# Ancient Science: Derivatives and integrals of realtime data

This blog is mostly devoted to researching about the truth and how that truth or Brahman as it is called in ancient Sanskrit literature becomes this reality around us. But, I am sure you have noticed that this blog title reads more like mathematics in data analytics. Why is this so? As I have written in the blog “Data accumulation based systems vs logic based systems“, reality around us can be seen as “data-based systems” that forms paths in the raw unmanifested data and progresses because of various reasons. This path then comes into existence as “individual beings” in the reality around us. So, naturally the first question that comes to mind is “How does that raw, unordered data start to attain order and a path and how does that path attain an awareness and progress or extend?” So, what does derivatives have any implication on this question?

To understand this we need to understand derivatives from a different perspective. We are all taught derivatives in school as dx/dy where we compute what the change in ‘x’ is when ‘y’ changes by a delta dy. So, given we observed the subsequent values of x as {x1, x2) when the values of y were (y1, y2), then we say dx/dy is (x2-x1)/(y2-y1). This is when we look at x and y as numbers or any mathematical concepts such as functions. What if we do not have a mathematical representation for change? Does this imply that, there can be no relation between changes of the two concepts? Let’s take for example the change in wind blowing and the movement of the trees. Is there no relation between the changes of the wind and the tree’s swaying? Practicality says otherwise. Sure, we can try to model these two behaviours as mathematical functions and then compute the relation. But representing these as regular mathematical functions and hence computing a direct derivative of the representative functions to understand the relation is practically impossible given the irregularity in their motion. Such scenarios, in our current state of definition of mathematics is computed using derivatives on small approximated polynomials that are integrated to arrive at a solution. i.e., we need to compute deltas for very small changes in time for the wind and the swaying of the tree (this is the limits mathematics) and then integrate the relation between these individual changes to understand the relation. What needs to be understood here is that relations computed in this manner is best an “approximation” and not the exact. Trying to compute in this manner in real time takes up a lot of processing. Hence we keep getting stuck with trying to get more and more compute and yet not be able to get the continuity that is present in nature. Yet, when we look at ourselves, we can usually predict the relation between the two and move away from swaying trees and falling branches to prevent catastrophe and I am pretty sure we work at a much lower speed than any computer we have. So how do we do it?

If we go by the fact that our brains are modelling reality and in real time computing various parameters even though our brains work at a much lower speeds than any computer, then it is time we asked ourselves what is the difference between what we have represented in the external mathematical language and the internal representation, that the external representation is very complex to compute while the internal representation compute works very fast at lower speeds. So, rather than look at nature in this manner i.e., as mathematical functions, how else can we look at it to make this better for real time computation and better for computation of irregular behaviour that is usually found in the real world. As I have indicated “Modelling reality with dhyanam“, we do not need to compute accurate values to perform everyday actions. We typically work with approximations and yet do it with much better accuracy than computers that have the ability for highly accurate computations. The best example of this can be found in the actions such as driving, walking, running etc. None of these types of actions can be smoothly done by any of the robots created by us. I believe “fast optimal derivative computation” is primarily the reason we can easily compute the approximation and is the basis of most of our actions and existence. This is done not based on the way we have it in mathematics but as a function expressed by accumulation and precipitation of data.

As I have explained in many of my blogs and books, what we put out as science and mathematics is just an external communicable representation of “what we know internally in a format we understand these things internally”, albeit a very faded version of it. Hence it should follow that even derivatives and integrals are just external representation for something that we inherently automatically do and render. It is just that we have not realised it consciously as to how we do it. When we see the cooking shows, one of the concepts that they have is called “deconstructed dish” where the individual components are laid out separately instead of assembled together. We can view the way we compute derivatives within ourselves in a similar manner. The mathematical formulas are a representation of the derivative as some function of variables, where as we compute it as the data that would be generated from those functions directly and leave it at that instead of creating functions out of that data.

So, how do we compute and view derivatives different from a function. This can be understood when we look at my explanation for “Mina rashi“. To understand this, let’s take a very simple example of road degradation as vehicles are driven on them. All of us have had the unfortunate experience of driving on roads in which ruts, that have formed because of the regular driving of heavy vehicles on the same paths on the roads. Similar to the below:

We all know that these are formed by the gradual accumulation of the wearing of road surfaces by the force exerted by vehicles travelling on the road. I am sure a lot of functions and theorems exist to model this wear and tear so that it can be compensated in design of the roads. Yet we do not succeed in completely eliminating the problem. So, what does this have to do with derivatives. This gives the integral output of small changes over time on the road surface. This may not be represented by regular mathematical functions in paper or representation by determinate variables such as x and y that can be used to compute changes, but however this is a prefect representation in the form of accumulated individual data points rendered in reality that shows the changes w.r.t time. If we had taken photos of this over regular intervals and created a time-lapse gif from it, it would have given the derivative function represented as pictures rather than a well-defined mathematical function. Something similar to this is how we compute changes and derivatives in real life. Derivatives and integrals as an accumulation of data point changes. In fact we should ask ourselves what makes us think that the “road does not know about changes and derivatives”? After all it has perfectly rendered the changes, just not in the mathematical form that we consider as intelligence, but in a completely different representation as pure data which is more apt rather than the approximated function? But, does that make it right or wrong or intelligent or non-intelligent? Note, I have called it “knowledge or knowing” rather than “intelligence”. “Knowledge is completely different from intelligence”. “knowledge is knowing what is present” and intelligence is describing knowledge.

What we need to realise is that there is a vast expanse of raw data that is varying across the expanse in various properties and this is the indeterminate Brahman. How can related data (in whatever property) from this expanse be picked up, a movement simulated, knowledge and subsequently intelligence created in it? We need to accept that our intelligence is created because of the knowledge contained in that vast expanse of data rather than that raw data being created because of our intelligence!!! It should further be realised that intelligence is really required only because of limitations in knowing all the knowledge that is contained in that raw data. Had we had the capability to know without actually having to extrapolate the knowledge we have to apply to other situations that we do not know, we would not have had the need to create descriptions and intelligence. We would just have sensed and known them. But, given this limitation in knowing and knowledge, we extend using intelligence.

What is even more important to understand is that inspite of our intelligence, and inspite of the actions that we perform, it is based on the accumulation of changes that reality is progressing further not because of our intelligent actions. That is the shift in knowledge that is required to understand this correctly. Our actions and intelligence can be increment or decrement to these accumulations, but it is only via such accumulations and precipitations that progress is got. So, how are these accumulation of changes got? This is the integral of derivatives computation that we have inherent in the working of reality.

So, how does this raw data organise itself into selves and hence individuals? This is where the concept of Mahadeva and Shakti arises. When we read many interpretations of the Sanskrit literature we find that the “concept of Shakti and Mahadeva” is always separated and explained as if they are different. I find that this is the first and foremost concept that needs to be understood and has to be understood in unison and should not be separated. One cannot exist without the other. Shakti basically means capability. Capability cannot exist without a subject that has the capability and this is where the Mahadeva comes into picture. Maha-deva translated literally is “prime energy”.

Energy as I have described in the book “Surya Siddanta: Emergence of empirical reality” is truly the underlying potential for variance in the vast inactive raw data. What this means is, if we take a specific instant region in the raw data. Further if there is present an ability to read the data at the next instant region to that specific region, is there a potential for these two to be different or is there a change between these two data values? To take even further, we try to ask, “is there a potential for the change to be a particular type of change and does this change have a sequential continuity as I keep going further down that given path”? That “specific type of change” then becomes the “prime energy” or “Mahadeva”. Shakti is then the capability of detecting that specific change in that vast raw data that forms the Mahadeva and be able to observe it. And hence arises the concept of the “self observing itself”. The Shakti of the Mahadeva observing itself to exist.

If that observation by the Shakti of the Mahadeva starts persisting or starts having what is called “smara”, then we are looking at a situation where we keep overlaying one change over by the next change similar to the road example we have above. Thus, at any point if we are able to observe the whole rather than just the changes we have detected as data-set what is in mathematical terms represented by “integral of derivatives”, represented in an accumulated form of data. This now takes on a knowledge such as “the change represented by the data-set is a spike” or “the change represented by the data-set is a regular change” and so on. This is “jnanam or knowledge”. Again to be noticed here that the reason this knowledge can be concluded is because at some point we have limited and translated the data-set, but the data-set by itself is continuous, albeit with a gap. Hence, it is said in the Sanskrit literature that the reason for knowledge to exist is because “a gap is detected” rather than “continuity being detected”. Thus the subsequent “jnanam” obtained becomes para jnanam or the remote knowledge. Thus we get the jnanam and para jnanam by the concept of integral of derivatives of the raw data which is present in the Brahman which then goes on to accumulate further and attain a rendering to form this real world around us.