The Language of Mathematics

[Mentat]

I found another of my old threads, from PF2, and decided that I would like everyone's opinion on this topic again...

Some have said that mathematics is a way of description that was invented by man.

Some say that mathematics is causal, and that the universe conforms to mathematics, instead of the other way around. I have a problem with this idea because of the points in This Thread (http://physicsforums.com/showthread.php?threadid=2424).

I personally believe that mathematics is a descriptive language - the best of them - that some are fluent in and others are not. It is a universal language, and is the only one that is without flaw (the only flaw would be in our understanding of mathematical principles). I do not believe that mathematics is man-made, but rather that it is universe-made.

But I want to see your opinions.

Note: Please give the reason for your choices, unless that reason is already covered in this post.

[wuliheron]

I choose all of the above and none of the above. Whatever mathematics may or may not be, the word is most definitely used to denote a descriptive shorthand language people use. Whether natural or man-made makes no difference whatsoever to its application and, hence, in that context is a moot point.

Alexander's mysticism is deep and rich, not unlike a twelve layer chocolate cake or a fresh cowpie. However, we already have a bulletin board dedicated to mysticism and I try not to encourage him to get to deep into it on the philosophy bulletin board. [:D]

[Mentat]

Originally posted by wuliheron
I choose all of the above and none of the above. Whatever mathematics may or may not be, the word is most definitely used to denote a descriptive shorthand language people use. Whether natural or man-made makes no difference whatsoever to its application and, hence, in that context is a moot point.

Alexander's mysticism is deep and rich, not unlike a twelve layer chocolate cake or a fresh cowpie. However, we already have a bulletin board dedicated to mysticism and I try not to encourage him to get to deep into it on the philosophy bulletin board. [:D]

Well, alrighty then. I'm glad to have your opinion, though I suspected this kind of response from you to begin with [:)].

[Mentat]

Again, I urge those of you that vote to give your reasons, unless they are already covered in my post - in which case, you should indicate this as well.

[Kerrie]

i believe mathematics is human discovered but is the language of the universe, geometry especially in my opinion is extremely descriptive of our universe...

[drag]

Greetings !

Good thread Mentat !

My opinion is that mathematics is indeed
a discriptive language. It is somewhat unique
in this role though. The reason for this
uniquness is the fact that when people
created this abstract system they wanted
to use the most basic ellements inherent in
our reasoning, rather than just discribe the
observed. The result of this was a system
that had very few and very basic axioms that
seemed to match precisely the most basic patterns
we observe in the Universe. It also meant that
this system could evolve and create many
patterns that appear to be greatly similar to those
that we find in nature and can discribe those.

What do I mean by basic ellements ?
Well, one basic ellement of all reasoning systems
we had so far is the existence of separate entities.
Others are space, time, laws/relations that control
the entities and possibly more.

Now, while these may seem totally basic and
inescapable for any reasoning - they, in fact, have
no real reasonable justification because any such
attempt based on the reasoning systems we're
aware of so far will be self-referential.
(And for Mentat: In this case this is deductive
reasoning - if I want to explain any of these
concepts I need a reasoning system and any such
system, I'm aware of at least, has these basic
components. In fact, the requirement of a reasoning
system to construct arguments is by itself basic
and self-referential.)

An intresting point is that although math is
man-made, the basis for this system in fact
lies in the data that we observe (what we may
call the observable Universe). Of course, we
probably have no way of knowing or proving
weather tommorow might bring a new type of
observation that will mathematicly be meaningless,
because it will not have the same basic concepts
(and weather that is at all possible is also
an intresting question).

Doubt or shout ! [:D]

Live long and prosper.

[Alexander]

Math obviousely is a cause of objects and phenomena in universe.

Say, take a rainbow - what causes it? Raindrops? Nope (there is no rainbow in raindrops). Sun light? Nope - because there is no RAINBOW in light yet (indeed, look at Sun).

What makes a rainbow is DISPERSION (=difference) of speed of light (for different frequencies) in water. All properties of rainbow mathematically follow from dispersion function (which in turn mathematically follows from inertia of electrons responding to variable e/m field (called light)).

Or take an atom. Where does it come from? Definitely not from electron or proton (indeed, there are NO atom neither in electron nor in proton). Atom is simply the mathematical solution for a wave trapped in 1/r potential. Harmonics of this wave (n=1,2,3...) are what we call s, p, d... orbitals.

So, "objects" and "phenomena" are at CLOSE LOOK just mathematical solutions of more basic mathematical object (say, wave) in given mathematical circumstances (say 1/r potential). Just because mathematics is simply a logic of existense.

The problem with layman understanding of math is that he CAN NOT look close (not enough mathematical education) to see that.

[drag]

Alexander, you're talking about the relation
of math and science. What is being discussed
is the relation of math and everything, not
just observation (of course you could say
there's nothing but observation, however, what
about things we haven't observed yet ?).
It is indeed possible that some new type
of observation will not at all be discribable
by math(it could be fundumentally impossible of
course, but that in turn is probably unprovable),
and hence the separation does exist.

Doubt or shout ! [:D]

Live long and prosper.

[selfAdjoint]

I voted for man-made. I know some, like Penrose, are Platonists and believe math is prior to the universe.

Here is what I think. Mathematics is a collection of ideas, ideas existing in human minds. But mathematical ideas have a property most ideas do not; they are well-defined. This means they have sharp properties and can be communicated between people without loss of sharpness. Compare this to other beloved ideas like "Justice" or "Democracy".

Now the relationships exist, at least approximately out in nature. I suppose there is a 3-4-5 triangle out there somewhere. But that is not mathematics, mathematics is when people think about such a triangle and say Aha! 3^2 + 4^2 = 5^2!

[LogicalAtheist]

I would assert the claim that math is not tied to humans whatsoever.

This could be studied well, and shown to certainly be of value. In fact, history alone helps with alot of evidence that math is NOT merely a certain species' way of looking at the world.

Thus the answer which follows evidence is it is a universal system

[plus]

Originally posted by Kerrie
i believe mathematics is human discovered but is the language of the universe, geometry especially in my opinion is extremely descriptive of our universe...


I agree.

Although it is not complete as shown by Godel.

[LogicalAtheist]

Humans did discover math. This implies math existed before humans. Indeed I have seen evidence which supports this.

Besides, this is also supported by nearly all of science. That math is "universal".

Indeed I could post here an experiment one could do to support this. As simple as it is!

[drag]

Greetings !
Originally posted by LogicalAtheist
Humans did discover math. This implies math
existed before humans. Indeed I have seen
evidence which supports this.
You mean you took a stick and poked at it ? [:D]
Originally posted by LogicalAtheist
Besides, this is also supported by nearly all
of science. That math is "universal".
Indeed. Supported, not proved (just like everything else). [;)]
Originally posted by LogicalAtheist
Indeed I could post here an experiment one could
do to support this. As simple as it is!
Please do !

Peace and long life.

[Alexander]

Originally posted by selfAdjoint
I voted for man-made. I know some, like Penrose, are Platonists and believe math is prior to the universe.

Here is what I think. Mathematics is a collection of ideas, ideas existing in human minds.

Nope. Math is just a logic coming from existence of objects. That is why any existing object obeys mathematics.

[wuliheron]

Originally posted by Alexander
Nope. Math is just a logic coming from existence of objects. That is why any existing object obeys mathematics.

Ahhh, then everything is logical and nothing is absurd! What a revelation, you should start your own religion! [g)] [g)] [g)]

[Royce]

Well...., Math is such a complex subject. But to ge to the point I think pure math is a development of man. An abstract system of reasoning with numbers and symbols that at first developed to make keep track of trade and production. Simply counting objects or amounts of things for trade and then learning to manipulate the numbers. Arithmetic and plain geometry certainly discribe real natural systems. One apple + one apple = two apples and the relationship of a circle's diameter and circumference are not the invention of man nor are they really abstract thoughts.
On the other hand number theory and algebra are pure abstractions of the human mind and are in no way representative of any natural phenomena, but based on logicical rules of relationships and maniplulations of abstract symbols not related to any real, natural occurrence. I voted that math is man made, an invention of man existing only in man's mind; but, having said that I agree completely that it was at first based on natural, real phenomina.
Man invented the names and later symbols 1,2,3....

[Iacchus32]

Sounds like the mocking birds are all out in force! ... Nahh, we all have better manners than that now don't we? ... Oh the disdain! Oh the disdain!

What you're referring to here is Capitalism anyway.

[Tom Mattson]

I voted "descriptive language--man made". It is an abstract system like logic that exists only as a mental construct. However, as Ontoplasma (where is he?) used to point out, mathematics is more than just a language, it is a science in its own right.

[FZ+]

I too voted Descriptive Language, man made. I think of maths as a subjective, but self-consistent conceptual model of real laws of the universe. Mathematics is founded on axioms and definitions than cannot really be proven as always true in the real world. It is an ideal of how the universe should be, and an assumed truth with which we can make extrapolations (predictions). The study of mathematics is based on finding the implications of our mathematical axioms. But is mathematics a science? I don't really think so, as it is a self-contained system that is not really falsifiable by evidence. The application of the model is checkable, but the fundamentals of the system itself is not.

[Tom Mattson]

Originally posted by FZ+
But is mathematics a science? I don't really think so, as it is a self-contained system that is not really falsifiable by evidence. The application of the model is checkable, but the fundamentals of the system itself is not.

You are right in that mathematics is not falsifiable. I meant that mathematics is a discipline that is systematically pursued for its own sake, and not just a language used by physicists.

[Mentat]

Originally posted by Alexander
Math obviousely is a cause of objects and phenomena in universe.

Say, take a rainbow - what causes it? Raindrops? Nope (there is no rainbow in raindrops). Sun light? Nope - because there is no RAINBOW in light yet (indeed, look at Sun).

What makes a rainbow is DISPERSION (=difference) of speed of light (for different frequencies) in water. All properties of rainbow mathematically follow from dispersion function (which in turn mathematically follows from inertia of electrons responding to variable e/m field (called light)).


Yeah, this is obviously a physical phenomenon. And, as mathematics has no physical force, it could not possibly be the "cause" of a physical phenomenon.


Or take an atom. Where does it come from? Definitely not from electron or proton (indeed, there are NO atom neither in electron nor in proton).


This reasoning is getting just rediculous (no offence). It is obvious that atoms don't come from electrons or protons, they come from the relationship between both.


So, "objects" and "phenomena" are at CLOSE LOOK just mathematical solutions of more basic mathematical object (say, wave) in given mathematical circumstances (say 1/r potential). Just because mathematics is simply a logic of existense.

The problem with layman understanding of math is that he CAN NOT look close (not enough mathematical education) to see that.

But all you have shown is that mathematics has done a beautiful job of describing the phenomena that exist in the Universe, as it is.

If the Universe were different, the logic itself would be different.

[Royce]

Your right mentat, Alexander has the cart before the horse. Talk about inconsistant resoning. Alexander has math causing the universe instead of describing it and making models of it which any scientist worth his salt repeatedly says and admits that the discription and model is not complete or exact.
Before you form your new religion of MATH, better open your holy bible THE TEXT BOOK and read it again Alexander. You've missed some very important points and misinterpeted a number of different passages and quotes.

[wuliheron]

Originally posted by Royce
Your right mentat, Alexander has the cart before the horse. Talk about inconsistant resoning. Alexander has math causing the universe instead of describing it and making models of it which any scientist worth his salt repeatedly says and admits that the discription and model is not complete or exact.
Before you form your new religion of MATH, better open your holy bible THE TEXT BOOK and read it again Alexander. You've missed some very important points and misinterpeted a number of different passages and quotes.

Alex knows perfectly well he has it backwards and is a mystic. You are sadly mistaken if you think you can convert him! Encouraging him to carry on about it on the philosophy bulletin board only supports his particular brand of mysticism over other kinds, which are not allowed to post here. However, its a unique situation because he has so little in common with the average mystic, and so much more in common with philosophers. Kinda a strange bed fellow to say the least. [6)] [6)] [6)]

[LogicalAtheist]

Royce - This place isn't here so you can convert people to your mythology, or bring us down with your antics. Try the yahoo chats for religious mythology.

[drag]

Originally posted by LogicalAtheist
Royce - This place isn't here so you can convert people to your mythology, or bring us down with your antics. Try the yahoo chats for religious mythology.
Royce, don't listen to him...[;)]

[jammieg]

I voted other, although the 3 previous choices were interesting views the dictionary is simply more defining.

Mathematics n. : the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. - Random House dictionary

Math is quantified reasoning.

[eNtRopY]

Like any language, mathematics is completely abstract. It should be no more suprising that we can describe physical phenomena using mathematics than we can with English.

What do expect? Mathematics was conceived (is still being conceived) by people who only know the ways of this universe. Therefore, it only seems natural that it would bear resemblance to phenonema of this universe. This should tell us that there is inherent limitation to the language of mathematics because it is included in the set we like to call our universe. We all know from Gödel's theorem that within a system there will always be theorems that cannot be proven or disproven using only the rules and axioms of that system....

I've seen an agent punched through a concrete wall. Men have emptied entire clips at them and hit nothing but air, yet their strength and their speed are still based in a world that is built on rules. Because of that, they will never be as strong or as fast as you can be.

eNtRopY

[wimms]

I voted for man-made description.

My opinion roots to disrespect of speciality of human position in the universe - man constantly tries to put himself into center of it.
So he found that universe is consistent. So he found a language that is consistent. Now he preaches that the language he found is fundamental of existence. Then, in tiny subscript, he mentions, oh yeah, that language describes unlimited possible worlds but we live in only one of them.

We follow boolean logic to reason. Math is also boolean. Mostly because it started from reflecting integer counts of things. At fundamental levels, we don't have that clear quantities. Yet, again, man claims boolean logic is the only possible one, because 'it is invented here'.

Math revolves around equations. Thats conservation laws hardcoded. Symmetries to be found. Now that this is found in universe aswell, its 'obvious' that they are one.
If there was different reasoning logic and based on that different math, would it be less likely to describe the world? What are the prerequisites to describe the world? Internal consistency. Thats about it, the rest is details of complexity.

But I agree that there is something underlying it all, some call it logic, some call it math. Yet there is a difference whether you try to find what universe IS compared to how it behaves. Math is good in describing how it behaves, but that doesn't mean universe is congruent with that description. imo.

[Alexander]

Originally posted by Royce
Your right mentat, Alexander has the cart before the horse. Talk about inconsistant resoning. Alexander has math causing the universe instead of describing it and making models of it which any scientist worth his salt repeatedly says and admits that the discription and model is not complete or exact.
Before you form your new religion of MATH, better open your holy bible THE TEXT BOOK and read it again Alexander. You've missed some very important points and misinterpeted a number of different passages and quotes.

You are dead wrong - either because you don't know origin of math, or you can't see a forest because of trees under nose.

Math originates from logic (it is logic). Logic originates because "stuff" exists (exists = "1", "true", "+", "yes", etc, lack of = "0", "false", "-", "no", etc). ANYTHING EXISTING no matter how complex it is thus by DEFINITION of logic obeys logic - and thus obeys math no matter how complex math is. We call this obedience "natural laws" (of conservation, of relativities, etc) and "natural objects" (raibow, atom, electron, galaxy, etc) and "natural forces" (actually just conservation interactions).

Plain and simple. Boy, how nearsighted can people be!

[wuliheron]

Originally posted by Alexander
You are dead wrong - either because you don't know origin of math, or you can't see a forest because of trees under nose.

Math originates from logic (it is logic). Logic originates because "stuff" exists (exists = "1", "true", "+", "yes", etc, lack of = "0", "false", "-", "no", etc). ANYTHING EXISTING no matter how complex it is thus by DEFINITION of logic obeys logic - and thus obeys math no matter how complex math is. We call this obedience "natural laws" (of conservation, of relativities, etc) and "natural objects" (raibow, atom, electron, galaxy, etc) and "natural forces" (actually just conservation interactions).

Plain and simple. Boy, how nearsighted can people be!

Now all you need do is define truth, then you can enlighten us all. [g)]

[Mentat]

Originally posted by LogicalAtheist
Royce - This place isn't here so you can convert people to your mythology, or bring us down with your antics. Try the yahoo chats for religious mythology.

If you would have people listen to your reasoning, LogicalAtheist, than you must be open to listening to someone else's - not just dismiss them as mere "antics", used to "convert" you to some mythology.

[Alexander]

Originally posted by wuliheron
Now all you need do is define truth, then you can enlighten us all. [g)]

As Marx said, truth is what complies with facts (observations).

Look up the definition of truth (dictionary may help in that).

[Mentat]

Originally posted by Alexander
You are dead wrong - either because you don't know origin of math, or you can't see a forest because of trees under nose.

Math originates from logic (it is logic). Logic originates because "stuff" exists...


Exactly!! You have just proven yourself wrong. "Logic originates because stuff exists, not the other way around (not "stuff exists because of Logic").


ANYTHING EXISTING no matter how complex it is thus by DEFINITION of logic obeys logic - and thus obeys math no matter how complex math is.


First of all, you are using self-referential logic here (in saying that logic obeys logic). You are just provoking any of the members here to bring up Godel's theorem, which shows that no system can be used to describe itself without running into paradox.


We call this obedience "natural laws" (of conservation, of relativities, etc) and "natural objects" (raibow, atom, electron, galaxy, etc) and "natural forces" (actually just conservation interactions).


If you would stop preaching that the natural laws and objects are "obeying logic", you'd realize that that's all you are doing, preaching.


Boy, how nearsighted can people be!

Yeah, but we still love ya.

[Mentat]

Originally posted by Alexander
As Marx said, truth is what complies with facts (observations).

Look up the definition of truth (dictionary may help in that).

Truth is what complies with observation? Bull. Heard of Quantum Mechanics?

[Alexander]

Again you MISUNDERSTAND. Logic originates NOT because stuff exists, but because something exists. Sorry for poor english.

Logic originates not from objects but from an EXISTENCE itself. Anything which has the property "to exist" shall obey logic - simply because logic is derived from labeling an existence as "1", "+", "true", "yes", etc.

Thus, any object/subject/phenomenon which exists SHALL comply with logic (math). It shall interact with other objects only as logic (=math) allows.

This is exactly what we see in universe. Only allowed by math phenomena and objects can exist.

Say, math allows a wave to slosh in 3-dimensional 1/r potential hole only very certain way (called spherical harmonics, by the way). This is exactly what we see. We call such standing wave by label "atom" and label harmonics by a word "orbitals" . First allowed by math harmonics (n=1) is labeled by us as "s orbital",second allowed by math (n=2) harmonics - as "p orbital", etc. Shape, size, appearance, etc - all properties of these harmonics are governed by math.

[Mentat]

Originally posted by Alexander
Again you MISUNDERSTAND. Logic originates NOT because stuff exists, but because something exists. Sorry for poor english.

Logic originates not from objects but from an EXISTENCE itself. Anything which has the property "to exist" shall obey logic - simply because logic is derived from labeling an existence as "1", "+", "true", "yes", etc.

Thus, any object/subject/phenomenon which exists SHALL comply with logic (math). It shall interact with other objects only as logic (=math) allows.

This is exactly what we see in universe. Only allowed by math phenomena and objects can exist.

Say, math allows a wave to slosh in 3-dimensional 1/r potential hole only very certain way (called spherical harmonics, by the way). This is exactly what we see. We call such standing wave by label "atom" and label harmonics by a word "orbitals" . First allowed by math harmonics (n=1) is labeled by us as "s orbital",second allowed by math (n=2) harmonics - as "p orbital", etc. Shape, size, appearance, etc - all properties of these harmonics are governed by math.

Are you still preaching, Alexander? No offence, but I don't have any time for being preached at. It is just as logical to say that math is just an accurate description of reality, as to say that reality obeys math. In fact, the Hurdles (http://physicsforums.com/showthread.php?s=&threadid=2424) that I have presented show some serious flaws in assuming the latter.

[Alexander]

Mentat, did you take atomic physics? Do you understand atom?

[Mentat]

Originally posted by Alexander
Mentat, did you take atomic physics? Do you understand atom?

Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?

I haven't gone to college yet, but I have a healthy understanding of physics for my age (15), I think.

[Tom Mattson]

Originally posted by Alexander
Mentat, did you take atomic physics? Do you understand atom?

Perhaps not, but I have and I say he is doing fine. Just answer his rebuttals, if you can.

[ahrkron]

You're doing great, Mentat.

I am a High Energy Physicist, and I think Alexander is not keeping up with your rebuttals to his faith.

[Mentat]

Thank you, Tom and Ahrkron. It didn't feel quite right for me to be debating with Alexander on my own.

[plus]

Originally posted by Mentat
Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?

I haven't gone to college yet, but I have a healthy understanding of physics for my age (15), I think.

Age should not come into question with this pure debate, although it does not seem necessary to have too high a level of understanding of physics for this argument.

[drag]

Greetings !

Purhaps at this partially "critical" stage
of the discussion it may be worth noting
that despite the apparent fact that math
is the best discriptive language we appear
to have so far for the type of observation
data we have - it's not that good at it's job ! [g)]

Starting from the "simplest" problems of Newtonian
Mechanics and up to the most difficult problems of
modern physics, math is certainly not perfect.
The simplest example is the 3+ body problem that
appears to be unsolvable by mathematics. Also, every
time you use integrals, for example, you're making
approximations and these are often your only way
of adressing what you observe. I'm not even beginning
to discuss stuff like the Chaos theory according to
which we can only get multi-level approximations.

The point I'm trying to make, if that's not clear
enough yet, is that if math had a direct connection
to the Universe you'd expect it to be able to explain
it better, wouldn't you ? [;)]

Live long and prosper.

[Alexander]

Originally posted by Mentat
Truth is what complies with observation? Bull. Heard of Quantum Mechanics?
A little. What about it?

[Alexander]

Originally posted by Mentat
Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?

Which rebuttals? I don't see any. Please, 1)state clearly what you want to claim. 2) provide logical or factual substantiation.

I haven't gone to college yet, but I have a healthy understanding of physics for my age (15), I think.


Good. Tell me then wnat happens if you throw a wave into 1/r potential hole?

[ahrkron]

Tell me then wnat happens if you throw a wave into 1/r potential hole?

Do you mean a physical, real wave? or when you write down the equation for it?

[Alexander]

Originally posted by Tom
Perhaps not, but I have and I say he is doing fine.

That is interesting. So, one does not have to understand physics to judge what is correct in it and what is not?

Why do we have schools and colleges then, if anyone can just say that he does not need to know relativity theory simply because he has "healthy understanding" that relativity is wrong.

I radically disagree that ignorance is a proof.

[Alexander]

Originally posted by ahrkron
Do you mean a physical, real wave? or when you write down the equation for it?

Mathematical wave. Energy conservation law for a wave is called Shred equation.

[ahrkron]

Originally posted by Alexander
That is interesting. So, one does not have to understand physics to judge what is correct in it and what is not?

His arguments attack the logic of your claims. IMO, he is doing much better than you are in that department.

Why do we have schools and colleges then, if anyone can just say that he does not need to know relativity theory simply because he has "healthy understanding" that relativity is wrong.

This does not correctly capture the logic structure of what he said.

I radically disagree that ignorance is a proof.

Again, nobody is saying that "ignorance is a proof". You either need to read posts better, or be more careful with your logic.

[ahrkron]

Originally posted by Alexander
Mathematical wave.

OK, how do you produce a "mathematical wave", how do you "throw" such an object?

Energy conservation law for a wave is called Shred equation.


And that is relevant because... ?

[RuroumiKenshin]

Originally posted by Kerrie
i believe mathematics is human discovered but is the language of the universe, geometry especially in my opinion is extremely descriptive of our universe...

I agree with Kerrie. Mathematics is a language that describes the universe, but none the less is man made. We can't think outside of our number sense because its very natural for us to see relationships between physical objects. When you think about it(that is, when you think about the temporal lobe structures involved), it is a very fascinating sense.[;)]

[drag]

Greetings !

Alexander, how come you're not responding to
what I said. I mean, if math rules the Universe
it's just a tiny little bit strange that it
can't even precisely and directly discribe
a system of 3(or more, of course) bodies circling
each other ? [;)]

Live long and prosper.

[Tom Mattson]

Originally posted by Alexander
That is interesting. So, one does not have to understand physics to judge what is correct in it and what is not?


What are you talking about? No one is saying that. Mentat is talking about something far more fundamental than the Schrodinger equation or atomic physics.

You aren't even paying attention, and meanwhile everyone is running circles around you. Get in the game, man!

[jammieg]

I can still blow my nose without knowing calculus, but would I want to?

With sureness of communication, the more atypical a view and the more relevance that view has on things, the less people will listen to it sometimes even repel from it. If you want people to listen to your views, don't be so sure Alexander- leave a bit of room for being wrong and a bit for letting others fill in the blanks with their unique views and above all be honest. In less you are quite sure, but then you had better gives some good evidence or reasoning for it.

[Mentat]

Originally posted by Alexander
A little. What about it?

Well, if you accept the Uncertainty Principle, then you know that the exact state of a particle-wave is never exactly defined. So, while I (a being composed of wave-particles) appear to be sitting at my computer (this would be an "observation"), it is not entirely so.

[Alexander]

Originally posted by Mentat
Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?


Which counter-argument(s)? You have not stated any one yet. At least I can't find it in your recent posts.

If you did then I probably ovelooked it (or you have deleted it before I look at it), so please state it again and in clear and logical way, ok?

[Alexander]

Originally posted by Mentat
Well, if you accept the Uncertainty Principle, then you know that the exact state of a particle-wave is never exactly defined. So, while I (a being composed of wave-particles) appear to be sitting at my computer (this would be an "observation"), it is not entirely so.

You are wrong. You are soooooooo big (at least 50 kg, I assume), that you wave function spreads soooooooo negligibly even during maaaaaaaaany ages of our universe. You will be sitting practically there way after yior computer and everything around long decompose due to non-related to spread of wave function reason.

[Mentat]

Originally posted by Alexander
Which counter-argument(s)? You have not stated any one yet. At least I can't find it in your recent posts.

If you did then I probably ovelooked it (or you have deleted it before I look at it), so please state it again and in clear and logical way, ok?

Well, first of all, if you look - in the "Hurdles" thread and this one - for my posts which contain a quote from you, you will find my "rebuttals" that I speak of.

In fact, I see no reason to restate all of the hurdles to your idea, just read them here: Hurdles thread (http://physicsforums.com/showthread.php?s=&threadid=2424&perpage=15&pagenumber=1).

Note: Also be sure to read the add-ons of Tom and wuliheron (and possibly others, those are just the two that I remember).

[Mentat]

Originally posted by Alexander
You are wrong. You are soooooooo big (at least 50 kg, I assume), that you wave function spreads soooooooo negligibly even during maaaaaaaaany ages of our universe. You will be sitting practically there way after yior computer and everything around long decompose due to non-related to spread of wave function reason.

You still have to defer to probability, no matter how negligible. Besides, my point is that not all is as it seems (or how it is "observed"). There may be a fourth spacial dimension. We may never actually "observe" it, but that doesn't mean that it doesn't exist.

[Mentat]

Just keeping the post up in the first page, and awaiting Alexander's response...

[Royce]

Your doing great mentat. Keep up the good work; but, you are fighting a futile battle that is impossible to win. If you can corner Aleander to the point that he actually has to answer a rebuttal he refuses to accept your answers or logic. But it is good exersize. Just don't butt your head against the brick wall named Alexander to long or hard.
You blew me away when you said you were 15. I would never have guessed from your writting or logic/philosophy that you were that yong. Well done, my friend.

[heusdens]

As to my answer (mathematics is a man made descriptive language) it was challenging to take the other alternative, that it is made by the universe.

The challenge is that we certainly claim that certain rules of mathematics are universal, that is they are the same to all inhabitants of the universe.

But in the same way we can state that the laws of physics are universal, cause they describe to the same physical world.

Physics is closely attacted to mathematics and extensively uses mathematical concepts.

[Alexander]

Originally posted by Mentat
Well, first of all, if you look - in the "Hurdles" thread and this one - for my posts which contain a quote from you, you will find my "rebuttals" that I speak of.


1) Non-physical Hurdle:

Mathematics has no physical presence (nor does logic, for that matter).


Define "physical presence".

[Alexander]

Anti"hurdles" continues. (Educating beginners about physics and math).

Originally posted by Mentat

You can say that electromagnetism (for example) is causal, because it can exert *physical* force on objects.

Mentat, next time when you claim something, make sure you know well what you are talking about, ok? Otherwise others have to waste their time explaining your errors in understanding how things actually work.

Force is not a "physical" object/subject. It is a pure mathematical phenomenon.

You need to learn origin of force (and ESPECIALLY of e/m force). It is all mathematical, there is no "physics" here. Force is just a time derivative of momentum: F=dp/dt. We simply label the rate of change of momentum by a symbol "F".

This labeleing does NOT mean that force "physically" exists. It does not.

Force has been eliminated out of list of "physical" objects since it was found that there are no forces in nature, but there are interactions of objects obeying certain mathematical symmetries (which we call conservation laws).



Mathematics, on the other hand, exists only in the metaphysical (or the realm of concepts).



Incorrect. Mathematics is way "physical" phenomena (like forces) and "physical" properties (like mass, for instance) emerge to existence. Say, if the rate of change of momentum in interactions would be zero, then there would be no "forces" in our world.

[ahrkron]

Originally posted by Alexander
Anti"hurdles" continues. (Educating beginners about physics and math).

Spare us the condescending comments. They don't make your position any less weak.

Force is not a "physical" object/subject. It is a pure mathematical phenomenon.

It is you who needs to straighten his definitions Alexander.

Directly from webster:

1a : having material existence : perceptible especially through the senses and subject to the laws of nature <everything physical is measurable by weight, motion, and resistance -- Thomas De Quincey> b : of or relating to material things.

If you want to say that force, mass, weight or heat are not perceptible through the senses, or that they are not subject to the laws of nature, go ahead; otherwise, you have to abide to the definition.

Forces, temperatures, speeds, frequencies, energy and the like are physical, whether you like it or not.

[Edit: a bracket, as usual]

[Tom Mattson]

Originally posted by Alexander
Mentat, next time when you claim something, make sure you know well what you are talking about, ok? Otherwise others have to waste their time explaining your errors in understanding how things actually work.


LOL

Alex, for someone who is totally lost in this discussion, you certainly have not lost your confidence.


Force is not a "physical" object/subject. It is a pure mathematical phenomenon.


You're begging the question here. Mentat is challenging you on this very point! Namely, that you are missing the distinction between abstract and concrete. The position he holds is that the mathematical relationship (an abstract object) describes the physical force (a phenomenon mediated by concrete objects).


You need to learn origin of force (and ESPECIALLY of e/m force). It is all mathematical, there is no "physics" here. Force is just a time derivative of momentum: F=dp/dt. We simply label the rate of change of momentum by a symbol "F".


That is just a definition. Again, you are confusing the label with the "real thing".


This labeleing does NOT mean that force "physically" exists.


Of course the label does not mean the force physically exists. The experimental evidence means that the force physically exists.


It does not.


It does so.


Force has been eliminated out of list of "physical" objects since it was found that there are no forces in nature, but there are interactions of objects obeying certain mathematical symmetries (which we call conservation laws).


The ability of humans to formulate mathematical descriptions of natural phenomena does not stop those phenomena from being natural (or "physical"). Nature does not care if we can do math. It exists independently of math.


Incorrect. Mathematics is way "physical" phenomena (like forces) and "physical" properties (like mass, for instance) emerge to existence. Say, if the rate of change of momentum in interactions would be zero, then there would be no "forces" in our world. [/B]

If you are lost in a desert and have not had water for a long time, a tall, cool glass of spherical harmonics will not save you. You need physical water for that.

No, Alex, mathematics is not "physical". At least, no one here has proven that it is.

[Alexander]

By the way, Tom, it occured to me that you interrupted my conversation with Mentat and does not even let him talk to me. Why do you do that?

I recall that in the past you also did not let others to continue their reasoning.

Can you be more civilized about that and let other people to continue expressing their OWN opinion?

[Alexander]

Originally posted by Tom
No, Alex, mathematics is not "physical". At least, no one here has proven that it is.

LOL. ([:D])

Define "physical".

[Alexander]

Originally posted by ahrkron
Forces, temperatures, speeds, frequencies, energy and the like are physical, whether you like it or not.



Let's do some THINKING here (it never hurts).

Define "force", for example. (Feel free not to use laymann blah blah blah like: "something that pushes or pulls". We are in physics forum here, so adhere to accurate definition (as you advised by the way).

[Alexander]

Originally posted by Tom
You're begging the question here. Mentat is challenging you on this very point! Namely, that you are missing the distinction between abstract and concrete. The position he holds is that the mathematical relationship (an abstract object) describes the physical force (a phenomenon mediated by concrete objects).


What? Concrete objects? Virtual photons (and virtual gravitons) are "concrete" objects? Tell us about them. What is their origin? Why do they behave certain way?

Also, what makes you think that they are NOT mere mathematical consequences of deeper reality - as everything else with known origin is?

[Mentat]

Originally posted by Alexander
Define "physical presence".

For a simple definition: The ability to exchange energy, and interact physically with other physical objects.

[Mentat]

Originally posted by Alexander
Mentat, next time when you claim something, make sure you know well what you are talking about, ok? Otherwise others have to waste their time explaining your errors in understanding how things actually work.


Why can't you just get to the point, without condesceding comments? If it's so simple to you, you should have no problem convincing me.


Force is not a "physical" object/subject. It is a pure mathematical phenomenon.


Force doesn't exist, but the curvature of spacetime does. According to alot of the candidates for the T.O.E., all of the "forces" can be explained as curvatures of spacetime itself. That doesn't mean that it is only a mathematical phenomenon, it means that it requires different mathematics (Riemann Geometry, for example) to describe it.


Force has been eliminated out of list of "physical" objects since it was found that there are no forces in nature, but there are interactions of objects obeying certain mathematical symmetries (which we call conservation laws).


So what? The "interaction of objects" is still a physical process, that is described by mathematical symmetries.


Incorrect. Mathematics is way "physical" phenomena (like forces) and "physical" properties (like mass, for instance) emerge to existence.


I know that this is your opinion, but that doesn't mean it's true. In fact, you are contradicting yourself, as you said that there were no physical phenomena (just mathematical properties), and then you said that mathematics is the way that these "physical phenomena" came into existence.


Say, if the rate of change of momentum in interactions would be zero, then there would be no "forces" in our world.

No, if there were no "forces" in our Universe, then the rate of change of momentum would be zero.

[Mentat]

Originally posted by Alexander
What? Concrete objects? Virtual photons (and virtual gravitons) are "concrete" objects? Tell us about them. What is their origin? Why do they behave certain way?


Why are you construing a "why" question as though it were scientific? Science doesn't answer "why" questions.

[Mentat]

Originally posted by Tom
You're begging the question here. Mentat is challenging you on this very point! Namely, that you are missing the distinction between abstract and concrete. The position he holds is that the mathematical relationship (an abstract object) describes the physical force (a phenomenon mediated by concrete objects).


Thanks Tom! This is the biggest "hurdle", in my opinion, and cannot be overcome.

You see, Alexander, if you deny that there is a difference between the abstract and the concrete, then you make known that you are an idealist, not a scientist.

[Mentat]

Originally posted by Alexander
Let's do some THINKING here (it never hurts).


You don't need to weaken your position any further with these kind of comments, Alexander. Lifegazer was just recently banned, and he didn't start out so many of his posts with condescending comments, like you.

[Alexander]

You don't like thinking? I do. It never hurts to think, to analyse, to investigate in depth cause(s) and reason(s) things behave certain way.

Say, what is the definition of a force?

[ahrkron]

Originally posted by Alexander
You don't like thinking? I do. It never hurts to think, to analyse, to investigate in depth cause(s) and reason(s) things behave certain way.

Drop the attitude.

[Perspectives]

Mathematics is an explanation of existence. Its complexity and level of relevance depends on need. Mathematics is to existence what the footprint is to the foot. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.

[wuliheron]

Originally posted by Perspectives
Mathematics is an explanation of existence. Its complexity and level of relevance depends on need. Mathematics is to existence what the footprint is to the foot. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.

Mathematics is symbolic of the footprint itself from a classical viewpoint. No matter how accurate our mathematical description of something might be, we cannot prove beyond a shadow of a doubt the thing itself really exists except by pointing our finger at it. When all is said and done, we can only point to a real footprint to prove they exist. Mathematics alone cannot prove anything exists in reality, thus it is considered symbolic.

A bird in the hand is worth two in the bush
And, in turn, the two in the bush are (for all I can determine) worth an infinite number of mathematical white rabbits.

[Perspectives]

Mathematics in its finest detail are composed of symbols and relationships between them. It is truly an expression of the tangible. However, most proven things cannot be held in the hand or seen by the eye but due to things in existence that can, we believe. These things are a model of what is from our perspective and while they are not the things, they like an echo are a part of it. Our existence is composed of all the things that are and the Mathematics are revealed to describe them. Without an object to examine we cannot apply math to it.

[Royce]

Ever notice how when Alexander feels he's being ganged up on and he thinks he's losing and arqument or debate he starts getting insulting. Very mature for a materialistic scientist, don't you think.

[FZ+]

Royce: It is also immature to make wry comments as to someone else's maturity from the sidelines.

Hmm...[g)]
(FZ+, now aged 4 [mental age])

[Mentat]

Originally posted by Alexander
You don't like thinking?


I don't like someone's insinuating that I, or any other member here, is not doing so. Insulting others, in this way, serves absolutely no purpose, except to irritate others.

[Mentat]

Originally posted by Perspectives
Mathematics is an explanation of existence. Its complexity and level of relevance depends on need. Mathematics is to existence what the footprint is to the foot. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.

Very good post. I like the analogy (of the foot and the footprint) too. I've been trying to defend a similar position against the belief that mathematics can actually "tell the Universe how to behave", or that there is no physical reality, but rather just mathematics.

[Perspectives]

What is possible and not is an enigma. I’m not speaking of why a person cannot flap its arms and fly like a bird. That we know is not possible. Why? We’re not equipped to do so and no one has reported it. Surely I would shout at the top of my lungs, ”I can fly like a bird, if I could.”

No, this is about the impossible being created out of nothing. On the one hand something that has not been discovered before, or should I say created, is new. Since it is new and a construct of the mind. Can we claim it never was therefore it is ours, created out of nothing? If we say YES, then we can say we operate outside of that which has been divined as ours back yard, our existence. If we say NO it has always been and it is predefined and impossible not to find if we exercise our mental ability.

When a lion drags down a deer, it does not empirically measure the deer’s health, size or weight. For the lion it is food and it will last how ever long it lasts. That is the lions existence and it’s mental extension to food. We on the other hand have selected the entire world as our food stores. We select a 32 oz. Steak, a baked potato, sour cream and a salad. That’s supper and we are satisfied. We check our mental pockets or our actual pockets and know how much money we have. We can eat till Thursday and we get paid Friday therefore we have a day of hunger or we can eat less expensive meals. I guess we should have had a hot dog instead of that large steak. We think of these things, our food supply in abstract terms days, money, where and what we eat. We developed these concepts out of want, not need. We could have still bartered or been self-sufficient. But we wanted more therefore we developed a system and nurtured friendly relations. We developed concepts that are extensions of more primitive existences. Families of Hippos allow little birds to pick parasites from their bodies, cooperation.

Where do we draw the line between saying “I did this out of nothing, it never was and it never could be at this time in this place except by me?” I claim this victory for myself at this point in existence. All may be true, except and it was specified, someone else could have discovered it, somewhere or sometime different.

But the essential point is not that it was discovered but that “what claim may be made regarding its preexistence?” Did these things exist before creation or were they there to create?

Mathematics is an expression of our existence as is physically portrayed through the universe. We merely model and explain what it is doing. If we developed a model of something that never was, or could not ever have been and has no relevance in existence then it can never be.

I believe existence and our comprehension of it as is called Reality, is only limited by our ability to emulate it through our mental constructs and exposure to others for consideration.

[wuliheron]

Originally posted by Perspectives
Mathematics in its finest detail are composed of symbols and relationships between them. It is truly an expression of the tangible. However, most proven things cannot be held in the hand or seen by the eye but due to things in existence that can, we believe. These things are a model of what is from our perspective and while they are not the things, they like an echo are a part of it. Our existence is composed of all the things that are and the Mathematics are revealed to describe them. Without an object to examine we cannot apply math to it.

Mathematics is meaningless unless we translate it into natural language. Ask yourself, "What is five?" Without reference to natural language concepts and the ability to physically point to "five" of something the word has no meaning. Thus the interpretation of mathematics and, indeed, logic itself has no meaning outside of natural langauge.

Natural language is repleate with vague terms and contradictions. Unless you can clarify these terms and contradictions, at least those that apply to mathematics and logic, any assertions you can make about mathematics and how it applies to the real world are pure speculation. Considering the evidence of the last century especially, the idea that any single view of mathematics covers everything is patently absurd. [g)] [g)] [g)]

[Perspectives]

While it is true mathematics is the chosen tool for the formal expression of physical phenomena, to most if it ‘s implications and indeed it’s implied consequences are not revealed through words and a story then it will not matter. I am most familiar with Einstein’s Special Theory of Relativity in both the math and his eloquent verbal expression of it. However his General Theory of Relativity is Mathematically beyond me at present and after that the implications that I must derive from it and finally I will not be able to express it verbally till I get the other two straight.

So considering the bridge that must be created between the abstractions of mathematics to the verbalization of its consequences, I agree with you. We do need to be able to properly express in non-mathematical terms the things revealed by mathematics.

Regarding why mathematics can be used to express all phenomena, I hold despite the many varied branches that may be needed, mathematics is a tool that is intrinsic to humans. And that it is very much applicable to all physical phenomena. We may need to create new abstract tools in the future that are mathematical in nature but nonetheless they will be mathematics. I therefore submit, formally expressed notation will be used that abstractly represent the relations in nature and it will perform the service of revealing nature’s inner workings. Mathematics and only mathematics in all its form is necessary and implicit in discovering nature’s mechanisms.

[wuliheron]

Originally posted by Perspectives
Regarding why mathematics can be used to express all phenomena, I hold despite the many varied branches that may be needed, mathematics is a tool that is intrinsic to humans. And that it is very much applicable to all physical phenomena. We may need to create new abstract tools in the future that are mathematical in nature but nonetheless they will be mathematics. I therefore submit, formally expressed notation will be used that abstractly represent the relations in nature and it will perform the service of revealing nature’s inner workings. Mathematics and only mathematics in all its form is necessary and implicit in discovering nature’s mechanisms.

Mathematics can be highly accurate and precise, but whether or not this implies it reflects reality in some sense is unknown. Its a bit like saying my yardstick is highly accurate and precise, therefore existence must be a yardstick, and everything must be capable of being measured by a yardstick. I should be able to measure my mother's love for me using my yardstick, or even the value of life itself.

Note that within mathematics itself, there is no clearly superior form of mathematics which describes reality better than another. In physics, Quantum Mechanics does a good job but only on a statistical basis that does not make any conclusive statement about the ultimate nature of existence. In other words, the evidence is against the idea no matter which way you turn. The only way available currently for this idea to hang on by a toe nail, is through the undifferentiated or indeterminate nature of existence we observe. If we cannot determine the precise nature of reality, then at least a small chance exists all our other observations are misleading due to our limited perspective.

[Perspectives]

Post from: Wuliheron

“Mathematics can be highly accurate and precise, but whether or not this implies it reflects reality in some sense is unknown.”….

”Note that within mathematics itself, there is no clearly superior form of mathematics which describes reality better than another.”…

“The only way available currently for this idea to hang on by a toe nail, is through the undifferentiated or indeterminate nature of existence we observe.”…

“If we cannot determine the precise nature of reality, then at least a small chance exists all our other observations are misleading due to our limited perspective.”…
__________________________________________________ _________________

I agree with you, we cannot know the precise nature of Reality since it is variable and interpreted from our perspective. Indeed our interpretation of Reality is subjective though the use of our Mathematics.

Mathematics can be the cause of two forms of interpretation, one a perspective and two a thoroughly incorrect application. I’m not sure there is much difference between them but there is a surety involved here, our observation of Reality in itself affects the outcome.

The interpretation of Reality is one point in the search and Mathematics is the other. It is difficult enough to, by some mystical event, discover a new or corrected view of reality, prove it in-principle through formal methodology, and then interpret what you’ve got. Lesley Groves has been quoted as having said upon viewing the first detonation of the atomic bomb, “ We’ve won the war, we have the biggest stick on the block,” whereas Robert Openheimer was quoted as reciting a passage from the Gita Bhagwat, “ I am become death…”

This is not math or science but a demonstration of perspectives regarding a pivotal event in history. After all the math and science two men regard the result from two entirely different perspectives.

There are times Mathematics, Reality and Humankind are as disparate as wind, rain, and earth and sometimes, maybe as close as the tree that gains the benefits of the three.

[drag]

Hmmm...[:((]
Alexander doesn't want to play with me...[:(] [*(]

[Mentat]

Originally posted by drag
Hmmm...[:((]
Alexander doesn't want to play with me...[:(] [*(]

Yeah, I'm getting the same feeling. [:(]

[wimms]

Give him a break. Hes becoming impatient and took some time to chill.

Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?

When I first encountered Fourier series I was baffled, you can dismantle wavesignal of any shape whatsoever into finite number of components, that can sometimes be awfully compact equation. Any kind of patterns in signal results in reduction of complexity of equation. The more repetitions, the simpler it becomes. Complexity of equations increase only in case when signal approximates towards completely acausally random noise.

Math is so powerful these days, that they seek for methodology to actually find equation for any given photo of any complexity. Its all about compression ala DNA. Given space of nearly infinite possibilities, find equation that produces exactly that given image.

I guess one could describe in full detail, shape, colors, smell and all, actual bull's shjt floating in the waterpool with wave equations. Some QM is 'piece of cake' in comparison. Question is merely in finding which of infinite possible equations best fits observable reality. Thus impression creeps in, if math is so powerful that it can describe about anything, how can math be actually cause for anything? What then constrains its infinite flexibility? And most importantly, why in this particular way?

Then, equations are merely dormant relations, 'curvature'. To make them alive, one needs to put in some values, 'matter'. Only then can equations 'take off'. Only if 'matter' and 'curvature' were in mutual interaction, creating and changing each other, like mass and spacetime, could there be some justification to why we observe only small subset of possibilities. In that sense, theories of chaos are fascinating. As I understand it, they have capacity to actually create new math from dumbsimple initial conditions, upto complexification beyond imagination.

[wuliheron]

Originally posted by wimms

Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?

Paradox.

[drag]

Greetings !
Originally posted by wimms
Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?
Of course there are things math fails to
discribe. In fact, modern mathematics is
full of approximations of nature with few
direct discriptions. The simplest example
I offered Alexander and got no response is
that of 3+ bodies orbiting each other due to
the force of gravity.

Live long and prosper.

[Perspectives]

The universe is an orderly and predictable environment that is reality. I’m sure the O and P statement will bring howls. Our attempt to emulate and capture the rules of the environment is through the discovery of the interrelationships that exist. We do this by creating symbolic relationships that when applied are predictive in nature, we call this mathematics. If math predicts in any reasonable manor the mechanics and mechanisms of the universe then we are merely illuminating that which is from the logic that is already there.

As regards what we call Reality, it is a subjective interpretation, verbal as much as logical, of our formal proofs. Half empty or half full, which is right?

[wuliheron]

Originally posted by Perspectives
The universe is an orderly and predictable environment that is reality. I’m sure the O and P statement will bring howls. Our attempt to emulate and capture the rules of the environment is through the discovery of the interrelationships that exist. We do this by creating symbolic relationships that when applied are predictive in nature, we call this mathematics. If math predicts in any reasonable manor the mechanics and mechanisms of the universe then we are merely illuminating that which is from the logic that is already there.

As regards what we call Reality, it is a subjective interpretation, verbal as much as logical, of our formal proofs. Half empty or half full, which is right?

Both are true, the glass is half empty and half full and that is the paradox. The universe is incredibly predictable and inordinately unpredictable else we would not be discussing the issue. Your argument is nothing less than a variation on the Anthropic Principle. That in itself is as humorous as it gets for the sciences and philosophy.

[Eh]

Why does this remind me of Lifegazer threads?

[Alexander]

Originally posted by Perspectives
Mathematics is an explanation of existence. Its complexity and level of relevance depends on need. Mathematics is to existence what the footprint is to the foot.

Small but impotrant correction: Behavior of existing objects is to mathematics what the footprint is to the foot.

[Alexander]

Originally posted by wuliheron
A bird in the hand is worth two in the bush
And, in turn, the two in the bush are (for all I can determine) worth an infinite number of mathematical white rabbits. [/I] [/B]

Wulli - no offense - how much expertise in math do you have?

The reason I am asking is that sometimes people with no or little expertise in some field try to judge that field and get wrong conclusion.

[Perspectives]

The qualifications for evaluation of the subject matter is elusive and every bit as consensus as the subject it’s self. We’re examining philosophy, theoretical physics, theology if you’re inclined, and of course mathematics.

I think, like the blind men each describing an elephant, the allegory fails to bring into account their area of expertise. It seems the most important part of the story is that they are blind, as if they could see they would immediately know what they see. Since all humans have some unique attributes that color their judgment each man would probably see something different. Scientific methodology tries to eliminate subjectivity from the evaluative process; therefore man should see the same thing. Yet we may have asked a subjective question, too unscientific to use an objective measure.

Mathematics without question is a methodology, just like a man is male. Math is a tool to assist our understanding of the Universe and a tool to assist us to build a house. We don’t care about the Universe when we build our house and we don’t think of houses when we consider the Universe. We just use it to justify our work. Especially at those levels we’re not standing far enough from the subject to illuminate it.

I believe that we have touched on many of the important points of the argument and as is equally important assisted each other in understanding individual perspective. At various levels we’re all right to some degree. This subject is important and not just an academic exercise since it’s conclusions could lead to innovation. Especially if one can get our mind around what Mathematics is. Then we can consider what it isn’t.
[:)]

[Alexander]

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

[Mentat]

Originally posted by Alexander
Small but impotrant correction: Behavior of existing objects is to mathematics what the footprint is to the foot.

Step outside of your religious hold to this unproven idea, and you will realize that you are preaching against the definitive notion of mathematics itself. I've been doing research into what mathematics is, and it seems that everyone (including expert mathematicians) recognizes mathematics as a tool for understanding physical reality.

[Mentat]

Originally posted by Alexander
Wulli - no offense - how much expertise in math do you have?

The reason I am asking is that sometimes people with no or little expertise in some field try to judge that field and get wrong conclusion.

And herein lies one of your greatest character flaws. An Indian mand (from India), revolutionized Mathematics, after having only read a basic mathematics textbook (I forget his name, but I'm sure you're familiar with him). It doesn't take an extensive education in a field, to question an "expert's" of understanding of it.

[Tom Mattson]

Originally posted by Alexander
So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

This has nothing to do with anything in the discussion. No one is saying that accepted physical theories are "wrong".

[FZ+]

Originally posted by Alexander
So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?
In an ideal would, they would nod in agreement, but not discard GR. Rather, they would agree that inevitably there would be improvements to the theory, but it's the best around at the moment.

[Perspectives]

I agree with FZ

Of course not, But I would expect the layman to support his or her position. I suppose it depends on the physicist level of tolerance. The layman has clearly stated their level of competence is “Not an expert.” Having said that, he or she should defend their position and put it to the test. Experts are public targets for all to test and they should be ready to defend. I agree bearding the Lion in his own den is not prudent. Either the layman has a hypotheses, I would at least expect this level of challenge, or he will be shown the door. One does not need to be recognized in a discipline to participate just recognize that professionals don’t always play nice.

[Alexander]

Originally posted by Mentat
Step outside of your religious hold to this unproven idea, and you will realize that you are preaching against the definitive notion of mathematics itself. I've been doing research into what mathematics is, and it seems that everyone (including expert mathematicians) recognizes mathematics as a tool for understanding physical reality.

Goog. Keep searching. Learning is a wonderful process.

What is the origin of this "tool"?

[Mentat]

Originally posted by Alexander
Good. Keep searching. Learning is a wonderful process.


Yeah, you should try it sometime. Of course, that would mean letting go of your religious belief for a while... Oh well, I guess we should leave learning to us "laymen", as experts apparently have no use for it.


What is the origin of this "tool"?

An empirical pattern of behavior that one observes in the Universe. This pattern is not absolute (see my new thread (http://physicsforums.com/showthread.php?s=&threadid=2740)), but it is deeply engrained in the human psyche, and set of beliefs.

[Alexander]

Originally posted by Tom
This has nothing to do with anything in the discussion. No one is saying that accepted physical theories are "wrong".

Incorrect. Some people here with little experience in math or in physics (or even in both!) try to JUDGE the RELATIONSHIP between math and physics. Not ask questions or suggest opinions, but to JUDGE.

Only those who not only do undestand (in reasonable depth) BOTH physics and math and have reasonable EXPERIENCE in mastering both physics and math, but also have good experience in dealing with RELATIONSHIPS and interconnections between them - only those can JUDGE about relationship of math and physics.

[Tom Mattson]

Jeez, you really don't get it.

You originally said:

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

I repeat: This has nothing to do with anything here. No one is suggesting that any physical theory is wrong or that any physical theory should be discarded.

Originally posted by Alexander
Incorrect. Some people here with little experience in math or in physics (or even in both!) try to JUDGE the RELATIONSHIP between math and physics. Not ask questions or suggest opinions, but to JUDGE.


That is not the same as what you said earlier.

Also, Mentat is asking questions and suggesting opinions. You are the only one doing the judging.

Mentat is reasoning, you are preaching.

[Alexander]

Originally posted by Mentat
Yeah, you should try it [learning] sometime.

[b]


I love it very much. I am even getting paid for it by government (being a full time scientist and educator).



Of course, that would mean letting go of your religious belief for a while...

Oh, no, that would be hard to do. My long experience in learning universe and solving many puzzles about it made me very closed minded believer in facts and logic.

Unlike some "wide open" minds.[;)]

[Hurkyl]

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what?

What if a layman walked into a physics conference and objected to someone's claim that "1 + 2 = 4"... would you still dismiss his objection based simply on the fact he's a layman?


The error you are accused of making is not up in the lofty stratosphere of scientific knowledge buried under such complicated equations that 10 years of study are required to even understand the equation in error. The error of which you are accused occurs down in the lower levels, in your philosophical interpretation of mathematical logic... a field outside of your primary field of study. I'm not sure why you keep bragging about being a government paid scientist, unless you're just trying to win the argument with the "I'm smarter than you" approach.

[drag]

Originally posted by Alexander
Goog. Keep searching. Learning is a wonderful process.

What is the origin of this "tool"?
What's the origin of a Monopoly game ?
Is it there because it is the fundumental
truth that discribes modern economics ? [;)]

Peace and long life.

[wimms]

Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations? (wimms)
Originally posted by wuliheron
Paradox. Whats so hard about describing it? P = ~P

drag:
Of course there are things math fails to discribe. In fact, modern mathematics is full of approximations of nature with few direct discriptions. The simplest example I offered Alexander and got no response is that of 3+ bodies orbiting each other due to the force of gravity. There is a difference between what humans are able to describe using math now, and what is possible to be described when sufficiently advanced. Math is developing.
What math doesn't do is explain. It helps finding relationships between descriptions, definitions.

Too often there are many ways to describe same thing. Take for eg square wave. Very simple thing, on-off switch with finite timing for each state. Simple formula would do. But if you dismantle it into fourier series, it appears that there is one main harmonic sinusoid, and infinite amount of odd higher harmonics with decreasing amplitudes all summed. And if square wave were single on->off cycle, like when you switch off your lights? Then main harmonic is infinitely low frequency sinusoid.

So we can describe act of switching off the lights as 'spontaneous emitting of summ of infinite amount of odd harmonics of infinitely low frequency main sinusoid, where each consecutive harmonic has specifically decreased amplitude'. Yeah, that sure helps understanding act of pressing the button. Or even better, after detecting all that harmonic stuff, we deduce that math creates a peculiar event of infinite harmonics..

But if you can define anything, then you can do that in mathematical symbols, and its automatically inside math, relations describable at least, even if not yet resolvable or explainable.

[Mentat]

Originally posted by Alexander
I love it very much. I am even getting paid for it by government (being a full time scientist and educator).


That is not learning, that is teaching. They are, in fact, opposite sides of the coin. You are paid to teach, and this is good. But you should not have abandoned learning to pursue teaching.


Oh, no, that would be hard to do. My long experience in learning universe and solving many puzzles about it made me very closed minded believer in facts and logic.


While it's nice that you admit to being closed-minded, I don't much care for the implication that I am not using logic or facts. I (along with Tom and ahrkron) have used logic to counter your belief, but you have closed your mind to it (for some reason that I just don't understand).

[FZ+]

Originally posted by Tom
Jeez, you really don't get it.

You originally said:

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

I repeat: This has nothing to do with anything here. No one is suggesting that any physical theory is wrong or that any physical theory should be discarded.

Exactly. Only that if the layman describes the scientific theories as only a description of the universe that should be open to change as our knowledge develops, instead of an absolute law, he is completely correct. After all, that is what differentiates science from religion.

[Mentat]

Originally posted by Hurkyl
What if a layman walked into a physics conference and objected to someone's claim that "1 + 2 = 4"... would you still dismiss his objection based simply on the fact he's a layman?


The error you are accused of making is not up in the lofty stratosphere of scientific knowledge buried under such complicated equations that 10 years of study are required to even understand the equation in error. The error of which you are accused occurs down in the lower levels, in your philosophical interpretation of mathematical logic... a field outside of your primary field of study. I'm not sure why you keep bragging about being a government paid scientist, unless you're just trying to win the argument with the "I'm smarter than you" approach.

Hurkyl, how did you get so perfectly succinct? I am staggered every time I read one of your posts - wishing I could portray my thoughts so perfectly, in so few words, as you do. Kudos.

[Hurkyl]

I think it comes from years of participating in threads that look like this one on various forums. IMHO the only way to have any chance of getting through to the other side is to break things down to basic elements, so I've had practice. [:)]

[Alexander]

Originally posted by drag
Greetings !

Of course there are things math fails to
discribe. In fact, modern mathematics is
full of approximations of nature with few
direct discriptions. The simplest example
I offered Alexander and got no response is
that of 3+ bodies orbiting each other due to
the force of gravity.

Live long and prosper.

Sorry for missing your post. There are many other important things to do (research, paneling, teaching, etc) beyond PF in my life. Sometimes I have plenty of time and can respond to all posts, but sometimes unpostponable duties come across.

The above example given by Drag is typical example of misunderstanding mathematics and thus making wrong conclusion about mathematics.

While solution (for 3 and more bodies) exists and can be calculated say, using a computer, it does not have a specific name (like, say, r(t)=arctan(sin(1/t)), or Gudermannian function, or elliptical integral, etc).

We just say that the solution is not "analytical". In fact only very and very few solutions are analythical.

Some other kinds of solutions are catastrophic solutions, chaotic solutions, imaginary solutions, wave solutions, etc - many of which are considered by laymann to be "no solution" - just because they look unusual or suspicious to a laymann.

Finally, some equations may have NO solution (say, the system x=1, x2=2) or infinite number of solutions (say, equation (x2-1)=(x+1)(x-1)).

[Sting]

Mathematics - Description

Also an artform but my head is hurting so I won't go into any philosophical discussion [:)]

[Alexander]

Originally posted by Mentat


[From] An empirical pattern of behavior that one observes in the Universe.

Not exactly. I would say, from empirical property "being able to exist" and "being able not to exist".

The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

Existence is logic, so to speak.

[Alexander]

Originally posted by Sting
Mathematics - Description

Also an artform but my head is hurting so I won't go into any philosophical discussion [:)]

Description can't predict. Math can.

[Sting]

Description can't predict. Math can.

True, a description can't predict but I can see where mathematics both describes and predicts.

[Sting]

Wait, giving slightly more thought as not exacerbate my headache, isn't there a connection between description and prediction?

[Alexander]

Not much. Unless you use logic (=math).

[Hurkyl]

logic (=math)

Just curious how you justify the '=' in your statement, not to mention how logic alone can take you from description to prediction.

[Mentat]

Originally posted by Alexander
Not exactly. I would say, from empirical property "being able to exist" and "being able not to exist".

The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

Existence is logic, so to speak.

You are contradicting yourself. When will you see the contradiction. Let me spell it out for you:

First you said that the origin of logic is the labeling of the states of phenomena (which I agree with), then you said that everything existing obeys logic. This is a contradiction.

[Mentat]

Originally posted by Alexander
Description can't predict. Math can.

Math is a description.

[Mentat]

Originally posted by Sting
True, a description can't predict but I can see where mathematics both describes and predicts.

Prediction is just a form of description (particularly, the one that pertains to things that haven't happened yet).

[Tom Mattson]

The multiplicity of these threads is getting troublesome. I have already addressed the following comment, but not even I can find where!

Originally posted by Alexander
Description can't predict. Math can.

That is false. With mathematics, we can describe:

1. Physical states.
2. Time evolution of physical systems.

If we can accurately describe a physical state at one spacetime point, and if we can accurately describe the time evolution, then we can accurately describe the physical state at any spacetime point, including those in the future.

That sort of description is called a prediction.

[wimms]

Originally posted by Alexander
The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic. You are talking about presence and absence. How can you label something that does not exist?? And then use as justification to fundamentals of logic itself? Absence or lack 'of it' presupposes existence of it and thus at least imaginable presence. And what does my absence from a party has to do with fundamentals and 'obeying logic'? [;)]
Where is the glue between 'existence' and 'obeying logic'??

Besides, what makes "0" fundamental logic/math entity? What makes "false" entity at all? Fundamental to math and logic is equivalence, '=' sign, validation operator. All else is endless crusade to get that '=' sign somewhere with maximum bang effect. Shuffling nicknames left and right doesn't make a reality, its just tailoring a suit to a shape of it. You are saying that suit makes a Man. Most say that suit fits a Man, and many suits fit.

[Sting]

Prediction is just a form of description (particularly, the one that pertains to things that haven't happened yet).

Yes, as soon as I posted that, I realized the ambigious nature of that statement (but the headache is gone and I can at least think logically [:)])

[Mentat]

Originally posted by Tom
The multiplicity of these threads is getting troublesome. I have already addressed the following comment, but not even I can find where!


Imagine how that would be compounded if you and one other member were engaged in back-and-forth debate on two threads (at the same time) that had started to be about exactly the same thing. This is the situation that drag and I found ourselves in (on the "Purpose" thread and the "Cause-and-effect" thread).

[Mentat]

Originally posted by Sting
Yes, as soon as I posted that, I realized the ambigious nature of that statement (but the headache is gone and I can at least think logically [:)])

[:D]

It happens to the best of us (which is why it has yet to happen to me [6)]).