The Hurdles to the Causal Mathematics Hypothesis

[Mentat]

Back in the old PFs, I made this thread to get rid of an idea that was continually side-tracking threads. I thought it was, for the most part, effective, but it appears that this is not the case. So, I have found the thread on the PF Archive C.D., and reposted it here:

The following are the Hurdles to the Causal Mathematics idea (which is the idea that Mathematics creates the phenomena of the Universe), as posted in PF 2.0:

1) Non-physical Hurdle:

Mathematics has no physical presence (nor does logic, for that matter). You can say that electromagnetism (for example) is causal, because it can exert *physical* force on objects. Mathematics, on the other hand, exists only in the metaphysical (or the realm of concepts).

2) The Dictionary Hurdle:

The American Heritage dictionary of the English Langauge defines mathematics as:

The study of number, form, arrangement, and associated relationships, using rigorously defined literal, numerical, and operational symbols.

The Webster's Dictionary defines it as:

The logical study of quantity, form, arrangement, and magnitude; especially the methods for disclosing, by the use of rigorously defined concepts and symbols, the properties of quantities and relations.

In both of these, it uses the term "study". The word study (according to the aforementioned dictionaries, and a thesaurus) is synonymous to research, observation, or the pursuit of knowledge.

3) The Unconscious Hurdle:

It appears that Alexander would have one believe that the Universe "conforms" to the laws of logic and mathematics. This would imply that the Universe "knows" what those laws are. Unless Alexander wishes to make a case for a "conscious Universe", this is another problem for his hypothesis. (Note: I have added Hurdle #3. It did not appear in the original thread).

In closing, any hypothesis with such giant objections would quickly be discarded by any scientist. But, of course, these are not objections at all, if anyone can prove them invalid.

 

[wuliheron]

Alexander's mysticism about everything ultimately being mathematics is nothing new, in fact, it is one of the leading candidate theories attempting to explain Quantum Mechanics. The assertion that mathematics has no physical presence is unproven and clear arguments with physical evidence to the contrary exist.

As for the universe having to be "conscious" of the mathematics that underlie it... that is utter nonsense. Even consciousness itself could be nothing more than another manifestation of mathematics. You are attempting to make an a priori assertion about the idea that axiomatically discounts the idea. You are, of course, welcome to have your own opinions about the idea, but your argument here amounts to nothing more complex than two little kids on the playground shouting at each other:

Is so! Is not! Is not! Is not!

If you really wish to talk about the subject instead of just shouting contradictory assertions at each other, it might be helpful to reframe your arguments along the lines of reductio ad absurdum, that is, that his ideas are no more or less rediculous than a number of alternatives.

 

[Mentat]

Originally posted by wuliheron
Alexander's mysticism about everything ultimately being mathematics is nothing new, in fact, it is one of the leading candidate theories attempting to explain Quantum Mechanics. The assertion that mathematics has no physical presence is unproven and clear arguments with physical evidence to the contrary exist.

There are theories that suggest that mathematics has the ability to mold the Universe?

As for the universe having to be "conscious" of the mathematics that underlie it... that is utter nonsense.

No, I didn't say that. I said that, in order for the Universe to conform to mathematics, it would have to be conscious. There's a difference.

Even consciousness itself could be nothing more than another manifestation of mathematics.

Not by the accepted definitions of the term "mathematics". Remember, the language that we are using to discuss these things relies on defined terms. As Alexander himself has pointed out, many times in the past, the terms need to be defined before any rational argument can take place about them.

If you really wish to talk about the subject instead of just shouting contradictory assertions at each other, it might be helpful to reframe your arguments along the lines of reductio ad absurdum, that is, that his ideas are no more or less rediculous than a number of alternatives.

No, his ideas are no more rediculous than many others, but I'm not arguing against others right now, I'm arguing against his.

 

[ahrkron]

I think the strongest of Mentat's "hurdles" is the second one. Mathematics is defined as a description. There's no way around that.

What Alexander refers to can at most be stated as "all concepts in math correspond to real entities, the interaction of which causes everything", which is a metaphysical assumption about the degree of validity or the description.

 

[Mentat]

Originally posted by ahrkron
I think the strongest of Mentat's "hurdles" is the second one. Mathematics is defined as a description. There's no way around that.

What Alexander refers to can at most be stated as "all concepts in math correspond to real entities, the interaction of which causes everything", which is a metaphysical assumption about the degree of validity or the description.

Good point, ahrkron.

 

[ahrkron]

in fact, it is one of the leading candidate theories attempting to explain Quantum Mechanics.

What are you talking about? The only possibility I can think of is Max Tegmark's idea of the "Ultimate ensemble", but even that does not rely on attributing causal powers to math, but on the idea that all self consistent structures are realized in nature.

The assertion that mathematics has no physical presence is unproven

The matter does not even require a "proof". It is a much simpler matter, since it comes from the definition of math. If you want to refer to a different concept, you need to use a different word.

and clear arguments with physical evidence to the contrary exist.

Show us one.

it might be helpful to reframe your arguments along the lines of reductio ad absurdum, that is, that his ideas are no more or less rediculous than a number of alternatives.

That is not what "reduction ad absurdum" means.

 

[wuliheron]

Originally posted by Mentat
There are theories that suggest that mathematics has the ability to mold the Universe?

Sure, one of the better theories attempting to explain Quantum Mechanics is that information itself is a material substance. Other leading theories propose everything is geometry or logic, albeit, rather strange geometries and logic.

No, I didn't say that. I said that, in order for the Universe to conform to mathematics, it would have to be conscious. There's a difference.

Whether any different or not, such a statement is an a priori assumption which can easily be turned on its head to assert that, "In order for the universe to be conscious it must conform to mathematics." In addition, it can also be argued that you can not have consciousness without mathematics and vice versa, that both involve symbolic logic or reasoning at the very least. In fact, if Alex really wanted to he could simply argue that consciousness is an illusion of mathematics.

Not by the accepted definitions of the term "mathematics". Remember, the language that we are using to discuss these things relies on defined terms. As Alexander himself has pointed out, many times in the past, the terms need to be defined before any rational argument can take place about them.

Natural language is finite and of limited usefulness, especially when discussing such extreme metaphysical concepts. Just because the english language does not have words for concepts that other languages do possesses does not mean those concepts don't really exist. As much as I admire and espouse using dictionary definitions, I also acknowledge their limitations. To do otherwise is patently absurd.

No, his ideas are no more rediculous than many others, but I'm not arguing against others right now, I'm arguing against his.

My point is that you are not arguing against his idea, all you are doing is espousing an alternative by default and using shaky arguments that can easily be totally trashed. By merely using the english dictionary definitions you are asserting the dualistic worldview that is the origin of the english language. Mathematics, however, is not limited to dualism and contains many concepts that defy english language definitions.

In other words, by asserting as you are that The Map (mathematics) is not the Territory, you are axiomatically excluding the possibility that the map is actually a piece of paper made from a tree someone cut down from within the territory. Thus, the map is and is not the territory, the map both is shaped by and, in turn, shapes the territory.

Again, dictionaries are wonderful tools except when you forget they are only tools and start to worship them as the word of God or somesuch.

 

[drag]

Originally posted by wuliheron
Is so! Is not! Is not! Is not!

I summed it up better - Doubt or shout !

 

[quantumdude]

Since I have a lot of experience in these threads, let me add to your list.

Originally posted by Mentat
1) Non-physical Hurdle:

2) The Dictionary Hurdle:

3) The Unconscious Hurdle:

4) The Post Hoc, Ergo Propter Hoc Hurdle

Post hoc, ergo propter hoc ("After this, therefore because of this") is a logical fallacy that assumes a causal connection between two things that are simply coincidental, or that reverses the direction of causality.


5) The No Perfect Equation Hurdle

If someone claims that math creates things in the universe, then a perfectly reasonable request would be, "Please present the equation that does it." Indeed, I have made this request many times, but still have not gotten it. Every equation we have is an imperfect model, and so cannot be a candidate for the creator of anything.

 

[wuliheron]

Originally posted by Tom
Since I have a lot of experience in these threads, let me add to your list.

4) The Post Hoc, Ergo Propter Hoc Hurdle

Post hoc, ergo propter hoc ("After this, therefore because of this") is a logical fallacy that assumes a causal connection between two things that are simply coincidental, or that reverses the direction of causality.

5) The No Perfect Equation Hurdle

If someone claims that math creates things in the universe, then a perfectly reasonable request would be, "Please present the equation that does it." Indeed, I have made this request many times, but still have not gotten it. Every equation we have is an imperfect model, and so cannot be a candidate for the creator of anything.

6) The Emotional Context Hurdle

Mathematics has nothing to say about emotional context, and without context its meaning and application cannot be assertained.

 

[Mentat]

Originally posted by Tom
Since I have a lot of experience in these threads, let me add to your list.



4) The Post Hoc, Ergo Propter Hoc Hurdle

Post hoc, ergo propter hoc ("After this, therefore because of this") is a logical fallacy that assumes a causal connection between two things that are simply coincidental, or that reverses the direction of causality.


5) The No Perfect Equation Hurdle

If someone claims that math creates things in the universe, then a perfectly reasonable request would be, "Please present the equation that does it." Indeed, I have made this request many times, but still have not gotten it. Every equation we have is an imperfect model, and so cannot be a candidate for the creator of anything.

Excellent additions, Tom. Your input here is highly appreciated.

 

[Mentat]

I've just noticed that I forgot entirely about Godel's Incompleteness Theorem, which clearly shows the flaw (or "incompleteness") of mathematics. If mathematics cannot describe itself, and yet it is the producer of all reality, then mathematics is not real .

 

[Mentat]

Alexander, I don't want this to seem like a bunch of members are just ganging up on you, you are expected to attempt a counter-argument to any/all of the arguments here presented.

 

[wuliheron]

Originally posted by Mentat
I've just noticed that I forgot entirely about Godel's Incompleteness Theorem, which clearly shows the flaw (or "incompleteness") of mathematics. If mathematics cannot describe itself, and yet it is the producer of all reality, then mathematics is not real .

Wrong! The Incompleteness Theorem demonstrates that you cannot prove mathematics is the basis of reality. Thus it leads back to the Paradox of Existence.

 

[Mentat]

Originally posted by wuliheron
Wrong! The Incompleteness Theorem demonstrates that you cannot prove mathematics is the basis of reality. Thus it leads back to the Paradox of Existence.

That's exactly what I was saying.

 

[quantumdude]

Originally posted by wuliheron
Wrong! The Incompleteness Theorem demonstrates that you cannot prove mathematics is the basis of reality.

The incompleteness theorem says that any formal system at least as complicated as arithmetic is either incomplete or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality" is to make the same mistake that Alexander is making: confusing concrete objects and abstract objects.

 

[drag]

Originally posted by Tom
The incompleteness theorem says that any formal system
at least as complicated as arithmetic is either incomplete
or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality"
is to make the same mistake that Alexander is making:
confusing concrete objects and abstract objects.

Indeed.

 

[Mentat]

Originally posted by Tom
The incompleteness theorem says that any formal system at least as complicated as arithmetic is either incomplete or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality" is to make the same mistake that Alexander is making: confusing concrete objects and abstract objects.

Good point.

 

[Hurkyl]

Also, the second theorem states that any similarly complicated formal system that can deduce its own consistency must be inconsistent.

 

[wuliheron]

Originally posted by Tom
The incompleteness theorem says that any formal system at least as complicated as arithmetic is either incomplete or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality" is to make the same mistake that Alexander is making: confusing concrete objects and abstract objects.

In other words, any system we use that is at least as complex as arithematic must be taken on faith to a certain extent.

Sorry if I'm sounding redundant, but this leads inexorably back to the paradox of existence. Beneigth the level of arithmatic lies metaphysics, which also must be taken on faith. Including the metaphysical idea that existence is "concrete" and mathematics is "abstract."

 

[quantumdude]

Originally posted by wuliheron
Beneigth the level of arithmatic lies metaphysics, which also must be taken on faith.

In what sense is arithmetic "beneath" metaphysics?

Including the metaphysical idea that existence is "concrete" and mathematics is "abstract."

So then it is metaphysics, not incompleteness, that takes this to the paradox of existence?

 

[drag]

Originally posted by wuliheron
In other words, any system we use that is at least as complex as arithematic must be taken on faith to a certain extent.

Sorry if I'm sounding redundant, but this leads inexorably back to the paradox of existence. Beneigth the level of arithmatic lies metaphysics, which also must be taken on faith. Including the metaphysical idea that existence is "concrete" and mathematics is "abstract."

Yeah, but while this may be relevant to reality
when Alexander says math is it, it's not
relevant to the subject in general, I think
(beyond being another example of a reasoning
system that can not explain its own origin).

Live long and prosper.

 

[wuliheron]

Originally posted by Tom
In what sense is arithmetic "beneath" metaphysics?

So then it is metaphysics, not incompleteness, that takes this to the paradox of existence?

Arithematic is built upon metaphysics, precisely the kind you advocate. Of course, these metaphysics are based in turn on observation and whatnot, but they remain metaphysical concepts nonetheless. The belief that reality can be described using rational constructs is an inherently metaphysical idea.

Incompleteness leads back to these metaphysical foundations, which, in turn lead back to the paradox of existence. It is this continuous and apparently unavoidable thread of evidence that makes the paradox of existence a likely candidate for the source of all metaphysical ideas.

Originally posted by drag
Yeah, but while this may be relevant to reality
when Alexander says math is it, it's not
relevant to the subject in general, I think
(beyond being another example of a reasoning
system that can not explain its own origin).

Live long and prosper.

No, it is critical in the sense that when one is talking about vague and poorly defined concepts you can still often reduce them down to a single connundrum. As far as I am concerned, Alex is just talking about the paradox of existence. He can argue otherwise of course, but so far all of his arguments involve not only vague terms, but an attempt to seriously redefine the english language to favor his metaphysics. In fact, not only to redefine the language to favor metaphysics, but his particular brand of mysticism.

This is patently absurd. Words are used for communication, outside of that context what you do with them is your personal affair.

 

[Alexander]

Looks like almost nobody here understands Goedel theorem. Thus the wrong conclusions this thread is choke full of. Can you guys lift your fingers and learn more about it?

In brief: it says that out of rich enough bunch of axioms you can build a conclusion which is impossible to prove by these axioms only, but which nevertheless is CORRECT conclusion.

It simply means that math is open (more rich than the axioms it started with) yet always CORRECT.

And that math is correct we see each and every day - it makes correct predictions of behavior of things in universe. We use math to predict behavior of unexisting yet devices and mechanisms with owerwhelming success.

 

[wuliheron]

Originally posted by Alexander
Looks like almost nobody here understands Goedel theorem. Thus the wrong conclusions this thread is choke full of. Can you guys lift your fingers and learn more about it?

In brief: it says that out of rich enough bunch of axioms you can build a conclusion which is impossible to prove by these axioms only, but which nevertheless is CORRECT conclusion.

It simply means that math is open (more rich than the axioms it started with) yet always CORRECT.

And that math is correct we see each and every day - it makes correct predictions of behavior of things in universe. We use math to predict behavior of unexisting yet devices and mechanisms with owerwhelming success.

Mathematics do not make predictions... people make predictions. Sometimes we use math incorrectly and make false predictions because math as we know it is not a perfect system for making predictions.

 

[Alexander]

Originally posted by wuliheron
Sometimes we use math incorrectly and make false predictions...

Exactly. Whom to blame for incorrect usage of math?

Here is the hint (in case if you did not get it yet):

... because human as we know it is not perfect for making predictions.

 

[ahrkron]

Originally posted by Alexander
In brief: it says that out of rich enough bunch of axioms you can build a conclusion which is impossible to prove by these axioms only, but which nevertheless is CORRECT conclusion.

This is a wrong account of the theorem. I'm aware you are trying to "make it simple", but this description shows some misconceptions on your part.

1. "out of rich enough axioms you can build conclusion"... no. Actually, what Godel's theorem says is precisely the opposite: that there are statements you cannot build out of these axioms.

2. (same phrase). You need to distinguish between the statements you can form in the system, and the coclusions that can be obtained from the axioms.

3. "which nevertheless is CORRECT conclusion". No. It talks about a true statement that is NOT a conclusion of the axioms.

It simply means that math is open (more rich than the axioms it started with) yet always CORRECT.

You have a confusion between "correct" and "true". Also, your use of "math" is ambiguous.

If by "math" you mean "all possible consequences of a given set of axioms". I have to ask, which axioms?

Also, if that is the case, then of course all such consequences are "correct", this means that all of them are true (within the axiomatic system you chose). However, Godel's theorem deals with the converse: not all true statements in the system can be derived from the axioms.

And that math is correct we see each and every day

Nobody here says that math is "incorrect". However, that just implies that math is a good description. It has nothing to do with its causing anything.

What do you call "math", Alexander?
A set of axioms plus their conclusions?
The "structure of interactions" between physical entities?
The "study" of anything?
The description of what we observe?

(I know you don't see it as either of the last two, but I wanted to include them as possible options).

 

[wuliheron]

Originally posted by Alexander
Exactly. Whom to blame for incorrect usage of math?

Here is the hint (in case if you did not get it yet):

... because human as we know it is not perfect for making predictions.

Point out one thing is "perfect." Otherwise I shall assume it another of your myths.

 

[pelastration]

No myths WULI ... MONEY !

These interesting questions will be solved by .A.M.M.M. (Alexander Mathematical Master MIND) in a minute or two: http://feynman.physics.lsa.umich.edu/strings2000/millennium.html and http://www.qub.ac.uk/mp/questions/questions.html . That's only warming up ;-)

For other members, this is the main question: Are all measurable dimensionless parameters that characterise the physical universe calculable in principle or are some merely determined by historical or quantum mechanical accident and uncalculable?

IMHO, ... why does AMMM says that we can calculate everything? .. and here top physicists even think some parameters might be UNCALCULABLE !

And AMMM will become a very rich man since he can earn one million dollar from the Clay Institute for EACH solutions on special questions.

If AMMM can find already tonight the solution on the Riemann Hypothesis he really makes money NOW.
That's reality!
http://www.claymath.org/Millennium_Prize_Problems/Riemann_Hypothesis/

Go ahead AMMM ... All PF is supporting you! ... only maybe some other members will try to cheat ... and will try to find the solutions before you :/ . In such case - winning 1,000,000 $ instead of you - we will ask the moderator to kick them of PF ! I promise!

Small suggestion, Alexander don't use below exposed logic to give the answers to those money-making questions:

Originally posted by Alexander in: what does physics describe?
Universe comes from physics, physics comes from math, math -from logic. Logic comes from just fact of existense.
So, universe obeys math simply because objects in universe exist.

Something is seriously wrong here!

 

[Mentat]

Originally posted by Alexander in: what does physics describe?
Universe comes from physics, physics comes from math, math -from logic. Logic comes from just fact of existense.
So, universe obeys math simply because objects in universe exist.

Originally posted by pelastration

Something is seriously wrong here!

Many things are seriously wrong here, but one of them is the fact that he has created a loop (universe comes from logic, which comes from the fact of existence (=universe)).

 

[Alexander]

Originally posted by Mentat
Many things are seriously wrong here, but one of them is the fact that he has created a loop (universe comes from logic, which comes from the fact of existence (=universe)).

Thank you. Finally at least some people began to understand WHY math is so powerfull in predicting behavior of objects in universe.

Simply because math is indeed a logic of existence I as said many times before. Anything existing (object, phenomenon, concept, etc) can be labeled as "yes", or "1", or "+", or "truth", and the lack of thereof - as "no", or "0", or "-", or "false".

So any object which has the property to "exist" then shall obey logic (math) by definition.

Is not this obvious? I spend a lot of words trying to explain this clear issue to everyone yet only very few people understood. Most as one can see from above and other threads keep parroting: "math can't be correct because it is just a description, a human construct". Well, math is correct (otherwise it would not be so overwhelmingly used almost everywhere), and it is correct simply because anything which has the property "to exist" shall obey it by definition (see above).

 

[quantumdude]

Originally posted by Alexander
Most as one can see from above and other threads keep parroting: "math can't be correct because it is just a description, a human construct".

Not one person has said "math can't be correct". Your straw man arguments are getting old, Alex. Why not try logic for a refreshing change?

Well, math is correct (otherwise it would not be so overwhelmingly used almost everywhere), and it is correct simply because anything which has the property "to exist" shall obey it by definition (see above).

This is total nonsense. You can't form an a priori definition of what it means "to exist" or "to be physical". Any formulation of that concept is contingent on observatonal evidence and is subject to revision. Indeed, the concept has been revised many times as new discoveries have been made.

The truth of the matter is that no one knows why mathematics is so successful in describing physics, despite the fact that some of the best minds have pondered it.

 

[Alexander]

Originally posted by pelastration


IMHO, ... why does AMMM says that we can calculate everything? .. and here top physicists even think some parameters might be UNCALCULABLE !

Pela, do you understand the difference between mathematics and CALCULABIBITY? I clearly see that you dont. Mathematics prohibits "calculability" in many cases. Let's say that two quantities x and y are defined as inverse of each other: x=1/y. Then no matter what values x and y have, they can NEVER be equal to zero both. Suppose, x is spread of energy and y is spread of time. If they are entangled by mathematical definition then there is no way to have spread of both to be zero. So, energy and time can only have limited mathematical presicion, so to speak. Thus any quantity which requires accurate values of BOTH energy AND time will be undefined (uncalculable in principle).

And AMMM will become a very rich man since he can earn one million dollar from the Clay Institute for EACH solutions on special questions.

Thanks to both russian and especially US government (whom I helped to solve a few good puzzles) I am already very rich man. By the way, those puzzles were solved contrary to your poor advice:

Small suggestion, Alexander don't use below exposed logic to give the answers to those money-making questions

Finally, I share your concern that

Something is seriously wrong here!

I think it is because of lack of understanding of how math works.

Knowledge is power, ignorance is darkness!

 

[Hurkyl]

Thus any quantity which requires accurate values of BOTH energy AND time will be undefined

I hereby define a complex number x + i y to be an Alexandrian of a particle iff x is the energy of the particle and y is the time at which the energy is measured.

That certainly looks defined to me (even if no complex number is ever an Alexandrian of any particle)

 

[Alexander]

Yes, and if we then introduce Herculian function as y=ix then it is easy to show that applying Alexandrian to Herculean function makes the value of Herculean zero: x+iy=x+i(ix)=x-x=0



I love the power of math!