One and infinity

What is one is a question that cannot be answered, similar to what is infinity. According to current knowledge even the universe us finite. Therefore we cannot find something physical that is infinite.

What about one? If universe consist of one unbreakable object, we cannot say anything about it. We always need other things to say something of something.

Suppose there are two marbles in the universe to find distance between them, we need a ruler. To say something about the marbles we need other objects.

So if we have two marbles still we can't say something. What about three or ten. What is the minimum needed to say something about a set of objects. I think it is not possible to answer even this.

We do make concepts like entropy but cannot say the minimum necessary to have a concept. Entropy is a statistical factor of a large number of objects. How large? we don't know.

Achilles and Tortoise Paradox

Achilles and Tortoise Paradox. The paradox is Achilles and tortoise will have a race. The tortoise is given a head start say 100 meters. Suppose both started running at the same instant. It will take some time for Achilles to run the 100 meters. In this time the tortoise will have moved ahead say 10 meters. Then Achilles will need a further time to catch up the tortoise. When Achilles reaches the next point the tortoise has moved a further small distance. So, when Achilles reaches some point the tortoise has reached, he will have to go farther. Therefore, Achilles need to go to infinite number of points to overtake the tortoise, which, is impossible. So, he will never overtake the tortoise.

In reality commonsense says this cannot be, Achilles will easily overtake the tortoise. Therefore this is a paradox.

Is it? The problem is that we assume that space and time are continuous entities which can be divided indefinitely. It is not so. Time and space are discrete. The locomotion is not a smooth one where it can be divided in to infinitely. The movement is in jumps. At one stage Achilles will jump over the tortoise.

Compressing multi dimensions to one

1,2,3.....is an infinite series. 2,4,6..... is also an infinite series. The total of both are equal to infinity. But strangely second one is not larger than the first one. Similarly there can exists a function that can transform each point in a two dimensional space to a single dimension. Similarly infinite dimensional space can be transformed to a single dimension.

Is this a contradiction? Can we transform space time to a single dimension. Or are there many Infiniti. Some Infiniti larger than others?