Solution to pascal’s wager

For those who don’t know, Pascal’s wager is an attempt to make a logical argument for believing in god. The idea is that if you agree that heaven has infinite value, it follows that if your belief is that the probability god exists is greater than 0 (and even Richard Dawkins would only rate himself at 6 out of 7 in the strength of his belief that god does not exist) then the value of believing in god is infinite, because any non zero number multiplied by infinity is infinity – if you assign a probability of 0.01 of god existing then the value of believing in him to reach heaven is 0.01 * infinity = infinity. For more information, check out the wikipedia article.

Allowing the possibilities of states that have infinite value (such as heaven) implies that any decisions that can both potentially lead to reaching these infinitely valuable states necessarily have equal value. For example, exercising for 50 minutes and punching one’s self in the face are both of equal value to someone who believes that the probability of reaching heaven after doing either of these things is not exactly 0.

Assigning a future state the value of infinity in decision systems has a very powerful destructive effect. Because a future state of infinite value has a non-zero probability of being reached, all the parent nodes have infinite value too and that will ultimately lead to the current node also having infinite value, meaning that there will be indifference to all current decisions. Thereby making it not much of a decision system anymore because it has no way to discern between any choices.

Those who do believe in states of infinite value but don’t believe that all decisions that don’t rule out the possibility of reaching all values of infinite states have equal value are forced into resolving the contradiction. Either they must accept that essentially all decisions have equal value to them, or they must deny the existence of the possibility of states that have infinite value – it’s not consistent to hold both beliefs. And it’s my belief that denying the existence of states of infinite value is the most intuitive decision that most people already agree with. I don’t have any proof that this is the correct assumption, but I think most people would agree with me that anything that results in almost all decisions having exactly the same value is not valid.

While adding in a new rule for decisions systems is a heavy handed approach to solving what seems to be a small problem in Pascal’s Wager, it actually solves the problems of the destructive forces infinities have on decision systems.

At this point you may be thinking “but wait, if heaven does last infinity long and each year has a value greater than 0, it’s value must be infinite”. In that case I would like to outline how it is possible that even though heaven can last infinitely long, it does not necessarily have infinite value even though each year has a positive value. Consider the series 1/2 + 1/4 + 1/8 + … Does it add up to infinity? It doesn’t, here’s a visual proof

Things that have an infinitely long existence in the temporal realm do not necessarily have infinite value even though each instance of that point of time has a value greater than 0.

Similarly, you can assign a probability distribution of the value of an unknown entity such that it never adds up to infinity. E.g. the probability it is worth 1 is 1/2, the probability it’s worth 2 is 1/4 and so on. This is another way to assign a positive probability to all possible values of an unknown entity without requiring you to be absolutely certain that it is not worth more than a given amount (i.e. not needing to assign a probability that it has a value above x to be exactly 0).

In summary, this post is meant to outline the fact that you must either accept that almost all decisions have the same value or that states that have infinite value do not exist.


Consciousness is not at the Core of Problem Solving

Learning to walk takes some time. There’s a reason for this: walking actually requires you to solve simultaneous equations. Yes, that’s right. It’s incredibly difficult math. It’s only recently that engineers have been able to build a robot that can walk on uneven terrain with four feet. I am yet to see one that can do so on TWO feet. There is Asimo but that only works on flat surfaces and so isn’t very impressive. To program a robot that can walk you need many gyroscopes in. Ray Kurzweil touches on this in Age Of Spiritual Machines
“To predict where the ball will go, and where the fielder should also go, would appear to require the solution of a rather overwhelming set of complex simultaneous equations. These equations need to be constantly recomputed as new visual data streams in. How does a ten-year-old Little Leaguer accomplish this, with no computer, no calculator, no pen and paper, having taken no calculus classes, and having only a few seconds of time? The answer is, she doesn’t. She uses her neural nets’ pattern-recognition abilities, which provide the foundation for much of skill formation.”
This assertion that she is not solving the equations is wrong. She is solving the equation but only in a way that doesn’t lend itself to being expressed in math. The solution to the simultaneous equations are in her brain unable to be expressed by her. Some people struggle with expressing emotions. I argue that we also struggle expressing the solutions of complex equations we solve.

To think it is pattern recognition is absurd. No two balls ever take the same path, how can it use pattern recognition? To transform the ball’s path into a previous pattern we’ve seen would be more computationally expensive than solving the simultaneous equation. It wouldn’t allow us to predict the path of a ball in windy conditions or when the ball has spin or anything of the sort.

The conscious mind does not give us unrestricted access to the computations our neurons are doing. Why would anyone believe it could? You can’t access the part of your brain that’s telling your heart to beat or your stomach to pump food. We can only observe a tiny fraction of our minds and how it functions. This makes many people uncomfortable because they identify with “their” conscious mind and enjoy living in the fantasy world in which they have absolute conscious control over their decisions, fueled by the illusion that is free will. If I say “why did you choose to play football instead of doing your homework?” saying “I don’t know” leaves many unsatisfied. As though not knowing is a reason to not have done that. There is a lack of consistency because if people were asked how they were walking (and express it in computer language or math) they would be unable to yet one wouldn’t expect that person to then stop walking.

I don’t fear doing something without a reason for it becoming consciously apparent to me and neither should you. You’re really blocking your own intuition and your greatest weapon – the unconscious (subconscious) mind. A recent article I read on this subject was about crows solving problems without planning their actions. I’m going to interpret the results differently. When we do things on the fly is called improvisation.  I think that what we call planning is actually just improvisation in a virtual world that we have constructed by imagining it. In other words, the same processes in our unconscious mind (the processes of solving the problem at hand) when we are in the real situation than the imagined one. It’s just that we are storing the improvisations we made in the virtual world in our memory so that once we encounter the real scenario we have already had a head start spending time improvising the answers. It is not that when we plan things it is our conscious mind overseeing this whole thing.

Now one mind say that my point is wrong because the conscious mind is the one that solves improvisation problems but this is not true. I see it as the unconscious mind solving problems then that solution rising up (“falling down “is perhaps the language I should have used) to the level of consciousness. The conscious mind then swiftly takes credit for solving this problem. It reminds me somewhat of the quote “good artists copy, great artists steal”. This quote was brought to my mind for unknown reasons but I still feel its relevant. I don’t need to be able to express justification for everything I do in order to be satisfied with it.

I’m guilty of separating the brain into conscious and unconscious parts. This isn’t quite right. Our brain is just one big mush of neurons and somehow it works.  To split it up in this way isn’t going to be very successful.

We Are All Unique Xor Equal

We cannot be both unique and equal. It is a contradiction. It is a fantasy that many people have. When they want to be individuals they tell themselves they’re unique. And when they feel threatened by those in more powerful positions they say that everyone is equal.

The reality is that no one is equal. Every atom is my body is arranged differently to everyone else. We are equal in terms of rights the governments give us but there are special cases. Journalists are often given different rights in order to keep reporting. To say that you are equal to someone else is false. This may seem like pedantry but to me it seems essential to avoid confusion. It’s fine you just it as shorthand for “you have been awarded the same rights as me by the  government” but most people genuinely think we are inherently equal in some way which is dangerously wrong.