Moving Up in the World

I first need to explain what I mean by World Reference Frame or WRF and Personal Reference Frame or PRF.

By WRF I mean the standard directions relative to the world, or at least relative to your own local area of the world.
There are three axes involved :
1) the North-South axis,
2) the East-West axis and
3) the Up-Down axis.
Any motion you make can be resolved into components on each of these three axes. You are going a certain amount North or South, and at the same time a certain amount East or West and at the same time a certain amount Up or Down. The phrase ” a certain amount” may in many instance mean zero.
And it doesn’t matter which way you are facing or whether you are standing, or sitting in a car, or curled up in a ball, the world doesn’t care. North is North, East is East, Up is Up and so on.

[I realize that to be more “mathematical” I could named the axes the North axes, the East axis, and the Up axis, and that what we call motion to the South could be called a negative amount of motion to the North.]

By PRF I mean the standard directions relative to your self. The three axes involved are :
1) the Frontward-Backward axis ( or Forward-Backward if you prefer ),
2) the Right-Left axis, and
3) the … the uh … hmmm.
And there is my problem. We don’t seem to have a word in English for the third PRF axis, at least I don’t know one. It is no good telling me ” it is the Up-Down axis you big dough head”. The Up-Down axis is a WRF axis. The WRF Up-Down axis only aligns with the third PRF axis I am talking about when we are standing upright. But we are not always standing upright.

So I am going to suggest the term Headward-Footward to describe the thrid PRF axis.

Now when you have a set of WRF axes and a set of PRF axes this is what you can do with them.
When you are standing upright facing North your PRF Frontward-Backward axis aligns with the WRF North-South axis, your PRF Right-Left axis aligns with the WRF East-West axis. If you are standing upright facing East then your PRF Frontward-Backward axis aligns with the WRF East-West axis and your PRF Right-Left axis is negatively aligned the the WRF North-South axis. By negatively aligned I mean Right is South and Left is North, rather than positively aligned which would have Right being North and Left being South. In all these situations your PRF Headward-Footward axis is aligned with the WRF Up-Down axis.
If you were to stand on your head and face North then your PRF Frontward-Backward axis remains aligned with the WRF North-South axis, but your PRF Right-Left axis will now be negatively aligned with the WRF East-West axis. And your PRF Headward-Footward axis would be negatively aligned with the WRF Up-Down axis.

You can imagine positioning yourself any way you like, lying face down with you head to the east, on your back with you right arm stretched to the north, anything you like, and figure out how your PRF axes align with the WRF axes.

Now all this positioning and aligning sounds complicated and perhaps even confusing to many. But this is simple routine stuff in the study of vectors and coordinate systems and that sort of math. So why do we find it complicated ?

Perhaps some may find learning these topics difficult because our language does not have a word for the Headward-Footward axis. And does our language not have a word for the Headward-Footward axis because our motion is done by walking upright and therefor Headward-Footward is always the same as Up-Down when we are in motion ?

We live in a three dimensional world, and we must move around in it. So it seems a bit odd to me that our language has not developed a word for the third PRF axis.

Is there a practical application for such a word. I think so. Someone lying face down on a toboggan going downhill can be said to be going headward. Some people may say he is going forward, but I think that is inaccurate. Forward in this case would actually mean the tobogganer was going deeper into the snow.

Perhaps there is such word in English but I just don’t know it. I would be interested to hear of one.
Also, do any other languages have such a word ?

RCM 20200103

This is just a bit of a mild rant about the word Infinity. I may move it into the Math Wing of the house.

The Word Infinity

Sometimes the general public uses a word differently than how it is used by people in some specialized discipline.
For example in mathematics “irrational” does not have anything to do with being unreasonable. It means not being a ratio of two integers.

Another example is quantum leap. When used by the public, which may not be as often as it once was, it is generally used to mean a huge change in something, a giant step forward in some endeavour. Maybe people have a vague idea that the word quantum has something to do with nuclear physics and nuclear physics has

something to do with atomic bombs and atomic bombs make really really big explosions. So quantum must mean really really big.
Except quantum means really really small. In fact a quantum is the smallest possible amount of something.

I have no objection to the use of irrational to mean unreasonable or even crazy. It is common. It expresses an idea that both the speaker and the listener almost always understand in the same way.

I do object to the misuse of quantum. But I am not too concerned, I havent heard it used for quite some time now. Maybe people know better now.

But now to the topic of this story. The word infinity is in a different class. I believe it is misused by the general public and sometimes by specialists who should know better.

Collections of ‘things’, or Sets, have a certain number of ‘things’ , or Members, in them. I think the term Elements may also be used.
For example I have just now come back from my refrigerator where I counted the number of eggs it contains.
I have 13 eggs in my refrigerator. The Set of Eggs in My Refrigerator has 13 Members.

If you object that eggs traditionally come in boxes of 12, so how can I have 13, then I must inform you that they may now be purchased in boxes of 18. Is that a quantum leap in egg marketing ?

The number of eggs is limited, it is called Finite.
I think “Finite” is a good word.

When the number of things is not limited, when it may increase without limit, then it is called Infinite, which is simply the opposite of Finite. An example is all the integer numbers. They increase without limit. You can never run out of numbers, there is always one more. And because there is always one more, there is alway

two more, and so on.
I think “Infinite” is a good word.

That is not to say it is not sometimes misused. For example some one might gush poetically about how the grains of sand in the world are infinite. But they are not. There is a really really big number of grains of sand, but it is not infinite.
Consider this : can all the grains of sand in the world weigh more than the whole world, which includes those grains of sand ? Of course not.

So let us calculate.
According to Reference.com
https://www.reference.com/science/much-grain-sand-weigh-90bad4f39f93ac7b
” An average grain of sand weighs approximately 50 micrograms”.

According to the JPL Ephemeris
https://ssd.jpl.nasa.gov/?planet_phys_par
the mass of the earth is 5.97237 x 10^24 Kg.

So even if the earth was made of nothing but grains of sand, which it is not, so this number will be an outrageous upper limit, the number of grains of sand would be 5.97237 x 10^24 Kg / 50 ug which is 1.194474 x 10^32 grains of sand. or written out in full
119447400000000000000000000000000 grains of sand.

Now that is a big number, but it is not infinite. Also we know the world is not made of sand alone. Sand is only a tiny fraction of that number.
You may find other estimates on the internet for the number of grains of sand in the world, for example here https://www.quora.com/How-many-grains-of-sand-are-there-on-Earth-and-how-many-stars-are-there-in-the-universe, which gives 10^25 and 7.5 x 10^18 as possible answers.

In any event, it is not infinite, just really really big.

But that sort of thing, although annoying, is not what bothers me most.
What bothers me is when people take the good adjective word “Infinite” and turn it into a noun by addint “ity” to it. I dont think “Infinity” is a good word. Oh, you can find it in the dictionary and in math text books, but I dont like it. I prefer “increase without limit” and so on.

Consider the movie “Toy Story” when the spaceman toy says ” To Infinity….and Beyond !!”. I know, it is just a kids movie, and I should not over analyze it. But even if Infinity was a place, which it is not, and that you could get to it, which you cant, how could you go beyond it ? My main objection is that Infinity is not a place. It

is not a size. And it is especially not a number. I just dont think it is a good word.

If I were to flex a bit and use it as a word then I would define it by saying “Infinity is the promise that you can never run out of numbers”.

Which appears in my list of aphorisms posted a few days ago.

RCM 20200102

I have placed a new story called Proverbs into the Philosophy Ground Floor. It was originally on my personal FaceBook page.

I have put a new story, called Aphorisms, into the Philosophy wing Attic. It is a collection of what I fancy to be clever little sayings. Some day I will publish the stories that go with them. This may be backwards, perhaps even a bit outrageous like a band issuing a collection of greatest hits before issuing any other records at all. But they may serve as discussion points.