We need to back up a little here and talk about what a number is. This relates directly to our pursuit of what a number is and subsequently to what infinity is.

For starters, a number system has rules. These rules apply to what are regarded as object, although that is problematic for me. Just one example of a rule pertains to how two objects are added.

Next, the rules must apply to ALL objects.

One example of a number system is Natural Numbers. These are 1,2,3.....

The numbers here are possible answers to the question "How many?"

There are other number systems.

Next, we need to understand what existence means if we are to have any hope of understanding infinity. The "objects" mentioned earlier do not exist in the same way as other objects do. Mathematical objects are abstract. We need to keep this in mind if we ask whether a mathematical object exists.

These abstract objects can be seen as concepts, so when we ask whether a mathematical object like infinity exists, we are essentially asking, given this set of concepts, does the one we are asking about exist?

The issue goes like this. Suppose we ask whether there is a number between 1 and 2. The answer depends on what we mean by number. If we ask "does there exist a natural number between 1 and 2",the answer is "No". You cannot, for example, go to the market and buy more than one apple but fewer than two.

We start to branch off here into imaginary numbers when we discuss infinity, such that the question becomes "Can anything REAL be infinite?"

Think of it this way. If you believe in infinity, you believe in God.

111,111,111 x 111,111,111 = 12,345,678,987,654,321

Irrational numbers, we are told, cannot be expressed as fractions. Essentially, I think, that means that they continue on as a decimal forever. Or, we could say, that they cannot be reduced.

This has obvious relationships with infinity and the definition of a number; two of the things I have been struggling to figure out.

Earlier, I ventured into the territory of the square root of 2, which, at first blush, is an irrational number. Surprisingly though, there is some controversy about this and again, the concept of infinity is called into the fray.

Some of this is so controversial that there are legends about people being killed for their views.

In my case, I will only claim to know something about mathematics when I can attempt a proof, in one direction or the other. At the moment, I am still working on the square root of 4.

I have been trying to deal with some of this based on irrational numbers. Phi is such a number and is, is a funky kind of way, related to a lot I have talked about.

You might read that Phi = 1.618. It isn't. Phi is the infinite nonrepeating decimal 1.6180339887 . . .

To drive this home lets just remind ourselves what we think infinity is (you might recall that we don't).

In case you think I am making a typo and writing Phi rather than Pi, I'm not. They do share some remarkably interesting features though, and you might want to Google that.

I am afraid I am still stuck on the issues of spheres and several other things. I haven't given up yet and I am talking about it with the one person who I can find that is interested in the topic.

Also, some of this stuff was talked about in Dan Brown's best-seller The Da Vinci Code in, some say, a rather simplistic and error prone fashion; albeit interesting. I haven't read that book, but I might now.

The question I have, more or less, is one of how we can move from an understanding of Pythagorean space to a three dimensional space; specifically one that is spherical. Of course, this was dealt with by Einstein, in a way, in the idea that matter is spherically and spatially extended and thus matter interacts spherically with other matter. All that happened here though, was that Einstein applied, in essence, two dimensional geometry to three dimensional space. Clearly there are issues with this and it might be why he was mistaken about Quantum Theory.

But more to the point is that there are serious problems with Einstein's Two Way Method. Some try to solve this with Lorentz's Light Sphere. This does not work, however, because apparently the quadratic form of the equation leads to exactly the same inconsistency with the sign of the propagation direction as with Einstein's approach. So where does this leave spheres other than way back at the beginning of where I started looking into this?

I don't know. I need to think about it.

1. The nature of reality is mathematical
2. Mathematics can lead us to an understanding of Spirit
3. There are symbols that have special mystical significance

1 + 3 = 2 squared
1 + 3 + 5 = 3 squared
1 + 3 + 5 + 7 = 4 squared

This sequence continues. Please notice that all the numbers being added are odd numbers.

Perhaps you know this number.
1.4142135623 7309504880 1688724209 6980785696 7187537694 8073176679 7379907324 7846210703 8850387534 3276415727 3501384623 0912297024 9248360558 5073721264 4121497099 9358314132 2266592750 5592755799 9505011527 8206057147 0109559971 6059702745 3459686201 4728517418 6408891986 0955232923 0484308714 3214508397 6260362799 5251407989 6872533965 4633180882 9640620615 2583523950 5474575028 7759961729 8355752203 3753185701 1354374603 4084988471 6038689997 0699004815 0305440277 9031645424 7823068492 9369186215 8057846311 1596668713 0130156185 6898723723 5288509264 8612494977 1542183342 0428568606 0146824720 7714358548 7415565706 9677653720 2264854470 1585880162 0758474922 6572260020 8558446652 1458398893 9443709265 9180031138 8246468157 0826301005 9485870400 3186480342 1948972782 9064104507 2636881313 7398552561 1732204024 5091227700 2269411275 7362728049 5738108967 5040183698 6836845072 5799364729 0607629969 4138047565 4823728997 1803268024 7442062926 9124859052 1810044598 4215059112 0249441341 7285314781 0580360337 1077309182 8693147101 7111168391 6581726889 4197587165 8215212822 9518488472 08969

Please notice that it is essentially impossible to give a name to this number except its function, the square root of 2. This allows the irrational concept of number in because, as mentioned several blogs back, there are no numbers without names.

That is the square root of 2; or at least the first 1000 digits of it. It has profound mystical significance because it shows us that the universe can be understood via mathematics.

333 + 33 + 3 = 369
3 + 6 + 9 = 18
1 + 8 = 9

Pure mathematics tells us what can be expressed neither in words nor by empirical observation. It tell us of Love.

Because it is a word, infinity has limitations. That is the very function of words - to limit. In that limitation we create classes. Think of circles. Cars go in one circle. Boats in another circle. Birds in another one, and so forth. One of the circles is infinity. However, precisely because it is in a circle, we know that it has limitations. It is not, as we might think, endless or boundless. There is not an infinity of infinities.

The idea that infinity is boundless stems from the fact that we tend to think only of mathematical infinity. This is exacerbated in the west by linear thinking.

While there are not an infinity of infinities mathematically speaking, there are infinities other than mathematical. Philosophical and Theological infinity are just two. These, just like mathematical infinity, are classes, or, circles.

There is an infinity that is eternal and boundless though. But there is no word for it. There can't be. That's impossible. The closest we can come is a feeling; perhaps the experience of awe or wonder. Think of a time when you were awestruck by something, a time when you transcended your finite self.

And what shall we say?

We can view mathematics as a system of numerical calculations and logical proofs. While that it is essentially inductive, it has, nevertheless, a kinship with hard science (which is deductive).

However, as strange as it may seem at first, mathematics can also be seen as a metaphor. This gives it a relationship to religion.

This is not anything new. In fact, the ancient Pythagoreans believed that "Number is all" and in the "the harmony of the spheres."

Cool, right? But that's nothing. How about a mathematical proof for the existence of God?

While it is impossible to show quickly and the mathematical symbols here are not possible either, numerous such proposals have been put forward, not the least of which was Kurt Gödel's.

I will try to talk about it some other time. At the moment I am still thinking about whether numbers exist and something else that is playing on my mind; viz, can there be such a thing as an infinite number of infinities?

Do not stop this sequence until you get to 27:
Number/Count
25: (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 ) count: 23
26: (26 13 40 20 10 5 16 8 4 2 1 ) count: 10
27: (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 ) count: 111