infinities for StainlessS

[feisty2]

recently I noticed StainlessS signature

"Some infinities are bigger than other infinities", but how many of them are infinitely bigger ???

StainlessS, maybe u already know the answer to that question, or maybe not if ur major is not quite relevant to natural science, anyways I guess it's an intriguing question

if u already know the answer, ignore my post, if not, the answer to ur question is:

infinites come in orders, for instance 1.0001^x is a higher order infinity than x^1000 when x goes toward infinity, u can prove it by recursively applying L'Hôp's rule to the limit for 1000 times, what it really means is that 1.0001^x accelerates infinitely faster than x^1000 as x gets larger and larger, so 1.0001^x is "infinitely bigger" than x^1000 tho both are going toward infinity as x itself goes to infinity, another example here is 0.001x and 1000log(exp(x) + 1), they are infinities of the same order as x approaches infinity, which means 1000log(exp(x) + 1) accelerates faster than 0.001x but faster only for a constant ratio, so 1000log(exp(x) + 1) is a bigger infinity than 0.001x as x skyrockets to infinity but not "infinitely bigger"

infinity is a relative and "dynamic" concept unlike constants like 100 or 1234.56 which are dead "static", ur question is incomplete, "but how many of them are infinitely bigger (than what exactly ?) ???"

well for a lot of known infinities like x^1000, there are infinite infinities infinitely bigger than them

[StainlessS]

Thanx master Feisty, but of those, how many of them are infinitely bigger than all of the rest put together, ??? :)

EDIT: I never expected any kind of answer to that, was just a daft question.

[microchip8]

the word infinity implies "no end". Thus one infinity cannot be "bigger" than another since both have no end at all (or they won't be called infinities). Asking how many of them are infinitely bigger makes no sense, since these infinities go on forever

[Sparktank]

I'll take the interpretation as infinity meaning "endless".
In our observable universe, we've already discovered how things can be infinite, or rather, limited in knowing given our limited capabilities in this universe.

However, if we perceive that things can be infinite and unknowable, then what is to stop us from thinking there is an alternate universe, much like our own, but with different values of what we perceive to be the point where infinity starts?
Their perception could, indeed, be larger than our own measurement.

But, that also creates a paradox of other infinities (alt unis) being larger the two parties already measured, thus skewing the perceived values of infinity to be either of greater significance; which could, consequently, make our own perceived values to be totally inconsequential.

If we were to omit the unobservable, we could make our own results mean something again, when, in fact, it means nothing; since, we can't do much beyond the point of infinity, anyway

Thus, we've come full circle: infinity is always infinitely more bigger than any given infinity. Unless, it's our own. Then it's just the same old infinity we were born to know.

tl;dr: 42

[microchip8]

the "many world" interpretation of a multiverse is a well studied part of physics. As with most theories, it has its backers and those who oppose it. At our current point in time, it is still untestable, directly or indirectly. However, it solves some fundamental problems (and also creates others). I'm mostly neutral about it, but if it's true, the "whole" could be an infinite network of universes all with their own constants

I try not to think too much about infinity, or I'll go mad like Cantor :p

[Sparktank]

If we can tap into those other verses, I wonder which one has gone further in the realms of video/image processing.
Cheap, affordable and amazing nn upscaling.

[burfadel]

Pi is said to go to infinite decimal places, but infinite kind of becomes finite in practice once you apply a radius, and the distance change of those decimal places become shorter than the planck length. In this scenario, the infiniticity of the pi decimal is directly proportional to the radius. The smallest distance change on the circle then becomes a modified planck length, since any observable change can only occur at steps of pi times the planck length of the radius.

Finite infiniticism.

[johnmeyer]

I wish I could find a book I was given back in the mid 1960s called "Beyond the Google." This is before anyone knew what a Google was: it was a totally foreign word.

The book was about various mathematical ideas and conundrums, and one chapter was about the concept of infinities. As I remember, the mathematician who wrote it made the same claim that Feisty is making, namely there are different levels of infinity. However -- and this is why I wish I could find the book -- it was not at all obvious to a mere engineer like me what it took to get to a higher level of infinity. For instance, infinity + infinity still equals infinity. As I remember (and this is now at least half a century ago) infinity * infinity still equalled infinity. It was only when you got to exponentials, like infinity ^ infinity, that you got to a "more infinite" infinity.

Even back then, I was more bent on practical things, and found much of the discussion in the book a little like the "how many angels fit on the head of a pin" debate that medieval monks apparently wasted their time discussing.

[StainlessS]

"how many angels fit on the head of a pin"

I guess that if it were an infinitely large pin, then you could fit on it a helluva lot of angels (similarly, if the angels were infinitely small).

Its quite amusing that my current sig prompted such discussion.

I am a clinical "idiot savant", Infinitely gifted at being stupid. :)

[Midzuki]

I wish I could find a book I was given back in the mid 1960s called "Beyond the Google." This is before anyone knew what a Google was: it was a totally foreign word.

Don't you mean GOOGOL instead of "google"?
Because in the mid 1960s surely there was no such thing as a half-ässed search engine that was worshipped as the god of the millennial generation.

[Midzuki]

the "many world" interpretation of a multiverse is a well studied part of physics. As with most theories, it has its backers and those who oppose it. At our current point in time, it is still untestable, directly or indirectly. However, it solves some fundamental problems (and also creates others).

Therefore it is FALSE and can be safely sent to the garbage can =)

[StainlessS]

Don't you mean GOOGOL instead of "google"?
Absolutely correct Midzuki, here is list of hits for the book:- https://www.google.co.uk/search?client=firefox-b&dcr=0&ei=d015WunxKqiYgAbm6bOADA&q=%22Beyond+the+Googol%22&oq=%22Beyond+the+Googol%22&gs_l=psy-ab.3...37496.38693.0.39034.0.0.0.0.0.0.0.0..0.0....0...1c.1.64.psy-ab..0.0.0....0.vg6jnVtLOL8

[feisty2]

Thanx master Feisty

lol I'm still an undergrad so ain't no master (which is for grads) for me

[microchip8]

Therefore it is FALSE and can be safely sent to the garbage can =)

well, the same can be said about string theory, yet people don't want to give up on it :p

[microchip8]

Its quite amusing that my current sig prompted such discussion.

I am a clinical "idiot savant", Infinitely gifted at being stupid. :)

nice to have a break from encoding at times :)

[StainlessS]

lol I'm still an undergrad so ain't no master (which is for grads) for me

Ah young sir, I guess you misinterpret, I meant in same context as used by TreeBeard (Young Master Gandalf):- https://www.google.co.uk/search?q=young+master+gandalf&ie=utf-8&oe=utf-8&client=firefox-b&gfe_rd=cr&dcr=0&ei=Fnd5WrCBObLHXvi_tKAM

Master, Noun:-
Used as a title prefixed to the name of a boy not old enough to be called ‘Mr’

Seems to be more in English than colonial usage.
(that usage not mentioned at all in my old pop-up Wordweb dictionary, which usually denotes different US, Brit usages).
EDIT: Sort of gender opposite to Miss, although is a little archaic and nowadays seldom used even in the UK.

EDIT: To Below post,
skilled practitioner of a particular art or activity
that context would also not be unwarranted.

[feisty2]

Okay,,, I was tryna be ironic, I knew "master" in ur context is not "a person who holds a second or further degree from a university or other academic institution" which is the one in my context, I thought u were calling me a "master" for "a skilled practitioner of a particular art or activity", but guess I got it wrong anyways:)

[wonkey_monkey]

the word infinity implies "no end". Thus one infinity cannot be "bigger" than another since both have no end at all (or they won't be called infinities). Asking how many of them are infinitely bigger makes no sense, since these infinities go on forever

Most mathematicians would disagree with you.

https://www.khanacademy.org/math/math-for-fun-and-glory/vi-hart/infinity/v/proof-infinities

[johnmeyer]

Don't you mean GOOGOL instead of "google"?

Because in the mid 1960s surely there was no such thing as a half-ässed search engine that was worshipped as the god of the millennial generation.Thank you for that! I kept searching for the book and couldn't believe it wasn't listed. Because the search engine name is everywhere, I forgot how to spell the actual term on which the company name is based.


Mathematics and the Imagination: Beyond the Googol (https://www.amazon.com/Mathematics-Imagination-Edward-Kasner/dp/0671208551)

[edit]

A few sample pages (https://books.google.com/books?id=-bXDAgAAQBAJ&pg=PA27&lpg=PA27&dq=%22Beyond+the+Googol%22&source=bl&ots=REfzXdXU4M&sig=cILSRHZjbGV_ZQR-F7ituWZpX38&hl=en&sa=X&ved=0ahUKEwiQxd6f2ZHZAhXHqVQKHV8kByUQ6AEIPzAG#v=onepage&q=%22Beyond%20the%20Googol%22&f=false).]

Page 44 is where he starts talking about properties of infinity, and how subsets and supersets are still the "same level of infinity" (my term, not his). Page 47 is the page I remember, where he derives a new level of infinite.

[feisty2]

I wish I could find a book I was given back in the mid 1960s called "Beyond the Google." This is before anyone knew what a Google was: it was a totally foreign word.

The book was about various mathematical ideas and conundrums, and one chapter was about the concept of infinities. As I remember, the mathematician who wrote it made the same claim that Feisty is making, namely there are different levels of infinity. However -- and this is why I wish I could find the book -- it was not at all obvious to a mere engineer like me what it took to get to a higher level of infinity. For instance, infinity + infinity still equals infinity. As I remember (and this is now at least half a century ago) infinity * infinity still equalled infinity. It was only when you got to exponentials, like infinity ^ infinity, that you got to a "more infinite" infinity.

Even back then, I was more bent on practical things, and found much of the discussion in the book a little like the "how many angels fit on the head of a pin" debate that medieval monks apparently wasted their time discussing.

it's actually pretty obvious, the order (or what u called "level") of infinites is not defined by basic arithmetic operators like u thought, stuff like "infinity + infinity" is typically indeterminate, which means the result of "infinity + infinity" could be anything from negative infinity, an arbitrary constant or positive infinity, and "infinity - infinity", "infinity * 0", "infinity / infinity", "1 ^ infinity", ... are likewise indeterminate, the definition of the order of infinities is not that convoluted as u thought, it's actually pretty straight forward

given
https://i.imgur.com/YQnFhNg.png
https://i.imgur.com/1ueKLuk.png
where "a" could be an arbitrary constant or +-infinity

if
https://i.imgur.com/pfY9uG7.png
then f(x) is a higher order infinity than g(x)

if
https://i.imgur.com/pLflhYD.png
then f(x) and g(x) are infinities of the same order

if
https://i.imgur.com/jIVuy2y.png
then f(x) is a lower order infinity than g(x)

it's really just newbie level math, I learned it a few years ago in high school, and it's the prerequisite stuff before real/complex analysis or calculus, and u must have had courses like that if u did major in engineering, I mean I get it if u engineering folks never had advanced math like number theory or differential manifold, but ur claim of u majored in engineering and had no idea about the basics of calculus is oh so not convincing

[johnmeyer]

Feisty, check out the links in my post above that I was writing while you were posting. It provides a link to pages of the book I referenced, and does a great job describing infinity and how you can get to new levels of the infinite.

[feisty2]

well the infinity in that book is a different form of infinity, I was talking about infinity in calculus, the book concerned more about infinity in set theory, I think infinity in calculus should be the more appropriate kind of infinity here since StainlessS asked about "bigger infinity" not "denser infinity" (stuff like countably infinite/uncountably infinite)

[StainlessS]

Was that astronaut "Buzz", talking bollocks ? :- https://www.google.co.uk/search?q=to+infinity+and+beyond&ie=utf-8&oe=utf-8&client=firefox-b&gfe_rd=cr&dcr=0&ei=HvJ5WqzPL7SN8QeMxabYAg :)

[johnmeyer]

well the infinity in that book is a different form of infinity, I was talking about infinity in calculus, the book concerned more about infinity in set theory, I think infinity in calculus should be the more appropriate kind of infinity here since StainlessS asked about "bigger infinity" not "denser infinity" (stuff like countably infinite/uncountably infinite)
Infinity as used in calculus, like the examples you used which are similar to how calculus derivatives are derived, is really easy stuff that even a simple-minded Midwest guy like me can understand. If we limit he discussion to that view of infinity, we won't have to delve into the metaphysical aspects of what it means to have an infinity of infinities.

[microchip8]

Most mathematicians would disagree with you.

https://www.khanacademy.org/math/math-for-fun-and-glory/vi-hart/infinity/v/proof-infinities

Most? you speak for most? as said in the video, it deals with countable numbers. But it is impossible to count all *real* infinities out there because there will be infinite possible infinities in between and not in between. As said in the video, does light have infinite moments? If so, you can't count it due to infinity... in other words, it's endless no matter how much you add to it, i won't make it any bigger. So when I said it has "no end", I was referring to this so the question "how many are infinitely bigger" becomes meaningless

[feisty2]

some (or maybe most I dunno) physicists argue that the measurable space and time are discrete, there's no measurable time shorter than Planck time and no measurable space smaller than Planck length, which makes our measurable universe countably infinite, or not, the universe might not be infinite to start with, no one knows if there's anything more 47 billion light years away..

[microchip8]

we measure distances with light. If the universe is truly infinite, there will always be light that can never reach us. So if we only use light to measure it, we will never be able to prove its infinity or not. I think we may need something else

[feisty2]

We could use something else to measure the universe but I'm not sure if that would outperform light since most physicists agree that light speed should be the upper bound of speed in our universe

[microchip8]

well, I don't know if this can be done so don't quote me on it, but maybe entanglement between particles can be used? they "communicate" instantly regardless of the distance, so it "appears" as if they do it faster than light but they really don't (so they don't break the speed-of-light stuff and Einstein's theories).

Another thing is, if the universe is infinite, it also invalidates a few theories that say at some point the universe will start to shrink until it reaches a singularity that explodes at some point and creates a new universe. An infinite universe will take an infinite amount of time to reach such a singularity, so you might as well give up on it

but like you said, we don't know (yet) if the universe is infinite or not

[Midzuki]

well, the same can be said about string theory, yet people don't want to give up on it :p

Please define "people" :)

https://en.wikipedia.org/wiki/Peter_Woit

[microchip8]

Please define "people" :)

https://en.wikipedia.org/wiki/Peter_Woit

Leonard Susskind, Gerard 't Hooft, Hawking, Holger Nielsen, and others

(PS: I root for loop quantum gravity (LQG)) :p

[StainlessS]

Microbes discussing the bowl of soup that they inhabit.

[microchip8]

Microbes discussing the bowl of soup that they inhabit.

this made me LOL big time! thx for that ;)

[wonkey_monkey]

some (or maybe most I dunno) physicists argue that the measurable space and time are discrete, there's no measurable time shorter than Planck time and no measurable space smaller than Planck length, which makes our measurable universe countably infinite, or not, the universe might not be infinite to start with, no one knows if there's anything more 47 billion light years away..

Planck length/time are not held to be "smallest measurable units." They are - roughly - the scales at which quantum effects dominate, but they don't - as far as is known - hold any special physical significance.

It's generally held that space and time are continuous (special relativity would be an unholy mess if they weren't).

Microbes discussing the bowl of soup that they inhabit.

And crawling on the planet's face
Some insects called the human race
Lost in time, and lost in space
And meaning (me-ea-ning...)

[feisty2]

I never said space and time are discrete, they might be continuous and there might be a tiny period of time even shorter than Planck time, but it would be immeasurable, I do remember there was a discussion a few years ago that some big ass physicists gathered up and discussed if the actual universe itself (not the measurable universe) should be discrete or continuous, both sides had their reasons and there wasn't a definite answer

however about the measurable universe, I think its universal that most physicists would agree that it should be discrete, https://www.quora.com/What-is-the-smallest-possible-unit-of-time
https://www.quora.com/What-is-the-Planck-length

[feisty2]

special relativity would be an unholy mess if they weren't

maybe u already know this, but we woulda had a dominant unified field theory long by now if relativity and quantum mechanics were fully compatible... (there are some attempts of UFT currently like string theory, LQG, but none of them is really dominant and universally accepted)