Bayes as the definitive of reality (refer to chapter in books or wiki), logistic regression, decision trees, or you might use something else… You may even use a distributions system like SVM or god forbid rule based systems…
If you understand this computation above, then it will be easy for you to understand the continuous version. Let dinner be a continuous variable, we can still write the same expression
IG(Dinner; private email to wife) = H(Dinner) - H(Dinner|private email to wife)
and it would have the same meaning. How far are we from the truth. This idea, btw, is indeed partially inspired by the name Information Gain, which also goes by Kullback-Leibler divergence when computed over distributions. The above formation exactly with the exception that "private email to wife" is a distribution, say, perhaps, my emails are generated randomly.
KL( Dinner|private email || Dinner )
But KL divergence does point us to some other interesting characterizations. Divergence--distance without some properties of distance. Namely that it is not a metric distance:
* Nonnegative dl(x,y)>=0:  yes
* Indiscernability: dl(x,y)=0 iff x==y: yes
* Symmetric dl(x,y)==dl(y,x): NO
* Triangle inequality dl(x,y)+dl(y,z) >= dl(x,z): NO
This has some serious implications regarding this formulation of privacy. Somethings that we naturally think should make sense do not.
Let's say I have two emails, e1 and e2, and let's say dinner is still the subject of intense TLA investigation:
KL(d;e1) + KL(d;e2) != KL(d;e1,e2)
All private information must be considered together, because considering them separately would yield inconsistent measurement of privacy loss
Let's say there're two secrets, d1 is my dinner choose and d2 is my wife's dinner choose
KL(d1;e1,e2) + KL(d2;e1,e2) != KL(d1,d2; e1,e2)
All secrets must be computed together, because computing IG separately and adding is not equal to the total information gain.
Let's say we have an intermediate decision called Mode of Transportation (mt), and it is a secret just like my dinner choice.
KL(mt;e1,e2) + KL(d ; mt) != KL(d; e1,e 2)
The intermediate secret can be calculated, but again, it must be calculated carefully and not by additive increase of IG.
Bummer, but fascinating!! But we we must make some choice about how to proceed. Knowledge about the nature of information (and especially electronic information), I believe, informs us about how we make choice in our privacy laws:
  • Should the whole data be analyzed all at once?
  • or should we only allow each individual's data be processed all at once?
  • or should we only allow daily data of everyone to be processed together?
  • or should we only allow daily data  of each individual to be processed separately?
Each of these choice (and many other) impact the private information loss due to clandestine activities.