smallest size a space can occupy

No, but maybe I'm talking Alpo.

"Spandex..."

s-p-a-n-d-e-x = e-x-p-a-n-d = noun = verb

Omigosh. There goes my askiom.

What was wrong with spandex in its original form? Someone took it away why?

Oh. It expanded to another page.

I thought what I was asking, rhetorically I think is the word, was pointing out that theres no more sense in talking how small a space can be a space than how large a space or spaces can be a space or spaces. And, how could you ever know you had a boundary to measure from that remained a boundary once you decided on a boundary...if it was ever a boundary. Something like that. Yes you could say you had a point, or the last point, but you could never know you had either. So the point itself, of maximum contraction or expansion, is all in the mind while the construct of expanding, or contracting is not, I think. Except for wearing apparel or silicon valley houses.

Guest,

I think you got apples and oranges going there, so let me see if I can untie the knot...

Geometry is a set of logical thermos that allow us to describe certain aspects of our reality. In geometry, we're taught that a point has no dimensions. A point is not "a thing." Rather, it's more like an adjetive... "We are talking about this exact location here." It does not and cannot have dimensions. It just means "right, exactly here."

Later, in algebra, we take on the concept of areas and volumes with equations, especially inequalities, where we say "the locus of all points that are less than or equal to x,y..."

What you are proposing is something like the old Achilles Arrow chestnut, where Achilles shoots an arrow at a tree, and since we can half the distance over-and-over the arrow never gets to the tree. This is of course, based on faulty logic (even in mathematics), do a Google search, I'm sure the correct proof is out there.

Now let's move away from fundamental math and move more toward the physical sciences. In this realm, I think calculus-based math does very well at explaining the real world, but we don't really need to go there. Anyway, the question is asked "What is the smallest possible space." In other words, what is the smallest actual 3-dimensional volume that can exist. Keep in mind here that we are not asking "What is the smallest volume that the human mind can imagine." We're saying "screw imagination!" In the real Universe, what is the smallest volume that can possibly exist.

The true answer: "We don't know!" Of course, there are some good possibilities, such as Plank's length³, but we really don't know. Surprisingly, not only does it take vast amounts of energy to traverse the cosmically large, it also takes vast amounts of energy to traverse the cosmically small - hence the price tags of things like the CERN super-collider. Devices like the one in CERN, due to come online in 2008, are the types of machines needed to investigate the super-ultra small.

So, what if we're like a little, animated man on our computer screen - he thinks that his Universe is smooth and un-granular, because he can't tell the difference between one pixel or another. So he reasons that the smallest space that can exist is two pixels. Are we in the same situation? I'm not sure. However, the answer to these types of questions belong to the realm of nuclear physics and the physical sciences, and not the abstract concepts of mathematics.

Does this help any?

are not the abstract concepts of mathematics the source of nuclear physics as well as the basis of physical sciences? do we not have to resort to the concepts of mathematics to resolve any conceptual perception of this topic?

joshua

Yes, but pure math is sterile and leads to nowhere. As I said in my post, sooner or later the experiments and observations must be made. It's like trying to do astrophysics without using a telescope.

And if you need math, it's more likely than not you'll need calculus, which is more flexible than algebra or geometry where describing reality is concerned.

Hi Vermin,

It is Sunday morning, I am taking my two "drugs", coffee and the (new one) CR4 forum and I read your # 106 posting. I am telling to myself that this Vermin guy is a very smart one (having the same views as myself) but my controversy watchdog flagged the answer #108.

....but pure math is sterile and leads to nowhere. As I said in my post, sooner or later the experiments and observations must be made. It's like trying to do astrophysics without using a telescope........you have written.

Tell Mr. Fourier that his sterile math researches in the series field have no practical application and try to imagine his answer.

Also, I have forgotten the name of two astronomers who have found a planet (Pluto, I think) with their pencils, not telescope.

Have a nice and fertile day

"Have a nice and fertile day"

No! NO! One vermin is more than enough for the world.

What magnification were those pencils anyway? I think I need a couple of dozen. Please send COD.

......What magnification were those pencils anyway?

It is from high school time, the math professor, who was teaching astronomy, too, told us that the two guys discovered the planet by calculation before being seen, on tip of the pencil, as he used to say.

Now, if we start, again, that discution of the smallest space (for the tip of the pencil)....

A fertile day (in ideas) for you, too.

"The discovery of Pluto was rooted in a misconception. Before it was found, scientists believed that its existence had been indirectly determined through discrepancies observed in the orbit of Uranus thought to be the result of gravitational interactions with a more distant planet. However, Pluto is not massive enough to affect the orbits of the planets, and the discrepancies eventually turned out to have been caused by an overestimation of the mass of Neptune.

Observations of Neptune in the late 19th century caused astronomers to speculate that Uranus' orbit was being disturbed by another planet in addition to Neptune."

So your teacher was, for the most part, correct.

While we're on the subject of pencils, lets note that the eraser should not wear out before the pencil.

Now back to the smallest space paradigm. The smallest space can not be smaller than any single particle that occupies it. Therefore, we're right back to the same old question: what's the smallest particle? Answer: we don't know and I'm not so sure we ever will. Let's take vermin's halving analogy (flight of the arrow). Given that a particular particle exists, then, by its very existence, it must be such that (by some means) we could split it, then split it again, which of course leads to an ad infinitum discourse. At some point we reach an A. Priori position, that is, the proposition is knowable a priori if it is knowable independently of experience. This we can't do (yet).

I am flying, next Thursday, to Europe, I have a lot of chores to do before that: replace the door to the shack in the back yard, to finish the door bell electronics ( I bought a $19 ding-dong and I am spending two days modifying it to my specs – a one like that would cost me $59!), and so… Now, I am looking for trouble with my "smart" observations…but this is me…

You wrote:

……The smallest space can not be smaller than any single particle that occupies it. Therefore, we're right back to the same old question: what's the smallest particle?

But who talks about smallest particle? The initiator of this thread asked about the smallest space. And, because inside this smallest space there is NOT a smallest particle – which you decided that:

-what's the smallest particle? Answer: we don't know and I'm not so sure we ever will

therefore, because of being empty, we, for sure, are not obstructed by dividing this smallest space to an even smaller size, until we cannot see it

________________________

Everybody has an horizon of his views. For some, the horizon is broad, and for some it is narrow. For some, the horizon is narrowing and narrowing until it becomes, from a line – just a point. Than, this guys will tell you, with aplomb: this is my point of view!

"But who talks about smallest particle? The initiator of this thread asked about the smallest space. And, because inside this smallest space there is NOT a smallest particle – which you decided that:"

"Space" is the substance of particles! There can't be one without the other (sounds like a song I remember). If you subscribe to the BB, then you must admit that space precedes matter. Can you conceive of matter existing in the absence of space? Even in the void of deep space there is at least one particle in each cubic meter of space (jump on me if I'm wrong on this). In other words, there is no space that does not contain at least some matter.

It's easy to suggest that (as some have posted) that the lower limit is a Planck³, but if that's true then the BB began AT a dimension of a Planck³. Otherwise, we're back to the proposition of "no one knows!!!" (and I repeat: yet).

Addendum to previous post:

indel said in post #113 "But who talks about smallest particle? The initiator of this thread asked about the smallest space. And, because inside this smallest space there is NOT a smallest particle"

I said in post #116 "Can you conceive of matter existing in the absence of space?"

Answer: It cannot! Therefore it's reasonable to assume that matter itself creates space (going back to the BB theory). This reinforces what I said earlier that a space cannot be any smaller that a particle that occupies it (or creates it).

The first thing (according to the Standard Model) that appeared at the moment of the Big Bang was energy, not matter.

Here's a nice little piece on the discovery of Pluto.

"When the British tried to stake their claim in this momentous discovery, the Paris Academy of Sciences was in an uproar."

Leave it to the Brits...

"Scholars' opinion has been moving in recent years to increased awareness that Leverrier's open prediscovery publication of his predictions merits his credit, heretofore too long denied, as sole mathematical discoverer of Neptune".

indel said in post #111, that his math teacher said "two guys discovered the planet by calculation before being seen, on tip of the pencil, as he used to say". Looks like he was right:

"Le Verrier had a wife and children. He died in Paris, France and was buried in the Cimetière Montparnasse. A large globe sits over his grave. He will be ever remembered by the phrase attributed to Arago: "the man who discovered a planet with the point of his pen."

Just for that, I'm going to go out and get pregers!!!

I totally agree with you! I think we are talking more about semantics than we are about the real issue.

I, too, know the story of how Pluto was discovered. All I'm saying is that if after doing the math, they had just said "oh, well, that's that" and had just walked off, there would have been very little point in doing the figures. The next step was for someone to go to the telescope and prove what they had found.

Also, if I remember correctly, the reason why they did the math in the first place was that tiny discrepancies were being discovered in the motion of other planets.

Sterile might have been a poor choice of words. I'm just saying that sometimes math can lead to a reality that has nothing to do with our reality. It's not wrong, it's simply a mathematical reality.