Posted on 11/30/2004 6:21:11 PM PST by betty boop
Which slant?
Well, bless you safisoft. This is a reasoning debate, and by your standards I take it that you've dismissed yourself.
don't know that I can fathom this, as I don't know what an "allele" is. [g]
true. God is not done with me or you or men in general or Israel in particular. I meant something rather narrower. Sacred text ends with the new testatment--at the point where it is no longer a specifically jewish story. There have been some great jewish and christian writings over the last 2000 years since John completed Revelations. But none have been considered to be Sacred Text. That's all I meant.
Romans 11
13I am talking to you Gentiles. Inasmuch as I am the apostle to the Gentiles, I make much of my ministry 14in the hope that I may somehow arouse my own people to envy and save some of them. 15For if their rejection is the reconciliation of the world, what will their acceptance be but life from the dead? 16If the part of the dough offered as firstfruits is holy, then the whole batch is holy; if the root is holy, so are the branches.
17If some of the branches have been broken off, and you, though a wild olive shoot, have been grafted in among the others and now share in the nourishing sap from the olive root, 18do not boast over those branches. If you do, consider this: You do not support the root, but the root supports you. 19You will say then, "Branches were broken off so that I could be grafted in." 20Granted. But they were broken off because of unbelief, and you stand by faith. Do not be arrogant, but be afraid. 21For if God did not spare the natural branches, he will not spare you either.
The reason I wanted to post about numbers was that I found your idea of an essay about numbers and eternity quite interesting, but I found your approach a little trouble some, namely equating real numbers to eternity (i.e. infinity.) I assumed at some point you would talk about the infinte number of digits required to represent an irrational number in a decimal system of notation. So let me offer this for your consideration.
It is a problem that caused great scandal in the Pythagorean Brotherhood more that 2500 years ago. Reportedly it drove some Pythagoreans mad, even to the point of riot and murder.
Pythagoras is most famous for the Pythagorean theorem: the square of the hypotenuse of a right triangle is equal to the the sum of the squares of the other two sides. So the finite length of the hypotenuse is the square root of the sum of the squares of the other two sides.
Now take an isosceles right triangle. The legs which are at a right angle to each other are one inch long. What is the length of the hypotenuse? Exactly the square root of 2. The square root of 2 is an irrational number. It cannot be expressed as the ratio of whole numbers. The philosophy of the Pythagorean Brotherhood was based on the idea of rational numbers. When they discovered irrational numbers, some of them went mad.
Does that mean that the square root of two is infinite? Look at that isosceles right triangle again. What is the length of the hypotenuse? The length of that finite line segment is exactly the square root of two. If the square root of two were an infinite number, it would take you an infinite amount of time to draw that hypotenuse. But it doesn't. You can draw it quite easily without exhausting all the lead in your pencil.
It turns out that irrational numbers aren't very mysterious after all. The are very mundane things. We use them all they time. We can hold them in our hands. They are finite.
I think you have offered some other ideas about eternity in this thread that are very profound. I have also offered some suggestions that may have possibilities for further development: process, direction, division by zero, infinitesimals, etc. Why have mathematicians forbidden division by zero? What are they afraid of? Well, I think they are afraid of eternity. And maybe in some sense we should all be afraid of eternity. Or at the very least approach it with due respect.
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You bet.
I also think of it in a similar way. Something with the direction that the two take. There is, of course, theology that ends in the personality of man, because that's where it begins. So where things begin is also a difficulty.
In their most famous works, both Augustine and Calvin begin with the difficulty of a beginning. Neither resolve it by getting rid of one for the other. That's smart. Otherwise you'd have 100% God and no man or 100% man and no God.
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two reasons for the paradigm shift away from the arian heresy imho involve man and creation. as to man the problem with the college dictum "Man is the measure of all things."--is this. Man is a very poor/imprecise/fuzzy measure. After all what kind of man are we talking about that is doing the measuring. Is the man short fat tall skinny, black brown yellow or white, an embryo, baby, child, teenager, young adult, middle aged adult, oldster, a doctor, lawyer indian chief, joiner, macdonalds burger flipper, massai warrior. How about a group of men or a group of groups. Hey maybe he is a she or a hermaphordite. ugh. It was a madhouse when I went to college 30 years ago. And worse today according to Tom Wolfe's new book (which I havn't read.) Man is the measure of all things is a hopeless measure even as measure. It doesn't work. Better to set all the measurements out to infinity/eternity/. Infinitely wise, good, powerful, omniscient, omnipresent etc. God is the measure of all things. This is a measure people can work with--and draw a plumb line. Lord have mercy on me for I have too often not loved or trusted you enough. amen.
The problem with the cynics' line of the 19th century "if God did not exist then man would invent him." is that its too smart by half.
As to the creation side of things scientists have hit a wall that has humbled them.(I've seen a link recently
http://www.nypl.org/research/newton/reason.html
to presentation by the new york library of the writings of newton that included his arian heresies as well as his scientific writings.)
as this point I quote from this link:
http://www.tothesource.org/4_14_2004/4_14_2004_printer.htmific writings
In the late 1970s the astrophysicist Robert Jastrow recorded this state of affairs in a book entitled God and the Astronomers. There he argued that the convergence between Genesis and cosmology should cause agnostic scientists to sit up and take notice, and even be a little worried. In one memorable passage in his book Jastrow wrote:
At this moment it seems as though science will never be able to raise the curtain on the mystery of creation. For the scientist who has lived by his faith in the power of reason, the story ends like a bad dream. He has scaled the mountains of ignorance; he is about to conquer the highest peak; as he pulls himself over the final rock, he is greeted by a band of theologians who have been sitting there for centuries.
Well said! In days of old, the prophets, speaking under inspiration of the Holy Spirit, (Third Person of God) would always qualify their prophecy by saying, 'thus saith the Lord,' so there would be no mis-understanding on the part of the listener or reader that the messenger was NOT God, but only the bearer of tidings.
When John The Baptist came on the scene, perhaps the last of the prophets who spoke under the inpiration of the Holy Spirit, he testified of the coming AND the presence of Christ Himself, the Second Person, who would speak directly to man.
When our Lord Jesus began his office, he spoke as one having authority within Himself, not once using the the phrase, 'so saith the Lord,' for this was the Lord Himself speaking to man, and few there were that were willing to understand that it was the day of their 'visitation.'
I suppose it was expected that the Jews, already conditioned for centuries to receive messages from the Third Person through another human, had great difficulty accepting the new paradigm, the concept of Emmanuel, God with us, speaking for Himself in the Second Person directly to mankind.
Of course, I don't think the Jews were condemned for not accepting God in the flesh, as they were locked into the law which said that they were to kill a blasphemer. In retrospect, it can be said that if the Jews did not abide by the law, there would have been no crucifixion. No crucifixion, no perfect sacrifice. No perfect sacrifice, no fulfilling of the law. No fulfilling of the law, no final atonement, no redemption.
If there were no final atonement, we'd all still be involved in blood sacrifices and cleansing the temple every year. I think it can also can be said that many of the Jews were blinded to the radiance of Christ lest they understood WHO He was and would NOT have crucified Him.
I think it was easier for the Greeks, and the gentiles in general, to accept the paradigm, for they had no such law to prevent them from understanding the logic and sequential (expanding) revelation of God to mankind. Again, if it were not for the obedience of the Jews to the law, we would not be having this conversation.
I think Plato would have delighted and rejoiced in knowing that the Word became flesh IN the microcosm, not AS the microcosm.
bttt
IEEE computer arithmetic allows division by zero.
Ordinary arithmetic forbids division by zero because there is no consistent definition of such. Extending the number system (by adding infinity and minus infinity as in IEEE) creates more special cases than the single "can't divide by zero" case. One loses the cancellation law for example. (IEEE arithmetic isn't a field so this doesn't matter as much.)
Otherwise your program blows up. If your define this in a special way in the context of computer programing, it's permitted. But I wouldn't try this on a test in math class unless you like arguing with math teachers.
Extending the number system (by adding infinity and minus infinity as in IEEE) creates more special cases than the single "can't divide by zero" case.
As you point out these are special cases in the context of a practical application involving computers. Computer aren't used in most math classes and traditional classes don't even allow handheld calculators.
Division by 0 in the real numbers is undefined because that is not a real expression. Neither is division by zero permitted in the hyperreal numbers which do have positive and negative infinitestimals and positive and negative infinitely large numbers. But you can in this context divide by infinitesimals and infinitely large numbers as long as the express in not indeterminant.
I thought you might get a kick out of the excerpt from Philo of Alexandria because it sounds so close to Max Tegmark's Level IV Parallel Universe based on radical mathematical Platonism. For Lurkers:
According to the Aristotelian paradigm, physical reality is fundamental and mathematical language is merely a useful approximation. According to the Platonic paradigm, the mathematical structure is the true reality and observers perceive it imperfectly. In other words, the two paradigms disagree on which is more basic, the frog perspective of the observer or the bird perspective of the physical laws. The Aristotelian paradigm prefers the frog perspective, whereas the Platonic paradigm prefers the bird perspective....
A mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would correspond not to a single frame of it but to the entire videotape. Consider, for example, a world made up of pointlike particles moving around in three-dimensional space. In four-dimensional spacetime--the bird perspective--these particle trajectories resemble a tangle of spaghetti. If the frog sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix. To the frog, the world is described by Newton's laws of motion and gravitation. To the bird, it is described by the geometry of the pasta--a mathematical structure. The frog itself is merely a thick bundle of pasta, whose highly complex intertwining corresponds to a cluster of particles that store and process information. Our universe is far more complicated than this example, and scientists do not yet know to what, if any, mathematical structure it corresponds.
The Platonic paradigm raises the question of why the universe is the way it is. To an Aristotelian, this is a meaningless question: the universe just is. But a Platonist cannot help but wonder why it could not have been different. If the universe is inherently mathematical, then why was only one of the many mathematical structures singled out to describe a universe? A fundamental asymmetry appears to be built into the very heart of reality.
As a way out of this conundrum, I have suggested that complete mathematical symmetry holds: that all mathematical structures exist physically as well. Every mathematical structure corresponds to a parallel universe. The elements of this multiverse do not reside in the same space but exist outside of space and time. Most of them are probably devoid of observers. This hypothesis can be viewed as a form of radical Platonism, asserting that the mathematical structures in Plato's realm of ideas or the "mindscape" of mathematician Rudy Rucker of San Jose State University exist in a physical sense. It is akin to what cosmologist John D. Barrow of the University of Cambridge refers to as "pi in the sky," what the late Harvard University philosopher Robert Nozick called the principle of fecundity and what the late Princeton philosopher David K. Lewis called modal realism. Level IV brings closure to the hierarchy of multiverses, because any self-consistent fundamental physical theory can be phrased as some kind of mathematical structure.
Wow! indeed, Stripes! Thank you for this most excellent post! I certainly will be reflecting on it. Liebnitz is an amazingly creative and penetrating thinker, one of the all-time greats. You know the philosphers claim him, too.
Understood, Doc. But my own experience does not extend much beyond working in terms of the decimal and binary systems (and I'm still "binary light"). And so I am thankful for your discussion of finite-continued, periodic-continued, and non-repeating-continued fraction expansions. There is "no decimal in the binary system," and so I wondered what binary expansions describing, say, a transcendental would look like. I think you may have given me a clue.
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