Editing 2947: Pascal's Wager Triangle

{{comic
| number    = 2947
| date      = June 17, 2024
| title     = Pascal's Wager Triangle
| image     = pascals_wager_triangle_2x.png
| imagesize = 740x802px
| noexpand  = true
| titletext = In contrast to Pascal's Wager Triangle, Pascal's Triangle Wager argues that maybe God wants you to draw a triangle of numbers where each one is the sum of the two numbers above it, so you probably should, just in case.
}}

==Explanation==
{{incomplete|Created by a BOT WHO BELIEVED THE N BOTS ABOVE HIM - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
The comic is a conflation of {{w|Pascal's Wager}} and {{w|Pascal's Triangle}}. It's structured as a layout that emulates Pascal's triangle, an infinite triangle of numbers where the top number is 1 and each value below is the sum of the adjacent number(s) above it. The second row has two 1s (each the sum of the single 1 above), and the third row has a 1 (the sum of a single 1 in the second row), a 2 (the sum of both 1s above it), and another 1, and so on. It plays important roles in binomial expansion, probability theory, and other areas of math. While {{w|Blaise Pascal}} did not invent the triangle, it is named after him (an example of {{w|Stigler's law of eponymy}}).

<center>
{|style="text-align: center; vertical-align: bottom; border: none;"
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|colspan=5| 
|colspan=2 style="width: 60px; height: 40px;"|…
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''seed''</span><br/>'''1'''
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|colspan=2 style="width: 60px; height: 40px;"|…
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''… + 1''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''1 + …''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|…
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|colspan=2 style="width: 60px; height: 40px;"|…
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''… + 1''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''1 + 1''</span><br/>'''2'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''1 + …''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|…
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|-
|colspan=2| 
|colspan=2 style="width: 60px; height: 40px;"|…
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''… + 1''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''1 + 2''</span><br/>'''3'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''2 + 1''</span><br/>'''3'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''1 + …''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|…
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|-
|
|colspan=2 style="width: 60px; height: 40px;"|…
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''… + 1''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''1 + 3''</span><br/>'''4'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''3 + 3''</span><br/>'''6'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''3 + 1''</span><br/>'''4'''
|colspan=2 style="width: 60px; height: 40px;"|<span style="color: #CCC">''1 + …''</span><br/>'''1'''
|colspan=2 style="width: 60px; height: 40px;"|…
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|-
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|colspan=2 style="width: 60px; height: 40x;"|⋮
|colspan=2 style="width: 60px; height: 40x;"|⋮
|colspan=2 style="width: 60px; height: 40x;"|⋮
|colspan=2 style="width: 60px; height: 40x;"|⋮
|colspan=2 style="width: 60px; height: 40x;"|⋮
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|}
</center>

Pascal's Wager is a philosophical argument proposed by the same Pascal. Essentially it says that if God exists, both the rewards for believing in God and the punishment for nonbelief are infinite; if not, the cost of belief and benefit for nonbelief are negligible. Therefore, if there is a finite possibility that God exists, however small, one should believe in God. One problem with that is that there may be more than one God to believe in, even if only one truly exists. Which one of all the possible Gods should you choose to believe in could be problematic, if the real God insists that you only believe in Him and punish you for believing in any other gods (even if you somehow also believed in Him). A further problem is that committing to any particular belief in a deity is not a totally zero cost option, and thus affects your life in many needless ways if you subscribe to any particular practice of religion not actually required by any extant god(s), even if any of them exist in the first place.

The comic merges the two Pascalian concepts: each Cueball is wagering his proof of a god or gods to the Cueballs below him, thereby creating Cueballs that believe in the sum of the number of gods of the Cueballs above them. In the second row, the two Cueballs each believe in one god, as intended by the original Cueball. However, in the third row, the Cueball in the middle interprets the two proofs offered to him as proving the existence of two gods. Theoretically, this expansion would continue for all integers as the triangle grows, giving rise to a belief in escalating numbers of gods going down and towards the middle of the triangle. This is clearly not the intent of the first Cueball, who simply wagered the proof of his one god, but he has no control over the situation below him. 

It is unclear why the Cueballs behave in this fashion, instead of treating all the proofs as proving the existence of the same god. Perhaps each one rewords their arguments for god(s) sufficiently to make them sound different than other gods. This is not without precedent. Scholars of comparative mythology believe that the religion of Proto-Indo-European peoples splintered into many disparate religions of Europe and West Asia; for instance, {{w|%2ADy%C4%93us#%22Sky-Father%22_epithet|Dyeus phter}} (sky father) became Zeus in Greece and Jupiter in Italy.

This comic may be referencing a common counterargument to Pascal's Wager — that it works equally well for ''any'' hypothetical god which offers eternal paradise for one action and eternal damnation otherwise. This can even include hypothetical gods with contradictory criteria for entrance into paradise. In this case, the Cueballs apparently chose to believe in all the deities they've heard of in order to cover their bases.

The title text suggests that everyone should draw a proper Pascal's Triangle, since there is a possibility that God wants you to do so, and if they do then the benefits of pleasing God or the costs of displeasing God could be high, whereas if they have no such desire then there is minimal cost to drawing one anyway. The failing of this logic is that God may have a positive preference for you ''not'' to draw a Pascal's Triangle (though at least according to the Catholic Church this is unlikely, as Pascal himself is on the way to {{w|beatification}}.)

Pascal's Wager was previously mentioned in the title text of [[525: I Know You're Listening]].

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[Cueballs, each holding some document, are shown in a triangular arrangement, with arrows pointing from upper to lower Cueballs:]
:[At the top, row 1 has a Cueball, unnamed but described below as "C1", holding a piece of paper with a crossed-square shape possibly resembling a Punnet Square diagram and with a speech-bubble]
:C1: Hey, you two below me! Here's a proof that you should believe in my god!
:[Two arrows lead diagonally down-left and down-right from C1 to the second row, having two similarly drawn Cueballs (differing only by slight changes in pose) described here as "C2" and "C3"]
:C2 & C3: I'm convinced! Hey, you two below me! Here's a proof that you should believe in my god!
:[Two arrows lead down from each of Row 2's Cueballs to three similar Cueballs on Row 3, "C4", "C5" and "C6", the central Cueball being the target of arrows from both of the predecessors, and the speech-bubbles partly obscuring the predecessor Cueballs and the lines of the arrows]
:C4 & C6: I'm convinced! Hey, you two below me! Here's a proof that you should believe in my god!
:C5: Ok, I believe you both! Hey, you two below me! Here's a proof that you should believe in my '''two''' gods!
:[Two further arrows lead down from each Row 3 Cueball to a total of four Row 4 Cueballs, all but the edge ones having two incoming arrows, "C7" to "C10"]
:C7: I'm convinced! Hey, you two below me! Here's a proof that you should believe in my god!
:C8 & C9: Ok, I believe you both! Hey, you two below me! Here's a proof that you should believe in my '''three''' gods!
:[C10 has no visible bubble, as there is no room for one in-frame, and is itself also slightly obscured by C9's bubble, but would logically be considered to have a "believe in my (singular) god" monologue]
:[Continuing the pattern, Row 5 has "C11" to "C15" Cueballs (with only a small amount of leg visible above the lower edge of the comic frame), each is led to by diagonal arrow(s) originating from the Row4 Cueballs]
:[C11 and C15 have no visible speech bubbles, due to being even more edge-adjacent and C15 even reaching off the edge of the frame with his 'punnet paper', but can be assumed to have a "believe in my god" statement]
:C12 & C14: Ok, I believe you both! Hey, you two below me! Here's a proof that you should believe in my '''four''' gods!
:C13: Ok, I believe you both! Hey, you two below me! Here's a proof that you should believe in my '''six''' gods!
:[No further arrows or Cueballs can be visible, and no further speech-bubbles obscure Row 5, but without any reason to believe they aren't just off frame]

:[Caption below the panel:]
:Pascal's Wager Triangle

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Multiple Cueballs]]
[[Category:Math]]
[[Category:Religion]]