# The riddle of infinite number

I can’t believe i’m reading this…explaining this to you is like talking to a kindergartner. Don’t you see how irrelevant the symbol on the die is? It represents a number…when that face of the die lands facing up, you read the symbol and interpret it as the number you see. Again, Duh.

You damn well can distinguish succesive throws. Instead of recording 1 data point for each throw (the value), you record 2. the first data point holds the throw #, and and the second holds it’s value (1,2,3,4,5 or 6). Now you can easily distinguish throws that are the same value. Oddly, this is both obvious and intuititive for anyone but you.

You took 2 paragraphs to explain that there are a finite number of positions in a stick? a stick’s size is quantized because it can only be made from a whole # of atoms.

The only meaningful conclusion I can draw from your posts is that a real life function must choose from a finite set because you can’t physically represent an infinite # of digits. That is a true, if basic conclusion. However, that doesn’t influence how random the number coming fro the function is. The set does not represent all possible values, but randomness is not defined with respect ot all possible values, hence the dice example. a die has only 6 values, but it can generate a random number within that set.

This is a lot like saying that math exists for a machine that will never gain entropy, but you can never build it. It’s true, but it’s nothing stunning or orignial.

1. Spots and shapes on the sides of objects are not numbers, despite your insistence to the contrary.
2. There are no positions on a line unless they are made.
3. A line is not composed of points.
4. An infinite set of digits is a romantic idea. Shapes and spots are made and defined by their shape and spottiness. They are not out there waiting to be discovered. Where then, is this infinite number of shapes and spots called digits?
5. Marking each throw of a die with a different mark ensures that all throws of the die are logged. However, how does mathematics present this task?

JJ

1. Spots and shapes on the sides of objects are not numbers, despite your insistence to the contrary.
2. There are no positions on a line unless they are made.
3. A line is not composed of points.
4. An infinite set of digits is a romantic idea. Shapes and spots are made and defined by their shape and spottiness. They are not out there waiting to be discovered. Where then, is this infinite number of shapes and spots called digits?
5. Marking each throw of a die with a different mark ensures that all throws of the die are logged. However, how does mathematics present this task?

JJ

1. Spots and shapes on the sides of objects are not numbers, despite your insistence to the contrary.
2. There are no positions on a line unless they are made.
3. A line is not composed of points.
4. An infinite set of digits is a romantic idea. Shapes and spots are made and defined by their shape and spottiness. They are not out there waiting to be discovered. Where then, is this infinite number of shapes and spots called digits?
5. Marking each throw of a die with a different mark ensures that all throws of the die are logged. However, how does mathematics present this task?

JJ

Not unless it is axiomatic, ie1. assumed,
2. or taken as self-evident,
3. or believed it so based on our experiences,
4. or an artificial concept defined into being,
5. or something deemed necessary by beauty.This is a fundamental gap, a teeny weeny gap, but nonetheless a gap between the concepts in our minds and the correspondence to reality. It is an impossible gap to breach by ‘logical’ means, ie by inference or deduction, but nonetheless can be reasoned. In some sense we can never ‘know’ what is reality. We are forever separated by this tiny gap.

And one justification or evidence that our abstraction or artificial concepts can possibly be true is that it works. So although we may not know that a line is indeed a set of points, but when assumed so, I can infer and derived even unintuitive things which later correlates well with our experiences.

BTW a point is also an axiomatic concept.

A line is not composed of points for this reason.
If a line is made of points then between any two points comes a third, positionless point. Therefore, a line made of points is a line where points do not define positions. This is not a line.
JJ

I might have lost a post somewhere.

Anyway. a line is not made of points: Between any two positioned points on a line lies a third, positionless point. A line with positioned and unpositioned points is not a line.

JJ

For some reason my post is not appearing. I will try again.

A line is not composed of points because between any two positioned points there is a third unpositioned point. A line where points are unpositioned is not a line.

JJ

For some reason my post is not appearing. I will try again.

A line is not composed of points because between any two positioned points there is a third unpositioned point. A line where points are unpositioned is not a line.

JJ

1. It doesn’t matter that they aren’t numbers, because they rpresent numbers. The die is imaginary…the die is just a real world analogy of a set of 6 elements with the values {1,2,3,4,5,6}. you pick one of the numbers with each random throw.
2. If it is a line in the physical world, that’s true. You point is…
3. Oh really? a line is defined as all POINTS that satisfy the equation of the line. for the line Y=2X, any point such as (0,0) and (1,2) is a solution of the equation and a point on the line.
4. that’s why we have numbers wiht more than one digit, smart guy. you can easily take a finite number of digits and repeat it infinitely. You can’t necessarily write it down, though.
5. i just explained that…each throw has 2 peices of information. you can accomplish this with a simple tally chart.

what is the distinction between a point and a position? Why is it relevant? You seem to be saying that we can’t represent an infinite range of values by any physical means, because we live in a finite univrse. If so, then we’ve been over that…you can still draw a random element from a finite set.

Now, what does this mean for the real world? well, if you had a true random number generator which retrun any possible value from 0 to 1, with no limit to the # of decimal places, how would we interpret it’s answer? we’d round the random number off to whatever precision we needed for our application. Maybe for a computer you’d need random 128 bit numbers, whereas for a dice game you’d only need a 3 bit number. My point is, if you build a random number generator that picks from the set of 128 bit numbers or 3 bit numbers or whatever, you get the same result.

A line is not sufficiently defined by being composed of points in the absence of their separation and position.
Therefore, a point must have a position.
Between any two positioned points, there lies a third unpositioned point.
Therefore, a line of points is not a line if points are both positioned and unpositioned.

JJ

Wow, youa re so wrong on that last count.

a line is a describption we apply to the set of points that solve a linear equation. That’s it. no positioned points bullshit. Look it up…the mathematical definition of a line is just what i said.

It is defined ONLY by points. You, Mister getting-to-the-root-of-mathematics-which-i-know-nothing-about, should be able to see that. positioned points…goddamn…you need to lay off the bong and take some middle school algebra.

I don’t know how youc an draw a distinction between point and position. a point is defined by it’s position. that’s why they are represented wiht ordered pairs.

A point is not defined by position. There can be positioned or unpositioned points. A point, like a line,is not a mathematical structure, derivation or concept.

JJ

No…NO NO NO

A point is defined only by it’s position…that’s it. look it up.

You may be refering to a point that is “on” an object vs. a point out in space. In that case, you’re undertanding is flawed. The point is not “on” anything. it is stinng at location (x,y,z). The volume or area may enclose the point, but that is a property of the object, NOT of the point.

You are wrong about that second concept too…points, lines, and areas are STRICTLY mathematical concepts, because there is no physical analog. They exist only in our imagination, and the rules of math have precise definitions for each. In the real world, everything is 3 dimensional…only in theory is there an object with 2,1 or 0 dimensions.

Between any two positioned points on a line lies a third unpositioned point. Signifying a number to a dimension, like 3D, or 2Dimensional, does not describe volume, lines, planes or anything else. Mathematics describes NOTHING that we are familiar with. We merely associate our experience to a symbolism that gives us the result we are looking for.

JJ

what does “unpositioned” mean? you mean a line composed only of whole numbers has non whole numbers between the marked points? doesnt make sense

do you mean that every time you think you have two points that are right next to eachother there is in fact another point, and another thousand points in between those two that you initially didnt see? so what a point is infinitely small in theoretical graph land.

well it describes which of those things you are talking about. a line is one dimensional, because it only goes left or right, one dimension. a plane is two dimensional because you can go left and right and also up and down. thats 2 dimensions. what do you mean here?

have you heard of the pythagorean theorem? apparently not because you wouldnt have said this if you did. finding the length of a third, unknown side of a right triangle is a technique so freaking useful for finding distances to things wed probably still be wearing togas talking about aristotleian science, with gigantic rolls of measuring tape as far as the eye can see if it hadnt been discovered.

JJ…stop it…your’e making stuff up again. Your positioned point idea, your concept of dimensions, all that is totally made up. I suppose it’s a way to look at the world, albeit a stupid way, but that does NOT mean it is the mathematical definition as laid out in numerous textbooks.

A point IS a position. That’s all it is. They are two names for the same concept. A point contains no other information. That’s it…

A line is the shape that describes the set of all solutions of a linear equation. A point that is on a line is one happens to be a member of the set of points that defines that line. Of course, we do not need to have a list of all the points on the line to know what it is. Only two points are necessary to define the relation that describes the line.

A plane is a similar expansion…all lines perpendicular to a certain vector descriobe a plane. Only 3 points, 2 lines, or 1 vector are necessary to describe the plane.

A 3D “space” or hyperplane" is the set of all planes that are perpendicular to a certain 4 dimensional vector. We live in such a space, so we know of only one of them…this one.

Do you see the hierarchy? a “positioned” point on a line is a meaningless concept in this defintion.

You are corrrect in repeating what i said that 0,1,2,4,4+ dimensional objects are strictly imaginary. Math that describes things in 3 dimensions describes what we are familiar with. I really don’t see how this supports your point, though.

The only thing you seem to be saying so far is that we cannot represent an infite number of positions in the real world. It is true that we cannot subdivide a stick smaller than the subatomic particles.
But, if you can document all these finite lengths the stick could be, and choose on of them at random, then choice would be random wrt the set it was picked from…so you would have chosen a truely random length from all possible lengths. This is just like breaking the stick in a random place.

See, the key here is that a random number generator is only used for applications of math. These applications only require a certain precision (i.e a certian number of decimal places), so a random number generator does not have to pick from all possible values to give a useful random result. In fact, it’s silly to even expect a random number generator to make a random number from a truely infinite set, because neither theory nor application of math has any use for the result, nor any way to represent it.

I incorrectly stated before that you could draw a random number from a bounded but infinite set…I explained before that as the number of elements in the set approaches infinity, the probability of any one being picked approaches zero. the limit implies that you would never be able to make a random choice, because any choice of a number with finite length would be a biased, and thus non-random choice.

There can be no random numbers.

An unpositioned point is the same type of entity as an unpositioned line, plane, or any other unpositioned object.

Forget it…I’m sorry JJ, but this is not worth my time anymore. If you want to live in your own fantasy universe, go right ahead. I no longer care enough to try and educate you. Just do me a favor and don’t get a job that involves any more math than what you can do with your 10 fingers.

If anyone else would like me to explain the nature of space and geometry as it is defined and agreed upon in modern mathematics, then feel free to chime in.

1. Mathematics is logcial
2. John Jones disagrees with mathematics
3. John Jones disagrees with logic
4. John Jones is not logical.

Define:
Logic-a system of reasoning

1. John Jones is being unreasonable

Do you understand this, JJ?