Occam’s Razor is an important principle of scientific
epistemology. The Encyclopedia Brittanica explains:
“Pluralitas non est ponenda sine necessitate, ‘Plurality should not be posited without
necessity.’ The principle gives precedence to simplicity; of two competing
theories, the simpler explanation of an entity is to be preferred. [1]”
In this article, we will focus on a particular class of applications for
Occam’s Razor: the class of applications where it is used to select the null
hypothesis. The null hypothesis is the hypothesis on a question that we assume
to be true, by default, unless an alternate hypothesis on the question is
satisfactorily proven. To clarify this, let us proceed immediately to an
illustrative example.
Illustration: The Veracity of
Jack and the Beanstalk
You finish telling a child the story of Jack and the Beanstalk, a story involving giants, immense climbable
beanstalks, geese that lay golden eggs, and other bizarre phenomena. The child
asks: ‘Is that story true?’ How do you respond?
Well, the veracity of the story
is dependent on the source of the story. Did the story come from someone’s
imagination? Or was it actually based on an eyewitness account of actual events?
Thus, our question is: What is the origin of the Jack and the Beanstalk story?
Let us say that we entertain two competing hypotheses as possible
answers to this question. They are:
1. The story came from the active
imagination of a storyteller.
2. The events in the story
actually occurred on another planet and the eyewitness account of those events was
communicated to the originator of the story on Earth via interstellar,
telepathic brain waves.
It is unlikely that we could satisfactorily prove either one of these
hypotheses. If we treated both of these hypotheses equally, than our response
to the child’s query would have to be: ‘I have no idea’.
This is a highly
unsatisfactory answer though because we do in fact have an idea: even in the
absence of satisfactory proof, one of the hypotheses just seems a lot simpler
and more plausible than the other, which is pretty outlandish. Applying Occam’s
Razor, we select this simpler and more plausible hypothesis as the null, or
default, hypothesis, and the other hypothesis as the alternate hypothesis.
Our
setup now looks like this:
Question: What is the origin of
the Jack and the Beanstalk story?
H0 (null): The story came from the
active imagination of a storyteller.
H1 (alternate): The events in the story actually
occurred on another planet and the eyewitness account of those events was
communicated to the originator of the story on Earth via interstellar,
telepathic brain waves.
Because we cannot satisfactorily prove H1, H0 remains standing, and we
can tell the child: ‘I strongly suspect that the story came from the active
imagination of a storyteller, and hence isn’t a true description of actual
events’. Much more useful and satisfying than just proclaiming utter ignorance!
Anthropogenic Climate Change
The proper selection of the null hypothesis is an important part of
answering many scientific questions. One such question is that of whether human-caused
greenhouse gas emissions could cause disastrous global climate change in the
future if continued unabated. I would set up this question as follows:
Question: What was the primary
cause of the global warming that the Earth has gone through since the 1970s?
H0: The primary cause was not
human-caused emissions of greenhouse gases, but rather was a ‘natural’ cause or
set of causes, that would have happened even without any human interference.
H1: The primary cause was
human-caused emissions of greenhouse gases.
Why do I choose the skeptical position as the null
hypothesis? Isn’t this just indicative of my particular bias? I do so because
the ‘natural’ explanation of global climate change is in fact the simpler
explanation of the phenomenon. This is because we know that the Earth’s climate
has changed significantly and relatively frequently in the past, long before
humans were in a position to emit any significant quantities of greenhouse
gases. We also know that humans have been spuriously blaming themselves (or
their sins) for negative changes in the weather since the beginning of human
history. Thus, the simplest explanation is that this recent bout of global
warming has a natural cause, and that humans are once again blaming themselves erroneously
for changes in the weather, as has happened multiple times throughout the Earth’s
and humanity’s history.
The selection of the null hypothesis for this question is
very important, given how complicated the Earth’s climatic system is. Due to
this complexity, I don’t think that any well-informed person can honestly say
that either of these hypotheses has been satisfactorily proven. Treating both
hypotheses equally is not a good option, because then we would be forced to say
‘I have no idea’, which is not a very useful response when deciding whether implementing
anti-emissions policies would be a good idea or not. Setting up the hypotheses
as I have allows us to say: ‘I suspect that most of the observed global warming
has been due to natural causes, not human-caused greenhouse gas emissions, and
hence we should not implement any anti-emissions policies for the moment.
However, if more convincing evidence favouring the emissions hypothesis came to
light, I would be willing to change my opinion accordingly.’
The Existence of God
Occam’s Razor can help us answer this age-old and
much-discussed question. I would set it up as follows:
Question: Does God exist?
H0: No, there is no omnipotent sky ghost (God) in
existence.
H1: Yes, there is an omnipotent sky
ghost (God) in existence.
Why do I set the atheistic position as the null hypothesis?
The first reason is because, given our current knowledge about how the world
works, it is the simpler explanation. We can already satisfactorily explain
many seemingly mysterious phenomena by employing the principles and findings of
physics, chemistry, biology, and other sciences. Given this, the simplest hypothesis
is that there is an as-yet-undiscovered scientific,
non-omnipotent-sky-ghost-dependent explanation for the mysterious phenomena
that we still cannot explain satisfactorily.
The second reason is because it is impossible to prove a
negative. If religious people had their way and the existence of God became the
null hypothesis, it would be impossible to prove them wrong, no matter what
evidence came to light. For this reason, it is infinitely fairer, for these
kinds of ‘existence’ questions, to put non-existence as the null hypothesis.
In addition, if religious people insisted that the existence
of God should be the null hypothesis, for consistency’s sake the same should
apply to the question of the existence of other magical creatures. We would
have to accept the existence of the tooth fairy, unicorns, talking
garden-gnomes, leprechauns, and Santa Claus, for the simple reason that is
impossible to satisfactorily prove that any of these things don’t exist.
A group of people called Agnostics think that the two hypotheses
regarding the existence of God should be treated equally; neither should be the
null hypothesis. The problem here is that a consistent Agnostic can never say
that anything doesn’t exist, because it is impossible to prove a negative. To
be Agnostic just with regards to God is arbitrary and illogical; to be logically
consistent you have to be Agnostic with regards to any being whose existence cannot
be satisfactorily proven, including the aforementioned other magical creatures,
such as Leprechauns.
If you have no idea which, if any, of the scores of magical
creatures that people have dreamed up over the centuries exists, how do you
know which actions to take in regards to these creatures? Do you pray to God?
Sacrifice to Poseidon? Pay homage to Vishnu? Follow rainbows in search of the
Leprechaun’s pot of gold? In practice, most so-called Agnostics will take no
action related to any magical creature, including God, and thus seem to assume,
like Atheists, that these things don’t actually exist, unless proven otherwise.
Agnosticism, in practice, usually proves just to be a more socially-acceptable
form of Atheism, with little difference in actual content. This is for the
best, as a consistent Agnostic, not sure which of the thousands of potential gods
to pray to, or whether to chase rainbows and hunt Unicorns or not, would
probably quickly go insane.
Government Intervention
We can apply Occam’s Razor to the desirability of political
action as well. I would set up such questions as follows:
Question: Should the government engage
in coercive intervention x?
H0: The government should not engage
in coercive intervention x.
H1: The government should engage in
coercive intervention x.
Why set non-intervention, the libertarian position, as the
null hypothesis here? In a theoretically pure free-market society, every
individual would be free from violent coercion or harassment when it came to
taking the actions they deemed most conducive to their material and mental
well-being. They would similarly be free to engage in voluntary exchange involving
each others’ services or material possession, as long as the transaction was
deemed beneficial and worth engaging in by both parties.
The simpler and more plausible general hypothesis is that
this regime of individuals being allowed to pursue their own well-being in the
best way they know how and of mutually beneficial exchanges with others will in
fact be the regime most conducive to most individuals’ well-being. It is
certainly simpler and more plausible than the other possible general hypothesis,
which is that a regime where all individuals’ lives are completely controlled by
a centralized, coercive power will be the one most conducive to most
individuals’ well-being. This is especially true given the extensive and pretty
one-sided empirical evidence we now have with regards to the negative effect of
totalitarian regimes on individuals’ well-being.
Given this setup, if we cannot satisfactorily prove that the
government intervention in question will increase the relevant individuals’
well-being more than it decreases it, we retain the null hypothesis and opt for
laissez-faire in this instance.
But again; why the need for a null hypothesis at all? Why not
just treat both hypotheses equally. Because
either the government intervenes or it does not; there is no ‘neutral’, or ‘I
don’t know’, option available. If you don’t take a position on the question at
hand at all, then you’re basically just supporting whatever the majority of the
more active people have decided.
The Standard of Proof
I have used the term ‘satisfactorily proven’ a number of
times throughout this article, referring to what must be done in order to
reject the null hypothesis and accept the alternate hypothesis in its place.
The level of certainty of a proof for it to be ‘satisfactory’, or the Standard
of Proof, is a subjective determination, and will vary person by person and
instance by instance. For example, in criminal trials the null hypothesis is
innocent, and in order for the court to accept the alternate hypothesis of
guilt, it must be ‘proven beyond a reasonable doubt’. This strong standard of
proof makes the null hypothesis difficult to reject. By contrast, in civil
suits, the standard of proof is ‘balance of probabilities’, meaning that it
doesn’t really matter what the null hypothesis is, because if there is even a
shred more evidence for the alternate hypothesis than for the null hypothesis,
the alternate is accepted.
How do we decide what standard of proof to set? This will
depend on how much simpler and more plausible the null hypothesis is over the
alternate hypothesis. It will also depend on how bad the consequences of
erroneously rejecting the null hypothesis, balanced against the consequences of
erroneously retaining it, would be.
Conclusion
Null hypothesis selection using the principle of Occam’s
Razor is an important part of the scientific method. For many questions, it is
important to select the default hypothesis properly because we do not have the
luxury of waiting for all possible evidence to be collected before making a
determination. ‘I have no idea’ is a pretty useless position to take when it
comes to deciding upon concrete actions. Often we must decide one way or the other
without delay, and in the absence of sufficiently definitive proof one way or
the other, this means relying on the default hypothesis.
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