On the matter of mathematics, I think we are largely in agreement. Perfect is nearly impossible. Consider this statement of your own. As you stated: “no two people will understand what they are reading in exactly the same way .”

Where I think we differ is on how our abstractions affect our mathematics. The concept of a discrete unit is itself an abstraction. For a discrete units to exist in our minds, we must presume, for example, that all apples are equally tasty and nutritious, that none contain worms or rot. If a grocery store violates that assumption, its customers will complain.

Unless we choose to coin gold and silver, to use a currency that has value in and of itself, then money is wholly an abstraction. So long as they are recognized as currency, we are indifferent as to the condition of paper currency and coins. We just try to replace our currency before it wears out.

As you suggest, mathematics exists as a subset of our language. Language exists to communicate our thoughts. Because our thoughts begin as abstractions from reality, even with mathematics, we can communicate only so well.

You end with a criticism of Christians that deserves further comment.

It is interesting how Christian like to cherry pick the Bible. They will accept the 10 Commandments as true, but ignore the commanded punishments (e.g death by stoning). According to this article, there are not exactly 10 commandments, since are both abstract language and numbers involved. For this reason, and others, there are several different denominations. Different groups cherry pick the bits that are pleasant and either do not read the rest, choose to ignore what it says, or “hand wave” it away.

As you noted yourself, we each interpret what we read differently. Because we each have our own unique vision and viewpoint, this is an inevitable fact of life. Because we are also weak, serious misinterpretations and cherry picking of the Bible are difficult to avoid.

Are all the commandments equal? We think in quantities. We set priorities. Some commandments do, for example, actually seem to have more weight than others. Some commandments direct us to love God. Some commandments direct us to love each other. Nonetheless, God wants us to obey all His commandments — not just those we think important.

Note that there is a profound difference between the Old and the New Testaments. When the Old Testament Hebrews tried to live by the Law, they found it impossible to live perfect lives. Yet each sin requires punishment — or a sacrifice to God for the remission of our sins. In recompense for their sins — to appease the Almighty — the Jews and others made innumerable sacrifices. Yet nothing they could do was enough. So they felt compelled to come to the alter and to sacrifice again and again.

The New Testament established a new covenant. With the New Testament, we do not ignore the punishment for sins. We recognize that price has already been fully paid. Jesus paid the price.

With Jesus’ death we see an illustration of our inability to model discrete quantities. Jesus offered up His Life only once, but His Sacrifice paid the full price.

So what is left for us to do? Our task is to accept His Gift for the remission of our sins. Our command is to do as He said, to love God and each other.

“When we take a measurement in the real world, that measurement is an approximation. We cannot exactly measure two pounds, two inches or two quarts. We can only measure abstractions with infinite accuracy. Thus, because money represents an abstract concept, two dollars is exactly two dollars. ”

Notice how all of these examples are measurements of the non-descrete (analog) kind. The reason money can be measured exactly is not because it is abstract, it is because the units are descrete – just like the apple example that I give above.

One can say the same thing for any book, including the Bible, since that book must be written down in a language and language is abstract. No two people will understand what they are reading in exactly the same way from each other or in the same way as the author(s).

Actually, it is words like “tall” as in a tall building are fuzzy and non-precise. Is a man who is 6 feet in height tall? For the sake of argument, let us suppose he is. What about five foot eleven? 5′ 10″? If you say a man is 6 foot tall, then you know much more precisely the man’s height. We can do the same thing for measuring colors. If we say the apple is red we are not being as precise as we would be, if provide a range of light frequency and define that as red. In fact, if we define colors by wave frequency, then we can program a computer to distiguish colors to arbitrary precision. The same will apply for measuring the rate in which a container is overflowing. If we say “rapidly” we get some idea of what is meant, but if we give a nearly exact rate in say liters/second we can get a much more precise measurement. In principal, we can measure all non-descrete items down to their Planck units (i.e. the smallest possible length, time) and anything smaller than those units are meaningless (there is no information smaller than those units – very similar to the concept that you cannot make anything colder than absolute zero.) Ultimately the Universe is composed of descrete units of space, time and energy.

It is interesting how Christian like to cherry pick the Bible. They will accept the 10 Commandments as true, but ignore the commanded punishments (e.g death by stoning). According to this article, there are not exactly 10 commandments, since are both abstract language and numbers involved. For this reason, and others, there are several different denominations. Different groups cherry pick the bits that are pleasant and either do not read the rest, choose to ignore what it says, or “hand wave” it away.

Amen to that, Will. That will save the world.

So many Christians seem to forget that “Christ” is a title, and not a person.

I don’t oppose Christ, in the least. I pursue Christendom.

Personally, I believe no one apple is like another, so you can add as much as you like but still not prove anything other than you can add : )