Models Lacking Mathematics tend to be Fragile
Glorification of Mathematics results in Neglect of Attention
Attention’s Mathematical System = Data Stream Dynamics
Matter operates in Linear Time; Attention in Spatial Time
The initial papers in this Notebook identified what we deemed as insurmountable gaps in the Chemical Model for both Life and its origin. For example, cells, the undisputed building blocks of all life forms, are a holistic system, i.e. the meaning of the parts is only determined by their relationship to whole. A sense of time is necessary to form a holistic system. Chemical reactions don’t have the requisite sense of time.
To fill this gap and others, we proposed a model. According to our model, Attention’s information digestion process provides the temporal sense that is necessary for Life’s holistic system. While our reasoning is sound, there have been innumerable well-argued theories that address similar issues. Yet none of these models have found wide-spread acceptance.
Why were these eloquent expositions too fragile to survive the vicissitudes of time? Could it be because they lacked a mathematical foundation?
In the attempt to fill this gap, this article presents a cursory examination of the mathematics of Attention. This unique mathematical system operates in a unique dimension of time which belongs to a unique realm of existence – Attention’s Realm of Experience. According to our model, Life exists at intersection of the Realm of Matter and the Realm of Attention1.
Before proceeding forth, let’s summarize our position with some algebraic-like statements. Biologists are generally committed to a chemical, hence exclusively material, explanation for Life. They believe that material systems on the early Earth became ever more complex. Emergent properties were associated with this growing complexity. The eventual result was Life.
Life = Emergent Feature of Matter’s Growing Complexity?
Under this perspective, Life is a merely a function of matter; nothing else: No hidden ingredients.
Life = ƒ (Matter)?
(The question marks at the end of the equations indicates a certain amount of uncertainty.)
However, all life forms from the single-celled bacteria to multi-cellular humans, have an intentional relationship with information that enables survival as a unit. An essential feature of this intentional relationship is the ability to sense, observe, monitor and then adjust to the environment. Following convention, let us employ the term ‘Attention’ for this entire intentional relationship, not just sensing.
Attention’s interactive quality is observable on an almost minute to minute level with many life forms. Amoeba approaching nutritious environments and avoiding toxic ones. Sunflowers turning to face the sun. Chickens hunting and pecking for food pellets. Me deciding what word to use.
While Life possesses the ability to monitor (Attention) and adjust (Intention) to an ever-changing environment, Matter does not have this same ability. Matter reacts to environmental information, but does not interact. Not possessing this ability, Attention is not a function of Matter.
Attention ≠ ƒ(Matter)
However living systems have both a material basis and an intentional relationship with information. Therefore Life is a function of both Matter and Attention
Therefore, Life = ƒ (Matter, Attention)
It is a common understanding from the average person to brilliant scientists that humans and indeed all life forms possess Attention. Attention enables us to first monitor our environment through our senses and then make deliberate movements to adjust to immediate conditions. Why do the material scientists ignore this crucial ability or subordinate it to mechanistic chemical processes?
The previous paper dealt with one psycho-cultural reasons for this scientific blind spot – the scientific stigma associated with vitalism. While there are many others, these motivations don’t interest us here. Eloquent books have been written on this topic. Yet the scientific materialist dogma remains and even becomes stronger with each new AI machine.
Let us suggest another relevant reason. Life’s non-material, information-based component has up to this point yet to have a mathematical system of her own. Having your own Math lends incredible prestige in the scientific community. Indeed many material scientists along with their philosophers hold the belief that if a field of inquiry cannot be described by a mathematical system, it is not worth studying - not even considering the discipline a science.
This glorification of mathematics has an illustrious history. Starting perhaps with the influential Pythagorean school in ancient Greece, Galileo revived this worship of precise numerical relationships a few thousand years later in Renaissance Italy. Rather than inference or circumstantial evidence, direct quotations reveal the esteem held for mathematics.
“The Laws of Nature are but the mathematical thoughts of God.” Euclid (circa 300 BCE), the Greek who founded geometry with his influential book, The Elements.
Indicating his reverence, Galileo stated, ”Mathematics is the language with which God has created the Universe.”
Since Galileo, an unbroken chain of illustrious scientist mathematicians has shared this awe and reverence for mathematical clarity. In modern times, both Albert Einstein, the founder of relativity theory, and Paul Dirac, the founder of quantum electro-dynamics, have reiterated the same theme, even elevating mathematics to a divine level.
From Dirac: “If there is a God, he is a great mathematician and he used very advanced mathematics in creating the Universe.”
Why doesn’t Attention have a mathematical system? Even though Attention related behavior is observable, heretofore it has not been quantifiable. This is a fatal flaw for radical empiricists. Unquantifiable phenomena are not subject to mathematical rigor – the god of material science. If a phenomena can’t be quantified, it does not exist.
Interestingly, while precise mathematical formulations are able to describe material interactions with great precision, they have been impotent before living behavior. Rather than admit that a different type of mathematical system might be needed, scientists have conveniently, perhaps lazily, attempted to apply material mathematics to living systems. This futile attempt to fit Matter’s square peg into Life’s round hole has led to ignoring the immaterial features of Attention, for instance our intentional relationship with information.
However, this liability has been addressed. Attention has its own mathematical system – Data Stream Dynamics. The system is the mathematical realization of Attention’s image overlay process (IOP). Living systems employ the image overlay process to digest information, i.e. transform environmental data streams into a useful form2.
What do these data streams consist of? On the cellular level, the receptor-effector proteins in the cell’s membrane (IMPs) fire in response to environmental images that match their precise configuration. In such a way, IMPs provide Attention with data streams of 1s and 0s, or their biological equivalent. These IMP-generated cellular data streams are the building blocks of all the sophisticated data streams that occur in multi-cellular systems, like us (at least, according to our model.)
On or off, these data streams are binary, hence quantized3. These data streams also have built-in identity, i.e. the image of the IMP that is firing. Just like the data streams, these IMP-derived images are the building blocks of all the images that living systems employ to organize reality. For instance, the image of our mother is constructed from the firings of billions upon billions of IMPs in response to image matching (protein with environmental input).
In addition to data streams and images, IMPs also provide the building blocks of our sophisticated sensory-motor network. Receptor IMPs sense the environment (matching images) and then effector IMPs react to this sensory input. Deriving from the cell’s sensory-motor apparatus, we see an apple and then grasp and eat it, if we are hungry.
Attention is required to conduct this symphony of stimulus-response to transform mere notes into the living music of monitor and adjust. Accompanying Attention is the temporal sense that is requisite for transforming Matter’s atomistic systems into Life’s holistic systems. This temporal sense is also associated with and necessary for a sense of self and other. This sense of identity is required for mere survival.
This cellular identity is also associated with Conscious Awareness. As such, the Cell’s capacity for Attention provides the building blocks for our sense of Self – Consciousness etc. The Attention of cellular groups join together to form the Attention of multi-cellular organisms, e.g. our Consciousness. Similarly, the Attention of multi-cellular life forms join together to form dis-embodied organisms, such as flocks, packs, tribes and countries.
As the building blocks of data streams (analytics), images (mental constructs), our sensory-motor network, and Consciousness itself, this IMP-Attention network is very important indeed. It is easy to see why IMPs are more closely related to cellular intelligence than is the nucleus with its DNA. Without genetic instructions, we might become hopelessly lost and die eventually. But without the ability to sense and react (monitor and adjust), every living system is dead in the water.
Due to the crucial importance of IMPs as the cell’s sensory-motor apparatus, Attention aligns with the rhythmic firings of the tens of thousands of proteins found embedded in every cellular membrane. Only able to attend to one data stream (or more likely one composite data stream) at a time, Attention is either on or off regards any data stream. This capacity for Attention can be quantified as a 1 or 0. Just as the IMP data streams are quantified and quantized as 1s and 0s, so is Attention4. Data Stream Dynamics operates on these binary data streams to determine the natural rhythms of Attention.
Besides being quantified and quantized, Attention exists in its own dimension of time5 – the Spiral/Circular time of Experience. This temporal dimension is orthogonal (perpendicular) to the usual material dimension of time. Life exists in spatial time – the interaction of material time with experiential time.
Our clocks and bodies are locked into Matter’s ‘horizontal’ time zone. This zone is objective, moves obsessively forward, is singular and complete. It is the time of Calculus, the ultimate mathematical system of Matter.
In contrast, our experiences only exist in the ‘vertical’ time zone. This zone is subjective, repetitive, partial and requires memory, hence a sense of time and Attention. It is the temporal dimension of Data Stream Dynamics, the mathematical system of Attention.
For Attention to even exist, she had to raise her head above Matter’s flat realm to begin to perceive patterns, such as those generated by the interaction of space and time. Attention’s out-of-the-body Experience generated a new dimension of time – by logical necessity6. However Attention’s temporal dimension is not independent of Matter’s time zone, but rather intimately linked.
Together, due to the magic of Attention, the two temporal dimensions generate a spatial time. Those locked in Matter’s flat time plane can’t even conceive of the spatial time generated by the interaction of the two. But this spatial time zone is the one in which we experience both living and dying. Less poetically, we can only experience things (events, objects, etc.) in spatial time.
Both Matter and Attention have their own mathematical systems and time zone which interact to define their own Realms of Existence. The objective, inexorable and complete horizontal time zone of molecules and objects is associated with Calculus, the mathematics of Matter. Together, they define the laws of the Molecular Realm of Matter.
The subjective, contextual and partial vertical time zone of Experience is associated with Data Stream Dynamics, the mathematics of Attention. Data Stream Dynamics applied to the vertical time zone reveals the patterns of Attention’s own Realm of Experience.
Indeed Attention applied to Matter yields Experience. As such, Attention requires Matter to have an Experience. In reverse, Matter requires Attention to be Experienced. In such a way are the two Realms of Existence mutually interdependent.
(Attention -> Matter) -> Experience
Matter requires Attention to be Experienced
This mutual interdependence is an indication that the parts belong to a holistic system, where the meaning of the parts is not innate, but is rather determined in relation to the whole. In this case, the interaction of subjective Attention and objective Matter define our Universe.
Cells, hence all living systems, are also holistic systems. Is this parallel similarity between the holistic systems of Life and the Universe just random? Or does it instead have some greater meaning?
We have talked about Attention as a singular entity. Yet it has many features, e.g. a temporal sense. Functionally, Attention is a synergy. The Synergy includes attention, intention, feelings and mind as an executive function. This Synergy has been hiding in another dimension and realm of existence ever since Life’s origins. Could this be why scientific geniuses haven’t invested their own Attention in this omnipresent feature of existence?
1 This topic is developed and dealt with in more detail in Notebook 40: ‘The Realm of Attention’.’
2 For more detail, check out Notebook #48:1, Intro: Life’s Information Digestion System.
3 While these so-called Raw Data Streams (IMP-generated) are binary, hence quantized, the more useful (digested) Derivate Data Streams are fractional, hence rational.
4 There is experimental support for this thesis. Researchers in France have done experiments that have conclusively exhibited that Attention is not continuous, as in flow of Consciousness. Rather their extensive work has clearly demonstrated that Attention comes in discrete pulses at the level of micro seconds (thousandths of a second.)
5 This topic is developed and dealt with in more detail in Notebook 51:2 ‘Time’s Two Dimensions’.
6 We suggest that this ‘miracle’ was not the result of the emergent properties of self-organizing Matter, but rather due to the Universe infusing the early Earth’s molecules with Attention. More in our next article #50:6, ‘The Providence Model of Life’s Origin’