In a commencement address, Carl Sagan commented on the photo, deriving a deep meaning that still hangs on my shoulders every time I look at the stars and is the inspiration for this blog, “A Pale Blue Light” [1]

Look again at that dot. That’s here, that’s home, that’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every “superstar,” every “supreme leader,” every saint and sinner in the history of our species lived there – on a mote of dust suspended in a sunbeam.

The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.

Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.

The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand.

It has been said that astronomy is a humbling and character-building experience. There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we’ve ever known.

Ever Since I read this article, I grew to become obsessed about the Universe, the mechanics, and the philosophical beliefs of humanity.  I could easily end this blog by saying “we are inferior to the Universe because our minds and civilization will never compare to the awesome capacity of space, and time”  While I believe we are infinitely inferior, knowledge is much like a disease of irrationality.  Knowing anything allows us the hope of knowing something “more.”  But giving up the search for further knowledge is going against everything that we believe.

This blog is written about astronomy from an amateur astronomers point of view.  Most of the time I will keep the level of physics to a high/middle school level (basic algebra) however, in certain articles, I may advance the math to a College level.

Sources (Wikipedia: “The Pale Blue Dot”):

[1]^ Sagan, Carl (1994). Pale Blue Dot: A Vision of the Human Future in Space (1st edition ed.). New York: Random House. ISBN 0-679-43841-6.

Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions. You would like to attain faith, and do not know the way; you would like to cure yourself of unbelief, and ask the remedy for it. Learn of those who have been bound like you, and who now stake all their possessions. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. Follow the way by which they began; by acting as if they believed, bless yourself with holy water, have Masses said, and so on; by a simple and natural process this will make you believe, and will dull you—will quiet your proudly critical intellect…

Now, what harm will befall you in taking this side? You will be faithful, honest, humble, grateful, generous, a sincere friend, truthful. Certainly you will not have those poisonous pleasures, glory and luxury; but will you not have others? I will tell you that you will thereby gain in this life, and that, at each step you take on this road, you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognize that you have wagered for something certain and infinite, for which you have given nothing.^[9]

Pascal’s Wager first argues that believing in God is more morally acceptable and will make you “honest, humble, grateful, generous, a sincere friend, [and] truthful.” (lines 2-5 paragraph 2)  I will not go into this here, it deserves a post of its own.  I will simply say: there is nothing to suggest that believing in God is necessary for honesty, humbleness, gratefulness, etc.  Until my next article “Morality Part I”, pick up an excellent book by one of the most irritating evolutionary scientists in the world: The Selfish Gene by Richard Dawkins.

Cutting the fat off the bolded quote translates into something like: “[Believing in God will show you that] you have wagered [a finite sum] for [an infinite gain] for which you have gained nothing.”

I believe this passage, as with most of Pascal’s work, to be a genius tid bit of logic.  It is an excellent way for Christians to convinve ex-Christians and other Christian-biased believers, but convincing a truly agnostic or atheist person to believe in a deity is impossible to do with Pascal’s wager.

Suppose I were to ask you “what is the greatest football team?”  Depending on your following of sports, you may assume I mean an NFL, College, or little league team.  Some people may answer “Florida State,” while others answer “The Eagles” or “The little birds”  The truth is, the question is too general and varies depending on the person who is asked.  Similarly, ask a Christian what God or gods  they believe, and they say “the Christian ‘God’” Ask muslims what God or gods they believe, and they say “Allah,” ask Jews what God or gods they believe, and they will answer “Yahweh or Jehovah.”  The point I am making, is that the wager is not limited to a single God when trying to convince a wider audience.  A true atheist or agnostic should answer , if asked what God they believe, “I do not believe in a God” this is similar to someone saying “I do not follow football.” For some atheists and agnostics, there is no bias, simply no feeling on the matter.

The statement I made earlier presents a certain presumption “What God or gods do you beleive in?” This assumes God exists in the present.  But most Gods are omnipresent.  This means that God is an all-present and timeless entity.  Assuming that all God or gods are this way, we must wonder if the God or gods we believe today are even the correct God or gods.  What if the true “God” had one chance to make himself known, and he spoke to a person who was later: trampled by a wooly mammoth, run over by a chariot, or run over by a car?  With this person would end the true Gods power, knowledge, and any chance of us knowing him.  Similarly, what if the true God is not discovered until the year 2456, what reason does the Pascal wager give me to believe in God if I am completely uncertain of which God to believe?

Since the number of gods: past, present, and future are unknown.  Trying to argue to a truly unbiased point of view would be like trying to convince a person to wager a large finitite amount, say $100,000.00 (total offerings and a life time devoted to a belief) against a n-sided-die whose outcome, if z, would gain them infinite paradise.  If n was any number from 1 to infinity and z was any number from 1 to n.  The chances of picking the right God is literally undefined, unknown, and is as likely to be infinitely improbably as probable…  [Proof 1]

[Further Explanation] Since we do not know how many God or gods are out there.  We must average the total possible chances for every God scenario.  While starting at the chances for 1 God is not necessary since we already know more God or gods, real or fake, exist than 1, it does not matter since we will be dealing in infinites. (It should be said that this decision, though it does not impact this scenario, would be more impactful to my argument since a lower number would grant a higher chance that you would pick the right God or gods.)

1 to infinity for n means there could be anywhere from 1 to an infinite number of gods.  Since we can only beleive in one god, z is the God in which we believe in.  z can be any number 1 to n because z must be a number that falls within the number of gods (n) which happen to “exist.”

[Proof 1] Suppose that the range of the die was 1-3 (a traditional D3 if there were 3 gods)  The chances of me picking the right one would be 1/3.  If there were 3 possible scenarios, 1,2, or 3 gods, then there would be a (100% +50% +33.33…%)/3 chance that I would choose the right one.  If I take an average of this, then there is a %61.11… chance that I choose the right God if there are an unknown of one to three gods to choose from.  If this were generalized for all numbers n=1-infinity (anywhere from one to an infinite number of gods), then the template would be:

LIM[sum(1/n,1,n)/n,n=1,infinity]

The sum(1/n) adds all possible chances of choosing a correct God.  This includes all values for the number of possible gods (n).  The 1,n bound inside of the sum() indicates that 1 to n will be added using the probability term 1/n.  Dividng by n outside of the summation is to take the average of the total chance of picking a God.  To perform this calculation, the summation inside will be calculated first.  If the summation inside is less than infinity, the Pascal Wager is likely to be unproven because there are an infinite number of chance-combinations.  If the numbers are the same, there is a suggestion that the Pascal’s wager could be wrong or right, but the calculation shows that there is not enough mathematical evidence to take part in the wager.

In mathematics, a limit is said to either diverge (approach infinity) or converge (approach a finite number).  The idea of a limit is to figure out what happens as a sequence of numbers approaches infinity.  The summation 1/n diverges (approaches infinity) because 1/1+1/2+1/3+1/4+1/5+…1/99+…1/9999999+ 1/… approaches infinity.  An easy way to see this is to group the sequence of numbers (1/1 + 1/2) + (1/3+1/4) + (1/5+1/6)+…  In this sequence, notice that every pair of numbers is greater than the last number in the preceeding pair. [1] So the sum of pair 2:  (1/3+1/4) is greater than 1/2 (the last number in the preceding pair).  This follows with pair3 where (1/5+1/6) is greater than 1/4, the last number in pair2.  Because the pairs are always greater than the last number in the last pair, the value of the number can be said to increase without “bound” and diverge away from any finite number and towards infinity.

Since we must divide the total chance “by infinity,” the number of probabilities involved in every scenario of gods, we are left with an undefined function that neither proves the Pascal’s Wager or confirms it.  In essence, the math shown here shows that the Wager has so many unknown variables that convincing someone who is truly agnostic or an atheist is absolutely impossible.