Is it possible to describe any number without reference to another number or by using a formulae such as adding / subtracting etc?

[Awatso]

Good morning,

I was thinking about this on a dog walk yesterday ( it makes the passage of time fly by) .  How would I describe to someone for instance what the number 4 is without using other numbers or by applying something like addition or subtraction etc.

Obviously you cannot say it is the number between 3 and 5 as that uses other numbers to define it.  Then I thought about drawing 4 lines.   But then of course I am mentally counting them as a draw them, and know when to stop in the addition.

Next I thought of dice  with their 1 to 6 in different patterns.    4 could be always that pattern of the 4 dots, which would negate any counting in the "description".

The problem with that technique is of course you can't extrapolate it for a general principle.  Imagine pattern matching  12 556 987 2444 98763  as a number,  or even worse,  0.0025.

At that point I thought I would give up, I am not a mathematician, and thought I would ask someone more experienced. So I joined this forum.  Hello by the way.

Is there a way of describing a number simply without using maths and its constituents? I am guessing not but I might have missed something obvious.

Many thanks for any input, I am on a dog walk soon and will think about the twin paradox to make the time go faster.

 

[studiot]

51 minutes ago, Awatso said:

Good morning,

I was thinking about this on a dog walk yesterday ( it makes the passage of time fly by) .  How would I describe to someone for instance what the number 4 is without using other numbers or by applying something like addition or subtraction etc.

Obviously you cannot say it is the number between 3 and 5 as that uses other numbers to define it.  Then I thought about drawing 4 lines.   But then of course I am mentally counting them as a draw them, and know when to stop in the addition.

Next I thought of dice  with their 1 to 6 in different patterns.    4 could be always that pattern of the 4 dots, which would negate any counting in the "description".

The problem with that technique is of course you can't extrapolate it for a general principle.  Imagine pattern matching  12 556 987 2444 98763  as a number,  or even worse,  0.0025.

At that point I thought I would give up, I am not a mathematician, and thought I would ask someone more experienced. So I joined this forum.  Hello by the way.

Is there a way of describing a number simply without using maths and its constituents? I am guessing not but I might have missed something obvious.

Many thanks for any input, I am on a dog walk soon and will think about the twin paradox to make the time go faster.

 

 

Don't give up, you have had the same thought as one of the greats of 20th century maths. Kolmogorov

So welcome and keep thinking.

Quote

https://en.wikipedia.org/wiki/Kolmogorov_complexity

Kolmogorov randomness defines a string (usually of bits) as being random if and only if every computer program that can produce that string is at least as long as the string itself.

Basically Kolmogorov is saying that a number is random if the shortest algorithm (read what you meant by describing a number) for arriving at that number is writing down the number itself.

So for instance 1234567890 and 0 and 1 are all random numbers.