Category Archives: real

Talking about the world

This text is part of the text “Rebooting Humanity”

(The German Version can be found HERE)

Author No. 1 (Gerd Doeben-Henisch)

Contact: info@uffmm.org

(Start: June 5, 2024, Last change: June 7, 2024)

Starting Point

A ‘text’ shall be written that speaks about the world, including all living beings, with ‘humans’ as the authors in the first instance. So far, we know of no cases where animals or plants write texts themselves: their view of life. We only know of humans who write from ‘their human perspective’ about life, animals, and plants. Much can be criticized about this approach. Upon further reflection, one might even realize that ‘humans writing about other humans and themselves’ is not so trivial either. Even humans writing ‘about themselves’ is prone to errors, can go completely ‘awry,’ can be entirely ‘wrong,’ which raises the question of what is ‘true’ or ‘false.’ Therefore, we should spend some thoughts on how we humans can talk about the world and ourselves in a way that gives us a chance not just to ‘fantasize,’ but to grasp something that is ‘real,’ something that describes what truly characterizes us as humans, as living beings, as inhabitants of this planet… but then the question pops up again, what is ‘real’? Are we caught in a cycle of questions with answers, where the answers themselves are again questions upon closer inspection?

First Steps

Life on Planet Earth

At the start of writing, we assume that there is a ‘Planet Earth’ and on this planet there is something we call ‘life,’ and we humans—belonging to the species Homo sapiens—are part of it.

Language

We also assume that we humans have the ability to communicate with each other using sounds. These sounds, which we use for communication, we call here ‘speech sounds’ to indicate that the totality of sounds for communication forms a ‘system’ which we ultimately call ‘language.’

Meaning

Since we humans on this planet can use completely different sounds for the ‘same objects’ in the same situation, it suggests that the ‘meaning’ of speech sounds is not firmly tied to the speech sounds themselves, but somehow has to do with what happens ‘in our minds.’ Unfortunately, we cannot look ‘into our minds.’ It seems a lot happens there, but this happening in the mind is ‘invisible.’ Nevertheless, in ‘everyday life,’ we experience that we can ‘agree’ with others whether it is currently ‘raining’ or if it smells ‘bad’ or if there is a trash bin on the sidewalk blocking the way, etc. So somehow, the ‘happenings in the mind’ seem to have certain ‘agreements’ among different people, so that not only I see something specific, but the other person does too, and we can even use the same speech sounds for it. And since a program like chatGPT can translate my German speech sounds, e.g., into English speech sounds, I can see that another person who does not speak German, instead of my word ‘Mülltonne,’ uses the word ‘trash bin’ and then nods in agreement: ‘Yes, there is a trash bin.’ Would that be a case for a ‘true statement’?

Changes and Memories

Since we experience daily how everyday life constantly ‘changes,’ we know that something that just found agreement may no longer find it the next moment because the trash bin is no longer there. We can only notice these changes because we have something called ‘memory’: we can remember that just now at a specific place there was a trash bin, but now it’s not. Or is this memory just an illusion? Can I trust my memory? If now everyone else says there was no trash bin, but I remember there was, what does that mean?

Concrete Body

Yes, and then my body: time and again I need to drink something, eat something, I’m not arbitrarily fast, I need some space, … my body is something very concrete, with all sorts of ‘sensations,’ ‘needs,’ a specific ‘shape,’ … and it changes over time: it grows, it ages, it can become sick, … is it like a ‘machine’?

Galaxies of Cells

Today we know that our human body resembles less a ‘machine’ and more a ‘galaxy of cells.’ Our body has about 37 trillion (10¹²) body cells with another 100 trillion cells in the gut that are vital for our digestive system, and these cells together form the ‘body system.’ The truly incomprehensible thing is that these approximately 140 trillion cells are each completely autonomous living beings, with everything needed for life. And if you know how difficult it is for us as humans to maintain cooperation among just five people over a long period, then you can at least begin to appreciate what it means that 140 trillion beings manage to communicate and coordinate actions every second—over many years, even decades—so that the masterpiece ‘human body’ exists and functions.

Origin as a Question

And since there is no ‘commander’ who constantly tells all the cells what to do, this ‘miracle of the human system’ expands further into the dimension of where the concept comes from that enables this ‘super-galaxy of cells’ to be as they are. How does this work? How did it arise?

Looking Behind Phenomena

In the further course, it will be important to gradually penetrate the ‘surface of everyday phenomena’ starting from everyday life, to make visible those structures that are ‘behind the phenomena,’ those structures that hold everything together and at the same time constantly move, change everything.

Fundamental Dimension of Time

All this implies the phenomenon ‘time’ as a basic category of all reality. Without time, there is also no ‘truth’…

[1] Specialists in brain research will of course raise their hand right away, and will want to say that they can indeed ‘look into the head’ by now, but let’s wait and see what this ‘looking into the head’ entails.

[2] If we assume for the number of stars in our home galaxy, the Milky Way, with an estimated 100 – 400 billion stars that there are 200 billion, then our body system would correspond to the scope of 700 galaxies in the format of the Milky Way, one cell for one star.

[3] Various disciplines of natural sciences, especially certainly evolutionary biology, have illuminated many aspects of this mega-wonder partially over the last approx. 150 years. One can marvel at the physical view of our universe, but compared to the super-galaxies of life on Planet Earth, the physical universe seems downright ‘boring’… Don’t worry: ultimately, both are interconnected: one explains the other…”

Telling Stories

Fragments of Everyday Life—Without Context

We constantly talk about something: the food, the weather, the traffic, shopping prices, daily news, politics, the boss, colleagues, sports events, music, … mostly, these are ‘fragments’ from the larger whole that we call ‘everyday life’. People in one of the many crisis regions on this planet, especially those in natural disasters or even in war…, live concretely in a completely different world, a world of survival and death.

These fragments in the midst of life are concrete, concern us, but they do not tell a story by themselves about where they come from (bombs, rain, heat,…), why they occur, how they are connected with other fragments. The rain that pours down is a single event at a specific place at a specific time. The bridge that must be closed because it is too old does not reveal from itself why this particular bridge, why now, why couldn’t this be ‘foreseen’? The people who are ‘too many’ in a country or also ‘too few’: Why is that? Could this have been foreseen? What can we do? What should we do?

The stream of individual events hits us, more or less powerfully, perhaps even simply as ‘noise’: we are so accustomed to it that we no longer even perceive certain events. But these events as such do not tell a ‘story about themselves’; they just happen, seemingly irresistibly; some say ‘It’s fate’.

Need for Meaning

It is notable that we humans still try to give the whole a ‘meaning’, to seek an ‘explanation’ for why things are the way they are. And everyday life shows that we have a lot of ‘imagination’ concerning possible ‘connections’ or ’causes’. Looking back into the past, we often smile at the various attempts at explanation by our ancestors: as long as nothing was known about the details of our bodies and about life in general, any story was possible. In our time, with science established for about 150 years, there are still many millions of people (possibly billions?) who know nothing about science and are willing to believe almost any story just because another person tells this story convincingly.

Liberation from the Moment through Words

Because of this ability, with the ‘power of imagination’ to pack things one experiences into a ‘story’ that suggests ‘possible connections’, through which events gain a ‘conceptual sense’, a person can try to ‘liberate’ themselves from the apparent ‘absoluteness of the moment’ in a certain way: an event that can be placed into a ‘context’ loses its ‘absoluteness’. Just by this kind of narrative, the experiencing person gains a bit of ‘power’: in narrating a connection, the narrator can make the experience ‘a matter’ over which they can ‘dispose’ as they see fit. This ‘power through the word’ can alleviate the ‘fear’ that an event can trigger. This has permeated the history of humanity from the beginning, as far as archaeological evidence allows.

Perhaps it is not wrong to first identify humans not as ‘hunters and gatherers’ or as ‘farmers’ but as ‘those who tell stories’.

[1] Such a magic word in Greek philosophy was the concept of ‘breath’ (Greek “pneuma”). The breath not only characterized the individually living but was also generalized to a life principle of everything that connected both body, soul, and spirit as well as permeated the entire universe. In the light of today’s knowledge, this ‘explanation’ could no longer be told, but about 2300 years ago, this belief was a certain ‘intellectual standard’ among all intellectuals, the prevailing ‘worldview’; it was ‘believed’. Anyone who thought differently was outside this ‘language game’.

Organization of an Order

Thinking Creates Relationships

As soon as one can ‘name’ individual events, things, processes, properties of things, and more through ‘language’, it is evident that humans have the ability to not only ‘name’ using language but to embed the ‘named’ through ‘arrangement of words in linguistic expression’ into ‘conceived relationships’, thereby connecting the individually named items not in isolation but in thought with others. This fundamental human ability to ‘think relationships in one’s mind’, which cannot be ‘seen’ but can indeed be ‘thought’ [1], is of course not limited to single events or a single relationship. Ultimately, we humans can make ‘everything’ a subject, and we can ‘think’ any ‘possible relationship’ in our minds; there are no fundamental restrictions here.

Stories as a Natural Force

Not only history is full of examples, but also our present day. Today, despite the incredible successes of modern science, almost universally, the wildest stories with ‘purely thought relationships’ are being told and immediately believed through all channels worldwide, which should give us pause. Our fundamental characteristic, that we can tell stories to break the absoluteness of the moment, obviously has the character of a ‘natural force’, deeply rooted within us, that we cannot ‘eradicate’; we might be able to ‘tame’ it, perhaps ‘cultivate’ it, but we cannot stop it. It is an ‘elemental characteristic’ of our thinking, that is: of our brain in the body.

Thought and Verified

The experience that we, the storytellers, can name events and arrange them into relationships—and ultimately without limit—may indeed lead to chaos if the narrated network of relationships is ultimately ‘purely thought’, without any real reference to the ‘real world around us’, but it is also our greatest asset. With it, humans can not only fundamentally free themselves from the apparent absoluteness of the present, but we can also create starting points with the telling of stories, ‘initially just thought relationships’, which we can then concretely ‘verify’ in our everyday lives.

A System of Order

When someone randomly sees another person who looks very different from what they are used to, all sorts of ‘assumptions’ automatically form in each person about what kind of person this might be. If one stops at these assumptions, these wild guesses can ‘populate the head’ and the ‘world in the head’ gets populated with ‘potentially evil people’; eventually, they might simply become ‘evil’. However, if one makes contact with the other, they might find that the person is actually nice, interesting, funny, or the like. The ‘assumptions in the head’ then transform into ‘concrete experiences’ that differ from what was initially thought. ‘Assumptions’ combined with ‘verification’ can thus lead to the formation of ‘reality-near ideas of relationships’. This gives a person the chance to transform their ‘spontaneous network of thought relationships’, which can be wrong—and usually are—into a ‘verified network of relationships’. Since ultimately the thought relationships as a network provide us with a ‘system of order’ in which everyday things are embedded, it appears desirable to work with as many ‘verified thought relationships’ as possible.

[1] The breath of the person opposite me, which for the Greeks connected my counterpart with the life force of the universe, which in turn is also connected with the spirit and the soul…

Hypotheses and Science

Challenge: Methodically Organized Guessing

The ability to think of possible relationships, and to articulate them through language, is innate [1], but the ‘use’ of this ability in everyday life, for example, to match thought relationships with the reality of everyday life, this ‘matching’/’verifying’ is not innate. We can do it, but we don’t have to. Therefore, it is interesting to realize that since the first appearance of Homo sapiens on this planet [2], 99.95% of the time has passed until the establishment of organized modern science about 150 years ago. This can be seen as an indication that the transition from ‘free guessing’ to ‘methodically organized systematic guessing’ must have been anything but easy. And if today still a large part of people—despite schooling and even higher education—[3] tend to lean towards ‘free guessing’ and struggle with organized verification, then there seems to be a not easy threshold that a person must overcome—and must continually overcome—to transition from ‘free’ to ‘methodically organized’ guessing.[4]

Starting Point for Science

The transition from everyday thinking to ‘scientific thinking’ is fluid. The generation of ‘thought relationships’ in conjunction with language, due to our ability of creativity/imagination, is ultimately also the starting point of science. While in everyday thinking we tend to spontaneously and pragmatically ‘verify’ ‘spontaneously thought relationships’, ‘science’ attempts to organize such verifications ‘systematically’ to then accept such ‘positively verified guesses’ as ’empirically verified guesses’ until proven otherwise as ‘conditionally true’. Instead of ‘guesses’, science likes to speak of ‘hypotheses’ or ‘working hypotheses’, but they remain ‘guesses’ through the power of our thinking and through the power of our imagination.[5]

[1] This means that the genetic information underlying the development of our bodies is designed so that our body with its brain is constructed during the growth phase in such a way that we have precisely this ability to ‘think of relationships’. It is interesting again to ask how it is possible that from a single cell about 13 trillion body cells (the approximately 100 trillion bacteria in the gut come ‘from outside’) can develop in such a way that they create the ‘impression of a human’ that we know.

[2] According to current knowledge, about 300,000 years ago in East Africa and North Africa, from where Homo sapiens then explored and conquered the entire world (there were still remnants of other human forms that had been there longer).

[3] I am not aware of representative empirical studies on how many people in a population tend to do this.

[4] Considering that we humans as the life form Homo sapiens only appeared on this planet after about 3.8 billion years, the 300,000 years of Homo sapiens make up roughly 0.008% of the total time since there has been life on planet Earth. Thus, not only are we as Homo sapiens a very late ‘product’ of the life process, but the ability to ‘systematically verify hypotheses’ also appears ‘very late’ in our Homo sapiens life process. Viewed across the entire life span, this ability seems to be extremely valuable, which is indeed true considering the incredible insights we as Homo sapiens have been able to gain with this form of thinking. The question is how we deal with this knowledge. This behavior of using systematically verified knowledge is not innate too.

[5] The ability of ‘imagination’ is not the opposite of ‘knowledge’, but is something completely different. ‘Imagination’ is a trait that ‘shows’ itself the moment we start to think, perhaps even in the fact ‘that’ we think at all. Since we can in principle think about ‘everything’ that is ‘accessible’ to our thinking, imagination is a factor that helps to ‘select’ what we think. In this respect, imagination is pre-posed to thinking.

HMI Analysis for the CM:MI paradigm. Part 3. Actor Story and Theories

Integrating Engineering and the Human Factor (info@uffmm.org)
eJournal uffmm.org ISSN 2567-6458, March 2, 2021,
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Last change: March 2, 2021 13:59h (Minor corrections)

HISTORY

As described in the uffmm eJournal  the wider context of this software project is an integrated  engineering theory called Distributed Actor-Actor Interaction [DAAI] further extended to the Collective Man-Machine Intelligence [CM:MI] paradigm.  This document is part of the Case Studies section.

HMI ANALYSIS, Part 3: Actor Story and  Theories

Context

This text is preceded by the following texts:

Introduction

Having a vision is that moment  where something really new in the whole universe is getting an initial status in some real brain which can enable other neural events which  can possibly be translated in bodily events which finally can change the body-external outside world. If this possibility is turned into reality than the outside world has been changed.

When human persons (groups of homo sapiens specimens) as experts — here acting as stakeholder and intended users as one but in different roles! — have stated a problem and a vision document, then they have to translate these inevitably more fuzzy than clear ideas into the concrete terms of an everyday world, into something which can really work.

To enable a real cooperation  the experts have to generate a symbolic description of their vision (called specification) — using an everyday language, possibly enhanced by special expressions —  in a way that  it can became clear to the whole group, which kind of real events, actions and processes are intended.

In the general case an engineering specification describes concrete forms of entanglements of human persons which enable  these human persons to cooperate   in a real situation. Thereby the translation of  the vision inside the brain  into the everyday body-external reality happens. This is the language of life in the universe.

WRITING A STORY

To elaborate a usable specification can metaphorically be understood  as the writing of a new story: which kinds of actors will do something in certain situations, what kinds of other objects, instruments etc. will be used, what kinds of intrinsic motivations and experiences are pushing individual actors, what are possible outcomes of situations with certain actors, which kind of cooperation is  helpful, and the like. Such a story is  called here  Actor Story [AS].

COULD BE REAL

An Actor Story must be written in a way, that all participating experts can understand the language of the specification in a way that   the content, the meaning of the specification is either decidable real or that it eventually can become real.  At least the starting point of the story should be classifiable as   being decidable actual real. What it means to be decidable actual real has to be defined and agreed between the participating experts before they start writing the Actor Story.

ACTOR STORY [AS]

An Actor Story assumes that the described reality is classifiable as a set of situations (states) and  a situation as part of the Actor Story — abbreviated: situationAS — is understood  as a set of expressions of some everyday language. Every expression being part of an situationAS can be decided as being real (= being true) in the understood real situation.

If the understood real situation is changing (by some event), then the describing situationAS has to be changed too; either some expressions have to be removed or have to be added.

Every kind of change in the real situation S* has to be represented in the actor story with the situationAS S symbolically in the format of a change rule:

X: If condition  C is satisfied in S then with probability π  add to S Eplus and remove from  S Eminus.

or as a formula:

S’π = S + Eplus – Eminus

This reads as follows: If there is an situationAS S and there is a change rule X, then you can apply this change rule X with probability π onto S if the condition of X is satisfied in S. In that case you have to add Eplus to S and you have to remove Eminus from S. The result of these operations is the new (successor) state S’.

The expression C is satisfied in S means, that all elements of C are elements of S too, written as C ⊆ S. The expression add Eplus to S means, that the set Eplus is unified with the set S, written as Eplus ∪ S (or here: Eplus + S). The expression remove Eminus from S means, that the set Eminus is subtracted from the set S, written as S – Eminus.

The concept of apply change rule X to a given state S resulting in S’ is logically a kind of a derivation. Given S,X you will derive by applicating X the new  S’. One can write this as S,X ⊢X S’. The ‘meaning’ of the sign ⊢  is explained above.

Because every successor state S’ can become again a given state S onto which change rules X can be applied — written shortly as X(S)=S’, X(S’)=S”, … — the repeated application of change rules X can generate a whole sequence of states, written as SQ(S,X) = <S’, S”, … Sgoal>.

To realize such a derivation in the real world outside of the thinking of the experts one needs a machine, a computer — formally an automaton — which can read S and X documents and can then can compute the derivation leading to S’. An automaton which is doing such a job is often called a simulator [SIM], abbreviated here as ∑. We could then write with more information:

S,X ⊢ S’

This will read: Given a set S of many states S and a set X of change rules we can derive by an actor story simulator ∑ a successor state S’.

A Model M=<S,X>

In this context of a set S and a set of change rules X we can speak of a model M which is defined by these two sets.

A Theory T=<M,>

Combining a model M with an actor story simulator enables a theory T which allows a set of derivations based on the model, written as SQ(S,X,⊢) = <S’, S”, … Sgoal>. Every derived final state Sgoal in such a derivation is called a theorem of T.

An Empirical Theory Temp

An empirical theory Temp is possible if there exists a theory T with a group of experts which are using this theory and where these experts can interpret the expressions used in theory T by their built-in meaning functions in a way that they always can decide whether the expressions are related to a real situation or not.

Evaluation [ε]

If one generates an Actor Story Theory [TAS] then it can be of practical importance to get some measure how good this theory is. Because measurement is always an operation of comparison between the subject x to be measured and some agreed standard s one has to clarify which kind of a standard for to be good is available. In the general case the only possible source of standards are the experts themselves. In the context of an Actor Story the experts have agreed to some vision [V] which they think to be a better state than a  given state S classified as a problem [P]. These assumptions allow a possible evaluation of a given state S in the ‘light’ of an agreed vision V as follows:

ε: V x S —> |V ⊆ S|[%]
ε(V,S) = |V ⊆ S|[%]

This reads as follows: the evaluation ε is a mapping from the sets V and S into the number of elements from the set V included in the set S converted in the percentage of the number of elements included. Thus if no  element of V is included in the set S then 0% of the vision is realized, if all elements are included then 100%, etc. As more ‘fine grained’ the set V is as more ‘fine grained’  the evaluation can be.

An Evaluated Theory Tε=<M,,ε>

If one combines the concept of a  theory T with the concept of evaluation ε then one can use the evaluation in combination with the derivation in the way that every  state in a derivation SQ(S,X,⊢) = <S’, S”, … Sgoal> will additionally be evaluated, thus one gets sequences of pairs as follows:

SQ(S,X,⊢∑,ε) = <(S’,ε(V,S’)), (S”,ε(V,S”)), …, (Sgoal, ε(V,Sgoal))>

In the ideal case Sgoal is evaluated to 100% ‘good’. In real cases 100% is only an ideal value which usually will only  be approximated until some threshold.

An Evaluated Theory Tε with Algorithmic Intelligence Tε,α=<M,,ε,α>

Because every theory defines a so-called problem space which is here enhanced by some evaluation function one can add an additional operation α (realized by an algorithm) which can repeat the simulator based derivations enhanced with the evaluations to identify those sets of theorems which are qualified as the best theorems according to some criteria given. This operation α is here called algorithmic intelligence of an actor story AS]. The existence of such an algorithmic intelligence of an actor story [αAS] allows the introduction of another derivation concept:

S,X ⊢∑,ε,α S* ⊆  S’

This reads as follows: Given a set S and a set X an evaluated theory with algorithmic intelligence Tε,α can derive a subset S* of all possible theorems S’ where S* matches certain given criteria within V.

WHERE WE ARE NOW

As it should have become clear now the work of HMI analysis is the elaboration of a story which can be done in the format of different kinds of theories all of which can be simulated and evaluated. Even better, the only language you have to know is your everyday language, your mother tongue (mathematics is understood here as a sub-language of the everyday language, which in some special cases can be of some help). For this theory every human person — in all ages! — can be a valuable  colleague to help you in understanding better possible futures. Because all parts of an actor story theory are plain texts, everybody ran read and understand everything. And if different groups of experts have investigated different  aspects of a common field you can merge all texts by only ‘pressing a button’ and you will immediately see how all these texts either work together or show discrepancies. The last effect is a great opportunity  to improve learning and understanding! Together we represent some of the power of life in the universe.

CONTINUATION

See here.

 

 

 

 

 

 

 

 

STARTING WITH PYTHON3 – The very beginning – part 3

Journal: uffmm.org,
ISSN 2567-6458, July 10, 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email:
gerd@doeben-henisch.de

CONTEXT

This is the next step in the python3 programming project. The overall context is still the python Co-Learning project.

SUBJECT

After a first clearing of the environment for python programming we will now focus a little bit more on the structure of the python programming language. Generally python is not different to any other programming language: there are different kinds of objects and different kinds of operations with these objects, and a certain order how to proceed.

PHILOSOPHICAL CONSIDERATIONS

To be able to write code it is not necessary to do philosophy. But as you will see shortly (and hopefully) it can add some more helpful knowledge by widening your view of what you are doing.

What you want to do while programming is to write some lines of code in the python language to enable some computing process.

Usually you will do this because you have some model in your head which you want to translate (encode, implement) in a python script which can be processed by the python interpreter who talks with the computing machinery.

The computing machinery is some real machine which matches the general (mathematical = philosophical) concept of an automaton called Turing machine.

From a Turing machine we know that one has to distinguish between input values which can be read in and being processed according to a finite set of computable rules and output values of these computations. The output values can also be understood as stored values, which can be read again. Input and output values can have an explicit address of some location where they are stored and a content (= value) at this location. Thus the processing rules can select an address and either read the associated value or write a value into the associated location.

Within this mathematical framework of a Turing machine the values represent objects and the computable rules represent possible operations with these objects.

It is possible to combine elementary values located in individual addresses to more complex values and to combine individual computable rules to more complex operations.

In the first moment this description of a Turing machine can appear  to be too simple to be useful for anything interesting, but as the history of Logic, of Mathematics as well as Computer Science has revealed to us, this simple concept can do anything what we can think of to be computable (a complete different story is that of quantum computers. It has still to be clarified whether the definition of ‘quantum computer’ is compatible with that of a Turing machine).

Taking the journey from a Turing machine to the python programming paradigm as defined in the language then we find a rich set of different types of values as well as a rich set of different types of operations (methods), often object specific.

Let us have a first look to the value (object) types numbers, strings, and sets.

Remark: the following information about numbers you get directly from the python manuals, which you can find associated with the entry for python 3.7.3 if you press the Windows-Button, look to the list of Apps (= programs), and identify the entry for python 3.7.3. If you open the python entry by clicking you see the sub-entry python 3.7.3 Manuals. If you click on this sub-entry the python documentation will open. In this documentation you can find nearly everything you will need. For Beginners you even find a nice tutorial (Alternatively you can have a look to the python web page to the tutorial where you will find this information too).

VALUES (OBJECTS) AS NUMBERS

In our everyday world numbers occur usually as certain symbolic expressions like ’99’, ‘-62’, ‘6.23’, ‘2.3*10^4’ etc. From Mathematics we have learned that there are different kinds of numbers defined which obey different kinds of rules.

Thus we have in everyday life integers, rational numbers, real numbers, irrational numbers, complex numbers to mention the most common types.

While numbers as such have no special meaning they can be used to quantify certain properties like temperature, weight, length, clock-time, velocity, etc.

In python there are three distinct numeric types built in: integers, floating point numbers, and complex numbers. Integers have internally an unlimited precision. Example:

>>> print(23**23)

20880467999847912034355032910567

>>> print(234**23)

3104307401943398225947002752118451297846365869366575104

>>> print(2345**33)

1639509557347018492896272198387903513810572353466749818375721601077990329493344735781232477165758609771728515625

Information about the precision and internal representation of floating point numbers for the machine on which your program is running is available in sys.float_info:

>>> import sys

>>> print(sys.float_info)

sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)

Complex numbers have a real and imaginary part, which are each a floating point number. To extract these parts from a complex number z, use z.real and z.imag.

>>> z=complex(2.33,-2)

>>> z

(2.33-2j)

>>> z.real

2.33

>>> z.imag

-2.0

>>> z=complex(2.33,-2)

>>> z

(2.33-2j)

>>> z.real

2.33

>>> z.imag

-2.0

There are additional numeric types like fractions and decimals that hold floating-point numbers with user-definable precision.

The different operations with these numeric types are the following ones:

A population p=1200 citizens increases by incoming people migPlus=500 to 12500.

>>> p=12000

>>> migrPlus=500

>>> pnew=p+migrPlus

>>> pnew

12500

With a birth rate br=0.015 and a death rate of dr=0.018 the population will change in a year like

>>> p=12500

>>> br=0.015

>>> dr=0.018

>>> pnew=p+(p*br)-(p*dr)

>>> pnew

12462.5

If one would assume that the birth br and death dr rates are linearly distributed over the year one could compute some average per month like:

>>> (p*br)/12

15.625

>>> (p*dr)/12

18.749999999999996

The floor operator ‘//’ turns a float number into the next integer which is smaller:

>>> (p*br)/12

15.625

>>> (p*br)//12

15.0

>>> (p*dr)/12

18.749999999999996

>>> (p*dr)//12

18.0

>>>

The remainder operator ‘%’ delivers the ‘rest’ of a division instead of the fraction as in a usual division:

>>> 12/8

1.5

>>> 12%8

4

The ‘abs()’ operator abstracts from possible negative signs:

>>> abs(-7)

7

>>> abs(-7.2)

7.2

The ‘int()’ operator turns a float number into an integer:

>>> int(7.2)

7

>>> int(-7.2)

-7

And the float operator ‘float()’ turns an integer into a float:

>>> float(7)

7.0

>>> float(-7)

-7.0

With the power operator ‘pow(x,y)’ one can raise x to the power of y:

>>> pow(2,3)

8

>>> pow(2,5)

32

>>> pow(3,3)

27

Alternatively one can use the expression x**y:

>>> 2**3

8

>>> 2**5

32

>>> 3**3
27

The next possible continuation you can find HERE.