Ideas and relationships: using limits to work towards infinity. Neil Keleher.

What is zero parallax?

How to account for viewing error to measure change, create change and to understand

Zero parallax means knowing how things relate. When you know how things relate (and how those relationships change over time) you have the basic building blocks of understanding.

Why acquire understanding?

Understanding means you can do things without needing to think (or inquire) about how to do them. The necessary knowledge is "pre-thought" or "pre-learned".

When you run into problems, understanding is what helps you figure out the problem and deal with it. If you don't have understanding then the first part of solving any problem is acquiring the necessary understanding. That means learning how things currently relate and figuring out how things are supposed to relate. Or figure out how things are supposed to relate and then notice how they currently relate. The difference between the two states is the problem.

The better you are at acquiring understanding (and using it) the more independent you can be. And, perhaps ironically, the better you can work with others.

So what is parallax?

Parallax is viewing error. Or it's a difference in what is perceived based on differences in viewing angle.

One person looks at a clock, the old fashioned kind with arms that move relative to a fixed back plate, and sees that it's three o'clock. Another person looks at the same clock but from the side and sees that it's two minutes past three.

It's not so much that one is correct. What's more important is that the views match, but failing that, understanding how viewing angle affects what is perceived.

If each is aware of how the other relates to what is being viewed, viewing angle can be corrected for.

Dangers can arise. Say both people correct for viewing error?

As an example, say that person A asks person B for the time. Seeing B's relationship to the clock, A accounts for the parallax so that when B tells him it's 3:02 he corrects it to 3:00.

But, suppose that B is aware of his relationship with the clock, understands that that affects how he views the time and so he instead of telling A that it's 3:03 he tells him it is 3:02.

Because of this double correction the error is compounded.

And so an important part of accounting for parallax or "zeroing parallax", is knowing or pre-arranging who corrects for parallax.

This is why "clear references" are so important.

Zero parallax is when viewing error is accounted for.

Zeroing parallax requires an understanding of relationships and clear references!!!

As a real world example of the importance of having a fixed end point, if two firefighters are trying to couple two lengths of hose, each one holding on to the end of a length of hose, if both move their hose relative to the other, it's harder for them to couple the hoses. So one looks away. He or she acts as a reference. The other firefighter can then easily connect their hose end to the unmoving hose end.

If you've ever used excel, the spreadsheet program, or any other spreadsheet program, you use a fixed reference all of the time, perhaps without even realizing it. The a1 cell is generally the reference for all other cells. Unless you are using relative references where the currently active cell is the reference (and all other cells are either above, below, or left or right of this cell.)

Right marker!

In the army, marching in neat rows and columns, the person at the right front was called the right marker. Unless told otherwise, he/she was the one that we adjusted our position to and maintained our position relative to so that we kept our nice neat rows and columns.

The clock is a fixed reference point

When viewing a clock, the clock is generally viewed as the fixed part of a relationship. If you are observing someone else's relationship to the clock, then the clock is fixed and you can measure the person's position relative to the clock (and thus determine parallax if required.)

To further underestand the idea of fixed reference points, generally with old fashioned clocks, the clock is positioned so that the 12 is uppermost. This is so obvious that most of us take it for granted. But it is because this positioning is so "stable" that we can take it for granted. This can be one of the benefits of stability.

So zeroparallax is in part based on understanding how we relate. But it's also about having clear references. Which part of the relationship is being used as the reference point?

How to measure consistantly (and avoid measurement error)

I first learned about parallax in chemistry class. Our teacher was Ms Klobature. She taught us that when measuring liquids using a beaker (or whatever the specific apparatus that was used for measuring was called) we had to view the measurements with the vessel level and with our eyes level with the surface of the liquid. This was the reference position that made all of our measurements consistent because they were made using a fixed reference point. Note, she could have defined it as 89 degrees above the horizontal. The point was if we knew it, and could find it, we could use it, consistently.

A relationship needs something to relate

An important idea in all of the above examples is that a relationship needs two things in order to exist.

I'll suggest here that a relationship relates two, and only two things. Looking at a clock, the relationship includes ourselves and the clock.

Why limit a relationship to two connected things?

Because it makes it easy to define a particular change. In addition, if there are more than two related things, it means we can look at each relationship in relative isolation if we choose. If there are more than two connected "things" we can look at each relationship individually. And we can sum all of the relationships with the idea of a system.

So what is the term general term for the two things that a relationship connects?

Ideas are the basic building blocks of relationships

This bears further explanation but the term I use to refer to the things that a relationship connects is [idea]. A relationship connects or relates ideas.

A relationship can also be viewed as an [idea].

We tend to think of ideas as imaginary. Or in some cases as viruses. And both can be true. Note that another term that I've come across recently and that can be used in a similiar way is holon. A holon is something that is whole in and of itself but at the same time part of something bigger. A holon can be a system which is part of a bigger system. It can be a component part which is part of a system.

Why ideas can be more useful than holons

I like the term idea a bit better because it includes thing that we can imagine as well as things that are real. And so it can be used to describe something as it is taken from the imagination and made real. And it can also be used to describe the reverse process where something real is made imaginary, such as when we learn to understand something.

Something else about ideas, and this is no less true for holons, is that they are infinite, unlimited. As a friend once said to me: "There are plenty of ideas to go around". And that's an important part of understanding also, the idea of infinity.

Just because something is infinite doesn't mean that it is big

Mathematicians and physicists tend to think of infinity as something really big.

That's a "limited" view of infinity.

If you have a glass of water, that water is bound by gravity and the shape of the glass itself. And while the individual molecules of that volume of water have freedom to move relative to each other within the bounds of the glass, they are ultimately limited by the glass.

Upturn the glass and the water falls due to gravity. Now it is no longer limited by the shape of the glass. While in midair, it is no long limited by the shape of the glass. It is unlimited in the number of possible relationships. When the mass of water lands on the floor it becomes partially bound or limited. The surface of the floor limits or constrains it, but there are no limitations to how it spreads out. So while the puddle of water is less unlimited compared to when it was in midair, there is still an aspect of limitlessness even when it is on the floor (and in the same way, within the glass there are some ways in which the water is also unbound).

Defining the square of infinity (or "infinity squared")

So infinity can depend on your point of view. And it might be appropriate, when required, to think in terms of degrees of infinity. As an example of this on a larger scale, we tend to think of ourselves as limited by time and space. What if we could become infinite or unbound by time? Or what if we could become infinite or unbound by space. If unlimited in both time and space, this could be a reasonable way of defining what infinity squared means.

Why the tangent of a 90 degree angle is infinite

Looking at triangles, they are traditionally defined as having angles whose sum equals 180 degrees. In a triangle with one right angle, the tan of one of the angles that isn't 90 degrees is the ratio of the opposite side over the adjacent side. As the angle approaches 90 degrees, this means the triangle is getting close to having more than 180 degrees. Tan is infinite for angles of 90 degrees because there are no triangles with that possibility.

Another way to put it is that the relationship, that of a triangle, no longer holds true and as a result the ratio is no longer constrained by the relationship. Hence the tangent for that angle is any number possible.

Just one of an infinite number of ways of making money without using your own money

Yet another example that inspired me to think more about what infinity means comes from rich dad's Robert Kiyosaki. He'd often use examples where he'd use other peoples money to make money. He'd then say he had an infinite rate of return, implying that the rate of return was very big.

What made more sense to me was that he used one of an infinite number of ways of making money from money using other peoples money. if you define rate of return as the rate of return using your own money then using someone else's money you are no longer getting a rate of return. The relationship and terminology no longer applies. Hence it is unbound or infinite.

How infinity relates to understanding

So how does this apply to zero parallax or more importantly understanding?

We tend to be limited by what we don't understand. Problems generally involve a lack of understanding. And so the first step in solving any problem is understanding. That can include understanding the desired state, how things should work, and the current state where things aren't working. When both are understood, it can be possible to fix the problem.

Learning generally involves the use of limits

Another way to look at it is that the process of understanding generally involves using limits.

We can use limits to cut a complex system into bits (say into relationships and/or ideas) so that we can ingest those bits and build a model of that system within ourself. This is generally called learning. The more we learn, the better we understand. The interesting thing is, as we learn something, once we've built a model of the thing we are learning inside of ourself, we no longer need the limits we used to learn it.

As an example, learning to ride a motorcycle, we practiced in a car part with no other traffic around. We further created limitation by focusing on learning little bits at a time, say how to stay balanced, how to stear, how to use the brakes. As we learned more and more the restrictions were reduced. We no longer focused just on stearing or just on braking. Eventually, we passed our test and were no longer bound by the car park. We could now ride a bike on the road. We were working towards infinity, being unlimited.

The more we understand, the more free, the more unlimited, the more infinite we become. In real terms the more freedom we have to express ourselves using what we understand.

We can use limits to define ideas, relationships and of course systems.

The trick is in using limits to gain understanding. How do can we use limites to increase our understanding? By using them to define relationships and ideas (and systems).

When we clearly define these things, they are easier to ingest and learn. Once we've learned the thing (the system) that is made up of those interconnected ideas and relationships, we no longer need the limits that define them.

Limits are imaginary

Limits for the most part are imaginary. We can define them as we choose. We can redefine them. We can release them completely.

Because limits are "imaginary" we can always call them up again if we need them. Or we can divide what we are learning or have learned in different ways. This is roughly equivalent to viewing a clock from many different viewing angles so that from any viewing angle we can account for parallax. We thus become more less limited, more infinite.

These tools can be used when learning our body, our mind, even ourselves as well as the things outside of ourselves. The better we understand ourselves, the more freedom we have to express ourselves, becoming more infinite in the process.

Published: 2019 04 24
Updated: 2021 01 19
Use limits to define ideas and relationships. Once these have been learned, you no longer need the limtis. You thus work towards being unlimited i.e. infinite. Neil Keleher, Sensational Yoga Poses.

Zero Parallax

First principles

Basic principles

ideas as units of meaning: and as the potential for change