who's hand is in this picture?
A Mathematically Rigorous Proof That I Spent Too Long Writing
welcome to university math: dnp hand edition
(no, don't leave, you'll be fine i promise)
to begin, we need a statement to prove. we have two options:
- the hand is dan's hand
- the hand is phil's hand
now, for most proofs in university math, you are told a true statement, and you must show why it is true using logic rules, definitions, and theorems. but, we do not know which of these statements are true, so we have to find out.
to prove that a statement is true, we must show that it is always true for the situation presented. to show a statement is false, we must present a single instance where the statement is false (also known as a counter example).
a quick not scary math example:
definition: a prime number is only divisible by 1 and itself.
statement: all prime numbers are odd
(this is false, because 2 is a prime number and it is even. you don't even need to check if there's any others, all you need is one single case where it isn't true to disprove it)
so now that we have a little background on proofs and how to prove and disprove them, we go back to our two statements.
the thing with this situation is, one of them must be true (unless you're gung-ho on someone else holding dan's face while phil takes a picture on his phone of dan in his glasses, in which case, i applaud your commitment, but in actuality this proof will cover that option too)
the full statement we have is: dan is touching his face or phil is touching dan's face
now, because this is Real Life and we have a picture where a hand is touching dan's face, we know already that one of these options is true (as mentioned above) but! using symbolic logic you could also come to this conclusion.
this type of statement is an 'or' statement, and if you're curious, you can look into 'truth-tables' and see why, but at least one of the options must be true.
back to the proof at hand (bah-duhm-tss)
okay. now, proofs also must be 'general' in order to mean anything, really. these are statements of truth of the universe, not just for individuals. so, we will prove this generally.
we have 2 people involved, so individual 1 (dan, the owner of the face and potential face toucher) will be labelled as 'D' , and individual 2 (phil, the possible face toucher who does not own the face) will be labelled as 'P'. thus, this can be true for any such D and any such P.
so with our 'or' statement, in order to prove it, we pick one of the options and say that it is not true, and we have to show then that the other is true.
step 1: let's assume this is not P's hand. (assumption)
step 2: thus, it must be D's hand. (what we take from our assumption)
step 3: now, if it is D's hand, we look at what a hand on one's own face is capable of appearing like. (a definition or true fact about step 2)
the position in the given photo shows the hand with a thumb on the cheek, and a finger on the forehead. so, we find an example of a person with their fingers in the same position (or close to) and see if this supports our claim.
consider:
now, with this image, you can clearly see how the subject's right hand has the thumb on the temple and index finger on the top of their head, however, it is a close enough position for our case.
from the view of the camera, the closest finger to the camera is the edge of the pinkie. in fact, it will always be the closest finger to the camera in this position, assuming the subject has all fingers and no additional appendages.
step 4: we now compare this to our photo (we verify if this holds to our claim or contradicts it)
in our photo, the closest appendage to the camera is the edge of the thumb.
step 5: thus, it cannot be the case that D is touching their own face. (what the evidence says)
step 6: as we assumed it was not P's hand and have shown it cannot be D's hand, and as this is an 'or' statement both of these claims cannot be false, we can therefore conclude it must be P's hand. (our conclusion: re-stating the statement and assumptions and conclusion)
step 7: we verify that P is true (optional step but in beginner proofs you generally show why your case works)
to do this, i will show a picture of a person touching another's face, and compare it to our image.
consider:
now, this image is not exactly the same, similar to above. however, P's left thumb is on the cheek, with their index on D's temple. the closest appendage to the camera (if it were in a similar perspective as our original) would be the edge of the thumb.
comparing it to our original:
our comparison holds.
thus, we can conclude that the true claim in this statement is that P must be touching D's face, which, in particular means that:
phil is touching dan's face in the image
thank you for partaking in phannie mathematics. we now know. i am not sorry.
bonus:
phil has a hitchhikers thumb and dan doesn't so why was this necessary at all 🤡
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Between commissions I finally managed to finish this OC set of parent characters! If the looks aren't enough to show you who their kid is, the background colors match them ^_^ but of course more details below!
Name: Thuban
Name origin: The former pole star, before the north star (Polaris), it's name means "Large snake" and is referred to as the “Dragon's tail”
Pronouns: He/him
Age: N/A
Relation: Raised Polaris, though they're not related by blood and have a somewhat distant relationship, until he suddenly went MIA
Weapon: Spear (Same as Polaris's)
Ethos (Power): N/A
Flaw power is based on: N/A
Notes: Make no phallic jokes about the large snake thing and you'll be rewarded
Name: Ananke
Name origin: A moon of Jupiter, named for the mythological spirit of necessity, inevitably, and compulsion
Pronouns: She/her
Age: -
Relation: Bella's mother, she raised her to be a warrior
Weapon: Bardiche
Ethos (Power): Indomination (The ability to freeze the movement of objects and people, and lock them in place)
Flaw power is based on: Her strict enforcement of obedience through authoritarianism, and a lack of concern for the wishes of others
Notes: She believes in tough love. It's better in the long run to give your kid strength rather than affection.
Name: Rhea
Name origin: A moon of Saturn named after the Titan known as the mother of the gods
Pronouns: She/her
Age: 38
Relation: Saiph's mother, though she gave him up to the guild when he was very young
Weapon: None
Ethos (Power): None
Flaw power is based on: N/A
Notes: Was unable to take care of a baby at the time, and gave Saiph to the guild. She wishes she'd visited beyond that but it's probably too late now...
Name: Arche
Name origin: One of Jupiter's moons, it's name comes from the muse of new beginnings and is associated with springtime
Pronouns: He/him
Age: 7
Relation: Saiph's half-brother. Neither currently knows the other exists
Weapon: None
Ethos (Power): None
Flaw power is based on: N/A
Notes: He's just a little guy. He likes flowers and playing with toys. He wants to be a cool hero like his dad
Name: Poerava
Name origin: A star in Tucana, the Maori word for a black pearl of mystical beauty and perfection
Pronouns: She/her
Age: -
Relation: Al's mom. She mostly raised him on her own while her husband was with the knights.
Weapon: None
Ethos (Power): None
Flaw power is based on: N/A
Notes: Probably the best parent of the bunch if we're being real.
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