Introduction - Human Body as Doughnut Analogy

• Traditional view: human body like doughnut with central hole (mouth to anus)
• Reality more complex: humans have multiple holes (nostrils, ears, pores, etc.)
• Subatomic level: gaps between molecules, 60 billion neutrinos from Sun pass through thumbnail every second
• At molecular scale, human body just loose constellation of atoms/molecules

Defining Minimum Hole Size

• Established minimum: 20-60 millionths of meter (width of human hair)
• 60 micron wide spaceship could enter pores like giant craters
• Cannot continue through vasculature or slip between molecules
• Creates distinction between different types of holes

Through-Holes vs Blind Holes Classification

• Through-holes: GI tract (mouth to anus) - can thread 60 micron string completely through
• Blind holes: pores, urethras, nipples, ears, hair follicles, birth canals, sinuses
  • Can be entered but eventually dead-end at narrow capillaries
  • Only permeable by things smaller than single blood cell
• Examples of blind hole limitations:
  • Eyeball: blocked by conjunctiva
  • Sinuses: dead-end at same ostia entered through
  • Ear: airtight eardrum blocks passage at 60 microns
• Total blind holes: millions (counting all pores and hair follicles)

Philosophy of Holes

• "Hole" is colloquial, fuzzy, imprecise term
• Refers to disparate, unreconciled things without single mathematical definition
• Holes might not exist - ontologically parasitic (depend on something else to inhabit)
• Demonstration: bowl → drinking glass → plate transformation
  • Shows blind holes can disappear without closing anything
  • Through-holes (like doughnut) cannot be removed without cutting/gluing

Human Body's Connected Pathways

• Mouth connects to both blind and through holes
• 60 micron traveler: mouth → esophagus → exit, OR mouth → trachea → dead-end in lungs
• Pharynx: area behind mouth, warms/moistens/filters air
• Nasal pathway: nostril → nasal vestibule → nasal cavity → pharynx → trachea
• Nostrils and mouth connected: string can go mouth/nose → butt

Additional Connected Openings

• Eustachian tube: middle ear to nasal cavity, normally collapsed
  • Controls air pressure, opens when swallowing/yawning ("popping ears")
  • Not through-hole due to eardrum blockage
• Lacrimal punctum: 4 openings (one near each eyelid)
  • 1/3 millimeter wide, drain tears into nasal cavity
  • Why nose runs when crying (tears, not snot)
  • 60 micron string could thread: punctum → tear ducts → nasal cavity → pharynx → anus
• Total external openings: 8 (2 nostrils, 1 mouth, 1 anus, 4 tear ducts)

Topology and Homeomorphisms

• Topology: studies properties that persist without ripping apart
• Homeomorphism: gentle continuous transformation (stretching/squashing, no cutting/gluing/ripping)
• Coffee cup ↔ doughnut example: both have 1 through-hole
• Blind holes can be erased through homeomorphism (topologists don't count them)
• Through-holes cannot be massaged away

Topological Puzzles and Solutions

• Two-hole donut with rod: can manipulate so rod goes through both holes
• Intertwined loops: can be untangled by inflating bulb section

Mathematical Definition of Homeomorphism

• Bijective function: one-to-one correspondence between points
• Continuous: cuts must be mended perfectly, points return to same neighbors
• Material cannot be added/subtracted
• No smooth sliding along abrupt fissures

Counting Human Body Holes

• Result: Human body has 7 through-holes at 60 micron scale
• Not doughnut, but "seven-hole doughnut"
• Topologically equivalent to 4 pairs of pants sewn together at waists
• "Bodysuit for spider"
• Transformation: legs become nostrils (2) + tear ducts (4) + mouth (1), inflate into head/body shape

Variables Affecting Hole Count

• Piercings: each adds 1+ holes
  • 2 holes if piercing goes through existing through-hole
• Supernumerary lacrimal punctum: some people have >4 tear duct openings
  • Each additional one adds another hole to standard 7
• Accessory ostia: up to 50% of people have extra holes connecting sinuses to nasal cavity
  • Creates additional through-holes
  • Most people unaware unless serious sinus problems/extensive scans

Final Answer

• Blind holes: millions (at least 5 million)
• Through-holes: 7 at birth (standard), varies with individual anatomy
• Individual variation due to accessory ostia unknown without medical imaging
• Paradox: can define hole properties rigorously, study Pluto craters, but few know true hole count of own body