I know, I just like to pretend I'm one of those boys that doesn't care school...I don't like it, but I do care about it!
Different Types of Infinity, arithmetic vs geometric vs exponential growth also energy vs power
- Thread starter Vovk
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There are plenty more.In fact, the common definitions are basically,
let Aleph_0<Aleph_1<Aleph_2<..., where Aleph_0 is the number of natural numbers. (These are generally called the cardinal numbers.)
(Most think Aleph_1 is the cardinality of the continuum, though no one has proven this yet.)
Anyways, from what I can make of the OP, you're basically saying that one function is "more infinite" than the other if it dominates the other; that is, f(x)/g(x)->0 as x grows large. They have the same "sort" of infinity, infinity basically just means "larger than any real number" in calculus terms, but yes, one function dominating the other can be quite useful when it comes to engineering like this. While you lack rigor in understanding what larger infinities *mean,* you bring up some very good points, and I wouldn't blame you for not quite understanding, it's pretty much impossible to if you haven't studied calculus in formal terms.
(Oh, and geometric growth *is* exponential growth.)
hah, math pwned. thanks for the correction Yeah, my last calc class was 4 years ago and I wrote this at 3 in the morning after being angered at folks doing the whole "look at my infinite energy" dance.
both examples would give a countable set of numbers (single source of power and a source of power which makes sources of power) and are the same order of infinity (aleph_0). I suppose I should have titled the rant: "Some functions grow much faster than other functions - also your dinky 'free energy' setup is stupid".
Infinity is infinity... there's no "this infinity is bigger than that infinity".
100 MJ/t forever is more infinite than 10MJ/t forever.
It doesn't matter how long you wait, you'll always have 10 times as much energy with the former.
Haha I've turned into the exact opposite. I used to 'like' math (as anyone who took math in a public school can *yawn*), then found practical uses, thought "hey I finally found a purpose for XXXXXX", then realized who cares, this is the real world, no one cares if you can triple integrate crap if you're good with people and can think realistically.
To the OP, I think there's people that play FTB to explore, those who build the most technologically intricate thing they can, those who just want FUSION/MAX EU/t, those who just want a nice way to release creativity/ kill stress. I know personally, I get ZERO joy out of building Ultimate Solar Loops (nor do I find builds like this impressive at all), and I'd like to think most players of GT think this way as well (not that it's a bad thing if you don't mind you), I have build plenty of inefficient power sources, just for a challenge and to learn/add something new to my world.
While this is a mod pack put together by maybe a few individuals, it contains the visions, playstyles, ideas, and beliefs of many many many people (individual mod makers). If everyone were to play the exact same way, there wouldn't be any need for several mods, as one single groups of mod makers could achieve what was desired. No idea if that's what we're talking about anymroe. How you doing?!
Another nifty cool "infinite" loop I'm definitely going to pull off is renewable Thorium and even Tungsten and Plutonium with as little as 4 uranium! So as long as you never consume any uranium in the facility then you'll have those three things coming in with just a little tin and a lot of power. (get a lava fab going and you can run about 15 or even 16 centrifuges spitting out your reactor fuels without digging holes day/night just to keep reactors reacting!) If you want to hop in the fun with me then check out my thread for server details. Among other cool "infinite" things I want to do on a mass scale!
Sadly not so great at math anything past the basic addition, subtraction, multiplication, and division tend to go over my head. when it comes to mathmatical formulas tend to lose me. although I can measure and understand the basic american measurements. I do know a little about the metric system.
I always have to start at those smaller, inefficient infinite power loops or basic solars or UE windmills. I bugs me because I know I can use the materials more efficiently, but it isn't possible until the inefficient infinite sources turn those first resources into the more efficient sources. You're right, though. Things can ramp up rapidly. A single run from a UE fission reactor can supply you enough energy to replace a good chunk of the investment. I haven't run the actual numbers yet, but it only takes a few runs before it becomes profitable from an energy standpoint.
Honestly, I can't see the difference between nuclear power generating a massive amount of EU or MJ, depending on how it is harnessed, powering a UU factory or MFR mining laser and the hated EE2 system of "free" resources. You have an initial investment in resources which is quite high, and it takes quite a large amount of EU/EMC to upgrade or build new reactors/collector flowers. The more you produce, the more you produce, the more you produce until mining/quarrying is nearly pointless. The power system requires quite a bit more initial work to create the automation, but otherwise, what's the substantive difference? It all ends up being free at some point, even if you never get into UU or MFR laser. A system of quarries in a mining age is just as infinite at a certain point. Hell, EU/MJ into new resources gives a defined price to each item in the game and is just EMC with a few extra steps added.
From this angle, the only true balancing factor in any modpack is the efficiency at which you reach the highest levels of these kinds of infinity. This translates into time being the only true resource as always. However, I speak from a purely objective view. There is a second, even more precious, resource that cannot be inherently found within Minecraft or any mod.
This resource is the fun factor. Or !FUN! factor, as it may be. !FUN! comes from Dwarf Fortress. The unofficial motto of DF is, "In a game with no way to win, the only fun can be found in how you lose." In MC, the majority of people seem to have a losing condition of "Survival becomes Creative". Not many are proficient in architecture or design. Not everyone has a programmer's mindset to create amazing redstone contraptions. However, everyone will come to a point where they no longer have fun with a world. Maybe through egregiously dying and losing their equipment as in a currently active thread or through achieving Creative Survival or completing their masterwork factory or building or some other condition. Many players found the EE2 method too fast, and their worlds lost their fun too soon. Many consider GT too slow, and their worlds lose their fun before they achieve a "winning" condition. However, the exact opposite is just as true. Many players loved the EE2 method. Many love the GT method just as much. This only proves that the journey from fresh world to a world of lost fun is the only subjective resource.
Therefore, the most successful mods are the ones that balance the time until a world is lost against the method of losing. As this ratio approaches infinity, which is a different metric for each player, a mod approaches immortality. Of course, no single game or mod can be immortal, but the right balance can approach it as stated. My children still play Super Mario World, a game that was published before any of them were born. Outside of video games, look at chess for a much more tried example.
Summation: Large or small, the math of infinity, as it pertains to games in general and Minecraft in specific, breaks down at the point of the player. Thus the only measurable infinity in an unwinnable game is the number of ways you can lose.
Honestly, I can't see the difference between nuclear power generating a massive amount of EU or MJ, depending on how it is harnessed, powering a UU factory or MFR mining laser and the hated EE2 system of "free" resources. You have an initial investment in resources which is quite high, and it takes quite a large amount of EU/EMC to upgrade or build new reactors/collector flowers. The more you produce, the more you produce, the more you produce until mining/quarrying is nearly pointless. The power system requires quite a bit more initial work to create the automation, but otherwise, what's the substantive difference? It all ends up being free at some point, even if you never get into UU or MFR laser. A system of quarries in a mining age is just as infinite at a certain point. Hell, EU/MJ into new resources gives a defined price to each item in the game and is just EMC with a few extra steps added.
From this angle, the only true balancing factor in any modpack is the efficiency at which you reach the highest levels of these kinds of infinity. This translates into time being the only true resource as always. However, I speak from a purely objective view. There is a second, even more precious, resource that cannot be inherently found within Minecraft or any mod.
This resource is the fun factor. Or !FUN! factor, as it may be. !FUN! comes from Dwarf Fortress. The unofficial motto of DF is, "In a game with no way to win, the only fun can be found in how you lose." In MC, the majority of people seem to have a losing condition of "Survival becomes Creative". Not many are proficient in architecture or design. Not everyone has a programmer's mindset to create amazing redstone contraptions. However, everyone will come to a point where they no longer have fun with a world. Maybe through egregiously dying and losing their equipment as in a currently active thread or through achieving Creative Survival or completing their masterwork factory or building or some other condition. Many players found the EE2 method too fast, and their worlds lost their fun too soon. Many consider GT too slow, and their worlds lose their fun before they achieve a "winning" condition. However, the exact opposite is just as true. Many players loved the EE2 method. Many love the GT method just as much. This only proves that the journey from fresh world to a world of lost fun is the only subjective resource.
Therefore, the most successful mods are the ones that balance the time until a world is lost against the method of losing. As this ratio approaches infinity, which is a different metric for each player, a mod approaches immortality. Of course, no single game or mod can be immortal, but the right balance can approach it as stated. My children still play Super Mario World, a game that was published before any of them were born. Outside of video games, look at chess for a much more tried example.
Summation: Large or small, the math of infinity, as it pertains to games in general and Minecraft in specific, breaks down at the point of the player. Thus the only measurable infinity in an unwinnable game is the number of ways you can lose.
Countable Infinities are for example N (Natural Numbers, {1,2,3,...}, sometimes also containing the 0), Z (Integer Numbers, {...,-3,-2,-1,0,1,2,3,...}) and Q (Rational Numbers = Z/N).
A group of numbers is countable, if all members can be brought into definite order, where any number can be defined as the n-th number of that group.
N: Easy, since you can simply match N -> N (1 is the 1st number, 2 the 2nd number, ...).
Z: Easy with a small trick: 0,1,-1,2,-2,3,-3,4,-4,..., so -4 is the 9th number in the line.
Q: A bit trickier: Write a matrix with 0 in the top left corner. Expanding to the right in the top row follows Z, expanding down in the leftmost column follows N. The remaining fields are then filled in with the top number divided by the left number. This will construct all possible members of Q (remember its definition as being Z/N). Now for counting the numbers you have to draw diagonals over this matrix from up right to down left. The first one only hits the 0 (first column, first row). The second one hits 1 (second column, first row) and 1 (first column, second row). The next one hits -1 (third column, first row), 1/1 (second column, second row), 2 (first column, third row). And so forth and so forth. Via this method every number has its definite place. You can expand the definition to remove doubles from the list. Easiest would be to never hit the first column except for the 0. This would keep numbers like 1, 1/1, 2/2 counted separately. You could also expand the definition, that only numbers are counted after being reduced completely which were not counted before (so 1/1 wouldn't be counted, since 1/1 = 1 and 1 had been counted beforehand). But no matter which definition you use, members of Q can be counted, so Q is part of the countable infinities.
The rational numbers are not the same as the positive and negative integers, and both are actually countably infinite. With the integers, you start at 0 and count 0, 1, -1, 2, -2, 3, -3, ...
With the rational numbers you create a two-dimensional array with the integers along both axes, and the array occupied by the quotient of the numbers making each entry's co-ordinates. You can iterate through that in a regular and defineable way, thus they are countable.
The real numbers, however, are not countable. There is no process you can come up with that can generate all the real numbers.
EDIT: That's what I get for not reading the second page before replying >_>