What is discrete? And continuous? Why we need both of these ideas? How do they relate to each other?? And how it manifests itself in physics?
Discrete. What it is? By this word we mean something intermittent, consisting of unrelated no parts between each other. These parts represent some integrity, quite easily distinguishable from anything else. for instance, stone and dog. Further to the idea of this “whole” added the idea of its not uniqueness. Several stones, many dogs. And this can already be framed as an idea multitudes. Discrete set. At this level, the idea may already be divorced from the specifics., whether stones, whether dogs. Further, and those, and others you can think. This is how it appears natural number idea, developing then until countable set. It is with these ideas that the notion of discreteness turns out to be associated in mathematics. Every number in the set of all natural numbers, one side, quite individually, distinguishable from another. On the other hand, has its place in this set, all numbers line up. Because another idea is already invisibly present here.. The idea of order, followings. The concept of ordering for a discrete set is still quite ephemeral.. It is external to the very elements of this set. They can be built in one, then in a different order. But in the set of natural numbers this order already installed. AND is established he by operation, actions. Items, when there are a lot of them in a heap, can be added and subtracted. This is how addition and subtraction operations appear in the set of natural numbers.. Addition creates an ascending order, clarifying the concept “more”. Subtraction, respectively, maintains descending order. Then the multiplication operation is added to these actions, and then division. Here the last of the arithmetic operations creates the track, linking the idea of discrete with a completely different idea, the idea of continuous.
Continuous. The idea of a continuous arises naturally from the experience of handling sufficiently large solids and liquids.. Continuous is also possible “interrupt”, split into parts. Only these parts remain in all similar to the whole. And in the case of liquids, it is easy to combine them again and get the same original whole.. Moreover, you can divide the continuous in an arbitrary place. Even more, the idea of the continuous manifests itself in objects, which associate something with something. for instance, belief, a thread, the cloth. Pull one end — the second one will definitely feel.
If individual items, as a whole, gave birth to the idea of an integer, then formalization of the concept of continuous matter gave rise to the idea of geometry. Geometric steel elements figures, having volume (three-dimensional; stone plate), surface (two-dimensional, in particular flat; canvas, paper), lines (having only one dimension; nor) and points (unmeasured). The concept of a point was formed as a development of the concept of an object, all dimensions of which are vanishingly small. Line and surface concepts were formed the same way, only two or even one size become vanishingly small, respectively. Operations in geometry are also available. Somewhat identical to operations with numbers, somewhat different. Further development of geometry, its fusion with set theory led to, that the order in the sequence of the formation of these concepts has changed to the exact opposite. At the heart of all concepts of geometry, of necessity, the concept of a point turned out to be, and therefore the usual idea of it as an object with vanishingly small dimensions turned out to be little satisfactory. You can not introduce a concept with the help of other concepts, which will be based on the same concept. Below I will dwell on this in more detail..
Quite a long time much of the difference between these two ideas, the number and geometry of the continuous was not noticed. Number as such naturally entered geometric concepts. Dimension concept, comparing, eg, lengths of two lines, was one of the starting points in the formation of the idea of geometry. Indeed, one of the properties of a continuous is precisely the ability to divide it into parts (including, equal) and, hence, talk about the number of these parts. And the very unification of objects into sets according to some criterion already carries one of the basic features of measurement. It is about choosing a unit of measurement. The symptom is described, according to which the set. for instance, stone. This is the definition of the unit of measurement in this simplest case.. for instance, one stone. The counting is not carried out further., namely stones. On the other hand, subjects, which we believe, even when they seem very far from geometry, you can also sometimes be divided into parts. This division operation expands the concept of a natural number, introduces fractional (rational) numbers. Then, that with the help of a rational number it is possible to write down the measurement result of any continuous segment it seemed obvious before Pythagoras discovered incommensurable segments in one of the simplest geometric figures – right triangle, whose legs are equal to units. According to the legend, Pythagoras sacrificed a hundred bulls to the gods on this occasion.. It was truly a major discovery.. The chasm between two ideas, the idea of discrete and the idea of continuous declared itself in full voice.
What is this abyss? Her name is infinity. The concept of infinity appears already during the formation of the idea of a natural number. Any subsequent number in the series of natural numbers can be obtained by adding one to the previous one. And you can do this an infinite number of times.. Limit, upon reaching which you will have to stop, not. This infinity was called potential, precisely in the sense of the potential for an unlimited increase in the number of natural numbers. Since continuity, for example a line, can also be imagined continuing infinitely, then such infinity turns out to be naturally inherent in the idea of a continuous. On the line, you can place marks at equal intervals and assign an integer to each. In this way the set of integers is naturally immersed in the continuity of the line. Each such segment, unit of measure, you can continue to divide over and over again and this is how rational numbers arise. And the impression is made, that in this way you can mark each point of a continuous line. But this impression is completely deceptive.. Because between any rational numbers, no matter how close they seem on a continuous line, always there are infinitely many unmarked points. And this another infinity, actual. To number these points of a continuous line, new numbers were invented, other than rational — irrational. There are infinitely many of them on any, an arbitrarily small line segment. It is this infinity that separates the discrete set of rational numbers and the continuous set of points of the line, also called the set of real numbers. it just a statement of the fact of the difference between discrete and continuous, the inability to get the last from the first. These are two different ideas. Various methods have been developed to work with this actual infinity with the help of a more understandable and familiar potential infinity., first of all, limit concept. But you need to understand well, what these methods are not able to remove this chasm, fundamental difference between the two ideas.
On the other hand, there is some relationship between these two ideas and it is quite transparent. It's about the nesting ratio. Discrete is obviously a subset of continuous, all its infinity is contained in continuity, embedded in it. And the continuous at the same time is the external organizing for the discrete in terms of establishing and preserving in the discrete one and the same order. As a matter of fact, the ratio here is the same, as between integrity and its arbitrary parts. It is this relationship that ultimately manifested itself in physics. It manifested itself as the presence in physics of two descriptions of the world, two approximations, which complement each other, and none of which can claim to be a complete and exclusive description of the real world. This is a classic (relatively speaking, fundamentally continuous) and quantum descriptions of the world. The first is based on the idea of the world, about the universe as one, integral object. The second appeared later, as a result of realizing, that even with the integrity of the world, any our knowledge about it is knowledge only about its highlighted specific parts, commonly referred to as events.
It will be useful here to return to the discussion of the concept of a point and the hierarchy of concepts., related to the idea of continuity (integrity) with an increasing number of dimensions. In its development and search for its justification mathematics came to the situation, when it is based on turned out to be a set, sets of arbitrary elements, the only property of which is the property of their existence. Out of touch with the concept of time! Just a concept “there is”, wherever and whenever. And this concept is formalized under the name “element” or “point”. The concept of time is just formed on its basis., adding new properties to a set of such elements, organization of orderliness in it. Time is seen as a sequence of such elements (points), in which pairwise connections are established “earlier – later”. Causal relationships. It is the presence of cause-and-effect relationships between individual events that makes us combine all these events into integrity.. Ie. in continuity, continuum. Into a single universe.
With this approach, the set of events must be identified with a discrete set of points, nested in continuity, ensuring the inviolability of the connections between them. Thus, point idea, from which geometry also begins, gets a very clear image, unrelated to size (their absence). Concept “point” associated with the concept “event”. No other additional explanations required. Then, that most events, which we operate when describing the world are complex, divisible by other events, does not matter. Naturally, our descriptions of the world line up in a series of approximations. In every such approach, events, considered as further indivisible, associated with a mathematical concept, pure idea, “point” . These points, and other elements of the continuum (also points), designed to record connections between events, all together become the image of the world at this level, space-time. Another choice “indivisible” events — another image, other space-time, roughly describing the world.
When the experiment made us understand, that we are facing events, which cannot be further divided, with elementary events, we had to realize, that such a set of events can (and need!) describe not the only continuum that unites them, and the whole infinite set of continuities compatible with a given set of events. This is how quantum mechanics came to physics..
I want to emphasize, what questions like: “And what is the real world really, which of the possible continua?”, “Indeed, this continuum is one, or the world is all continua?” etc. don't make much sense. Peace, Universe, as a set of elementary events in a single copy. All events! In our past, present and future. No multiverse. The presence of causal relationships between events requires us to consider them nested in continuity. And that, that our description of this continuity is possible only in an infinite number of ways, this is already a property of not the world as such, but the limitations of our capabilities, as parts of this world.
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Your words “…Peace, Universe, as a set of elementary events in a single copy. All events! In our past, present and future. No multiverse …”
With your design, we are deprived of the Choice. And although he is very limited, but still there. Pity, but there is little space for communication, to turn the discussion. All Past and Future occur simultaneously in the NOW moment. This is exactly the same, as a two-dimensional sectional figure, three-dimensional cone, moving through the plane, there is a flat circle. And if you imagine, that this flat circle is a creature of a two-dimensional plane, that's it(creature) exists NOW, but the whole three-dimensional cone, like his past and future, also exists at the same time and NOW, as the object of the next dimension. Likewise, the sequence of discrete states of our body (or the universe), from birth to death, there is a body of the fourth dimension, which we call Time. Mother! talk to, not write. And it seems, it's so simple.
Sorry, but you are trapped in a very old and stable paradigm of containing space (and time too). For you “dimension” something external to the universe. For me “dimension” there is a result of the process, which I, or someone (or something, it doesn't matter) we use to build an image of the world. The number of measurements in this case is not more than the number of reference objects or phenomena, available in the same world, which I need, for, to make this description comprehensive (but even without that, to describe something more than once, ie. adequate to the world). The difference in views is huge. Nor time, no space as ideas divorced from the world, independent are not suitable for this. This is what I am writing about. And you about the sequence of states of the Universe… View articles “The universe as a whole” and “Evolution and static nature of the Universe”, it says about it.
Author
… “For you, a “dimension” is something external to the Universe”. I do not know from what you made such a conclusion. If in truth, then I try to talk about measurements in your language, where in the majority of measurements we mean the degree of freedom. In fact, by measurements I mean the level of development of Consciousness. And those people, who look into the past and predict reliably to some extent the future, have more developed (four-dimensional) Consciousness. In fact, with the help of Consciousness, they move along the fourth dimension of Time. You disagree?
The trouble is, that the words are the same, and the meaning is different in them. For me expressions, You are using, raise questions about every word you use. Take “…with the help of Consciousness, they move along the fourth dimension of Time…”
“Consciousness” — what's this? How does it allow “move”? “Move” == “change position, a place” (I must also indicate, what and how this provision is described). What is the relationship of the most complex concept “consciousness” to change place?
AND “time”, what's this? Road, along which something can move back and forth? So this is the idea of time as an INTEGRATING entity, to the world, events unrelated… From here I made my conclusion.
Developed consciousness is certainly a good thing.. Allows both your own and someone else's experience to be remembered (look into the past), and realize that a lot can be predicted practically from 100% reliability (predict the future). But it is not directly related to displacement. (sorry, displacement, associated with the satisfaction of the desires of consciousness, I don't want to drag in here).
Honestly, I do not want to continue the discussion in this direction. Your ideas, set out on your site, alien to me. Terminology (notice, in every article I try to clearly define the meanings of the words used) does not serve to clarify anything, and vice versa, substitutes other concepts for the words I use here. I am ready to try to clarify that meaning, which I put in them, if any of my statements seem to be incomprehensible or incorrect. In the latter case, of course, you need to argue your opinion. But I do not want to analyze the difference between your views and mine on this site..
Author
You cling to words. “…with the help of Consciousness they move along the fourth dimension of Time ... ". Well this is … clear, that displacement is understood as the ability to draw information about the past or future. Therefore, in this style of yours, of course it is useless to debate. But, this is your site and I leave you alone with your delusions.
Vladimir, Do you consider it more important, How to describe the world, than WHAT is he ?
Shakes, of course your ability to combine physical meaning and mathematics. I've read a lot on this subject of popular science ... and the best, seems to. But you – the most SCIENTIFIC thing I understand. Your idea about the field is very promising and broad.
I would like to know your opinion about, is there any direction in mathematics, Arrow ? Does a math object follow an arrow ? (Think, not). If not, then is it possible to set a condition for this Arrow to follow the main mathematical objects in your mathematical space? If yes, then maybe, try ? It would be something new, which is – development of consciousness.
I was very glad to be fluent (even so, because there is not enough knowledge in detail) familiarize yourself with your topic. Probably, You are a very smart person. thanks.
thanks for the comment.
What is the world? Everything, what can we say about him in “meaningful” form.
Ie. formulating statements about it based on well-tested examples from this very world.
And this is always a description of the world. Not more. But no less. Nothing else is available to us.
All our knowledge about the world is somehow reflected only in our languages (books, music, dancing, etc. etc.)…
Mathematics grows out of our experience of describing the world as adequately as possible to it. As far as we could.
This is a collection of ideas, generalization of our experience of existence in the world. And this is part of our language.
And it happens, incorrect or meaningless statements appear from time to time. But then from them
sooner or later get rid of.
Is there in mathematics “arrow”? I'm not very clear, what do you mean by that.
If we put into this concept the presence of a hierarchy of mathematical ideas, growing in the form
wood from a small number of basic ideas, as having a direction from simple ideas to complex
— that yes, there is. And this very thought
I tried to convey to the reader in the first volume of the book “Foundations of physics. Introductory chapters”.
Articles on the site say about it “On the foundations of mathematics” and “Hierarchy of concepts in geometry and physics”.
And little by little in others.
I do not know, have you read this book. If not, then read. In it, the questions raised on this site
set out, I think, much better. Just because, that this book has grown as a generalization and development
in a single statement of all articles presented here.
You deleted my comment. What did not suit ?
I have not deleted your comment. Just for some reason, all comment notifications of days 20 pour into spam,
but I didn't pay attention to it. Only today accidentally looked.
thanks.
For a detailed answer. I will try to read. To you, probably, hard to imagine, what is the real number of people, ready and able to assimilate at least the basic of the material you offer.
When I asked you about the Arrow, I meant a little different….but your proposal to interpret the Arrow in mathematics as a hierarchy of ideas, rather more productive.
More on the article – you have, I think, the last paragraph is very short. Therefore, the previous reader too, as I, tripped over him. I also want a bit of freedom of choice in this only world. )
Really, the last paragraph in this article is very short.
And its content to the main text of the article has only an indirect relationship.. As a seed for reading OTHER articles.
About freedom. Real and imaginary. As far as I understand, we are talking about the so-called “Free will”, “The freedom to choose your own destiny”.
The uniqueness of the universe as a set of related events by no one
does not deny this freedom. A look at the universe “outside”,
as the only universe, viewed as a single whole
not only is it not available to us otherwise, than an abstract IDEA, this look
we MUST also combine with the concept of EVOLUTION of each selected PART of this integrity. And in this sense, the awareness of unity for each part of her past, present and future, embedded in integrity does not contradict the awareness of evolution in the EXTERNAL FOR THE MOST SELECTED PART (in particular, human) WORLD.
Roughly my thought can be expressed as follows:
When looking at the life of any person “outside” as integrity (and this is quite accessible to us in relation to people ALREADY LIVING HIS LIFE)
we can state, that this whole life corresponds to THAT CHOICE,
which this person DOES IN THE PROCESS OF THIS LIFE. Well, and circumstances external to a person, of course. For some, his choice may seem more defining his life., than external circumstances. For some, circumstances were crucial, even
completely excluding for a given person the possibility of any “free will”…
However, in all cases, when life is lived from start to finish
it's no more (but not less) as a set of events in this life and the connections between them, as “inside a person”, so with “outside world”.
The question is logical — what place is left for “Free Will”?
There is enough space for this concept.…
Events, the components of our life are HUGE in the sense of breaking them down into elementary, further indivisible events. And so they and their connections
quite different concepts are reasonably put into correspondence, than an individual
elementary event. Yes, these new concepts arise as a hierarchy
based on the simplest (mathematics in this sense is only the MOST CLEAR
an example of organizing this kind of hierarchy). At a certain level of this hierarchy, concepts such as “life”, “behavior”, “act”,
“habit”, “character”, “fate”. “SOUL” eventually.
Where is "here “free choice”? I will answer with a Russian proverb:
Sow an act — you will reap the habit.
Sow a habit — reap character.
Sow character — reap fate.
And I will also offer this funny way to look at the time..
When looking from the outside at a person's life, already gone, we may well
unfold the arrow of time and reason like this:
Killed by an avalanche in the mountains. This could only happen if
for some reason this man got into the mountains. Ie. do “reverse selection” — among all the possibilities of fate who just came to the mountains.
etc. and so on.
The connections are binary, and in each pair you can change the cause and effect.
Until birth — to somehow live life you had to be born first… Death becomes the beginning, and the birth is the end of a chain of events called “life”.
Ie. when looking at the totality of events and their connections FROM OUTSIDE, as finished, dedicated PART OF THE ONE WORLD, considered as an integral part of space-time, the arrow of time for her may be
changed to the opposite without problems. Only our own life, the evolution of our society makes the choice unambiguous.
Say, we remember the past and do not know the future (his).
Is it so? Do we remember everything? Something yes, but something is not. And it happens,
which we cannot understand, was it that “remember” real or “fancy”…
Do not know the future? truth?
Tomorrow will be a new day and a new night. The earth will continue its way around
Suns, and the moon around the earth. This is EXACT knowledge, at least, for many thousands of years from “today”… Well such examples of exact knowledge,
What will happen, regardless of our choice whether, or in general existence, you can bring a set. All our CONSCIOUS part of life is based precisely on PREDICTION, CHOOSING A WISHED FUTURE.
This choice is based on the knowledge of possible connections in the chains of events..
Do it like this – will it. You will not do – it will be. there is, of course, also the outside world, who also makes his choice, including for us too.
After all, our “separateness” from the world is nothing more than an illusion… Very well grounded, but still an illusion.
thanks. Right, did not count on such a detailed answer.
Difficulty always arises when trying to demonstrate something in detail.. There is always a question – limit ourselves only to PHYSICAL realities, or attract something else, what is not material….but I always want to attract. But it is then that the need for hermetic comparisons arises.. And they – are always led to be shot …or, least, begging for him.
I will not say, that I figured out your position regarding freedom of choice. Understood so, that evaluating the whole process (how do you say – outside), we still appreciate the past. Then it all happened like this, how did it happen. And freedom of choice, you can say, Not anymore.
but, who is this Observer, which evaluates OUTSIDE ? If he is able to look OUTSIDE, probably he is not in any of the possible frames of reference of our world. It is unlikely that he distinguishes the past from the future.. Unfortunately, more clearly I cannot express some sucking concern from your answer. Sorry for the man, who is doomed to know something in advance for thousands of years.
And here's another question – why do you consider cause-effect to be a symmetric biner ?
In my opinion, this chain is directed along a certain arrow. Or by Meaning. An integral part of this meaning is novelty.. In principle, nothing is repeated.
thanks.
P.S. To know, honestly, I do not believe in the certainty of the Past. The further it is from me as an Observer, the more probabilistic aspects it has…
but, this is no longer a very physical topic. But you were the first to mention the Soul)).
You didn’t pay attention to that, that the case of considering the COMPLETED life of a person
(or not human, but any part of the world) ANOTHER person, continuing to live it
also look “outside”.
But it is not “outside” for the WHOLE UNIVERSE, which is impossible.
This description, one part of the world from the point of view of another part of the world. What is only possible.
Yes, this description is not accurate, in the sense of listing all events without exception
in “life” (completed) some highlighted part of the world. It will be approximate,
some set of KNOWN events. But this sequence will be a sequence
events with cause-effect relationships.
The arrow of time in this sequence, taken regardless of the observer's time arrow (another
human) may well be reversed. Yes, in relation to the history of creatures (ie. actually
to the concept “life”) this approach seems strange — because before you die you have to be born,
is not it? but, in descriptions at the level “events with links” not a clue “life”, not a clue “to be born”,
and other similar ones simply do not exist yet. Not defined. How concepts are not defined “soul”, “choice” etc..
And I am considering the FULL history of the highlighted part of the world, you are not considering ONLY THE PAST. You consider everything —
and the past, and the present and future of THIS SELECTED PART.
And what is in herself, in this story defines these concepts — “past”, “the present”, “future”? Only that, which event do you name “begining”, and which one “end”. YOU ASSIGN.
YOU will bring your arrow of time into this story…BUT she became the past
AS A COMPLETED WHOLE, as the chain of events you know. The past for YOU.
The arrow of time for the living is precisely determined at the level of these, complex concepts, type no. to be born”, “die”, “live”.
In the foundations of physics, the arrow of time is always determined at the most elementary level in two ways..
But it is obligatory for all chains of events at once. Chosen for one — Chosen for the WHOLE UNIVERSE.
Here the solution to such questions as the absence in the universe of symmetry between matter and antimatter,
and related to this issue.
The opposite choice is possible, but in fact does not change anything for the entire universe.
we, our life, the existence of our society by this existence and the concepts that describe it,
complex events, but made up of entangled simple chains CHOOSE one of two possible directions. We choose by our very existence as parts of a single world. By this we also define the arrow of time and at the lowest level. Elementary event level.
Probability and randomness are no longer concepts related to events and their connections.
And to the OPPORTUNITY TO EXACTLY DESCRIBE these very events and their connections. They are inevitable for a very simple reason. —
over any finite number of discrete events, smaller set of ALL events in the Universe,
the description of a LARGE set can only be a PART of the POSSIBLE descriptions. And in relation to
to continuity all the more. This is about the need to introduce the concept “probability”.
Accident necessarily arises then, when we have “a lot” events without specifying them,
as part of the exact number, and in terms of causal relationships between them.
I do not know, has my position become clearer for you?…
Yes. thanks. Your position has become clearer to me. You again bothered to give a very detailed answer.
And now I realized this is what :
1. Point history (object, areas) and its surroundings can be viewed by the Observer as a whole (in fact, determined) history. Although approximately. The arrow can be deployed. History can be described including. the language of mathematics.
2. Probability refers to the ability to describe an event. And not for the event. Since there are always more reasons for the event, how can this be taken into account.
3. The arrow is still chosen arbitrarily from two directions. Although a reservation is made, what for elementary events. And it's a matter of the choice of the researcher, the use of analytical tools.
Boom for “life in general” rather it is psychological and it is broader than physical concepts.
It seems to me, you can come to that, that only the Observer has freedom of choice. Every Observer, of course )). And a series of events in any, even in any small area – mathematical object, containing some guaranteed truth (because of “really was”) and “something else”.
And if this is even something like this, then the question arises. Our most advanced mathematical objects describe “ALL THIS MIXTURE” or just that, which is guaranteed to be true, and the rest is not determined in any way.
There is one more question “sideways”. And what is the PHYSICAL and not the mathematical meaning of probability ? But interesting is not that, what everyone says anyway, what do you think ? This also applies to the understanding of discrete, for that matter.
When you write your books and articles on this site, probably, You are pursuing a very important goal for you. Especially, taking into account the depth of penetration into the material. And she's not that, to do another tutorial.
Thanks again for the non-trivial and detailed answers.
Think, what book “Foundations of Physics - Introductory Chapters” could give more detailed answers to your
questions.
The development of science has already shown quite clearly, that many concepts, at a certain stage
introduced as basic, completely independent, may be (and should be!) rethought
as grown out of a set of completely different, “more fundamental”.
Example — temperature concept. Important, independent concept, characterizing
state of matter. And the concept is secondary, characterizing the distribution of small particles,
constituting this substance in terms of velocities.
Necessary only there and then, when there is no way to track these particles separately.
The particle has no temperature. There is simply no way to define such a property for it..
Many of these particles have it.
Why am I giving this example? We describe the world only roughly. But the most accurate description
in any approximation is achieved in terms of mathematics. Sometimes these are the same terms for different approximations., sometimes different. The larger the events in question, the more often new, generalizing concepts.
But this does not negate the need to keep the description in a reliable framework every time.. It's difficult,
very hard.
Where is that track, which will lead from the simplest concepts of physics to the concepts of psychology? She's not there yet.
But already there, at least in general terms, the path from physics to chemistry as no longer a separate science and,
Further, to biology. Will continue. And if you look at history as a description of a collection of events?
Why is she not a part of physics? And psychology will someday find a place in this hierarchy of dialects of language about properties
Of the world… Dialects, with their terms, their rules for the use of these terms in “phrases” statements
about the properties of the World.
This is what the physical meaning of probability is.? And he is different in different approximate descriptions of the world.
Different in different formulations of the question in the same approximation. Different.
But there is also something in common. This is always a way of describing that single, or somehow limited group, selected in the aggregate,
which is certainly wider than this group. As a share of taken into consideration (limited by something — conditions
experiment, circumstances, or someone's chosen conditions) description capabilities in relation to
to all other possibilities, which are also always somehow and somehow limited.
Purpose of my site… There are several.
To provide an opportunity for a wide range of interested persons to get acquainted with that picture of the World, which I formed for myself, working in physics.
It is possible to help someone in understanding the things that caused him problems.
It is possible to help someone separate myths from reality.
It is possible to see your own shortcomings in the presentation…
And there is also the displeasure of, that too much is poured out on the masses
half-truths and lies about the state of science…
Our world is discrete and only discrete. Continuity is called discrete continuity – the smallest changes in the world continuously replacing each other. More details on the website https://www.litres.ru/book/v-a-sarkisov/filosofiya-diskretnogo-mira-69275800/.