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The Infinity Problem - by John Prytz

“There is a fifth dimension beyond that which is known toman. It is a dimension as vast as space and timeless as infinity. It is themiddle ground between light and shadow, between science and superstition, andit lies between the pit of man's fears and the summit of his knowledge. This isthe dimension of imagination. It is an area which we call the Twilight Zone.”

―Rod Serling


There are numerous nearly incomprehensible scientificconcepts we have lots and lots of trouble wrapping our heads around. There arephysics concepts like quantum mechanics; extra / hidden dimensions andrelativity theories; biological concepts like the mind / brain duality, freewill, self-identity, and the nature of consciousness; there's the mathematicalconcept of the square roots of negative numbers; and metaphysical /philosophical issues like why is there something rather than nothing or whatexactly is the nature of reality? 


But one of the most mathematical / physics / theological/ philosophical conundrums is the concept of the infinite, or infinity. That'sup for discussion this round.


All infinities are equal, but some are more equal thanothers.


Basic Definitions


*Nothing: Nothing is defined here as the total absence ofall mass and force particles (i.e. - electrons, photons, etc.). That's nothing.


*Infinity: Infinity means that no matter how far you go(in time or in space), you can always go farther. That's infinity.


Basic Premises


*No thing can create itself.


*From nothing, nothing comes.


*Only from something, some things comes.


*Something can't be created out of nothing.


*There are no spatial / temporal boundaries or walls.


*If N, then N+1.


Infinity and Mathematics


“... for one of the nicest things about mathematics, oranything else you might care to learn, is that many of the things which cannever be, often are. You see it's very much like your trying to reach Infinity.You know that it's there, but you just don't know where-but just because youcan never reach it doesn't mean that it's not worth looking for.”

―Norton Juster


“A googolplex is precisely as far from infinity as is thenumber 1... no matter what number you have in mind, infinity is larger still.”

―Carl Sagan


“There was a young fellow from Trinity,

Who took the square root of infinity.

But the number of digits, Gave him the fidgets;

He dropped Math and took up Divinity.”

―George Gamow


“Unity joined to infinity adds nothing to it, no morethan one foot to an infinite measure. The finite is annihilated in the presenceof the infinite, and becomes a pure nothing. So our spirit before God, so ourjustice before divine justice.”

―Blaise Pascal


“It is known that there is an infinite number of worlds,but that not every one is inhabited. Therefore, there must be a finite numberof inhabited worlds. Any finite number divided by infinity is as near tonothing as makes no odds, so if every planet in the Universe has a populationof zero then the entire population of the Universe must also be zero, and anypeople you may actually meet from time to time are merely the products of aderanged imagination.”

―Douglas Adams


When it comes to pure mathematics, we know that there arean infinite number of negative numbers; an infinite number of positive numbers;an infinite number of even numbers; an infinite number of odd numbers; aninfinite number of values between any two consecutive whole numbers (likebetween 10 and 11).  We know aboutinfinity in mathematics, that, for example, Pi has an infinite number of placesafter the decimal point. We know that there's an infinite number of lines thatcan be drawn between any two places.


But all of that is just pure abstraction with little ifany connection to real existence and practical matters and associatedoperations.


Infinity and Physics


“The finite is annihilated in the presence of infinity,and becomes a simple nothing.”

―Blaise Pascal


“Infinity is a floorless room without walls or ceiling.”



*Time and Space: The basic premise here is that no matterhow far you go, temporally or spatially, you can go even farther. In otherwords, if N, then N + 1.


*Matter and Energy: The basic rule here is the First Lawof Thermodynamics. Matter / energy can neither be created nor destroyed. Theobvious implication is that therefore matter / energy has infinitely existed.


*Infinity can be either unbounded or bounded. Infinity isunbounded like in the case where two parallel lines that just extendindefinitely without ever meeting. Infinity can be bounded. For example theEarth is bounded in that it is finite, yet you can travel around it in time andin space an infinite number of times. 


*And even some scientists who should know better looselythrow around the term "infinity" or "infinite" with ratherreckless abandon as in stating or referencing "infinite density" or"infinite temperature." That's just nonsense.


Infinity and Theology


“I am incapable of conceiving infinity, and yet I do notaccept finity. I want this adventure that is the context of my life to go onwithout end.”

―Simone de Beauvoir


“By confronting us with irreducible mysteries thatstretch our daily vision to include infinity, nature opens an inviting andguiding path toward a spiritual life.”

―Thomas More


“The poetic notion of infinity is far greater than thatwhich is sponsored by any creed.”

―Joseph Brodsky


*Either a deity or deities exist or they do not exist.


*If a deity or deities do indeed exist, then they areeither eternal or created by a previous deity or deities.


*If a deity or deities are eternal, everlasting, foreverexisting - that's equivalent to infinity.


*If a deity or deities are created, that of necessityleads to an infinite regress.


*Therefore, no matter how you slice and dice, there's atheological infinity to be dealt with, all the more so when many theologiespromise an eternal afterlife existence.    


*However an eternal afterlife existence would be aneternal boring hell. Unlike the Vulcan philosophy of events having an InfiniteDiversity in Infinite Combinations (IDIC), there's actually only possible afinite diversity in finite combinations. Thus, in an infinite / eternalafterlife, you're going to eventually endless repeat what you have alreadyendlessly and repeatedly done before. Boring.


Infinity and Philosophy


“The fear of infinity is a form of myopia that destroysthe possibility of seeing the actual infinite, even though it in its highestform has created and sustains us, and in its secondary transfinite forms occursall around us and even inhabits our minds.”

―Georg Cantor


“I cannot help it - in spite of myself, infinity tormentsme.”

―Alfred de Musset


“Man is equally incapable of seeing the nothingness fromwhich he emerges and the infinity in which he is engulfed.”

―Blaise Pascal


“The last function of reason is to recognize that thereare an infinity of things which surpass it.”

―Blaise Pascal


“It is good a philosopher should remind himself, now andthen, that he is a particle pontificating on infinity.”

―Ariel Durant


“If any philosopher had been asked for a definition ofinfinity, he might have produced some unintelligible rigmarole, but he wouldcertainly not have been able to give a definition that had any meaning at all.”

―Bertrand Russell


“Here is this mass of jelly - three pound mass of jelly -that you can hold in the palm of your hand, and it can contemplate the vastnessof interstellar space, it can contemplate the meaning of infinity, and it cancontemplate itself contemplating the meaning of infinity.”

―Vilayanur S. Ramachandran


*It is even claimed that God (as a representation of somedeity and the supernatural) couldn't from His infinite past arrive at"now" to do whatever God wanted to do "now". Hogwash!


*So, the philosophical / meta-philosophical question is,if there is an infinite past, can you ever arrive at now? It's all too easy.


*The Timeline: In an infinite timeline there are aninfinite number of events, each of which is finite (i.e. - like the event thatis you). Here's a useful analogy. Let's assign each unique and finite event aunique number. How many unique numbers are available to be assigned? Well weknow from the above that there are an infinite number of unique numbersavailable which would take an infinite amount of time (an infinite timeline) tocount off those infinite number of unique numbers.


*No matter where you are on an infinite number-line, youcan make progress, say by counting forward from say 100 (where you are) to 150(where you want to be "now"), or backward for that matter from 150 to100.


*You can arrive at any specific event on an infinitetimeline just as you can arrive at any specific unique number in the infinitenumber-line. No matter where you are on an infinite timeline, you can makeprogress towards "now" by going say from Saturday to Sunday; Januaryto February; 2001 to 2002, etc.


*One additional aside, you don't actually have to make progressto arrive at "now", whenever you are you are at the present or the"now".

Science librarian; retired.

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