Thread: "warning speculation" Relative Mathematics

Originally Posted by Conway

What is or is not infinite is relative to the observer

No. Something either has an end or it doesn't, it doesn't matter what the observer's point of view is. There are different "sizes" of infinity, but there are no multiples of infinity. Your idea of 0.1infinity doesn't make sense, just like "a tenth of a hole". It's either a hole or it isn't. It's not half a hole, or 2 hole. Similarly with infinity.

"Near infinity" is like "almost pregnant", it doesn't mean anything. Any quantity that you consider " nearly infinitely large" is vanishingly small in comparison to an infinite number of other quantities. It is not even in the top 1% of quantities.

Originally Posted by Conway

Why are we debating the existence of this concept [of infinity]?

We are debating it because you are confusion the physical world (which does not have anything infinite) with a mathematical concept.

I don't propose to discuss your ideas regarding zero until the framework you created for you ideas makes some sort of sense.

It is fair enough that you wish to take bit by bit, the "framework" before continuing on. You yourself gave examples as to the relativeness of size. "10 sugar grains v.s. 10 sugar cubes." If I am a giant, 10 cubes are equivalent to 10 grains. But my perspective is not that of a giants. 10 infinite cubes are, or are not, infinite to my perspective. But to the giant that changes. Relative to his size, ergo perspective. Almost pregnant does exist. It only depends on what point the "sperm" and "egg" are considered to be a baby. So then if the sperm is only millimeters "away" from the egg....then one is "almost" pregnant. I am willing to set aside the issue of infinite. Assuming I still have your attention....let's start with one of the first axioms given.

Do you then agree or disagree with the following statement, and why....

Space is the labeling of quantities of dimensions.

Or if you wish an alternative starting point....

Numbers are symbols used to represent space and value of given things.

If this is not what a "number" is, then what is a number?

Originally Posted by Archie

No. Something either has an end or it doesn't, it doesn't matter what the observer's point of view is. There are different "sizes" of infinity, but there are no multiples of infinity. Your idea of 0.1infinity doesn't make sense, just like "a tenth of a hole". It's either a hole or it isn't. It's not half a hole, or 2 hole. Similarly with infinity.
"Near infinity" is like "almost pregnant", it doesn't mean anything. Any quantity that you consider " nearly infinitely large" is vanishingly small in comparison to an infinite number of other quantities. It is not even in the top 1% of quantities.

@Archie: I do not think that you are trolling, even if I know that Conway must be.
You may come to regret the quote above.
Elementary Calculus: An Infinitesimal Approach by Jerome Kiesler is available as a free download at here.
The whole book is free, but so is each separate chapter. Chapter is a great introduction to both infinitesimals and infinite hyperreal numbers. I think you will be surprised by what you find there in light of your quote above
J.K was one of the greatest model theorist of the twentieth century. You can see hyperreal infinite numbers put on a firm foundation.

Originally Posted by Plato

You may come to regret the quote above.

Hardly. I haven't studied infinitesimals or hyperreals in detail, but they are non-standard analysis and therefore not relevant.

Edit: I was going to amend this post before Plato's distasteful outburst. I think infinitesimals or hyperreals are relevant inasmuch as their development is a fine example of how non-standard analysis can be carried out. But they don't form any part of the OP's ideas as far as I can see, and are therefore not relevant to his framework or what he's trying to do with it.

Originally Posted by Archie

they are non-standard analysis and therefore not relevant.

Sorry, my mistake. I though you were serious.
Then none of this, in fact none of mathematics is relevant according to you then.
Sorry my mistake again, YOU ARE A TROLL.

It doesn't matter how far away a sperm is from the egg. The earliest you can possibly consider them to be a baby is when the egg is fertilised. But if you wish to claim that "almost pregnant" exists, you can consider my analogy to be flawed. There is no such thing as "nearly infinite".

Originally Posted by Conway

You yourself gave examples as to the relativeness of size.

Size, not the infinite. An infinite cube is infinite to everybody and everything, no matter how large they are. Perhaps in mathematics, a similar idea would be calling a number "nearly irrational". It simply doesn't make sense. Either it is a ratio of two integers or it is not, there is no grey area nor any concept of "if we went a little further we'd reach it". The whole point of the infinite is that you can never reach it.

I'm loathe to set aside the issue of the infinite, because and discussion of zero is going to need it. It seems to me that you have a confused idea of "infinity" being a very, very large number. It is not a number at all.

Originally Posted by Conway

Space is the labeling of quantities of dimensions.

Space is not a process, but dimensions are a property of space. But I think we can gloss over any differences there - the problems come later.

Originally Posted by Conway

Numbers are symbols used to represent space and value of given things.

Numbers are not symbols. Numerals are symbols that are used to represent numbers. Numbers are mathematical objects in their own right, just as are squares and circles. They don't represent values, they are values and they don't represent space at all. Again space has properties such as distance, and we can make sense of distance by defining a unit and then counting how many of those units make up the distance we are interested in. But the numbers themselves don't represent the distance.

Your claim seems similar to suggesting that squares, circles and triangles represent pictures, when in reality the squares and circles are patterns we see in pictures that allow us to make sense of them.

Originally Posted by Plato

Sorry my mistake again, YOU ARE A TROLL.

now now Plato...you be nice to Archie...
else you're going to bed with no dessert...

Denisb

I have not forced anything on anyone. They may read it at their inclination. I also literally gave a fair warning as to the nature of the speculation in this idea. So then clearly I am trolling no one. I have posted this idea on more than 3 forums. 15 or so.....physicsforum banned for good reason. I posted in the wrong thread. While they are not much on forgiveness, I still clearly broke a rule. If you wish I can link all the times I have posted it. You will find, I hope, that I have tried to be polite and listen to others.

Plato

It seems to me you are the only one making rude post. Of course by replying back to you I evidence a tiny piece of the troll inside of me. LOL.


Archie

I like and agree with your statements.

[they are values], [Again space has properties such as distance, and we can make sense of distance by defining a unit and then counting how many of those units make up the distance we are interested in. But the numbers themselves don't represent the distance.]

So then why NOT represent in a given "numeral" (I think you nit pick but....) with both "pieces" of information at the same time. Unit and value. In fact I am saying that this is done with a "numeral" whether it has a "unit" or not. By using the "numeral" one to represent my apple", Then through information contained on "apple" I can derive a "unit". The information of space and value exist in all things. It is only how we use it, and or represent it, is different. I suggest we represent both bits at the same time. Why not?

Finally I did not intend to suggest that space was a process. "quantities of dimensions" exist with or with out a human to perform a process. But the word space is ONLY applied when a human intends to make use of "quantities of dimensions". Therefore a process is necessary in order to call it space.

Originally Posted by Plato

a great introduction to both infinitesimals and infinite hyperreal numbers. I think you will be surprised by what you find there in light of your quote above

It's curious, is it not, that the first chapter of that book explicitly states that all hyperreals are either finite or infinite and that all infinite hyperreals are greater than all of the reals. This means that what I wrote above is entirely true, even in the hyperreals.

I think you should stop trolling.

Any number(except zero) is either finite or infinite, but it is only so from a given reference point. Zero. There are small infinites just like there are large infinites. Value and size are all relative to position on the number line, again relative to a perspective. These are the same ideas used by Einstein, only applied to mathematics. Space and Time(a value), are two things in one. The space time continuum. Or space time manifold...mathematically speaking. As I stated, all things are two things in one. Space and Value.

Originally Posted by Conway

Any number(except zero) is either finite or infinite, but it is only so from a given reference point. Zero. There are small infinites just like there are large infinites. Value and size are all relative to position on the number line, again relative to a perspective. These are the same ideas used by Einstein, only applied to mathematics. Space and Time(a value), are two things in one. The space time continuum. Or space time manifold...mathematically speaking. As I stated, all things are two things in one. Space and Value.

I'm afraid that all of this is just wrong. Einstein's idea was that all physical laws should be the same for any observer - no more and no less. That has nothing to do with the number line, it is a qualitative statement about the universe. All real numbers are finite, and they are finite "relative to" any other real number.

Originally Posted by Conway

So then why NOT represent in a given "numeral" (I think you nit pick but....) with both "pieces" of information at the same time. Unit and value. In fact I am saying that this is done with a "numeral" whether it has a "unit" or not. By using the "numeral" one to represent my apple", Then through information contained on "apple" I can derive a "unit".

I'm not being picky at all. You seem confused. He's a good illustration of various numeral systems:

Then there are other numeral systems that are not decimal systems. Roman numeral, Babylonian numeral, Mayan numerals, etc.. The "size" of a number can be different in each one of these.

The reason we don't represent units within numbers is that numbers are far more general. It is this generality that gives them there power. There is certainly archaeological evidence to show that originally numbers were considered as one with their units: the mark for 3 sheep being different to the mark for 3 cows, for example. But this approach was discarded many thousands of years ago when it was realised that numbers can be abstracted and doing so gives them power.

Although a newcomer here I have been on the receiving end of Plato's acerbic tongue.

However I find nothing either rude or offensive in his statement in post#18.

In fact thank you Plato for the link, I had not heard of the good professor Kiesler and have downloaded the text in the hope (and expectation) that he will tell me something new to me.

This thread is posted in the Math Philosophy section which is presumably meant for discussion rather than just presenting a fomal mathematics sequence of statements, such as you would find in a proof or the solution to a problem.
So it is a shame that conway has adopted a non engagement discussion style and, as Dennis has pointed out, has already acted similarly elsewhere.

So to infinity.

Before you can say what infinity is or is not or 'near infinity' or approaches infinity means you have to have a working definition of infinity that provides properties we can compare with.

As an applied mathematician I can confirm that the concept of near infinity is very well developed in applied maths and engineering to the extent that our understanding of electric circuits, aeroplane flight, chemical calculations, themodynamics and many more fields depend utterly on it.

So, archie, I am happy to discuss near infinity with you, although I am not sure it is on topic in this thread.
To be honest I don't know what is on topic in relation to conway's ideas since he won't answer questions about them or discuss them and, as so far presented, they are unintelligible.

We should not fall out over this but rather demonstrate that we are capable of holding a rational discussion, even if conway will not.

My contribution:

Deleted Replies? - Page 2

post#20

This has been anything but a non-engagement style on my part. ( I evidence post number 7 ). I evidence post (number 9) for proof of the troll in Plate. It appears you have not read the entirety of this post studiot. Further I was the person making the statement that near infinity existed. It was Archie that was claiming it did not. Why did you not atlest try to be polite and read the entirety, instead of jumping to conclusions. Archie and myself were getting along fine with out you coming in and trolling it up, but I suppose your buddy Plato needed help with his own trolling. Finally post one statement by me studiot that was not rational. Again, let's move this TALK to actual mathematics. I challenge you studiot to post not a single more word. Only post equations, such as one that I can not solve using my own axioms. I will also move from this point with out any words. Lets just do math, will that be rational enough for you. Will you consider that to be an honest engagement. Do you know of any equations I can not solve with this set of axioms? I think not.