Loki

The Nordic equivalent of Hermes and Mercury was known as Loki. His father was Fárbauti, a "hacker", and his mother was Laufey, possibly a silvan nymph. Like the Greek and Roman gods his connection with bounds is that he often ignored them. There is a discription of him given in an Icelandic saga about Gylfi, the first king of Sweden,

"Loki was cute and alluring* in appearance, bad by nature, very duplicitous in manner. He surpassed others in that wisdom which is called craftiness with devices for all things; he would even bring the Æsir into a complete quagmire and often he would free them with fabrications." - Gylfaginning, 33

Loki was a slippery character who did not engender trust and probably was responsible for the downfall of the gods. He had a fate similar to that of Prometheus.

(*edit: fríður og fagur can be translated as "beautiful" and "enchanting" but, allowing for changes over time, "plain" and "simple" might be a better fit. A modern translation for fríður is "peace." vélar and vélræðum → "devices" and "fabrications," at least that seems to be the impression.)

Problems with Analyzing Data with Cyclical Error

There may be some doubt concerning the rate of global warming which is due to the nature of the temperature measurements. For statistical data one usually encounters a normal distribution but with temperatures there are both daily and annual cycles in the data. This can bias the estimate of global warming as seen by what happens to the data in the following example. The solid line is the true curve, the dots are the data and the dashed line is the estimated trend based on the data. Notice that the slope is greater for the estimated trend. This increases the time necessary to make accurate estimates of the rate and rate of change of global warming. When analyzing the data one has to be on guard against subtle errors.

Naive Impressionism in Ancient Times?

I found some passages in the Bible which touch on naive impressionism.

and said, “Assuredly, I say to you, unless you are converted and become as little children, you will by no means enter the kingdom of heaven. (Matthew 18:3)

When I was a child, I spoke as a child, I felt as a child, I thought as a child. Now that I have become a man, I have put away childish things. (1 Corinthians 13:11)

Paul may have seen naive impressionism as somewhat lacking. Perhaps this was due to his background. The ancient Greeks also may have viewed Hermes, the younger brother of Apollo, as somewhat naive.

Christ's message was one of renewal/rebirth.

Commons vs Lords

COP15 dealing with global warming is taking place in Denmark. There are two aspects to the problem. First, what is actually happening and, secondly, what should our response be. Whatever the cause of global warming, our response will primarily be an economic and political solution and perhaps we should consider the difference between economics and politics and how they might work together. In ancient times economics dealt with "rule of the home" while politics concerned itself with management of the city-state. There is still this division today in the separation of microeconomics and macroeconomics. The first deals with local problems while the latter deals with more general problems. The difficulty that we are having with global warming might be that the two approaches are out of balance.

In nature one finds a similar division between Special Relativity and General Relativity. Special Relativity is local while General Relativity deals with weaker but more "global" forces that ultimately dominate. These are the Commons and Lords of Nature.

We can probably do something similar with economics and global warming and try to get the two systems to work together better. The question is, "Are we up to the task?"

Beyond Relativity

The weakest assumption in the derivation of the Lorentz Transformation is Einstein's assumption that the speed of light is a universal constant. This assumption is validated by the null result of Michelson-Morley experiment. The conclusion that there is no ether may not be justified. The validity of the Lorentz Transformation suggests that the observed change to the speed of light for a given relative velocity is neglible. If this were not so naive impressionism suggests that one can still find a transformation between the two reference frames which is similar to the Lorentz Transformation. An expression for A can be found by plugging the two values for the speed of light into the formula for the addition of velocities and solving for A. One then gets the following results where Δc is the change in the observed value of the speed of light,

Relativity and Naive Impressionism

How can we justify the assumption of symmetry used in the derivation of the Lorentz Transformation? It appears to be a form of naive impressionism or the belief that what is true for one is true for all. But it appears to fit the facts. The Michelson-Morley experiment gave a null result on the measurement for the velocity of the ether. The speed of light appears to be independent of the Earth's motion throughout the year at least for the value of the Earth's orbital velocity. Relativity has proven to be a useful tool for scientific research. But it seems to validate the simplistic worldview and the possibility of making a false assumption.

One could view Ockham's razor as a form of naive impressionism. But it is an economy measure. One has to seek a balance between ignoring the lack of evidence to the contrary and unnecessarily complicating an explanation of the facts. Making unjustified assumptions raises doubts.

The operational rule of the scientific community appears to be naive impressionism with doubts. So we are justified in saying, "Don't trust them." As a matter of expediency, however, this may be the best way of proceeding, but under the circumstances one needs to show that the use of Relativity is justified in a particular case and that the results are reasonable. The assumptions break down if there is an asymmetry in the point of view of the observers. This may be the explanation of the imaginary values in the transformation for velocities exceeding the speed of light. Strong gravitation may bias the transformation and Einstein attempted to address this in the General Theory of Relativity. Special Relativity may still be the best first approximation to the laws of the Universe.

Special Relativity & the Lorentz Transformation

In Special Relativity the Lorentz Transformation allows one to convert measurements such as distances and times made in one frame of reference to those of another. It is easiest to derive the transformation when the situation is symmetric, i.e., changing between the two frames of reference doesn't alter any of the parameters involved. The same transformation can then be used for both reference frames. Consider two spacecraft headed directly towards each other with a relative velocity of v. We can use unprimed variables for measurements made by the first spacecraft and primed variables for the second. In both cases the transformation is L.


The transformation is assumed to be linear and can be represented by four components of a matrix which only depend on the relative velocity.





By noting that a point in the second spacecraft doesn't move relative to itself while it appears to be moving with velocity -v to the first spacecraft, we can deduce B. The method can be generalized to find the any velocity, V', as it appears to the second spacecraft if its value for the first spacecraft, V, is known. This is the formula for the addition of velocities.



















With L the same for both reference frames we can use it twice to make a transformation from the first to the second spacecraft and then back again to the first. Since we should get the original values back the result is the identity matrix. Doing the multiplications and equating terms gives two more terms of the transformation leaving only one unknown, A.














This is as far as symmetry will take us. To go further Einstein had to assume that the speed of light was a universal constant. This is not unreasonable if space is homogeneous. We just have to be careful about directions though. A ray of light moving along the common line of the spacecraft will appear to be moving in different directions to the two observers. Let's say that it moves away from the first and towards the second. This allows us to simplify the expression for C and determine an expression for A.














We then have to use the minus sign so that the direction of time will be the same in both frames of motion.









So we have found the transformation in this particular case. We can use other transformations to convert to situations that are less symmetrical.














This derivation indicates that Relativity doesn't impose any constraints on time travel. There are transformations which will convert positive changes in time to negative ones. But at the same time they will also convert positive energies into negative ones. So it seems likely that if one could travel back in time one would find oneself in an antimatter universe which would be extremely hazardous.