My post is primarily a philosophical one–not one that’s focused on biology or even statistical theory, although I do mention them quite alot in the argument. I did not claim to be a 7 day creationist, nor an evolutionist. I also do not claim to know any more about biological theories than a high school graduate who took an AP course. That being said, this is the main point of my post:

I don’t believe that all creationists are anti-intellectual. Sure, many creationists we know of will accept the bible and the literal use of the word “day” with absolute faith, and as a result there is no room for discussion about scientific evidence that suggests the contrary (you can’t discuss theories about the big bang or the origins of the universe, which I find absolutely fascinating): hence a lack of intellectual discussion due to failure to find common ground. However, two creationists may be able to engage in a mutually interesting, though non-scientific, discussion about the Garden of Eden and the creation account in the bible. They may also be arguing about interpretation. This is all an intellectual exercise, no less than scientists arguing about the theories of evolution. Just because the majority believe in one thing doesn’t make the minority less intellectual. They simply use different axioms.

More importantly however, note the key words that I used in the previous paragraph: “evidence” and “suggests”. The scientific paradigm is one that rests on the burden of “proof”. However, unless you are in a purely mathematical field (i.e. playing with abstract ideas), scientific “proof” rests on inductive axioms that can never really be “proven”. It can only be supported by statistical evidence and models constructed based on such statistics, and much of it rests on the assumption that what was observed in the past still holds today. At least, this is how it’s done in the engineering discipline, in theory and in practice. You can only engage in an intellectual discussion if both of you believe in the theories/models/techniques behind it. And personally, I wouldn’t be employing models at work if I did not believe in them (with high probability  ). As I said before, I am not a biologist and am therefore unfamiliar with how much evidence exists to support different evolutionary statements about the origins of different species that exist today or in the past. That analysis is up to the experts in the community. However, my claim is that the scientific philosophy rests on these fundamental assumptions about observability and regularity.

Along those lines however, I am also stating that “miracles” by definition cannot be scientifically proven (except with a set of probability zero or near zero) because they are things that are observed perhaps only once in a lifetime, if at all. If miracles could be reproduced in practice, they would cease to be miracles and at best would be scientific “phenomenons” (i.e. things that can be made to occur, but the cause is not well understood). 7-day creationism (if true), Noah’s ark (if true), Jesus’s resurrection from the dead (if true), would fall under the category of “miracles”. They must be accepted by faith because they are inherently non-reproducible.

What is my conclusion? Basically, open-mindedness. I am not asserting that you have to doubt what you currently believe, whether by religious faith or by scientific faith. I am not advocating some type of relativism. However, it would probably benefit you to put on two different thinking caps when discussing issues of religion versus issues of science, because they rest on two fundamentally different axioms that seem to be contradictory, but at their core are not. A scientist should be able to resolve the idea of “miracles” , since not everything is reproducible (at the moment at least, e.g. the Planck epoch of the Big Bang). Likewise, I do not see a reason for a Christian to take offense when entertaining ideas based on observation and statistics, including evolution. After all, you probably use similar assumptions all the time in your card games or dice games. All else being equal, if God exists, so do unreproducible miracles. If He does not, or He simply chooses not to intervene with the universe that He created, then our best guesses can only be constructed by what is more or less, regularly observed.

So here’s when the thought occured: why is it that people seem to always draw a binary (black or white) line between when it is right to terminate a potential life, and when it is wrong? As I see it, pro-lifers are very rigid with regard to a “moral line” and believe that upon conception, a new life is born. Hence, knowingly removing this life, whether by a morning after pill or by late term abortion, is equivalent to murder. However, some pro-choicers similarly draw a rigid “lawful” line, who believe that abortion at any stage should be tolerated, prior to childbirth. And then we have people in between, the fuzzies: For example, 3rd trimester abortions are wrong, but stem cell research and early stage abortions are ok. Or abortion only in cases of rape, incest, or health hazard should be legal. Or whatever else is out there.

Regardless, this is a very complicated issue, but at the risk of sounding offensive, here are a few things that I’ve been hearing underneath the arguments:

Pro-choice on the surface:
-Nobody’s pro-abortion, but a women should be given the right to make decisions regarding her body and her future, especially in poor economic situations. It’s not something to be taken lightly, but the option should be open.

The hidden assumption:
-A fetus is most likely unaware of its own existence, and thus there is nothing logically different from aborting a fetus (at any stage, morning after or late-stage), versus using a condom. Therefore, what is most important is the impact it has on the lives of cognizant beings, primarily the mother.
-Marginally pro-choice people who also believe in the “sanctity of life” simply believe that the mother’s well-being trumps the life card in most cases, after factoring in subsequent utility losses from childbirth due to anticipated parental neglect or abuse, or financial hardships.

Criticism:
-In a poorer country where safe abortion techniques do not exist, is killing a baby 1 minute after childbirth (due to severe perceived hardships) any different from abortion? A related question is whether the “morality” of abortion and “baby-killing” is contingent upon the technological advances of that community. If so, what is the “guiding principle” behind moral laws?
-Why not reform foster care and adoption agencies instead?

Pro-life on the surface:
Upon conception, the fetus is a life with greater value than any type of pain in and after child-rearing and should therefore be protected.

The hidden assumption:
-There is some intrinsic value placed on human life, given by some greater power or principle such as a moral God. Moreover, this intrinsic value begins at the point of conception.

Criticism:
-Those who don’t believe in the same “God-given right to life” at conception are likely not to reason in a similar manner, and thus convincing the agnostic, and even some of the religious, community in such a manner is meaningless.
-Most arguments that are aimed at making people realize the “faultiness” of the alternative rely on slippery-slope arguments, ironically, similar to the “criticism” I described above for pro-choice (baby-killing).

Solution?

This type of “drawing-the-line” problem occurs not only in abortion, but occurs on many different moral issues as well. Why is this the case?

Well, let’s consider a type of  “penalty function” for abortion, a continuous, monotonically increasing function over fetal age, where using a condom and avoiding conception is perfectly moral, and killing a baby after it is born is perfectly immoral (equivalent to a full-scale murder). This reflects a type of “grey scale” morality, where you can be only 40% wrong, or 60% wrong, with respect to abortion.

Somewhere along the line, every person sets a threshold, where above that threshold, the value of morality is quantized to “right”, and below the threshold, as “wrong”, i.e. you are either 0% wrong and 100% wrong. I’m not saying that there aren’t people who are go-in-betweens, who might conceptualize multiple levels of “wrongness” for key stages of development (as they have been so  defined by our society), but why is a fluid mechanism design not well accepted in the community? Well, viewing morality as a semi-fluid model is too similar to paying taxes using “tax brackets”. It counts the effect, not the reason, as the basis for moral law.

Fluidity obscures morality simply because morality transcends quantitative analysis. It is at its very heart qualitative: a principle of matters, a spirit of the law, a condition of the heart. It is not so much quantitative, although the effects of immorality can be measured quantitatively. Had there been two Hitlers, one who came into power in Germany, and another who had power only to kill 10 innocent people, would this be a proper metric for evaluating the “badness” of Hitler? Sure the effects of the first Hitler was far more devastating, but at the heart of the matter the two men were the same. One just had a power amplifier attached to him.

Tune in next time as I try to quantify other unquantifiable axioms.

The famous example is that of a garage that is 9 feet long, a ladder that is 10 feet long when “stationary” (but remember, it is only “stationary” relative to some frame of reference), and a mover that is holding the ladder and moving at a relativistic speed. If you are in anyway familiar with relativity, Lorentz contraction says that if an object is moving at a speed on the order of the speed of light (relative to your frame of reference), it will begin to look shorter to you. So let’s say that this ladder is moving at a speed of 3/5*c relative to the observer, such that its length shrinks to 8 feet. The garage has doors located in the front and back that are initially open, but when the ladder enters the garage, the doors immediately close. Then they open before the ladder exits the garage. From the observer’s point of view, there is no contradiction, because the ladder 8 feet long can fit within the garage.

But what if you were viewing it from the mover’s point of view? In his world, the garage is moving at 3/5*c, so its length shrinks to 7.2 feet. However, the ladder is 10 feet long! Can he actually fit inside the garage then? Well, thanks to the relativity of simultaneity, there is no contradiction based on what he sees moving at such high speeds. The mover will actually see the front door open, then the back door open. After he slides through, the front door closes, and then the back door closes. Pretty weird.

Now my friend went ahead and proposed another example, to which I might have an answer but will need to verify. Suppose that from the observer’s point of view, the back door is closed. The front garage door open, and the ladder goes in. Then the doors close, and the mover immediately stops moving after the doors close. What will happen inside the garage when the ladder suddenly expands?

I will leave this to the reader as an exercise.

However, one shortcoming of this model is that the ship game is treated as a one-shot game, which does not take into account the changes that may occur in human thought and behavior over time. For example, suppose that Joker started the game at 6pm, and the ships are set to detonate at midnight. You are aboard one ship, and you know that the other ship has no intention to blow you up. However, you feel morally obligated to keep the other ship alive as long as possible, in case batman does intervene successfully. Would you end up blowing the other ship up? Well, if you ultimately want to live, you would probably want to blow the other ship up a few seconds before midnight, granted that batman has not yet succeeded. However, at 8pm, you may want to hold onto your remote and wait to see the outcome.

In this entry, I will use a simple mathematical model to predict the change in human behavior over time as a function of their sense of urgency.

Partition the game into T discrete time periods (not necessarily equal) during which Batman has a fixed, independent probability Z of intervening successfully. Call the value of life X, and the value of obeying ones conscience Y. (In our game matrix, we will use 0 for clear conscience, and -Y for a guilty conscience.) If batman successfully intervenes with Joker’s plan first, then the game ends, and both ships survive with clear consciences. The game also ends if one ship destroys the other ship, or vice versa, but the surviving ship is left with a guilty conscience. Finally, we will also assume that if both ships flip the switch during the same time interval, then both ships are annihilated, but no moral consequences are felt.

Some Trivial Cases:

Case X > Y, Z = 0. Suppose that batman does not exist, and people do not have a conscience, or a conscience that is worth less than life. Then Joker’s repeated game has a dominant strategy: blow the other ship up as soon as you get the trigger.

Case Y > X, Z = 0. Suppose that batman does not exist, and people have a collective conscience greater than life. If the penalty of violating the conscience exceeds that of dying, then the dominant strategy is to wait until midnight, and let Joker blow them up.

A more interesting case, the game of hope:

Case X > Y, Z > 0. Here batman has a chance Z during each time interval of saving both ships. Hence, at the beginning of the game, the value of the game is a geometric sum from t = 0 to T-1 of Z(1-Z)^t. Provided that batman defeats joker, the resulting utility derived by both ships is X, since both conscience and life are satisfied. Hence, at each time interval t between 0 and T-1, the matrix is given by:

where the bottom right entry is the expected value derived if both ships decide never to pull the trigger.

When t becomes large enough, the value of not blowing the other ship may become less than X – Y, which leads to a weakly dominant strategy of blowing up the other ship. Note that in the very last interval T-1 (right before midnight), the game reduces to:

Hence, if the chance of batman’s intervention is greater than (X-Y)/X, the dominant strategy throughout the entire game is to not blow the other ship. However, if the chance of batman is smaller than (X-Y)/X, somewhere along the way, maybe at 10pm, or 11pm, or 11:30pm, the expected value of not pulling the trigger will become less than pulling the trigger. The best strategy then becomes to blow the other ship up, because it is time to give up hope on Batman.

The game of paranoia

However, this game can be extended once more! Suppose that you also know that the other ship is also reasoning using the same selfish game theoretic principles as you are. You know that at 10pm, both of you are going to give up hope on Batman, and hence blow each other up. In this case, your real deadline is not midnight, but rather 10pm! What happens then? Should you try to blow the other ship up at 9:59pm, knowing that if you do not, then you will die?

However, the other ship also knows that you are thinking this, and hence decides that it would be better to blow you up at 9:58pm. I mean, 1 minute is not enough for Batman to intervene right?

Using this argument recursively, we see that this game becomes one of paranoia, and a dismal game this is! Each ship comes to the conclusion that it is best to press the trigger upon getting it, to minimize the chance of the other ship pressing it first!

The game of mutual trust or cooperation

I do not have a nice rigorous argument for this, but: If there were such a thing as a game of cooperation, it seems likely that the two ships will talk to one another at t=0 and decide to throw out the triggers, even if each ship values life over morality. (Of course, the movie suggests that they did so for moral reasons.) By tossing out the triggers on each ship at time 0, granted that Batman has a sufficiently high probability of intervening, they play a one-shot game based on the expectation that Batman will successfully intervene before midnight. Furthermore, by preventing an extended game, they avoid the terrible equilibrium induced by paranoia.

Of course, because the ships are unable to talk to each other, this decision can only be reached based on some form of “mutual trust” or “faith in humanity”.

—-

Other notes:

In reality, each human has a different weight attached to life and morality, but here I simplified the problem into a symmetric game assuming that the law of large numbers reduces the variance of each ship’s collective value system, such that the utilities are nearly identical.

Also, Joker could have been lying, just for the heck of it. But such a game would not be meaningful to play, would it?

Finally, does anyone really know the probability that Batman will pull through?

The Justice Router: A New Approach to “Fair” Queueing

Inspiration

For a whole year, I have been living off of Verizon DSL and sharing my connection with 8 people. Verizon is pretty lame; it caps our upload at approximately 10kB/s, meaning that between the 8 of us, resources are scarce. Unfortunately, among the 8 of us, there are resource hogs who like to download 5 movies at a time while BT-ing 3 other movies, which floods our network with tons of ACK packets and slows our internet speed to a complete halt. To give you an idea of how terrible this situation is: my average ping time is around 1/2 second. On a bad day, my ping time is around 3-5 seconds.

First of all, I am very respectful toward network usage. If I find that the ping time goes above 200-300 milliseconds, I will graciously cancel one of my two downloads or turn off AIM. Moreover, when I am playing a game, I make sure that I do not download or upload anything. My upload rate is usually below 2kB/s at a “busy” time.

Unfortunately, just because you follow rules of your own doesn’t mean others comply to it. I decided to go talk to people individually about network usage. Unfortunately, one particular person, who will go unnamed for now, gave me an attitude. Apparently I can’t talk sense into some people. To this day, he still hogs the bandwidth without regards to others.

Thanks to him, I’ve developed a new idea for queueing/packet-switching networks. I propose a method which I call Justice Routing.

Some background information

Normally, when people describe a fair queueing system, their aim is to get packets through the network with a speed proportional to their length. Therefore, every packet (of the same type) has equal transmission rate in bits/second. Most packet-switching networks have priority classes for video/sound/data packets. Streaming video packets generally get high priority, because the application on the other side needs to constantly buffer these packets to provide high quality of service (good display). Fair queueing and priority queueing are age-old problems, but they fail to address the bigger problem in a shared network–that is, network hogs.

Why does network hogging increase latency so drastically? To analyze this, we assume an M/G/1 queueing system and notice that the waiting time is proportional to the second moment of a packet service time, and inversely proportional to 1 – (arrival rate/service rate). Never mind the first part; the second part (inverse proportionality) is more important. Suppose someone is uploading ACK packets at a rate of 500 every second on average, and the router can process 1000 packets per second on average. Then 1 – (arr/serv) = 1 – 500/1000 = .5. Take the inverse, and we get 2. Now suppose someone adds a couple BT’s to his downloads and uploads at a terrifying rate. Now we have 950 packets being sent out every second. The service rate is still 1000 per second. Now we get a factor of 1/(1-950/1000) = 20! Our waiting time has increased tenfold, even though the total upload rate has not even doubled. Try increasing the upload rate another 50 packets/second, and you get an infinite waiting time! Notice that you get a much better performance downloading at half your rate than you do at full rate, hence having 1 or 2 concurrent downloads is considered good manner, while flooding the network with 8 downloads is very bad manner. Fortunately, buffers are limited in size and often smartly designed so that they drop packets if queue sizes grow too large. Using an exponential backoff mechanism (e.g. TCP/IP) for retransmission, we’ll never have infinite waiting time. But we will still have terrible 10 second waiting times. WHATEVER SHALL WE DO???

Solution–The Justice Router

The Justice Router will analyze the source and type of each incoming packet and keep a counter for each source. Every few seconds, the router will compare the counters with a certain threshold and then reset the counters. If Mr. Bacon’s counter number is higher than the threshold, his computer will receive a violation. His upload will be capped at a lower rate each time a violation is received. Violations are handed out ever so often, so that eventually a stubborn network hog will have his connection reduced to a very small fraction of the total bandwidth. However, if he behaves himself, his violations will eventually go away after some time, and full network capacity will be restored. While administrators often block or disconnect people for flooding, this router will administer justice by itself.

Unfortunately however, the design of the Justice Router is inherently “merciful.” If a person’s upload is capped, he will be less likely to receive a violation. Below a certain rate, he will no longer receive any more violations. Thus the router’s violation scheme ought to be adaptive. The next section describes a scheme for harsher sentencing.

Three-strikes-and-you’re-out

In order to exact greater punishment, I propose the three-strikes-and-you’re-out policy. When Bacon receives “mercy” for the first time (i.e. his upload cap goes below the violation threshold), he will receive a strike. After the cap increases again and decreases below the threshold, he receives another strike. After three strikes, Bacon is disconnected from the router for the same amount of time that he has been connected since the beginning of his router farm life. If there was a year of Bacon, there will be a year without him, and everyone will be happy and healthy. Now keep in mind that after Bacon is readmitted to the router, the router still keeps track of his complete history. If within the next 30 minutes, he gets 3 strikes, Bacon will be out of the Justice Router for another 1 year and 30 minutes.

Justice is served with a plate of ham and spicy pork.

1) The theory of evolution is often viewed at a very macroscopic model with too many unknown variables and is thus difficult to verify, even if the probabilistic principles driving various aspects of the theory are sound.

At the top level, you have natural selection determining which animals “tend” to survive and which “tend” to die. This is largely based on the existing environment and the survival and propagation of a particular species, which is correlated with certain “favorable” traits obtained through either mutation or sexual reproduction. Note that the number of factors (e.g. environment, interactions and behavior, genetic traits) are huge and therefore very difficult to analyze jointly. Experiments can only verify that certain aspects hold statistically in isolation (or using only a small subset of factors). Complete, joint experimentation is too complex and takes too long to conduct.

2) There exists a truly probabilistic element in the universe, namely, that particles exhibit probabilistic wave functions.

I’m not a physicist, but from what I know that according to quantum mechanics, before observing any particle, the particle exists only as a probabilistic wave function which collapses upon observation. It is entirely possible (though not probable) for a baseball to be thrown horizontally and yet curve upward into space. In any case, to analyze sexual reproduction or gene mutations at the quantum scale is intractible. Hence evolution is still modeled based on statistical experiments at a higher level. Hence, while some mistaken quantum physics to support the theory of evolution, this is not true, though it is philosophically “consistent” with evolution.

3) What is often measured is the “average case” or “high probability” behavior, not the “ground truth”.

This is hopefully self-explanatory and is related to the above argument (intractibility). A simple illustration is brownian motion (the precise behavior of molecules) for an object at rest (a macroscopic, average behavior). One might perform kinematic experiments based on modeling the object as a whole, instead of accurately measuring the precise locations and trajectories of its individual particles.

4) The laws guiding the universe are assumed to be stationary.

Stationarity is a concept derived from the theory of random processes which states that what has happened, is happening, and will happen in the future (as time goes to infinity) will always follow the same distribution. Stationarity is an extremely important assumption required for the scientific method to hold, since, given that a result is validated, then it has always held in the past, holds in the present, and will always hold in the future. Otherwise all experimental results are meaningless.

5) 3-4 makes a strong case against young earth creationism, but only “with high probability”.

Stationarity can make a strong case against young earth creationism for two reasons: it supports the big bang with high probability. If the physical laws have always held as they do now, based on astronomical data there should be a singularity (with very high probability) around 13-14 billion years back in history. It also makes a case for the accuracy of radioactive carbon dating.

6) Interestingly, young earth creationism is also consistent with scientific theory based on 3 and 4.

Why? If the world indeed operates based on nondeterminism, then however negligible the probability of young earth creationism, there is still a non-zero probability that universe arranged itself accordingly in 7 days, just as there is a negligible (but non-zero) probability that the universe exists in its current state at the present time! To understand this, one needs to remove the paradigm of thinking in terms of “wholes”. We are not discussing the average behavior of macroscopic objects, but rather each individual quark, boson, muon, etc. in the observable universe. The reason why our observed universe has near zero chance of existing is a simple consequence of the sheer number of particles in the known universe, and the fact that they each exhibit probabilistic wave functions.

Hence, even if observable evidence points to the big bang “on average”, the universe need not always behave “on average”. Christians believe that with God all things are possible (though not necessarily probable)–and in this case God needs only operate within His own designed physical rules! Hence young earth creationism is consistent with scientific theory under the “guidance” of a non-quantum Cause.

7) Young earth creationism can not be experimentally verified. (i.e. it is philosophically valid, but can not be considered science.)

Unfortunately, due to its extremely low probability of occurence, it is nearly impossible to experimentally validate the 7 days of creation theory. The only tools that can be used to support young earth creationism is suggestive evidence (e.g. almost every nation had a “dragon” in its mythology/folklore, suggesting that humans might have lived among dinosaurs). Otherwise, it must be accepted by “blind faith”.

Another way to think about it is the following: If you saw a “miracle”, could you repeat it?

Conclusion: I am not the most eloquent writer, but hopefully this post has helped you to think “outside the box” regarding the debate that has been all over the news since… 1844. And hopefully those of you who are on different sides of the spectrum can develop an appreciation for one another’s viewpoints.

http://www.michaelrighi.com/2007/09/01/arrested-at-circuit-city

… and the system fought hard to convict him.

He managed to win the trial.

 http://www.michaelrighi.com/2007/09/20/success/

Kudos Michael, and thank you for bringing this corruption and injustice into the public spotlight.