Toot…

One of the most ridiculous thing I’ve ever heard how some people claim that evolution is just a theory. Sure it is a theory, but it is not just a theory. It is a scientific theory, as well as a scientific fact.

In common day to day usage, some of us use the word theory as a synonym to speculation and opinion. However, for a scientific hypothesis to be recognised as a scientific theory, it has to be able to withstand the scrutiny of peer reviews by the academics in the field.

Before we can establish any hypothesis, we must have a set of axioms of which the hypothesis can be built on. Axioms, or postulate, are propositions which are not proved, and are considered to be self-evident. For example, it is meaningless for me to ask you to prove to me a + b = b + a, or 2a is even (if a is an integer), as they are axioms and are considered to be self-evident.

However, I have to clarify, I am not saying that all the axioms are true, and or can never be proven. For example, the Parallel Postulate states:

If a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, intersect on that side on which are the angles less than the two right angles.

For those who can’t seem to get the meaning at the first quick glance (I am one), let me put it down in words much more easily understood. Given two lines (which are seemingly parallel), if a third line intersect those two lines, and the angles at any side of the line does not sum to 180°, then the first two line given will eventually intersect, if extended indefinitely.

Parallel Postulate is a postulate which holds for Euclidean Geometry. There exist non-Euclidean Geometry which satisfy all the other axioms but not the Parallel Postulate, such as elliptic geometry or hyperbolic geometry. As a point of interest, the simplest form of elliptic geometry is a sphere, and the shortest distance between any 2 points on a sphere is along is geodesic, or it’s Great Circle. This is the reason why, if you look at the map, airline routes are not straight, but curved. This is the result of showing a surface of the globe, which is non-euclidean on an euclidean surface.

Now that we are clear on what axioms are, let me continue on how the axioms are used. Since axioms are the defining properties of a system, we can utilise these properties to prove or disprove hypotheses within that system. One of the more interesting way of proving something is by reductio ad absurdum, or proving by contradiction. Using this method, if we want to prove a case, we assume that the opposite is true, then prove that the assumption leads to a contradiction, and hence proving that the case is true. For example, consider the proof of irrational numbers.

Define: irrational numbers are number which cannot be expressed by the a ratio a/b, where a and b are integers and coprime (meaning they have no common factor other than 1).

Assume that √2 is a rational number, hence it can be expressed as √2 = a / b

Hence, (a / b)² = 2

a² / b² = 2

a² = 2b²

Therefore, a² is even since a² = 2b² .

Since, a² is even, then a must be even.

Since a is even, it can be expressed as a = 2k.

Substituting the a = 2k into a² = 2b², (2k)² = 2b².

Hence, 2b² = 4k²

b² = 2k²

Therefore, b² is even since b² = 2k² .

Since, b² is even, then b must be even.

BUT, if both a and b are even number, they cannot be coprime, as they share the same factor 2.

Therefore, assumption that √2 is a rational number leads to a contradiction.

Therefore, √2 is an irrational number.

Another method of proving or disproving something is through hypotheses, experimentations and observations. The data collected by the observations are facts. If facts support the hypotheses, through statistics, we can calculate the confidence level that those hypotheses are true. Now, if a lot of observations shows that a hypothesis is true, then our confidence grow. Hence, a theory can be accepted. A theory explains a certain observations and make predictions on the future outcome. However, if a theory is proven to be inconsistent with certain axiom, it will be proven false.

Having said this, certain axioms might just really be conjectures, and in time, they may be proven to be unfounded. For example, if we only consider Newtonian mechanics, it is self evident that mass can travel faster than the speed of light, as all we have to do is to apply force. Now with the understanding of relativity, we now know that speed of light is the ultimate speed barrier, and hence the “self-evident” assumption that mass can travel faster than the speed of light is actually false.

When conducting an experiment, or formulating a theory, any assumptions must be stated. In some cases, the assumptions are in fact conjectures, such as the law of conservation of energy, of which the cause of the phenomenon is yet to be proven, but has be consistent in countless observations. Another famous conjecture, although now proven, was Fermat’s Last Theorem (it was a conjecture, despite its name).

Since experiments and theories are based on conjectures or assumptions, it is important to keep the number of assumptions as little as possible, since having more means having more chance that the experiment can be proven false. This is because if any of the assumptions were to be proven false, the experiment would be render useless. This is essentially the idea of Occam’s Razor, which states that “entities should not be multiplied beyond necessity”.

After a long winded, at yet greatly summarised introduction to the scientific method, let me go back to the original topic: why it is ridiculous to call evolution just a theory. Anybody who has an adequate high school knowledge of science could have told you this, although I do agree that many people do not have adequate high school knowledge of science. For those of you who still do not understand why it is so, I urge you to have a look at Evolution as Theory and Fact on Wikipedia. It has much much more explanation than I can ever include in this article. It is interesting that most of those people who criticise the theory of evolution are well, hardcore theists.

I thought it would be interesting to try to determine the axioms used by certain groups of theists in their explanation of this world. The the bible for example. Let’s consider the two conjectures below:

1.I am the Alpha and the Omega, the First and the Last, the Beginning and the End. (Revelation 22:13)
2.But you are the same. Your years will have no end. (Psalm 120:27)

Anybody with a hint of common sense would have detected that those two conjectures are contradictory. One say that there’s a beginning and an end, and the other one say that there is no end.

The above is but one out of the many examples of contradictory conjectures in the bible. Of course, I think somebody can come up with a certain sets of theological internally consistent axioms of which further proves can be built on. However, even if this is achieved, it would be meaningless in explaining the world because, well, it does not explain this world!
Although, I guess they can find comfort in seeing and accepting the world based on the certain conjectures, written centuries ago, before the existence of the scientific method. Of course, you can argue science and religion and be coexist and still be consistent.

Let me draw an analogy: even though the world is spherical, a lot of time, we still use euclidean geometry, oh say, in civil engineering. If we assume that non-euclidean geometry and euclidean geometry cannot coexist, does that make euclidean geometry true and non-euclidean geometry false in explaining the world? Or does that mean the civil engineers are just a bunch of people (who happen to be the ones building your houses) who don’t understand basic geometry?

No! The reason why euclidean geometry is still used is because it gives a good approximation to the boundary we are working in. It is somewhat, but not exactly, the same as why Newtonian physics is still applicable in our life, even though we have a more precise theory. No sane engineer will tell you that he believes the world is flat, and no sane engineer will be willing to lobby the government, or change the school syllable, to make you think that the world is flat!

However, this is not the case with religion. The reason why religion cannot coexist is because there is only one universe that both science and religion are trying to explain. Some theists will tell you that their religion is the one and only truth, and their holy book is internally consistent and flawless. To the more extreme, some theists are willing to kill to prove a point.

Ever wonder why there aren’t any militant atheist who claims that atheism is the one and only truth, and he will kill you if you do not embrace atheism?