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.

alex

[CraigS]

OMG ..!!…

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

[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 (Carl)]

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]

Originally Posted by 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.

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 (Carl)]

Originally Posted by 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

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]

Originally Posted by 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

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]

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

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

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.

It's not the case.

Some sets are infinite; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by , has infinitely many elements, and we cannot use any normal number to give its size. Nonetheless, it turns out that infinite sets do have a well-defined notion of size (or more properly, of cardinality, which is the technical term for the number of elements in a set), and not all infinite sets have the same cardinality.

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 ?

Cheers

[renormalised (Carl)]

Originally Posted by 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

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 (Carl)]

Originally Posted by 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 ?

Cheers

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]

Originally Posted by CraigS

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

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]

Originally Posted by leon

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

Leon

Hi Leon;

Not sure, but I think the YouYubes Alex was referring to are in this thread.. (Post #1).

Very worthwhile viewing !

Cheers

[sjastro]

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

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

Steven