The Gumball Analogy

1st October 20221st October 2022 Dave Rowlands 2 Comments

Introduction

You are presented with a jar full of gumballs. There are no broken gumballs inside the jar, they are all whole gumballs. Most sceptics and atheists will have heard the Gumball Analogy already. It’s a pretty common analogy used by sceptics and atheists who have discussions on places like Twitter, Facebook, and YouTube. Fans of The Atheist Experience will certainly recognise it, as it’s an argument created, used, and popularised by Matt Dillahunty. Though I have also had people mention that it was Tracie Harris that first created it. The analogy then went on to be used by many other sceptics and atheists in the community.

As you can probably guess from the title of the article, and that opening paragraph, that will be the focus of the article. For those looking for a complete rebuttal to the Gumball Analogy, I’m afraid you’ll probably be disappointed. I will be taking a critical look at the analogy, and pointing out where I think some people go wrong using it. But I will also be commenting on what I think it gets right, as I think there are some valid points to be made using the analogy. While I know that most people are probably familiar with the analogy, I’ll still begin with a description of the analogy. Then follow that with a look at what the analogy is claimed to show.

The Gumball Analogy

As stated at the very beginning of the article, you are presented with a jar full of gumballs. Inside the jar there are only whole gumballs. The jar is packed to the top with these gumballs. The only thing we know about the jar of gumballs is what we can see. We have no way of knowing how many gumballs there are in the jar, at least not without opening it up and counting them. There is one thing that we can tell though. There will be an odd or an even number of gumballs. With all of the gumballs being whole there can be no fractions involved, only whole numbers. This means that it must be odd or even, because whole numbers are odd and even. So, the question asked to us is, are there an odd number of gumballs in the jar or an even number?

What the Analogy Intends

The analogy is intended to show a couple of ideas. One of the first things it is intended to show is the idea of the burden of proof. We cannot know how many gumballs are in the jar, nor can we know whether the number of gumballs is odd or even. As stated previously, we must open up the jar and count them to get this information. Showing that proof is needed in order to support any claim about the state of the number of gumballs. Both how many are in there, and whether there is an odd or even number in there.

Another focus of the analogy is belief states. There are several things about belief states that the analogy is used to argue for. One thing that is intended to be shown is that we should proportion our beliefs according to the evidence. If we consider what we can know about the jar just by looking at it, then the only thing that we seem to be justified believing is that there is an odd or even number of gumballs. This is something we can reason about the jar based simply on how numbers work, and does not necessarily need empirical evidence to support. It is analytical in nature, and true based on definitions alone. Any other beliefs about the state of affairs concerning the number of gumballs appear need empirical support in order to be reasonable.

The analogy also intends to show that belief states are binary. Meaning that someone either believes something or does not believe that something. You either believe the gumballs are an odd number, or you do not believe it is an odd number. The same when it comes to belief about whether it is an even number. The statement ‘there is an odd number of gumballs in the jar’ is a proposition, and can only be true or false.

The statement ‘I believe the number of gumballs is odd’ is a proposition about your belief state, and just as with ‘the number of gumballs is odd’, this proposition too can only be true or false. In both examples of the proposition there is no middle ground, it can only be true or false. Just as the number of gumballs can only be odd or even. To argue for a middle ground would be to break the law of excluded middle. The same can be said for the statement ‘there is an even number of gumballs in the jar’ and ‘I believe there is an even number of gumballs in the jar’.

It also intends to show that not believing one proposition does not mean that you believe the opposite proposition. Not believing that there is an even number of gumballs in the jar does not automatically mean that you believe there is an odd number of gumballs in the jar. Which certainly does seem to be case, it is possible to not believe both propositions describing the odd-ness or even-ness of the gumballs in the jar. So, while there may be no middle ground when it comes to believing they are odd or believing they are even, there is a middle ground of not believing either.

Burden of Proof

There may be other things that the analogy intends to show, but these are the things I most commonly heard attributed to it. From atheists and sceptics, as well as when I’ve heard Matt Dillahunty speak about. So, these are the main things I will focus on. Let’s begin first with the analogy’s representation of the burden of proof. I am currently working a script doing a deep dive in ideas about the burden of proof, so I will save a more detailed explanation for that. For this video I’ll just focus on what the analogy represents.

As stated earlier, when it comes to what we can know about the number of gumballs there is very little. We cannot know the number of gumballs in the Gumball Jar, nor can we whether that number is odd or even. At best we could make a guess. This means that any claim we make about the number of gumballs is at best a guess. It would also be a guess that is not based on any evidence. Therefore, if we want to be good sceptics, we should withhold belief in any claim made about the number of gumballs in the jar. Why would wanting to be a sceptic imply that?

This can best be summed up by a statement popularised by Matt Dillahunty, ‘I want to believe as many true things as possible, and as few things as possible’. The statement represents, at least in part, the motivations of many sceptics. The desire to avoid believing false things, the desire to avoid falling for scams, and that kind of thing, also plays a part. Of course, there can be, and will be, other motivations when it comes to individuals, this statement describes the motivation of scepticism as well. At least, a certain kind of scepticism. Radical Scepticism is a different matter, but the average sceptic and atheist is not working from Radical Scepticism, but a more general scepticism.

So, in my opinion, the gumball analogy can work pretty well as an analogy for showing the burden of proof and scepticism. There is one thing that should be avoided when arguing this though. The analogy does not show that only empirical evidence can suffice as evidence, only that empirical evidence is necessary before we should accept or believe certain claims. The idea that we can discover that there is either an odd or even number of gumballs in the jar through reason alone shows that there are things we can deduce without empirical evidence. Plus, if the analogy is intended to be used as evidence for scepticism, or for beliefs being binary, or for atheism meaning a particular thing, then the gumball analogy is also evidence that arguments and analogies can considered as evidence for certain things.

Belief States

Next up is its use in arguing that beliefs are binary, or that belief states are binary at least. To recap the argument, it’s the idea that you either believe the gumballs are odd or you don’t, and as a separate matter you either believe that gumballs are even, or you don’t. As stated previously, this is based on expressing those beliefs as propositions, and adhering to the Law of Excluded Middle. Which argues that a proposition is either true or false, and there is no middle ground.

This argument is true of course. If your belief state is expressed propositionally, then you either believe or you don’t. There is only the true or false option, and as stated it would break the Law of Excluded Middle to offer a middle ground. So, it seems reasonable to accept this argument. However, this ignores certain things when it comes to beliefs. Things that the analogy actually goes on to argue, while ignoring them for this particular part.

The reason that the analogy ignores these ideas is because it being used to support a very specific claim. That specific claim being that you are either a theist, or you are an atheist. You either believe God exists, and are therefore a theist. Or you do not believe, and are therefore an atheist. Which this argument seems to support. Job done, right?

Well, no, unfortunately not. This argument might support how an individual is using the terms, or give some explanation of why they are using terms that way. However, it does not support that there is a fact of the matter regarding the term atheism. It does not support that there is a fact of the matter that atheism must be used this way, any more than citing a dictionary supports that there is a fact of the matter that atheism must be used a certain way. We will look at this in more detail later, but for now let’s return to the idea that beliefs are binary and there is no middle ground. So, are beliefs only binary?

Are Beliefs Binary?

When we look at purely in the sense of a proposition then beliefs do appear to be binary. The proposition describes the existence of a psychological state in the agent. That psychological state either exists or it doesn’t exist. However, when we speak about beliefs we don’t always speak of them in the context of the existence of the psychological state. We generally speak about them in terms of our attitude towards the proposition. These attitudes are not based on Classical Logic.

Consider a question like ‘Do aliens exist?’. How would you answer that question? Some might answer ‘I think so’, some might answer ‘I don’t think so’, and others might answer ‘I’m not sure’. There may be variations in the wording, but they are the general attitudes that one might have when answering the question. This sort of idea also applies to the question ‘Does God exist?’, as well as many other similar questions. If we were to honestly reflect on how we actually think about our beliefs, we would see that we rarely speak about them in terms of whether a particular psychological state exists.

They are usually thought about in terms of certainty, credence, confidence, and as admitted by the gumball analogy without admitting to it, there are neutral positions on certain topics. As the gumball analogy states, it is possible to have a neutral position. Not believing one proposition does not mean you believe the opposing proposition. Admitting that when it comes to beliefs, they are not the binary idea that many arguing using the gumball analogy are putting forward. It is possible to be uncertain about certain claims, and this includes the claim of God’s existence. If the gumball analogy is applied to belief in God, it becomes obvious that it is possible to be neutral on the position of God’s existence.

Purpose Driven

Which brings us to the problem with this part of the argument. It is driven by a specific purpose. That purpose is to argue that atheism and theism are binaries. And that atheism is based solely on not believing God exists. It is driven by the idea that atheism is a lack of belief in god or gods and that’s it. The analogy tries to show this using poor logic driven arguments. Its purpose is to show that atheism is, or can be, a neutral position. While also arguing that there are no neutral positions when it comes to belief in god. The argument, in essence, contradicts itself due to its desire to argue for what could be considered ideological purposes.

The sceptic and atheist using this portion of the analogy is more than happy to throw reason, scepticism, and logic, out the window in order to protect the claim that atheism is a lack of belief in god or gods and that’s it. They are also willing to ignore counter evidence, counter claims, and counter arguments, in order to defend that belief. Which undoes the good work that the burden of proof analogy does with the analogy.

The Failure of the Analogy

It is here that the analogy breaks down and fails, and there really is no need for it. Using the analogy to argue for anything about what atheism must mean will always fail. As will any other argument for why atheism must mean a certain thing. Regardless of what meaning is being put forward. Which causes what is, or at least could be, a good and helpful analogy to break down, and weakens it. Using this analogy to argue for what atheism must mean also promotes bad scepticism. Which is in opposition to its use for promoting good scepticism. Undoing the good work that its promotion of scepticism does.

One thing it does highlight is that some sceptics and atheists are no less susceptible to starting with a conclusion and forming evidence to support it. The position that atheism is a lack of belief in god or gods and that’s it is assumed. And then the analogy is used to support it. As well as the idea that there are no neutral positions when it comes to belief. Both of these things are assumed before the argument, and the argument tailored to those conclusions. Something that not only sceptics and atheists criticise in those outside of those circles, but promote avoiding within those circles. Again, undoing the good work the analogy does when promoting the idea of the burden of proof.

No Need For It

There really is no need for it either. Words work in such a way that different groups can use words and terms differently. If someone wants to identify as atheist, and make that identity ‘someone that lacks a belief in god or gods’, then they really are free to do so. Will there be others that argue again that usage? Of course, there will, that is simply par for the course. Will there be people that argue that there are other ways of using the term atheist? Of course, there will. The gumball analogy can also be used to argue for those other ways of using the term atheist. Just as it is used for the idea that lack of belief is the definition of atheism.

However, none of those arguments have any kind of authority over how the term must be used. There simply is no authority on how the word must be used, except in a contextual sense. My video ‘Atheism: A Tale of Two Usages’ goes into detail about why there is no such thing as a one true definition of atheism. As well as why there cannot be such a thing as one true definition of atheism. Unless one wants to promote the idea as a form of dogma. Which is not something that atheists and sceptics should be doing. Something that I would imagine that most sceptics and atheists would agree with, and I often see them arguing against.

Conclusion

So, to conclude, I would argue that the gumball analogy is useful, and makes some good arguments. The problem comes when people try to extend that beyond what the gumball analogy can be argued for. It comes when people use it to argue for what atheism must mean, or how the word must be used. Or when used to argue against the idea that beliefs are binary and there is no middle ground. Doing so ignores how beliefs actually work when it comes to claims and propositions. And does so in the face of evidence on how they work when it comes to claims and propositions. It puts dogma before good reasoning, something that goes against good scepticism.

It should be important for a sceptic to remember something mentioned by David Hume. That we ought to proportion our beliefs to the evidence. By clinging on to certain arguments the gumball analogy is used to promote, the sceptic and atheist is not proportioning their belief to the evidence. Instead, they are proportioning the evidence to the belief. They are also willing to throw their scepticism out the window in favour of that belief. If the idea of the gumball analogy is to promote good scepticism, then these arguments should be dropped. As they most certainly are not supported by the gumball analogy.

There is obviously much more that I could say about the ideas here, but I am doing my best to try to keep the length of my articles down. This article does, hopefully, give some idea of where and why the analogy breaks down. At least in how it’s used by many atheists and sceptics. Which is a shame in my opinion. As there are some strong ideas and arguments that can be made from it. The problem comes from overreach by the wielder of the analogy.

Thanks for reading, hopefully there has been some food for thought here. Don’t forget to check out my video on ‘Atheism: A Tale of Two Usages’ for why arguments about what atheism and atheist must mean are non-starter arguments. It also discusses why I think these arguments are not only pointless, but harmful to good scepticism and the atheist community in general. See you soon, take care all!

Comments (2) on “The Gumball Analogy”

RealestRealist says:
11th June 2023 at 5:50 pm
“Not believing that there is an even number of gumballs in the jar does not automatically mean that you believe there is an odd number of gumballs in the jar. Which certainly does seem to be case, it is possible to not believe both propositions describing the odd-ness or even-ness of the gumballs in the jar. So, while there may be no middle ground when it comes to believing they are odd or believing they are even, there is a middle ground of not believing either.”
This is an assertion. Because belief is neurological, to characterize atheism as an “absence” of belief, a “lack” of belief, or “nonbelief,” as opposed to disbelief, the implicit claim here is that a distinct neurological state that is neither belief in p nor belief in the negation of p exists in reality.
Certainly, there is a linguistic distinction between the statements, “I do not believe in gods” and “I believe there are no gods.” However, this is insufficient to substantiate the existence of a distinct neurological state in reality. As far as I can tell, “nonbelief” and disbelief are as different as couches and sofas, flapjacks and pancakes, or pants and trousers. That is to say, they are different in expression only. This is a distinction without a difference fallacy.
I also understand the concept of “nonbelief.” However, this is also insufficient to substantiate the existence of a distinct neurological state in reality. Without empirical evidence, I have no good reason to think that “nonbelief” is any more real than are gravitons, tachyons, and wormholes. These are all very interesting abstract hypothetical concepts. However, they remain hypotheticals because we do not have empirical evidence of their existence. Just because we can conceptualize something–just we can imagine “nonbelief” as being separate and distinct from disbelief doesn’t mean that this is the case. Existence is not a predicate. This is an existential fallacy.
I recognize that this is how the term “atheism” is defined. However, one cannot define a distinct neurological state into existence any more than one can define a deity or anything else into existence. It either exists, or it doesn’t. This is an appeal to definition fallacy.
Not knowing that something is true does not preclude belief that it is true, nor does the fact that a belief is unjustified. Just because we agree that one has insufficient evidence or good reason to warrant belief, does not mean that belief isn’t present anyway. This is an ought-is fallacy.
The problem with the famous gumball analogy is that it is just an elaborate fallacy of begging the question. It doesn’t actually demonstrate that it is objectively true that not believing there are an even number doesn’t mean instead believing that there are an odd number. As a counterargument, I’ll provide my own analogy. When one flips a coin, the odds of the result being either “heads” or “tails” are exactly the same–just as in the aforementioned analogy. Thus, we can agree that no one knows what the result of any such coin toss will be, nor does anyone have any evidence or good reason to justify believing that the outcome will be one side versus the other.
Yet, when the coin is tossed, no one ever says, “I don’t know,” even though this is this is the case. One simply calls “heads” or “tails.” However, if belief informs action, and an “absence” of belief provides no impetus for action, then any action taken (including willful absention) is evidence of the presence of some belief. It may be insufficient or inconclusive evidence; however, it is evidence. Indeed action entailsbelief. We can agree that this belief that the result will be one face of the coin versus the other is unjustified and irrational; however, it is present to inform the action of calling that result. Perhaps this belief is caused by a recency bias, or by a gambler’s fallacy where we think a particular face is “due,” or because of how question is posed, or because of any number of things. However it is formed, it is present.
The same could very well be the case in the gumball analogy where one irrationally believes on the subconscious level that it is more likely than not that the number is odd or even–despite having no evidence and no good reason for it. And, this could occur, as it does in the case of the coin toss, despite one being aware on the conscious level that one can neither predict the result nor be justified in believing one versus the other. Neither not knowing nor being unjustified preclude the possibility of the presence of belief.
To look at it another way, in order to know definitively that belief is absent or present would require that we first be able to positively identify specific beliefs within the human brain, which we cannot presently do. However, because belief informs action, and action entails belief, we can infer the presence of belief based on actions taken. Being derisive toward people who believe in the existence of s deity (action) is evidence of the presence of belief in the nonexistence of any deity. Arguing against the existence of a deity (action) is evidence of the presence of belief in the nonexistence of any deity. Abstaining from participation in religious practices and traditions (action) is evidence of the presence of the belief in the nonexistence of any deity. Dismissing the claimed existence of any deity (action) is evidence of the presence of belief in the nonexistence of any deity.
If atheists wish to assert that a distinct neurological state of “nonbelief” exists in reality, they, as the claimants, have the burden of proof for this assertion.
If atheists wish to assert that “nonbelief” is genuinely different from disbelief, they, as the claimants, have the burden if proof for this assertion.
If atheists wish to assert that their actions are informed by some other belief, they, as the claimants, have the burden of proof for this assertion.
I have yet to have been presented with any empirical evidence to support the claimed existence of a distinct neurological state of “nonbelief” or any independently verifiable means by which one might differentiate between “nonbelief” and disbelief. The null hypothesis is to proceed as though something does not exist unless there is sufficient evidence to substantiate its claimed existence; and a distinction that does not manifest in reality is indistinguishable from a distinction that does not exist. I await empirical evidence to substantiate this claim. I have been presented with conceptualizations, definitions, explanations, rationalizations, analogies, and personal anecdotes. I have faced a litany of logical fallacies, deflection, distraction, and evasion…but not a scrap of actual evidence despite the fact that multiple clinical studies have already substantiated a genuine neurological distinction between the brains of atheists and religious people using fMRI. All I am asking for is for the next logical step of substantiating a distinction between the brains of atheists expressing “nonbelief” and those expressing belief in the nonexistence of gods.
As it stands, as a (potentially subconscious) belief in the nonexistence of god(s) actually explains the actions of atheists expressing “nonbelief” whereas an actual “absence” of belief does not, this remains a better hypothesis than the alternative.
If you prefer syllogisms, I’ll provide two:
P1) To possess the knowledge that a particular belief is absent requires that one be able to be able to positively identify specific beliefs in the brain.
P2) We have no means by which to positively identify specific beliefs within the brain.
C) To possess the knowledge that a particular belief is absent is a logical impossibility.
We can, however, infer the presence of belief based on actions taken.
P1) Disbelief in p signifies belief that p is false. (by definition)
P2) Belief that p is false signifies belief that the negation of p is true. (principle of the excluded middle)
P3) The neurological condition of “nonbelief” in p is the equivalent of disbelief in p. (null hypothesis)
C) The neurological state of nonbelief in p signifies belief that the negation of p is true.
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1. Davidian says:
  14th June 2023 at 3:32 pm
  //This is an assertion. Because belief is neurological, to characterize atheism as an “absence” of belief, a “lack” of belief, or “nonbelief,” as opposed to disbelief, the implicit claim here is that a distinct neurological state that is neither belief in p nor belief in the negation of p exists in reality.//
  Yes, consider any other dichotomy wehre you’re unsure of the answer. Has anyone ever given you a choice between two meals, for example, and you’re unsure what you prefer? Or even the choice of do you want to do [enter thing here] and you’re unsure if you do or you don’t?
  Not believing something is true or false is entirely possible.
  //Certainly, there is a linguistic distinction between the statements, “I do not believe in gods” and “I believe there are no gods.” //
  There is a logical distinction too.
  ¬Bp (not believing in gods existence) could be because you B¬p (Believe no gods exist) or because you are also ¬B¬p (not believing in gods nonexistence) and are therefore sustpending judgement.
  //However, this is insufficient to substantiate the existence of a distinct neurological state in reality.//
  Do you have any studies that show it is impossible to be uncertain and therfore suspend judgement on a proposition?
  I know a person might be going A B A B A B with their thoughts on the matter, and therefore suspend judgement until they know more but that is a different kettle of fish.
  I do agree, however, that one could make the statement that for practical purposes there is little difference, e.g. someone suspending judgement vs someone in the state of disbelief in gods would seem generally similar in the sense they don’t pray, go to church etc.
  I talk about this a little in do non-theists live as atheists: https://www.answers-in-reason.com/religion/atheism/do-non-theists-live-as-atheists/
  //I recognize that this is how the term “atheism” is defined.//
  There is no single way atheism is defined. The popularism of the non-belief definition is a relatively recent phenomenon though it does have older roots. The normative definition is the belief or proposition gods do not exist. https://www.answers-in-reason.com/philosophy/atheism-as-a-proposition/
  There are many definitions though: https://www.answers-in-reason.com/religion/atheism/evolution-of-atheism/
  We happen to prefer the propositional use to the “lack belief” definition, but our preference doesn’t stop language being fluid.
  //Not knowing that something is true does not preclude belief that it is true, nor does the fact that a belief is unjustified. //
  Indeed, Knowledge is a subset of belief, but not having knowledge can still mean you believe.
  However, that is refering to epistemic knowledge, and if you’re answering a proposition with “i don’t know” it is more about uncertainty than knowledge. Thus, it means you’re not affirming p or ¬p and therefore are suspending judgement.
  //Just because we agree that one has insufficient evidence or good reason to warrant belief, does not mean that belief isn’t present anyway.//
  agreed, we can have unjustified beleifs, and we can have justified beliefs. We can even have arational beliefs.
  // This is an ought-is fallacy.//
  I am not sure I see how. Perhaps this is to do with a conclusion you have made about Dave’s article which isn’t necessarily in tune with the article itself.
  //The problem with the famous gumball analogy is that it is just an elaborate fallacy of begging the question//
  How is it begging the question?
  //Yet, when the coin is tossed, no one ever says, “I don’t know,” even though this is this is the case. One simply calls “heads” or “tails.” However, if belief informs action, and an “absence” of belief provides no impetus for action, then any action taken (including willful absention) is evidence of the presence of some belief. It may be insufficient or inconclusive evidence;//
  This is kind of a false equivalence. When people yell heads or tails they are guessing.
  Much like in gumballs when you have to guess how many are in the jar. I doubt anyone trully beleives there are 849 in the jar. They are just guessing.
  With a coin flip, it is mostly guessing.
  Sure, some might watch the coin and try and judge which side it will land on based on rotation.. or some might just like heads or tails for some reason and just call that regardless.
  //The same could very well be the case in the gumball analogy where one irrationally believes on the subconscious level that it is more likely than not that the number is odd or even–despite having no evidence and no good reason for it.//~
  Could being the operative word.
  Also, something you in your subconcious isn’t the same as something actively in your mind.
  A belief is a positive attitude towards a proposition, something accepted as true, something concluded is most likely the case or thought most probable etc.
  a “Subconcious belief” seems more like you unconcious set of expectations about the world. From a psychological perspective they are less specific and more generalised. These are commonly known as Schemas or scripts.
  So you might have general beliefs about a place being dangerous or the value of a gender/race..
  but having a Schema about gumballs being odd is incredibly unlikely as it is oddly specific.
  This could only really be built by repetition of having this examined loads of times, always being odd and building a sort of cognitive bias in your brain. You might not conciously know why you think it is odd, but that comes to the forefront of your mind… at which point you have a belief and you’re not suspending judgement.
  //If atheists wish to assert that a distinct neurological state of “nonbelief” exists in reality, they, as the claimants, have the burden of proof for this assertion.//
  //If atheists wish to assert that “nonbelief” is genuinely different from disbelief, they, as the claimants, have the burden if proof for this assertion.//
  Non-Belief: ¬B¬p ^ ¬Bp
  Disbelief: B¬p ^ ¬Bp
  There are different types of not believing: https://www.answers-in-reason.com/philosophy/different-types-of-not-believing-the-law-of-excluded-middle
  A baby doesn’t believe because it lacks the cognitive abilities to consider the proposition and believe either way
  and agnostic doesn’t beleive because they suspend judgmenet
  an apatheist doesn’t beleive because they don’t care to examine the propsition and so on.
  //If atheists wish to assert that their actions are informed by some other belief, they, as the claimants, have the burden of proof for this assertion.//
  Sure, I agree with that.
  I don’t even hold to non-belief atheism anyway. I am happy to be an atheist that believes no gods exist and I justifiy why here: https://www.answers-in-reason.com/religion/atheism/why-do-i-believe-no-gods-exist/
  //Stuff about null hypothesis//
  The null hypothesis isn’t about belief, it doesn’t deal with existence or relate to theism/atheism.
  The null hypothesis is the conclusion drawn if there is no (significant) difference between variables.
  In fact, its not even drawn, its part of the initial set up and relates to H1-Hn.
  Without a valid H1 there is no H0.
  H0 is never accepted, just not rejected.
  A bit more on the null hypothesis: https://www.answers-in-reason.com/religion/atheism/misunderstanding-the-null-hypothesis-and-knowledge/
  Though I have a script I am working on for as video about this in more detail.
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