Infinity

[xelasnave]

Bert,s movies reminded me that thinking about infinity has had many casualties over the years.
I think about it a lot but so far I have avoided madness in my view.
However something presented when I was trying to work out a formula to express energy at a point in a void..a mind exercise in so far as I cant go to such a place to observe the energy...anyways I started trying to calculate the possible number of trajectories that could pass thru a point ..finally I have concluded that the number of trajectories is infinite....I thought to add energy that could be observed and a probability ....so as to somehow rightly or wrongly observe the energy passing a point in space.... however before I could add e or p it occured to me what ever is multiplied by infinity and that can only produce an infinite answer ...so energy at a point must be infinite...
I think that is math OK but then how can you divide infinity to have mass??? I conclude time is the only thing that can be considered but how I dont know yet:P:P:P:P.

alex:D:D:D

[CraigS]

OMG ..!!…

.. and here's bojan being worried about science gone wrong !

:shrug: :P :)

[avandonk]

Alex it is my humble opinion that the ones that fell by the wayside were functional autistics at best. To have worthwhile gedunken experiments takes a mind that has studied all the current knowlege in great depth. It needs a very good grasp of the underlying mathematics. If you do not know what an elliptical integral is that is dealing with discontinuities and thus infinities it is an impossible task.

This is about where I lost interest in pure mathematics as I was too busy dealing with reality.

I have trouble keeping up with and understanding what has already been discovered.

A simple theorem. A finite mind cannot comprehend an infinite anything.

Another question I was asked a long time ago. Has the human mind enough intelligence to understand itself?

Godel says NO!

I think that the Universe by it's inherent indeterminism at quantum and chaotic levels and sheer size overcomes all the paradoxes that are inherent in any closed logical system.

Bert

[renormalised]

Infinity is a relative term.....it's either exceedingly large, or as small as anything can be...simply because both ends of the spectrum can be divided up into an indeterminate number of times. As can everything in between.

It's best summed up by the a line written by William Blake (in Auguries of Innocence)....

" To see a world in a grain of sand, And a heaven in a wild flower, To hold infinity in the palm of your hand, And eternity in an hour"

[xelasnave]

I thought that would get you thinking.
Dont worry however my respect for real physics and science goes in step with my frustration not to master most of it.
However I have concluded even nothing must be made up of a lot of something.
I do find the history of the development of ideas exciting as well as the people their personalities etc. thats why I enjoyed the movie.
I like the concept of an infinite universe but even our observable universe is for human purposes infinite,,even if it isnt it may as well be... just our galaxy is big beyond most folks comprehension.
I cant get over the various subjects in math (anything really) one needs ...
alex

[xelasnave]

I looked at all the elliptical integral information I could find and read it.
So far I have no idea how to use it... and to be honest I dont know what the formulaes are saying.

Only in Wiki which has too many blue side tracks... I usually end up learning about something I wasnt looking for.
I should do a new thread and post a link but I saw a great vid re liquid behaviour on the space station...they had spheres of water floating..injecting them with air ..all sorts of interesting things...needless to say I saw it as supportive of my ideas whatever they may be...it is all in how you see things but I look at thoses spheres of water etc and imagine them held in a system I imagine....but thats not science I know that but as simple as these spheres appear try and describe all that goes on math wise..so many actions to record if one were to record all the complexity wow..but no doubt that can be done.

As simplistic as my approach may be it is clear that if we were to try and quantify the energy you could not use the geometric reality that the number of trajectories is infinite... although if you think about it we think of trajectories coming from a point and so when we imagine where they end up we see them as then separated by a distance... all that means is we have trajectories we have overlooked...anyways I must use a big but finite number rather than infinity to multiple e and p ... all this simply to understand nothing ... this I can see as my lifes work studying nothing and everything to end up knowing nothing about everything and everything about nothing... came with nothing saw everything in nothing and saw nothing in everything.

alex

[Barrykgerdes]

Infinity is infinity. We as humans have no way of expressing it. To say it is large or small is to immediately give it a finite dimension. Just live with it and accept that it has no dimension!

Barry

[renormalised]

Barry, you don't get what I wrote. It's both large and small but it has no limits. It does have a dimension...it's infinite.

We say that the smallest possible unit of length and time are the Planck length and Planck Time (both approx 10^-43 cm or sec in size). But how do we actually know that...it's the smallest we can measure and the smallest our present theories allow for. Even now, they're talking about the graininess of spacetime being even smaller than the Planck Length. That then begs the question...how can you get something smaller than the supposedly smallest possible unit of measurement?? How small can small get?? Conversely, how big can big get?? What happens at these scales to everything??.

Something to think about:)

[sjastro]

Actually we can. There are concepts such as "countable infinite sets" and "uncountable infinite sets". Ever wondered that the set of natural numbers and integers are both infinite sets yet intuitively there are twice as many numbers in the set of integers.

This topic has been discussed previously.

Regards

Steven

[Barrykgerdes]

Sorry Carl and Steven

You have both decided to give infinity a meaning that it hasn't got.

A standard human mind trait that must try to explain something that can't be explained. To say that infinity is smaller than smallest or larger than largest is still giving it a meaning that is not infinity. Once the mind can understand infinity most of the other bounding consepts we have will start to have a new meaning.

Barry

[sjastro]

So the great mathematicians of the 19th century such as Cantor etc. were incorrect to give infinity a meaning.

http://en.wikipedia.org/wiki/Uncountable_set
http://en.wikipedia.org/wiki/Countable_set



It's not the case.



Regards

Steven

[CraigS]

Has the formalised mathematical definition of infinity, (ala Cantor, Godel,etc), ever resulted in productive outcomes for society ?

Has a meaningless explanation about "something that can't be explained", which somehow leads to a somewhat irritating "bounding concept" that gives other things "a new meaning", resulted in something productive which society can use ? :question:

Cheers

[renormalised]

You still don't get it:)

Take a time period of 1 second....how many time intervals can we divide that 1 second up into??. Take a time period of 1 billion years....how many can we fit into an infinite period of time??

Infinity is both small and large. Small and large are bounds of scalar convention, not bounds of length, volume, area, time etc etc. Something can be infinitely large or small. Anything can be divided up into an indeterminate number or quantity of whatever you chose it to be divided up in.

It's what Steven is trying to get at.....say you have a set N, that has 10 integers (the numbers 1-10) in that set. Common sense would tell you that it is finite in size and there is only 10 numbers there. But you would be wrong.....what you have there is an infinite set of numbers. The cardinality equals 10 (because there are 10 integers within the set). However, for every integer (1-10) there is an infinite number of elements, n, that each integer can be divided up into and that have values between 1 and 10). You have defined set points for the beginning and the end of the integer sequence, however you have an infinite number of possible values present between those end points.

[renormalised]

Well, if you take the infinities which occasionally crop up in QM and are renormalised in order to cancel them out, then the mathematics that relies on their existence has produced things like the silicon chip, the transistor, radar, GPS, computers etc etc etc. :)

[sjastro]

At this stage no, but today's pure mathematics may become tomorrow's physics or applied mathematics.

An example of a mathematical theory of infinities which is used by theoretical physicists today is convergence testing of a series containing an infinite number of terms.
Even though a series may contain an infinite number of terms, it may converge to a finite value.
This is particularly important in solving certain partial differential equations used in physics and engineering. The "raw" series solution usually contains an infinite number of terms. If the series diverges it cannot be a solution to the equation.

Regards

Steven

[CraigS]

Hmm interesting … I would've said that without a doubt, unless Cantor, Godel, Boltzman, Turing, etc formalised thinking about dimensionality, as it relates to the concept of infinity, then vast amounts of technologies and development would never have happened.

Solutions to pdes are bread-and-butter housekeeping in engineering projects !

Barry's assertion that infinity has been assigned meaning is fine by me, if it has ultimately resulted in tools which reinforce the theory everytime I turn on my computer, use a phone, go for an NMR/MRI etc, etc …

Cheers

[leon]

Bugger me, I was lost after the first sentence, however very interesting reading.

Leon

[bojan]

Anyone have read Fred Hoyle's "Black Cloud"?
The person most affected by new ideas was Professor Kingsley (he didn't only went mad, he actually died... while if they had put the simple gardener into a learning machine instead (Joe Stoddard), all would have been fine :-)

[CraigS]

Hi Leon;

Not sure, but I think the YouYubes Alex was referring to are in this thread.. (http://www.iceinspace.com.au/forum/showthread.php?t=67311&highlight=Dangerous) (Post #1).

Very worthwhile viewing !

Cheers

[sjastro]

Engineers apply the end product but some poor bugger still had to solve the equations for you.:lol:

Steven

[CraigS]

Check out the YouTubes in the thread I just posted … get some popcorn (and a beer), and sit back and watch !! (They really are very good).

cheers

[renormalised]

Haven't read it yet, but wouldn't mind grabbing a copy. Imagine a spacefaring, sentient being that consisted of a black cloud of particles.

[CraigS]

That should read 'youse' !
:lol: :)

Cheers

[renormalised]

Speaking of which.....

From plasma crystals and helical structures towards inorganic living matter (http://iopscience.iop.org/1367-2630/9/8/263/fulltext)

[CraigS]

Wrong thread Carl .. should've been in the 'Anti-science Hysteria' thread.

Authored by Alvenic Russian poets, eh ?

Cheers

[renormalised]

Maybe, but it's interesting nevertheless.

[CraigS]

Man, they start with a model .. ie: organic life structures and functions ie: DNA reproduction, metabolism, etc and then apply an external field to crystal dust grains in plasma:

.. and then draw simularities with the straw-man analogy, (organic life), and then use it to recommend a SETI program ?

What to make of this ?

Cheers

[renormalised]

Didn't say it was theoretically sound or even empirically correct, just that it was interesting (in the context of the novel "Black Cloud", and a sentient cloud of particles).

It's hard to make anything of it unless there have been further experiments and observations. What, though, if it's found to have veracity. They may have overstepped the mark with some of their statements, but the only way to confirm or deny their hypotheses and their implications is to repeat the experiments and to do the necessary observations.

If it's BS, then that's what it is. If not, well, then we have to start looking at the implications of their original finding and the further results.

I haven't read the article in full as yet, so I'm not going to comment on the veracity of the research.

[xelasnave]

I am not convinced that we can have infinitly small...infinity does not respond to subtraction or addition...clearly if something is infinitely small it could be added to and the impact could be noticed whereas infinitly big does not respond this way.
I dislike the Universe being described as infinite if we subscibe to a big bang start ...you cant double and redouble any number to reach infinite...any doubling can only amount to finite.
Driving thru the bush today it occurred to me even here on Earth no tradjectory could be observed without observing energy..photons come from an infinite number of tradjectories and I suspect there would be no tradjectory along which energy did not flow...
I am not trying to prove anything here (in support of you know what) but its something one does not think about and when you do ...well I find the prospect hard to get my head around thats all.

alex

[renormalised]

Why not.....there's no physical law or principle denying it or preventing it from existing.

You can't add to something infinitely small and make it infinitely large, or any size at all for that matter. Adding an infinity to an infinity still only makes it an infinity. In defining a large and small infinity, you have to set an arbitrary point somewhere between the two that delineates between large and small. Remember what I wrote earlier, large or small are conventions of scale, not vector (numerical) conventions.

[xelasnave]

QUOTE=renormalised;744792]Why not.....there's no physical law or principle denying it or preventing it from existing.

You can't add to something infinitely small and make it infinitely large, or any size at all for that matter. Adding an infinity to an infinity still only makes it an infinity. In defining a large and small infinity, you have to set an arbitrary point somewhere between the two that delineates between large and small. Remember what I wrote earlier, large or small are conventions of scale, not vector (numerical) conventions.[/QUOTE]

Thanks Carl I didnt ignore what you said Carl but I guess I find infinitely small a more difficult idea..I try to visualise concepts in an imagined reality and go into a russian doll thinking with infinitely small...I mean how could they make such a small doll... large is an easier concept...I could see thinking about infinitely small sending one crazy whereas infinitely big less so ...

Sort of related trivia which some may or may not be aware of...the Sun over a year marks out the sign for infinity in the sky from our point of observation...I guess that would have been picked up very early ...must check when that symbol first appeared.

alex

[renormalised]

Yep, that "sign" is the analemma...the path the Sun traces through the sky over the course of a year. Looks like the "infinity" symbol:)

I have no problems with visualising either small or large.

[xelasnave]

It is a wise man who can imagine a stick without ends:thumbsup:

alex:):):)

[renormalised]

Not necessarily....just someone with a good imagination:)

[xelasnave]

I often sit under the stars and try Carl (during long exposures you really dont have to do anyhting the gear does it all so there is time a plenty to think and look up)...and so I start following that stick and looking for an end takes you strange places ..I pierce countless objects with it;)..stars planets worlds that may or may not be there... I have poked it thru the edge of the universe but got lost when I found myself outside it:eyepop:.
But having got used to one stick I am now trying to see how many you can stick thru the universe...and find the number of sticks must be infinite...from a geometric point of view...and that is thru one point mmm how many points could we fit in the universe...

Been studying my math and it is great ..actually looking at infinity from that approach...sets etc.
But in so doing I can see the strenght of maths (the tests etc) must give one almost absolute confidence in it... the boundaries have been tested like no other science.

alex:):):)

[CraigS]

Not only tested, but in many cases … proven (see theorem (http://en.wikipedia.org/wiki/Theorem), axiom (http://en.wikipedia.org/wiki/Axiom)).
The principles and axiomatic proofs are repeated time and time again, everytime we derive a resultant, or develop technology/tools via mathematical logic. (http://en.wikipedia.org/wiki/Mathematical_logic)

Why, or how, anyone can think they can refute the rationale behind mathematical logic completely escapes me.:shrug:

The application of this maths to the physical world, is a reasonable line of query.
:)
Cheers

[xelasnave]

I realized how I really am into numbers.. my math is not advanced but I use it.. I ran a business on math... thanks for the pointers Craig.

I am dangerous with any weapon in my hand but I would love to wield math with common sence as my shield.

alex

[renormalised]

They think they can refute it, Craig, because they have absolutely no understanding of it in the first place. If they understood the logic, even something as simple as 1+1=2, they'd know why they can't refute the rationale.

[xelasnave]

How did the romans get by? You would have to run your budget counting on your fingers.
alex

[renormalised]

Their maths was a bit more complicated than that:)

In more ways than one!!!!

Thank god for the zero!!!:)

[xelasnave]

You would have had to be a genius to do a simple multiplication it seems to me... anyways I will look into their math history more but I read a little today ..mmm yes zero so simple now but before it...
alex

[CraigS]

In my travels, I have seen refutation of the applicability of maths, in this case, Relativity, to the real world. The "logic" employed was based on Aristotlean logic (and other philosophical streams). If the maths was not based on observed phenomena (dilation, length contraction), then logically, the perceived resultant of this maths (ie: the physical technology), can be deduced to simply operate independently of the maths.

The maths works ok in isolation, but is unrelated to the functions of the physical technology because of the perceived lack of evidence of the phenomenon on which it was predicated. (Never mind that Lorentz contracted particle bunching calculations work and GPS systems are adjusted for time dilation).

So, it seems that we humans merely stumbled upon ways to make particle accelerators "just work" independently of any mathematical formalism used in their construction.

Such logic completely disregards everything we (reasonably) take for granted !

That such people/thinking can exist, is beyond the incomprehensible !

Cheers

[renormalised]

Like I've mentioned so many times.....a great many just can't handle certain subjects because their minds don't work in a way that they can understand those subjects. They still think the Earth is flat, is at the centre of everything and we have crystal spheres and epicycles...their minds are still stuck in ancient history whilst their bodies are in the 21st Century.

[xelasnave]

I am sure members think I am joking when I say there is a flat earth site....here is the link...here words fail me.http://theflatearthsociety.org/cms/

alex

[xelasnave]

I had to look at their forum:eyepop:...dam good stuff:rolleyes::screwy:...but this is typical.
http://www.theflatearthsociety.org/forum/index.php?topic=49614.0
:lol::lol::lol:
what can you say? could any of these folk be neighbours or work coleagues ...
alex:):):)

[sjastro]

Very "enlightening" Alex.

It has always puzzled me how pseudosciences operate under the principle that bashing mainstream science is a validation of one's own ideas.

Regards

Steven

[renormalised]

Using mainstream science as a punching bag makes them feel good about themselves. It's a crutch to help make them forget about how intellectually inadequate they all are :):P

Just like school bullies:)

[renormalised]

However, being frank about this, just like their TBolts/EU brethren, they're a joke. A bunch of modern idiots following the psychotic babble of 19th Century crackpots.

Most would have to join something like this as a bit of a laugh...if they were serious about it...........

[xelasnave]

Steven on the basis that it takes a man to admit where he has gone wrong I say that I have been guilty of such an approach, fortunately the sites I carried on so badly are gone and hopefully all that I have said with it. So only my rants on iceinspace remain and here I will demonstrate certainly a more enlightended alex.
And Steven I have you for the great part to thank you have always kept me honest.
My gravity trip has been most strange teaching me many things one that perhaps I present differently to the humble person I hold as my self image.
And strangly my thinking about trajectories has me thinking how to define them and guess what I see them represented by wave forms even though I dont see wave forms in my reality and then I seperate them into packets and realise each of those packets could be represented as one cycle of a wave... and I then thought maybe there is something in string theory after all...so who would think this day would ever arrive...
Doesnt mean that I still wont ask questions but the more I learn the more questions it is a geometric progression of demand for information.
But how good is the net to be able to chat with folk of like minded intererests.
I came to this site for astronomy so this forum is a great thing for me.
I joined Physics.org years ago to read but felt out of place where as here its ok.

Thanks again Steven you have made a massive contribution to my ability to learn.

alex

[xelasnave]

Carl as I said to Steven I have been guilty of such bad behaviour...I have never felt intellectually inadequate or inadequate in any way which I regarded as self confidence others regarded as standoverish...Carl you also have been inspirational as have so many here I can never thank everyone enough.

I am in the bush been alone for how long I dont know and this is my only outside contact at the moment so sorry for getting personal. I have got only one solar panel 100 amp battery which is flat and I get to transmit if the Sun shines for a while...so no surfing radio tv etc is why you guys get a bucket load ..sorry.

alex

[xelasnave]

I can see why this could do ones head in.
Having determined geometricaly the trajectories are infinite we need to measure the energy in both directions so we now need to multiply infinity by two...however to bring a finite in would be to limit the end limit of a tradjectory to a lenght the same as the diameter of the observable universe..which would be a huge number ... but as high as the probability of infinite energy arrived at from the suggestion of infinite probability that probaility may not occur at a certain point in time therefore a real observation may reveal no energy packet can be observed from any tradjectory or no energy at all...
Glad I got that off my chest.
Just enjoying the math stuff I have been reading.
alex