Clarifying Infinity

Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.

Re: Clarifying Infinity

Postby nameless on June 27th, 2017, 8:04 pm 


Sure; only that which is perceived exists, there can not be anything that exists that is not perceived.
'Infinite/eternal' cannot exist besides as empty words! There is "For all intents and purposes 'infinite'!" or "Might as well be 'infinite'"! Metaphoric/poetic.
Like the answer to how many protons exist in the One (unchanging, ALL inclusive) Universe, ever? Yeah, it's a big number, but still finite.
'Infinite/eternal' are poor terms for "all there is!"!
'Eternity' would be an endless string of moments, but as Plank moments are literally 'timeless', you can string every one and still = 0! 'Eternal' is a crap word for 'timeless'!
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Re: Clarifying Infinity

Postby Lomax on June 27th, 2017, 8:09 pm 

Just a reminder that this is the mathematics subforum. It's fine to define "infinite" as "all there is" over on metaphysics but in mathematics it's a well-defined term, with particular properties.
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Re: Clarifying Infinity

Postby scientificphilosophe on July 2nd, 2017, 4:50 am 

I want to thank everyone for their posts on this topic as I have certainly learned a lot from it, but my 2 overall impressions from the various arguments made so far are that
• there are valid points on both sides of the debate
• there only seems to be one generic abstract circumstance where you might be able to add to infinity – and that is where there is a lack of completeness within the set definition and both the set and sub-set are infinite.

I’d like to test out my summary to see if you agree – accepting my layman’s language.

I have been approaching the issue of infinity from practical real-world scenarios, of which there seem to be two main possibilities, (neither of which we can be sure about), the size of the Universe, and Time. Other respondents have been approaching the subject from abstract mathematical principles and concepts.

Before continuing I’d like to clarify one point related to definition which has surprised me and seems to have caused a measure of confusion. Some people have used the term ‘complete’ to mean ‘bounded’ as opposed to ‘unending’ whereas I have used it to mean an unbroken sequence. The example that caught my eye was that all numbers between 1 and 2 was deemed a complete sequence, whereas 0 to infinity was ‘incomplete’ but I find that the terminology is confusing, (even if it is official mathematical jargon). The infinite sequence of fractions between 1 and 2 seems just as ‘incomplete’ as the sequence from 0 to infinity even though we may say that all relevant numbers are populated - which is why I would have used the term unbounded – reflecting the unending nature of infinity.

To now look at specifics, much seems to depend on the nature of the sets we are discussing. If we take the example of ‘all even integers running to infinity but starting a 6’ there is an assumption on the part of most people that at the ‘infinite end’ of this complete sequence – there is no limit, but an assumption at all even numbers are still present in the set. In this case you cannot add to the ‘infinite end’ because all relevant numbers are already present. Indeed if there was an end to the sequence to allow an add-to it would have to represent a finite set.

On the same principle you cannot add to Hilbert’s hotel because you can’t have gaps in the floor sequence and if it already runs to infinity then you can’t add to it by going upwards – the core scenario. Equally, you cannot add to the infinity of space if it is already infinite, and the only way to add to history is by moving the infinite timeline forwards.

We could add to the ‘finite end’ of the even number sequence by adding 4 or 2, and this would imply a direction of travel in my terminology, but this would change the set definition to one of ‘all positive even integers’, and if we change the set definition again we could also create more gaps in the set which might be filled – but in relation to the original definition, the same basic circumstances would not change. The original set becomes a sub-set which is also infinite but you can only add to the limited end which has a boundary/limit.

There are very few sets which can avoid a boundary or limit of some sort. Even if we said that the overall set definition was all numbers, we would still be setting a boundary by (for instance) denying duplicates etc.
So the one generic abstract circumstance where you can potentially add to an infinite set is by creating gaps in a set that is unbounded – ie. by not placing a limitation on the set through a definition, and yet this is very difficult to avoid.

In acknowledgement of this I tried to describe such a scenario in layman’s language as ‘a random sub-set of numbers, running to infinity, within the broader set of all numbers’. Here we have gaps in the sequence that runs to infinity but it is still infinite – so in theory you could potentially add to it within the larger set, and still not break the definition of the sub-set. But is that absolutely true?

Just because it is difficult to define a random set of numbers that runs to infinity, doesn’t mean that you have avoided imposing a boundary. Most people will say that such a random set of numbers has to be stable, (not constantly changing), because if it were, there would be no basis on which it could be sensibly discussed.
From this starting assumption, once the initial random selection is made no ‘add-to’ can be truly random because it has to avoid numbers that are already selected/present. The add-to must apply a different definition that now includes specific limitations, not the original unlimited one. Is this really adding to the infinite?
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Re: Clarifying Infinity

Postby Brent696 on July 18th, 2018, 10:45 pm 

SP,

I realize this post is a year old, and I have skimmed through a bit and I think I would like to make an observation.

In this universe, there is an underlying dynamic structure, the patterns of forces to which the phenomenal world obeys. This dynamic structure, although mathematicians may have their own word for it, but it is THAT realities to which our written formulas merely are descriptive, is part and parcel of this universe.

In another universe, with different dimensional qualities would they not have another math, one which describes their particular universe.

So Math, as we know it, is part of this finite universe, wherein all supposed "infinities" exist merely as "Potentials", meaning that they really do not exist.

Infinity, that which is beyond addition or subtraction, does not exist within this universe but it's existence would be beyond this universe, which is why,

Our math does not work against it.

When we come to that Infinity, this universe and all its math is dissolved, non existent.

So a discussion of a true Infinity, relates to our math through one number alone and that is 1, not 1 of, but 1 period.

So, there's the math that can describe an absolute Infinity [1] where there is no other.

If this has been addressed I apologize
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Re: Clarifying Infinity

Postby DragonFly on July 19th, 2018, 1:44 am 

Brent696 » July 18th, 2018, 9:45 pm wrote:So a discussion of a true Infinity, relates to our math through one number alone and that is 1, not 1 of, but 1 period.


For 'One', see Parmenides or the Block Universe.

Maybe this link will work (let me know): http://s664.photobucket.com/user/austintorn/media/PARJ%20791/Page-01jpeg_zpsf2bc6de4.jpg.html?sort=9&o=0
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 1:54 am 

My understanding of infinity is based upon simply logic. I read something of the block universe many years ago but as it is not my source, I would not know how other aspects of that theoretical model aligns with mine. I really don't know how to say this as people keep trying to categorize me somehow but my knowledge is not based on parroting some theory I read.
Infinity can only be understood when we are willing to let the finite universe be dissolves of any sense of reality since it lacks any permanence.
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 1:55 am 

I'll check it out tomorrow
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 2:07 pm 

Brent696 » July 18th, 2018, 11:54 pm wrote:... my knowledge is not based on parroting some theory I read.


I hope you wouldn't pick a brain surgeon who brags that their ignorance of prior art is proof of knowledge.

There is in fact 140 years of mathematical formalization of infinity. Without the mathematical theory of infinite sets you couldn't get functional analysis off the ground, and QM is based on functional analysis (Hilbert spaces, Lebesgue integration, etc.) So at the very least we can say that physics uses math that's based on mathematical infinity.

How mathematical infinity relates to the actual physical universe (as opposed to contemporary physics) is as yet unknown.
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Re: Clarifying Infinity

Postby BadgerJelly on July 19th, 2018, 2:11 pm 

In math some infinities are bigger than others. Although I have no idea how mathematicians use them to cancel each other out?
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 2:15 pm 

BadgerJelly » July 19th, 2018, 12:11 pm wrote:In math some infinities are bigger than others. Although I have no idea how mathematicians use them to cancel each other out?


Don't know what you mean by canceling each other out.

Cantor's theorem gives us an endless hierarchy of ever larger cardinalities. The set of natural numbers is infinite, the power set (set of all subsets) of the naturals has larger cardinality, the power set of that has still larger cardinality, and so forth.

https://en.wikipedia.org/wiki/Cantor%27s_theorem
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Re: Clarifying Infinity

Postby BadgerJelly on July 19th, 2018, 2:23 pm 

Neither do I understand. Was something I heard a physicist say once when doing complex calculations. I’ll just assume he made a bad analogy until I find out otherwise.
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 2:27 pm 

BadgerJelly » July 19th, 2018, 12:23 pm wrote:Neither do I understand. Was something I heard a physicist say once when doing complex calculations. I’ll just assume he made a bad analogy until I find out otherwise.


Ah well physicists are not constrained by rigorous math. Just as Newton used the idea of limits to work out gravity, even though it took mathematicians another 200 years to fully formalize the theory of limits. Likewise, physicists play fast and loose with math in order to build theories that conform to observations.

In modern times, renormalization is the idea that physicists can "get rid of infinities" in certain calculations in order to get the right answer. The mathematical rigor of such procedures is not their concern, nor should it be.

https://en.wikipedia.org/wiki/Renormalization
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 2:59 pm 

Dragonfly
>>>>For 'One', see Parmenides or the Block Universe.<<<<<<

Block does not fit my views at all, but it is not the first time someone has tried to imply it of me.

Permenides, although I can follow his logic well, we take exactly opposite conclusions. In denoting the the space assigned to temporal reality, he dies the existence of the space favoring the reality over the void.

His sees the temporal and it takes him to the void, but then he inadvertently swings back to its all one and real.

To me he is logical until he makes that 180
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 3:35 pm 

Someguy1,

>>>>>>>I hope you wouldn't pick a brain surgeon who brags that their ignorance of prior art is proof of knowledge.

There is in fact 140 years of mathematical formalization of infinity. Without the mathematical theory of infinite sets you couldn't get functional analysis off the ground, and QM is based on functional analysis (Hilbert spaces, Lebesgue integration, etc.) So at the very least we can say that physics uses math that's based on mathematical infinity.<<<<

First, since I meditate (think deeply) about the Omnis, which are much older than 140 years, perhaps infinitely so, then I am not without inspiration. Further there are no defects in the Infinite, brain surgeons are simply not required, neither do they or their patients exist.

Let me try one more to create a visual because you guys just don't seem to get what I am saying,

There are two Infinities, One infinity of Being, that is who and what I refer to as God but don't tell anyone here that.

And there is an Infinity of Nothing, a depth as it were of NON-being. This is the Nothingness from which all of this universe arose, the motions of time and space and all mathematical patterns of which our symbolic language merely describes. It is this foundation of infinity non-being that appears in physics equations where infinity co-aligns with the factors, the irritation of leading to string theory as to cancel out such infinities.

These infinities to be are just the nothingness out of which the universe springs, there is information added to the nothingness, in the same way a medium that is silent, when put under compression, gives rise to sound. So Nothing, being compressed into specific vibrations, resonates.

Those resonate waves are the patterns that mathematicians describe by their symbolic language.

The Infinity of non-being, from which the universe arises as compressed nothingness, shows up to mathematicians as these underlying "potential" infinities in their math.

The true Absolute Infinity of Being, exists beyond (transcendent to) this universe and its inherent nothingness, but it is the source of the information that leads to non-being's or nothingness's compression.

So, you say math has infinities, but, as a thought experiment, the closest we can come to an actual infinity which be a singularity, so hold a singularity in your hand. Wait, wait, there is no longer any time, nor space, nor you, everything stops and only the singularity exists because IT and you cannot exists in the same context.

Now a singularity would be descriptive of an Infinity of Being, the descriptive of non-being infinity would be a black hole. There again, everything stops, even time, even math.

>>>>>>>>How mathematical infinity relates to the actual physical universe (as opposed to contemporary physics) is as yet unknown.<<<<<<

This would be the non-being infinity of nothing, also why math produces larger and smaller infinities (relatives), a potential infinity or even numbers it supposedly bigger than the potential infinity of prime numbers,
potentialities are not realities, even of the temporal kind, this kind of math is merely reflecting upon that infinite base of non-being that underpins this temporal reality.
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 4:30 pm 

Brent696 » July 19th, 2018, 1:35 pm wrote:... brain surgeons are simply not required, neither do they or their patients exist.


@Brent696, I hope that neither you nor I never have to face the nonsensical bullshit of that statement.

Brent696 » July 19th, 2018, 1:35 pm wrote:Let me try one more to create a visual because you guys just don't seem to get what I am saying,


I speak for nobody but myself here. Or anywhere else.

Brent696 » July 19th, 2018, 1:35 pm wrote:There are two Infinities, One infinity of Being, that is who and what I refer to as God but don't tell anyone here that.


No question that there is a theological infinity. But that's not the infinity that was the subject of the thread. As this thread is in the Mathematics section of the forum, the discussion is presumptively about mathematical infinity. You seem to think this is the theology section.

Brent696 » July 19th, 2018, 1:35 pm wrote:And there is an Infinity of Nothing,


"Oh I got plenty o' nothin', and nothin's plenty for me."


Brent696 » July 19th, 2018, 1:35 pm wrote:Those resonate waves are the patterns that mathematicians describe by their symbolic language.


Bullshit. I've studied mathematical infinity and nothing of what you mention is discussed anywhere. You're just ignorant or prevaricating about mathematical infinity. If ignorant, I'd be happy to walk you through the basics. But it's not theology.

Brent696 » July 19th, 2018, 1:35 pm wrote:The Infinity of non-being, from which the universe arises as compressed nothingness, shows up to mathematicians as these underlying "potential" infinities in their math.


Word salad.

Brent696 » July 19th, 2018, 1:35 pm wrote:The true Absolute Infinity of Being, exists beyond (transcendent to) this universe and its inherent nothingness, but it is the source of the information that leads to non-being's or nothingness's compression.


With croutons.

Brent696 » July 19th, 2018, 1:35 pm wrote:So, you say math has infinities,


Um, yes. If you had curiosity I'd tell you about them with enthusiasm. But I suspect this is not an interest of yours.


Brent696 » July 19th, 2018, 1:35 pm wrote: but, as a thought experiment, the closest we can come to an actual infinity which be a singularity,


Yes, in physics. Math is not physics. Always good to hold that in mind when discussing infinity.

Brent696 » July 19th, 2018, 1:35 pm wrote:so hold a singularity in your hand.


Why? True singularities are just a mathematical idealization. Physicists just say that "the physics breaks down" in a region around a singularity. They don't claim a singularity is real, only that we don't know what happens there physically. You are making a strawman argument to claim that physicists are claiming singularities are real as opposed to simply regions where the theory breaks down.

Brent696 » July 19th, 2018, 1:35 pm wrote:Wait, wait, there is no longer any time, nor space, nor you, everything stops and only the singularity exists because IT and you cannot exists in the same context.


I'm really glad weed is legal in my state but your line of discourse is late-night stoner philosophy, if even that.

Brent696 » July 19th, 2018, 1:35 pm wrote:Now a singularity would be descriptive of an Infinity of Being, the descriptive of non-being infinity would be a black hole. There again, everything stops, even time, even math.


It's just a region where our physical theory breaks down. It has no more meaning than that. You're just making all this up.

Brent696 » July 19th, 2018, 1:35 pm wrote:>>>>>>>>How mathematical infinity relates to the actual physical universe (as opposed to contemporary physics) is as yet unknown.<<<<<<

This would be the non-being infinity of nothing, also why math produces larger and smaller infinities (relatives), a potential infinity or even numbers it supposedly bigger than the potential infinity of prime numbers,
potentialities are not realities, even of the temporal kind, this kind of math is merely reflecting upon that infinite base of non-being that underpins this temporal reality.


Pass the bong, dude.
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 4:48 pm 

Someguy1,

Thanks for clarifying your position,
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 4:59 pm 

Brent696 » July 19th, 2018, 2:48 pm wrote:Someguy1,

Thanks for clarifying your position,


Do you understand that we're in the Mathematics section of this website? And that if we were in the Theology section, if they have one, I would not make these comments? Can you understand that?
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 5:09 pm 

Then as infinity is beyond the limits of mathematics perhap the whole thread belongs in theology. And I can say that without being rude and belittling. Sorry to interrupt this one year dead air thread.
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Re: Clarifying Infinity

Postby DragonFly on July 19th, 2018, 5:14 pm 

Brent,

Info+'Nothing' = Info; 'Nothing' is the least 'infinite' of anything because 'it' can't be [no there, what… no properties) and can't add to the Info.

As Parmenides warned, 'Nothing' cannot even be meant. 'Nothing' cannot be an entity.

His 'One' is a changeless All, as is the Block Universe, both being like a 'movie' playing stills, with past and future already complete in it (how was it produced?) which is the eternalist notion of time. 'Presentism' is the opposite, with the past totally gone and the future not yet made, we ever living in the smoothly rolling 'now', as the present. A 'Growing Block' is a mixture, with the future not yet made but with the past kept around.

A big problem with Presentism is Einstein's relativity of simultaneity. See Lee Smolin; he likes Presentism. Perhaps we can allow for time fronts proceeding at different rates to save or local 'now'.

Actual 'infinities' are out; they cannot be capped. Potential math 'infinities' diverge/converge 'forever'.

'Nothing', as shown, is a goner.

Other impossibles are very likely to be Stillness (even the Blocks transforms or moves us through it), Fundamentals having Parts, Beginnings, Ends, One (total solidity), free will, things outside of Totality, consciousness dualism, absolute space, absolute time, and He.

'Random' appears to be possible; Anton Zeilenger has shown it as nature's bedrock to a three-sigma quality. In our universe, event still unfolded as they had to; one would have to rerun the universe to see different results due to 'random'.

— St. Austin
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 5:22 pm 

Brent696 » July 19th, 2018, 3:09 pm wrote:Then as infinity is beyond the limits of mathematics perhap the whole thread belongs in theology.


The portion of the the subject of infinity that lies beyond mathematics belongs outside a discussion of mathematics.

The portion of the subject of infinity that lies WITHIN mathematics, should be discussed in the section on mathematics.


Brent696 » July 19th, 2018, 3:09 pm wrote:And I can say that without being rude and belittling.


You're not being rude or belittling. You're just ignorant of the modern mathematical theory of infinity. If you'd like to discuss it, it's one of my favorite topics.

Oh you mean I was being rude and belittling. Well I'm a longtime student of crankology. I recognize word salad when I see it and I label it as such. Guilty as charged.

Brent696 » July 19th, 2018, 3:09 pm wrote: Sorry to interrupt this one year dead air thread.


Hey if you want to talk about mathematical infinity, let's do that!
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Re: Clarifying Infinity

Postby Braininvat on July 19th, 2018, 5:30 pm 

"With croutons. "

Sigh.

I am really trying to get across, in multiple forums, that ineffables and theological speculations ( or revelatory wisdom, depending on your perspective I guess) only lead to tears if you launch them in science forums or analytic philosophy forums. Only in Religion or maybe the Arts threads are things set up for more poetic and mystical insights.
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 6:16 pm 

BIV,

I know, I know, the thread was so old and Infinity, like truth, draws out me head from me hole. But I thought to respond more mathematically. At least to Dragonfly anyway. But had the OPer used a plural rather than a singular "infinity", I would not contest that this whole thread does not belong in the science forum section. Furthermore if you look at the OP itself, this should become obvious. And yet, if binary coding can be considered science and math, then I am capable of working back from that format.

Dragonfly,

<https://en.wikipedia.org/wiki/Binary_code>

""""""The modern binary number system, the basis for binary code, was invented by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire. The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi."[1] (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the I Ching through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.[2][3] Leibniz saw the hexagrams as an affirmation of the universality of his own religious belief.[3]

Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing.[4] Leibniz was trying to find a system that converts logic’s verbal statements into a pure mathematical one. After his ideas were ignored, he came across a classic Chinese text called I Ching or ‘Book of Changes’, which used a type of binary code. The book had confirmed his theory that life could be simplified or reduced down to a series of straightforward propositions. He created a system consisting of rows of zeros and ones. During this time period, Leibniz had not yet found a use for this system................
...........Another mathematician and philosopher by the name of George Boole published a paper in 1847 called 'The Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra. Boole’s system was based on binary, a yes-no, on-off approach that consisted of the three most basic operations: AND, OR, and NOT.[13] This system was not put into use until a graduate student from Massachusetts Institute of Technology by the name of Claude Shannon noticed that the Boolean algebra he learned was similar to an electric circuit. Shannon wrote his thesis in 1937, which implemented his findings. Shannon's thesis became a starting point for the use of the binary code in practical applications such as computers, electric circuits, and more"""""""""

<https://en.wikipedia.org/wiki/IEEE_754-1985>

"""""""IEEE 754-1985 was an industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008. During its 23 years, it was the most widely used format for floating-point computation. It was implemented in software, in the form of floating-point libraries, and in hardware, in the instructions of many CPUs and FPUs. The first integrated circuit to implement the draft of what was to become IEEE 754-1985 was the Intel 8087.

IEEE 754-1985 represents numbers in binary, providing definitions for four levels of precision, of which the two most commonly used are:

Level Width Range at full precision Precision[a]
Single precision 32 bits ±1.18×10−38 to ±3.4×1038 Approximately 7 decimal digits
Double precision 64 bits ±2.23×10−308 to ±1.80×10308 Approximately 16 decimal digits

The standard also defines representations for positive and negative infinity, a "negative zero", five exceptions to handle invalid results like division by zero, special values called NaNs for representing those exceptions, denormal numbers to represent numbers smaller than shown above, and four rounding modes."""""""""

Since the thread is titles "clarifying Infinity" (singular), and not plural, I assumed this to refer to that absolute infinity that would exist beyond the limitations of math and all of its subsets of potential infinitie(s).

Hence the need to delve just a bit beyond math that comes about with the universe to that function where a contrast between binary infinities could create all the worlds within a computer as a "something" and a "nothing" work together to manifest multiplicity.
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 6:30 pm 

IEEE-754 is not the real numbers. It's the floating point numbers. Very different things. You can't represent arbitrary real numbers on computers.
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Re: Clarifying Infinity

Postby DragonFly on July 19th, 2018, 6:37 pm 

Brent,

'Binary' is the base 2 number system: 0, 1, 10…

'Hexadecimal' is the base 16 number system: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10…

No big insight here. On/off 'transistors' were amenable to binary; reading half-bytes of 8-bit bytes was amenable to hexadecimal.

Special computer codes for math exceptions are fine, allowing the programmer to intercept and handle them instead of having the computer crash.

If an I had an infinite file of records coming in, my 'end-of-file' exception would never have shown up and so I guess that program of mine would be still running, since the machine has infinite memory.

TOE = 0/0.
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 7:09 pm 

Well, perhaps I did not do it right, I was in a crunch, ideally I wanted to show there that binary as 1 and 0 had more to do with a positive (information) and a negative (void), than merely being the symbols they appear to be as if binary could also be 1s and 2s.

But that's it for me, beyond that I can not understand any math than can address a true absolute Infinity, I respectfully bow out a failure and I will leave you your abilities to clarify what does not exist for you.
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 8:55 pm 

Brent696 » July 19th, 2018, 5:09 pm wrote:
But that's it for me, beyond that I can not understand any math than can address a true absolute Infinity, I respectfully bow out a failure and I will leave you your abilities to clarify what does not exist for you.


It's not all that bad. You're raising a good point. I have this question in my own mind. We do have this wonderful theory of the infinite going back to Cantor, and frankly back to Archimedes and Eudoxus. Mathematics has always been able to deal with infinity one way or another; and in the 1870's Cantor literally overnight brought the world into a new stage of our ability to symbolize the infinite.

But what about the physical world? Physics often talks about infinities, such as at the heart of singularities in spacetime, or infinitely many possible worlds in the multiverse, or the infinities of renormalization. Well, those aren't really mathematical infinities. They're "physicists doing math," which is a frequent source of confusion. Physicists aren't required to do rigorous math, and they don't. So people should be careful of getting their math from physicists.

And what about the "real world out there," as if we're so certain there even is such a thing. But let's say there is. What do we know about whether anything in the real world is actually infinite? And then supposing it is? What is the relationship between the infinities of the real world. and the strange infinities of mathematical set theory?

These questions interest me. And I try to help sort out the concepts, the physics versus the math on the one hand, and the physics versus the "real world" on the other.

But you know Georg Cantor, the German mathematician who created set theory and the modern mathematical study of the infinite, was a religious man. He showed that there was an infinite hierarchy of infinite sets, each one a larger infinity than the one before. Cantor believed that the ultimate set above all those levels, the set that encompasses all sets, was God.

Today, Cantor's math permeates all of mathematics. And his theology is forgotten. I think that if he came back, he'd be disappointed. Cantor took God seriously. Maybe he was on to something.

So @Brent696 I do recognize that there's a connection between the spiritual infinity and the mathematical infinity, with the physical infinity lying somewhere between the two. I think I was having a hard time catching the drift of your argument and was pushing back on parts of it that didn't make sense to me.
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Re: Clarifying Infinity

Postby Brent696 on July 19th, 2018, 9:59 pm 

>>>>>>I think I was having a hard time catching the drift of your argument and was pushing back on parts of it that didn't make sense to me<<<<<<<

So am I gingerly pulling the chair back from the table to sit back down, last time I had food thrown in my face and was told I didn't belong. Now are you inviting me back, I just want BIV to take note, this really was a long dead thread,

>>>>>>>It's not all that bad. You're raising a good point. I have this question in my own mind. We do have this wonderful theory of the infinite going back to Cantor, and frankly back to Archimedes and Eudoxus.<<<<<

"Theory" is ok with me, I figure if I am truly right, we will one day see it or we will one day will not, I might even be both right and wrong. But I do have my own views and may or may not agree with these guys.

>>>>>But what about the physical world? Physics often talks about infinities, such as at the heart of singularities in spacetime, or infinitely many possible worlds in the multiverse, or the infinities of renormalization. Well, those aren't really mathematical infinities. They're "physicists doing math," which is a frequent source of confusion. Physicists aren't required to do rigorous math, and they don't. So people should be careful of getting their math from physicists.<<<<<

Aren't physicists those guys who are trying to tell us matter is traveling back in time, no, no, don't believe anything they tell you, next they will be telling us a cat can be both dead and alive, In the REAL? world my girl friend is either pregnant or she's not, don't go messing around with my head. (Jokes)

It SEEMS, once physicists opened the door of "probabilities", not they can do damn well whatever the hell they please with their math.

But once Mathematicians opened the door to statistics and game theory, now they also can do whatever the hell they want with their math.

Now that's just a layman's view, I'm the visual thinker, my wife is the accountant and she has the talent for making numbers grew, not me. But Infinities, as I understand how they are used in conjunction with universal realities, exist on paper as it were and potentially. In math class we learned that multiplying 4 or 8 times infinity left only infinity, but that is never a reality, it simply describes a "relationship" between infinity and finite math. In odds, probabilities, and the like, I can see quotients of infinity being used to re-contextualize abstracts. (OK that last sentence was even hard for me, it may not be the exact language mathematicians use but I always suppose if you think about it, you can grasp what I mean assuming I'm close enough) But ultimately and absolutely, such infinities do not and cannot exist as in physical reality.

For example, a potential infinite number of even numbers. as a potential this is a reality within a potential equation, but it is never a reality in the physical (real) world. This Universe, the same universe that is manifesting finite attributes from top to bottom, from the life of a fruit fly to the death of our sun to the end of the expansion and final collapse, I see finite attributes reigning. And this might be a bit of logic, but if everything within this universe is finite, then the universe itself, as the parent so to speak, is also finite.

This finitude is not abstract, the very conditions of existence depend upon the time and spatial dimensions. Math would not be superior to time and space but rather as they are constants which define the universe, they provide the underlying structure from which math is derived.

Thus any True Infinity, one that might actually exist, must exist transcendent to this universe. What help in understanding this transcendent reality is when we stop thinking of the universe as an addition, as if creation truly added something, but rather in the infinity of nothing, nothingness was squeezed down by imposed limitations.

IOWs, the universe would be happening all at once, but when the speed was restricted to the speed of light, that allowed for a separation of time units. The limitation of the speed of light allows and creates time. What I am proposing is upside down from how we normally think of it.

Most of the questions you pose can only be answered when the attribute of Infinity and the attribute of the finite are kept strictly apart, this means that ultimately such potential infinities in math do not really exist.

Anyway its late, perhaps this will give you something to think about.
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Re: Clarifying Infinity

Postby someguy1 on July 19th, 2018, 10:21 pm 

Brent696 » July 19th, 2018, 7:59 pm wrote:>>>>>>I think I was having a hard time catching the drift of your argument and was pushing back on parts of it that didn't make sense to me<<<<<<<

So am I gingerly pulling the chair back from the table to sit back down, last time I had food thrown in my face and was told I didn't belong. Now are you inviting me back, I just want BIV to take note, this really was a long dead thread,


I haven't read the rest of your response yet. But I want to make clear a crucial distinction between my comments and BIV's.

* If I'm sometimes snarky or sharp (rude? eye of beholder) it's because this is an online forum and not the Oxford debating society. A little give and take is within the rules. I like free speech and would never tell you not to post here. I might make uncomplimentary remarks about your work but whenever I speak I speak only for myself.

BIV on the other hand is a moderator, and what he says goes.

So I make no warranty that BIV won't give you a hard time for writing the post that I invited you to write! If so, I apologize. I did give you a hard time earlier about being off-topic for a math discussion. But for me, that's more of a debating point. When BIV says the same thing, it's the law.

Hope this clarifies things. Now here comes BIV with his baseball bat! (jk BIV!)
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Re: Clarifying Infinity

Postby Braininvat on July 20th, 2018, 9:44 am 

it's just a baguette that sat out too long.

No, really, I'm glad to see an old dead thread resuscitated. Truth be told, "with croutons" made me laugh.

On the dead cat, physics never intended that as anything but a thought provoking conundrum, it's not meant to be taken literally. Just the presence of adjacent atoms will cause decoherence, no other observer is needed.
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Re: Clarifying Infinity

Postby Reg_Prescott on July 20th, 2018, 10:03 am 

Braininvat » July 20th, 2018, 10:44 pm wrote:i

On the dead cat, physics never intended that as anything but a thought provoking conundrum, it's not meant to be taken literally. Just the presence of adjacent atoms will cause decoherence, no other observer is needed.



Not meant to be taken literally? Oooohhh, I'd disagree there, old pal.

It was meant to highlight (what some see as) the absurdity of orthodox quantum mechanics. Taken literally, it exposes the absurdity of extrapolating from the quantum level to the macro level.

And that, I suggest, is precisely how Schrodinger meant it to be taken: as a reductio ad absurdum.


Actually, Einstein (as you probably know) proposed a thought experiment very similar -- something about gunpowder -- even before Schrodinger, I believe, to achieve the same effect: namely, the theory, as it stands, is ridiculous. It fails to meet, what Albert considered to be, scientific norms of causal-explanatory goodness.
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