Does It Make Sense To Say That Something Is Almost Infinite? If Yes, Then Why?

[DRACO]

I remember hearing someone say "almost infinite" in this video. As someone who hasn't studied very much math, "almost infinite" sounds like nonsense. Either something ends or it doesn't, there really isn't a spectrum of unending-ness. In this video he says that ''almost infinite'' pieces of verticle lines are placed along X length. Why not infinit?

https://www.youtube.com/watch?v=7Yq8nqIn2X8

 

 

[Flummoxed]

 

I remember hearing someone say "almost infinite" in this video. As someone who hasn't studied very much math, "almost infinite" sounds like nonsense. Either something ends or it doesn't, there really isn't a spectrum of unending-ness. In this video he says that ''almost infinite'' pieces of verticle lines are placed along X length. Why not infinit?

https://www.youtube.com/watch?v=7Yq8nqIn2X8

 

 

 

If its from a mathematician, infinities make the maths easier. ie If a number tends towards infinity and you divide a value by it, then you know the answer will tend towards zero.

 

Infinite space has philosophical meanings, like never ending, or never ending as far as we can tell. The visible horizon of the universe 13.8billion ish years away does not mean the universe ends at 13.8 billion light years away. It could just keep going for ever or have some slight undetectable curvature, that brings you back to where you started like on the surface of a very large sphere. 

[DRACO]

If its from a mathematician, infinities make the maths easier. ie If a number tends towards infinity and you divide a value by it, then you know the answer will tend towards zero.

 

Infinite space has philosophical meanings, like never ending, or never ending as far as we can tell. The visible horizon of the universe 13.8billion ish years away does not mean the universe ends at 13.8 billion light years away. It could just keep going for ever or have some slight undetectable curvature, that brings you back to where you started like on the surface of a very large sphere. 

So, in that video, at 1:23 is it correct to say that 'infinite pieces'' of vertical lines instead of ''almost infinite pieces''?

[balagna]

1) I think conversely. everything is  almost finite. (but this is a part of philosophy,you need formulization and usage for reality)

2) I disagree to that video,after 3th dimensions are not convincing. 

3) as a matheatician, I do not prefer to say that math is easy or difficult. 

 

...

Edited June 10, 2020 by balagna

[DRACO]

1) I think conversely. everything is  almost finite. (but this is a part of philosophy,you need formulization and usage for reality)

2) I disagree to that video,after 3th dimensions are not convincing. 

3) as a matheatician, I do not prefer to say that math is easy or difficult. 

 

...

So, is two dimensions made of infinite number of one dimensions, as stated in 1:23?

[balagna]

we need some instructions ,and to connet some other contexts each them

like this 

 

 

 

vector space X is said to be finite dimensional if there is a positive integer n such that X contains a linearly independent set of n vectors whereas any set of n + 1 or more vectors of X is linearly dependent. n is called the dimension of X, written n = dim X. By definition, X = {O} is finite dimensional and dim X = 0. If X is not finite dimensional, it is said to be infinite dimensional

In analysis, infinite dimensional vector spaces are of greater interest than finite dimensional ones. For instance, C[ a, b] and 12 are infinite dimensional, whereas Rn and en are n-dimensional. If dim X = n, a linearly independent n-tuple of vectors of X is called a basis for X (or a basis in X). If {et, ... , en} is a basis for X, every x E X has a unique representation as a linear combination of the basis vectors

This is sometimes called the canonical basis for Rn. More generally, if X is any vector space, not necessarily finite dimensional, and B is a linearly independent subset of X which spans 2.1 Vector Space ss X, then B is called a basis (or Hamel basis) for X. Hence if B is a basis for X, then every nonzero x E X has a unique representation as a linear combination of (finitely many!) elements of B with nonzero scalars as coefficients. Every vector space Xi:- {O} has a basis. In the finite dimensional case this is clear. For arbitrary infinite dimensional vector spaces an existence proof will be given by the use of Zorn's lemma. This lemma involves several concepts whose explanation would take us some time and, since at present a number of other thin~s are more important to us, we do not pause but postpone that existence proof to Sec. 4.1, where we must introduce Zorn's lemma for another purpose. We mention that all bases for a given (finite or infinite' dimensional) vector space X have the same cardinal number. (A proof would require somewhat more advanced tools from set theory; ct. M. M. Day (1973), p. 3.) This number is called the dimension of X. Note that this includes and extends Def. 2.1-7. Later we shall need the following simple [1]

[1] Kreyszig,Erwin Kreyszig ,INTRODUCTORY FUNCTIONAL ANALYSIS WITH ~ APPLICATIONS,wiley&son's

 

 

 

 

some more broad instructions exist in algebra. and then , go to geometry and / or physics ..

 

then try to connect all the relevancies each them without going far away from the reality.

Edited June 10, 2020 by balagna

[balagna]

I'm still waiting for a payoff I've demonstrated within a context in the past

what do you mean by this sentence?

are you waiting a reply to your previous comment?

[balagna]

I don't even know right now. These public forums are not a good place to be spilling all my regimes. 

you are really not understandable.

I can also see,that you do not understood yourself,too.

Edited June 10, 2020 by balagna

[balagna]

I have a universe-like topological system that can be expressed in numbers giving precise behavior similar to a big bang. Big bangs in this context in fact have variations which are size dependent, and only for the first few moments of a stellar mass black hole at this point can be comparable to fitting 13 billion years in a event horizon accelerated time vacuum of about 10^-21 years

1) topology: I think that while,it has its own mathematical definition privately to this case,this word seems semantic.

2) big bang: I do not deal with this definition in the current position. so,I am unable to draw a meaningful message here about this issue.

3) black hole: yes! this has high potentiality to be relevant to this thread, but again I do not deal with it in the current position.

....

some specific conclusions.

if you;

1)think that you have found some important scientific clues or findings ,then do not post here .(if I were you). prepare it well ,and submit it to a scientific journal.

2) think that you have invented something, then please be informed that you are strictly advised NOT to share it anywhere except official filing to patent institıtes. 

Edited June 10, 2020 by balagna

[Flummoxed]

So, in that video, at 1:23 is it correct to say that 'infinite pieces'' of vertical lines instead of ''almost infinite pieces''?

 

The video starts by discussing 0th dimensions and adding them in a infinite straight line to produce 1 dimension.

 

Whilst the video has that horrible robotic voice, and claims from the outset not to be teaching maths, the 0th dimension concept is interesting. I didnt get to the end of the video, 

 

I am not a mathematician, but I guess the 0th dimension could be viewed a little like an interconnecting membrane between points in space. Or viewing the 0th dimension as the planck scale for amusement https://en.wikipedia.org/wiki/Planck_length you could add an approaching infinite amounts of planck lengths in a straight line giving a 1 dimensional line, then adding x y z dimensions, to get three dimensional space.

 

Polymath???

[sluggo]

Draco;

Unfortunately, mathematicians don't always have grammatical skills to match their math skills. "almost infinite" is in the same category as "almost pregnant", etc.

The intended meaning of any statement containing 'infinite', depends on the context.

Using a dictionary or thesaurus, you find 'figures of speech' for emphasis or drama.

Math is (supposedly) a formal language with rigid definitions, (in an ideal world).

The definition of 'infinite' in the mathematical sense is: without limit or immeasurable.

It's a relation or condition, not a quantity. This is the common problem of attempting to use it as a quantifier.

If you research "mathematical limits", you will find another nonsensical phrase, "approaches infinity".

I have asked how this is done, on various forums, with no responses.

If 'it takes an infinite amount of time', then 'it never happens'.

[Mutex]

Infinity is interesting, but it is also really just an abstract, it simply means 'something without bounds', numbers are also abstract (a 6 does not exist in reality), but infinity is not really even a number.

 

Nothing is infinite! literally.. The only thing that can be considered by itself as infinite is nothing.. 

 

Although having said that, it could be that the Universe itself 'goes forever' (without bounds), and it could actually be the case that the amount of matter in the universe AND the amount of space that the matter exists in could be infinite.

 

But even if the entire universe contained only the mass of a single electron, then the Universe would still be infinite (without bounds or borders), that is our universe that contains a single electron mass would have finite mass (the mass of the electron), but the 'NOTHING' that the electrons exists in (space) is infinite, at no point at any distance away from that electron is there NOT SPACE. 

 

SO the only thing that can be infinite is nothing. 

 

You just cannot consider 'infinite' to be 'VERY LARGE' or 'VERY SMALL' or very far away, or 'almost' anything. Because infinite does not have anything to do with size.

 

Infinity is handy for use in mathematics (again, because of strict rules and definitions), but in science and physics it's not really 'a thing', if your physics equations results in infinities that generally means you are getting something wrong. 

 

So if you are doing calculation son black holes and you start getting infinities out of your equations, either your physics is wrong, or your assumptions are wrong. 

Nature does not do infinities, (except possibly for nothing, and the universe). But locally (such as black holes), if you get infinities it's probably wrong. 

 

Mathematically you may be able to put matter into zero volume but just like in computer science if you start dividing by zero's you get an error (divide by zero error), if you introduce concepts like matter in zero volume you will get infinities (garbage) as an output.

 

It's upsetting to me that in modern times (past 50 years ish), that theoretical physics has started to consider infinities as a valid conclusion and are embracing infinities as opposed to understanding that the infinities they get show that they are wrong.

 

This is probably a good part of the reason why physics and cosmology are in crisis today and have been really struggling for many, many years. 

[balagna]

Infinity is interesting, but it is also really just an abstract, it simply means 'something without bounds', numbers are also abstract (a 6 does not exist in reality), but infinity is not really even a number.

 

Nothing is infinite! literally.. The only thing that can be considered by itself as infinite is nothing.. 

 

Although having said that, it could be that the Universe itself 'goes forever' (without bounds), and it could actually be the case that the amount of matter in the universe AND the amount of space that the matter exists in could be infinite.

 

But even if the entire universe contained only the mass of a single electron, then the Universe would still be infinite (without bounds or borders), that is our universe that contains a single electron mass would have finite mass (the mass of the electron), but the 'NOTHING' that the electrons exists in (space) is infinite, at no point at any distance away from that electron is there NOT SPACE. 

 

SO the only thing that can be infinite is nothing. 

 

You just cannot consider 'infinite' to be 'VERY LARGE' or 'VERY SMALL' or very far away, or 'almost' anything. Because infinite does not have anything to do with size.

 

Infinity is handy for use in mathematics (again, because of strict rules and definitions), but in science and physics it's not really 'a thing', if your physics equations results in infinities that generally means you are getting something wrong. 

 

So if you are doing calculation son black holes and you start getting infinities out of your equations, either your physics is wrong, or your assumptions are wrong. 

Nature does not do infinities, (except possibly for nothing, and the universe). But locally (such as black holes), if you get infinities it's probably wrong. 

 

Mathematically you may be able to put matter into zero volume but just like in computer science if you start dividing by zero's you get an error (divide by zero error), if you introduce concepts like matter in zero volume you will get infinities (garbage) as an output.

 

It's upsetting to me that in modern times (past 50 years ish), that theoretical physics has started to consider infinities as a valid conclusion and are embracing infinities as opposed to understanding that the infinities they get show that they are wrong.

 

This is probably a good part of the reason why physics and cosmology are in crisis today and have been really struggling for many, many years. 

 

first,it will be good to say ,I think you do not have sufficient mathematical skill

You need to formulize the thing whatever you say,therefore you are definitely lacking.

please be informed that infinity is not alone.

you need something to describe it for instance you need a serie, a sequence or a function. 

then you will be able to describe infinity.

thus,almost all of your this explanations is NOTHING.

[balagna]

 

Draco;

Unfortunately, mathematicians don't always have grammatical skills to match their math skills. "almost infinite" is in the same category as "almost pregnant", etc.

The intended meaning of any statement containing 'infinite', depends on the context.

Using a dictionary or thesaurus, you find 'figures of speech' for emphasis or drama.

Math is (supposedly) a formal language with rigid definitions, (in an ideal world).

The definition of 'infinite' in the mathematical sense is: without limit or immeasurable.

It's a relation or condition, not a quantity. This is the common problem of attempting to use it as a quantifier.

If you research "mathematical limits", you will find another nonsensical phrase, "approaches infinity".

I have asked how this is done, on various forums, with no responses.

If 'it takes an infinite amount of time', then 'it never happens'.

 

you do not have  mathematical skill to interpret this issue.

Edited June 13, 2020 by balagna

[Flummoxed]

Infinity is interesting, but it is also really just an abstract, it simply means 'something without bounds', numbers are also abstract (a 6 does not exist in reality), but infinity is not really even a number.

 

Nothing is infinite! literally.. The only thing that can be considered by itself as infinite is nothing.. 

 

 

Infinity has mathematical and philosophical meanings.

 

Examples of infinties with other definitions eg. Mathematically N/0 is undefined or non computable. The calculation of numbers, that can not be computed without infinite decimal places. PI for example could be regarded as examples of infinities. 

 

Infinity is a definition of something that is unattainable either numerically, or in terms of spacetime coordinates.

 

Nothing is not a mathematical definition. If you focus on the vacuum nothingness of space, you find it is full of quantum fluctuations, all the way down to the planck scale, perhaps the 0th dimension for the purposes of this thread.

 

Tending towards infinity is a useful mathematical idea which allows mathematical simplifications in the derivation of formulaes. You will remember from university that many of those formulae used in calculus are derived by assuming infinties, or tending towards infinity or zero.  

 

 

 

 

Although having said that, it could be that the Universe itself 'goes forever' (without bounds), and it could actually be the case that the amount of matter in the universe AND the amount of space that the matter exists in could be infinite.

 

You just cannot consider 'infinite' to be 'VERY LARGE' or 'VERY SMALL' or very far away, or 'almost' anything. Because infinite does not have anything to do with size.

 

Infinity is handy for use in mathematics (again, because of strict rules and definitions), but in science and physics it's not really 'a thing', if your physics equations results in infinities that generally means you are getting something wrong. 

 

Nature does not do infinities, (except possibly for nothing, and the universe). But locally (such as black holes), if you get infinities it's probably wrong. 

 

Mathematically you may be able to put matter into zero volume but just like in computer science if you start dividing by zero's you get an error (divide by zero error), if you introduce concepts like matter in zero volume you will get infinities (garbage) as an output.

 

 

 

Are you not contradicting yourself a little here. 

 

If the maths comes up with infinities when a mathematical theory is stretched beyond breaking point, then a new theory might be required. 

 

Standard spacetime dimensions, might not be all there is. String theory which I am not keen on introduces lots more dimensions. The 0th dimension above could be regarded in a number of different ways. Playing with the idea of it as a membrane (m theory), which connects all points in spacetime, is interesting. The number 0 revolutionized our counting. https://www.history.com/news/who-invented-the-zero#:~:text=Sumerian%20scribes%20used%20spaces%20to,century%20B.C.%20in%20ancient%20Babylon.

 

Introducing a 0th dimension as a membrane, without shape or definition is interesting to play with, both mathematically and philosophically. Perhaps ascribing a minimum size at the planck scale, and also connecting to all points in space to different degrees tending all the way to infinity. Space time grows out of an undefined infinte 0th dimension

 

Disappearing down a wormhole and warping ideas with entanglement ie the ER = EPR conjecture does a a 0th dimension help at all????? 

 

Edit at c infinite space and time or zero space and time in what reference frames??

Edited June 13, 2020 by Flummoxed

[sluggo]

you do not have  mathematical skill to interpret this issue.

How did you get appointed as a role model for society?

[Mutex]

Infinity has mathematical and philosophical meanings.

 

Examples of infinties with other definitions eg. Mathematically N/0 is undefined or non computable. The calculation of numbers, that can not be computed without infinite decimal places. PI for example could be regarded as examples of infinities. 

 

Infinity is a definition of something that is unattainable either numerically, or in terms of spacetime coordinates.

 

Nothing is not a mathematical definition. If you focus on the vacuum nothingness of space, you find it is full of quantum fluctuations, all the way down to the planck scale, perhaps the 0th dimension for the purposes of this thread.

 

Tending towards infinity is a useful mathematical idea which allows mathematical simplifications in the derivation of formulaes. You will remember from university that many of those formulae used in calculus are derived by assuming infinties, or tending towards infinity or zero.  

 

 

 

Are you not contradicting yourself a little here. 

 

If the maths comes up with infinities when a mathematical theory is stretched beyond breaking point, then a new theory might be required. 

 

Standard spacetime dimensions, might not be all there is. String theory which I am not keen on introduces lots more dimensions. The 0th dimension above could be regarded in a number of different ways. Playing with the idea of it as a membrane (m theory), which connects all points in spacetime, is interesting. The number 0 revolutionized our counting. https://www.history.com/news/who-invented-the-zero#:~:text=Sumerian%20scribes%20used%20spaces%20to,century%20B.C.%20in%20ancient%20Babylon.

 

Introducing a 0th dimension as a membrane, without shape or definition is interesting to play with, both mathematically and philosophically. Perhaps ascribing a minimum size at the planck scale, and also connecting to all points in space to different degrees tending all the way to infinity. Space time grows out of an undefined infinte 0th dimension

 

Disappearing down a wormhole and warping ideas with entanglement ie the ER = EPR conjecture does a a 0th dimension help at all????? 

 

Edit at c infinite space and time or zero space and time in what reference frames??

 

 

 

Infinity has mathematical and philosophical meanings.

 

Examples of infinties with other definitions eg. Mathematically N/0 is undefined or non computable. The calculation of numbers, that can not be computed without infinite decimal places. PI for example could be regarded as examples of infinities. 

 

Infinity is a definition of something that is unattainable either numerically, or in terms of spacetime coordinates.

 

The question then is 'is mathematics physics?', and yes Infinity has math and philosophical meanings, I would say that math is not in itself physics, it is just a good language to describe things in physics (the real world), by using the abstract and 'by definition' mathematics, as the language of communications.

 

N/0 is only undefined in your don't use infinity (infinity is the definition of how many zero's goes into one), I would say it's is non-computable because infinity is not a number. (but numbers can be infinite, as you said such as Pi, or the number of numbers between 1 and 2). 

 

You can do that with numbers and math, especially if you have a definition of a value without bounds (infinity) that can be used in mathematics to describe irrational numbers and division by zero.

 

But how does that apply beyond the world of math and philosophy? In the real world, in nature and in physics? (that's the philosophical question).

 

So what is infinite in the real world ?

 

 

Nothing is not a mathematical definition. If you focus on the vacuum nothingness of space, you find it is full of quantum fluctuations, all the way down to the planck scale, perhaps the 0th dimension for the purposes of this thread.

 

'Nothing' is tricky, particularly in theoretical physics, it is true it is not a mathematical definition (but zero is, as are all numbers, they are abstract, so what nothing 'is' is more a philosophical question. 

 

"If you focus on the vacuum nothingness of space" then you focus on the something (vacuum) nothingness of something (space). So you are not really dealing with nothing. 

 

I'm assuming your are talking about the Casimir effect when you talk about 'full of quantum fluctuations', I don't buy that argument, it's an interesting effect but I don't accept the conclusion that the effect is caused by quantum particles or fluctuations popping into existance and applying a force to the metal plates. I see the effect to be simply electric and magnetic forces between the charges present on the metal plates causing the observed attraction.

 

If that was not the case where is the entire class of instruments being developed to study and investigate and characterise these quantum fluxuations?

That is I do not accept based on the available evidence that we do in fact get something from nothing (vacuum nothingness of space).

 

But to truly have nothing, you would not no space or time or energy or gravity. But even then you still could have completely empty space.

 

Imagine you had a box made out of a hyperthetical shielding material that existed at absolute zero, blocked all EM radiation, blocked 'gravity' and all energy, you take out all matter from inside the box (perfect vacuum), so within the walls of the box exists nothing (no heat, no light, no gravity, no matter) even then you have 'SPACE' betweeen the walls of the box, the box does not collapse to zero size, it is just a box with NOTHING in it, but you can still measure a length of space within the box (the box has a size). 

 

But even then the length of space you have in the box is finite (say your box is 1 meter per side), you can fit a 1 meter ruler inside the box. That is inside the box is bound by the box itself. 

 

I was trying to say earlier that the 'box' of our universe has no bounds, so nothing (space length and nothing else) could be infinite, the universe could be infinite in extent, and if populated with matter that matter could also be infinite. But it is possible to have a finite amount of matter in an infinite universe of nothing but space.

 

If the maths comes up with infinities when a mathematical theory is stretched beyond breaking point, then a new theory might be required. 

 

 

 

This is a thorny point (at least for me), is it a 'mathematical theory' or a mathematical description of nature? Is the math the science? Or the theory? 

My argument against math being the science/nature is that if you get infinities from the math it is going to be the math that is misapplied or applied as an 'ideal' (abstract). 

 

My argument is that nature will not let you do something that will result in infinities, so something you can do with math you cannot do in the real world, if you stretch the mathematical 'theory' such that you get infinities I think it is the application of the math that is the problem and not nature.

 

If I put zero ohms across a charged capacitor I will get infinite current, according to perfectly working math and ideal components that nature does not allow you to do. Does that mean ohms law, or coulombs law are broken and we need a new theory or new math? I would say we do not. Nothing wrong with the theory or the math, but you still get infinities out, if you consider nature as abstracts (ideal components).

 

So zero volume with matter in it would be for me an example of applying abstracts to the reality of nature, So to say that you can apply relativity and mathematically put matter in zero volume, you get the impossible infinities (density/volume) in the singularity in a black hole. 

 

Does that really happen in nature? I would say it is just like the zero ohm resister and charged capacitor, you will not get the infinities that the math implies. 

 

As for dimensions of space and the 0th dimension, you have to ask yourself what qualifies as a spatial dimension and a time dimension?

In that subject I have a different perspective of space and time that is a non-geometrical perspective.

 

but even with a geometrical perspective you need to consider (or I do) what is common between X,Y,Z and time X,Y,Z are directions, and a length and that length is an absolute (no negatives). SO I consider the common factor to be length (of space and of time), and due to the speed of light being constant (in all reference frames), that length property is the same (in any direction and in any time if geometrically treated). 

 

So my question would be what qualifies 0th dimension or higher dimensions as dimensions at all? do they have a direction and a length property? Do they have length properties such to keep c constant? Does a direction qualify as a dimension? if so would there not be an infinite number of them, far more than X,Y,Z 3 dimensions with is a minimal number of values to define a location (plus time for when to show up!). But there is no reason why could not go in any direction and define that direction as a dimension.

 

Now I fully understand that you, just like myself have always understood as space being 3 dimensional and geometrical in nature and 'curved and warped' by matter/mass. I understand that it is hard to conceptualise otherwise. 

 

But for me, I see the model of space and time far more simply explained and understood that space is fundamentally a length property, and what is relative about relativity is the difference in the length property from the observed to the observer, and having little to do with the relative locations or paths between to two reference frames.

 

The temperature at your place relative to the temperature at my place is not a function of the relative locations or paths between your place and my place, although I can define it as such, and I can mathematically justify that relative difference in those terms. 

I find it more interesting to consider simply that the temperature at your address is different from mine, and then explore those differences in terms of the nature of space (temp) at your location relative to the nature of space at my location. (but not as a function of your position relative to me). 

 

The only difficulty of this treatment (non-geometrical) is not intrenched the geometrical model is. (but it does save on 4D geometric calculus).. 

Now I think I'm way off topic, but thanks for the comments and post.