Computers are not capable of generating random numbers, instead they generate "pseudo-random" numbers based on a seed. The same seed will always yield the same number if you use the same function. In a nutshell, when working with computers you seed the random number generator to a specific number, and for every number the computer produces it increments the seed by 1. You basically have a list of numbers with a seed corresponding to an index, if the generator is not reseeded it will gradually return a subset of this list, starting at the initial seed.

If you really want to analyze "seed science" you are going to have to break down Minecraft world generation, by determining the pattern of random number function calls and then finding optimum values for these functions that result in good landscape. After you have a set of choice numbers you then have to analyze the list of outputs of the random number generator, looking for subsets that contain these choice numbers.

The only way you will be able to find correlations between two seeds resulting in a good map would be from a list of outputs from functions seeded with these seeds. It would be very difficult to find correlations using the seeds alone, and still difficult without memorization of the Minecraft world generation process. The only plausible way to find correlations using only the seeds would be to reverse engineer the random number algorithms and determine why they produce similar outputs; but this would be extremely difficult.

Yes, sure. High school algebra students who just can't get enough of their homework, and CRAVE MORE would be welcome recipients of this knowledge.

I never saw the OP post something that would imply he was not part of this demographic. Additionally, someone with a knowledge of the smelting process would never have to ask another question of this type, they would know how to calculate the most efficient method of smelting given the available resources possible. You can argue against this point all you want, but because the math is solid you are simply debating the psychology of the recipient of the knowledge. Some will find the knowledge useful and answer additional questions on their own, others won't and will continue asking questions they cannot answer themselves.

Does anybody care when they are trying to decide anything practical in-game? No. they care about the linear equation telling them about end product, because that is what actually determines how much wood to go get.

Does the exponential equation answer the OP? No. The process itself will help him get more out of his wood, but he does not need to know or use the equation, and in fact, your equation alone cannot actually get him the information he needs. Only the linear one can.

I mean, I talk about less relevant stuff than this fairly often in this forum. That is fine. It is academically interesting. But claiming that the exponential one is somehow equally useful or correct for answering anybody's question is definitely wrong.

In and of itself, the end result is more immediately useful than the process, I do agree with you on that. However, that does not mean we should disregard the process; just because we have used the process to derive a useful end result does not mean it should be banished from memory and replaced with the result. There are plenty of reasons why we should know why an object moves, not simply that it does move.

Yes, the process does not directly answer the OP's question. But if someone posts a homework question do you simply provide the answer? No, you show them how to arrive at the answer. Minecraft is not homework, and charcoal smelting is a fairly insignificant topic, but that does not reduce the benefits of understanding the process. Additionally, Exponential equations are not extremely useful either, but the procedure they describe is.

@ Tainted_wolf
The issue you are discussing was resolved several posts up, please read the entire thread before posting.

ANY amount of logs as an input, using either your method or planks, will result in a linearly determined output of charcoal (different slopes).

3 logs, 6 logs, 401 logs... you can plot any of them. That is infinitely many points.

With respect to the end result function that is correct. However, with respect to the process function, you still get a curve. A point on the end result function equates to two points on the process function, as an interval on the process function describes how to produce a given amount of charcoal with an initial amount of charcoal. Between these two points you have an interval containing a curve.

The progress is constrained to non-linear batches of smelting (IF you start with nothing). But the end product as compared to the beginning product is still entirely linear. If you always use charcoal instead of planks to fire the furnace, you simply end up with a different slope to your linear output function.

If you use coal to jumpstart the whole thing, though, or if you are like any normal person who will ever play the game, and only need a fixed rate of charcoal for your gameplay, then your batch process is irrelevant. You would start out immediately at the linear ceiling in one case, and in the other case, you would very rapidly stop expanding your charcoal stores, and would create a rolling process where you smelt the same amount each time from then on.

Even if you always use up all your charcoal, and then start from scratch again, there would never be any reason to actually perform any calculations using exponential terms. Again, you have found an exponential phenomenon, yes, but it is irrelevant to anything anybody would ever need to know.

Let's say I fuel my furnace with charcoal, when there are only 8 charcoal remaining I throw in a stack of logs to make more charcoal with which to fuel my furnace. From your point of view, we are sampling two points, which of course result in a line. However, it is really the interval [1,2] on the graph of y=8^x, the range of which is [8,64]. Or it is the interval [8,64] on the graph of log(8,x) = y if you prefer the inverse function. This is indeed a curve, just because it is not apparent on a small scale does not mean it does not exist.

Quote from smurfsahoy »

The relevant thing to know mathematically, even if you use your process, is the linear rate of end product you can expect. The process doesn't have to be understood mathematically at all. All you have to know is "always use charcoal to fuel the furnace."

Nobody is arguing the existence of something that is non-linear. What we are arguing is that no exponential phenomenon have anything to do with an answer to the OP's (or any other practical) question.

So you're saying that nobody has to know why an object moves if you push it, only that it does move?

Your "answer" answers the question "How much coal can you recursively smelt, given an infinite amount of wood, one coal, and a furnace, using the result of each smelting to smelt the next series?" Nobody is asking this question. This is critical. Problem solving requires providing an answer, but you haven't started with the correct question!

ORLY?

Let's say you start with 439 logs and want to smelt them all into charcoal in the most efficient manner possible, without outside fuel sources.

Using my method:

Convert 1 log into 4 planks, use those 4 planks to smelt 6 logs into charcoal.
You now have 432 logs and 6 charcoal.

Use the 6 charcoal to smelt 48 logs into charcoal
You now have 48 charcoal and 384 logs.

Use the 48 charcoal to smelt the remaining 384 logs into charcoal.
You now have 384 charcoal, for a smelting power of 3072.

Using your method:

Let x = charcoal and y = logs turned into planks

x + y = 439
x = 6y

6y + y = 439
y = 63 (approx.)

You will turn 63 logs into planks to smelt 376 charcoal, these 376 charcoal yield a smelting power of 3008.

My method is more efficient than your method.

Now, if you plot out the graph of charcoal over total wood you will see a line; this is because of conversion of wood to charcoal is 1-1 and will always result in a line, there is no way around this. However, the process of obtaining charcoal in the most efficient way possible does result in a curve if you plot the growth of the charcoal over the course of the process. This is because charcoal is more efficient than planks and it therefore makes sense to smelt charcoal with charcoal, resulting in that wonderful curve.

Once again, I was pointing out the behavior of the process of obtaining charcoal, you were pointing out the behavior of the end result of this charcoal. The ends are not greater than the means, as the means determine how much of the ends you can produce.

Nope, it will follow something exactly like that RED, linear line, except as you point out, obviously discrete, not smooth. but that has nothing to do with it being linear or not. It just means you can only use integers in your linear equation.
-snip-

I was referring to this post

Quote from M-L-BeastZ »

Quote from Tainted_wolf »

Quote from M-L-BeastZ »

Then get some logs, smelt them into charcoal, and you'veexponentiallylinearly increased your smelting resources.

Fixed it for ya.

Sorry, this annoys me, as I am a math major.

1 coal to 8 charcoal

8 charcoal to 64 charcoal

64 charcoal to 512 charcoal..... Given you have the resources and time to do that.

You start with one charcoal, you can smelt eight. With those eight you can smelt another 64, with those 64 you can smelt 512. The graph would have output charcoal on the y axis and smelting "rounds" on the x axis. The equation y=8^x would model the charcoal growth, yielding this graph

Depending on how you interpret the problem both a linear model and exponential model would match. Both are correct in their respective situation.

Sequence =/= an equation. (It can be described by an equation, yes) Sequences are simply sets of numbers, therefore if you calculated out the sequence of numbers, it would be a geometric sequence but it is linear growth, just look at the equation you put down.

To begin with, I never said anything about exponential growth. I was pointing out that charcoal growth is not linear. If you interpolate the points on the graph of a geometric sequence you will get the graph of an exponential growth equation. Also, I'm pretty damn sure that charcoal growth in minecraft is discrete, therefore a geometric sequence and a discrete exponential growth equation would be equally suited to modelling it.

Now, using that nice graph you provided

Red is linear growth, green is exponential growth. An interpolated geometric sequence would match the green curve. Still don't believe? Here's the nth term formula for a geometric sequence:

Hey, what do you know, an exponential growth equation!

So, to recap:

[*:1hax107d]Charcoal growth is discrete
[*:1hax107d]Charcoal growth is not linear
[*:1hax107d]Charcoal growth could be modeled by both a geometric sequence and an exponential growth equation
[*:1hax107d]I never said anything about charcoal growth being exponential in my original post.
[*:1hax107d]Your original correction of exponential to linear was incorrect, the original poster was indeed right

0

For lighting, make street lamps with fences and glowstone.

0

If you really want to analyze "seed science" you are going to have to break down Minecraft world generation, by determining the pattern of random number function calls and then finding optimum values for these functions that result in good landscape. After you have a set of choice numbers you then have to analyze the list of outputs of the random number generator, looking for subsets that contain these choice numbers.

The only way you will be able to find correlations between two seeds resulting in a good map would be from a list of outputs from functions seeded with these seeds. It would be very difficult to find correlations using the seeds alone, and still difficult without memorization of the Minecraft world generation process. The only plausible way to find correlations using only the seeds would be to reverse engineer the random number algorithms and determine why they produce similar outputs; but this would be extremely difficult.

0

0

0

Works for me, if it doesn't work for you check out my website C:\Users\ITAmember\Website\, it explains lots of this stuff.

0

This is your best bet. I would recommend showing how to calculate where to place each block given an equation and scale.

0

I never saw the OP post something that would imply he was not part of this demographic. Additionally, someone with a knowledge of the smelting process would never have to ask another question of this type, they would know how to calculate the most efficient method of smelting given the available resources possible. You can argue against this point all you want, but because the math is solid you are simply debating the psychology of the recipient of the knowledge. Some will find the knowledge useful and answer additional questions on their own, others won't and will continue asking questions they cannot answer themselves.

0

In and of itself, the end result is more immediately useful than the process, I do agree with you on that. However, that does not mean we should disregard the process; just because we have used the process to derive a useful end result does not mean it should be banished from memory and replaced with the result. There are plenty of reasons why we should know why an object moves, not simply that it does move.

Yes, the process does not directly answer the OP's question. But if someone posts a homework question do you simply provide the answer? No, you show them how to arrive at the answer. Minecraft is not homework, and charcoal smelting is a fairly insignificant topic, but that does not reduce the benefits of understanding the process. Additionally, Exponential equations are not extremely useful either, but the procedure they describe is.

@ Tainted_wolf

The issue you are discussing was resolved several posts up, please read the entire thread before posting.

0

With respect to the end result function that is correct. However, with respect to the process function, you still get a curve. A point on the end result function equates to two points on the process function, as an interval on the process function describes how to produce a given amount of charcoal with an initial amount of charcoal. Between these two points you have an interval containing a curve.

0

Let's say I fuel my furnace with charcoal, when there are only 8 charcoal remaining I throw in a stack of logs to make more charcoal with which to fuel my furnace. From your point of view, we are sampling two points, which of course result in a line. However, it is really the interval [1,2] on the graph of y=8^x, the range of which is [8,64]. Or it is the interval [8,64] on the graph of log(8,x) = y if you prefer the inverse function. This is indeed a curve, just because it is not apparent on a small scale does not mean it does not exist.

So you're saying that nobody has to know why an object moves if you push it, only that it does move?

0

6 charcoal -> 48 charcoal -> 384 charcoal is not linear in any way. Try again.

0

ORLY?

Let's say you start with 439 logs and want to smelt them all into charcoal in the most efficient manner possible, without outside fuel sources.

Using my method:

Convert 1 log into 4 planks, use those 4 planks to smelt 6 logs into charcoal.

You now have 432 logs and 6 charcoal.

Use the 6 charcoal to smelt 48 logs into charcoal

You now have 48 charcoal and 384 logs.

Use the 48 charcoal to smelt the remaining 384 logs into charcoal.

You now have 384 charcoal, for a smelting power of 3072.

Using your method:

Let x = charcoal and y = logs turned into planks

x + y = 439

x = 6y

6y + y = 439

y = 63 (approx.)

You will turn 63 logs into planks to smelt 376 charcoal, these 376 charcoal yield a smelting power of 3008.

My method is more efficient than your method.

Now, if you plot out the graph of charcoal over total wood you will see a line; this is because of conversion of wood to charcoal is 1-1 and will always result in a line, there is no way around this. However, the process of obtaining charcoal in the most efficient way possible does result in a curve if you plot the growth of the charcoal over the course of the process. This is because charcoal is more efficient than planks and it therefore makes sense to smelt charcoal with charcoal, resulting in that wonderful curve.

Once again, I was pointing out the behavior of the process of obtaining charcoal, you were pointing out the behavior of the end result of this charcoal. The ends are not greater than the means, as the means determine how much of the ends you can produce.

0

I was referring to this post

You start with one charcoal, you can smelt eight. With those eight you can smelt another 64, with those 64 you can smelt 512. The graph would have output charcoal on the y axis and smelting "rounds" on the x axis. The equation y=8^x would model the charcoal growth, yielding this graph

Depending on how you interpret the problem both a linear model and exponential model would match. Both are correct in their respective situation.

0

To begin with, I never said anything about exponential growth. I was pointing out that charcoal growth is not linear. If you interpolate the points on the graph of a geometric sequence you will get the graph of an exponential growth equation. Also, I'm pretty damn sure that charcoal growth in minecraft is discrete, therefore a geometric sequence and a discrete exponential growth equation would be equally suited to modelling it.

Now, using that nice graph you provided

Red is linear growth, green is exponential growth. An interpolated geometric sequence would match the green curve. Still don't believe? Here's the nth term formula for a geometric sequence:

Hey, what do you know, an exponential growth equation!

So, to recap:

[*:1hax107d]Charcoal growth is discrete

[*:1hax107d]Charcoal growth is not linear

[*:1hax107d]Charcoal growth could be modeled by both a geometric sequence and an exponential growth equation

[*:1hax107d]I never said

anythingabout charcoal growth being exponential in my original post.[*:1hax107d]Your original correction of exponential to linear was incorrect, the original poster was indeed right

0