Vector of Parameters: This is a set of variables or conditions that characterize the system or scenario. They can be input conditions, system states, or any other relevant metrics that describe the system. 

Objective Function: This is a mathematical function that quantifies how far the current system's performance is from the desired performance. The goal is usually to minimize or maximize this function. 

Constraints: These are the bounds or limitations within which the system operates. In engineering problems, constraints can arise from physical limitations, safety requirements, budgetary restrictions, etc. The solution must satisfy these constraints.

Mathematical Treatment of the Axioms of Physics

Rigorous Foundation of Schubert's Enumerative Calculus

Topology of Algebraic Curves and Surfaces

Analysis of Solutions of Variational Problems

Birch and Swinnerton-Dyer Conjecture

Hodge Conjecture

Navier–Stokes Existence and Smoothness

P vs NP Problem

Riemann Hypothesis

Yang–Mills Existence and Mass Gap

No Definitive Formulation

No Stopping Rule

Solutions Are Not True-or-False

No Immediate and No Ultimate Test

Every Solution is a 'One-Shot Operation'

No Enumerable (or Exhaustively Describable) Set of Potential Solutions

Every Wicked Problem is Essentially Unique

Every Wicked Problem Can Be Considered to Be a Symptom of Another Problem

The Existence of a Discrepancy Representing a Wicked Problem Can Be Explained in Numerous Ways

The Planner Has No Right to Be Wrong

Radioactive waste disposal

Liberation from fossil fuel dependency

Language extinction

Weltverständlichmachung

Unf*cking the Wohnungsmarkt

...

...

...

...

The Clock Reform

https://github.com/python-constraint/python-constraint

https://github.com/timnon/pyschedule

Note: install the most recent fork, (e.g. pip3.10 install "pyschedule"@git+"https://github.com/ppoile/pyschedule/#subdirectory=src")

eight queen problems

map coloring problem

#Adam has one hour time on Monday and Wednesday, three hours time on Thursday and fours hours time on each weekend day, Eve has two hours on Tuesday, three hours on Friday and four hours on each weekend day.  Define pyschedule resources with correctly defined periods and horizons.

#Monday: Adam x 1
#Tuesday:  Eva x 2
#Wednesday: Adam x 1
#Thursday: Adam x 4
#Friday: Eva x 3
#Saturday: Both x 4
#Sunday : Both x 4

from pyschedule import Scenario, solvers, plotters, alt

# Define the scenario
S = Scenario('household_chores', horizon=15)  # Two weeks

# Define the resources, resource costs are not obligatory but it's more fun with them
adam = S.Resource('Adam',periods=[0,3,4,5,6,7,11,12,13,14])
eve = S.Resource('Eve',periods=[1,2,8,9,10,11,12,13,14])

kitchen=S.Resource('kitchen')

# Define the tasks and their durations
task_costs = {
    "meal1": {"length":1,"delay_cost":1},                # 1 hour, schedule towards beginning of the week
    "meal2": {"length":1,"delay_cost":1},             
    "meal3": {"length":1,"delay_cost":-1},               
    "meal4": {"length":1,"delay_cost":-1},               # 1 hour, schedule towards end of the week
    "bake": {"length":2,"delay_cost":0},                  # 2 hours (1 cake)
    "sleeping_room": {"length":2,"delay_cost":0},  # it seems there is a bug for tasks longer >1 
    #"CSR1": {"length":1,"delay_cost":0},          # one way how to address the bug is to split long tasks into sub-tasks coupled by tight preference constraints
    #"CSR2": {"length":1,"delay_cost":0},          # 
    "bathroom": {"length":2,"delay_cost":0},       # 2 hours
    "living_room": {"length":3,"delay_cost":0},    # 3 hours
    "clean_kitchen": {"length":3,"delay_cost":0}   # 3 hours
}

tasks={}
# Define alternative resources for each task
for task,costs in task_costs.items():
    print(task,costs)
    tasks[task] = S.Task(task,length=costs['length'],delay_cost=costs["delay_cost"])      #create new task
    tasks[task] += adam | eve               #assign resources to newly created task

#additional task-resource attributions
tasks["clean_kitchen"]+=kitchen
tasks["meal1"]+=kitchen
tasks["meal2"]+=kitchen
tasks["meal3"]+=kitchen
tasks["meal4"]+=kitchen
tasks["bake"]+=kitchen

#tight precedence constraints
#S += tasks['CSR1'] <= tasks['CSR2']

#optional tasks
#tasks['playground'] = S.Task('playground',length=2,schedule_cost=-1)
#tasks['playground'] += alt(adam,eve)

#additional constraints
S += tasks['meal1'] < tasks['clean_kitchen'] 
S += tasks['meal2'] < tasks['clean_kitchen'] 
S += tasks['meal3'] < tasks['clean_kitchen'] 
S += tasks['meal4'] < tasks['clean_kitchen'] 
S += tasks['bake'] < tasks['clean_kitchen'] 

# Solve the scenario
solvers.mip.solve(S,msg=1,kind='GUROBI')

print(S)
print(S.solution())
print(adam.periods)
# Plot the schedule
plotters.matplotlib.plot(S)

• Latin "solutio": Meaning a loosening or unbinding. This comes from the verb “solvere,” which means to loosen, untie, or dissolve.
• Latin "solvēre": This is a compound of “sol-,” a variant of “se-” (apart), and “luere” (to wash or to loosen).

Howard Gardner :: Frames of Mind / The Theory of Multiple Intelligences

David Goleman :: Emotional Intelligence : Why it can matter more than IQ

Singer et al. :: A Piaget Primer: How a Child Thinks

Murray & Herrnstein :: The Bell Curve: Intelligence and Class Structure in American Life (Achtung! Controversy)

Nick Bostrom :: Superintelligenz

Carlo M. Cipolla: The Basic Laws of Human Stupidity

connect the dots so You obtain the requested geometric patterns (e.g. square and triangle)

observe Your cognitive processes (if anything interesting "happens", note it on a piece of paper for further discussion)

do not hurry, You have all the time You need.

Breath slowly and deply

Word of warning : You now enter the path of intelligence enrichment. While some teachers say that the path of intelligence is the path leading to the highest joy, a more pragmatic ones would assert that being smarter just makes one more sad.

And potentially also mad

the "bad" errors (often happen only once)

the "innocent" (unpleasant but useful minor misstep) 

Turn to Your neighbour, discuss the question "what was the worst error (e.g. the biggest fuckup) You ever did/caused in Your life". After 5 minutes, each couple will be asked to present at least one such error to the plenum.

Agricultural Societies

Ancient Egypt

Mesopotamia/Babylon

Ancient China

Ancient India

... remarkable counting abilities, such as Shakuntala Devi: she was able to multiply two 13 digit numbers in 28 seconds in 1980

... intuitive understanding, such as Srinivasa Ramanujan: he wrote down nearly 3.900 new results (theorems, identities and equations)

... insight into abstract structures, such as Alexander Grothendiek: he worked on a rebuilding of algebraic geometry

calendar

religion: Nile river god Hapi

measuring device

landmeasure

measure unit

legth and area calculation

decimal system

binary counting system

fractions

Eye of Horus: geometric theory

accurate value of pi

Pyramid - the golden ratio, right angle

Pythagoras

right-angled triangles

the harmonic serie

Euclid

300BC "The Elements": axioms

Archimede

the decimal place-value system

0 and infinity

pi

Brahmagupta

negative numbers

unknowns in equations

trigonometry

Al-Khwarizmi

algebra

Pythagoras Musica Universalis

Rhythms and intuitive counting

Musical notation and polyphony

12-Tone music and Arnold Schönberg

Stochastic music and Iannis Xenakis

Algorithms and generative music

Crosslink between phonology, music and mathematical description

Semantics and symbol manipulation

logics and reasoning

Mediator of mathematics

Vectorization of language

Vectorization, stochastic and noise

IQ test

Turing test

Q+ model?

Non-computational problems

Q-learning is a model-free reinforcement learning algorithm that enables an agent to learn an optimal policy for decision-making. It works by estimating the Q-values (action-value function), which represent the expected cumulative reward for taking an action in a given state and following the best future actions. The agent updates Q-values iteratively using the formula:

Classical Conditioning: Involves pairing a neutral stimulus with a meaningful one to elicit a similar response (e.g., Pavlov’s dogs salivating at the sound of a bell).

Operant Conditioning: Involves learning through rewards or punishments, where behaviors are strengthened or weakened based on their consequences (e.g., Thorndike’s Law of Effect).

Vicarious means experiencing something indirectly, through someone else, rather than firsthand. It comes from the Latin vicarius, meaning "substitute" or "acting in place of another."

Individuals learn by observing others being rewarded or punished for a behavior.

Example: A student is more likely to participate in class if they see a peer receiving praise for doing so.

Learning happens by watching others and imitating their behavior, even without direct reinforcement.

Example: A child learns aggression by observing an aggressive adult (c.f. "The Bobo Doll Experiment")

Howard Gardner :: Frames of Mind / The Theory of Multiple Intelligences

David Goleman :: Emotional Intelligence : Why it can matter more than IQ

Singer et al. :: A Piaget Primer: How a Child Thinks

Murray & Herrnstein :: The Bell Curve: Intelligence and Class Structure in American Life (Achtung! Controversy)

Nick Bostrom :: Superintelligenz

Carlo M. Cipolla: The Basic Laws of Human Stupidity

Can You think of other examples of unsupervised learning and/or clustering ?