Infinity

[EricMartello]

Originally posted by: Estrella
After reading half the stuff you put up OP, would you rather argue about philsophy or mathematics?

I'm not here to argue, just here to discuss my Infinite Scaling theory...

 

[DrPizza]

See, that's where you're wrong. Scientists do NOT use the term theory the way you do. "I absolutely do understand what scientists expect from a solid theory, and in time, my theory may or may not "work" for them. As long as it works for me, that's all I care about." Those two consecutive sentences are not compatible. You do NOT understand what scientists expect from a solid theory, or rather, you cannot call your absurd thought a scientific theory.

Here's a simple place to read what "theory" actually means in science. here

Then, come back and explain how your conjecture "is predictive, logical and testable."

Time isn't anything, it didn't begin with the "big bang" (also a theory), it began with the human mind, and that's the ONLY place time really exists.

Are you saying that space isn't anything, it didn't begin with the "big bang", it began with the human mind?? Space and time are inseparable from each other. Another suggested reading to get your feet wet: here

"complex over-my-head math..." Calculus isn't *that* complex. It's pretty simple actually; most of my students comment that it's surprisingly simple compared to my pre-calculus course. Over your head? Well, you said it, not me. But, calculus has been around for hundreds of years. Perhaps if the concepts of limits are over your head, then continuing a lengthy thread about the subject is about as productive as me having a lengthy thread about brain surgery.

We're not talking about math here, so much as we are discussing concepts.

Just because it's not arithmetic doesn't mean it's not math. Infinity is a mathematical concept that has been studied very well. You don't just get to say "well, in my opinion it's not math, therefore I'm free to be ignorant of the mathematics."

 

[DrPizza]

Originally posted by: Estrella
Where is the thread on your sig? Could it not be represented as I put it? "!=" meaning not equals, like in Computer Science.

0.9999... = 1 (of course)
When I saw the !=, I knew it meant "doesn't equal". But, it reminded me of my sig (which I see on occasion) that says, "0.99999... = 0!" The "!" not meaning an exclamation

 

[DrPizza]

Wait a second... EricMartello... aren't you the person who had the conspiracy theory that the Tunguska event was caused by Nikolai Tesla?! :laugh: here

Then, there's this thread... here
Quiet humorous, especially when the creative fictional writing begins toward the end of the thread.

And, this thread, when you start whining about being accused of fraud and denying it, while providing evidence that proves some amount of fraud on your part. Come to think of it, didn't you get a lengthy vacation for your comment having to do with a sweet chocolatey snack in that thread?

 

[Estrella]

syntax syntax sytanx

 

[EricMartello]

Originally posted by: DrPizza
--- SNIP ---

Wait a second... EricMartello... aren't you the person who had the conspiracy theory that the Tunguska event was caused by Nikolai Tesla?! here

Um....WTF?

Then, there's this thread... here
Quiet humorous, especially when the creative fictional writing begins toward the end of the thread.

And, this thread, when you start whining about being accused of fraud and denying it, while providing evidence that proves some amount of fraud on your part. Come to think of it, didn't you get a lengthy vacation for your comment having to do with a sweet chocolatey snack in that thread?

Wow! What a concept: this is not my first post on these forums! Congratulations, you've discovered something that has eluded the best minds of our time. I can see bright futures for your students, with a fountain of intelligence such as yourself guiding them along!!!

That aside, what are you doing in this thread? OH! That's right, you're TROLLING!

 

[DrPizza]

Originally posted by: EricMartello

Originally posted by: DrPizza
--- SNIP ---

Wait a second... EricMartello... aren't you the person who had the conspiracy theory that the Tunguska event was caused by Nikolai Tesla?! here

Um....WTF?

Then, there's this thread... here
Quiet humorous, especially when the creative fictional writing begins toward the end of the thread.

And, this thread, when you start whining about being accused of fraud and denying it, while providing evidence that proves some amount of fraud on your part. Come to think of it, didn't you get a lengthy vacation for your comment having to do with a sweet chocolatey snack in that thread?

Wow! What a concept: this is not my first post on these forums! Congratulations, you've discovered something that has eluded the best minds of our time. I can see bright futures for your students, with a fountain of intelligence such as yourself guiding them along!!!

That aside, what are you doing in this thread? OH! That's right, you're TROLLING!

Nahh, not trolling. Merely pointing out that there's no reason whatsoever to take this thread seriously. (Not that this wasn't evident in the first post)

 

[EricMartello]

Originally posted by: DrPizza
Nahh, not trolling. Merely pointing out that there's no reason whatsoever to take this thread seriously. (Not that this wasn't evident in the first post)

You actually fall into several of these definitions:
http://www.urbandictionary.com/define.php?term=troll

I am sure AT is proud to have you as a member.

 

[PowerEngineer]

Originally posted by: EricMartello

Originally posted by: DrPizza
Nahh, not trolling. Merely pointing out that there's no reason whatsoever to take this thread seriously. (Not that this wasn't evident in the first post)

You actually fall into several of these definitions:
http://www.urbandictionary.com/define.php?term=troll

I am sure AT is proud to have you as a member.

Yes, we certainly are proud to have Dr Pizza as an AT member and valued contributor to HT!

Finally, after all the statements you've made in this tread, I've found one (after flushing the sarcasm) that I can wholeheartly agree with.

:thumbsup:

 

[CP5670]

I don't have time to read this whole thread, but infinity can be considered a number by just adding it to the set of available numbers. It then becomes an abstract object in some space with a bunch of rules you can apply to it, just like any other number. The wikipedia article on compactification has a nice explanation of this. In complex analysis and abstract algebra, infinity is frequently used as a full blown number in this way, since a lot of results become simpler and more "natural" in such a framework.

 

[Eeezee]

Originally posted by: EricMartello


Infinity is a concept, not really a construct. It's more philosophical than mathematical, and what is the basis of science? Math, and what I am saying is that using the concept of infinity to make theories work is essentially invalidating them.

You say this, yet some very advanced equipment is able to work thanks to being able to use infinity in physics. You're bringing in a philosophical argument where it really doesn't belong.

I'm not a philosopher, so I'm not sure where the logical fallacy is, but it has to be there. For example, let's say you want to cross a room. First you must travel a distance equal to have the length of the room. Then you must travel half of the distance. Then you must travel half of that distance. Continue infinitely and you will never reach the other side of the room. Therefore, travel is impossible.

Do you see why that doesn't work?

 

[Eeezee]

Okay, read through a few more pages and this is what I have to say

1) This doesn't belong on HT. You're discussing philosophy, and typically HT has more scientific topics.

2) You're trying to apply philosophy to science and math, which has historically not worked well. It's your right to ask these types of questions, but you may not like the answer; using infinity may remove significance in a philosophical sense, but it is still a useful tool for mathematics. Trust me when I say that it is important and that it certainly does not make any subject meaningless.

3) There is much evidence supporting the idea that space-time is finite anyway.

 

[EricMartello]

Originally posted by: Eeezee
You say this, yet some very advanced equipment is able to work thanks to being able to use infinity in physics. You're bringing in a philosophical argument where it really doesn't belong.

I'm not a philosopher, so I'm not sure where the logical fallacy is, but it has to be there. For example, let's say you want to cross a room. First you must travel a distance equal to have the length of the room. Then you must travel half of the distance. Then you must travel half of that distance. Continue infinitely and you will never reach the other side of the room. Therefore, travel is impossible.

Do you see why that doesn't work?

If by philosophical you mean that it requires you to think beyond accepted bounds, then it sure is. Your example has already been cited before in this thread, and all it shows is there are an infinite number of positions between two points...but it's worth noting that if you were traveling, your physical size would limit the smallest increment of space you could travel. If your scale was halved along with your incremental steps, then for all intents and purposes, the line segment would be infinite to you.

Okay, read through a few more pages and this is what I have to say

1) This doesn't belong on HT. You're discussing philosophy, and typically HT has more scientific topics.

2) You're trying to apply philosophy to science and math, which has historically not worked well. It's your right to ask these types of questions, but you may not like the answer; using infinity may remove significance in a philosophical sense, but it is still a useful tool for mathematics. Trust me when I say that it is important and that it certainly does not make any subject meaningless.

3) There is much evidence supporting the idea that space-time is finite anyway.

1) Once again, you're not the first person to say that and I still don't agree.

2) You got that backwards. Scientists are trying to apply math and science to a problem whose structure is infinitely variable. I have nothing against the 'scientific' answers that have been given in this thread, but they do nothing to answer any of my questions. Again, it would be the other way around - the people who think scientifically are the ones who reject anything that doesn't fit into their idea of "reality". Someone such as myself is open to...ahem...an infinite number of possibilities.

3) The idea of time itself sure helps things make more sense to us. I don't think it really exists beyond the human mind, and to use something as arbitrary as "time" in science is somewhat ironic, if not counterintuitive.

 

[StopSign]

Yes there are infinitely many points between two points on a number line. It doesn't matter what your physical size is if distance is always measured from a point to the destination point. Say you're measuring from a point on the tip of my toe to the wall, and when scaling down, you use that point as my anchor point. It doesn't matter how big or small I am because the physical size of a point never changes and the number of points between the point on my toe to the wall is always infinite.

My questions is this: SO WHAT?

 

[Gibsons]

Originally posted by: EricMartello

3) The idea of time itself sure helps things make more sense to us. I don't think it really exists beyond the human mind, and to use something as arbitrary as "time" in science is somewhat ironic, if not counterintuitive.

There's the second law of thermodynamics. Or Feynman diagrams.

 

[EricMartello]

Originally posted by: StopSign
Yes there are infinitely many points between two points on a number line. It doesn't matter what your physical size is if distance is always measured from a point to the destination point. Say you're measuring from a point on the tip of my toe to the wall, and when scaling down, you use that point as my anchor point. It doesn't matter how big or small I am because the physical size of a point never changes and the number of points between the point on my toe to the wall is always infinite.

My questions is this: SO WHAT?

What you said is true by definition. If we choose two fixed points and a standard reference for the distance between them, then that distance will always remain the same. To put it simply, a centimeter is a centimeter.

Now our perception of distance or length is based on our relative size to objects. Since we do not physically get "bigger" or "smaller" in terms of changing position on the scale, our position becomes our reference point for measurement. The problem here is that we're trying to apply a measurement based on what may as well be a random reference point.

What you can understand with Infinite Scaling, is that we could be anywhere on this scale, and there will always be something of infinitely "larger" and "smaller" scale to us. This means that using relative size as reference a point limits the scope of the whole measurement system to the point on the infinite scale from which the reference points are defined.

Let's pretend that humans existed on two extreme scales - B for BIG and s for small. On one scale humans are so "large" that a planet would be the size of a molecule, and on the other end humans are so "small" that to them an molecule is the size of a planet.

Now the humans in group B have a centimeter unit in their measurement system, as to the humans in group s. If we compared the two centimeter units' relative length, the the group B humans' centimeter is vastly longer than that of the group s humans. Yes, we could scale up group s to the scale of B so that the units "match", but in doing so we show the general irrelevance of measuring distance.

So that is what I'm attempting to explain here. Make sense?

 

[Gibsons]

Originally posted by: EricMartello

Let's pretend that humans existed on two extreme scales - B for BIG and s for small. On one scale humans are so "large" that a planet would be the size of a molecule, and on the other end humans are so "small" that to them an molecule is the size of a planet.

Now the humans in group B have a centimeter unit in their measurement system, as to the humans in group s. If we compared the two centimeter units' relative length, the the group B humans' centimeter is vastly longer than that of the group s humans. Yes, we could scale up group s to the scale of B so that the units "match", but in doing so we show the general irrelevance of measuring distance.

So that is what I'm attempting to explain here. Make sense?

Nope.

Unless you're just saying that units of measurement are arbitrary, but that's not exactly news.

 

[trevinom]

Originally posted by: EricMartello
Let's pretend that humans existed on two extreme scales - B for BIG and s for small. On one scale humans are so "large" that a planet would be the size of a molecule, and on the other end humans are so "small" that to them an molecule is the size of a planet.

Now the humans in group B have a centimeter unit in their measurement system, as to the humans in group s. If we compared the two centimeter units' relative length, the the group B humans' centimeter is vastly longer than that of the group s humans. Yes, we could scale up group s to the scale of B so that the units "match", but in doing so we show the general irrelevance of measuring distance.

So that is what I'm attempting to explain here. Make sense?

So let me get this straight. What you are saying is that the concept of 'measuring' distances is irrelevant? All your B and s humans have to do is handshake, come to some understanding of what their 'centimeter' is that makes sense to the both of them, rename it UC (Universal Centimeter) and continue boogeying. The only irrelevance I see is that they don't come to an understanding until a common framework is found. When B and s meets up with H (Humongous human beings)...all they have to do is rename UC (Universal Centimeter) to another common term TUC (Truly Universal Centimeter) and we're still in business, still relevant.

What's your point?

 

[StopSign]

Originally posted by: EricMartello
What you said is true by definition. If we choose two fixed points and a standard reference for the distance between them, then that distance will always remain the same. To put it simply, a centimeter is a centimeter.

Now our perception of distance or length is based on our relative size to objects. Since we do not physically get "bigger" or "smaller" in terms of changing position on the scale, our position becomes our reference point for measurement. The problem here is that we're trying to apply a measurement based on what may as well be a random reference point.

What you can understand with Infinite Scaling, is that we could be anywhere on this scale, and there will always be something of infinitely "larger" and "smaller" scale to us. This means that using relative size as reference a point limits the scope of the whole measurement system to the point on the infinite scale from which the reference points are defined.

Let's pretend that humans existed on two extreme scales - B for BIG and s for small. On one scale humans are so "large" that a planet would be the size of a molecule, and on the other end humans are so "small" that to them an molecule is the size of a planet.

Now the humans in group B have a centimeter unit in their measurement system, as to the humans in group s. If we compared the two centimeter units' relative length, the the group B humans' centimeter is vastly longer than that of the group s humans. Yes, we could scale up group s to the scale of B so that the units "match", but in doing so we show the general irrelevance of measuring distance.

So that is what I'm attempting to explain here. Make sense?

It makes no sense what so ever. All measurement units are derived from reference measurements. The "foot" was derived from an actual foot of some nameless person and it happens to be 12". What are inches? Inches are 1/12 of a foot. Not your foot. Not my foot. Mr. Nameless's foot.

I fail to see how scaling has anything to do with this. The centimeters from B and s are not the same centimeter and are *probably* not called the same thing in their respective worlds. The centimeter is a standard unit of measurement IN OUR SCALE. It doesn't matter how big you scale us.

What you're thinking is that "a centimeter is X amount of distance in the universe and therefore if you increase the scale, the distance changes and 1 cm takes up more space than before." That is incorrect. It is not a measure of distance in space at a subatomic level and nowhere in its definition does it say that. It is a reference measurement in our current scale and nothing more, with the reference being 1/100 of a meter, while the meter is a SI unit based on some random length that was decided upon hundreds of years ago.

You're not explaining anything. You're distorting your own understanding of the universe with your "Infinity Theory."

 

[imported_AndyT]

I believe that this thread is a fine example of the concept of "Infinity". It goes on and on.......

 

[DrPizza]

Actually, as far as there having been arguments in mathematics about infinities, and whether or not these invalidated some of our studies in science and mathematics, the OP is correct. These arguments were hashed out in the late 1800's, early 1900's. The mathematicians were, for a while, sort of split into two different camps. Some of them more notable names in the argument were Kronecker, Brouwer, Cantor, Hilbert, Weyl, Russel, and Whitehead. I can't recall who was on which side; it's all detailed quite nicely in the book "Pi in the Sky - Counting, Thinking, and Being" (John D. Barrow) which is a nice blend of mathematics and philosophy, albeit a boring read at times. It was one of the books I had to read at school while other teachers were reading various fictional pieces. I delighted in harassing a couple of people about the "uselessness of reading fiction" when there's so much excellent non-fictional literature available which had all of the same story elements - I actually get to learn something, rather than read for pure entertainment. Although that isn't my actual opinion about fiction, it was fun to play that side of an argument.

 

[Blouge]

>we could scale up group s to the scale of B so that the units "match", but in doing so we show the general irrelevance of measuring distance.

Well, the centimeter has no universal significance. It has to be backed up by a standard - such as an actual object whose length we declare to be a centimeter, or it has to be reproducible by anyone through a standard procedure, like having a beam of light travel over a period of time in which 43534534534 vibrations of a Cesium atom occur. I think for mass there might even be a real object in a vault somewhere that defines the international standard for a kilogram.

Suppose that we had an object X whose length we declared to be The Centimeter. Then if we measured another object with a ruler and found it to be a centimeter, the only way to verify that with absolute certainty that it's a centimer would be to bring it to object X and compare it directly. However, in practice we've found that the world approximately follows Euclidean geometry, and we can manufacture rulers and distribute them all over the world and that seems to work very well in practice.

I think if we doubled the size of the entire universe, and every object therein, and adjusted the physical constants that contain or are related to distance units, then absolutely no one would notice. This is scale invariance. Object X would double in size, but since it defines The Centimeter, other objects that doubled in size would yield the same measurements. In this sense, measurements are irrelevant. They are simply labels that humans stick on distances for convenience. The distances don't care what measurements you happen to label them with today.

AFAIK physics tends to ignore the idea of scaling invariance, while other invariances play a big role - time invariance (resulting in conservation of energy), translational invariance (conservation of momentum), and rotational invariance (convservation of angular momentum). I'm not sure why scale invariance is overlooked.

BTW, I think one theory competing with the idea of the universe continuously expanding is that the universe and space are staying the same; it is the atoms that are actually shrinking. It's hard to tell the difference between the two scenarios.