Problem & Solution [content & code transfered to public under conditions of Wizzion Public Licence v. AE53] by DDH / Design & Computation - Perspectives in Engineering - Studio @ Old TU Berlin building
Meta-Problem
What problem is worth time of Your life ?
problem(s)
picture of "problem", black background
A problem P can be defined as a situation or scenario where a particular system, device, or process is not performing as desired, leading to suboptimal or undesired outcomes. In a design & engineering context, P is typically framed in terms of:
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.
etymology of the term 'problem'
From Middle English probleme, from Middle French probleme, from Latin problema, from Ancient Greek πρόβλημα (próblēma, “anything thrown forward, hindrance, obstacle, anything projecting, a headland, promontory”), from προβάλλω (probállō, “to throw or lay something in front of someone, to put forward”), from προ- (pro-, “in front of”) + βάλλω (bállō, “to throw, to cast, to hurl”).
[note the etymologic similarity to word "project": from Latin projectum ‘something prominent’, neuter past participle of proicere ‘throw forth’, from pro- ‘forth’ + jacere ‘to throw’)]
Alltag problem(s)
Divide in couples and discuss with Your colleagues cases when You use the word problem in daily life. Pose Yourself questions like "What was the last problem I solved ?", "What was the last problem I didn't manage to solve "? etc.
Hilbert problem(s)
dalle-e 3: essence of hilbert problem "topology of algebraic curves and surfaces", black background
The Hilbert Problems are a set of 23 mathematical challenges presented by the German mathematician David Hilbert in 1900. Aimed at defining future research directions, these problems span various areas of mathematics. While some were clearly stated, others were more open-ended. Over the decades, a majority of these problems have been resolved, significantly advancing mathematical knowledge. Some led to the establishment of entire new fields of study. Unresolved - as of AE53 - Hilbert problems:
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
Millenium Problems
dall-e 3: 'generate picture which illustrates the best the essence of "riemann hypothesis"'
The Millennium Problems are seven mathematical challenges established by the Clay Mathematics Institute in 2000, each with a prize of one million dollars for a correct solution. These problems represent some of the most persistent and critical unsolved issues in mathematics, spanning areas such as number theory, geometry, analysis, and fluid dynamics. Only one of the problems, the Poincaré Conjecture, has been solved so far. Unresolved - as of AE53 - ones are:
Birch and Swinnerton-Dyer Conjecture
Hodge Conjecture
Navier–Stokes Existence and Smoothness
P vs NP Problem
Riemann Hypothesis
Yang–Mills Existence and Mass Gap
wicked problems
dall-e 3: "essence of wicked problem, black background"
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
13 teacher-proposed D&C problems
This is the set of problem(s) to which I expose all my D&C students since AE50.
Hopefully, at least 1 will be "solved" during my lifetime, 2 during Your lifetime and 3 during lifetime of my children.
Closing the Door to Hell
The "Door to Hell" or the Darvaza Gas Crater is a natural gas field located in the Karakum Desert in Turkmenistan. It has been burning continuously since 1971 when it was set on fire by Soviet geologists to prevent the spread of methane gas after a drilling rig collapsed into it.
Status: solvable
Approach: CAD, scientific modeling, few telephone calls, trip to Turkmenistan
H-microfusor
The core of the microfusor is a solid carbon-based magnetic confinement lattice similar to hobberman's sphere filled with hydrogen isotope fuel.
H-microfusor is a reactor for deuterium/tritium nuclear fusion whose size does not exceed 1 cubic meter and which is able to persist in the breakeven state (Q>=1) for at least 1 second.
The central problem of roboethics is defined as follows: AI & robot engineers aim to construct beings which will transcend the faculties of human beings, on the other hand, some unethical acts should be made impossible to execute for such artificial beings (Hromada, 2011)
Note: the central problem is equivalent, mutatis mutandi, to much more famous "AI Alignment" problem
Fremen Stilsuit
The Fremen stilsuit, native to the desert planet Arrakis *, is a marvel of engineering. Designed to conserve moisture, this full-body attire reclaims sweat, breath, and waste, converting them into drinkable water. Its black, skin-tight material is layered to reduce heat exposure and prevent water loss. Tubing systems distribute reclaimed water to catchpockets, from which the wearer can drink. Breath filters purify and reclaim moisture, while a nose plug ensures no moisture escapes. Built for desert survival, the stilsuit ensures the Fremen can thrive in Arrakis' harsh environment, making the most of every precious drop of water.
* also known as Terra, Gaia or Zem etc. during AD and AE epochs
Inspiration: Frank Herbert, Dune
Young Lady's Illustrated Primer
The Primer is an almost magical, book-like solarpunk artefact with embedded personalized adaptive generative teacher avatar so advanced that it is able to catalyse, by means of education, a transformation of a traumatized orphan into a Queen.
Status: solvable (provided that there is at least one vacant 👑 around)
Approach: fine-tuning of Large Language Models, speech technologies, Raspberry Pi
Inspiration: Neal Stephenson (Diamond Age: or Young Lady's Illustrated Primer)
Cracking the Voynich Manuscript
Voynich Manuscript is a corpus of unknown origin written down in unique graphemic system and potentially representing phonic values of unknown or potentially even extinct language.
Geodetic dome providing a protective membrane around highly diversified biosphere above, around and below Berlin's Tempelhofer Field.
Status: solvable
Approach: material research, architecture, corruption
Self-optimization of communities and societies
Interconnect processes of opinion aggregation, expertise integration and decision-making so that at least some future social and political systems are more equitable, adaptable and less prone to "extinction through stupidity".
Status: wicked
Approach: try in smaller community, then expand
Common Eco(log|nom)ical Protocol
Common Ecological Protocol is a SDG *-inspired set of positives ("DOs") and negative ("DON'Ts") principles establishing a planetary-wide Nash equilibrium between all human, institutional, corporate, artificial and organic agents.
* SDG = United Nation's Sustainable Development Goals
Approach: Game-Theoretical and Agent-based simulations
Status: wicked but solvable through (enforced) consensus
Space Elevator
dalle-3: "picture of space elevator platform attached to artificial island in equator region with strongly intertwined carbon nanotube fiber, black background"
A space elevator is a proposed transport system connecting Earth's surface directly to space using a tethered cable. Primarily envisioned to reduce exorbitant rocket launch costs, it aims to provide sustainable and energy-efficient space access. The concept requires a geostationary anchor in space and a base on Earth, connected by a carbon nanotube or similar high-strength cable. Centrifugal forces from Earth's rotation keep the cable taut. Elevator cars, powered by solar energy or lasers, would climb this cable.
Status: uncertain but decidable
Approach: material research, modeling, fractal architecture
The Tangle
The tangle is circle with 1m radius containing different vertically stacked herbs, veggies, fruits and mushrooms which maximize nutritive yield beneficial for human all year long and minimizes the amount of external intervention.
Inspiration: Neal Stephenson (Anathem)
Aquatic Alternative: The Aquarium
The Seed
picture of "the seed", the universal nano-assembler in process of creating its own copy. has tree-like, fractal form of a dandelion seed with the MEMS nanocomputer at its base, spherical buckyball energy source in the middle and many robotic arms on the top
The Seed, or Universal Nano-Assembler, is a programmable, portable, self-sustainable matter compiler of non-organic origin able to reorganize molecules of its envelopping substrate in such a manner that it is able to create its own copy in less than one hour.
Status: nature can do it
Approach: MEMS, DNA-computing, nanotech, protein design, AGI
Inspiration: Eric Drexler (Engines of Creation)
Elliptic Curve Discrete Logarithm Problem
dall-e 3: 'picture of bilbo passing to frodo the scroll with a PSI symbol on it, saying "the ring is yours"'
Unsolvability of ECDLP is the pillar on which modern asymmetric cryptography (e.g. cryptocurrencies, communication with products of military-industrial complex etc.) stands.
Status: uncertain and potentially meta-unsolvable *
Approach: apt install sagemath, pen & paper, hope
* proof of ECDLP unsolvability is equivalent to solving the P = NP Millenium Problem
10 student-proposed D&C problems
picture showing depictions of these problems "Radioactive waste disposal", "Liberation from fossil fuel dependency", "Language extinction", "Weltverständlichmachung","unf*cking the wohnnungsmarkt", "the clock reform" in different segments of the picture, black background
Radioactive waste disposal
Liberation from fossil fuel dependency
Language extinction
Weltverständlichmachung
Unf*cking the Wohnungsmarkt
...
...
...
...
The Clock Reform
Taxonomy of Problems
solved
P is considered to be SOLVED if we know that it doesn't have a solution and/or know at least one solution which satisfies our needs.
unsolved
picture of "problem about which it is impossible to find out if it can be solved or not", black background
Unsolved problems are problems for which we neither have a solution, nor know whether such solution can be found.
solvable
P is solvable if, at some point in time, a proof will be provided that solution to P can be found.
unsolvable
P is unsolvable if, at some point in time, a proof will be provided that P does not have solution.
fatal
illustration of "unsolvable and undecidable problem which leads to madness", black background
Problem P is "fatal" if no proof could ever be provided whether P is solvable or unsolvable.
It is impossible to tell about problem if it is "fatal". That's why it is fatal ;)
solution(s)
etymology of the term 'solution'
The word "solution" has its roots in Latin, deriving from the word “solutio.” The etymology can be broken down as follows:
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).
Over time, the meaning of "solution" has evolved and broadened. In English, it has been used since the 14th century to refer not just to the act of dissolving a substance in a liquid, but also to the means of solving a problem or answering a question. The sense of finding an answer or explanation encapsulates the idea of resolving a complex situation, untangling its components to reach a clear understanding or resolutionIn summary, the etymology of "solution" reflects a journey from the physical act of loosening or dissolving, through to the more abstract notion of resolving problems and finding answers.
Advice 0
Used as a general rule in chemistry; the old alchemical principle "similia similibus dissolvuntur" meaning "like dissolves like" refers to the ability of polar or non polar solvents to dissolve polar or non polar solutes respectively.
Engineer's solution
In engineering, the solution S is that vector of P which minimizes (resp. maximizes) the value of objective function F.
Exercise 0: Paper Airplane Optimization
After the break, we will make a little exercise in "Paper Airplane Optimization".
What parameters define the "paper airplane design space"
What will be the primary objective ? What could be a secondary, tertiary, etc. objective ?
What other criteria and constraints could be involved in deciding which design is the optimal one ?
Multi-objective Optimization
In multi-objective optimization, optimize for two or more objectives in the same time.
Problem & Solution
In engineering, a problem P is defined by an objective function that needs to be optimized, a vector of parameters that can be adjusted, and constraints that must be satisfied.
The solution S is the optimal set of parameter values that achieve the desired optimization while staying within the bounds of the constraints.
Meta-Problem
What problem is worth time of Your life ?
problem(s)
picture of "problem", black background
A problem P can be defined as a situation or scenario where a particular system, device, or process is not performing as desired, leading to suboptimal or undesired outcomes. In a design & engineering context, P is typically framed in terms of:
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.
Hilbert problem(s)
dalle-e 3: essence of hilbert problem "topology of algebraic curves and surfaces", black background
The Hilbert Problems are a set of 23 mathematical challenges presented by the German mathematician David Hilbert in 1900. Aimed at defining future research directions, these problems span various areas of mathematics. While some were clearly stated, others were more open-ended. Over the decades, a majority of these problems have been resolved, significantly advancing mathematical knowledge. Some led to the establishment of entire new fields of study. Unresolved - as of AE53 - Hilbert problems:
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
Alltag problem(s)
Divide in couples and discuss with Your colleagues cases when You use the word problem in daily life. Pose Yourself questions like "What was the last problem I solved ?", "What was the last problem I didn't manage to solve "? etc.
etymology of the term 'problem'
From Middle English probleme, from Middle French probleme, from Latin problema, from Ancient Greek πρόβλημα (próblēma, “anything thrown forward, hindrance, obstacle, anything projecting, a headland, promontory”), from προβάλλω (probállō, “to throw or lay something in front of someone, to put forward”), from προ- (pro-, “in front of”) + βάλλω (bállō, “to throw, to cast, to hurl”).
[note the etymologic similarity to word "project": from Latin projectum ‘something prominent’, neuter past participle of proicere ‘throw forth’, from pro- ‘forth’ + jacere ‘to throw’)]
Millenium Problems
dall-e 3: 'generate picture which illustrates the best the essence of "riemann hypothesis"'
The Millennium Problems are seven mathematical challenges established by the Clay Mathematics Institute in 2000, each with a prize of one million dollars for a correct solution. These problems represent some of the most persistent and critical unsolved issues in mathematics, spanning areas such as number theory, geometry, analysis, and fluid dynamics. Only one of the problems, the Poincaré Conjecture, has been solved so far. Unresolved - as of AE53 - ones are:
Birch and Swinnerton-Dyer Conjecture
Hodge Conjecture
Navier–Stokes Existence and Smoothness
P vs NP Problem
Riemann Hypothesis
Yang–Mills Existence and Mass Gap
wicked problems
dall-e 3: "essence of wicked problem, black background"
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
13 teacher-proposed D&C problems
This is the set of problem(s) to which I expose all my D&C students since AE50.
Hopefully, at least 1 will be "solved" during my lifetime, 2 during Your lifetime and 3 during lifetime of my children.
Closing the Door to Hell
The "Door to Hell" or the Darvaza Gas Crater is a natural gas field located in the Karakum Desert in Turkmenistan. It has been burning continuously since 1971 when it was set on fire by Soviet geologists to prevent the spread of methane gas after a drilling rig collapsed into it.
Status: solvable
Approach: CAD, scientific modeling, few telephone calls, trip to Turkmenistan
H-microfusor
The core of the microfusor is a solid carbon-based magnetic confinement lattice similar to hobberman's sphere filled with hydrogen isotope fuel.
H-microfusor is a reactor for deuterium/tritium nuclear fusion whose size does not exceed 1 cubic meter and which is able to persist in the breakeven state (Q>=1) for at least 1 second.
The central problem of roboethics is defined as follows: AI & robot engineers aim to construct beings which will transcend the faculties of human beings, on the other hand, some unethical acts should be made impossible to execute for such artificial beings (Hromada, 2011)
Note: the central problem is equivalent, mutatis mutandi, to much more famous "AI Alignment" problem
Fremen Stilsuit
The Fremen stilsuit, native to the desert planet Arrakis *, is a marvel of engineering. Designed to conserve moisture, this full-body attire reclaims sweat, breath, and waste, converting them into drinkable water. Its black, skin-tight material is layered to reduce heat exposure and prevent water loss. Tubing systems distribute reclaimed water to catchpockets, from which the wearer can drink. Breath filters purify and reclaim moisture, while a nose plug ensures no moisture escapes. Built for desert survival, the stilsuit ensures the Fremen can thrive in Arrakis' harsh environment, making the most of every precious drop of water.
* also known as Terra, Gaia or Zem etc. during AD and AE epochs
Inspiration: Frank Herbert, Dune
Young Lady's Illustrated Primer
The Primer is an almost magical, book-like solarpunk artefact with embedded personalized adaptive generative teacher avatar so advanced that it is able to catalyse, by means of education, a transformation of a traumatized orphan into a Queen.
Status: solvable (provided that there is at least one vacant 👑 around)
Approach: fine-tuning of Large Language Models, speech technologies, Raspberry Pi
Inspiration: Neal Stephenson (Diamond Age: or Young Lady's Illustrated Primer)
Cracking the Voynich Manuscript
Voynich Manuscript is a corpus of unknown origin written down in unique graphemic system and potentially representing phonic values of unknown or potentially even extinct language.
Geodetic dome providing a protective membrane around highly diversified biosphere above, around and below Berlin's Tempelhofer Field.
Status: solvable
Approach: material research, architecture, corruption
Self-optimization of communities and societies
Interconnect processes of opinion aggregation, expertise integration and decision-making so that at least some future social and political systems are more equitable, adaptable and less prone to "extinction through stupidity".
Status: wicked
Approach: try in smaller community, then expand
Common Eco(log|nom)ical Protocol
Common Ecological Protocol is a SDG *-inspired set of positives ("DOs") and negative ("DON'Ts") principles establishing a planetary-wide Nash equilibrium between all human, institutional, corporate, artificial and organic agents.
* SDG = United Nation's Sustainable Development Goals
Approach: Game-Theoretical and Agent-based simulations
Status: wicked but solvable through (enforced) consensus
Space Elevator
dalle-3: "picture of space elevator platform attached to artificial island in equator region with strongly intertwined carbon nanotube fiber, black background"
A space elevator is a proposed transport system connecting Earth's surface directly to space using a tethered cable. Primarily envisioned to reduce exorbitant rocket launch costs, it aims to provide sustainable and energy-efficient space access. The concept requires a geostationary anchor in space and a base on Earth, connected by a carbon nanotube or similar high-strength cable. Centrifugal forces from Earth's rotation keep the cable taut. Elevator cars, powered by solar energy or lasers, would climb this cable.
Status: uncertain but decidable
Approach: material research, modeling, fractal architecture
The Tangle
The tangle is circle with 1m radius containing different vertically stacked herbs, veggies, fruits and mushrooms which maximize nutritive yield beneficial for human all year long and minimizes the amount of external intervention.
Inspiration: Neal Stephenson (Anathem)
Aquatic Alternative: The Aquarium
The Seed
picture of "the seed", the universal nano-assembler in process of creating its own copy. has tree-like, fractal form of a dandelion seed with the MEMS nanocomputer at its base, spherical buckyball energy source in the middle and many robotic arms on the top
The Seed, or Universal Nano-Assembler, is a programmable, portable, self-sustainable matter compiler of non-organic origin able to reorganize molecules of its envelopping substrate in such a manner that it is able to create its own copy in less than one hour.
Status: nature can do it
Approach: MEMS, DNA-computing, nanotech, protein design, AGI
Inspiration: Eric Drexler (Engines of Creation)
Elliptic Curve Discrete Logarithm Problem
dall-e 3: 'picture of bilbo passing to frodo the scroll with a PSI symbol on it, saying "the ring is yours"'
Unsolvability of ECDLP is the pillar on which modern asymmetric cryptography (e.g. cryptocurrencies, communication with products of military-industrial complex etc.) stands.
Status: uncertain and potentially meta-unsolvable *
Approach: apt install sagemath, pen & paper, hope
* proof of ECDLP unsolvability is equivalent to solving the P = NP Millenium Problem
10 student-proposed D&C problems
picture showing depictions of these problems "Radioactive waste disposal", "Liberation from fossil fuel dependency", "Language extinction", "Weltverständlichmachung","unf*cking the wohnnungsmarkt", "the clock reform" in different segments of the picture, black background
Radioactive waste disposal
Liberation from fossil fuel dependency
Language extinction
Weltverständlichmachung
Unf*cking the Wohnungsmarkt
...
...
...
...
The Clock Reform
Taxonomy of Problems
unsolved
picture of "problem about which it is impossible to find out if it can be solved or not", black background
Unsolved problems are problems for which we neither have a solution, nor know whether such solution can be found.
solvable
P is solvable if, at some point in time, a proof will be provided that solution to P can be found.
unsolvable
P is unsolvable if, at some point in time, a proof will be provided that P does not have solution.
fatal
illustration of "unsolvable and undecidable problem which leads to madness", black background
Problem P is "fatal" if no proof could ever be provided whether P is solvable or unsolvable.
It is impossible to tell about problem if it is "fatal". That's why it is fatal ;)
solution(s)
Engineer's solution
In engineering, the solution S is that vector of P which minimizes (resp. maximizes) the value of objective function F.
Advice 0
Used as a general rule in chemistry; the old alchemical principle "similia similibus dissolvuntur" meaning "like dissolves like" refers to the ability of polar or non polar solvents to dissolve polar or non polar solutes respectively.
etymology of the term 'solution'
The word "solution" has its roots in Latin, deriving from the word “solutio.” The etymology can be broken down as follows:
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).
Over time, the meaning of "solution" has evolved and broadened. In English, it has been used since the 14th century to refer not just to the act of dissolving a substance in a liquid, but also to the means of solving a problem or answering a question. The sense of finding an answer or explanation encapsulates the idea of resolving a complex situation, untangling its components to reach a clear understanding or resolutionIn summary, the etymology of "solution" reflects a journey from the physical act of loosening or dissolving, through to the more abstract notion of resolving problems and finding answers.
Exercise 0: Paper Airplane Optimization
After the break, we will make a little exercise in "Paper Airplane Optimization".
What parameters define the "paper airplane design space"
What will be the primary objective ? What could be a secondary, tertiary, etc. objective ?
What other criteria and constraints could be involved in deciding which design is the optimal one ?
Multi-objective Optimization
In multi-objective optimization, optimize for two or more objectives in the same time.
Problem & Solution
In engineering, a problem P is defined by an objective function that needs to be optimized, a vector of parameters that can be adjusted, and constraints that must be satisfied.
The solution S is the optimal set of parameter values that achieve the desired optimization while staying within the bounds of the constraints.
