BIAIMM

The Base Intelligence Architecture Instantiation Method for Mathematics

(BIAIMM) – A.K.A. the Ben and Jaxom method.

A small note: This document is written in a simple format. This is done so that this document will be friendly to anyone. The use of this format will also ease the process of translating this document into other languages.

Table of contents:

  • What is BIAIMM, and what does it do?
  • What is a spheroid – As a core element of BIAIMM, it is important to understand what this thing, a spheroid, is.
  • Note: Spheroids with a greater diameter that is approximately 2.5 time their lessor diameter are preferred. M&Ms are a great source of this type of spheroid. Yes, M&Ms are spheroids. 😉
  • Self-Guided Progression
  • Group Dynamic
  • Object Based Data

What is BIAIMM and what does BIAIMM do?

Before I wax overly verbose and wander happily down the nerd path, here is the short answer. BIAIMM is a tool. It builds a base mathematical architecture in the human mind. This is the base upon which all further math in a person’s life will be built. It sets the IQ for this field. The IQ built by BIAIMM will be between 115 and 160. Where a student lands between 115 and 160 is dependent upon the small details encountered during BIAIMM’s application.

Now, on to the nerd path.

What is BIAIMM?

BIAIMM is an intellectual tool. Tools are devices used to build things. Intellectual tools are used to build things in the mind.

When considering intellectual tools, mathematics is a good example. While mathematics in and of itself may be considered an intellectual tool, within the field of mathematics we find a host of intellectual tools. These tools start with the idea of a number line and basic numbers, proceeding along to calculus and beyond.

When we look at the founding history of mathematics, we find the human race using numbers simply to count things. When a returning hunting party began to come in view in the distance, before we could even discern who the individuals were, we looked at the number of hunters returning. Was the number of hunters the same as when they left? In this we find that before Homo sapiens had written symbols for numbers, the intellectual tool we now call mathematics was forming.

A short few thousand years later came geometry. With geometry, humanity began to use mathematics to create representations of the physical world. The effect geometry would have on architecture, economics, and our understanding of the world would change civilizations forever.

If you are wondering how geometry in ancient times changed economics, here is your answer.

  • A person’s political power was determined largely by an estimation of their wealth.
  • Wealth was determined by how much land you owned.
  • Geometry turned the hills, valleys, rivers, and not remotely square land into perfect squares.
  • These squares, flat shapes inscribed on clay tablets or pieces of papyrus, were then stood up on end like a tree.
  • The length of the roots of this square tree was then measured.
  • The longest root measure defined the wealthiest, most powerful person.
  • Having one number made it easier for politicians that could not do the math themselves to decide who was more important.
  • Thus, was the Square Root born!

So yes, geometry determined wealth and political power.

It is important to note the difference between an intellectual tool and an intellectual engine. An intellectual engine is used to move, transform, and even create things in the mind. From intellectual engines we derive answers. From intellectual tools we build the things we use to create these intellectual engines.

The difference between the two can blur. Sometimes the tools we use can be engines as well. So yes, some of the mind’s structures can be both. These structures contain dynamic elements, static elements, and elements that the human race at large has not yet defined. Happily, humanity does not need a clear understanding of all the minds elements. It is a bit like light. Even without a clear and complete understanding of its structure and function, humanity can see the world light touches and be warmed by its glow. So it is with these other structures of the mind as well.

I have digressed enough. 😉 We move on.

–

What does BIAIMM do?

BIAIMM is used to build an advanced engine for mathematics in the human mind. In simple terms this means it actually builds intelligence.

How does it accomplish this? That discussion begins below.

–

BIAIMM’s pieces and process:

Spheroids:

Spheroids are the first physical tool used in the BIAIMM process.

What is a spheroid? To clearly understand what a spheroid is, let’s start with a circle. Circles are round, perfectly round in fact. But circles are also 2 dimensional. This means flat.

When we make a circle 3 dimensional it becomes a sphere. The sphere is perfectly round as well, but round in 3 dimensions.

When we squish the sphere in any one direction, the sphere becomes a spheroid. So, A spheroid is a sphere that is squished. It can be squished a little, or a lot.

As an example, the earth is a spheroid. It is a little bit wider than it is tall. How much wider? The earth’s diameter is 26.4 miles or 42.4 kilometers more than its height. So, if you were in a boat floating on the surface of the ocean at the equator you would be 13.2 miles farther from the center of the earth than you would be if you were sitting on the north pole at sea level. And I have digressed enough for now. Back to BIAIMM.

M&M shape benefits:

Yes, M&Ms are spheroids.

An M&M resting on a flat surface is circular when viewed from the top. The same M&M viewed from the side forms an ellipse. This particular shape, called a spheroid, is of tremendous use when building base intellectual architectures in the field of mathematics.

Why Spheroids? Spheroid shapes are easily held in the human mind without adding stray data. Their 2-dimensional characteristics provide a sense of a top and sides. This sense of a top and sides in turn provides the spheroid with a perceived resting shape. This resting shape is especially important when building the base mathematical architecture. The resting spheroid becomes the core element of the concept of both what “1” is as a number and 1 is as a thing.

This resting shape provides a comfortable sense and perception of stillness when the spheroid is, on a surface, in the subject’s hand, or in the subject’s mind. There is no, what happens next. The conceptual endpoint is important. It is like a ball tossed into the air. Once the ball is caught, the mind is comfortable, the process is complete.

Self-guided progression:

The BIAIMM process uses self-guided progression. This is a core element. It is like an intelligent oven that knows when the cookies are done. The self-guided element here is allowing the child to come to you to ask what number comes next. This is necessary. If the BIAIMM is followed properly it will build the base intellectual architectures of the following:

  • numbers
  • objects – independent of object type
  • numeric progression
  • a number line
  • mathematics
  • and above all, what “1” really is.

If the method is not self-guided the children will still learn to count to 20, but the underlying architecture will be broken severely. They will learn to count by repeating a series of sounds you have given them and drilled them to memorize. The opportunity to build the base architecture for mathematics will be gone. If you think you can just add the missing parts later, you are catastrophically wrong.

Group Dynamic:

This process works optimally when preformed on a group of 2 to 5 children. With 2 to 5 children allows each of them is an individual. They will form a lose group as they work learning. They will feed on each other’s excitement. A natural competition will develop. And yet, they will happily help each other when someone forgets a number or needs to know what number comes next.

As they are all learning to count and building their intellectual architectures at the same time, they will benefit from observing each other’s attempts and progressions. Playing will the spheroids to see why they stand up when they spin them will inspire logical discussion and lead to scientific experimentation.

Object based data:

The meaning of Object based data literally is, relative to BIAIMM, objects created in the mind. These objects have many properties. All of these properties are important.

How to use BIAIMM:

(Base Intelligence Architecture Instantiation Method for Mathematics)

This is a short and very simplified walkthrough of the process

  1. Start with 2 to 5 children, (age 3 to 5).
  2. Bring them into a kitchen. Yes, there is a reason it is a kitchen.
  3. Show them some M&Ms.
  4. Give each child 1 M&M while you are talking and let them eat them.
  5. If they are not familiar with M&Ms explain what M&Ms are. Include in this explanation what is both on the inside and outside of the M&M.
  6. Ask them what they think of the M&Ms.
  7. Pick up 3 M&Ms in one hand.
  8. Place the other hand low enough that the children can see the upturned palm closely.
  9. Put the 3 M&Ms in the empty hand one at a time, counting them as you go.
  10. Example: “This is 1 M&M, 2, and now 3 M&Ms.”
  11. Tell them the following:
    1. 1, 2, and 3 are numbers. Numbers are how we count things.
    2. So, to help you all learn to count, every day after lunch, for the next 2 weeks, I will line up 20 M&Ms on the counter.
    3. (Note: After dinner works as well if lunch time is not really an option.)
    4. After I line them up, you can each have as many as you can count, up to 20, until you miss a number.
  12. Take the M&Ms to a table that is easily accessible by the children.
  13. Pile some of the M&Ms on the table.
  14. Take 20 of the M&Ms and line them up.
  15. Count the 20 M&Ms one at a time pointing at each one with your index finger as you count.
  16. Then tell the children:
    1. You know what else is neat about these?
    1. If you lay 1 down and spin it, it will stand up on end.
  17. Place 1 M&M on the table.
  18. Place your thumb and the side of the last segment of your middle finger on each side of the M&M.
  19. Spin the M&M by flicking your middle finger out straight. (As a note, it’s good to practice this before showing the children.)
  20. The M&M will stand up on its end if it is spinning at a good speed. Spinning them is actually quite easy with a little practice.
  21. Ask the children to see if they can figure out why the M&M stands up. Is it something about the friction on the table, maybe something about the M&Ms center of gravity, or maybe some other reason?
  22. Even if you have figured out why this works don’t tell the children. Thinking about why spheroids, (M&Ms), stand up when spun increases the intellectual energy and data resolution used in this process. It also helps children develop their analysis skills.
  23. The children will learn to spin spheroids to see if they stand up when they spin them. They will test this repeatedly in their efforts to develop an understanding of why this happens. This process of testing and observation develops an effective initial skill in using the scientific method. Developing this skill without even realizing they are working on skill building is of tremendous value. The joy they experience while learning is something that they will carry with them into their school years. It would be tragic to underestimate the value of this step in the process.
  24. Leave the children a few of the M&Ms to experiment with, practice spinning, and munch on. (Each child should be left with the same number of M&Ms.) Let them know they each have some to practice with. A group that plays well together is essential to this process. If the group is cohesive, they will spend a good part of their days helping each other learn to count.
  25. Let the children come to you to ask what number comes after 3, and so on. This is vitally important! If you try to teach the children to count by having them repeat the sounds of numbers to you, you will burn the cookies. Using the BIAIMM method will produce, in the child’s minds, visualizations of the spheroids, (M&Ms). These spheroids form the base of this advanced mathematical architecture.
  26. When the process is pushed instead by repetition, the fluid dynamic of the path of least resistance takes over. THIS IS BAD! It will then be easier for the children to just remember and repeat the progression of sounds. The advanced spheroid architecture in their minds would then not be properly formed, if formed at all. I do not currently have an effective method to fix such mis-formed intellectual architectures.
  27. The spheroid process creates an advanced mathematical architecture in the children’s minds. Numbers are conceived as collections of things rather than a progression of sounds. 2 becomes 2 spheroids rather than 2 being the sound made after 1 and before 3. They will see 3 spheroids in their minds when they think of 3. When it comes time to learn to add, 2 plus 3 adding becomes 2 spheroids and 3 spheroids that they see in their minds. They will then move these two groups together to get the answer. This architecture is a considerable advance over that of relating numbers to a progression of sounds. Here again, the spheroids are a tremendously useful tool. The simple and comfortably smooth shape of a spheroid is easily morphable into numeric architectures and objects. The children’s minds will casually change 3 spheroids, (M&Ms), into whatever else their mathematical calculations will later in life require.
  28. Each day, at the set time, line up 20 M&Ms on the edge of a counter. They should be slightly above eye level but still easily visible. (It is important to have the M&Ms above eye level but still visible on the front edge of the counter. This placement of the M&Ms directs the children’s minds inward to see the M&Ms they have been visualizing in their minds as they have learned to count.)
  29. Let the children count them as far as they want to go. Do not stop them if they miss a number. When they stop let them know which numbers, if any, they missed or got out of order. Congratulate them on their counting. Give them the M&Ms they correctly counted. Yes, up to the max of 20.
  30. Continue to do the daily counting, even after the children can count up to 20 comfortably. This allows the success they have had to become a bonus for the remainder of the 2 weeks. Continuing the daily counting for the entire time span of the BIAIMM process, even after they have succeeded, helps make numbers something they enjoy.

Progression from counting to formal mathematics

The process presented above is just the first part of the BIAIMM. After learning to count to 20 the BIAIMM process continues with 2 sessions of 1 and a half to 2 hours each in duration. These 2 sessions are used to teach a solid foundation in the following areas of mathematics.

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Fractions
  • Basic algebra
  • An introduction to mathematical bases.

My own testing and analysis indicate that the ideal age range for a subject’s participation in the BIAIMM training listed above is 3 to 5 years.

Below are some final notes of particular importance.

Intelligent people will understand that this method works well. Amongst these intelligent people there will be some who think that they understand the process completely. Knowing that they understand the process completely, they will then feel free to happily change the process to fit their own particular style. They will do this with the thought in mind that nothing is lost, no harm is done.

Within this thought that these people have, lies the rub. There are genius elements in this process. These genius elements will often be missed entirely. Even very bright people will usually miss them. Just a few of these genius elements here that will commonly be missed are:

  • Spheroids:
    • The shape of the spheroid is a core element in the establishment of the base intellectual architecture, or idea, of “1”.
    • The action of the spheroid’s resting shape stabilizes the subject’s intellectual architectures at multiple points during this process.
    • Viewing the spheroids at just above eye level during the daily counting part of this process directs the mind inward while counting, instead of just looking at the spheroids (M&Ms).
  • The self-guided method used here allows the numeric architecture to stabilize and continue to build comfortably in the subject’s mind as the learning to count progresses.
  • Placing the (M&Ms), spheroids on the edge of a counter during the daily counting allows the edge of the counter to represent a number line. As such, please place the spheroids at a fairly even, though not exact, distance from each other.

And for you Shakespeare nerds out there, Yes, I do know that the actual quote is

“Ay, there’s the rub!” ?

Thank you,

The Anomaly

–

Copywrite (c) 2020 Sean Rutherford. All rights reserved.