Important Math Question
 

What comes after:

Million
Billion
Trillion
?

And after that and after that and after that.

I have always wondered how the progression of numbers goes. I can remember a time when a million was a super big number, but now even a trillion is small.

Re: Important Math Question
 

It's based primarily on latin prefixes - see Numerical Adjectives site

Re: Important Math Question
 

http://www.unc.edu/~rowlett/units/large.html
http://www.uni-bonn.de/~manfear/large.php

Centillion is fricking huge. 10 to the 600th power. OMG people actually have thought these names up for numbers.


Million
Billion
Trillion
Quadrillion
Quintrillion
Sextillion
Septillion
Octillion
Nonillion
Decillion
Undecillion
Duodecillion
Tredecillion
Quattuordecillion
Quindecillion
Sexdecillion
Septendecillion
Octodecillion
Novemdecillion
Vigintillion
Unvigintillion
Duovigintillion
Quattuorvigintillion
Sexvigintillion
Septenvigintillion
Octovigintillion
Novemvigintillion
Trigintillion
Untrigintillion
Duotrigintillion = 10 to the 99th power

[ November 01, 2003, 03:38: Message edited by: Atrocities ]

Re: Important Math Question
 

Now I'm extremely curious. Why was it so important to find this information as the thread subject mentions? If you have just come across some money in excess of 1 trillion, please don't forget us little people.

Slick.

Re: Important Math Question
 

Atrocities! Spam! i'm shocked!

Re: Important Math Question
 

I have an excellent link on this topic that I have been looking for an excuse to post:

The Biggest Numbers in the Universe

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">It is really not spam though. It is an important question because growth. Currently there are about six billion poeple on our planet. In SEIV say you have a 100 planets roughly the same size, yet you only have 51 billion in population. Over time growth will inflate that number tremendously and say by the end of a good game, 200 systems with an average of 10 planets per system, and 5 billion on each planet, that number could top a trillion easy.

So that made me wonder how high a number could go. How many earth like planets, how many galaxies would it take to reach the hights of these numbers.

What was here before the universe? Nothingness, and if so, what caused the universe, and don't relay on the big bang either. Say that never happened. What else could create a universe with centillion stars or more?

Re: Important Math Question
 

can't create something out of nothing. logical impossibility.

that's the thing about nothing - by definition, you can't do anything with it - because there's nothing there to do anything with.

I sounded like Fyron! AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHHHHHHHHHHHHHHHHHHHH H!!!!!!!!!!!!!!

[ November 01, 2003, 06:36: Message edited by: narf poit chez BOOM ]

Re: Important Math Question
 

I thought you were Fyron, or at least a clone of him.

Ok imagine that the universe is without end. Can you conceive of this? Actually put your mind around the concept that the universe is endless. There are those who say that the universe is not endless but I say to them, if you can keep counting on and on until infinity, then so must be the size and scale of the universe.

If I had but one single wish that I could ask of God or whomever, and know that it would be granted, it would be to have the power of Q. To be able to roam the universe from beginning to end, from day one to the Last second. To create at will any object, place, thing, etc. To be GOD.

I for one feel that time and space are linked and that Time, all time, exsists in the same instant as our universe and that even though we preceive the passage of time, it is actually us who are moving through time and not time moving around us. Each nano second of time is a new reality, and each reality has a billion or more branches that it can follow. Quantum theory I believe it is called, a concept that I first though of when I was six. Long before I saw it on tv and on Star Trek NG.

I was shocked to find that others held the same concepts and had though of the same things that I had. This revolation so to speak also enlightened me to the fact that if I can imagine it, think it up, or create it then there are 100's of other people who have also done the very same thing.

Now put that into practical thought and apply it to the make up of the known universe. If there is one hundred people out of six billion that come up with the same idea, then the possiblity does exsist that out of a billion stars, there is one or two planets like earth.

I do not believe in UFO's, the alien kind, but doe hold out hope that there is life out their, but where and how far it is we will never know because of the shier vastness of space itself.

I never put much thought into numbers until I started to learn statistical process control (SPC) and then things started to make sense to me on a level that they had not before. Sure I can not spell worth a damn, but I can figure out complex things rather simply. Jig Saw Puzzles are easy for me. I was doing 1500 size puzzles in the first grade by my self. I can see thing in great detail as if looking at them in scematic form. I love blue prints and deck lay outs of ships and such.

And over the years I have grown fond of noting the reoccuring numbers in my life. Numbers that keep presenting themselves over and over and over again, but never for the lottery. http://forum.shrapnelgames.com/images/icons/icon10.gif

When you boil everything down to its core, mind over matter, its all about the numbers. Numbers are endless, and the fact that we know they exsist shows that we are atuned to something greater than ourselves. We have one of the keys to open the door to the universe and we have had it since our inspection as a race.

[ November 01, 2003, 06:59: Message edited by: Atrocities ]

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">I think it was Einstein who came up with the theory that space and time are linked. The closer you come to light speed, the slower time passed for you. However, time will still be passing at the same rate for all other people. So you could be travelling at near-light speed and experience a few seconds, while someone who wasn't moving at light speed would experience a year, or two years.

Therefore, if you are sitting still, you are moving faster through time than if you are moving. Barely, but a little bit.

The theory of space/time says that a photon of light at the instant it is released from say, a flashlight, would instantaneously also be at the farthest corner of the universe. Weird huh? But where is it if there is no end to the universe?

Re: Important Math Question
 

If the universe is infinite, then there are an infinite number of earth-like worlds, and infinite number of alien civilizations, and the sky would be not be blue but the color, brightness and intensity of your average sun 24/7. Half of infinity is still infinity!

Frankly, we could not survive an infinite universe. Of necessity the temperature would be far beyond what our bodies could stand. I mean, we are talking thermonuclear temperatures.

Since this is not true, the universe is not infinite.

Yep, centillion is huge, but it's pretty miniscule next to infinity.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Not true at all. Look at Hubble's Deep Field photographs sometime- you see entire galaxies that aren't even visible to the naked eye. Infititely sized means infinitely far away, as well. And heat? Do you feel any heat from the stars at night? Didn't think so, and those are the closest ones. Heat does trail off the further you get from an object.

Re: Important Math Question
 

Can't agree with you Phoenix-D. You are still underestimating infinity. In an infinite universe, there will be a star in every direction you care to point, in fact, an infinite number of them. Therefore, you are being bombarded by an infinite number of photons. True, each photon puts out an immeasurable amount of heat but that tiny amount is still there.

Do the math:

Infinity x immeasurable = ?

Re: Important Math Question
 

Ah, but most of the stars will also be at an infinite distance. If a galaxy can be receeded to an invisible pinpoint, smaller than stars even in Hubble's view, then I don't doubt a group of galaxies could do the same.

EDIT: in other words, most of the photons don't even reach any point you'd care to name. Or just haven't yet; light, whatever else it may do, does have a finite speed.

Infinite stars, true. But also infite space..

[ November 01, 2003, 17:18: Message edited by: Phoenix-D ]

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">And infinite time. http://forum.shrapnelgames.com/images/icons/icon12.gif

No limits to infinity, please.

Re: Important Math Question
 

Not to mention, infinite amount of stuff in the way! Anything from dust particles to Huge planets.

Since we're on the subject of math, does anyone know the formula for finding the area of a 4-dimensional sphere? Assuming an equal radius for all 4 axes...

(spelling)

[ November 01, 2003, 17:29: Message edited by: atari_eric ]

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">... which is also being bombarded by an infinite number of photons and has thus been heated up to stellar temperatures and is now emitting photons itself.

LOL... Just think, there are an infinite number of Shrapnel Forums discussing this very same subject. An infinite number of Grandpa Kims, an infinite number of Phoenix-Ds, an infinite number of Atari_Erics... and an infinite number of advanced aliens laughing their asses off at our silly antics.

I'm beginning to think that infinity is a total fiction invented by the human mind. The inherent contradictions won't allow its existence. It doesn't exist and cannot exist.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Sorry can't help you there but how about an additional question:

the formula for the 3D volume of a 4 dimensional sphere? This would be analogous to the area of a 3D sphere.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">And infinite time. http://forum.shrapnelgames.com/images/icons/icon12.gif

No limits to infinity, please. </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Actually even an infinite universe could have a finite start. And you are still leaving infite space out of the equation. If space is infinite, all the stars that would cause that problem could be on the "other side" of infinity. Photons aren't infinite, and with every step you loose energy.

Put it this way: it is entirely possible to have an infinite number of stars in an infinite volume- and still have each star so far apart that none of the others would be visible to the naked eye. Or to have each star several trillion light -millenia- away from each other.

Re: Important Math Question
 

if the universe is infinite in size, the distance between us and any galaxy will still not be infinite.

what if, at extreme distances, photon's degraded and were absorbed into the general background? infinite energy/infinite space = finite amount of energy/finite amount of space.

then you could have an infinite universe without being baked.

Re: Important Math Question
 

Okay, I give up. If you insist on putting limits to infinity I am unable to present a coherent argument. All I will say is you haven't thought it through.

ie: Where does that degraded photon energy go?
How do you know infinite space is possible without infinite time?

This is a great thought exercise for expanding your personal universe. Think about the ramifications of infinity long enough and it begins to collapse like a house of cards. Anything and everything is possible-- no, not possible but has occurred an infinite number of times.
So maybe the universe is infinite.

But I don't believe it. The universe is finite.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">As it happens, I'm not putting limits on. You're just disregarding the space argument..

Quote:

ie: Where does that degraded photon energy go? How do you know infinite space is possible without infinite time?

<font size="2" face="sans-serif, arial, verdana">The photon energy is lost, or absorbed. Some fraction is sent on, which then hits something else and repeats the process. Infinite number of photons..infinite number of barriers. And at any given time, only a finite number of those photons are actually arriving at any given point.

Quote:

This is a great thought exercise for expanding your personal universe. Think about the ramifications of infinity long enough and it begins to collapse like a house of cards. Anything and everything is possible-- no, not possible but has occurred an infinite number of times. So maybe the universe is infinite. But I don't believe it. The universe is finite.

<font size="2" face="sans-serif, arial, verdana">Try this thought exericise then. If the universe is finite- what happens when you reach the edge? I'd have an easier time beliving that -space- is infinite, even if matter isn't.

EDIT: word-level typos.

[ November 01, 2003, 23:07: Message edited by: Phoenix-D ]

Re: Important Math Question
 

i didn't say anything about infinite time, however, i do beleive time is infinite to. and i fail to see any ramifications of infinite time on my statement, nor do i see how my statement limits infinity.

Phoenix-D, would enough photons bump into each other for that to be how photons might degrade?

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">The same way that the Earth is finite in size, but there is no edge to fall off of.

Re: Important Math Question
 

yes, but there's an edge to launch a rocket off of.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Actually, energy never really goes away - it changes form (occasionally to matter), it goes to a different density over a different volume, but so far, every time someone somewhere has found a contradiction to that, it is later found that what was happening was a conVersion to a previously unrecognized form of energy.

Re: Important Math Question
 

This sounds like a good time to bring up the:

Cosmology FAQ

One argument against an infinite universe is that the universe seems to be cooling, i.e. the cosmic background radiation is growing weaker over time. If the universe is truly infinite, with an infinite number of stars, it seems that the universe will only get hotter over time.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">As Jack pointed out, the energy cannot be destroyed. Given enough time, anything that blocks and absorbs those photons will eventually re-radiate it out again.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">If the distance between us and any galaxy is not infinite then clearly the universe is not infinite in size.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">If the distance between us and any galaxy is not infinite then clearly the universe is not infinite in size. </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Err, not exactly. A universe being infinite in size doesn't preclude two things from being next to each other. http://forum.shrapnelgames.com/images/icons/icon7.gif

re: photon energy: true. The background actualy -cooling- probably precludes an infinite universe; it'd have to be either constant or increasing (unless all the non-visible stars are pulsing at the same time, but that is er, not likely).

Re: Important Math Question
 

I think he meant "if the distance between us and any one other galaxy is not infinite", meaning unless there is at least one galaxy that is an infinite distance away.

Re: Important Math Question
 

Once again I am going to step in and say that we are making very big statements about EVERYTHING THAT EXISTS when we personally have observed about... less than .00001% of .000001% of .000001% (I am being generous tonight!(also assuming that it is finite and can have a percent value for it)) of everything in the Universe and then stating that we know that ALL OF THE UNIVERSE is cooling so it can't be infinite.

Let's say the Universe is infinite. Then couldn't it quite possible have very small sections of it, oh say 10^999 square light year sections, that are in fact cooling due to their rapid expansion while others are absorbing tons of this radiation and heating up until *BOOM* they make their own big bang in a far far far distant not corner (infinite doesn't have corners) of the universe.

If you can neither create nor destroy matter and energy (and I'm not saying that is correct either but you have to have something to base stuff on) then in an infinite universe you have an infinite amount of energy and matter spread out over an infinite amount of space. But nothing says it has to be evenly spread. Some parts can be heating absorbing the energy until they reach a critical point then they release it while others are cooling off, then they switch off.

Infinity is not inherently linear it isn't nice and orderly. There is an infinity of numbers between any two numbers that can be named.

Quite simply the possibilities stagger the mind and we have no way and probably never will of knowing. So it makes for great arguments in forums all across the infinte space.

Oh... and just because something is infinite doesn't mean it has to include all sets and possibilites. The set of all real rational whole numbers is infinite but excludes things such as Pi, or fractions, etc. Yet it is still an infinite set. You can even make an infinite set with a beginning but no end.

Just because the universe is infinite does not mean that all possibilites are inherently capable of existing within it.

[ November 02, 2003, 04:00: Message edited by: Cyrien ]

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">You need to seriously rethink your entire argument. Even if there is an infinite amount of energy in the universe, it still propagates at a finite speed. It will take an infinitely long time to travel from a source that is an infinite distance away, so we will never see that energy.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">If the distance between us and any galaxy is not infinite then clearly the universe is not infinite in size. </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Err, not exactly. A universe being infinite in size doesn't preclude two things from being next to each other. http://forum.shrapnelgames.com/images/icons/icon7.gif
</font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Yea like IF said. If the distance between us and every other galaxy is a finite measurable distance like the original quote said then the universe is not infinite.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">I don't disagree with logic of your statement, but I do disagree with the sentiment behind your statement. Certainly, all of our theories on the subject of cosmology (and much else besides) should always come attached with the caveat "so far as we can tell". But just because we cannot know for certain is no excuse for saying that we can never know and that we shouldn't speculate, build theories and try our best to extend our knowledge, imperfect as our methods are.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Space is also expanding due to the mysterious force astronomers call "dark energy". It's an anti-gravitational form of energy that is accelerating the expansion of the universe. According to what I know of the theory, within several billion years, we will only be able to see stellar objects that are located in the Local Group, whose gravitational effects would overcome the anti-gravitational effects of dark energy.

This dark energy is believed to make up approximately 66% of the entire universe. Yet we know almost nothing about it. To say either that the universe is finite or infinite is pure guesswork. We know so little about the universe as a whole. For instance, only about 1% of the universe is made up of "normal" baryonic matter. The rest is dark matter and dark energy, which we know virtually nothing about. We need to find out more about these things before we can start formulating some hard theories about whether the universe is finite or not.

Don't get me wrong, I'm not discouraging debate and stuff like that. I'm just saying that even educated guesses are just that; guesses.

Renegade 13

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">I don't disagree with logic of your statement, but I do disagree with the sentiment behind your statement. Certainly, all of our theories on the subject of cosmology (and much else besides) should always come attached with the caveat "so far as we can tell". But just because we cannot know for certain is no excuse for saying that we can never know and that we shouldn't speculate, build theories and try our best to extend our knowledge, imperfect as our methods are. </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">I never said we shouldn't speculate. I enjoy the speculation. The problem comes when, as I have often seen happen in other forums discussing this and other topics, people start pressing things across as facts to prove themselves when it is all just theory and speculation. IE: the number of atoms in the Universe, how old the universe is, background microwave radiation proves this or that... quite simply we don't know enough to be making any statements on these things based on what we can and can't know. All of this needs to be taken with a grain of salt when you start talking about infinite v finite universe.

Sorry if you took what I was saying the wrong way but I was simply trying to nip that in the bud, since normally as soon as people start posting cosmological data it rapidly approaches that path.

The basic problem is one you can see in every field of science. Older theories have prominence because they are the ones the scientists grew up with and their body of work is based on. If you say it might be wrong then you say that your whole body of work that you have worked on your whole life might be wrong. Most people just won't do this. You can see it historically with great resistance to new ideas and ways until overwhelming proof shows it to be truer and the old false and it can't be ignored anymore.

I wonder how much further along we could be if we as a species could simply admit to ourselves and others when something that we have worked on our whole lives might be wrong. Add up the decades of resistance you get to each new idea before it is accepted and I bet it is quite a alot.

Re: Important Math Question
 

And Dark Matter theory is the perfect example of theories growing larger than maybe they should. It is the most largely accepted theory currently. But there are several other theories just as valid and accurate in the predictions for the actions of the universe that we can observe. They differ in what causes that and in their predictions for what we can't observe.

Yet Dark matter and energy is almost always what gets brought up. I know that we normally preface it as "this is just a theory" and quite correctly but the fact that we don't even bring up the others is itself a disturbing trend. If we don't even look at the alternatives will we notice when it starts being more accurate than the mainstream?

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Of course, the flip side of that would be like societal ADD.
Everything in moderation...

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Good points, and certainly true for a universe which is expanding at an accelerating rate, as our universe currently seems to be. Of course, in such a universe, the volume that we can interact with in any way is certainly very finite, so you throw away much of the appeal of having an infinite universe.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Sorry can't help you there but how about an additional question:

the formula for the 3D volume of a 4 dimensional sphere? This would be analogous to the area of a 3D sphere. </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Well in anwser to these little questions:
wwwDOTbright.net/~mrf/hierarchy(1).html
(Yikes can't use links with brackets!!!! DOT is a ".")

1. A hypersphere (4D sphere) has a 4D "Area" of
V⁴</font> = π²r⁴/2

2. A hypersphere (4D sphere) has a 3D "Surface" of
S³</font> = 2π²r³

Re: Important Math Question
 

O.K. now onto the subject of infinite energy in an infinite universe.

Well Space is expanding due to the cosmological constant (vacuum energy, quintessance, so on whatever you call it or think it is, it all makes up the value of Lambda. If you followed that tell me how! http://forum.shrapnelgames.com/images/icons/icon12.gif ). This means that there is an edge to even an infinite universe, at least from our viewpoint, it is where the 'speed' of the expansion between the viewer and another point in space (whatever it happens to be) exceeds the speed of light.

This means that even though the both viewer and the other point are 'stationary' light cannot travel from one to the other (even over infinite time). The fact that nothing can travel faster than the speed of light (don't even say Tachyons http://forum.shrapnelgames.com/images/icons/tongue.gif )is not a problem since nothing is, only the distance between the two points itself is changing.

Therefore even in an infinite universe you only get to see a finite volume of space. So only the Photons from objects in this volume can reach you, so no superheating problem! This also means that the cooling of space does not mean energy is being 'lost' only that the density of the energy is decreasing, same amount of energy larger volume.

Now i'm sure you are all wondering why I wrote all this, I don't know, no idea whatsoever.
Good Luck I hope you can follow this guys I'm not sure I can http://forum.shrapnelgames.com/images/icons/icon10.gif

[Edited for some clarity http://forum.shrapnelgames.com/images/icons/icon7.gif ]

[ November 02, 2003, 12:48: Message edited by: XenoTheMorph ]

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Not true at all. Look at Hubble's Deep Field photographs sometime- you see entire galaxies that aren't even visible to the naked eye. Infititely sized means infinitely far away, as well. And heat? Do you feel any heat from the stars at night? Didn't think so, and those are the closest ones. Heat does trail off the further you get from an object. </font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Plus an infinitely large universe does not mean infinite numbers of everything in it. You could have an infinite amount of space, with a finite amount of planets and suns, for example.

[edit] Oops - I responded to something on the first page thinking it was the whole conversation. Now I see the converstion has covered this ground. Ignore me.

[ November 04, 2003, 10:31: Message edited by: Ran-Taro ]

Re: Important Math Question
 

Let me preface this by saying I don't believe the universe is infinite. But the arguments given here against an infinite universe don't hold up. This is somewhat restating what others have already said, but maybe it will help to think of it this way.

If the universe is infinite, there are an infinite number of photons, but each photon is still a finite particle. It can only be in one point in the universe at any particular time. And you are finite as well. You only exsist in one point in space. Being hit with an infinite number of photons all at once would be bad. But for that to be possible one of these has to be true:

1. The infinite number of photons in the universe have to all be in the same place; just where you happen to be standing. Besides being an incredible piece of bad luck, this would be quite difficult to time. And if you managed it somehow, you'd be left with an infinite sized universe empty of photons, except where you are.

2. Every one of the infinite number of photons would have to exsist in every point in space simultaneously. Impossible since they are finite particles.

3. You would have to exsist in every point in space simultaneously.

The point is that over time, an infinite amount of time actually, you would be hit by an infinite number of photons. But at any particular point in time you are being hit by a very small, and very finite fraction of the total number of photons. Your perceived temperature is not dependant on the total number of photons to ever hit you, but on the total number of Photons hitting you at any particular point in time.

Geoschmo

[ November 04, 2003, 13:22: Message edited by: geoschmo ]

Re: Important Math Question
 

Hmmmm, I seem to have hit a problem here. My previous post started out as a statement showing why Phoenix-D was right, that an infinite universe would not be infinitly hot.

However, in my post I stated that any particular point in in infinite universe would contain not an infinite number of photons, but very small and finite fraction of the total number of photons in the universe. However, according to those that are supposed to know about this stuff, any fraction of infinity is still infinity. Of course mathematics also tells us that any number divided by itself is 1. Therefore infinity divided by infinity is simultaneously equal to infinity, and 1. (By the way, if noone has thought of that before I am going to name it the Geoschmo paradox. http://forum.shrapnelgames.com/images/icons/icon7.gif )

So I guess Phoenix-D and Grandpa Kim are both right. Glad we cleared that up.

[ November 04, 2003, 13:51: Message edited by: geoschmo ]

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Any fraction of infinity is indeed infinity so in any given piece of space in an infinite universe there are an infinite number of particles. But what is overlooked is they don't have to be photons or any particle we know of. One could say that in an infinite universe things advance to the infinitely large and infinitely small. Thus in any given point of space there exists an entire infinite universe composed of the infinitely smaller and smaller particles that make up that space.

The infinite universe would be infinetly large and infinitely small. http://forum.shrapnelgames.com/image...s/confused.gif That is more than my mind wants to take in atm. Sooo....

Re: Important Math Question
 

Geo - perhaps instead of fraction you should have used "finite portion of" - which is doable without having infinities in the portion. E.g., the set of whole numbers is an infinite set, while the set of whole numbers between 0 and 10 inclusive is a finite portion of the set of whole numbers.

Re: Important Math Question
 

Yes, finite portion might have been more correct. However, you still have problems trying to calculate the possible number of photons at any one point in space at any particular point in time.

The whole issue of infinity is probbably beyond our reach as a species anyway, except in a very theoretical discussion. Calculations involving infinity tend to break down into paradoxes. Perhaps the question shouldn't be whether the universe is infinite, but whether infinity even exsists. http://forum.shrapnelgames.com/images/icons/icon10.gif

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Once you have it limited to a finite volume, the task becomes much easier; the energy of a single photon is hv, where h is a particular constant (and depends on units) and v is the frequency of the photon. With the energy density of the light in that volume, and the freqency distribution in that volume (both measureable), the total number of photons can be calculated fairly readily.

If you are talking about an absolute point, rather than a volume, then the answer is trivial: 0. Photons don't seem to exist as points; they seem to exist as waves and particles.

Re: Important Math Question
 

<font size="2" face="sans-serif, arial, verdana">Infinity is not a number. It is a concept.

Dividing Infinity by Infinity is like dividing an apple by an apple.

[edit] However dividing infinity in half is not like dividing an apple in half. You would get two infinities, not two halves of infinity (because you cannot reduce something that is limitlessly big in size by dividing it, since the half would still, by definition, be limitlessly big).

Imagine trying to halve all the possible idea's in the world - both halves would still be limitlessly big, hence infinite.

My head hurts.

[ November 04, 2003, 20:59: Message edited by: Ran-Taro ]