Physical world and mental space ​

As easy to see from the examples in the previous sections, the closer the concept (idea) is to physical reality, the easier it is to find objects embodying it, and the denser its conceptual space.

In the previous section, we discussed that physical objects (individuals) are a very simple thing. They are something that can be touched, heard, smelled, measured (at least theoretically), that is, perceived by our senses or instruments. They have extent in space and time, spatial and temporal boundaries. Pay attention to "time" here: these objects are not simply given to us, they exist in time, and this existence has a beginning and an end! In the future, we will learn to differentiate between physically quite complex objects, sometimes unexpected, counterintuitive, that is, those whose existence is more contradictory to our "everyday" intuition.

All the other objects distinguished by our thoughts in the world were called "categories" in the previous section, and in this one we discussed their close connection with "ideas, concepts". We cannot touch them and register them in the physical world. They arise as our thoughts, exist only in our heads. For terminological unity, we will sometimes call all non-physical objects "objects of mental space". These are abstractions above physical objects, conceptualizing a wide variety of things.

Signs expressing ideas are also material, they exist in the physical world. Thinking about objects of mental space is a very material computation that physically occurs in our brains or in our computers. Signs can be extracted from the head, recorded, processed, then signs can be read, and thus the corresponding ideas (concepts) can be loaded into a person's head.

How not to get confused? Ask yourself what exactly you mean when you think about "this". Try to imagine "this" in the current context of your reasoning and ask yourself with which objects your object can interact. Then imagine this interaction. If your object interacts with other physical objects through its physical parts, then it is physical. If it interacts as an idea, by influencing thinking, it is an object of mental space (but do not forget that it is the idea that influences thinking, but any idea is presented as a sign!).

Suppose you are planning a "strategy presentation" for management. What concerns you now?

If you are worried about whether the flash drive will be readable, or the compatibility of the presentation format with the equipment, whether animated pictures and videos inserted into the slides will be displayed correctly - you are concerned about the presentation as a physical object, a file on a specific flash drive.

If you are concerned about the reaction to new ideas, if you are choosing the right ways to convey them to the managers even before you started choosing specific pictures and video clips (signs) - you are working in the mental space.

The main skills that should be formed in you as a result of mastering the material of this section are:

• distinguishing objects from ideas, concepts (while distinguishing physical objects from categories was taught in the previous section, and abstract categories from ideas were agreed not to distinguish);
• finding or tracing connections between physical objects and the ideas they embody;
• analyzing signs, names (especially poorly chosen ones) to determine what they refer to - an object or an idea, and also determining the mechanisms of this reference (references).

Let's discuss a number of examples again (some of them we have already discussed).

1. A specific table and "table" as a concept

Imagine the table you are sitting at right now. And now imagine the table in general, the abstract concept of a table.

The table you are sitting at can be touched; it exists in space and time; takes up space, has extent; it started to exist at some point (was created) and will end (collapse, become unable to perform table functions).

The "table" as a concept does not exist in the physical world. This is conceptualization, a generalized image that will appear in your head when you hear "table". The "table" as a concept emerged (was distinguished from the background) to refer to a generalized category of objects when there is no need or possibility to identify a specific table.

2. Conversation between me and you and "conversation in general," as a phenomenon

A conversation between me and you exists in the physical world, in reality (not right now, but it could have taken place in the past and can be easily imagined in the future). When it occurs in reality, it involves: me, you, and the air between us, through which sound waves travel. This conversation has a beginning and an end in time.

The "conversation in general," as a phenomenon, exists as a concept in the mental space, it is a generalized image, a description of a wide range of situations. The "idea of a conversation" never happens at any moment, in any place, this idea has no participants. When we talk about a "conversation in general," we imagine a set of the most characteristic features of a conversation - several interlocutors communicating verbally. But we cannot say whether sound waves are transmitted only through the air in the "conversation in general" or whether it involves a microphone and speaker of a phone, as well as computers, cables, antennas, and radio waves transmitting voice between phones.

3. Justice

You can always imagine specific physical embodiments of the idea of justice. These are situations in which justice is served, those situations where you will say, "yes, this is fair".

Children quarreled over a toy — you found a fair solution by giving one the toy and giving the other something else.

There is a well-known meme illustrating the phenomena of "justice" and "equality" easily understood situations in the physical world:

The word (sign) "justice" names situations from this set of situations of a fair state of affairs, each of which is tangible, audible, and finite. The concept of "justice" refers to a set of sensations or experiences common to all such situations.

Here, we started not from a specific example in physical reality, but from the concept, which exists precisely in mental space, and tried to imagine its embodiments in the real world. In principle, we succeeded in this as well as for the "table". But there are several important differences.

The density of the conceptual space for "justice" is lower than the density of the conceptual space for "table". In other words, for "justice," people can envision many more completely different situations, much more than the most advanced furniture designer can imagine different tables.

And among these situations, there will definitely be those about which someone (in the context of their culture, origin, education) will loudly cry out: "This is an outrageous injustice, some kind of shame!" You can easily come up with examples yourself. And there will be much more such protests than dissatisfied with fanciful design fantasies sold under the label "table".

4. Mathematical and physical objects

Abstract mathematical objects (number, line, set, derivative, and so on) obviously are objects of mental space. However, understanding why this is so, whether they are ideas or categories, how to correctly find their concrete physical embodiments (extensional) - requires real knowledge of the corresponding branches of mathematics, as well as the history of sciences. But for some objects, information about possible paths to find embodiments of these concepts is given even at an elementary level when these concepts are first introduced in school.

Let's be honest - philosophical discussions about the "reality" of mathematics do not cease. There are disputes about the type of science mathematics belongs to. Constructive and axiomatic approaches, infinity problems - all these fascinating questions we leave beyond the scope of our course.

Physicists are proud that the most abstract objects in the mental space of their science were created solely for the purpose of modeling reality, thus physics maintains strong ties with reality, which is even called "physical". Unfortunately, philosophical disputes also go on on this topic.

We will consider that mathematics and physics (fundamental transdisciplinary intellect stack used in the courses of SHSM) operate with objects of mental space, and their grounding in the real world occurs within the framework of ontology, logic, study/knowledge/research - other fundamental transdisciplinary disciplines of the intellect stack.