Vanquishing Infinity?

Well said, Vermin. They're sort of like the Decency League for Clothing Naked Singularities. But, infinity is absolutely needed in math.

Reminds me of a puzzle from an Issac Asimov magazine.I hope I get this right:

"Take a board, of some length, and cut it in half.The saw you use does not consume or waste any wood during the cut.It can also make an infinite number of cuts in an infinitely small interval of time.

Now, take one of the pieces, and cut it likewise in half, and put one half beside the first cut (uncut half) of the board.Take the remaining piece(1/4) and cut it in half.Repeat this process with all of the pieces until an infinite number of cuts are made. (in an infintely short interval of time).Now, add all of the pieces together:1/2+1/4=1/8, etc."

What is the result?

Nice alegory here. Except that, also for a question of definition and fundamentals of physics and engineering, there's no way an engineer or a physicist or even both together to have a beautiful secretary... a semi-slave stagiary working part time and dividing its time among the lab, the classes and pizza delivery at most...

eye ghyvve uhhp whutz uh "stagiary"?

A resident canon.

You hate a concept? I suppose if it's OK to have a "war on terror", it's OK to hate the concept of infinity.

But the way, Dirac's delta function shows that infinity * zero = 1. Which can be handy to know sometimes.

Perhaps I used the word"hate" too loosley for some readers.There are many interpretations, one of which is "dislike,".This is the context in which I meant it, not the gut churning,adrenaline pumping,red-lights flashing,tunnel-visioned psycopathic meaning. Sorry I did not mince my words more finely, to accomodate those that were reared in a different environment.I will try to be as unoffensive as possible, but I cannot allow for all contingencies due to my lack of worldliness.

I will also not take to bait to become political on an engineering subject, so give it a rest for the time being.

As far as my original statement, allow me to rephrase it.Replace the word "hate" with the word "distrust", in it's simplest form:Dubious ordoubtful.

Most of the replies have shed a little light onto the dark corners of my knowledge, and for them I am grateful, but still I need to dig furthur to appease my curiosity.

Any links to hasten my search will be appreciated.

Woof!!! Where to start... Try going to Wikipedia and searching on "Dirac's delta function." It's definition is there. I don't expect you to understand the math (by your admission), but just look at all the places that infinity is used within the equations. Integrals of functions can be taken from -∞ to +∞ and give real mathematical values, like 3.12 or 5,271 or something like that.

In math, infinity almost never leads to a dead-end. On the contrary, Using infinity is often the only way to a non-infinite answer. Again, the calculus make wonderful use of infinity to get real numerical answers to real-world problems.

Furthermore, the article you referenced was the converse issue. In this case the values don't give answers other than infinities - think of it as if you were trying to figure out the dimensions of something you were building and every time you added them up it came to zero. You'd be scratching your head over that - and that's sort of what they're doing.

Hi vermin,

I am not a Catholic..............but for some reason, I always remember this............evidently if a catholic is a sinner he could go to purgatory...........but, for how long.................the answer..........for infinity...............How long is infinity?.............the answer was........"If the earth was a ball of solid gold and an eagle was flying around our solar system and just touched his wing on the earth on every lap of the solar system he made........infinity is how long it would take to wear the golden ball away.

Even this example is not a real infinity (if we assume that just a few atoms of gold are removed from the golden earth in every touch of the eagle's wings). This is an extremely huge -but finite- number... but not infinity... Actually, infinity is a concept not easily comprehensible from the human perception, because humans -in their daily life- deal with measurable quantities and specific things of finite size. Infinity is sth far beyond the human perception and it is approached only by maths. And it's a big achievement for the human intelligence the capture of the idea of infinity.

It's really not easy to "define" infinity. One could say that it's a number bigger than any number you can imagine (no matter how big this number is). But this is sth somewhat misleading, as someone could imagine it as a huge number... One could say that an infinite quantity is sth that is not masurable, meaning that you should spend an eternity to measure a infinite quantity of things. But, again, what is "eternity"? It's an infinite large time duration (so the "infinity" issue comes, again, in the attempt of defining the "infinity"). So, the definition of infinity is sth difficult. We perceive the infinity issue -more or less- in a rather intuitive manner. However this intuitive manner is, also, misleading. As an example: we assume that two infinite quantities must be equal. This is not true though. There are infinities of the same "size" and infinities of different "sizes" (the so-called "Aleph"). I.e., in a way, there are infinities which are "bigger" than other infinities. This seems very "strange" in our intuitive way of thinking. That's why the infinity issue should be approached by maths.

I'm no Catholic, but as I understand it Purgatory was 'closed' during Vatican II... While it was 'open' my understanding is that purgatory was a place for those poor menial sinners who needed to finish 'scrubbing' their soul before they would be allowed into heaven, not a happy place but not an eternal destination, more of a lay-over at a podunk airport with no bar... all those mortal sinners on the other hand get to burn in hell for eternity, which is really not fair to the original sinners as they get to experience a longer infinity than the more recent crop of damned... tricky...

......tricky........

You can say that again..........but.........thinks????.........we had better not go there!

.....a lay-over at a podunk airport.......

or as we may say downunder:

.......somewhere out the back o' Bourke. (or similar, e.g......out bush somewhere)

.......some godforsaken hole .....or words to that effect with a few expletives.

.......somewhere out the back of beyond (out past Birdsville)

.......somwhere out in the mulga (covers approx 20% of semi-arid Australia where mulga trees (types of acacia) grow.

back of beyond......Simpson Desert........driest place on earth............freezing nights and temperatures can reach 60⁰C + in summer. If it does rain it becomes covered in wild flowers.

A typical mulga tree

Bourke 6 years without rain

Bourke after rain earlier this year.

Take a look at a discusion that took place in CR4 2 years ago...

The Mysteries Of The "Infinity" (Part 2)

The discusion is mainly between Tkot and me... And Tkot gives some very interesting points for the understanding of the difficult concept of "infinity"... I hope that you'll find it interesting and helpfull too...

My feeling on this article is that those guys don't get that the quantum world doesn't follow the same rules as the macro world... Quantum Mechanics and Relativity Theory are both studies of 'worlds' that don't obey Newtonian Physics... It's all the same world, so this poses some problems...

I am not a physicist or a mathematician so I will refrain from trying to give a clear explanation, though I will recommend some reading on the subject to help clarify the mess for other non-physicist types.

Driving Mr. Albert by Michael Paterniti: This book is a fantastic true story about returning Einstein's brain (in a tupperware container) to his family (granddaughter) by car from New Jersey to California, it also gives good basic explanations for Einstein's theories.

The Tao of Physics by Fritjof Capra: this book explains some of the more difficult concepts of the quantum world using concepts from eastern philosophy. It gave me a much clearer understanding of some of the seemingly conflicting concepts in quantum physics. It has been updated numerous times since its original publication in 1975 so make sure you look for the most recent edition you can find (I read the 25th anniversary edition which was published in 2000).

I also recommend checking your local library's video collection... I know Nova has done several good episodes on these subjects and they are geared toward the layman.

In my opinion the only concept more valuable to advanced mathematics than infinity would have to be zero... of course algebra left me feeling like I had mashed potatoes for brains so maybe I don't know what I'm talking about...

One more thing... I want to point out the ad next to this article 'Learn Telepathy. Gain Access To Hidden Knowledge Of The Universe. Learn Telepathy.'

I have to say that sort of thing encourages me to give a vote of no-confidence to the publication...

also don't forget to get your quantum pendant and learn more powerful hypnosis...

Infinity as a concept, I can accept;A mathematical symbol, A useful tool like imaginary numbers.Or Zero.It allows us to perform calculations that otherwise would be much more difficult or impossible.

Infinity as a reality is much more difficult to accept. Pi continues forever, but a bubble forms instantly.

Infinity is easy to see in everyday life. Take a drive on the Jersey Turnpike with my ex-wife reading the map....

saying that you accept infinity as a concept but not as a reality doesn't seem consistent.

numbers are a system, a language, a tool created to organize and process data concepts.... numbers are of man. an infinite, or a finiite amount is a concept of the system. either is a reality.

asking for examples of infinity outside the concept system is just ask difficult as asking for examples for a non infinite integer outside the system.... numbers infinite, or not, are concepts.

man is the measure of all things...

benbenben

Aside from the concept, which I can accept, are there any real life infinities?I suspect not.As I stated before, Pi continues for infinity, yet bubbles form fully anyway, instantly.We cannot absolutely define a circle, or sphere,yet they exist, so there must be a flaw in our logic or math somewhere.If Pi did not have an absolute value, circles, spheres, etc. would always be incomplete, always closing in on that final fraction of completness.This is they way it seems to me, intuitively, but as you say, sometimes intuition is wrong.

Anyway, good answer.You have come closer than anyone else to explaining infinity to me, a layman in the art of math.

The flaw is in us, not in infinity... it is our shortsightedness, shortlived'ness (I can make up words if I want to, you just shush) and general shortcomings that prevent us being able to conceive of a world outside our own limitations. The fact that we have a hard time comprehending infinity does not invalidate it, what is a more difficult concept for me is finity, the concept that something occupies such a small place (in time or space) that it cannot be measured is far more abhorent to me than something which is un-ending...

Our intuition is a product of our senses and our experiences, both of which are very limited. Remember once upon a time the concept of germs was inconceivable because we couldn't see them or feel them or taste them...

Nice thread by the way, this has been a very stimulating conversation...

Uh...bubbles don't form instantly. They have a time dependence.

Cheers.

Does infinity have a time dependence?

The point is:They do Totally and Completely form; they are not eternally trying to close the circle or sphere.Sorry you missed it in the context I tried to parlay.

a bubble isn't a number.

a bubble may be represented in nearly infinite ways using the language of numbers, but it is not an example of a number outside of the concept of a number, finite or otherwise.

benbenben

You're talking apples and oranges... Infinity arises in the calculation because there is no rational (math for ratio) correspondence between a circle's diameter and its circumference. Plain and simple. However, we find using Π a convenience because we can calculate with it to any limit of the precision we want.

Nice explanation... You've helped me to understand that pesky little greek letter a bit better.

I'm puzzled. What's up with the bubbles? They don't form instantly. You can find high speed video showing bubble formation.

Of course we can exactly define a circle. Pi has a definite value; it's just that we can't calculate it.

Perhaps we are trying to calculate pi in the wrong system... does pi work better in base 8 than in base 10? or maybe in base 6 or 13 or 3 or...? Has anyone ever tried to calculate pi in anything but base 10? I mean I'm sure someone has at somepoint even if only for a lark, but... can one of you more mathmatically inclined people comment on this thought for me?

pi in... base pi.....

Ok."Instantly" was a bad choice of words.What I was trying to get across was the fact that they do totally and completely form.They are not forever in search of the final value.Unless they are one heck of a powerful computer.Imagine all of the bubbles just on Earth.That's a lot of computing.Our most powerful computers are even now crunching away towards that final digit, which has to exist for bubbles to form.

Perhaps our linear measurement system is off a little bit.Maybe we cannot measure curved lines as accurately as straight ones, or visa versa.A straight line can be described as a segment of a circle with an infinite radius.Therefor every straight line has a certain amount of curvature to it.Has this been considered in calculating Pi?

And until we know the absolute final value of Pi, we cannot absolutely define a circle, nor can we square the circle.

I don't want to mess up your theory, but the circle has been squared for some time.

I suspect, however, that at some level, bubbles are forever changing.

Reference Please?

Here's the original translation. Gray did an update on this about 4 or 5 years ago.

Actually, the circle can be squared only to a specified accuracy.It cannot be exactly squared because Pi is a trancendental number.We cannot even define a circle except within the same restricitons,imposed by the nature of Pi.

A bubble, placed in free spacetime,with no interference from gravity or accelleration, or any other outside forces will totally and completely form.Keywords here are totally and completely.

If we cannot define a circle, the basic shape of everythng in our universe,(strings aside; although I suspect strings will someday be found to be composed of tiny spheres linked together, with strings composed of even smaller spheres), then how then can we describe reality?

Reality itself is very elusive, and appears to be a very good illusion.

Did you not see my post? The circle has been squared...exactly...these past 180 years. You cannot draw any deep philosophical significance from not squaring a circle when it has been squared. The method is perhaps not very practical, but that doesn't matter here.

Give me the EXACT area of a circle with a diameter of 4 inches.EXACTLY.No tolerance.Zero.None.

Cannot be done, because one of the factors, Pi, is transendental.It can only be calculated to a given tolerance.Therefor all calculations involving Pi can only have a certain specified tolerance.Admitedly, the tolerance is small after a couple of billion decimal points, but it is not EXACT.

Sorry. It has been done exactly. Try signing in and I'll gladly give you book and verse.

What is the absolute value of Pi? To the last digit.

I didn't say crap about pi. I said the circle had been squared. If you want pi, figger it out yourself. And, I don't give two hoots about the last digit. I don't even care about the 8th digit. What's your point, other than to be belligerent?

Here is my point,and I am not trying to be beligerent or combative:

How can you construct a square with the same area as a circle if you cannot define a circle?There are limits on the resolution of the definition of a circle, and by default, a square constructed to equal it's area has the same limits.

Those limits are defined by how far you carry Pi to obtain the circular area.

I obviously did a poor job of explaining myself, and simply wanted an explanation, not an argument or to offend anyone.

There are differences between construction and mathematical ideal. I can construct a straight line only to some tolerance, never perfectly. But, I can write an equation, and think of, a perfectly straight line.

I can define a circle. x² + y² = r² does the job nicely if the origin is 0,0.

Pi is a definite number. We simply cannot compute it, nor even express it except as π.

The circle has been squared, not by construction, but by fundamental principle. The principle is probably not useful at all, but it exists and invalidates any metaphysical conclusions to the contrary.

Sounds to me like the fundamental principle is metaphysical.We live in a physical universe.We cannot build all that we imagine, we are stuck with reality.It is not metaphysical to state that Pi is transcendental.It is a reality.To ignore this reality is to embrace fantasy, or the metaphysical.To take on faith that which cannot be proven in reality is unscientific.There is some aspect of Pi that we do not yet understand.I do not know what it is, but we are somehow off a little bit.Perhaps there are no absolutely straight lines in nature.Even a straight line has some curvature.A plane flying in a straight line from point A to point B actually flies in a curved path in one dimension.Imagine a longitude line on a globe.Compare this to a straight line thru the Earth from point to point.Perhaps it is this other dimension of Pi that we are not accounting for.I wll not argue that it is mathematically possible to do as you say,but it does not fit reality.Perhaps I am just too pragmatic or simply to dense to get it.

You're arguing that we live in a physical universe where we have to accept reality. Yet, you don't accept pi as good enough even though it is known to around 2 million digits? A little consistency, please.

Do you think that the last digit of Pi will ever be found?

I am not saying that Pi as a mathematical tool is not a reality,I am saying that the tool is imperfect when compared to reality

To create a square with area equal to the area of a circle is simple:Take the square root of the area of the circle..But first, we have to know the area of the circle.This involves Pi.So we can only get close to, but not exactly, the true area.

The circle has a true area, but we cannot calculate it exactly.

On the other hand, bubbles do form .Totally and completely form.Exactly.

If you do not understand this, I will chalk it up to my poor ability to expain the concept, not a lack of enlightenment on your part, or inconsistency of my ideas.

Not only do I not understand you, I don't believe your statements. I can square a circle. Exactly and perfectly. I don't know of anything useful to do with that, but I certainly can do it.

Pi is not a tool. It is a number. A defined number. It is not computable.

I am not enlightened. I wouldn't know enlightenment if I tripped over it. What is that anyway?

"To create a square with area equal to the area of a circle is simple:Take the square root of the area of the circle..But first, we have to know the area of the circle.This involves Pi.So we can only get close to, but not exactly, the true area."

The reason you keep having to deal with pi and reality is because you insist on believing that there is a rational relationship between the diameter and the circumference of a circle. THERE IS NOT RATIONAL RELATIONSHIP!!! Even though the circumference and the diameter are two parts of the same thing, they have no real relationship - It's like saying that there is a rational relationship between the size of an apple and the length of it's stem. Yes, they're both part of the same thing (the apple) but one is not related to the other.

Furthermore, how much do you want??? You can calculate pi to so many decimal places that the size of the delta is smaller than the smallest subatomic particle that exists - You can reduce the delta even further to a size that is impossible to exist according to quantum physics! At that point I think even you would be satisfied with the accuracy.

I get the feeling you really have a messed up conception between mathematics, time, space, geometry, and the real world - Pi is infinite because there is NO real relationship between the diameter and the circumference of a circle.

I really think you need to go back to square-one and separate your parameters into the correct piles... IMHO.

I still don't like Pi and you can't make me.Blaaah! So there!!

(I prefer cornbread, which by the way, is SQUARE)

this whole thing is getting way too serious for me.