John

http://www.shu.edu/html/teaching/math/reals/history/zeno.html

Jugs, the reason "it's all too much" is that it contradicts our senses, but it also makes reasonable sense. That's never an easy thing for our brains to work out.

Zeno came from a school of thought that claimed all motion was simply a series of illusions, shifting perceptions and opinions. In reality, according to this philosophy, all of the universe was fixed, never changing. According to the site I linked above, modern mathematics has enabled us to "solve" Zeno's problems to some satisfaction, but there is still some debate.

The problem with this, as with any philosophy this broad in implication, is that our mathematical system is based on how its various contributors over the centuries have perceived the universe, both concretely and abstractly. However, this belief in an unchanging universe claims that all our perceptions are false. If that's the case, then how can a system we came up with to describe our perceptions ever hope to prove or disprove the theory?

If you're going to be an ancient philosopher, be an atomist. At least they proved definitely right in the end.

Basically, given the information, the function is:

f(x) = x

on the interval [.999..., 1.000...1]. I know that's not exactly what abcd said, but we're dealing with points infinitely close to each other, so for all intents and purposes, that is the function.

lim x->n x

will always be n.

I asked the question about continuity because if the interval (as defined in a function) wasn't continuous, then taking the limit would not make sense intuitively.

If a function isn't continuous at a certain point, then the limit as the function approaches that point doesn't exist. You can work out the limit from either the left or the right, but since they won't be equal, by definition, the limit won't exist.

Those are my thoughts.

Edit: I forgot the answer the original question of the topic, heh. The answer is no. On a continuous interval, no matter which two points you choose, there will always be some point between them.

Light is unique. It shows properties of being both a wave and a particle, so perhaps attempting to deduce its means of travel using the rules for either is the wrong approach.

Read this. It might prove informative: http://www.olympusmicro.com/primer/lightandcolor/particleorwave.html

Depending on the experiment, light acts as either a wave or a stream of particles. In other words, it exhibits properties of both. Light is a strange thing. It requires no medium to travel, so far as I know.

I've not posted for a long time, and probably won't post again for a long time, but blike linked me to the site, so I guess I'll post my schedule, heh.

CSC 135: Object Oriented Programming I

ENGL 115: English Composition II

MATH 222: Analytic Geometry and Calculus II

PHYS 261: General Physics I

PHYS 261L: General Physics Lab I

PSYC 152: Introduction to Psychology

I'm also taking CHEM 124L (Inorganic and Analytical Chemistry Lab) this July, but oh well. Double majoring in physics and psychology.

I'm assuming you'll have access to a periodic table.

The atomic number of an atom will always be a whole number, because the atomic number is equal to the number of protons in the atom's nucleus (which is also equal to the number of electrons orbiting the nucleus). For example, if you look in the box containing sodium (Na) on your periodic table, you'll see that its atomic number is 11.

The mass number is usually written on the periodic table as a decimal number taken to a few decimal places. For instance, sodium's atomic mass number is 22.989770 (your periodic table might only take the number to three or four decimal places).

As I mentioned earlier, the atomic number is equal to the number of protons (or the number of electrons) in the atom. In order to find the number of neutrons, round the atomic mass to the nearest whole number (23 in sodium's case), then subtract the atomic number. Using this for sodium, you subtract 11 (the atomic number) from 23 (the atomic mass number). 23-11 = 12, so there are 12 neutrons in sodium's nucleus.

Welcome to the forums, Soulja. I hope you find the place acceptable.

"We are but packets in the internet of life." -Mike, UserFriendly.org

"640K should be enough for anybody." -Bill Gates

"How glorious it is -- and also how painful -- to be an exception." -Alfred de Musset

Let's hear it for Dyson Spheres! Woo...

If the universe is the result of an explosion in an empty vacuum, then wouldn't it follow that the universe is roughly spherical in shape? If so, then go back to the balloon.

The balloon is spherical, and it represents (without the curves around massive objects) the physical dimensions of our universe. The balloon is expanding. We reside on one side of the balloon. In order to find the center of the universe, wouldn't we just need to determine which object has the greatest redshift? That object would be moving in a direction directly opposite of ours, so (assuming the universe's expansion is roughly uniform, as it would be in this balloon scenario anyway) that would give us a direct line across the center of the universe. Perhaps that's what blike originally meant anyway. I don't know about Hubble's Law. In that case, just disregard my post here. Otherwise...?

Planetary colonization is an interesting prospect, and almost a default feature of any science fiction program. There are a few problems to be worked out, however, even if we do develop the technology to reach another world and set up a home on it.

The primary dilemma I'm imagining right now is the possibility of destroying life. Now, this could possibly easily be solved by the time we have the technology to reach other worlds, as we will possibly by then also have the technology to scan a world for life on the surface and below (this is all assuming we take the more environmentally friendly approach of *not* indiscriminately wiping out whatever we come across in order to colonize). However, what if the life form(s) on a given planet are not readily recognizable to us as life?

I'm reminded of an early episode of Star Trek: The Next Generation, in which a terraforming project mysteriously began having problems (such as scientists dying and so forth). As it turned out, the planet was covered in tiny crystalline particles which were only intelligent when existing in groups (for instance, grab a particle and it's simply there, but put it with about 500 others and it can attempt communication with you). The terraformers had noticed strange patterns of light emissions from the sands of the planet (where these life forms existed in a massive, highly intelligent group), but had not thought anything of them, since the scanners didn't read them as life at all. The small life forms were killing scientists and such simply in defense of themselves and their planet. Whether or not this exact instance is even possible in our universe, I don't know, but it still shows my meaning well.

Besides that problem, how about the politics? Mankind would have new territories to fight for, and the technology to make those wars very destructive. It would be wonderful, I'm sure, to kill ourselves off because we can't decide who gets to keep Mars (heh, this brings up another thought--what if some ancient, space-faring race has already claimed our solar system as its territory? That would explain the sightings of UFOs, if they are indeed alien craft--simply tourists, soldiers, or scientists, dropping in to check our progress now that we've taken baby steps into space).

I'm not sure what other problems would spring up, but I'm sure there would be many. ::shrugs::

Does this 10 GHz processor use 32-bit x86 architecture? Also, how many stages is this processor's pipeline? Sure, a chip can run at a huge frequency, but if the pipeline is too large, then this "superchip" will be inefficient, just as the Pentium IV is now.

I've spent a lot of time thinking about how people say the universe is so perfect, it must have been created. Perhaps my response to this was stated in the article, and I misunderstood, but here we go...

The Big Bang Theory, which I believe is the main non-Creationist (and even some Creationists believe it) theory for how the universe began, states that the universe started as a singularity--for any of you who might not know, a singularity is a point where gravity and density are infinite, where the normal laws of physics don't apply. Now, if this was what happened, then when the expansion began, any set of physical laws could have been created, randomly picked and such. Following this logic, why do we assume that our universe is the only one in which life such as ours could exist?

There are constants within our universe which, if they were modified only a tiny bit, would prevent stars from forming, or life from forming, or whatever. That's what scientists say, but why must we assume that a completely different universe, with different laws of physics, would be affected so much by having those constants set at a different value? Perhaps there's a universe somewhere where scientists are saying that if the cosmological constants were set to the values they have in *our* universe, life couldn't exist, or stars couldn't form, etc.

We are bound to imagining things as they are inside our universe. We can't predict what other randomly created universes might be like, because they're completely outside anyone's experience, assuming that one is from our universe.

Another way to think of it is to imagine your life as a series of occurrences that might have been different. For my life, for example, I would never have been born if my dad hadn't made a phone call through the operator and met my mom (who was the operator). He wouldn't have been in America to make that call if he hadn't moved here from England, and he might not have moved here if his dad hadn't died in 1983 (or maybe it was 1982?). Now, could I validly sit here and say that if those events had been different, then my dad would definitely never have had another son? Of course not. Said son might have been completely different than me, but he'd still be there, and he might have even started thinking about what it would have been like if events had been different in Dad's life. This method isn't the best, since it doesn't rival the complexity of the universe, but it still serves to illustrate my point.

I just thought I'd throw that into the mix, whether I worded it well enough for it to make sense or not. Have fun responding.

I still love you, though.

You're still limiting yourself to our current understanding of the universe. We've done things that were considered impossible by all logic a relatively short while ago, and cracking an encryption that seems uncrackable now will fall into that category, I think.

Heh, that's so sad.

I guess it would suck if someone harboraing ill intentions towards our government found a way to send the command from the outside, heh. Spy plane flying around, suddenly all its computers die, plane crashes, there you have it.

It is my belief that any encryption algorithm we create will ultimately be crackable. The human mind can work a way to crack any technology it creates to prevent cracking.

As for it being proven mathematically impossible, you're limiting yourself to our current understanding of mathematics. A while ago there was no 0, and/or there were no negative numbers, and/or there was/were no [insert most of the other stuff in our mathematical system]. Mathematics is evolving all the time, and using our current understanding of it to say something is certainly impossible isn't valid, in my opinion.

For the physics aspect, much the same applies, as was briefly mentioned in Radical Edward's earlier post.

My vote for Linux stands, although FreeBSD shouldn't be listed as a separate option, since it is, after all, a flavor of Unix.

Heh, seems my posts are mainly going to be links to others' knowledge, rather than my own knowledge.

For a good description of shock, check out this page:

http://www.nlm.nih.gov/medlineplus/ency/article/000039.htm

I'm sure most of you have heard and/or read the story by now, as it's been out for several months, but I still find it intriguing. I'm wondering what you all think about this development, and its implications. Perhaps this would be better placed in the ethics forum, however.

For those of you who haven't learned about the technique of controlling rats by remote, check out this article:

http://news.nationalgeographic.com/news/2002/05/0501_020501_roborats.html

I remember watching a television program about HIV and AIDS, which mentioned prostitutes in Africa who were apparently immune to HIV. The show had a wonderful 3D rendered sci-fi representation of the human body as a futuristic city, with all sorts of things traveling through, but that's unimportant here. I found an article online which briefly describes a similar trend:

http://www.aegis.com/news/newsday/1998/ND980701.html

Making body parts is a wonderful prospect for medicine, and I don't see any ethical problems there (or perhaps I'm just short-sighted).

As for full human beings, I don't know. The religious view that a clone wouldn't have a soul doesn't seem logical to me, assuming we even all have souls in the first place. A cloned human would be just another person developed in a womb and growing on this world. The fact that it would share DNA sequences with another person shouldn't preclude its possession of a soul. Aside from that, I see no real problems with cloned humans, as long as we remember to place more emphasis on the "human" part of that than the "clone" part. However, human beings do tend to value their individuality (this even includes those who spend their lives trying to imitate and impress other people), so I suppose that could pose a problem.

Humans tend to fear the unknown, and that's even true with new technology. Cloning is a pretty famous process now, but the idea of using that ability on ourselves still falls into the realm of enigma, so it tends to alarm and frighten most of us. If it comes into being, and human cloning becomes an everyday process, I'm sure we'll all grow used to it in a few years, and look back, laughing, at our concern over the ethical issues.

Of the posted options, I'll choose Linux. If you want customization, Windows doesn't come close. There are loads of window and file managers available to run with the X window system. If you want to talk about stability and vulnerability, then I've seen no evidence that Windows rivals Linux, except perhaps XP. And if Linux is vulnerable and unstable, at least a knowledgable coder has the chance to correct the problem for himself and post the solution on the Net for everyone else to download. ::shrugs::