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A diagram of all knowledge topics.

Topics (also Tech or Innovations) are part of knowledge.

There are around 300 innovations that can be discovered. Many of them have requirements, and many do not, so it's kind of a tech forest/grassland rather than a tree. Notably missing are innovations related to practical labors in the game (which will be added later in development).

Several innovations require innovations from other branches, and since all knowledge is individually tracked, that implies some investigators will need to be at least well-read if not skilled in various topics (there aren't currently joint research projects). There are some old and new mechanisms in place to ensure this happens.

There are 9 "branches" of the knowledge system.

Astronomy

Topic	Description
Geocentrism	The theory that the sun moves around the world
Heliocentrism	The theory that the world moves around the sun
	The variation of daylight with the season
	The rise of the sun according to the season
	The phases of the moon
	The path of the moon
	The rise of the moon according to the season
	The relationship between the moon and the tides
	The height of the tides, the moon and the sun
	The relationship between the lunar and solar year
Astrography	The creation of star charts
	Methods of empirical observation in astronomy
Astrolabe	The construction and use of the astrolabe
Stellar Spectroscopy	The classification of stars based on the light they emit

Chemistry

Topic	Description
	Methods for performing experiments systematically in the laboratory
	The preparation and use of adhesive materials
Oil of vitriol	The preparation of oil of vitriol
Spirit of niter	The preparation of spirit of niter
Aqua regia	The preparation of aqua regia
	The mixture of metals to produce alloys
	The classification of ores
	The classification of materials based on which elemental materials might form them
	The classification of alkali and acids
	The classification of combustible materials
	The construction and use of the ampoule
	The construction and use of the vial
	The construction and use of the alembic
	The construction and use of the blast furnace
	The construction and use of the retort
	The construction and use of the crucible
	The construction and use of laboratory ovens
	The construction and use of the beaker
	The theory and methods involved in evaporation
	The theory and methods involved in distillation
	The theory and methods involved in the extraction of a constituent liquid from one solution to another
Water Displacement	A precise description of buoyancy and water displacement

• Spirit of niter

Engineering

Topic	Description
The Pulley	The construction and use of the pulley
The Lever	The construction and use of the lever
	The reasons why the lever is effective
The Windlass	The construction and use of the windlass
The Screw	The construction and use of the screw
Models and Templates	The use of models and templates in engineering
The Warded Lock	The construction and use of the warded lock
The Tumbler Lock	The construction and use of the tumbler lock
The Siphon	The action of the siphon
Gears	The reasons why gears are effective
	The construction and use of water-filled sphere as a lens
The Crystal Lens	The construction and use of the crystal lens
The Funnel	The construction and use of the funnel
The Glass Lens	The construction and use of the glass lens
The Camera Obscura	The construction and use of the camera obscura
	The construction and use of valves
	The construction and use of the bellows
	The construction and use of the straight-beam balance
The Wedge	The reasons why the wedge is effective
	The use of water-based devices to tell time
	The use of lamination
The Wheel-and-axle	The reasons why the wheel-and-axle construction is effective
	The reasons why pulleys are effective
	The reasons why screws are effective
Screws	The construction and use of the screw
	The construction and use of the padlock
	The reasons why the lever is effective
Water clock reservoirs	The use of reservoirs in water-based clocks to improve their accuracy
Shadow clocks	The use of shadows to tell direction and time
Armillary spheres	The construction and use of armillary spheres
	The construction and use of the dioptra
	The construction and use of chain drives
	The construction and use of the verge escapement

Differential gears are a difficult innovation and a prerequisite for pointing chariots and astrariums.

Geography

Topic	Description
Surveying	The process of surveying land
Surveying staff	The construction and use of the surveying staff
Anemology	The forces that govern wind patterns
Econometrics	The process of economic data collection
	The placement of economic information on maps
Water cycle	The origin of rainfall through evaporation and condensation
	A world-wide cycle involving precipitation, oceans, rivers, and other forms of water
Cartography	The process involved in creating maps
Atlases	The collection of maps and other information together into a single text
	The process of the formation of deltas at the mouths of rivers
	The placement of geological information on maps

The geography innovations include several related to cartography.

History

Innovations for historians are, in part, writing forms like biography, and then any historian that reads a biography can start writing them as well. Innovations include comparative biographies describing multiple people, and matters of sourcing, etc.

Historians can start to understand how cultural differences and state bias affects source reliability and think a bit about social forces.

Topic	Description
Historical causation	The causes of historical events
Archaeology	The method of collecting and evaluating artifacts to learn about history and culture
Diachronic archaeology	The method of examining artifacts to determine how techniques have changed over time
Cultural history	The method of accurately and comprehensively describing cultures and civilizations
Comparative anthropology	The method of comparing and contrasting different cultures
Source reliability	The reliability of sources
Personal interviews	Using personal interviews as sources
Biography	The method of writing the history of a single individual
Autobiography	The method of writing a biography of oneself, particularly as it concerns a military campaign or adventure
Biographical dictionaries	The compilation of brief biographies into one large collection
Comparative biography	The method of compiling several biographies to compare and contrast the subjects' character and to gain insight into history
Cultural relativism	The role of cultural differences in source reliability and interpretation
Genealogy	The compilation of family lineages and methods of displaying them artfully
Alternate history	The exploration of how history would be different if some key past events had transpired differently
Sociology	The notion of bonds between members of a community
	The notion of historical, governmental and social cycles

Mathematics

• Symbol for addition

Topic	Description
Place values	Positional notation
	The idea of using symbolic notation for addition
Large Sums	Simple formulas for certain arbitrarily large sums
Equations	The technique of balancing and completion for solving equations
Scientific notation	Notation for very large numbers
Negative numbers	Notation for negative quantities
Zero	A symbol for nothingness
Division	An algorithm for dividing one number into another, possibly yielding a remainder
	The divergence of the harmonic series
Quadratic formula	A formula which solves quadratic equations
Completing the square	The solving of quadratic equations by completion of the square
Basic geometry	Geometric objects: points, lines, circles, triangles, and so on
	The computation of the volume of different pyramids
	The computation of the volume of a cone
	The computation of the volume of a sphere
	The computation of the surface area of a sphere
	The properties of similar and congruent triangles
Geometric mean	The relationship between the length of the altitude of a right triangle and the lengths of the segments into which it divides the hypotenuse
	The equality of the base angle of isosceles triangles
	The angles of triangles inscribed in a circle with one edge on the diameter
	The unique decomposition of a number into products of its prime divisors
	A triangular configuration of numbers relating to the successive powers of any sum
Chords	The properties of chords
Chord tables	A table of chord lengths indexed by angle
Sum-difference trig identities	Trigonometric identities relating to the sums and differences of angles
Pythagorean Theorem	The relationship between the lengths of the hypotenuse of a right triangle and the other two sides
Pythagorean triples	Examples of triples of small whole numbers which, when taken together, are the lengths of the sides of a right triangle
	Examples of triples of large whole numbers which, when taken together, are the lengths of the sides of a right triangle
	Examples of triples of very large whole numbers which, when taken together, are the lengths of the sides of a right triangle
	The relationship between the half chords of a triangle's angles, the opposite side lengths, and the diameter of the triangle's circumscribed circle
Irrational numbers	The existence of incommensurable ratios
Irrationality of root 2	A proof that the length of a diagonal of a square is incommensurable with its edge
Approximation of root 2	An approximation for the length of the diagonal of a square
Existence of pi	The relationship between the area of a circle and its radius, involving the ratio of the circumference of the circle to its diameter
Method of exhaustion	An approximation of the ratio of a circumference of a circle to its diameter, using the area of polygons and the method of exhaustion
Conic sections	The categorization and properties of conic sections
	The area enclosed by a parabola and a line
Algebra	Notation for abbreviating the unknown and other elements of an equation in a systematic and useful fashion
Systems of equations	Methods of solving systems of equations
	Methods for solving certain equations involving powers higher than the quadratic
Axioms	Axiomatic reasoning
Proof by contradiction	The method of proof by contradiction
Euclid's Theorem	A proof that there are infinitely many prime numbers
Euclidean Algorithm	An algorithm for computing the greatest common divisor of two numbers
	An algorithm for computing a number which has given remainders when divided by several given primes

Medical science

Medical innovations include dedicated hospitals with specialized wards, staffing, medical labs and treatment for many illnesses.

Topic	Description
Incision	The surgical method of incision
Excision	The surgical method of excision
Suturing	The surgical method of suturing
Draining	The surgical method of draining
Scraping	The surgical method of scraping
Probing	The surgical method of probing
Ligature	The surgical method of ligature
Bandages	The method of bandaging wounds
	The treatment of fractures
Traumatic injuries	The treatment of traumatic injuries
Veterinary medicine	The diseases of creatures
Herbal remedies	Herbal remedies
Mineral remedies	Mineral remedies
Pathology	The classification of disease
Toxicology	The classification of toxic substances
	The classification of fractures
	The classification of bodily fluids
	Cauterization
	Anesthesia
	The use of practice models in surgery
	The use of mud bags as surgical models
	The use of animals as surgical models
	The use of specialized surgical instruments
Needles	The construction and use of surgical needles
Anatomical studies	Anatomical studies for medical edification
	The anatomy of the eye
Disease and fouled water	The connection between disease and fouled water
	The method of physical examination in diagnosing illness
Prognosis	Determining the likely outcome given a patient's current status
	The notion of the exacerbation of a patient's condition
	Pulmonary medicine
	Remedies prepared from animals
Cutting for stone	The lithotomy surgery
Tracheotomy	The tracheotomy surgery
	Hernia surgery
	The distinction between acute and chronic conditions
Epidemiology	The theory of epidemic disease
Paroxysm	The notion of paroxysm
	The source of the voice

Natural science

Toady on natural science innovations:

And so on through the other seven branches - there are innovations in naturalist writings, for example, and then they can investigate specific critters with those in mind when they get down to work observing foraging behavior or performing dissections.

Naturalists can build a theory of rainbows using water-filled spheres and a camera obscura, and they can calculate the height of the atmosphere based on atmospheric refraction using the law of refraction (though it tries not to get into the actual shape of the world, since that might vary).

Topic	Description
Physical taxonomy	The classification of creatures by their physical features
Climactic adaptation	The way that creatures are suited to the climates in which they live
Migration	The migratory patterns of creatures
Foraging behavior	The foraging behavior and diet of creatures
Reproductive behavior	The reproductive behavior of creatures
Social behavior	The social behavior of creatures
Dissection	The dissection of creatures
Embryology	The embriological development of creatures
	The struggle for survival among creatures
Anatomy	The anatomical study of creatures

Philosophy

The specific view that a philosopher takes on, say, the nature of beauty or methods of education will depend on their individual/cultural values, where they apply, and a philosopher that encounters a philosophy book on beauty can then provide their own take (having acquired the innovation).

Toady on philosophy innovations:

For fields like philosophy, I've tried not to make judgments about which ideas are "right" or anything like that, but rather which subjects can be thought about at all.

Topic	Description
Value Agendas	Writers can push value "agendas" if they are skilled enough. Description format: The [worthlessness | value | nuances | nature] of [belief] Examples: The nature of truth - probably related to TRUTH The value of art - probably related to ARTWORK
Interpersonal Ethics	Discourse on ethics as applied to interpersonal conduct
Causation	The nature of causation
	Discourse on diplomacy
	Discourse on the meaning of individual happiness
	Discourse on economic policy
	Discourse on ethics as it regards the benefit of the state
	Discourse on the nature of perception
	Discourse on the nature of justification
	The relationship between objects and their properties
	Discourse on the nature of time
	Discourse on the nature of mind and body
	Discourse on ethics as applied to war
	Discourse on the nature of beauty
	Discourse on law
Grammar	Grammar
	Discourse on government
	Dictionaries
Formal Reasoning	Formal reasoning
	Discourse on social welfare
	Discourse on the nature of events
Education	Education, its forms and recommendations
	Discourse on the nature of belief
	Discourse on medical ethics
Whole and Parts	The relationship between wholes and parts
	The notion of etymology
Social Welfare	Social welfare, its forms and recommendations
	Economic policy, its forms and recommendations
	Syllogistic logic
	Hypothetical syllogisms
	Deductive reasoning

Unknown/unsorted

Topic	Description