We would like to invite everyone to discuss the material that has been presented during virtual conference Computability in Europe (5-9 July 2021).

The entire slideshow (with large sections of text from our paper draft) is available HERE.

We decided to submit it for discussion, because we are now working on a new publication devoted to **analog/continuous computations**, and all additional critical input, and each additional discussion will be for us very precious.

Thus, we will be grateful for any comments that may contribute both: the improvement of our text (which still is in the reviewing process), and the **development of our new ideas**.

To encourage you to read the whole slideshow, we put two representative (text) passages below:

**Two basic (general) meanings of analogicity**

When talking about analog computing, i.e. a kind of non-standard computing, there are two different (yet not necessarily separate) ways of understanding analogicity.

The first meaning, we shall call it AN-C, refers to the concept of *continuity*. Its essence is the generalisation (broadening) of digital methods in order to make not only discrete (especially binary) but also continuous data processing possible. On a mathematical level, these data correspond to real numbers from a certain continuum (for example, an interval of a form [0,1]), yet on a physical level – certain continuous measurable variables (for example, voltage or electric potentials).

The second meaning, we shall call it AN-E, refers to the concept of *analogy*. It acknowledges that analog computations are based on natural analogies and consist in the realisation of natural processes which, in the light of defined natural theory (for example physical or biological), correspond to some mathematical operations. Metaphorically speaking, if we want to perform a mathematical operation with the use of a computational system, we should find in nature its *natural analogon*. It is assumed that such an analogon simply exists in nature and provides the high effectiveness of computations.

In a short comment to this distinction, we would like to add that the meaning of AN-E has, on the one hand, a historical character because the techniques, called *analog*, which consisted in the use of specific physical processes to specific computations, were applied mainly until the 1960s. On the other hand, it looks ahead to the future – towards computations of a new type that are more and more often called *natural* (for example, quantum or computations that use DNA).

The meaning of AN-C, by contrast, is more related to mathematical theories of data processing (the theoretical aspect of computations) than to their physical realisations.

The categories AN-C and AN-E are not disjoint, as there are empirical computations that consist in processing continuous quantities. As such, they are AN-E, but also fall into the AN-C category.

**Empirical justification of AN-E computations**

AN-E computations are closely related to the theories of *empirical* sciences (e.g., physics or biology). This means that specific computations of this type could neither be specified nor physically implemented without reference to a specific theory of this type.

Typically, such theories are treated as a tool for accurate *description* of physical reality in terms of mathematical structures and operations. Thus, their cognitive aspect is highlighted.

From the *computational *point of view (or more precisely: from the implementation one) they can be treated as a *basis for realizing* certain mathematical operations by means of physical processes described by these operations. With such an approach, a particular theory is treated as something that *justifies *the physical implementation of certain mathematical-algorithmic operations. It is therefore a justifying theory for a particular type of AN-E computation.

Once again, **we invite** everyone to discuss our slideshow — Paula Quinon & Paweł Stacewicz.

I was wondering if anyone is planning (or maby trying) to replace single element of biological neural Network (in Some simple organizm) to find if “cyborg” is acting like its “normal” counerparts?

That would be some test for nessety/ role of analogicity/continousity for performance of (biological) neural Network.

If raplaceing many of biological (AN-C) elements with some kind of digital parts won’t change behawior of (simple) organizm, it could be some argument against big role of AN-C in construction of mind (in more complex organizm).

If you replace in some creature one (or many) elements of neural network with neural cell body taken frome diferent species (achieveing proper funcioning “hybrid”) , would IT be an example of AN-C?

On the other hand – there were projects of mapping neural networks of simplests organizm – does anybody tried to cut off some “simple” fragment (few cells) and compare its funcioning under biological/ phisical input with digital model of such arragment – to see if continousity in potencial gradient on one neuron really makes diferent in outcome when changes in bigger network (of a few elements) so when learning and performing tasks is concerned?