A postulate and three laws.

[Ronald Hyde]

We make a postulation: That in some deep sense

the World is made of mathematical relationships.

We state three laws:

<1> Every mathematical relation permitted by Logic must occur.

<2> Time is just a number, an integer.

<3> Everything that occurs in Nature is a function of Time.

 

<1> says that the World is a mathematical-logical construct, that any mathematical

relationship permitted by logic must occur in Nature. Logic is simple Boolean logic, which

can be applied to mathematical expressions.

 

<2> says that time is just an ordinary integer, its value is about 10^41 at present

and increasing by about 10^25 per second.

 

<3> says that everything that happens in Nature can be expressed as a function of time.

If F is a function that describes something in Nature, it is always F(t). If

F = F(t,x,y, z) then ultimately x = x(t), y = y(t) and z = z(t), so that anything that

happens in the World is strictly always a function of time.

 

This is all that we need to build a valid picture of the World, the rest is just deduction

and the application of logic, which is Boolean logic and mathematics.

[studiot]

Does not Godel's Theorem invalidate your proposal?

 

 

[Ronald Hyde]

Does not Godel's Theorem invalidate your proposal?

 

Do you know what Godel proved? He proved that any formal system is contained in a larger formal system.

That proof fits this view of the world to a T. It would mean there is only one Universe, the one described by

these principals, and it contains everything that could ever happen.

[studiot]

Do you know what Godel proved? He proved that any formal system is contained in a larger formal system.

 

I beg to differ.

[Ronald Hyde]

I beg to differ.

That really doesn't say anything. If you have a line of reasoning and some facts, please let us all know. What do you think that Godel proved?

[studiot]

That really doesn't say anything.

 

Yes it does, in standard London English it means that I disagree (politely).

 

 

Do you know what Godel proved? He proved that any formal system is contained in a larger formal system.

 

 

 

My understanding of Godel's theorem is that it leads to the opposite conclusion - that is there is no larger system that can contain everything.

 

 

 

However it is up to you to demonstrate the correctness of your proposal not for me to provide 'facts etc'

 

I am simply inviting you to test it against Godel's theorem.

 

 

Since your set of propositions is a formal system in the Godel sense and allegedly covers everything, where would you place the proof of the self consistency and the true but unprovable facts?

 

 

The danger of offering any form of universal set is that it runs into a Russel type paradox when Godel is applied.

Edited August 3, 2012 by studiot

[Ronald Hyde]

My understanding of Godel's theorem is that it leads to the opposite conclusion - that is there is no larger system that can contain everything.

 

No, that's not what it says. It says that any finite procedure cannot prove everything about relations among the natural numbers ( integers ), that

there are always things that are true, that can only be proven in a larger system. So there is an infinite hierarchy of logical systems related to

relations between the natural numbers. So it fits into this scheme very well, thank you!

 

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

 

And thank you for replying. I hate it when someone says something and has no intention of supporting it.

[qsa]

 

 

This is all that we need to build a valid picture of the World, the rest is just deduction

and the application of logic, which is Boolean logic and mathematics.

 

 

What are you waiting for then? What is an electron for a start.

 

 

 

 

 

[Ronald Hyde]

What are you waiting for then? What is an electron for a start.

 

The electron isn't a good place to start. It will take quite a few steps, levels of abstraction if you will, to get to the electron.

Better places to start would be using the Heavisides Unit Step Function and treat the Universe as an initial value problem, or to

build the Lorentz group up from more elementary groups and use it to construct a model. Ideally it would be nice to have a

model that could be run as a computer simulation, so that you could view, as it were, the first moments of Existence.

[qsa]

 

Better places to start would be using the Heavisides Unit Step Function and treat the Universe as an initial value problem

 

can you elaborate with more than just few lines, something useful.

 

 

 

[ecoli]

if time is an integer than how do you represent time between the seconds?

[studiot]

I'm sorry to tell you that if your reference genuinely states Godel as you have done, then you have been misled.

 

Firstly the theorem applies to more than numbers it applies to any system of logic that conforms to the formal definition.

 

In particular

 

In a system of logic or mathematics there must be true but unprovable statements and the self consistency of such a system cannot be proven true within that system.

 

You are implying from this that there must be a larger system which contains both the necessary proofs and the original system.

 

However this is not guaranteed by the theorem. It does not preclude it either.

 

Further the attempt to establish such a greater set, leads inevitable to an infinite series of such sets by application of the same theorem and finally to a Russell type paradox as I said.

 

By all means discuss, but please be less condescending about it.

[juanrga]

We make a postulation: That in some deep sense

the World is made of mathematical relationships.

We state three laws:

<1> Every mathematical relation permitted by Logic must occur.

<2> Time is just a number, an integer.

<3> Everything that occurs in Nature is a function of Time.

 

<1> says that the World is a mathematical-logical construct, that any mathematical

relationship permitted by logic must occur in Nature. Logic is simple Boolean logic, which

can be applied to mathematical expressions.

 

<2> says that time is just an ordinary integer, its value is about 10^41 at present

and increasing by about 10^25 per second.

 

<3> says that everything that happens in Nature can be expressed as a function of time.

If F is a function that describes something in Nature, it is always F(t). If

F = F(t,x,y, z) then ultimately x = x(t), y = y(t) and z = z(t), so that anything that

happens in the World is strictly always a function of time.

 

The three are plain wrong. Consider <2> any undergraduate textbook on basic physics explains, in the introductory chapters, that time is not a mere number. E.g. 200 does not represent time in physics. If you have not a textbook at hand start here with a discussion of what is a physical quantity.

 

This is all that we need to build a valid picture of the World, the rest is just deduction

and the application of logic

 

Already Pauli, the famous Nobel laureate, replied to arrogant statements as this in a very humorous way. His quote is very famous:

 

[Ronald Hyde]

I'm sorry to tell you that if your reference genuinely states Godel as you have done, then you have been misled.

 

Firstly the theorem applies to more than numbers it applies to any system of logic that conforms to the formal definition.

 

In particular

 

In a system of logic or mathematics there must be true but unprovable statements and the self consistency of such a system cannot be proven true within that system.

 

You are implying from this that there must be a larger system which contains both the necessary proofs and the original system.

 

However this is not guaranteed by the theorem. It does not preclude it either.

 

Further the attempt to establish such a greater set, leads inevitable to an infinite series of such sets by application of the same theorem and finally to a Russell type paradox as I said.

 

By all means discuss, but please be less condescending about it.

 

Sorry, I'm not trying to be condescending, but I think things through very carefully, so I don't appreciate it when I feel that someone is being glib or dismissive.

 

I know about this larger definition of Godels proof, but I wasn't trying to write a book about it. Our notion of a 'formal system' began with the mathematicians

of the Arabian Golden Era, who added the decimal point and zero to the Indian system of positional notation, so that the basic operations of arithmetic could

be performed by simple written procedures. They called these procedures 'algorithms', a word which we use today. They also found that they could substitute

x, y, z etc. for the actual numbers in an algorithm, perform operations with them and replace them with the actual numbers at the end of the operations.

This method of formal substitution is where we get the notion of a 'formalism'. All the operations of mathematics are defined over the 'natural numbers', i.e.

the integers. They also gave us the word Algebra which is a system of formal procedures for solving problems and expressing results.

 

So everything that I've said, and that you've said about Godels proof is true.

 

The three are plain wrong. Consider <2> any undergraduate textbook on basic physics explains, in the introductory chapters, that time is not a mere number. E.g. 200 does not represent time in physics. If you have not a textbook at hand start here with a discussion of what is a physical quantity.

Oh, it's you, you love to play the devils advocate, don't you. Consider a line from Porgy and Bess, "They been tellin' all you chillun, that the devil is a villun, but it ain't necessarily so".

I've read lots of textbooks, I have my own collection, including the wonderful Feynman Lectures. If the textbooks are all right why don't we have a complete description

of the world? Obviously there are some kind of shortcomings in the textbooks. And yes, I know about physical quantities and dimensional relationships, all those kinds of things,

so I'm going to tell you right now that the three are right, and if the text books differ they are wrong!

 

We live in a very strange world, a world where a billion people can be wrong and one person can be right. If he comes along and shows them the error

of their ways, he may become the hero of the hour, or he may have his head chopped off for heresy. That's the way it works.

[juanrga]

I've read lots of textbooks, I have my own collection, including the wonderful Feynman Lectures. If the textbooks are all right why don't we have a complete description

of the world? Obviously there are some kind of shortcomings in the textbooks. And yes, I know about physical quantities and dimensional relationships, all those kinds of things,

so I'm going to tell you right now that the three are right, and if the text books differ they are wrong!

 

<1> Textbooks' goal is not to provide "a complete description of the world". Their goal is much more modest and usually explained in the preface.

<2> You claim you have "read lots of textbooks" but you write "and if the text books differ they are wrong", which implies that you do not even know if the the textbooks differ from what you wrote [*].

<3> You can say otherwise, but your 'laws' continue being wrong.

 

[*] Yes they differ.

[studiot]

All the operations of mathematics are defined over the 'natural numbers', i.e.

the integers.

 

Actually this isn't strictly true.

 

It is certainly true that the natural numbers are very important in mathematics and operations such as induction can be defined/described in terms of them.

 

You should also be aware that there is a difference in mathematics between the natural numbers, which do not include zero, and the integers, which do.

 

However there are operations that are independent of numbers of any sort.

 

Translation, reflection as in 'the transitive property' and 'the reflexive property' are fundamental operations which are examples. There are many more, including some fundamental ones due to symmetries.

 

There are other operations such as counting, which can be defined as putting into one to one correspondence with N, which are certainly defined over the natural numbers, but cannot be applied to all mathematical objects, some are uncountable.

 

Having got that discussion on terminology out of the way let us fast forward from the ancient civilisations to the late 19th and early 20th centuries.

You have not addressed my point on Russell's paradox and the universal set in relation to your proposition.

Edited August 4, 2012 by studiot

[Ronald Hyde]

Actually this isn't strictly true.

 

It is certainly true that the natural numbers are very important in mathematics and operations such as induction can be defined/described in terms of them.

 

You should also be aware that there is a difference in mathematics between the natural numbers, which do not include zero, and the integers, which do.

 

However there are operations that are independent of numbers of any sort.

 

Translation, reflection as in 'the transitive property' and 'the reflexive property' are fundamental operations which are examples. There are many more, including some fundamental ones due to symmetries.

 

There are other operations such as counting, which can be defined as putting into one to one correspondence with N, which are certainly defined over the natural numbers, but cannot be applied to all mathematical objects, some are uncountable.

 

Having got that discussion on terminology out of the way let us fast forward from the ancient civilisations to the late 19th and early 20th centuries.

You have not addressed my point on Russell's paradox and the universal set in relation to your proposition.

You can start with a zero and a one, 0 & 1, if you wish they can be expressed if binary form. You also start with the basic mathematical operation of addition. You can make a new number by adding 1 to 1, and you can continue that indefinitely to make all of the natural numbers. You can define an inverse operation to addition, which is subtraction. You can define another operation which is multiplication and an inverse operation to multiplication, which is division. So just starting with 0 & 1, or even only with 1, you can define all the operations over all types of numbers, fractions, real numbers, you can extend the expressions to complex and imaginary numbers, ect.. So you can, by construction and definition build ALL of mathematics, including reflection, etc. , from just 1 and/or 0 and the basic operations of math.

 

I much prefer the definition of a set that is used in group theory, a group is a set with defined rules of combination. It can always be considered a 'member of itself' without any contradiction, it may have subgroups, which are members of it, and it may be a member of a larger group. In fact, it's very hard to define a group, perhaps impossible, which is not a member of a larger group. To me Russels paradox has always been a non-starter.

PS: This is why I know that time is a number; There are other operations such as counting, which can be defined as putting into one to one correspondence with N, which are certainly defined over the natural numbers, but cannot be applied to all mathematical objects, some are uncountable.

If it weren't the world would be a completely chaotic and disorderly place.

[Bignose]

<2> Time is just a number, an integer.

 

Consider the chemical reaction

 

CHCl₃ + Cl₂ --> CCl₄ + HCl

 

this reaction is known to have a rate constant that is half-order in the concentration of Cl₂

 

If for a given amount of CHCl₃ and Cl₂, you find that is takes 1 minute to complete the reaction, if you keep all the conditions the same except for halving the amount of Cl₂, how long does it take to complete the reaction? [math]\sqrt{2}[/math] minutes.

 

[math]\sqrt{2}[/math] is irrational and cannot be expressed using just integers. Doesn't this invalidate your postulate #2?

Edited August 4, 2012 by Bignose

[Ronald Hyde]

[math]\sqrt{2}[/math] is irrational and cannot be expressed using just integers. Doesn't this invalidate your postulate #2?

Not in the least does it invalidate it, since the basic unit of time is about 10^-25 seconds you can approximate that reaction rate very closely indeed in one minutes time.

[Bignose]

Not in the least does it invalidate it, since the basic unit of time is about 10^-25 seconds you can approximate that reaction rate very closely indeed in one minutes time.

 

But, why limit yourself to approximations with integers, when you have the wealth of irrational numbers available?

 

What about a perfect wheel (circle) with a radius of 1 m rolling at an edge speed of 1 m/s, how many seconds does it take to complete 1 complete revolution?

 

And why 10^-25? Why is that so special, why not 10^-26? or 10^-24? And why does it have to be limited to integers?

[Ronald Hyde]

And why 10^-25? Why is that so special, why not 10^-26? or 10^-24? And why does it have to be limited to integers?

It's that value because observation supports that value, or approximately that value. It seems to be the minimum

amount of time that it takes an interaction to happen. We have to go with what Nature tells us, not what our philosophers

think it should be like.

 

As for why it's limited to integers, consider that people have been using the notion of continuous time to describe Nature

since Newtons days, but about year 1900 that notion started breaking down, when the quantum was discovered. And it's

still breaking down. Because it's inherently wrong it causes problems. In describing the strong interaction the notion of

'lattice spaces' has been introduced, and calculations with them work very well, the notion of lattice space includes the

idea of discrete time, so consider that there may be something to what I am saying.

 

But the real reason for discrete, i.e. incremental time is that it makes the Universe into a structure which is logically consistent,

as well as consistent with observation.

[juanrga]

The basic unit of time is about 10^-25 seconds

 

Planck time is about 20 orders of magnitude smaller than that.

 

It's that value because observation supports that value, or approximately that value. It seems to be the minimum

amount of time that it takes an interaction to happen.

 

No. 10^-25 is not "the minimum amount of time that it takes an interaction to happen". From where you got that incorrect idea?

[studiot]

You can start with a zero and a one, 0 & 1, if you wish they can be expressed if binary form. You also start with the basic mathematical operation of addition. You can make a new number by adding 1 to 1, and you can continue that indefinitely to make all of the natural numbers. You can define an inverse operation to addition, which is subtraction. You can define another operation which is multiplication and an inverse operation to multiplication, which is division. So just starting with 0 & 1, or even only with 1, you can define all the operations over all types of numbers, fractions, real numbers, you can extend the expressions to complex and imaginary numbers, ect.. So you can, by construction and definition build ALL of mathematics, including reflection, etc. , from just 1 and/or 0 and the basic operations of math.

 

 

I am aware of how to derive more complicated number systems from simpler ones thank you.

 

Why do you choose not to use the conventional definitions?

That makes discussion really difficult and excessively protracted.

 

 

[Ronald Hyde]

I am aware of how to derive more complicated number systems from simpler ones thank you.

Then why did you say that all mathematical operations could NOT be defined over the natural numbers?

 

 

Why do you choose not to use the conventional definitions?

That makes discussion really difficult and excessively protracted.

Because I'm not a conventional person. I read whatever I can find on the subject, then I start reasoning about it myself,

I look at things in original ways, I re-arrange things until I see that they are related to other things, so concepts get

merged with other concepts we already know about. I can invent notation, systems of notation are very important in

understanding. That is the process of developing new insight, which people who don't develop new insight don't and perhaps

can't understand. Insight is the process of finding that many things have the same name, or that one thing has many names.

 

Planck time is about 20 orders of magnitude smaller than that.

Planck time is something someone pulled out of a hat. I have reasons beyond any stated that support the value I gave

as the 'natural unit of time', but I will make it all clear in time. You shouldn't believe everything you read in a textbook.

Some of it may be just plain wrong. Like it was before Planck discovered the Quantum.

 

In the meantime keep reading my original post until you understand every word of it. I think I made it quite clear how

everything that happens is function of time alone, and that time us just a number, and you will see that it all leads

to a logically consistent description of the World we live in.

Edited August 5, 2012 by Ronald Hyde

[Bignose]

In the meantime keep reading my original post until you understand every word of it. I think I made it quite clear how

everything that happens is function of time alone, and that time us just a number, and you will see that it all leads

to a logically consistent description of the World we live in.

 

No. It is NOT clear. I don't know if you intend this statement to sound incredibly haughty and arrogant, but that is how it comes across.

 

Please show us why 10^-25 is "the minimum amount of time that it takes an interaction to happen". Your original post does not address this at all. You keep using phrases like "We have to go with what Nature tells us", so why don't you actually cite evidence for this number?

Edited August 5, 2012 by Bignose