Jul 28, 2013

My design to implement PGP in commercial email system

PGP is great for privacy but rather hard to use for common users. I came up with a simple design that can be implement in main-string email system while preserving the usability. 
Take Gmail for example.
First Google should adopt zero-knowledge password proof for its account while asking users to choose recovery questions. To recover password, users will answer 3 secret questions and the password is encrypted with the answers. This ensures that users can recover password and get old emails back without letting Google know the password.
Then when users first log into Gmail, the browser will generate the keypair using JavaScript locally and encrypt the secret key with login password(with PBKDF2, etc). Then the user will upload the encrypted secret key and plain public key to Google. Because Google doesn't know your password, Google cannot server you a fake secret key, even though you download your encrypted secret key from Google every time you login.
When the users tries to send an email to another Gmail user B for the first time, B's public key will be downloaded from Google and signed by A. Any subsequent times when A tries to send email to B, A will not only download B's key from Google but also verifies the authenticity of B's key. This prevents MITM attack if Google is hacked or forced by law enforcement. (For advanced users, Google can present the option to manually verify the public key for the first email. )
To send email between Gmail and Hotmail, Google should be able to request a Hotmail user's public key from Microsoft server. To prevent spam, Microsoft should return some random public key for non-exist account and perhaps always return this fake public key for this non-exist account to prevent cross reference.
The only downside of this approach is that email providers are not able to filter spam or provide related Ads based on email content. Even this might be solved in the future because of private outsourced computation.

Jun 14, 2013

Newton's Worldviews in Relativity



Newton's worldviews in relativity
Isaac Newton, the authority of classical physics and Albert Einstein, the creator of relativity are two most distinguished physicists in human history. Their physics theories are fundamentally different and so are their worldviews and religious belief. In recent years, with the advancement of technology, relativity has been accepted as a more correct description of reality. Consequently, Newton’s worldviews and religious beliefs, which integrated deeply into his physics theory, are shaken greatly by relativity. In this paper, we will explore how Newton’s worldviews and religious views are manifested in his science and why most of them are no longer valid with the downfall of his classical theory of physics and the rise of relativity.
Newton’s science and his religious views are inseparable. In fact, contrary to popular belief, Newton was first a theologians then a scientist. Indeed, many believe that theology was Newton’s first love[1]. His science is only a way to provide evidence for his religious belief. In the second edition of Principia, while describing the system of planet, he concluded that “[such a system] could only proceed from the counsel and dominion of an intelligent and powerful Being”[2]. Newton reveals his three laws of motion and universal attraction in Principia not for their own sake; rather they are like handmaiden. He believed that by explaining the mathematical order of the universe, he could exhibit God’s will and power to the world and “bring humans to their knees in adoration of the creator”[3]
The claim that space is absolute is also fundamental to his laws of physics. Newton’s belief of space and time are fundamental to his religious views as well as his classical theory of physics. Newton believed that space and time are uniform and absolute. Newton defines time this way: “absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external”[4]. For space he claimed, “As the order of the parts of time is immutable, so also is the order of the parts of space… These are therefore the absolute places; and translations out of those places, are the only absolute motions.[5] These basic assumptions of space and time are basic to his physics theory. Hodgson argues that Newtown made this assumption because of his religious belief--space and time are “sensorium of God”[6]. Because God is infinite and eternal, so must be his sensorium. Working under this assumption, Newton built his entire theory. His theory matches with reality perfectly well at that time, and further verified the correctness of the assumption and his religious belief. After all, this is what Newton planned in the first place, namely using physics to convince general public the power of God.
Relativity assigns completely different properties to space and time. Relativity developed by Albert Einstein has been accepted as a more complete description of reality. He adopted the Lorentz transformation to relate measurements done in two different reference frames. Lorentz transformation is left multiplying a matrix to the space-time measurements in one frame.

 [7]
It follows that the time in a new reference frame (denoted as t’) is dependent on relative velocity between reference frames. In addition, in order to compute t’, all measurements (x,y,z,t) in the original frame have to be taken into account. Thus in relativity, all dimensions of space and time are entangled. Peculiar as Lorentz transformation appears to be, it has been verified by various scientific experiments. In daily life where motions of objects are greatly less than the speed of light, Newtonian physics will give the same description as relativity[8]. This means that the conclusions Newton drew are only approximation of reality. Although for practical purposes, we can say space and time are approximately uniform and absolute, the worldviews of those theories are distinct and cannot be approximated.
Time is not uniform or absolute in relativity. We can easily see from Lorentz transformation that as long as β, the relative speed measured in light-second is not 0, the measurements of time in two reference frames might not agree. In other words, an event that last two seconds in one frame might appear to be three seconds in another. This contradicts Newton’s claim that time flows equably through out space. We have established mathematically that time interval is dependent of reference frame and it is also confirmed by various experiments. Indeed, the difference of elapsed time called time dilation is observed in the Hafele–Keating experiment, in which atomic clocks were carried by several airlines and found to disagree with each other when returned[9]. Also, in Rossi–Hall experiment, Rossi and Hall confirmed the time dilation by comparing muons decay time with their observed decay time on earth when muons are moving in the atmosphere with high velocity[10].
Uniformity of time proposed by Newton is wrong beyond any hope of salvaging. Some readers might object that even though time might flow at different pace in different reference frames, it will always flow at a constant rate in a fixed frame - a weaker version of Newton’s claim. In other words, the elapse of time in different points in space is the same provided that one single reference frame is used. Unfortunately, those misunderstand what “flow equably” represents and have to review the definition of measurements. We empirically formulate that given a reference frame, we can use three space quantities x,y,z and one time quantity t to fully describe a event. The notion that we have a time quantity in addition to space quantities implies that this quantity is unique throughout space. We will use an example to illustrate why this weaker version of uniformity of time is meaningless. Suppose we have two arbitrary locations A and B. The claim is that time at A and time at B elapse in the same rate in one single reference frame. But what does time at A in this case mean? This is confusing because generally if we say time at A, what we mean is that time measured from an observer or reference frame centered at A. But in this case time at A means the time in this reference frame and at A merely indicates the event happened at A. Time at A and time at B are different names that refer to the same quantity. So long as we agree that there is one quantity called time in a reference frame, time has to elapse at one rate in this frame. Otherwise, time will not be a meaningful quantity in the reference frame; in other word, time does not exist. The existence of time and the consistency of the definition are beyond the scope of this paper. In this paper, we will assume in a single reference frame, we are able to describe an event with the four quantities. The weaker version of Newton’s claim is thus only a restatement of the premise and does not give any insight on the property of time.
The disagreement of time across different reference frames brings disasters to Newton’s religious belief. Newton believed that God is eternal, which means God exists throughout time. But since time is different to different reference frame, in which reference frame is eternity of God valid?  When we talk about the life span of an object, it is implied that the time is measured in its own frame. For example, in Rossi–Hall experiment mentioned previously, when we talk about the decay time of muons, it is measured in the reference frame intrinsic to muons. Now the trouble is to find the reference frame that is inherent to God. Until we can pinpoint which frame of reference God is using, any statement on the eternity of God is meaningless.
Similarly to time, space is not uniform or absolute.  Again, examine Lorentz transformation, we will find that x’ is dependent of relative velocities between two frames and all measurements in the original frame. This implies the dimension of an object such as x2- x1 in the original frame might be different in the new reference frame. Lorentz himself believed that this contraction[11] is a mechanical process caused by elasticity of the moving body. However, in relativity, we interpreted the contraction to be the contraction of space itself.
The counter-argument that space is uniform in one single reference frame or a special reference frame is invalid. If the claim that space is uniform and free of contraction in a single reference frame, is merely a restatement that space measurements exist, as we have discussed at length in time. Newton would object that saying space is uniform in any reference frame respectively might be meaningless, but if there exists a special reference frame, an analogy to his belief on absolute space, he can hold that in that special frame, space and time are uniform. The contraction we observed in any other frame of reference is just our misperceptions and does not reflect the true property of space. This argument is circular. Essentially it is saying that if an absolute frame of reference exists, space is absolute. Relativity is built based on the principle that every reference frame is equivalent in terms of physical laws and consequently physical phenomena. Relativity does not prove that the absolute frame does not exist, but removes the necessity for their existence as needed in Newtonian physics. Because the equivalency of reference frame, even if it did exist, there is no way to differentiate it to ordinary reference frames. It is like relativity removes the necessity of existence of ether, which physicists used to explain the propagation of electromagnetic waves. According to Occam's razor, which states that among competing hypotheses, the hypothesis with the fewest assumptions should be selected[12], there is no reason to believe such unobservable frame or absolute space to exist.
This contraction of space undermines the Newton’s picture of God. Newton believed that space is an attribute of God[13]. He also believed that God is immutable and absolute. It follows that God is immutable but his attributes are contractible; God is absolute but his attributes are relative. If God’s attribute can directly contradict the property of God himself, how can we say God is the perfect and rational being if he allows such inconsistency with himself? Furthermore, statements such as God is immutable can never be observed if this is the case.
Relativity undermines an important argument on God’s complete freedom based on space and time. Newtonians believed that because space and time are uniform is a piece of good evidence that God has complete freedom and is not bounded by reason. Clark presents Newton’s reasoning in the multiple-letter correspondents with Leibniz. If space is both uniform and absolute, every point in space is equivalent. That is, there is no reason for matter at one point to differ from that at another point. But the asymmetry does happen. For example, North Star is at the north but its counterpart “South Star” does not exist. North and South are two equivalent positions according to Newton; there should be no reason for the object in the North to differ from that of South. Perhaps surprising to contemporary readers, the reason behind this seeming physical paradox resides in the religious ground, God’s complete freedom. Even if two locations are equivalent, and there should be no reason for God to prefer one to the other, because of his complete freedom, he can choose to put one star at north but not south. This thought deeply troubles Newton’s contemporaries, such as Leibniz, because God’s has the infinitive wisdom and should act according to reason. The explanation from Newton’s side is that God dictates reason; if he chooses to put the star there, then his choice is the reason and the action alone is sufficient. In relativity, without the absolute and uniform space, Newton’s claim that God has complete freedom to do what he prefers becomes a claim not back up by any evidence or logic. If space is not uniform or absolute, one point in space can be differentiated from another; there might exist some reason for God to place matter heterogeneously as we observe. Therefore, there is no sufficient evidence to conclude that God can do what he prefers without any apparent reason. Relativity itself as a science makes no statement on pure metaphysics subjects such as God’s freedom.
Newton’s religious views were deeply integrated into his universal law of gravitation. The universal gravitational force as discovered and formulated by Newton could somehow act at a distance. Newton never explained the inner mechanics of the force or how one body can miraculously affect another body without any physical contact. This proper of gravitation is shocking as any other force known at that time require some physical contact one way or the other. Although he stated publically “I do not frame hypothesis”, he secretly believed such attraction is operated by God[14]. Newton believed that God is omnipresent in the universe and is actively governing the universe. The gravitational force is therefore a perfect evidence for this claim.
The new explanation of gravity in relativity undermines Newton’s belief on God even more. First the act within a distance is replaced by gravitational waves, which are actually the ripples of curvature of space-time. Such waves rid the necessity of invoking active involvements of God to explain the mechanism of gravity. In addition, it describes the effect of matter on space-time. Matter will not only curve the space-time but the curve will also be propagated outwards. Space-time in this case is behaving like a string and is clearly not absolute or uniform. Because space-time is constantly influenced by such gravitationally waves, and if God resides in space as Newton claimed[15], God himself will be subject to gravitational waves and will be constantly influenced by it. God thus becomes the object of gravity from the doer.
Relativity does not disprove the existence of God, but it removes the need of invoking God even more.  Although Albert Einstein believed in God and said, “God is subtle, but he is not malicious”,[16] relativity can explain most of the phenomena happened in the universe that it removes the necessity to invoke an external power. This is similar to Newton’s influence on society. Newton made “the world seem like an ordered, rational certain place, bounded by mathematically known laws that would stay in place forever”[17], even though he believed in an active God. With relativity, Einstein made the world seem more ordered, rational and certain than ever before and further removed the need of God. Albert Einstein himself believed that such elegant laws come from God. Newton had a similar argument that the laws themselves are the proof of existence of God. However, according to Occam's razor, if the existence of God will not influence the system in any way and have no consequence in the predictions, we have no need to include this additional object in our system.
 Establishing his religious view through scientific evidence backfired at Newton. The properties of space and time are determined scientifically in relativity and contradict with Newton’s views. When his physics system is proved to be incomplete and his fundamental assumptions wrong, most of his arguments on religion become automatically invalid, for example his argument on God’s complete freedom. Furthermore, some arguments are well constructed that the inversion of them are also true. For example, in the case of the absolute of God, because Newton links space and time to the attributes of God, the change of science automatically leads to the change of attributes of God.  Newton tries to facilitate a close connection between theology and science and is successfully at it. However, largely because the connection he builds, his religious beliefs are regarded as invalid in the new relativity age.



[1] Margaret Jacob, and Larry Stewart, Practical Matter, (London: Harvard University Press, 2004), 9.
[2] Isaac Newton, The Principia : mathematical principles of natural philosophy.( Berkeley, Calif: University of California Press,1999)
[3] Jacob, Practical Matter,17
[4] Newton, The Principia, 408-9
[5]Isaac Newton, Alexandre Koyré, and I. Bernard Cohen, Philosophiae naturalis principia mathematica. (Cambridge, Mass: Harvard University Press, 1972)
[6] Alexandre Koyré, From the Closed world to the Infinite Universe.(Baltimore and London: The Johns Hopkins University Press), chap. XI
[7] Unit length is light-second.
[8] See appendix.
[9] Hafele Joseph, and Richard Keating, Around-the-World Atomic Clocks: Observed
[10] Bruno Rossi, and David Hall, Variation of the Rate of Decay of Mesotrons with Momentum. (working paper., University of Chicago, Chicago, Illinois, 1941), 10.1103/PhysRev.59.223.
[11] It can be derived that it has to contract rather than expand.
[12] Merriam-Webster, "Occam's razor." Accessed June 5, 2013.
[13] Koyré, From the Closed world to the Infinite Universe. chap. XI
[14] Jacob, Practical Matter,13.
[15] Koyré, From the Closed world to the Infinite Universe, chap. XI
[16] Clark R.W, Einstein, (Hodder and Stoughton, 1979), chap. 14.
[17] Jacob, Practical Matter,9.






Bibliography
Alexandre, Koyré. From the Closed world to the Infinite Universe. Baltimore and London: The Johns Hopkins University Press.
Joseph, Hafele, and Richard Keating. Around-the-World Atomic Clocks: Observed Relativistic Time Gains. working paper., 1972. 10.1126/science.177.4044.168.
Margaret Jacob, and Larry Stewart, Pratical Matter, (London: Harvard University Press, 2004), 9.
Merriam-Webster, "Occam's razor." Accessed June 5, 2013.
Newton, Isaac, Alexandre Koyré, and I. Bernard Cohen. 1972. Philosophiae naturalis principia mathematica. [Cambridge, Mass.]: Harvard University Press.

Newton, Isaac, I. Bernard Cohen, and Anne Miller Whitman. 1999. The Principia: mathematical principles of natural philosophy. Berkeley, Calif: University of California Press.
Rossi, Bruno, and David Hall. Variation of the Rate of Decay of Mesotrons with Momentum. working paper., University of Chicago, Chicago, Illinois, 1941. 10.1103/PhysRev.59.223.
R.W, Clark. Einstein. Hodder and Stoughton, 1979.
Wikipedia, "Lorentz transformation." Accessed June 5, 2013.






Appendix




Mar 29, 2013

Natural and Artificial behaviors for College Students

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Natural and Artificial behaviors for College Students
In his text “College Pressures”, Zinsser examines the behaviors of college students nowadays and those of a decade ago. He argues that the unpredictability of life, exploration and enjoyment in college, and being true to feelings are natural and that the external control over life is artificial; he endorses this kind of natural over the artificial.

Mar 20, 2013

Nietzsche, Darwin, and Freud: Behavior and Morality of Modern Society

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Authors from the mid-nineteen century to twentieth century discuss how and why human behave as they do and their underlying reason. They try to understand the origin of morals and the purpose of civilization without the reliance on an external God. Nietzsche argues that morality is purely man-made while Darwin believes the formation of morality is an evolutional process. Freud formulizes two principles that dictate the behavior and morality of society. Their theories appear different or even contradictory; but, in fact, they are all related and complementary. Nietzsche’s argument is dominant when influence dictated by Darwin’s theory is negligible. Freud’s argument is comprehensive when we restrict time scale and take the results of Darwin’s theory for granted.

Mar 12, 2013

Fracking, Devil or Angel

 
Fracking, Devil or Angel
Hydraulic fracturing or fracking for short, is “a technique used to release petroleum, natural gas or other substances for extraction” (“Hydraulic fracturing”). In this paper, we only examine natural gas fracking, whose product is a mixture consisting largely of methane. To put fracking into simple words, it is a process where sand, water and other chemicals are pumped into the ground so that they will replace natural gas trapped inside of the rock. The gas will then be guided into a tube to the ground where it is eventually collected and transported by trucks.
In his post “5 Reasons Fracking Should Scare the Absolute Hell Out of You”, Jon Bowermaster calls for the scrutinizing and halt of fracking to ensure the safety of citizens living near the natural gas well. Allen Gilmer, on the other hand, strongly disagrees with Bowermaster. In the post “10 Reasons Fracking Improves American Lives”, Gilmer argues that fracking has brought overwhelming benefit to America. Each author believes his claim is not only scientifically accurate but also morally correct. Each argues on the grounds of the health of citizens, the environment of the state, the safety of people, and the economy of America, but come to drastically different conclusions. Further more, each author makes emotional appeals to readers in their arguments and asserts that his way is patriotic and the opponent is ruining America.