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Lets take the nuclear bomb as an example. The creation of this technology was by a group of people so pre-occupied with "could we" they never stopped to ask themselves "Should we?"

I'd like to suggest that tolerance is paramount with people we don't agree with today (ie: Webweebill) because the conflict of ideas is a necessary condition to learning, and getting ideas from all angles is a good thing. Let's encourage discussion rather than try to silence a few we don't agree with. Do we have to label things we don't agree with as crap?

Lets take the nuclear bomb as an example. The creation of this technology was by a group of people so pre-occupied with "could we" they never stopped to ask themselves "Should we?"

Though I like what I'm hearing from and agree pretty much with Abelian, I'd like to suggest that tolerance is paramount with people we don't agree with today (ie: Webweebill) because the conflict of ideas is a necessary condition to learning, and getting ideas from all angles is a good thing.

It is rocket science in terms of what we know today, in fact the materials & science behind it was serendipidously discovered by Fermi and others in an attempt to fill out the periodic table.

Knowledge has no morality either way and the people who drive applications for it like bombs are politicians and the people who elect them.

A typo, it should have read "It ISN'T rocket science" ...sorry about that.

Your comment is specious. The fact is, that by studying nature, one is going to find out how nature works. After that, developing a use for that knowledge is engineering. Knowledge has no morality either way and the people who drive applications for it like bombs are politicians and the people who elect them. The internet started as a military project. Does that make it bad or does the concept of ``bad'' depend upon how people use it?

There is serious investigation taking place into the possibility that all we see is only a small part of a much greater whole, specifically that our universe is only one of perhaps an infinite number of universes. It's part of a matrix of continuous "creation" for lack of a better, less religiously-charged phrase.

If that is the case, don't all probabilities begin to approach 100 per cent? Somewhere, somehow, a species of "pig" actually evolved the capacity to fly? There's actually an honest car salesman? The government is really there to help someone?

Silly examples, I know, but you see my point. What are the implications of it?[/quote


well from my perspective this is a vey religiously charged proposition. to deal with the scientific implications first though... for a multiverse of infinite universes to exist time as it is relative to your perception would have to cease to exist, it would only be a quantum system where your only point of reference for time would be your current manifestation. What I mean is that your birth and death way of life would become a sort of eternal state of existance. This seems impossible with the current model of the universe as generally accepted by science. If you were to think outside the box though, and focus on the possibe and accept the existance of such 'infinities' rather than closing your mind and saying it's impossible because there is no proof of such existance, then we have a debate because this universe and all it's laws would most definitely want to be eternal relative to all other universes. kind of like ego.

As for your flying pigs example, it wouldn't nessesarily happen in our universe, but in other universes it could be the norm. just because something is the norm for most universes doesn't mean it isn't impossible in whatever universe you're focusing on(1+1 will always be 2 not three because that is the law in this universe). take gravity for example, it is one of the laws that actually gives you a perception of what the universe is. I think gravity exists in the multiverse aswell. Not so much as it relates to matter but on a quantum level where only similar manifestations occur relative to the patterns that emerge. sort of like the similarities and difference from the dream world to the real world. perhaps the honest salesman would get a true sense of self worth because he subconciously knows that he is the only one not only in his universe but the multiverse aswell.

While there aren't any applications of Cantor's work on transfinite numbers I'm not going to say that they can't be applied in physics.

As a side note I take issue with your usage of "abstract concept" as you seem to be using it as "nonexistent". Abstract concepts may very well exist and they may exist independent of minds (Plato, Frege, et al).

If you don't already know that quantum mechanics is the basis of modern electronics, then you have far more to learn about that subject than I or anyone could teach you on a mere forum! Start with a basic textbook.
Even the transistor (the fundamental unit of integrated circuits) is based on electron tunneling, which is a quantum effect.

I think that's what I said but I'm not sure what you're saying. Are you saying that each new sphere has the same volume as the original or are you saying that the sum of their volumes are equal to the original?

This distinction, minimally, dates back to Aristotle in that infinity is always potential, never actual because we never "get there". This was Poincare's objection to Cantor's work.

Cantor's work is actually in contradiction to Aristotle's thesis here. From what I understand he does actually take time to argue why there can actually be an actual infinity but I haven't read his argument. What I can tell you is that actual infinity is essential to mathematics. Bertrand Russell found it necessary to assume the axiom of infinity; he tried desperately to avoid it but was unable to do so. ZFC also has as one of its axioms the axiom of infinity. So as far as mathematicians are concerned, infinity is not merely potential. An actual infinity seems to be indispensable to mathematics unless some able mind can figure out how to do mathematics without it.

Lets take the nuclear bomb as an example. The creation of this technology was by a group of people so pre-occupied with "could we" they never stopped to ask themselves "Should we?"

Knowledge has no morality either way and the people who drive applications for it like bombs are politicians and the people who elect them. The internet started as a military project. Does that make it bad or does the concept of ``bad'' depend upon how people use it?

Are we still talking about the reality and/or theory of an infinite universe, or are we just trying to show who is best at casting shadows on other peoples life perspectives?

Let's encourage discussion rather than try to silence a few we don't agree with. Do we have to label things we don't agree with as crap? Can we be a little nicer even when we beg to differ?

In short this is more of a philosophical question to answer why our universe.

There ARE plenty of applications of Cantor's work on transfinite numbers. Scientists in Physics and the rest of Science are just ignoring Cantor's work right now, because Cantor showed that the ZF axioms don't properly describe our world, and that really scares scientists, because it means that everything they know is "relative".

I'm saying that the sum of the 2 spheres is the same volume as the original. Each sphere will end up having half the volume of the original.

Now, let's argue the opposite: imagine that there is a finite distance, that we will reach, and at that distance, we cannot subdivide the ruler any more. Then we cannot measure that distance, because if we did, then we could cut it in half too. But then we cannot see that distance. The distance between the 2 ends of that subdivision are right next to each other. So that distance is 0. But then if we add all those subdivisions up, we are just adding zeroes to each other, and hence the total distance of the ruler is 0. But we know that the distance of our ruler is 1. That is a contradiction.

That is why Cantor's theorem relies upon a proof by contradiction. Our very system of counting must be self-contradictory, for it to work in the first place. But it doesn't have to be contradictory within its own system, only when comparing different levels of the same system.

If someone tells you how to make a weapon that will make you rich, but is easily copyable, and if ONE such weapon ever falls into the hands of terrorists, that would make it easy for any terrorist to kill thousands with one push of a button, would you give it to the military, knowing that at some point, it almost certainly will fall into the hands of terrorists? Or will you gamble that all the terrorists will be killed or incarcerated before that happens, and there won't be any more terrorists, before any of them gets hold of that weapon?

In my opinion, it would be clearer to say that modern electronics relies almost completely devices on ONE flexible type of device, semiconductor devices, such as the solid state transistor, which were based on quantum theory. It's a subtle difference. It's the difference between saying that vaccines are based on science, and vaccines are based on germ theory. One is a lot clearer than the other.

ZF is post-Cantor. I assume you are referring to Godel's theorem though that isn't problematic for physics as such - it just shows that mathematics is not reducible to formal systems.

That's incorrect. What makes the Banach-Tarski Paradox a "paradox" is the fact that it goes against our geometrical intuitions: the two spheres are both individually the same size of the original; the volume is doubled in the process.

I'm not entirely following you on this point. I think the supposition that, say, length has natural units (something derived from the Planck length) and that all lengths are some multiple of those natural units and therefore cannot be divided further. This doesn't imply you couldn't measure them per se, their measure would be "1" or to put it another way, you can't measure them but you can count them. Our forms of measurement then are reduced to forms of counting (a distinction that can potentially address some of Zeno's paradoxes.) So we aren't adding "0's" we'd be adding "1's". (Even if we were adding "0's" it still wouldn't necessarily be 0. This is how calculus proceeds by dividing up, say, the area under a curve into infinitely small parts and adds them up to get some value which isn't necessarily equal to 0.)

On Zeno, we can introduce this notion of "measuring" and "counting" and the concepts that go with them and suggest that some of his paradoxes are category mistakes of this kind. One of his paradoxes can be sketched in the following way:

Suppose I am at some point A and I want to arrive at some point B different from A. In order to do that I must get half way between A and B at some point C. Now in order to get to point C I must arrive at some half-way point we'll call D and so on. In this way I will never arrive at the next point.

The next point might be thought of as an intuition that comes from our counting methods. We always have a next number (1, 2, 3, 4, and so on) and we can specify what the next number is.

When dealing with sets that are "dense" such as the rationals, there is no next number; there are infinitely many rationals in between any two rationals. The notion of "next" only applies when we are counting, not measuring.

I'm not sure where you're even going with this. Proof by contradiction is a standard technique in mathematics and logic. It simply assumes some statement P, derives a contradiction from assuming that proposition and then concludes that P must be false.

I have news for you. Building an atomic weapon is not very difficult. It requires collecting enough fissionable material as close together as possible in a very short amount of time. This has been known for over half a century. The only thing which prevents any country (or group of terrorists) from constructing one is getting enough enriched 235U to make it. One needs only to calculate the probability of fission from an incident neutron as a function of energy to determine the volume of a sphere (or any other shape) of 235U required to go supercritical. (It doesn't have to be particularly efficient, so there is no reason to get fancy.) If the data weren't available, a peecee and a few data points would make the task fairly straight forward.

Stop appealing to emotional arguments. Those have zero merit and are a dead giveaway for a lack of any logic.

The real secrets of any concern here are designing efficient weapons and creating encrypted interlock schemes to prevent someone from making use of bomb which gets dropped but fails to explode. Even where encryption is concerned, encryption is not considered secure if it depends on hiding the encryption algorithm or the details of the implementation.

No one has the right to supress knowledge.

You seem to get the cause and effect backwards a lot. Quantum mechanics tells you what properties the materials must have to produce the phenomena needed for things like transistors and it also tells you all of the ways to change its properties to create lots of variations so that it's very flexible, as you put it. The choice of materials is dictated by the materials that exist in this universe which have the properties necessary to function as the equations predict. The choice of materials was not arbitrary and semiconductors were not discovered blindly by trial and error. Since there exists no theory which is an alternative to quantum mechanics, quantum mechanics and science are the same thing. Ditto for the germ theory, unless you dispute the existence of microorganisms or their responsibility for infections and disease AND have a better theory which explains germ theory as a subset.

The fact that I don't genuflect at its altar has nothing to do with lack of intelligence.

Consider the same sphere. But now, imagine that it is made of water, enclosed by a covering of infinitely thin, but infinitely strong plastic.

So I really don't see how it is possible to get more than we started with, even on a theoretical basis.

Fair enough. My main view is that if you ignore the emotions of it, it is still a moral argument,

That might be so. I just came across a lot of people who believed that the reason why terrorists cannot get atomic weapons is they cannot find out how to make them.

But that would rely on the encryption system itself being impossible to crack.

Fortunately, right now, no-one has yet put a method on the net, at least as far as I know, to crack public-key encryption systems.

But I'd still say that my pool-playing is based on mechanics, even if I didn't know any people who played pool without knowing anything about mechanics at all.

I think what you are trying to say is that the current design of semiconductors is an EXAMPLE of an application of quantum theory.

Your right knowledge has no morality until that knowledge becomes reality... kinda like VX Gas..