ISBN
978-3-00-037458-6
ISBN 978-3-00-042153-2
Monograph of Dr. rer. nat. Andreas Heinrich Malczan
It may seem bold or even audacious to compare the brain and today's computer already here, but a comparison could promote understanding of the similarities and differences. A major component of computers is memory cells. Initially, four bits were combined into one memory cell. A short time later, that number doubled. The bit width of the memory cells became a quality feature. Thus inevitably came the 16-bit computer, then the 32-bit computer. At present, 64-bit machines are the big seller.
In computers, the (internally installed) memories are identical to each other and have the same bit width. Thus, each memory cell of a 64-bit memory consists of exactly 64 bits.
The brain is different. On the one hand, the neurons of the primary and secondary cortex are one-bit memory. On the other hand, the Purkinj groups of the cerebellum are multi-bit memories, where the bit width is large but partly variable. This simply depends on how many parallel fibres are fed by one moss fibre.
On the other hand, a stored signal, whether stored as a one-bit complex signal in a cortical complex cell or as a multi-bit signal in a Purkinj group, is not necessarily active yet. This is another difference between data in computers and in the brain. In computers, there is no division into active and passive memory cells.
We have discovered that the primary cortex is made up of clusters. So, if such a cluster has n signal neurons. If each of these signal neurons can assume the values actively or passively, 2n different combinations are possible. Let us assume (purely theoretically) that each combination would become the signal of a Purkinj group of the primary cerebellum by imprinting. In this case, the system of cortex and primary cerebellum would generate a mapping of a total of 2n different value combinations of n cortex neurons into a set of 2n Purkinj groups. A mapping of n-digit binary values to 2n-digit binary values also exists in computer circuits. These are the column and row decoders. Both are address decoders.
The input of an address decoder of bit width n is an n-digit dual number. The output is a dual number with 2n dual digits. But the output has a special feature: Only one binary digit equals 1, the others are zero. The latter is not quite true for the Cerebellum. Also "address lines" with similar addresses are excited. In the beginning this may have been a kind of failure reserve to compensate for the neuronal death of a Purkinje cell. Later, when several Purkinje cells were combined to form a Purkinje group, this objective receded into the background and the main task of this secondary excitation of similar addresses became the intelligence foundation within the associative matrices. The receptive neighbour inhibition prevents too many address lines from being active at the same time.
The Cerebellum can be interpreted as a special address decoder. The n-digit input from the cortex is converted into an address of 2n binary values by the Purkinje group whose digital signature best matches the input, whereby only its own axon line is active, while the others would have to be zero. But in contrast to a digital address decoder, not all other axon lines are signal-free. This is because it is precisely the intelligence-creating property of the associative matrix to provide an output even if the input signal is similar to the digital signature and the Purkinje group's own signal is not drowned out by the external signal of the input. Thus, not only the address line is activated whose digital signature corresponds to the input, but also that line whose digital signature is sufficiently similar to the input. We want to call such an address decoder an analog address decoder.
While the direct Cerebellum works as an analog address decoder, the inverse Cerebellum is the inverse circuit. Therefore the inverse Cerebellum is an analog address encoder.
Now it becomes understandable why the series connection of primary cortex, primary cerebellum, secondary cortex and inverse secondary cerebellum results in the original input again. It is also clear that this sequential execution does not correspond to the multiplication of associative matrix and inverse associative matrix. The term associative matrix was already part of the fixed language range before the author exposed the cerebellum as an analog address decoder. In mathematics, only quadratic matrices are invertible. Therefore, every mathematician had to have his hair up at times when he read that the consecutive execution of a rectangular associative matrix with its inverse would again provide the original input. This misunderstanding should now be considered cleared up. To be more precise, one could say that the series connection of an address decoder with an address encoder delivers the original address again. And this series connection does not fulfill the basic rules of multiplication, so that the inverse cannot be the inverse of the multiplication. May group theorists deal with this topic more precisely.
The cerebellar address decoder now addresses a huge number of memory cells, each of which has only one bit width of one bit. While in the real computer the memory cells are divided into rows and columns and there are usually as many rows as columns, which is why a column decoder and a row decoder are needed, the cerebellum does not work with two dimensions, but only with one. So there is (per cortex cluster) only one column, but 2n rows. (Interpreted the other way round, it would also be correct: Only one row, but 2n columns).
However, this serious difference is quickly put into perspective when one considers that there is a huge number of cortex clusters that could theoretically be numbered. Then one would have a column number again, which would be equal to the cluster number. In this memory system, the cortex would quasi send the addresses as input to the cerebellum clusters.
An essential difference between the digital address decoder of computers and the cerebellar, analog address decoder is that the latter does not require its own circuitry. Each Purkinje group carries - finely hidden - the ability to independently determine from the input whether the n-digit cortical input signal applied to it sufficiently matches its digital signature, which is interpreted as an address. If this is the case, it activates its output line, which is a write line to a memory cell in the secondary cortex, and activates this cell. So in the Cerebellum, no programmer has to think seriously about where - i.e. at what address - he wants to store any binary data. The Cerebellum extracts the address automatically from the current input of the data. This ingenious solution is the reason why we cannot find a processor in the brain. The basic skills of a processor are integrated in the brain in each participating cell, whereby different neuronal cell types realize different subcircuits. Therefore, the system remains operable if its parts fail individually. Or it repairs itself by transforming proneurons into neurons of the required type.
And in the brain the difference between data and addresses is lost. The digital signature is the address. The data of the primary cortex are in the cerebellum the addresses of their locations in the secondary cortex. Analogous to the data of the secondary cortex, the secondary, inverse Cerebellum provides the addresses of the data in the primary cortex. The sequential connection of the direct and the inverse system enables the development of consciousness and thinking via signal oscillation, as will be shown later.
A simple example should clarify that the content of a memory cell can be used as an address. We consider the multiplication of natural numbers with exemplary 3 decimal digits. There are 999 such numbers. From them 999999 different products can be formed. If, for example, the product 369 * 472 = 174168 is stored in the memory cell with the number 369472, the address of the result is obtained by writing the two three-digit numbers one after the other, if necessary with leading zeros as in the case of 10 * 19 = 190, whereby the value 190 must be stored in the address 010019. Once each product has been stored, the answer to the question "How much is x * y?" can be determined by looking up the corresponding address with the number x * 1000 + y. Any (sequential) search is then no longer necessary. With binary notation, there is even no multiplication, because both factors are simply arranged one after the other in the dual representation.
It should be pointed out that not all possible complex signals are present in the cerebellum, but only real ones. Therefore the address decoder will have many address gaps. Later we will see that only selected signal combinations of mostly very few neurons - measured by the total number of signal neurons in the cortex cluster - are used to form complex signals. In this case, we speak of associative matrices with sparse coding, which contain a great many zeros. This is especially true for the primary cortex, as will be shown later in parts 3 and 4 of this monograph.
The exciting question now is which digital output is formed in the cortex from the analog signals of the receptors. And above all how this happens. Only the answer to this question will allow us to understand what modern computers cannot yet do. The reader will have to be patient here, because these answers are planned in the planned Part 3 and Part 4 of this monograph, which will be started in autumn 2012 at the earliest.
Since the term associative matrix has long been established in neurology and in the theory of neural networks, the author will continue to use this term, even though the associative matrix (according to his untested theory) is an address decoder. Likewise, the term inverse associative matrix will continue to be used for the inverse cerebellum, even if it does not refer to the inverse of matrix multiplication. It is only important that the successive execution of both results in the original input. Perhaps a separate language will emerge on this topic.
ISBN
978-3-00-037458-6
ISBN 978-3-00-042153-2
Monografie von Dr. rer. nat. Andreas Heinrich Malczan