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The inherent problem of scientific theories

The inherent problem of scientific theories is that there exists an infinite equally valid explanations. Why? Because in science, we never have perfect information. First, some background on Bayes’ theorem. Bayes’ theorem is used to judge how likely an event caused an observation, like how likely a test result means cancer. Yet, Bayes Theorem produces probabilities, not axioms. There is always a chance that our belief is wrong.

Statement of Bayes’ theorem. This says: the probability of A given B is the product of the probability of B given A and the ratio of the probability of A to the probability of B.

In science, Bayes theorem determines probabilistically if observations support a theory. However, an infinite number of theories can explain the observations. We can eliminate theories by testing, and we can judge how likely a theory explains observations, but Bayes Theorem is probabilistic, and we can never certain. For example, in physics, many theories successfully explain observations, like String Theory and the Standard Model. Yet an infinite number of other theories exist that explain all our observations, even though we haven’t thought of them yet.

OK, so our world understanding improves as we verify models, like if the Large Hadron Collider finds the Higgs… right? Theoretically, no. An infinite number of theories that are just as “probable” as the others still exist to be tested. All that was done was eliminate some of the theories. Subtracting anything from infinity is still infinity.

An infinite number of theories exist because we can never have perfect information about everything, both practically (we can’t be everywhere and observe everything) and theoretically. For example, the Heisenberg Uncertainty Principle states that the more one knows about a particle’s momentum, the less one may know about its position and vice versa. Even if one was momentarily omniscient, it’s theoretically impossible to know the prior state of every particle in the universe.

A simpler example: say my entire life, every swan I see is white. With reasonable confidence, I can assume that all swans are white. However, somewhere in the universe, there may be a black swan, disproving my theory. So then I could reasonably adjust my theory to say almost all swans are white. However, suppose I live in a region predominantly occupied by white swans, but really, black swans are the predominant type of bird. Or maybe black swans simply avoid me and my colleagues. How would I know?

In essence, while science finds theories that explain the observations that we see, we have no way of proving if it is the one correct theory. It’s probably wrong —all refuted theories in the past have been. We can never know the truth, and we can never have the real model of anything we don’t define ourselves. The best we can do is agree to use a model that works for humanity’s tiny set of observations.

For further reading on this topic:

The Similarity of Causal Inference in Experimental and Non-experimental Studies. Richard Scheines. 2005.

WHAT IS WRONG WITH BAYES NETS? Nancy Cartwright. 2001.

Causation: One Word, Many Things. Nancy Cartwright. 2004.

1 Comment

  1. Edward C said,
    September 20, 2011 @ 3:41 pm

    It has been said that logic makes a better servant than a master.

    In terms of a logical, provable state of knowledge we would do better by combining logic with the wisdom of the heart.

    Medical science now reveals that the heart is composed of 60-65% of neuron cells. It is an intelligence centre but it does not solve problems through logic.

    A logical intelligence centre cannot fathom eternity. The brain goes “tilt” and renders some broken concept of what eternity is. The heart has a connection with eternity and knows, in its own way, what eternity is.

    The heart knows that eternity cannot be put into words or explained in any logical fashion that does not fall short.

    The heart relates to eternity as an experience, such as “love is eternal”, which is not a concept that can be explained or proven. We know in our heart what affinity is and we know it does not need to be explained.

    The best things in life are free.

    Our consciousness, our emotional satisfaction, our belonging and loving and our giving and sharing all have more value than most of the stuff we want to analyze and prove.

    Never mind proving the seat of consciousness, but enter the inner awareness of consciousness and you are connecting with the human soul.

    To know a thing does not require logic. In fact, we know more from experience than we will ever know from a concept.

    Theories are conceptual constructs and they exist in the mind, and the human soul (mind & consciousness) plays with these concepts with relish. But, providing proof is a material exercise and it tries to reduce everything to a material existence.

    A virtual reality, such as the contents of a web page, cannot be proven. We do not accept (if we have any brain cells) the content of a web page as being proof. It exists in a virtual reality and the cup of coffee it shows you is a concept. We no longer look for proof on the web because the web cannot deliver proof. Instead of looking for proof we look for “truth.”

    You read what I say and you don’t know if anything I say has truth. You certainly can’t find proof, so you look elsewhere on the web for other arguements as you search for truth.

    In the end we all come back to accepting our own belief as to what is the truth. Some will rely on logic, others on experience, others yet on third party reports and experiences and in the end we form our own belief.

    Who is is right and who is wrong?

    It doesn’t really matter. We believe what we choose to believe and one belief is as good as another for that purpose. And if one belief is as good as another then why choose a belief of limited value?

    Why choose a belief that requires material proof? Why choose to be small through proof when it is limiting by excluding all aspects of a belief that does not fit the conceptual construct of material existence?

    I believe I am sick! Or, I believe I am strong! Neither belief requires proof in order to garner most of our attention, and yet choosing one of those beliefs is far more potent than any proof to the contrary. In a case such as this it is more a matter of having a change of heart than it is a change of mind.

    Do you need proof that someone loves you before you can love them? Do you need proof that your gift of charity on a street corner is going to do some good? If we waited for proof we would not have much of a life.

    When you weigh proof against having a life it comes up way short and even when proof proves itself it does not enrich our lives. It merely satisfy that analytical pert of our brain that wants to judge everything and create cubbyholes for all it finds.

    If you love theories and finding material proof of existence then the love you have for your chosen quests are far more important than the actual proof you may find.

    The best things in life are free. Love a little, love a lot. The rest is just exercise, and you can love the exercise, but let’s not take proof too seriously. Especially because it feeds the ego more than it feeds consciousness.