I have looked at data base management and applications, data-sets and their use in different contexts. I have looked at digital in general, and I have noticed that there seems to be a single split:
-binary computers, performing number crunching (basically), and behind this you find the Machine Learning, ML, DL, RL, etc at the root fo the current AI
-quantum computing, still with numbers as key objects, with added probability distributions, randomisation, etc. This deviates from deterministic binary computing but only to a certain extent.
Then, WHAT ABOUT computing "DIRECTLY ON SETS", instead of "speaking of sets" and actually only "extracting vectors of numbers from them"? We can program and operate with non-numerical objects, old languages like LISP and LELISP, where the basic objects are lists of characters of any length and shape have done just that decades ago.
So, to every desktop user of spreadsheets (the degree-zero of data-set analytics) I am saying: you work with matrices, the mathematical name of tables of numbers, you know about data-sets, and about analytics. Why would not YOU put the two together: sets are flexible. Sets are sometimes are incorrectly named "bags" because it sounds fashionable (but bags have holes, they may be of plastic, not reusable, sets are more sustainable, math is clean -joking). It's cool to speak of "bags of words", I don't do that. Sets, why? Sets handle heterogeineity, and they can be formed with anything you need them to contain, in the same way a vehicle can carry people, dogs, potatoes, water, diamonds, paper, sand, computers. Matrices? Matrices nicely "vector-multiply", and are efficient in any area of work, from engineering to accounting to any science or humanities domain. They can be simplified in many cases (eigenvector, eigenvalue, along some geometric directions operations get simple, sometimes the change of reference vectors gives a diagonal matrix with zeros everywhere except on the diagonal, by a simple change of coordinates (geometric transformation).
HOW DO WE DO THAT IN PRACTICE? Compute on SETS NOT ON NUMBERS? One can imagine the huge efficiencies gained in some domains, potentially (new: yet to be explored, maybe BY YOU? IN YOUR AREA). Here is the math, simple, it combines knowledge of 11 years old (basic set theory) and knowledge of 15 years old (basic matrix theory). SEE FOR YOURSELF ,and please POST YOUR VIEW on where and how to apply...
Preprint Matrices of Sets -Structures & Properties
Am in line with Aparna Sathya Murthy There are different levels of computing or computational methods.Number crunching is helpful for and used in any industry. Data crunching commonly involves stripping out unwanted information and formatting, as well as cleaning and restructuring the data. Analyzing large amounts of information can be invaluable for decision-making, but companies often underestimate the amount of effort required to transform data into a form that can be analyzed. Even accounting is much more than number crunching.
Computers are like humans - they do everything except think.
John von Neumann
You've raised a fascinating point about the nature and potential of computing. Indeed, computation is not merely about "number crunching" but can be a broader concept involving various types of data structures, including sets, lists, trees, graphs, and more.
In traditional digital computing, we do often work with numbers (or data that can be represented as numbers), but there's an extensive body of work in symbolic computation, which focuses on manipulating symbols rather than numbers. Languages like Lisp, as you mentioned, are well suited to this kind of computation. They have been extensively used in fields like artificial intelligence for tasks such as symbolic reasoning and natural language processing.
In modern computing, one significant application of set-oriented computation is in database management systems. These systems are designed to handle sets of records efficiently, and SQL, the standard language for interacting with databases, is based on the principles of set theory.
It's also interesting to note that machine learning, while often numerical in nature, does have aspects of set-oriented computation. For example, decision trees can be seen as operating on sets of instances, dividing them into subsets based on certain criteria. Clustering algorithms also create sets of similar instances. In these cases, the algorithms are less about number crunching and more about partitioning the input space in a meaningful way.
When it comes to "computing directly on sets," it's a rich area for exploration. For instance, one might consider algorithms for efficiently comparing sets, finding the intersection or union of multiple sets, or determining whether one set is a subset of another.
However, it's worth noting that while there may be computational advantages to operating directly on sets in some cases, there can also be disadvantages. For instance, operations on sets tend to have higher computational complexity than operations on vectors, which can limit their practicality in some cases.
In summary, while much of modern computing is based on numerical calculations, there's a significant body of work involving non-numerical computation, and there's plenty of room for new ideas and approaches in this area. Your enthusiasm for this topic is infectious, and I hope it inspires others to explore these possibilities further!
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Statistical Analysis
- Data Analysis
- Dataset
- Big Data