Energy/Math Discussion

[protovack]

David wrote:

I'm still waiting for someone to prove how information isn't energy.

I'm still waiting for someone to resolve the debate over whether matter really exists.

I've been waiting a long ass time

 

[zorn]

^^^ Huh? Of course it does. How is there any doubt about this?

I think this is what David, or at least I'm, getting at. The decimal expansion is not the same number. There will eventually be some discrepancy, no matter how small, to the decimal expansion of Pi.

Ah. I see -- you've got the idea that "concrete" "actual numbers" are necessarily finite decimal expansions. This is a bit confused, as I'm sure you'll see after reading through Euler's and Alphanumeric's posts.

In fact there's nothing natural or fundamental about decimal expansions at all; they just seem that way to you because you've grown up using them. It was actually only around the year ~1000 AD that people began to use this decimal way of writing numbers. Ancient mathematicians -- like the Egyptians and Greeks -- knew nothing of them, and only knew of numbers in terms of named numbers and fractions, eg "sixty five and a fourteenth."

Decimals are really quite complicated, abstract things. Think about what a decimal number is; it's not simple. What is "26.15"? I know what 26 is -- I can count out 26 things -- but what does the string of symbols "26.15" mean? If you remember how the decimal system is defined, 26.15 is defined ("abstractly") by

26.15 = 2*10 + 6*1 + 1*(1/10) + 5*(1/100)

ie, in terms of fractions. Fractions come first -- without fractions, there's no way to put meaning to a decimal number. And of course there's nothing that makes the fraction 1/10 any more "actual" or "concrete" than the fraction 1/3. So it's clear that decimal expansions don't provide a priveleged representation of a number, and why numbers with finite decimal expansions aren't any more 'concrete' than numbers without.

All numbers are fundamentally defined through what you termed "abstract" statements. Decimals are a convenient way of doing approximate calculations with numbers -- that's all.

 

[PGTips]

It was actually only around the year ~1000 AD that people began to use this decimal way of writing numbers. Ancient mathematicians -- like the Egyptians and Greeks -- knew nothing of them, and only knew of numbers in terms of named numbers and fractions, eg "sixty five and a fourteenth."

Some ancient cultures didn't consider 1 a number, nor 2. 1*1 = 1, which they didn't like, so they didn't think 1 was a number. 2*2 = 2+2, and they thought multiplication should "do more" than just addition, so 3 was considered the first "proper" number.

Obviously this reasoning is terribly flawed, because it considers any number with unique properties to not be a number. David often describes primes as "anomolies", as if they are errors in a problem, and that mathematics isn't "perfect" because such numbers exist.

Personally I take the opposite view. It is amazing that they do, and they should be studied. To consider them somehow an error, to be removed with careful tweaking of axioms is completely wrong IMO. It implies a desire for a system with no beauty or elegance, one of complete homogeneity and blandness. If you're after that, then I suggest a detailed examination of the smallest possible Field, {0}. Its terribly boring.

What makes mathematics so interesting and worthy of research is the unfolding elegance of some of the simplest ideas. "A number with no factors other than itself and 1". A prime. From something so simple (after all, its the very simple to have only 2 factors, itself and unity) has come some amazing results, far reaching into many areas of real world application too.

An old memory just sparked in my brain, and I remembered my first year "Numbers and Sets" lecturer, and that his website contains some very interesting articles directly related to these topics.

Sexyanon, and yes, even you David, might be interested in the following link, Prof. Gowers lays out a conversation between someone who denies the existance of Root 2, and someone who knows some maths :
http://www.dpmms.cam.ac.uk/~wtg10/roottwo.html
The discussion is developed further here :
http://www.dpmms.cam.ac.uk/~wtg10/decimals.html
Many other topics in a similar vein follow here :
http://www.dpmms.cam.ac.uk/~wtg10/naspage.html

Prof. Gowers has a Fields Medal (what is essentially a Nobel Prize in Mathematics) for work in Combinatorial Mathematics, and having had him as a lecturer (my first lecture ever if I remember correctly) I can tell you he's an immensely intelligent and insightful and his explainations do far more justice to the ideas we are trying to get across than I could possibly do, though some are pitched at university mathematicians, after all, he holds the opinion "Noone can really call themselves a mathematician if they don't have at least basic understanding of Banach Spaces", so beware the topics he gets technical in!!

 

[zorn]

"As a more physically scientific definition, information is possibly a property in physics. This is demonstrated by the phenomenon of quantum entanglement where information itself cannot travel faster than light, even if the information is transmitted indirectly. This could lead to the fact that all attempts at physically observing a particle with an "entangled" relationship to each other could slow down, even though they are not connected in any other way other than information.

Another such phenomenon is demonstrated where it was proven that in logic gates, an "AND gate" releases more heat than the "OR gate" does because information is destroyed in an AND gate and simply converted in an "OR gate". This discovery is an important development in research to create efficient and therefore less signal interference in quantum computers, as interference is a major roadblock.

This is often held contradictory to the traditional view that information is merely sensory input subjective to each organism or the human brain."

The bit about the limitation of information transmission to the speed of light is a red herring I think -- that just arises from the fact that nothing can affect events outside its light-cone. However the second bit relates to a very interesting apparent connection between thermodynamic entropy and information. It's long been realized that the second law of thermodynamics could perhaps be broken if you had a microscopic 'computer' which intelligently manipulated parts of the environment (cf "Maxwell's demon.") When people have tried to design physical systems that could do something like this, though, it's turned out that the computation mechanism produces more entropy than the computer's manipulation can save. There seems to be a tantalizing connection between the "information" that a system stores and the amount of entropy it produces. (In standard information theory the measure of information is called "Shannon entropy" b/c it parallels thermodynamic entropy in many ways...)

>>> "Information" is a much trickier concept to deal with scientifically... Without knowing how a message is supposed to be encoded in a system, you can't say anything about the information present.

But the information is present regardless...

Not exactly -- the definition of 'information' presupposes some semantics and encoding mechanism.

>>> What do you mean by "information is a property of energy"? Remember, energy isn't a "thing," it's a property of things, just like weight is a property of things.

Isn't that only one perspective though, why can't "things" be a property of energy as well?

No, that's what energy is. A given object (eg a particle) has some energy E, just like it has some mass M and some velocity v. Don't reify energy and treat it as some sort of thing... that's a common mistake.

 

[yougene]

Not exactly -- the definition of 'information' presupposes some semantics and encoding mechanism.

From what I understand information doesn't really have a clear definition. Just because a human can't make sense of the information present doesn't mean it hasn't been encoded.

No, that's what energy is. A given object (eg a particle) has some energy E, just like it has some mass M and some velocity v. Don't reify energy and treat it as some sort of thing... that's a common mistake.

You could look at objects as containers for energy, but what are the particles made of then?

 

[sexyanon2]

Please explain why you think you can cut a ruler into 4 equal pieces (since 1/4 = 0.25, a terminating decimal) but you can't cut it into three equal pieces.

I didn't say that. You're making assumptions.

And when you fail to do so, please reconsider your argument.

You're going to need to stop being so hostile if you want anyone to consider what you're posting.

As I said before, easy way to check. Put in Pi = 3.14 into your equations, and find your values for various cosmological constants. Then try 3.15 (the "real" value of Pi is between those two), and find your values of these constants. Now see if there has been a sufficent change for the equations to suddenly say something different.

Keep increasing the decimal length of your value for Pi and see if you can get rid of this sudden change. You reach this point WAY before 1.2 trillion decimal places.

On a big scale, you're correct. 3.14 and 3.15 won't make a noticeable difference. There still will be a difference, however small.

Check my gallery. There is an equation for Pi in there which is an expression involving 4 fractions. That is an expression for Pi in Base 16, as opposed to our Base 10. If you give me ANY "decimal" place for you want, I can tell you what it is in base 16. You want the 5th place? No problem. You want the billionth place, again, no problem. As you can see, that formula works for ANY n, there is no sudden "It doesn't work", so therefore the value of Pi must be a well defined on.

Can you give me the ending decimal?

In the "mathematical universe" 7*1/7 == 1, its absolute. Do you deny that this is right? If so, please point out where the error is.

I don't at all.

What is wrong with 1/3? I have 3 apples, I take away 1, I've got 2 left. The total number has decreased by 1/3. Now, by your logic, that isn't right, there is an error, because 1/3 = 0.33333......, which I therefore use exactly. Is there an error in my calculations? Is taking 1 apple from 3 not removing 1/3 the total?

Ah. Now we come to the discussion of systems. One apple is surely a system. But are 3 apples a system? I don't know physics and properties that well, but 3 seperate apples have different properties than a one apple system. The 3 apples are seperate. Now, does that make it a system? A system, in this sense, would be one object with specific properties. Three seperate systems, unless combined, are not one system.

Although, the discussion of "systems" would be a fun tangent, and I'd love to get into it. First we need to determine what a system is.

Follwoing your own logic no you can't. If you think that "1/3" doesn't exist then you are not cutting off 6.15cm from your ruler. Are you sure its exactly 6.15cm? What if its 6.1500001cm?

Ah. This is where the line is drawn. There is the idea of a third, and the concreteness of a terminating decimal. Although zorn posted something about this, so I'll come back to this after reading what he said.

The arguments which get from the axioms of mathematics to these results have been analyised, reanalyises, checked and rechecked by the best logisticians ever, the logic is flawless.

Can I see the arguments for these? If I add two apples together, I get two apples. Although, would I get a system of two apples? Or two systems of one apples?

Follwoing your own logic no you can't. If you think that "1/3" doesn't exist then you are not cutting off 6.15cm from your ruler. Are you sure its exactly 6.15cm? What if its 6.1500001cm?

Re-thinking this. If you have a 75 mm ruler. Cutting one third of it off would be cutting off 25 mm, right? Now, I don't know if this is a battle of semantics about to be brought up, but you didn't cut off a third, you cut off 25 mm. The idea of a third there is correct. You did cut a third from the ruler. Although why I have such a small ruler is beyond me.

Anyways, you concretely cut off 25 mm. Cutting off a third of the ruler would be an irrelevant idea. The IDEA, the concept, of a third, YES, has been cut off. But the concreteness, the actual cut off of the ruler was 25 mm.

But again, zorn said something about concrete and abstract in his post, so I'll need to take a look at that real quickly.

So to my post about the 1/3 of the apples, I instead say what I said above. But the idea of systems still interests me.

In reality, there are ALWAYS errors, but not from mathematics. You want Pi to 1 billion places? No problem, maths will tell you. 1000 trillion places? No problem, maths will tell you. 10^1000000000 places? No problem, maths will tell you.

I agree. That's what I've been saying, though. Mathematics is an ideal reality, while reality itself is imperfect.

In mathematics, every number can, and is, defined by the equations it solves. To deny that is either because you have insufficent schooling in mathematics (which is not a crime, and so asking for clarification is fine ) or a result of ignorance.

Maybe I'm guilty a little bit of both, so could you verse me a little? Like 1=1. That's defining 1 in terms of itself. Or 1=2-1. But there is this ideal scope that math holds. Adding two apples together in reality will give you two apples, no matter what. The proof for that is self evident, yes. But the proof in mathematics, I can see why that's not self-evident. All of math is based on ideal proofs (i believe), and there's nothing wrong with that.

Why do you represent reality using words?

Isn't our reality based on the tangeable? Can we use ideas, empirically, without any tangeability? Like God? Or infiniti? The convergence stuff we did in Calc this year wasn't explained in detail at all, so I'm fuzzy on the details. But what can you expect from High School math?

And yes, that was one long motha fuckin post. You deserve two post counts for that.

 

[sexyanon2]

Then 1/3 (which would actually be 1/10 in base three) has the decimal expansion 0.1. This is undoubtedly a terminating sequence of digits, and so you would consider this to be a 'real' number.

No. That's called rounding. Not a true terminating decimal.

And sorry, if your post has one more hostile remark, I won't respond back to your comments. You can either have a civilized debate or post attacks on the internet to boost your ego. "The ball is in your court".

 

[sexyanon2]

Ah. I see -- you've got the idea that "concrete" "actual numbers" are necessarily finite decimal expansions. This is a bit confused, as I'm sure you'll see after reading through Euler's and Alphanumeric's posts.

Did I cover it when I talked about the idea of a third? The idea of a third is ideal, or perfect. Taking away 25 mm of a 75 mm ruler would be a third. Sure, if you want to boost up the magnification, it would never be truly a third. But it's all relative.

And if I'm updating what I'm saying as I go along, I thank you guys for the insights.

All numbers are fundamentally defined through what you termed "abstract" statements. Decimals are a convenient way of doing approximate calculations with numbers -- that's all.

Ah. So anything past a natural number is an approximation or an ideal?

A prime. From something so simple (after all, its the very simple to have only 2 factors, itself and unity) has come some amazing results, far reaching into many areas of real world application too.

Like? Primes are fascinating, although I'm unsure of their significance.

And I'll check out those links, AN, after my brain wakes up a little more.

 

[PGTips]

On a big scale, you're correct. 3.14 and 3.15 won't make a noticeable difference. There still will be a difference, however small.

Of course a difference exists or 3.14 would be equal to 3.15.

My point was that Davids "We need to know Pi exactly or the entire nature of our understanding of the universe will change" view is wrong. Physicists currently use about 15 decimal places of Pi. Beyond that accuracy, nothing changes in the behaviour of systems and the experimental error in measurements is far more important. If it wasn't accurate enough, they'd use 20 places, 50 places, 100 places, till it was. There is't going to be an overnight revolution because someone calculates Pi to a few more billion places.

Can you give me the ending decimal?

Of course not, its a non-repeating decimal. Does that make it not a number? No, of course not. The links I posted explain how numbers can be defined by their decimal expansions.

Ah. Now we come to the discussion of systems. One apple is surely a system. But are 3 apples a system? I don't know physics and properties that well, but 3 seperate apples have different properties than a one apple system. The 3 apples are seperate. Now, does that make it a system? A system, in this sense, would be one object with specific properties. Three seperate systems, unless combined, are not one system.

Its 3. I am using apples to illustrate a point, not to bring in physical considerations. "Systems" are irrelevant. I had 3, now I have 2. What fraction have I lost? 1/3.

Can I see the arguments for these? If I add two apples together, I get two apples. Although, would I get a system of two apples? Or two systems of one apples?

Do you want the axioms or the derivation of 1+1=2 from the axioms? The derivation is 362 pages long of mathematics which gets highly complex.

As for the systems arguement, as before, you are making a pointless distinction.

The idea of a third there is correct.

This is all mathematics is, ideas. Concepts in our minds. Yes, in reality, some of these concepts do not apply, but in our minds, we are not confined by reality. Since there exists the idea of "1/3" and within the frame work of mathematics we've constructed is it consistent, then there exists the number "1/3".

Maybe I'm guilty a little bit of both, so could you verse me a little? Like 1=1. That's defining 1 in terms of itself. Or 1=2-1. But there is this ideal scope that math holds.

1 satisfies (x-1)=0. Sounds a little circular, but it is not. x^2+1=0 defines "i" and 3x-1=0 defines 1/3. If I get an equation (3x-1) where the x happens to be 1/3 I know that this (3x-1) is equal to 0. I know how this "1/3" behaves, and therefore can use it in equations.

The exact definition of 1 is a little more complex and is buried deep in the construction of numbers because of 1's unique properties.

No. That's called rounding. Not a true terminating decimal.

There is no rounding. If there is rounding then 0.1 is base 3 is not equal to 1/3, so 0.1-1/3 in base 3 has a non-zero value. What is it?

It is zero, therefore they are equal. There is nothing special about Base 10, it just happens we have 10 fingers. If we had 12 fingers, we'd have a base 12 system probably, and in that 1/3=0.4, 1/4 = 0.3. 1/5 would have an infinite decimal expansion.

If a number is rational (ie it can be expressed as a fraction) there ALWAYS exists a base in which that fraction has a terminating decimal. People cling to Base 10 as some kind of "universal base" because its so incredibly ingrained into their understanding, yet there is nothing special about it, just like 1 metre is not a special length, its just something thats the vresult of history.

Did I cover it when I talked about the idea of a third? The idea of a third is ideal, or perfect. Taking away 25 mm of a 75 mm ruler would be a third. Sure, if you want to boost up the magnification, it would never be truly a third. But it's all relative.

As you say, taking 1/3 from something in reality isn't perfect, but then neither is taking 1/2 from something, you'll always get error when you look hard enough.

Can you imagine some magical universe in which its possible to take exactly 1/3 from something? Or 1/2, or 1/7 or 1/3988? Well that would be the mathematical universe, where since we can imagine it, it is possible (within non-contradicting constraints).

Ah. So anything past a natural number is an approximation or an ideal?

Natural numbers are ideals too. But they are the closest link between mathematics and reality. All numbers are that, numbers, which are mental constructs. We happen to use the same words for them as in mathematics and reality. I could call 1 "alpha", 2 "beta", 3 "gamma" etc, and through exactly the same logic as the derivation of 1+1=2 arrive at alpha+alpha = beta. If I say "1+1=2" its just easier for people to follow. The numbers are representations of non-existant entities, we could call them anything we wish. Past history dictates that we happen to use the same names for the individual natural numbers as we do for objects.

Is that making much sense?

Like? Primes are fascinating, although I'm unsure of their significance.

Among other things, primes are the basis for all modern coding. Internet SSL systems use primes. Internet shopping wouldn't exist without prime research.

 

[Cex]

I didn't say that. You're making assumptions.

Here is a quote of you saying that you can cut a ruler into fractions that are represented by terminating decimals, but not into thirds:

I can cut 6.15 mm out of my ruler.

I cannot, however, cut my ruler into three 1/3's. I will never get exactly 3 thirds of my ruler cut... It simply does not exist in our reality.

You're going to need to stop being so hostile if you want anyone to consider what you're posting.

You consider that hostile? You ain't seen nothing yet, sonny-jim.

No. That's called rounding. Not a true terminating decimal.

This quote from you was in response to me saying that in base three, 1/3 = 0.1. This is not rounding at all. This is an exact mathematical expression. Perhaps you are a bit too used ot using the decimal system, and don't know how base three works? I'll explain it for you:

A 'base n' expansion of a number might be written in the form "ab.cde". What this means is "a*n + b + c*(1/n) + d*(1/n)^2 + e*(1/n)^3." For example, the decimal (base ten) expansion 32.4 means "3*10 + 2*1 + 4*(1/10)", which sums exactly to the number thirty-two-point-four.

Similarly, the base three expansion 21.12 means "2*3 + 1*1 + 1*(1/3) + 2*(1/9)". In decimal, this is the number 7.4444.......

Notice how in decimal (base ten) it's a never-ending number (what you'd call an unreal number), but in base three it is represented by the terminating expansion 21.12. This should make it clear why the process of expanding a number in a certain base doesn't really tell you very much about that number. I suggest you have a look at the first two links that AlphaNumeric posted.

And sorry, if your post has one more hostile remark, I won't respond back to your comments. You can either have a civilized debate or post attacks on the internet to boost your ego. "The ball is in your court".

Actually, I'll be as hostile as I like. Whether you read my arguments or not is up to you, but the fact remains that they're there whether you read them or not, and they're equally as compelling. If you choose to ignore them because you're afraid you might read something you don't like... well, that's up to you, but it seems like a very immature way to go about a debate.

 

[sexyanon2]

This is all mathematics is, ideas. Concepts in our minds. Yes, in reality, some of these concepts do not apply, but in our minds, we are not confined by reality. Since there exists the idea of "1/3" and within the frame work of mathematics we've constructed is it consistent, then there exists the number "1/3".

So then, 1/3 is equally an idea as the number 5 is?

See, what I'm getting at is: if you "remove a third" of something, either a third of a ruler or a third of 3 apples, are you literally removing a third? You're literally removing 25 mm or 1 apple. The idea surrounding this action that a 3rd is being removed still exists. But if someone tells you to remove a third of the ruler, you're going to need to get exact numbers in order to remove that portion of the ruler. Or you need the exact number in order to remove the one apple.

Beyond that accuracy, nothing changes in the behaviour of systems and the experimental error in measurements is far more important.

What about quantum physics?

There is no rounding. If there is rounding then 0.1 is base 3 is not equal to 1/3, so 0.1-1/3 in base 3 has a non-zero value. What is it?

It is zero, therefore they are equal. There is nothing special about Base 10, it just happens we have 10 fingers. If we had 12 fingers, we'd have a base 12 system probably, and in that 1/3=0.4, 1/4 = 0.3. 1/5 would have an infinite decimal expansion.

First, I don't understand the base 12 example.

Second, I'm not sure what the bases have to do with not rounding. Is 1/3 only .33 bar in base 10, but exactly .1 in base 3?

Do you want the axioms or the derivation of 1+1=2 from the axioms? The derivation is 362 pages long of mathematics which gets highly complex.

Maybe when I'm bored on a dark, stormy night I'll PM you for that.

If a number is rational (ie it can be expressed as a fraction) there ALWAYS exists a base in which that fraction has a terminating decimal. People cling to Base 10 as some kind of "universal base" because its so incredibly ingrained into their understanding, yet there is nothing special about it, just like 1 metre is not a special length, its just something thats the vresult of history.

I'm confused then. Is this some form of relativity? Some numbers in some bases, or "realities" of math, are ending, but can go on forever in other bases? Is there one base that has all numbers ending?

As you say, taking 1/3 from something in reality isn't perfect, but then neither is taking 1/2 from something, you'll always get error when you look hard enough.

Can you imagine some magical universe in which its possible to take exactly 1/3 from something? Or 1/2, or 1/7 or 1/3988? Well that would be the mathematical universe, where since we can imagine it, it is possible (within non-contradicting constraints).

I think I'm saying that fractions don't exist in reality (i'm not trying to be patronizing. only trying to figure out where my thoughts are). They're ideas.

Now if fractions are ideas, what seperates them from ending decimals or whole numbers? You can get a third of a ruler, or a half of a ruler, no problem. You just have to measure it first, thus you'd bring in real numbers, not ideas.

And by ideas I mean that they only exist in comparison. Hopefully I'm using the right words.

Taking away one apple from three apples can be seen clearly. You can then equate this idea into being a third of the apples being taken away. But without the one apple being taken away, the third of the apples being taken away is merely an idea.

Hopefully I'm making sense. These are new grounds for me plus I'm a terrible explainer.

Natural numbers are ideals too. But they are the closest link between mathematics and reality. All numbers are that, numbers, which are mental constructs. We happen to use the same words for them as in mathematics and reality. I could call 1 "alpha", 2 "beta", 3 "gamma" etc, and through exactly the same logic as the derivation of 1+1=2 arrive at alpha+alpha = beta. If I say "1+1=2" its just easier for people to follow. The numbers are representations of non-existant entities, we could call them anything we wish. Past history dictates that we happen to use the same names for the individual natural numbers as we do for objects.

Is that making much sense?

Nononono. Well, yes in that what you're saying makes complete sense. Alpha+alpha = beta. Yes, I agree. And pure mathematics with that is correct and fine by me.

But how are these entities unknown of they can be related to the real world? If I have one apple in a basket and I add another apple to that basket, I'll clearly get two apples. Now I can say I have .523 apples to measure one apple, but as you say, the numbers are mental constructs. Why not use our fingers?

Among other things, primes are the basis for all modern coding. Internet SSL systems use primes. Internet shopping wouldn't exist without prime research.

Like security?

Here is a quote of you saying that you can cut a ruler into fractions that are represented by terminating decimals, but not into thirds:

I've updated what I was saying. You can either take it or leave it.

About your base ideas, I talked to AN about that.

but it seems like a very immature way to go about a debate.

It's immature to expect the other person to refrain from throwing personal attacks due to wild emotions? Then is it mature way to approach a debate by attacking people?

Whether you read my arguments or not is up to you, but the fact remains that they're there whether you read them or not, and they're equally as compelling.

No. Incorrect. If you state something that is true while flaming someone, that person is more likely to disregard what you're saying because you're flaming them. You don't care?

Don't worry. Neither do we.

 

[Cex]

Second, I'm not sure what the bases have to do with not rounding. Is 1/3 only .33 bar in base 10, but exactly .1 in base 3?

Yes.

It's immature to expect the other person to refrain from throwing personal attacks due to wild emotions?

No, but it's foolish to ignore what someone has said because you're scared of reading something that offends you. I get heated when I debate, especially when I'm speaking to someone who is saying things that are plainly wrong. I realise now that you don't have, or claim to have, much expertise in mathematics, unlike the D-man. In that case I'm prepared to be patient - it's only when people claim to be experts, and still talk utter clap-trap, that I get annoyed.

 

[sexyanon2]

No, but it's foolish to ignore what someone has said because you're scared of reading something that offends you. I get heated when I debate, especially when I'm speaking to someone who is saying things that are plainly wrong. I realise now that you don't have, or claim to have, much expertise in mathematics, unlike the D-man. In that case I'm prepared to be patient - it's only when people claim to be experts, and still talk utter clap-trap, that I get annoyed.

Look how much substance was written there because of your emotions.

No, but it's foolish to ignore what someone has said because you're scared of reading something that offends you.

I'd be more scared of reading something covered up and smudged by emotions wailing out of control. Can you deny the futility and detriment on the quality of the argument and the productivity of it?

 

[David]

^^ Thanks for the reprival, and rational approach.

Yes.
No, but it's foolish to ignore what someone has said because you're scared of reading something that offends you. I get heated when I debate, especially when I'm speaking to someone who is saying things that are plainly wrong. I realise now that you don't have, or claim to have, much expertise in mathematics, unlike the D-man. In that case I'm prepared to be patient - it's only when people claim to be experts, and still talk utter clap-trap, that I get annoyed.

Yet, still you expect something from me, when I have never once been approached on the basis of logic, and rational discussion. It started with my opinion on Pi, which will always stand.

It's also foolish to assume things about others, and then to berate them endlessly with out even listening to their points. As far as you being patient, do you really think anyone fucking cares? You are nobody, and nothing. When you realize this, you'll probably be an old fucker on the academia payroll somewhere, and confused why no one listens to you, or if they do it's with bored reverence, because respect for what you have accomplished is so ingrained in the process of academia, which is the biggest farse of them all.

I find it amazing if someone doesn't agree with you, you automatically refuse to acknowledge they may know something, perhaps something you don't, or even something about what you are professed in.

Personally that post was aimed at everyone, so don't get your panties twisted. No one ever took the time to understand the point I was trying to make. I was flamed immediately. Which I returned, promptly. I am guilty of this, yes, but I refuse to deal with people that can't even hold a rational discussion on the internet. Which is why I now no longer respond to anything you guys make take part in. You guys sould really look elsewhere on the net, I've post a great site in the CE&P for news once. We are doing great things on that site with developing new approaches, and everything. Then again, do you guys understand the Gestalt approach.

You getting annoyed is funny, it makes you seem even more like an anally retentive bitch. You are still a student that doesn't know his ass from the hole he pulled his dick from. As far as actually work in the field, I doubt you have much, other than with math, which we have already gone over is farther from reality than most would believe. This is my argument against the way things are being done. You seperate, and categorize everything, but miss the whole picture that is right in front of you. You guys have no insight, and it's great you are going for maths, because I can see you guys doing much else, because of your lack of insight into reality from your posts.

Physics is about this insight, not chalk on the chalk board, and all that crap with symbolism, and irrational field's being applied as tensors. It's look at how things are correlating in reality, and understanding what is going on, and explaining what you see to everyone else.

Yes, this includes all of you. Zorn I don't know well enough to make that judgement, and personally if he's any way like his posting, I'd rather not. I hope he can still think on his own, instead of following his indoctrinational teaching.

 

[compact]

It started with my opinion on Pi, which will always stand.

You can make as many melodramatic posts as you want, but it's not going to change the fact that there is a unique real number which we call pi, and that it's value is determined explicitly and entirely by its defining properties.

 

[David]

^^ I love you soo much, you still keep using that word "define" improperly. Give me your address I'll send you a good book on defining things, and the tricks of language.

 

[PGTips]

started with my opinion on Pi, which will always stand.

As Compact says, this is the crux of your problem. You believe it is a matter of opinion about Pi. You keep mentioning logic, but do not get that "Pi" and all the related work were arrived at, step by step, through logic. Over the last 300 years that logic has been checked again and again and again by people who are better than you at both mathematics and logic.

You yourself said "Trust has no bearing in science.". Your opinion has no bearing on mathematics.

but I refuse to deal with people that can't even hold a rational discussion on the internet.

Perhaps you'd like to notice my last few posts in this thread which take the time to give (very long) explainations, links and attempt to answer each of Sexyanons (and your own) points and misconceptions. Sexyanon seems to be able to converse with myself, because he listens to what I have posted, and thinks about them. You do not.

You are nobody, and nothing.

A year from now, Cex, Euler and I will have degrees in mathematics (I'm not sure how far Compact is in his PhD) and you'll still be ranting about how amazing you are, and how you've got all the answers, all to no avail.

I think thats known as "Having the last laugh"

 

[PGTips]

^^ I love you soo much, you still keep using that word "define" improperly. Give me your address I'll send you a good book on defining things, and the tricks of language.

Give me your address and I'll send you a dictionary with the correct definition of "perfect", because your black hole description certainly wasn't.

So then, 1/3 is equally an idea as the number 5 is?

Excluding a typo I said "If it is consistent". You are free to define something in mathematics, provided that you can show it can then not be used to contradict something from previous work. Going about proving a new idea or method is consistant with other areas of mathematics is probably one of the most maticulous, painstaking things mathematicians do. Every possible use is considered and examined. Often a new idea can take a few years before its announced because they must make sure its consistent.

What about quantum physics?

Thats part of the "experimental error". If your quantum fluctuations change the values of a result in say the 9th decimal place onwards, you are going to have to take Pi to more than 9 places to make sure that almost all the error lies in the quantum fluctuations. If you take Pi to 15 decimal places, you've got errors 1 millionth the size of the quantum fluctuations. If you're really bothered, go to 20 places, and thats 100 billion times smaller. The slight discrepency of your taken value of Pi and the actual value means nothing, the quantum fluctuations of a system make it irrelevant.

But then that is physics, and has no bearing on wether Pi exists or not in mathematics.

First, I don't understand the base 12 example.

Binary is Base 2. That means you count 1, 10, 11, 100 etc. Since you can't have "2", you have to use 1's and 0's to count. In base 3 (perhaps called "Trinary") you count 1, 2, 10, 11, 21, 22, 100 etc
Work your way up to base 12 and you have (I'm going to use "A" to represnet the number ten and "B" to represent eleven)
1,2,3,4,5,6,7,8,9,A,B,10,11,12,......,19,1A,1B,20 etc

Rather than having our "digits" as 0,1,2,3,4,5,6,7,8,9, we have 0,1,2,3,4,5,6,7,8,9,A,B. This alters our digits expansions too, because I can have use A and B after the decimal point. Like 0.A.

To convert this to "normal" base 10, you'd do as Cex demonstrated. In Base 10 0.34 = 3/10 + 4/100. In base 12 0.A = A/12. This means in Base 12 0.4 = 4/12 = 1/3.

Therefore, just be introducing new symbols for eleven and twelve (nothing wrong with that is there?) I've subtely altered my way of representing numbers. The numbers themselves have not changed, just how I represent them (like a fraction and a decimal are 2 ways of representing a number), and it seems 1/3 can have a terminating digit expansion.

Can you now see why this shows the flaw in thinking "It must have a terminating expansion to exist"?

I'm confused then. Is this some form of relativity? Some numbers in some bases, or "realities" of math, are ending, but can go on forever in other bases? Is there one base that has all numbers ending?

Its to do with prime factors of both a Base you are working in, and the number in your fraction.

10 = 2*5, so Base 10 will only have terminating digit expansions for numbers whose ONLY factors are 2 and 5, like 8 =2*2*2, or 25 = 5*5.

If I have a Base 7 system, because 7 is prime, only numbers which are a power of 7 will have terminating decimals, so 1/7 = 0.1 and 1/49 = 1/(7*7) = 0.01, but anything which has another prime factor other than 7 will be non-terminating. 1/2 cannot be expressed as a terminating decimal!!

Better Base systems include Base 8, since its a power of 2 and Base 60. 60 = 2*2*3*5, so you'd get terminating decimals for 1/2, 1/3, 1/4, 1/5, 1/6, 1/12, 1/15, 1/20, 1/30, and all numbers which have prime factors 2, 3 or 5, like 1/9.

The ancient Babylonians used to work in Base 60, and I think its where we get out "minutes, seconds" from.

Base 10 is actually a very clumsy and bad base to use. People do not realise it because they automatically think in Base 10 and often cannot see how another system would work. As I said before, if we had evolved with 12 fingers, 1/3 would have a terminating decimal. Infact you'd probably be arguing the "non-existance" of 1/5 because in base 12 1/5 is an infinite digit expansion.

Now if fractions are ideas, what seperates them from ending decimals or whole numbers? You can get a third of a ruler, or a half of a ruler, no problem. You just have to measure it first, thus you'd bring in real numbers, not ideas.

You keep bringing up measuring a ruler, as if a mathematician needs to do that when he divides something by 5 or multiplies by 2/7. These are thought experiments where physical constraints don't apply.

Fractions are an extension of integers. They take the definition of integers and develop it further. Some fractions have terminating decimals, some do not. ALL have a terminating decimal in some Base system or other (though not at the same time).

Why not use our fingers?

Apples, fingers, its all good I just think apples are the traditional way of describing these things. That or oranges :D

Like security?

Yes. The method involves doing a mathematical operation which is easy to do one way, but hard to do the other. It wasn't thought one such thing existed that would be practical for computers, but then someone realised about primes. If you take 2 huge primes (100+ digits each) and multipply them together you get another huge number with only 2 factors. This can then be used to encode your data, and send it over distance. Should anyone intercept it, they can only read your data by "unlocking it" by knowing the prime factors of your "key". It takes a hell of a lot of trial and error to find these 2 primes. Its not unbreakable, but sufficently hard to put off people scamming for credit card numbers. Banks use numbers thousands of digits long!

Thats the vague idea, the specifics are a little more complicated, but I'll be happy to elaborate if you want

 

[Cex]

I'd be more scared of reading something covered up and smudged by emotions wailing out of control. Can you deny the futility and detriment on the quality of the argument and the productivity of it?

Well, yes, actually. My emotions never "wail out of control". Admittedly, if I were to say the things I do in real life, then I'd be guilty of being hot-headed, ill-tempered and not a particularly good debater. However the odd sly remark over the internet, when I have time to think about it and can post in a rational manner, is entirely different. I'm completely calm and serene as I type this, and if I called you a fuckwit (hypothetically, of course) that wouldn't change that at all.

Yet, still you expect something from me, when I have never once been approached on the basis of logic, and rational discussion.

I'd expect some semblence of humility when it's apparent that you're stubbornly arguing against five people, one of whom has a PhD, one of whom is working towards a PhD, and three of whom are soon to be holders of a Masters degree, all in the field that you're debating. Your comment "my opinion will always stand" reveals a lot about your character - it reveals that you're stubborn, bone-headed and will not give others' opinions a chance. All of your arguments involving maths (and some which don't) are fundamentally flawed, and we've pointed this out to you repeatedly. Yet you still keep repeating the same tired nonsense about terminating decimals and ideals. I've lost count of the number of times that we've tried to explain the the decimal representation of a number is not the be all and end all, but you keep ignoring it.

As far as you being patient, do you really think anyone fucking cares? You are nobody, and nothing. When you realize this, you'll probably be an old fucker on the academia payroll somewhere, and confused why no one listens to you.

Thank you for your calm, measured and objective opinion. Actually, I probably won't be on any academic payrolls anywhere. Unless something cataclysmic happens, I have no wish to go into an academic career. It's just something that I happen to find diverting, and useful, at the moment. Never mind though - it's ok to "make too many assumptions", right? After all, "you guys in the UK do that all the time"

I find it amazing if someone doesn't agree with you, you automatically refuse to acknowledge they may know something, perhaps something you don't, or even something about what you are professed in.

Without even a hint of a sensible argument to back them up, yes, I would assume that someone arguing against me knows less than I do. If they can convince we with a powerful argument which I can't make a case against, then I would admit that they know more than me.

You getting annoyed is funny, it makes you seem even more like an anally retentive bitch. You are still a student that doesn't know his ass from the hole he pulled his dick from.

I thought I was supposed to be the crazed, ranting, ill-tempered bigot who mouthed off at every opportunity? Calm down D-man, you'll give yourself a hernia.

As far as actually work in the field, I doubt you have much, other than with math, which we have already gone over is farther from reality than most would believe.

Where have I ever claimed that I do? I'm not the one professing to have solved the greatest problem in physics, and be well on my way to solving the greatest problem in maths, remember.

 

[Cex]

^^ I love you soo much, you still keep using that word "define" improperly. Give me your address I'll send you a good book on defining things, and the tricks of language.

Does this offer extend to me, also? I'll be glad to PM my address to you. I'll even cover postage.