Science and the public, Maths and Reality

Son Goku

I'm continuing the debate here, if it is okay with the Mods.

ISAW wrote:

Some people dont understand genetics. does this mean they can not have an opinion on whether a blastocyst is a person?

That is a moral issue, one which can be explained in largely everyday terms.
General Relativity is a mathematical construct which is expressed in terms of Tensors in curved backgrounds.
Most of these ideas don't even have an indirect analogue in everyday experience.
I'm not saying that General Relativity can only be understood by physicists, but a most of it's points can only be explained mathematically.
Even in Special Relativity the differences between Minkowskian and Euclidean geometry really only become apparent with an experience of the mathematics.
"An observer can only see the universe through a co-ordinate map which may exclude many points seen by other observers", is a statement that carries only a fraction of the true meaning of the mathematical concept it attempts to describe.
Mathematics is a language more suited for understanding the physical world than any other and it would be at best difficult for somebody who cannot "read" the mathematics to understand what is being described.

ISAW wrote:

And it is those people who pay the bills of scientists. They are after all public servants not scientists' servants and they answer to the public and not to other scientists.

Einstein and all most of the geniuses of General Relativity, Schwarzschild, Nordstrom, Kerr e.t.c., weren't paid for their work by the public.
They were usually paid for something else and worked on General Relativity as an interesting intellectual aside.

ISAW wrote:

Maybe we are on different wavelenghts. Science has its own internal system of peer review which determines great scientists and maintains standards within science. But that is not sufficient. The ultimate worth of a theory is in how it relates to things outside science.

I would disagree.
The ultimate worth of a physical theory is how well it can model reality.

simu

Son Goku wrote:

I'm continuing the debate here, if it is okay with the Mods.

Yes - that's perfectly acceptable.

planck2

Yes how can a theory of science relate to anything other than science, most theories of science don't relate to anything outside science except for example Feynman's summation over all possible paths approach to quantum mechanics which in recent years is being applied to finance.

Abortion and care of the elderly or disabled person reqiures is a moral question also so most people are entitled to give their view, but if one is in a debate on radiation effects from Sellafield who are you going to listen the british politician who tells you not to worry or the nuclear scientist and doctor.

ISAW

Son Goku wrote:

I'm continuing the debate here, if it is okay with the Mods.


That is a moral issue, one which can be explained in largely everyday terms.
General Relativity is a mathematical construct which is expressed in terms of Tensors in curved backgrounds.

If you believe mathematics is a formal language which exists independent of humans actually developing it then you have a very strong argument there. But I would hope you would accept that any formal construct is related to people who construct it. Would you not accept that meaning also involves interpretation and conception?

Most of these ideas don't even have an indirect analogue in everyday experience.

all the more reason for people to invent one!

I'm not saying that General Relativity can only be understood by physicists, but a most of it's points can only be explained mathematically.

Yes but youare bordering on fundamentalism. Can the Koran only be understood in Arabic or the Bible only in aramaic and greek?

Even in Special Relativity the differences between Minkowskian and Euclidean geometry really only become apparent with an experience of the mathematics.

If you are saying could Aristotle or Euclid understand the mathematical solutions to equations then I believe the answer would be yes. furthermore shuld they be given the present knowledge then they would in my opinion develop it in spite of their former ignorance.

"An observer can only see the universe through a co-ordinate map which may exclude many points seen by other observers", is a statement that carries only a fraction of the true meaning of the mathematical concept it attempts to describe.
Mathematics is a language more suited for understanding the physical world than any other and it would be at best difficult for somebody who cannot "read" the mathematics to understand what is being described.

In formal mathematical tems yes. But math isnt everything. You are pushing the envelope to suggest math describes all reality!

Einstein and all most of the geniuses of General Relativity, Schwarzschild, Nordstrom, Kerr e.t.c., weren't paid for their work by the public.
They were usually paid for something else and worked on General Relativity as an interesting intellectual aside.

Einstein became famous for relativity and I would argue got his position in Princeton mainly for that.

I would disagree.
The ultimate worth of a physical theory is how well it can model reality.

well now I think we are back to phenomonology. I wont retreat to a comfortable philospohical cul de sac. Let me first state that my position is that despite different perceptions I believe a "real world" exists out there independent of you and me.

But one could contend that while relativity demonstrated that commonsense notions of time, space and matter cannot be correct, it did not call into question the objectivity or casual nature of reality the way orthodox interpretations of quantum theory have done.

nesf

ISAW wrote:

If you believe mathematics is a formal language which exists independent of humans actually developing it then you have a very strong argument there. But I would hope you would accept that any formal construct is related to people who construct it. Would you not accept that meaning also involves interpretation and conception?

This has been on my mind recently, quasi-discussed it with simu, but I'll try and summarise it here.


Ideas and concepts are distinct from the mode of communication that is used to express them. This is a fundamental truth that most people fail to grasp. It's all about the concepts ppl!

But it does not justify a dismissal of a certain mode of communication. I'll put forward an analogy and you can refute me, this is something I want to debate


Take an emotion. Now take the idea of an emotion. Now lets just pick anger for the sake of it.

On one side I have an abstract painting depicting the artist's rendition of this concept.

On the other I have a poem depicting the artist's rendition of this concept.

Which is the more true? Which is the more accurate? Are they both the same? Is it not feasible that one "mode of communication" is not fundamentally better at expressing this idea?

Different modes suit different types of ideas. "Art" loosely works well with "simple and straightforward" concepts but more complex works can be over the head of someone who is not "trained" (be it formally or informally) in how to interpret the mode.


Maths is a language. It's the language of pure logic. This in it's own makes maths not an easy or very understandable topic. Maths gets very strange very fast once you step outside the "easily taught basic tenets" of it.

Take the whole question, what does 1 mean? We all know what 1 means but can you explain it perfectly in English? I've know I've yet to see a definition for it in English that matches my conceptual understanding in my head.

The concepts that maths can define are very different to the concepts defineable by English. Different tools for different jobs.


What's clear and understandable mathematically can often be extremely difficult to translate into English. Sometimes impossible. Same with art, sculpture etc. You can capture a "snapshot" of it in English, but trying to capture the entire concept in words? That's nigh on impossible.


I'm not sure if I'm making a lot of sense here.

Son Goku

nesf wrote:

What's clear and understandable mathematically can often be extremely difficult to translate into English. Sometimes impossible. Same with art, sculpture etc. You can capture a "snapshot" of it in English, but trying to capture the entire concept in words? That's nigh on impossible.

nesf has managed to sum it up here.
One could translate the mathematics into English, but very poorly.

ISAW wrote:

Yes but you’re bordering on fundamentalism. Can the Koran only be understood in Arabic or the Bible only in Aramaic and Greek?

I don't know, but I do know that General Relativity can only be understood in mathematical terms.
Just as poetry can't be understood mathematically.

Verbal languages simply didn't develop these concepts, mathematics did. That is the only reason mathematics is necessary, because without it you will not have the necessary "concept-background".

Of course the mathematical symbols only represent concepts but unless you are familiar with those concepts, such as exterior derivatives, Tensors, e.t.c., General Relativity would be almost, if not totally, impossible to explain.

In formal mathematical terms yes. But math isn’t everything. You are pushing the envelope to suggest math describes all reality!

I don't think it describes all of reality. I think it can give approximate models of the physical world.

Would you not accept that meaning also involves interpretation and conception?

Conception definitely. Interpretation, in a form.

You need maths to understand General Relativity.
Could somebody understand Yeats or Orwell without having a verbal language?
Maths is simply another language. However it is one that cannot be easily translated into others, because of the way it developed.
I'm not suggesting there is some "holiness" to mathematics, that only it contains Mother Nature's secrets.
I'm simply saying no other language transfers the concepts correctly or lends itself to physical thinking like mathematics.

ISAW

nesf wrote:

This has been on my mind recently, quasi-discussed it with simu, but I'll try and summarise it here.


Ideas and concepts are distinct from the mode of communication that is used to express them. This is a fundamental truth that most people fail to grasp. It's all about the concepts ppl!

Yes but do concspts exist independently of people.

NB. We are now moving off the special case of General Relativity and into the general case of the history and philosophy of science. Welcome to my world!
I don't know if you watch Bravo but they have had a show on late at night called the Ultimate fighting Championship. I feel a bit like Tito Otriz the ex world champion. He was not as good a striker as the boxers or kick boxers and did not tend to wrestle. He got someone on the ground and just kept elbowing them to the head and upper body. I think he called it tito's world. I also believe some Russian andre Arlofski I think dealt him a KO punch.

Anyway, after that brief aside in "reality" I would claim to be no more a specialist on HPS as on GR. I am interested in the debate not in "winning" any exchange.I would offer the following however. The philosophy of language can be IMHO as complicated as GR. history I believe shows that at the time of Newton not many people understood Calculus. Indeed Newton called it fluctions . It is Libnitz we have to thank for a superior notation the squigilly sign and words like "calculus" "derivative" "integral". For fifty years or so newtons gravity remained in Latin( and newton notation) until a lover of voltaires (Hortence Lapaute? she also has the Hydrangia plant named after her ) a mathematical savant who had read Libnitz calculusand translated Principa into French.

where am I going here. well I am trying to paint the picture of how such concepts were historically represented.

Now as to the language bit. Linguistics 101 would suggest that "6" "vi" and "six" represent the same thing - the number six. What a number actually is is central since mathematics is grounded in numbers. What one plus one is took bertrand Russel about sixty pages to derive by logic alone.

I think roland Barths and Noam chomsky were seminal on thjis stuff. i think chomsky refers to "interpretation" and "representation" and the other guy on words as to "signified" "signifier" and "sign".

But it does not justify a dismissal of a certain mode of communication. I'll put forward an analogy and you can refute me, this is something I want to debate

Take an emotion. Now take the idea of an emotion. Now lets just pick anger for the sake of it.

On one side I have an abstract painting depicting the artist's rendition of this concept.

On the other I have a poem depicting the artist's rendition of this concept.

they are two representations. But I think it is important to look into what they represent. "Anger" is an abstract concept like "truth" or "beauty". Now if you said the painting was of two items one on top of the other, the picture is of something more concrerte.
Unless of course the items are quarks and you can still call them "truth and beauty" or "top and bottom" depending onn whether you are American or European and most people will be none the wiser

Which is the more true? Which is the more accurate? Are they both the same?

they are different[/q] representations. But there is a sense that there is somthing really there. But whether the thing there is a particle or an emotion we have similar problems in fighting to define an "ultimate reality". I still think one problem to me is that people might consider you example as an abstract representation of an abstract concept but see say quarks as concrete and not as abstractions which in some sence they are.

Is it not feasible that one "mode of communication" is not fundamentally better at expressing this idea?

Yes. mathematics. Because it does away with nuance. But the thing "6" "six" or "vi" represents still has to be grasped even if we all agree to use "6"

Maths is a language. It's the language of pure logic. This in it's own makes maths not an easy or very understandable topic. Maths gets very strange very fast once you step outside the "easily taught basic tenets" of it.

I agree but one not even get complicated. People frequently disregard basic logic denying the antecedent or affirming a consequent for example.

Take the whole question, what does 1 mean? We all know what 1 means but can you explain it perfectly in English? I've know I've yet to see a definition for it in English that matches my conceptual understanding in my head.

We are at one with each other on this! I would suggest a counting number is a one-to-one relationship between a set of numbers and a set of objects in the real world. But now I just went into a circle didnt I? Well one can define a set.

The concepts that maths can define are very different to the concepts defineable by English. Different tools for different jobs.
What's clear and understandable mathematically can often be extremely difficult to translate into English. Sometimes impossible. Same with art, sculpture etc. You can capture a "snapshot" of it in English, but trying to capture the entire concept in words? That's nigh on impossible.
I'm not sure if I'm making a lot of sense here.

You are making sense to me. very interesting. But back to GR in poarticular. what the math does is to propose concrete formal descriptions. But even accepoting its limitations, only one solution of GR equations describes the Universe. The rest are incorrect. So which one is it?

nesf

I'll post a reply to ISAW in an hour or two. Stupid things need doing getting in the way of my idle self-indulgant ramblings on the nature of concepts


Apologies to simu for derailing this thread horribly but I think that there is some worthwhile discussion to be made here

ISAW

Please excuse any flippancy in advance. I think I listed my arguments on representation in my last reply.

Son Goku wrote:

nesf has managed to sum it up here.
One could translate the mathematics into English, but very poorly.

But shakespeare in Klingon might be quite acceptable?

I don't know, but I do know that General Relativity can only be understood in mathematical terms.
Just as poetry can't be understood mathematically.

well it can but all that iambic pentameter stuff takes the joy out of it. Unless you are a rapper of course

Verbal languages simply didn't develop these concepts, mathematics did. That is the only reason mathematics is necessary, because without it you will not have the necessary "concept-background".

But the whole of mathematics can be explained in terms of set theory cant it? and that in turn has 13 (is it?) basic rules. So is it fair to say mathematics does not have any formal additions and is an inductive development from very basic stuff. At the same time we seem to be stating here that mathematics has the power to deduce the concept of what the Universe actually is!

Now even a painter will draw your attention to the fact that there is another world which is not on the canvas. some of the clever ones even make you think that the other world which you cant see in the canvas is actually in the canvass somewhere.

Of course the mathematical symbols only represent concepts but unless you are familiar with those concepts, such as exterior derivatives, Tensors, e.t.c., General Relativity would be almost, if not totally, impossible to explain.

but "almost" is almost and "would" is would. although I accept the point. It is still importand to note however that GR suggests that something should be measured and then people go and measure it and sure enough it comes out as GR predicted and not as other theories did. Other than Gravitational lensing i cant think of other examples. and the theory seemed so "true" that the original eclipse experiment which apparently "verified" GR did no such thing. so much for objectivity in science!

You need maths to understand General Relativity.
Could somebody understand Yeats or Orwell without having a verbal language?

there have been deaf and dumb playrights and composers. a blind person could in theory hold a PhD in the visual arts. But I agree that language helps one think. there are two modes of language however. One is for communicating. the other is foir philosophising. talking to yourself is NOT like talking to others. when you talk to yourself you are juggling as many concepts as someone doing mathematics in their head. Now literature and numeracy extends that to formally communicate it to others as does speech. But maybe mathematics is more "efficient" "concrete2 or maybe "brief" at communication.

then we have two problems 1. the problem of what is being communicated and we can go off into "ideals" and "universals"

2. If efficiency or brevity is the issue how come the Germans have such long words? Is life really to short to learn German?

Maths is simply another language. However it is one that cannot be easily translated into others, because of the way it developed.
I'm not suggesting there is some "holiness" to mathematics, that only it contains Mother Nature's secrets.
I'm simply saying no other language transfers the concepts correctly or lends itself to physical thinking like mathematics.

I think you have summed the whole thing up very wellin euglish. I also think the kerner of the issue is probably in working out how the concepts mentioned in your last sentence above are represented translated communicated and interpreted. But one must also ask what these ideal "concepts" are.

simu

nesf wrote:

Apologies to simu for derailing this thread horribly but I think that there is some worthwhile discussion to be made here

I've added to the title to account for the expansion of the thread. (if there's a problem with this, PM me).

nesf

simu wrote:

I've added to the title to account for the expansion of the thread. (if there's a problem with this, PM me).

You're making it sound pretentious....

Son Goku

Okay, I'll sum up what I mean in this post.
Bare with me because, I'm a physicist not a philosopher.

The field equation in its truest form is the following:

where:


The point being, in general, that given:

you can obtain:


can then be used to figure out orbits, e.t.c.

Thats General Relativity. You can't really do it without a knowledge of Tensors. Any attempt to transcribe this into would just be a vague description.
Maths is just the best language to this in.
(I know I just explained the Field Equation using english, but I suggest you ignore that.)

ISAW wrote:

But even accepoting its limitations, only one solution of GR equations describes the Universe. The rest are incorrect. So which one is it?

Almost all of them are physically realisable solutions, that occur somewhere in the universe.

I could be missing a lot of what you're saying ISAW, I was never really one for philosophy.

nesf

Son Goku wrote:

Okay, I'll sum up what I mean in this post.
Bare with me because, I'm a physicist not a philosopher.

The field equation in its truest form is the following:

where:


The point being, in general, that given:

you can obtain:


can then be used to figure out orbits, e.t.c.

Thats General Relativity. You can't really do it without a knowledge of Tensors. Any attempt to transcribe this into would just be a vague description.
Maths is just the best language to this in.
(I know I just explained the Field Equation using english, but I suggest you ignore that.)

These look an awful lot simpler than they actually are btw. Each of those letters represent very complicated thingies.

Son Goku

Yes, for instance:


are the components of a Tensor which any two vector properties of matter and returns a number.
In greater generality it describes the flux of (alpha)-momentum across a surface of constant "Beta".

The entire field equation represents the coupling of its components with the components of the Ricci Curvature Tensor, which is a contraction of the Riemann Tensor, and the components of the metric tensor, which describes the mapping of vectors into one-forms in the resultant space.

In fact thats only half of it and I haven't even defined certain things.

nesf

This might get complicated/obscure, I'm not sure how well I can articulate this so if I stop making sense please feel free to quote the relevant section and I'll try and make it clearer.


Right. Ok think outside the box here....

All the examples you listed were translations from verbal/written language to another. There essentially is very little difference between them.

I can say an bróg and a shoe and I'm essentially saying the identical thing. It's unusual for a word not be shared by many languages. It's "rare". This applys to "common speak". As soon as we get into "technical usage" like in philosophy for English for instance, then we aren't translating the words straight over, we are translating the "concepts behind the words".

Now the thing is, translating from maths to english is like translating from art to english. They are distinctly different modes of communication. There are concepts in maths that cannot be logically defined correctly in english. Same as there is "styles of painting" that cannot be communicated in words, you need to see the painting, see the individual brushstrokes, see the physical nature of the painting to appreciate it fully. If you were not "aufait" with art then you'd "miss" a lot. You wouldn't be able to fully appreciate the entirety of the concept captured in the work.


I'm going to try and express my thinking on this in the form of a questions and answers. Hopefully I won't bore you to tears

What seperates a mathematician from a physicist?

Well, Son Goku touched on this already somewhere I think, there is a magical unteachable quality called "physical intuition" that seperates the people who are "good" at physics from the "drones" who merely reproduce the work of others.

This quality is the ability to look at a set of data or a mathematical equation and for it to "coalese" into a kind of conceptual mental framework which fit's reality well. It's not something that you can teach to others. It really is something you need to find for yourself.

Some people are born with it (they are extremely rare), everyone else has to put a lot of hard work in before they "get it". It's like with philosophy, when I was in my teens I used read Satre, Kant, Nietche etc and thought, hey this is easy, I "get" this. I could discuss any part of their books, I could "understand" what they said in their books.

But I didn't "get" it. I didn't have the experience and knowledge to appreciate the subtler points they made. I was blind to them. I still have copies of some of those books and there is my own notes written in them, and they embarass me. I can't believe how narrow minded I used to be. Then again, I'm still, to an extent narrow-minded.

It's summed up by my favourite quote with regard to education:

"Education is a progressive discovery of our own ignorance."

Will Durant (1885 - 1981)

An idea is independent of the mode of communication used to represent it. Why then do you insist on maths being needed to express GR?

An idea in my head is independent of the stirctures and limitations of mathematics or English or anything. I don't "think in mathematics" anymore than I think in "English".

But there is no way for me to transplant ideas straight and unfiltered from my mind to yours. It just doesn't work that way.

There needs to be some mode of communication between us. Be it I draw a picture, write an equation or as I'm doing here, ramble in English. The words in this post are a poor reflection of the concepts in my mind, I just can't fully express them.

That's the eternal battle with one's own mind. How can I help people see what I can see? All I can do is open their eyes, and hope they read/look at what I do with an open mind. It still doesn't mean that it's possible though.


The thing with the "concept" of GR is that it is more accurately a very complex conceptual construct that was built out of need to explain reality in a mathematically consistent way. It's conceptually built to suit mathematics, not English or any verbal language. Because the level of precision required in the concepts is very high.

What do I mean by precision of concept? Well basically, in order for me to "explain" GR to you in English, I'd have to invent words. Because the English language was never meant to express what I would want to express to you.

As I said, different tools for different jobs. I can't write a philosophical essay in art or mathematics. I can try and "represent" it in either mode.

But I would be unable to deliver the concepts involved correctly simply because philosophy is a discipline that needs to be expressed in written/verbal language.

I'm going to continue this over to the next post. I'm going to run out of space here.

nesf

But what is the point if you can't explain it in English?

Here's the crux of the problem. People assume that writing/verbal communication is the prime mode of communication.

It isn't. It's just one amoung many. It's a product of modern society that people are "brain washed" into thinking in terms of English instead of thinking in concepts. Thinking in terms of concepts is more difficult, you can't passively accept concepts like you can with English. If you "think conceptually" you need to be self aware and "think about things".

Lets face it, people don't want to do this.

Think of it this way. I can express something to another person through many many different means. The mode I choose restricts me. There is no form that doesn't. An artist is restricted by their canvas/medium, a mathematician by the logic of maths, a writer by the grammar of his language.

The true greats in intellectual circles are the ones who "transcended" their mode. These are ones that managed to turn the "limitations" of their mode into part of their expression. They weren't hindered by it, they changed it as they went along.

An explanation in English is not the goal of physics. Physics can't be explained in English. It needs it's own "language". Like most technical disciplines. It's not that English is inferior, it's just that it is the wrong "tool for the job".

Think of it like this.

I read a script for a play, then I watch a production of the play. Are they the same thing? Do they mean the same thing to me? Are the same concepts expressed in both? Is there a difference in the types of concepts that can be expressed?

For instance. On a character notation, it might say (in a depressed tone of voice) "blah blah blah". Now a gifted actor saying that line might elict from me a responce far above and greater than what I'd read on a page. He's given the concept "life" if you will. Both are equally valid modes, it's just that they are also very very different.

So ok, why pop science then? Why do people write these books that are basically wrong?

Scientists need to make a living and people don't want to learn a new mode of communication just so they can grasp the concepts involved. They expect it to be available in "English" because they have been made lazy intellectually.

Please stop, you are boring me now....

Ok so.

nesf

Eh, on reading it over again, I'm not sure if I'm making much sense there.

Earthhorse

Maybe you should repost your thoughts, in mathematical form.

nesf

Earthhorse wrote:

Maybe you should repost your thoughts, in mathematical form.

Eh, I ramble a lot. So meh, I'm not even sure if the above makes even any sense to other people. It's just an attempt at communicating something that's been stuck in my head.


Plus I really should flesh it out more. But I just get distracted by some other idea and go off on a tangent with that so....

Meh. I don't care tbh.

Earthhorse

Nah man, I'm only joking with you. It made perfect sense to me.

Fact is, every time someone posts on this thread I find myself agreeing with them. I can see precisely where both sides are coming from.