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How Math & Computations Permeate Everything!

 

Hello folks, creatives and science-centric people! Today bearing in mind my code programming refinement in Python I would like to grab the opportunity and explain how math and scientific programming are the missing keys to understand how we can model nature and the environment around us. So that we can understand them, especially when dealing with experiments, luck and games projected into AI and state spaces. But let’s start from the beginning.

 

As teenagers we were dealing with thoughts of using math to model casino games, to model maps, to model luck experiments or to find out the algorithms of slots or whether God plays dice with the world. We were assuming these things demand highly sophisticated knowledge of mathematical formulas and being disappointed by the lack of our access we could only dream of understanding the history, the beauty and the omnipotence of modelling the world with computational formulas.

 

Intermediate Python explains and solves these mysteries once and for all. It calls these methods Hacker statistics and I explain myself. Let’s say that this nature of modelling will later acquire AI resonance. There are two paths in solving computational problems, the analytical one and the simulating the process of it. The analytical one means modelling our problem with math, coming up with equations and program these equations into e.g. Anaconda and Jupyter Notebooks. Developing a numerical simulation process on the other hand, means we’re trying to hack the computations – the mathematical formulas – and via analyzing and programming state spaces we can model and understand phenomena without the necessity of trying to understand the math behind it, i.e. hacking the mathematical algorithm. How could we, understand, in other words? Just pay attention to the following.

 

1.) Modelling a problem

 

We’ll deal with the problem named “Empire State Building Simulation”. There is a ladder. There is a man climbing stairs or coming down of them. He rolls a dice and here’s the analytical framing of our first case study.

-Whenever he rolls the dice and comes up with 1 or 2, he comes down of one stair, straight to the previous one.

-Whenever he brings 3, 4, or 5, he rises one stair, one step up.

-Whenever he brings 6, he repeats the process.

-He can’t go below step 0 which is the ground.

-There is 0.1% chance of falling down the stairs.

-Can you calculate the chance of reaching step 60 and whether he’ll win that bet?

This is one of the many impressions we get when we try to use math to solve puzzles. For the sake of this article, we will compute a partly easier version of it. We’ll use a simpler but more powerful experiment for climbing stairs that is a coin toss.

 

2.) Scientific Programming with Python

 

Let’s say that instead of dice we use a coin toss. For every 0, name it “heads”, he stays constant. For every 1, name it “tails” he rises one stair. He will never fall down the stairs so we want to calculate his chance of reaching the 60th stairstep.

 

Pay attention to the Python code tested in Jupyter notebooks:

 

import numpy as np

np.random.seed(123)

tails = [0]

# 0=heads, 1=tails

for x in range(121):

    coin = np.random.randint(0,2)

    tails.append(tails[x] + coin)

print(tails)

 

The experiment runs 121 times using the range function, where we have selected the figure 121 through trial-error attempts, until we reach the desired step. Furthermore tails[3], tails[4], tails[5] doesn’t mean necessarily we reached the 3rd, 4th, 5th step respectively, this is the ideal scenario as it depends from the opposite coin toss results. tails[x] is a function that participates in our repetitive loop and we initialize this function with a zero figure that denoted being on the ground.

 

The algorithm outputs a list of 122 results (121 plus the initial configuration) where every figure, based on whether the coin toss brings 0 or 1, denoted as obvious the numbered step on the stair… The 122nd output is the first output indicated as 60th and we usually put many figures there until we reach it. This means our player has tossed the coin 121 times before he reaches the 60th step.

 

As soon as we come up with this list of numbers and we know the distribution possibly projected with plots in the matplotlib library as well we can start calculating chances! We can do many more calculations in partly different examples than the previous depending on the complexity of the problem.

 

3.) Generalization to applications

 

We used experiments in order to climb the stairs such as rolling the dice or tossing a coin. Can you truly imagine what would happen if we could change the experiment that denoted our purpose, the ladder and e.g. using the tree of tic-tac-toe, roulette simulations, loaded dice, use even the double-slit experiment in quantum physics via the distribution of electrons and a boundary limit deciding going forward or going backwards, numerical analogies of board games, playing slots, playing darts, playing mastermind, using the trees of chess variants...? We are eager of highly sophisticated science and use science and math to permeate everything but so far, it would seem impossible to study all that math. This doesn’t mean we don’t need math. To solve the previous examples, as it happens with every other scenario we need to map the possible outputs of the game, meaning to map the state space of the experiment or the game and simulate the process as Python coders…!

 

4.) More complex scientific puzzles

 

Earlier we used several games or we can even imagine of more complex scientific phenomena to determine of whether we go up or down the stairs. What could happen if we could change our purpose as well, meaning, subtract the ladder and use a phenomenon, art, science, whatever, to determine a decision of a more complex puzzle? Picking up the experiment and our decision-making process is not random but it depends on their feasibility as well. It simply has to make sense in other words…!

 

Let’s say we want to use the eigen vectors and the eigen values of the Schrodinger equation in quantum physics to determine web navigation! Choices like the previous ones can be fictional – games – or real – science.

 

Internet is being accessed via the electricity company and internet providers, telecommunication companies in other words. Telecommunications companies posses a map of the internet and a graph diagram of their connected nodes – graph theory. If the host is in the middle and the nodes represent our graph, the total resultant of the vector – not bigger than the distance of our globe – could determine the depth of our potential well of quantum physics if electromagnetic energy is what is actually being transmitted, in terms of not using sophisticated telecommunications and network knowledge to map the topology and the architecture of the network but use the Schrodinger equation in order to simulate network dynamics. The wave function here at a concrete depth of the potential well, denoted the signal of our node. Meaning, we use the eigen vectors and the eigen values of the equation of Schrodinger!!

 

Later on, studying Higgs and e.g. coming up with even more complex problems such as quantum cognition in the network instead of mere navigation, we can test of whether we can come up with even more complex situations and find out what fits and what doesn’t. Bridges can be numerous and ambition is present…

 

5.) Understanding Global Impact

 

Pick up whatever game or experiment you’d like – if possible several games and experiments but not all – and use it in your own decision making process of a single case study…! When we take decisions, when we enter an arena, we need to know the rules of the game. When we write e.g. books or write screenplays, we need to know the craft and the art of our job. In this last example I’ll use the invention of the science of medicine that is MRI (Magnetic Resonance Imaging). It can map concrete and specific functions of the brain as well as e.g. movements of hands but it is impossible so far to create a measurement device or a machine that could possibly map ballet pirouettes as brain functions. So, whether it’s true that only God knows such stuff, such machinery doesn’t exist and we seek to act as Men instead of God, real science progresses and we can come up with alternate ambitions and inventions as long as we stay with science and don’t substitute knowledge with myth. Even though that understanding movies and book characters via the math of quanta ‘could be’ impressive and it alternately proves writers are children of the universe…

 

6.) Conclusion – The Importance of Games & Reality

 

Are we dealing with a made-up construction? We should simulate games and here’s where epic fantasy goes vertical. Are we dealing with real world phenomena and problems? Science is an excellent field of glory. Coming up with outputs and graphical plots of our simulations, means we can proceed with more advanced calculations, the probabilistic character of nature, etc, and use our outputs now for sophisticated predictions and curve fitting or clustering analysis that is the case of AI.

 

Pay attention to an even more complicated example inspired by my epic science fantasy book!: We want to map the tree of a labyrinth that provides us with 3 different exit paths of different sizes – number of labyrinth doors passed -, we collect points and trophies during our routes and we want to calculate an optimization problem…!

 

Such kind of problems, of course, require competence on math, but require as well less fanatism with “great formulas” and better understanding of coding, numerical simulations and … Hacker statistics… 

 

The Idea

 

Measuring the World via Math & Technology

 

In the middle of being reorganized and disillusioned in terms of the limits of different forms and fields of creativity, it’s true that answers in life should be primarily science-focused… The time has come for me to apply them and I should introduce you to my will of developing a scientific project (Python based) using the power of digital platforms and social networks. Pseudocode-oriented, it’s also true that mere possession of an equipment may it be software, programming, math utilities, 15 different patterns of code running in multiple software, data studios, etc, does not turn the individual into a developer, AI scientist, data analyst, designer, math programmer, etc. Cultivations and scopes of science differ from one another…

 

Perhaps I should employ the power of a Blog-Website network and via my knowledge on Python, AI, math and experience with data-driven problems I should focus at:

 

A. Developing flow diagrams of pseudo-code

 

Pseudo-code with less emphasis on commands, even though they will exist, should be merged with the utility of selective naming of software and applications and only after a while, for the purposes of time management and the impossibility in terms of time and creative restrictions to develop platforms indefinitely.

 

B. Challenging and worldwide applications

 

May these be the study of games of luck, jungles, studying populations, multi-disciplinary areas of science, quantum and theoretical physics, market chaos, board games (imagine getting an equation for The Lord of the Rings table-game), complex creative puzzles, applications in data and AI, language models, digital marketing initiatives, deep learning or sentiment analysis, genetic algorithms or whatever challenges our minds and is waiting of being discovered and understood – including the overturning of our fears – should be included in a Python-centric pseudo-code project.

 

C. Emphasis on Narrow Vs General AI

 

Imagine of solving a problem or a computational formula and the fact that this could unlock the possibilities of solving thousands of other problems. Even if this is an utopy called General AI, it’s true that multi-disciplinary mindsets that focus in solving a specific one task bypassing several times the grand questions of science, they have at least unlocked certain degrees of freedom for thinking holistically.

 

D. Think Global – Act Local

 

In the 21st century where the media and the internet almost everyday demand a head on the platter, favoring objectivity versus universality not only tames fake fears and fake victories, it’s also focus-based on the tasks and the problems at hand.

 

E. Challenging computations

 

The applicability and the worldwide impact of math and science may not be what they seem. There are not errors in nature but only in the calculations of our minds, Neil deGrasse Tyson. We should take away the welfare veil from science and dare to approach our hidden sides. This means that choices of what to study, what to develop and what to analyze matter more than coming up with thesis statements. Questions are more important than answers.

 

Imagine now of a scientist that can unite all the previous with the predictability, curve fitting or calculations of modern AI. At the end of the day that it is AI as well that can interpret the world, science and technology should walk hand in hand.

 

Photo Courtesy of Easy-Peasy.AI