disproving infinity paradoxes; Hilbert’s Hotel?

[China Cat Sunflower]

It occurs to me, just thinking about exponential operations, that infinity: that is the ability for there to be no end to a process, is an essential ingredient in lots of common, around the house so to speak, functions. Lot's of really common little math thingies have to do with repeating decimals. So that begs the question: why the 33 1/3 rpm LP's? Is it a matter of dynamics?

Chris

 

[_Z_]

infinity is not purely conceptual in my mind. it it is then you have to replace it with something else - and that would have to have no limits too, in short you can only replace it with itself. if you don’t have infinity then what is beyond what ever we do have? there is always a beyond - but not beyond infinity.

the infinity lamp
this puzzle is a lot simpler than the hotel one, and i think we can resolve a few issues with it.
quote:
Question. Consider a very durable ceiling lamp that has an on-off pull string. Say that the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed?

Answer. The lamp could in fact be either on or off after infinitely many days. Information about its state after any finite number of days is not enough to enable us to extrapolate past infinity. What makes this question interesting is that it is possible give an argument that seems to indicate the lamp will be on, as well as an argument that seems to indicate the lamp will be off. On: "The light starts out off, and then we turn it on. Each time we turn it off again, we immediately turn it back on. Therefore it must ultimately be on." Off.- "Each time we turn the light on, we immediately turn it back off. Therefore it must ultimately be off." This type of lamp is called a Thompson Lamp.

firstly we may ask; what exactly is an infinite number set? in maths surely we are actually talking about open number systems! it is presumed that you can have an infinite set of natural numbers, yet in truth what is visualised is a very large number without end.this means that you can add for instance; injective or bijective sets, to the original infinite number set - add infinitum. you can keep adding sets because infinity is thought of as without end, thus another set can be added without detracting from that space [the open end].
in short then you cannot have an infinite number set, nor add sets to it. you can have open ended number systems or potential infinities just as we can have theoretical geometric shapes which begin and end at infinity.

thus you cannot have a lamp that can be switched on or off infinitely, nor an infinite amount of days to perform this task in.

 

[juantoo3]

Only got a minute, Z...

Question. Consider a very durable ceiling lamp that has an on-off pull string. Say that the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed?

See, what we are up against with puzzles like this is conflating a portion with the whole. Any portion of infinity cannot be infinity, it is a portion of and therefore must be limited. Someone else already mentioned the odd / even issue, so that if all we are looking at is the on / odd "set," or the off / even set, we are only looking at half of the picture and therefore an incomplete and not-infinite set. We are looking to use a sample to define the whole...in a social setting we would call this a "prejudicial assumption." Either infinity is an endless set, or it is a "total" set, depending on contextual usage. The thing is, one cannot add to infinity if it is totality. And if one can continue to add to an open ended set, this presupposes a potential end even if that end is always just out of reach, therefore not infinite. (one could choose not to add to the open end, in which case the open end must halt if only for a moment...) One cannot use an apple versus orange concept to describe something that encompasses not only all fruit, but all vegetation and all matter / energy. One cannot add an infinite subset to infinity (an infinite number of new guests to an infinitely full hotel). The subset is and always will be but a portion of infinity, therefore it cannot be appropriately called "infinite."

Let us consider from a somewhat different perspective, that of zero. What is zero? Zero is one of the most powerful forces in the universe...let us place your imaginary lamp into the black hole of zero, and play the on-off game for an infinite amount of time, and what will the outcome be?















Zero.

 

[seattlegal]

infinity is not purely conceptual in my mind. it it is then you have to replace it with something else - and that would have to have no limits too, in short you can only replace it with itself. if you don’t have infinity then what is beyond what ever we do have? there is always a beyond - but not beyond infinity.

the infinity lamp
this puzzle is a lot simpler than the hotel one, and i think we can resolve a few issues with it.
quote:
Question. Consider a very durable ceiling lamp that has an on-off pull string. Say that the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed?

Answer. The lamp could in fact be either on or off after infinitely many days. Information about its state after any finite number of days is not enough to enable us to extrapolate past infinity. What makes this question interesting is that it is possible give an argument that seems to indicate the lamp will be on, as well as an argument that seems to indicate the lamp will be off. On: "The light starts out off, and then we turn it on. Each time we turn it off again, we immediately turn it back on. Therefore it must ultimately be on." Off.- "Each time we turn the light on, we immediately turn it back off. Therefore it must ultimately be off." This type of lamp is called a Thompson Lamp.

firstly we may ask; what exactly is an infinite number set? in maths surely we are actually talking about open number systems! it is presumed that you can have an infinite set of natural numbers, yet in truth what is visualised is a very large number without end.this means that you can add for instance; injective or bijective sets, to the original infinite number set - add infinitum. you can keep adding sets because infinity is thought of as without end, thus another set can be added without detracting from that space [the open end].
in short then you cannot have an infinite number set, nor add sets to it. you can have open ended number systems or potential infinities just as we can have theoretical geometric shapes which begin and end at infinity.

thus you cannot have a lamp that can be switched on or off infinitely, nor an infinite amount of days to perform this task in.

Well, my answer would be MU! because there is no such thing as "after an infinite number of days."
Therefore, the best answer would be a question: Is the lamp on or off now? Yes, it is either on, or off. The funny thing is, where ever you are, it is "now."

 

[juantoo3]

Kindest Regards, Seattlegal!

Well, my answer would be MU! because there is no such thing as "after an infinite number of days."

Good catch! I missed this about "after" infinity, which you are correct, is not possible. I do have one question though...what is "MU?"

Therefore, the best answer would be a question: Is the lamp on or off now? Yes, it is either on, or off. The funny thing is, where ever you are, it is "now."

Should we wait and ask that cat?

 

[seattlegal]

Kindest Regards, Seattlegal!


Good catch! I missed this about "after" infinity, which you are correct, is not possible. I do have one question though...what is "MU?"

Short answer:

mu
1. The country code for Mauritius.
2. /moo/ The correct answer to the classic trick question "Have you stopped beating your wife yet?". Assuming that you have no wife or you have never beaten your wife, the answer "yes" is wrong because it implies that you used to beat your wife and then stopped, but "no" is worse because it suggests that you have one and are still beating her. According to various Discordians and Douglas Hofstadter the correct answer is usually "mu", a Japanese word alleged to mean "Your question cannot be answered because it depends on incorrect assumptions".
Hackers tend to be sensitive to logical inadequacies in language, and many have adopted this suggestion with enthusiasm. The word "mu" is actually from Chinese, meaning "nothing"; it is used in mainstream Japanese in that sense, but native speakers do not recognise the Discordian question-denying use. It almost certainly derives from overgeneralisation of the answer in the following well-known Rinzei Zen teaching riddle:
A monk asked Joshu, "Does a dog have the Buddha nature?" Joshu retorted, "Mu!"

Should we wait and ask that cat?

When you see that cat, please also ask it, "Why do cows say mu?"

 

[_Z_]

juantoo3
excellent description which completely agrees with where i am going here - thank you! i have had a seven page battle with mathematicians at another forum and they just don’t get it.
zero is interesting, someone said that the combined value of all energy in the universe is zero. the interesting thing about infinity is that you may produce as many zero’s as you like as long as they have no value they don’t create a paradox, then when we consider the above, that the universe itself emanates from zero, then infinity become a fascinating and interesting field of exploration - for me this includes creation and eminationary notions.

seattlegal

Well, my answer would be MU! because there is no such thing as "after an infinite number of days."

would you believe that in maths you can have omega plus one! so you can according to math have an after infinity - to wit i would agree is a ridiculous notion. i think the problem with math is that it toys with potential infinities but calls them actual - this is the main premise of this thread; that infinity cannot be defined mathematically. indeed it may even be the seat of divinity [i postulate].
so hands off science it belongs to us

 

[Tao_Equus]

So infinity is always beyond all efforts to observe as a whole. So is it like the cat and expands with observation, is infinity dependent on the observer? And what about the reverse of outward looking infinity, what about going inward through the microscope? Is there infinite space there too?

 

[seattlegal]

juantoo3
excellent description which completely agrees with where i am going here - thank you! i have had a seven page battle with mathematicians at another forum and they just don’t get it.
zero is interesting, someone said that the combined value of all energy in the universe is zero. the interesting thing about infinity is that you may produce as many zero’s as you like as long as they have no value they don’t create a paradox, then when we consider the above, that the universe itself emanates from zero, then infinity become a fascinating and interesting field of exploration - for me this includes creation and eminationary notions.

Have you considered this: Usually you can't divide by zero, because zero times any number equals zero. However, when you divide zero by zero, the answer could be an infinite amount of possibilities. {Creation from nothing?}

n=any nonzero number
0 * n = 0
therefore
0/n = 0
therefore
0/0 = n

Please remember that n/0 does not make sense, because 0 * anything ≠ n, because 0 * anything = 0​

 

[_Z_]

tao equus

So infinity is always beyond all efforts to observe as a whole

perhaps, as there are no xyz coordinates to observe from! i don’t think it is beyond our perception though - if i may. for me it is a thing of contemplation, we must begin at ‘infinity as incomparative’ then add and immediately take everything away e.g. add infinite being and mind, then remember that such things have entity or natures thence remove them leaving their zero value somehow therein. we can do this for absolutely everything we can possibly think of [after being reduced to component parts?], as it may be perceived as a kind of everything at zero value.
well that is how i see it anyhow.

And what about the reverse of outward looking infinity, what about going inward through the microscope? Is there infinite space there too?

perhaps you are referring to the infinitesimal? this is an infinitely small point of no substance or value [due to its size]. i am beginning to wonder if there are three basic natures and principles of existence and non existence [= reality]; infinity, the quantum and the infinitesimal. while betwixt and utilising them all is universality.

seattlegal

Usually you can’t divide by zero, because zero times any number equals zero. However, when you divide zero by zero, the answer could be an infinite amount of possibilities. {Creation from nothing?}

good point!
i have considered similar notions, very interesting - thank you. when we consider the totality of energy = 0 then it makes more sense as a real ‘force’ of creation/emanation. i would consider it so that from this base all things would arise autotelically [see below] i.e. all entities either actual or in terms of law and principle, would arize from their base ‘0’ value!
[1] autotelic
philosophy; possessing internal purpose: describes an entity or event that has within itself the purpose of its existence or occurrence.

 

[juantoo3]

Kindest Regards, Tao!

Thank you for joining the discussion!

So infinity is always beyond all efforts to observe as a whole. So is it like the cat and expands with observation, is infinity dependent on the observer?

I think in some sense infinity is dependent on the observer. For instance, the examples Z is positing stem from mathematical calculations...therefore the understanding created is limited by the mathematics. Z mentioned elsewhere about "omega plus," wherein I presume omega to represent infinity. This would represent a mathematical "fudge factor" to overcome the inherent stickiness surrounding the solution of infinity, at least hypothetically and confined to the realm of theoretical mathematics...not "reality."

And what about the reverse of outward looking infinity, what about going inward through the microscope? Is there infinite space there too?

This again provides a certain "stickiness." While it seems fairly well understood that even within the confines of a single atom there is a great deal of empty space, it seems to me that "infinity" is not quite appropriate in this sub-atomic realm...although I can grant that it may well be a "matter" of perspective. As we exist in a realm above and beyond that of a single atom (indeed, many many multiples of atoms), from our perspective infinity would not apply.

Now, we could easily wander into "what ifs" that reflect the concept that our "reality" is but an illusory dream of some god. If an atom is a mirror of a solar system, and there happened to be sentient beings existing on one or more satellites, then I suppose an argument might be made that "relatively speaking" that vast emptiness that would continue on into further atoms might be considered infinite.

This is why I hesitate to consider the vastness of the universe to be infinite in the "never ending" sense to be a little presumptive...that the universe may well have an end. Even so, that end is so very far beyond our personal reach that it may as well be for all practical purposes infinite. In the sense of "totality," whatever totality eventually figures out to be, I can see the universe as infinite. Everything that is of concern to us is confined within this totality.

 

[juantoo3]

Kindest Regards, Z!

excellent description which completely agrees with where i am going here - thank you! i have had a seven page battle with mathematicians at another forum and they just don’t get it.

Nor would I expect mathematicians to "get it." They are engulfed in their own dogma of hypotheticals. To hypothetically surmise is one thing...it is an exercise of the brain. To take for granted that a hypothetical is factual is where people...any people using any dogmatic hypothetical...get lost on their own tangent. This is why I still hold string theory and multiple universe concepts at arm's length until proven otherwise.

zero is interesting, someone said that the combined value of all energy in the universe is zero.

I would have to see this worked out to understand, I'm afraid it makes no sense to me.

the interesting thing about infinity is that you may produce as many zero’s as you like as long as they have no value they don’t create a paradox, then when we consider the above, that the universe itself emanates from zero, then infinity become a fascinating and interesting field of exploration - for me this includes creation and eminationary notions.

Something from nothing? Interesting concept. I am wondering if the reality is somewhere more in the middle...that zero is the balance to infinity, without both reality could not functionally exist.

so hands off science it (infinity) belongs to us

No harm, no foul, so long as it is understood that questioning the nature of infinity is an exercise to stimulate the mind and explore the vastness of mystery. Some here call it the mind of the unknowing, the mind of the seeker. It is when we decide we have found the answer that we often get ourselves into deep doo-doo. There's always someone happy to come along later and show us where and how we are mistaken in our assumptions.

 

[seattlegal]

Something from nothing? Interesting concept. I am wondering if the reality is somewhere more in the middle...that zero is the balance to infinity, without both reality could not functionally exist.

Well if you add up all the values of all the numbers in an all-encompassing numerical infinity, the net amount would be zero, because for every positive value, there is also a corresponding negative value. {Interesting, when you use zero as a reference point, you get a sort of positive/negative duality within the infinite singularity.}

 

[17th Angel]

disproving infinity paradoxes; Hilbert’s Hotel?

I prefer the Hilton...

 

[juantoo3]

Kindest Regards, Seattlegal!

Well if you add up all the values of all the numbers in an all-encompassing numerical infinity, the net amount would be zero, because for every positive value, there is also a corresponding negative value. {Interesting, when you use zero as a reference point, you get a sort of positive/negative duality within the infinite singularity.}

Thank you for the clarification. I presume this is still within the realm of theorhetical mathematics. Are these negative values assigned to "anti-" and / or "dark" matter / energy?

What continues to mystify me concerning the expansion of the universe is that more and more astronomers are coming to the conclusion that galaxies are speeding up as they race away from each other... I am not versed well enough to explain, but it seems this creates complications regarding theorhetical calculations regarding mass / energy on an universal scale.

 

[flowperson]

I prefer the Hilton...

Ermmm...would that be the "paris" Hilton ? Sorry.

flow....

 

[juantoo3]

Ermmm...would that be the "paris" Hilton ? Sorry.

flow....

GROAN...

 

[cyberpi]

Math is a language and languages have flaws. A flaw in math is infinity. The only thing infinite is nothing. Nothing is infinite. The moment anything is something... it is not infinite. Don't believe me? Infinity is realized by dividing something by nothing. Take a finite pie in your hands and divide it into pieces of nothing (zero). What do you get? Infinite PIE? Infinite pieces of PIE? Or... infinite pieces of nothing. As I said truthfully, the only thing infinite is nothing.

Perhaps it looks good on paper or appears sensible in mind (Western education) to say that there are an infinite number of primes, or an infinite number of odds, or an infinite number of evens; however, the reality is that to positively check something (as opposed to nothing) for prime, or odd, or even, requires dividing it... and the whacked out mathmetician already maintains that you have to divide something into pieces of nothing to get infinity. For example to find out if a number is even or odd requires dividing it by two. What is infinity divided by two? Uh-huh. Ok, so a pick a very large number and divide it by two. The number picked is not infinite. Infinity is neither even, nor odd, nor a number. Sorry, there are NOT an infinite number of evens, or odds, or primes, or numbers. It is a LIE to say that there is. It is a real, tangible, finite FALSEHOOD to say that numbers are infinite. Numbers are NOT infinite.

I'm sorry to ruin the math, but there are a finite number of numbers. You think I am wrong? Try writing down digits for the rest of your life. The number that you will have written down is finite. The only thing infinite is nothing, so the moment the very first digit was written down it was all over. The moment that there is any definition whatsoever to anything wherein it becomes something in this world, then it is finite. Nothing is infinite... the only thing infinite is nothing. Under no mathematically, scientifically, or humanly known circumstance has there EVER been something infinite, except in the whacked out minds of the followers of mathematics... and maybe a few other religions. The overwhelming majority in schools who oppressively learn the language will surely disagree with me. Fine... so name one thing that is composed or even potentially composed of something... that is infinite. Sorry... wrong. Zilch... nada... nothing. The only thing infinite is nothing.

A lot of people tend to relate God and infinity. Infinite wisdom, power, sight, potential, etc... but I find that God is something, whereas nothing is not.

 

[cyberpi]

the infinity lamp
this puzzle is a lot simpler than the hotel one, and i think we can resolve a few issues with it.
quote:
Question. Consider a very durable ceiling lamp that has an on-off pull string. Say that the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed?

Days are not infinite in number.

 

[cyberpi]

disproving infinity paradoxes; Hilbert’s Hotel?

i thought i would have a crack at this ole chesnut, see what you think?
here’s the infinite-hotel puzzle (also known as "Hilbert’s Hotel"); In a hotel containing infinitely many rooms, all of which are full, how do you find room for infinitely many new guests?

There is no hotel that can contain an infinite number of rooms.