It’s from 300 BC, and has remained largely unsolved.
If you don’t know the paradox here’s how it goes.
Let’s say you wanted to get to the fridge. You would first need to get 1/2 way there, and to get 1/2 you’d need 1/4, and 1/4 you’d need 1/8 and so on. In an infinitely divisible space, because there is no smallest unit, you could never accelerate from 0 to 1 m/s. How is this not true, other than that you’ve eaten from the fridge recently?
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Zeno’s paradox. It’s from 300 BC, and has remained unsolved, until recently. With calculus we were able to show that eventually Achilles will catch the Turtle. But this doesn’t seem possible to me? Perhaps I misunderstand what exactly was disproven.
If you don’t know the paradox here’s how it goes.
Let’s say you wanted to get to the fridge. You would first need to get 1/2 way there, and to get 1/2 you’d need 1/4, and 1/4 you’d need 1/8 and so on. In an infinitely divisible space, because there is no smallest unit, you could never accelerate from 0 to 1 m/s. How is this not true, other than that you’ve eaten from the fridge recently?
Okay, I did some research and realized that someone has mislead me. Only some of Zenos paradox were disproved. The paradox of infinite space is not disproven. We must still live with that brain twister:
If space is infinite, it would be impossible to move without moving at the speed of infinity, or instantaneous travel. If space is not infinite, what is between the smallest points, or perhaps more prudently, what are the smallest points?
Zeno’s paradox. They’re from 300 BC, and has remained largely unsolved, until recently with complex calculus. But this doesn’t seem possible to me?
If you don’t know the paradox here’s how it goes.
Let’s say you wanted to get to the fridge. You would first need to get 1/2 way there, and to get 1/2 you’d need 1/4, and 1/4 you’d need 1/8 and so on. In an infinitely divisible space, because there is no smallest unit, you could never accelerate from 0 to 1 m/s. How is this not true, other than that you’ve eaten from the fridge recently?
Its 2:30 am and for the last three weeks all I’ve been able to think about is a girl and in the last three days I’ve suddenly come to the realization that I have some of those very strong mushy feelings for her…
If it weren’t Zeno’s paradox I would find that response very disappointing. But in this case I find it exciting! I’ll gladly be patient for a well thought out response.
Quantum_Spirit wrote: If it weren’t Zeno’s paradox I would find that response very disappointing. But in this case I find it exciting! I’ll gladly be patient for a well thought out response.
Anyone else?
haha If i get the chance to think about it… I have mushy feelings and one special girl on my mind :S
Numbers and words can be manipulated. Many Biological questions can be simply answered. Because it just is with faith. Take the wind for example you can’t touch it but it’s there. The Plant Earth was formed when anti-matter and matter came together, a balanced equation. Cellular respiration is the opposite equation of photosynthesis. The air we breathe keeps us alive. Small to infinite and large to infinite. Keep it simple.
As intriguing as I find science to be, unfortunately, I am not very perceptive in the subject. Especially when you bring physics into the equation. Therefore, any stab I attempt to make at the paradox will be likely groundless and fairly unintelligible.
Okay, so if space is infinite, there is no incremental increase in speed. There is no smallest to point to move to. On the number line, there is an infinity between 0 and 1.
So if you want to move from point A to point B, your speed needs to increase incrementally, right? Well how do you that logically, when there is no smallest increment to start with?
If you were to teleport somewhere, instantaneously, that would be the “speed of infinity”, because it took no time to get there. It seems more prudent to say “potential” infinite speed, because there is no limit to the distance traveled.
It seems that scientists and physicists don’t bother with the philosophical implications of a possibly infinite space, and are determined to say the there is a smallest point. First there were cells, then molecules, then atoms, sub-atomic particles and now strings have all been deemed “the smallest point in the universe”. Let’s say they’re right, strings are the smallest points. What then? What’s between the smallest points? How can there be non-existence? How can there be travel between them?
Ahh, now your on to something…How is anything that we see possible? Somethings, may indeed defy logic, some even exhibit this characteristic. Quantum mechanics for one.
Take negative energy for instance. A very real thing, that is created by having two plates in proximity in empty space. In the vaccum, electrons and anti electron will pop in and out of existence. Briefly creating negative energy.
logic by human definition is infalliable, i believe the truth to understanding this paradox is more the wording and the dichotomy it presents to the human mind than its real mathematical inconceivability
mathematical calculations don’t deal with the reality, they deal in ether, ideas, concepts that supersede infinities.
For instance, the number one, holds an infinite number of parts, how can it possibly exist in any time frame? It can’t.
When you call yourself one, you are referring to an idea that binds yourself together. But in reality there is no boundary between your trillions of cells that coalesce to form the idea of you.
When you add two apples together they total two. But can never be equal.
Chaos is not predictable, it is random. But even complete randomness(chaos) can have parameters. And that’s how quantum mechanics work.
According to current quantum theory, there is a chance that your entire body could teleport to the other side of the universe, but there may not be enough time in the universe for that probability to occur.
The orbital path of electrons around an atom are described mathematically by asymptote. They are most likely to be found near the atom, but have the potential to be anywhere in the universe.
allow me some time to digest you’re responses
(its getting late my mind needs rest lol)
I’ll give you a decent response tommorow.. you’re quantum theory response seems akin to Zeno’s paradox, thats will take me a least the night to wrap my head around :)
If you were to walk to the fridge how would you get there?
You walk haflway, but to get halfway you first need to walk a quarter, and to walk a quarter you need to walk an eighth and so on. In an infinitely divisible space, there is no smallest fraction to walk first, you would need to skip “x” number of units to get anywhere. And that “x”, in relation to any point on the number line would contain an infinity, and thus could never be moved in any finite acceleration. And so, moving at the speed of 1m/s is actually moving at the speed of infinity….But’s that’s in an infinitely divisible space. Who’s to say we live in that?
Oh Quantum, I see why you needed me, the answer of course is to not to attempt to reach the fridge, but to have someone else fetch the required item for you. Thus conserving energy and giving you more time to think about other more important things, like what to have from the fridge next, or maybe what to have from the cupboard…
Now that is a much more difficult paradox to solve… though I find the practice of closing your eyes, waving your finger around and stabbing blindly at the menu very successful, if only because you almost always land on something you don’t want, and the thing you do want becomes blindingly obvious.
Ha, ha, aside from solving 2000 year old paradoxes we’ve managed to find a way to finally decide what’s for dinner before checking the fridge. Amazing, simply amazing Jessica!
lol, really what does this paradox make consider? How does it make you feel? Is it a good feeling or is it somehow annoying to think that we may have a finite universe or what? I’m a sucker for people’s opinions. They’re my brain’s lifeblood. :P
Personally, I think it’s about as relevant as whether my toilet seat is up or down when I scratch my nose. I think sometimes, this type of questioning is moot, I’m very much one for question everything, but when a question is so blatantly wrong, (because we can in fact get to the fridge) I see little point in trying to fathom it, as there is nothing to fathom. That, and I can’t stop vomiting, so I can’t say I feel much but achey and sick…
Perhaps this isn’t your mode of thinking, but really it’s supposed to show how living in an infinitely divisible universe is improbable. But then you have to consider living in a finite universe. The implications are just as great, for there would non-existence in between points.
But nowadays, things have become more illuminated with technology, and we KNOW that particles travel at the speed of infinity, since they manage to pop in and out existence.
Your welcome to think it’s all irrelevant, but you are a part of this world, and you are subject to the truth of the fabric of reality. How this affects you may be unknown, but affect you, it does.
I really don’t care right now. I’ve got enough ‘real’ stuff on my mind. I might care next week, but right now I really couldn’t care less. It isn’t really anything to do with the subject, you could give me any paradox and I’d have the same stance.
The non-existence is more relevant than you or I know. For instance, it would mean that our form of mathematics is flawed, because on the number line, there is an infinity both large and small.
—-0—-> Large infinity
(1/2,1/4,1/8…) Small infinity
With points of non-existence, we would need to incorporate this into our perception of reality, and the number “one” would no longer contain an infinite number of parts, for in reality is limited to “x” number of parts. So even the concept of a number would need to change fundamentally, when dealing with reality.
Quantum_Spirit wrote: The non-existence is more relevant than you or I know. For instance, it would mean that our form of mathematics is flawed, because on the number line, there is an infinity both large and small.
—-0—-> Large infinity
(1/2,1/4,1/8…) Small infinity
With points of non-existence, we would need to incorporate this into our perception of reality, and the number “one” would no longer contain an infinite number of parts, for in reality is limited to “x” number of parts. So even the concept of a number would need to change fundamentally, when dealing with reality.
Nothing is relevant unless made so or observed to be so.
for example being shot in the back of the head could be seen as irrelevant to the victim because he never had a clue about it. Therefore this will only become relevant if we look at it, and since according to chaos theory (i think correct me if im wrong) Atoms/molecules behave differently than expected when observed right? after this discovery WE made it relevant. before hand it wasn’t.
Ah, ****. I have no idea what happened there. It told me page load error, and when I reloaded a second time it wasn’t there. So I retyped, and then my message appears. Stupid computers!
Relevance is made by the subject, not the observer. The structure of a building is relevant to it’s integrity, much like the structure of reality is relevant to it’s outcome. Relevance is not based upon the observer, but the “idea” is created by the observer. Much like Einstein’s theory of relativity.
I really don´t see the big problem with this one. Acceleration and distance are two different things. You can easily accelerate trough all the steps even though you take one at a time.
When going to the fridge is the case i don´t see the big issue.
Also talking about speed and distance without relevance to a certain task can go on forever.
One does not need to wonder about these things even though they´re interesting. In our lives the relevance of speed and distance is clear. Not a huge issue.
Well, there’s something to what you say. But in my eyes, the relevance of infinity supersedes my own life…So killing the cat, is a moot point to me.
Although, finding answers is the key to the choice. I could spend my entire life studying physics and mathematics and never understand the fundamentals of this existence. So, it’s a difficult choice.
I’ve read one of your posts that was largely a bio, and it appears we share some commonalities. Now that I have the opportunity to converse with you, I find you intriguing. So, I added you to my friends list.
However, we don’t share all that similar an age, I am 22. Although I understand where your coming from, and appreciate the sentiment, I feel this paradox to be very essential to many things. I intend to follow it to a possibly large extent. Really, it depends where I can go with it. Which may be nowhere.
Quantum_Spirit wrote: Well, there’s something to what you say. But in my eyes, the relevance of infinity supersedes my own life…So killing the cat, is a moot point to me.
Although, finding answers is the key to the choice. I could spend my entire life studying physics and mathematics and never understand the fundamentals of this existence. So, it’s a difficult choice.
I’ve read one of your posts that was largely a bio, and it appears we share some commonalities. Now that I have the opportunity to converse with you, I find you intriguing. So, I added you to my friends list.
However, we don’t share all that similar an age, I am 22. Although I understand where your coming from, and appreciate the sentiment, I feel this paradox to be very essential to many things. I intend to follow it to a possibly large extent. Really, it depends where I can go with it. Which may be nowhere.
I understand the urge to follow these matters. It´s like figuring out things greater than oneself. I´ve been thinking about such matters for some years. It`s hard to find people really interested. I´m currently trying not to think too much about such matters as they seem to consume my life too much. Seems there is some link i need to find to get out of my current place. The search is on and i think it´s gonna be a long time before one is out of the woods again.
Although it´s really cool to wonder of the universe and it´s big questions one need to find some peace in life too. I had that a long time ago and i´m searching to get to the same state of mind. I´m not going back cause the only way is forward.
Hmm… Seems i´m just going to go on and on so i better stop..
Quantum_Spirit wrote: Okay, so if space is infinite, there is no incremental increase in speed. There is no smallest to point to move to. On the number line, there is an infinity between 0 and 1.
So if you want to move from point A to point B, your speed needs to increase incrementally, right? Well how do you that logically, when there is no smallest increment to start with?
If you were to teleport somewhere, instantaneously, that would be the “speed of infinity”, because it took no time to get there. It seems more prudent to say “potential” infinite speed, because there is no limit to the distance traveled.
It seems that scientists and physicists don’t bother with the philosophical implications of a possibly infinite space, and are determined to say the there is a smallest point. First there were cells, then molecules, then atoms, sub-atomic particles and now strings have all been deemed “the smallest point in the universe”. Let’s say they’re right, strings are the smallest points. What then? What’s between the smallest points? How can there be non-existence? How can there be travel between them?
So what exactly do you suspect? Why are you so adamant about finding an answer?
It sounds like they don’t have the answer so they’re saying “well than there has to be a smallest point” because its easier (and more reasonable, logical) than it would be to say “Hmm…maybe we’ve got something wrong here”
I wonder what else is wrong about our methods of reasoning…
It’s difficult to say because I’m not a physicist. But I suspect that there may be something very wrong with our methods of reasoning and observing. Time and space may be very different from our current ideas, but I’m not an expert. Einstein was. I’m sure at some point he heard the dichotomy paradox. I just don’t know what he thought of it…
An illusion perhaps? That is part of the intended purpose of Zeno’s Paradoxes. To show that the subjective world is an illusion and that we are all one. I agree with the universe being “one”, but I don’t know what to think of the illusion concept.
Time is the fourth dimension of space. If you think of a still frame of a three dimensional world, that is the world without time; locked in place. When you add time, it changes the function, and creates new forms of the previous three dimensional space.
Maybe time is like a great scrambling of a once still frame. Now it’s totally tangled and a huge mess of energy or “strings”. Have you ever seen fractal zooms?
Fractals are equations. That whole thing is like a graph of an equation. You can find some 3-d fractal zooms also. I don’t know how far they go because computers can’t really calculate infinity. They can calculate to very small points, but they can’t calculate infinity, unless…maybe if you had it continuously calculating….but I didn’t that’s what they do with pi…not sure about that.
Equations of what? Did I miss the part where you told me what they are equations of? I suppose I could just look it up myself, but I’m really discouraged today.
Xeno Dragon wrote: Whatever it is, I think this site figured out a way to inject heroin right into out eyeballs while we’re on it. It’s addicting as hell.
Yeah, I suppose its easier to say that than it is to say “I have developed a nasty habit of living in virtual land with people I will never meet”
It’s what you make of it. I’m really not concerned with the time I spend here, or the fact all this text is all in virtual space. If you think about it, your entire life is in virtual space, your head. Haven’t you seen the matrix? None of this has to be real. So where’s the problem in virtual land? Your consciousness is nothing else but a simulation of stimuli. Your senses aren’t really “truthful”, they’re just electrical signals interpreted by your brain, and can be fooled with things like a tv screen.
The only thing that’s really important in this world is knowledge. Nothing else matters, nothing else improves, it just changes.
And plus, the internet, is here to stay. And is one of the best things we could have done for society. So you might as well accept the virtual.
1. Yeah I’ve seen the Matrix (its a movie!), and I understand the concept of perception but I don’t think that my entire life is in my head. So I disagree with some of what you said.
2. Knowledge. AND growth AND love are also important. Among other things.
3. I don’t know if it IS here to stay. And I dont know if it is one of the best things. And no.
I wouldn’t expect you to agree. But the truth is, everything you know and understand is in your head. Even though the events took place in reality, your version exists only in memory, and that memory is from what really happened. The truth seems like it’s always far more complex than anything else.
Love is an extension of knowledge. There is no love without knowledge, and if there was I wouldn’t want it.
The internet has brought people together from all over the world, and brought with it many expansions of freedom of speech, like youtube.
Yes and it also disconnects people from reality (please don’t retort with “what is reality?”) it keeps people out of the moment and away from PEOPLE. It also aids social regression.
I don’t know if I want to get into the rest with you - I think it would just turn into a frustrating discussion.
right i’ve come into this uber late, so i apologise if this has been said before and i’ve missed it;
i think it’s a linguistical problem, not a scientific one. the problem isn’t that space may or may not be infinate, in my opinion the problem is that the vagrancies of the english language sometimes lead us down a blind alley. there’s a riddle that is another example of language being used to describe a mathematical problem to create a paradox:
Three people check into a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers that the room rate is $25 and gives $5 to the bellboy to return to the people. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the missing $1?
It’s interesting that you say it’s a semantic dilemma, as my father said the same thing. I think perhaps were just not looking at the same implications of the paradox. Perhaps you could explain what the language problem is?
this is where my ideas slightly fall down, i’m not exactly certain :P in know that in both cases the paradox element comes from the fact that describing an action as opposed to accounting it mathematically lead to a logical fallacy, but it’s hard to work out where. perhaps that in itself is the nature of a paradox (oooooo). the problem seems to lie in the division of space, and the description and rules we apply to those divisions. in nature the space between the fridge and my empty tummy is continuous, but in science it is divisible, and perhaps it’s the relationship between two irreconcilables that causes the paradox. or you could say that a paradox is merely a loop the loop of language, which in it’s truest form has no solution, and therefore the debate of it will only lead to pretentious postulating and extra paradoxes (and seemingly alliteration). you see, it makes us all look like idiots!!!
Yes, those are very similar conclusions to mine. Except I was pondering the concept of how it shows that our current mathematical languages are flawed, because they do not deal with the problems that occur with infinity. For whether space is or isn’t infinitely divisible, our concepts of mathematics are. And that leads to a paradox.
you managed to eloquently say the conclusion i was slowly struggling towards! it’s a really interesting dilemma, because it seems to imply that at some point in order to further our understanding of the universe we will have to either discover a particle which is indivisible, or completely redesign mathematics.
Jubilee wrote: you managed to eloquently say the conclusion i was slowly struggling towards! it’s a really interesting dilemma, because it seems to imply that at some point in order to further our understanding of the universe we will have to either discover a particle which is indivisible, or completely redesign mathematics.
YES! Finally someone who agrees with me! I’m so glad that I made this post now! Although we may not need to completely redesign mathematics. Perhaps just tweak it, here and there, or give an alternate form for dealing with infinity.
Or just completely redesign it, as the entire number line, which our mathematics are based on, contains an infinity at every single point, and continues to infinity in both directions. So, in either case, I’d say there’s some thinking to be done in this field.
i love that now you sound like some sort of crazy person who’s been harbouring a secret theorem that you aren’t allowed to mention at dinner parties because everyone laughs, you sound so vindicated! the thing i don’t understand though is how could we tweak maths to deal with infinity? surely that’s like trying to tweak lego bricks to deal with complex curves; it’ll only end in a mess that’s neither one thing or the other. perhaps it’s possible that the two things are just irreconcilable, because the only way we can understand and make formulae out of the universe is to quantify it, but the universe itself defies quantification (i think i just made that world up…). maybe there is an inherent limit to the knowledge of the universe it is possible for us in our present state to achieve?
“i love that now you sound like some sort of crazy person who’s been harbouring a secret theorem that you aren’t allowed to mention at dinner parties because everyone laughs, you sound so vindicated!”
Ha ha, yeah that pretty much sums it up.
I don’t know how to deal with the dilemma. I think the first thing to do would be getting myself educated in complex math and physics. But I’m not sure which I want to be more, a scientist or a journalist. Lately I’ve been leaning towards being a scientist and I could write books in my years of wisdom(40-60).
But if you think about this, our methods of quantifying aren’t real or objective. They’re ideas that place boundaries on reality, that don’t seem to exist. For if the number one contains an infinite number of parts, then it can never be summed up into one unit. Essentially that’s true, but if you are outside the set, then you can have the illusion of summing it up. But in essence, the number one is still infinite in capacity.
What does this bode for reality, and our understanding of subjectivity? Well I’m not exactly sure, but I intend to find out…
I want to hear your theories and I’m going to start posting a bunch of fractal zooms.
i’ve no idea how you could possibly find out, and i’m not entirely sure i see the relevence of the fractals to be honest. i can’t believe however that we are the first people to come across this, so there must be some theoretical or philosophical debate or research already going on, just a matter of finding it.
Jubilee wrote: i’ve no idea how you could possibly find out, and i’m not entirely sure i see the relevence of the fractals to be honest. i can’t believe however that we are the first people to come across this, so there must be some theoretical or philosophical debate or research already going on, just a matter of finding it.
Your right, we aren’t the first people to consider this. Watch the video with the green head in it. That tries to explain some of the implications of an infinite universe and the dichotomy paradox.
Many of the things they say are true, but don’t fully explain how and what these phenomena are understood to be. It’s all very interesting though.
i can’t watch the videos, they just aren’t loading. it’s probably my internet, it isn’t great. and you can answer ANY questions? in that case i should ask THE most important question of all; should i have cheese on toast or pasta for tea?
Well obviously, we live in an infinite universe and so, you’ve already eaten the toast, the cheese, and of course, you had the pasta for tea. So now, the tea is the only answer.
What are you talking about? The sequels were awesome! And neccessary. You wouldn’t say, star wars good, but the sequels were bad because they were sequels. That makes no sense! The stereotype against sequels is because film industries will rush scripts and movies so that they’re on the market before the public gets disinterested. Thank god that didn’t happen with the matrix or star wars.
nah, the sequels were alright but they were nowhere near as good as the original, i know they were aiming for comic book stuff, but they just took it too far in the wrong direction in my opinion, and got far too caught up in themselves. star wars was good, but you have to admit the best sequel ever was wayne’s world 2. clearly.
I don’t know but I saw Matrix talk up there - and did any of you know the actor who was originally meant to play Neo was Will Smith and he turned it down? Ha ha I kind of wish he wouldn’t have…it would have either changed his career (earlier) or the movie would have not been the same.
He had me at Fresh Prince, so every time I watch the Matrix I can’t help but wish it was Will Smith instead. Neo would have been way more bad-***.
I’m really sorry that neither of can watch this video. It suits this post far more than I would have hoped for. And I’m sure that both of you would find it interesting.
Xeno Dragon
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