X

[Slawbug]

Hmm. I think I see what you're saying, but I disagree completely, because if I understand you right, it really hinges on this statement

Originally Posted By: cfgauss

Math is the 'largest' set (by construction) in the 'space' of all sets of relationships.

that seems quite unfounded to me. How exactly is math the largest set in the space of all relationships?

[Alorael at Large]

I considered linguistics and computer science as other potentially deductive fields. I don't know enough about linguistics, but my impression is that, like physics, it's concerned with fundamental laws and how to apply them, not with abstract constructs of language with no basis in any real language. (Put differently, nobody sets out to create a language without nouns or verbs. Although, since I don't actually know the field, maybe they do and I'm just totally unaware.) Computer science... maybe. It's more concerned with actual processes that can be carried out by machines, but sometimes those machines are things that do not and maybe cannot exist.

 

cfgauss, I think we're not quite communicating, because I don't think I disagree with you. All sorts of things can be described by math. Math can't be described by all sorts of things, though.

 

Originally Posted By: cfgauss

Most of what pure mathematicians study are these relations abstractly, without context, but in principle it's always trivial to add context ("this is a C*-algebra" vs. "this is the C*-algebra of quantum mechanical observables").

Absolutely! But what other fields permit the study of anything abstractly, without context, always? You can get away with building up entire mathematical systems describing things that don't exist, possibly based on axioms that seem to be untrue in the context of reality. That's publishable! But try describing the role of alien hyperlasers in the mage-kings' resistance to social change during the Akkadian Renaissance won't get you very far even if the conclusions you draw are quite elegant.

 

—Alorael, who actually can think of another field that respects systems describing things that don't exist. The field is economics, and the economists don't like it when you point that out. Take that, current cultural whipping boy!

[Sullust]

I believe Godel would have something to say about this 'largest' set, namely that it doesn't exist...

[cfgauss]

Originally Posted By: CRISIS on INFINITE SLARTIES

that seems quite unfounded to me. How exactly is math the largest set in the space of all relationships?

Basically by definition. If you found things not in this space, and labeled them X_i, which were described by relationships, X_j ~ X_k for some j,k if X_j and X_k are related, then you could define a set X = {X_i}, and the orbit space of relations, R(X_i) = { x in X : X_i in x with x~X_i}. But then you could study X and the orbits R(X_i) with the usual tools of math, because this defines the set and relation structure. You can also easily impose any other structural requirements you need. So by contradiction we can show that this collection and relations not in the space of all describable things is in fact describable by the usual tools.

Although, incidentally, this is much larger than is needed for almost all problems. You can actually restrict yourself to things one can describe with basic first order logic and conditional probabilities and do almost everything. The things beyond this are the minority, and typically don't require much more (and are often related to the 'details' rather than the main ideas, and if you want to accept details without proof you may not need them).

Originally Posted By: demons will charm you

I considered linguistics and computer science as other potentially deductive fields. I don't know enough about linguistics, but my impression is that, like physics, it's concerned with fundamental laws and how to apply them, not with abstract constructs of language with no basis in any real language.

Like I said, the inductive/deductive view isn't as mutually exclusive as it seems. Induction is just staring in the middle of a deductive chain when you don't know the beginning, until you can find a plausible beginning (or beginnings) to deduce the things you want to know, and learned through induction.

It's a little more complicated when you're dealing with uncertain implications (e.g., a=>b, and a is 99.7% sure to be true), but it's definitely doable, and when done correctly you can use this to strengthen implications even though naively it would weaken them (e.g., a=>b=>c=>d... and each implication is less than 100% sure, the probability that the last one is true goes to 0 as the number of terms increases, but without much difficulty this can be strengthened so each implication increases the probability--this is called the scientific method ).

A very clear example of how this has specifically happened is seen in the history of physics. So I'll leave it to any book that covers the history of physics from the crazy philosophical nonsense of the 1700s to the more axiomatic physics of today!

Quote:

(Put differently, nobody sets out to create a language without nouns or verbs. Although, since I don't actually know the field, maybe they do and I'm just totally unaware.)

Believe me, they definitely do stuff like this! Making up perverse languages is something they do as often as the CS people make up perverse Turing complete languages! Although, sadly, since the field is still really new (as an actual science) there's still a lot of weird philosophical nonsense in it, so it's not as good as it could be.

Quote:

cfgauss, I think we're not quite communicating, because I don't think I disagree with you. All sorts of things can be described by math. Math can't be described by all sorts of things, though.

I'm not sure that means what you think it means? This statement is either vacuously true or vacuously false depending on the way you interpret it.

Quote:

Absolutely! But what other fields permit the study of anything abstractly, without context, always? You can get away with building up entire mathematical systems describing things that don't exist, possibly based on axioms that seem to be untrue in the context of reality.

But this doesn't matter. A specific system may not satisfy some particular set of axioms, but who cares? Every system is not described the same way. In modern science we have a notions of 'effective descriptions' where you don't (and maybe can't) know (or care) about the detailed, fundamental description, because the effective description can look alarmingly different than the fundamental one.

Examples of this are:
* Electromagnetism in matter. E&M in vacuum is a linear theory, E&M in matter can have all kinds of crazy nonlinear effects that someone who only knows E&M in vacuum might think are impossible. You can have lots of crazy optical effects using this, as well as other interesting effects.

* Quantum mechanics, which apparently violates unitarity when you measure things by having a 'wavefunction collapse', but the complete description involves no such thing. The horribly discontinuous, apparently laws of physics violating, collapse comes out as some weird limit of a system interacting with its environment.

* Cellular automata being turing complete, and being able to model any computation despite being normally described in terms of all kinds of bizarre math that has nothing to do with computations, and can't in any way be (obviously) applied to understand normal computers.

etc.

Quote:

But try describing the role of alien hyperlasers in the mage-kings' resistance to social change during the Akkadian Renaissance won't get you very far even if the conclusions you draw are quite elegant.

I have seen many papers, review articles, and textbooks that use colorful metaphors like this to describe any number of things .

And if you want to go as far as science fiction as historical/social commentary, then this has definitely been done! And taken seriously, too!

Quote:

—Alorael, who actually can think of another field that respects systems describing things that don't exist. The field is economics, and the economists don't like it when you point that out. Take that, current cultural whipping boy!

Actually, many of the systems physicists study don't exist. The reason they're studied is that they help us understand the systems that do because there are certain kinds of 'universal' behavior that show up in totally different types of systems, and because it helps us develop new tools and look at things from different ways, that can be used to solve 'real' problems. You could probably go as far as saying most theorists don't study 'realistic' systems most of the time--but that's good, not bad. And has clearly been very successful in developing new physics.

In fact, some of the 'unrealistic' systems we've studied have actually shown up in real life in effective systems described by condensed matter physicists.

Originally Posted By: Lt. Sullust

I believe Godel would have something to say about this 'largest' set, namely that it doesn't exist...

This really has nothing to do with what I am saying.
http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html
http://mathworld.wolfram.com/GoedelsCompletenessTheorem.html

[Slawbug]

Originally Posted By: cfgauss

Originally Posted By: CRISIS on INFINITE SLARTIES

that seems quite unfounded to me. How exactly is math the largest set in the space of all relationships?

Basically by definition. If you found things not in this space, and labeled them X_i, which were described by relationships, X_j ~ X_k for some j,k if X_j and X_k are related, then you could define a set X = {X_i}, and the orbit space of relations, R(X_i) = { x in X : X_i in x with x~X_i}. But then you could study X and the orbits R(X_i) with the usual tools of math, because this defines the set and relation structure. You can also easily impose any other structural requirements you need. So by contradiction we can show that this collection and relations not in the space of all describable things is in fact describable by the usual tools.

My bold. So basically you're saying that can study all of these relationships with math, because you have decided that math defines all relationships. That sounds like circular logic. Presumably you could study all of those relationships with history, if you also decide that history defines all relationships. What's special about math that makes it a priori the definition of all relationships?

[Dantius]

Originally Posted By: CRISIS on INFINITE SLARTIES

What's special about math that makes it a priori the definition of all relationships?

Because everybody is egotistical enough to think that it is their chosen field of study is the best and purest and awesome-est field there is, and that us plebeians should just shut up and be in awe of them. Historians do it, teachers do it, scientists do it, mathematicians do it, engineers do it, manual laborers do it, politicians do it, everybody does it.

They're all wrong, of course. But noone will admit it.

[Student of Trinity]

Math is a very small subset of history.

 

All the math that will ever be presented or studied will be expressed as thoughts by someone or something. Those thoughts are events, a very small subset of the events in all of history.

 

So, if we could only have perfect knowledge of history, we would know all of math.

[waterplant]

Originally Posted By: Dantius

Originally Posted By: CRISIS on INFINITE SLARTIES

What's special about math that makes it a priori the definition of all relationships?

Because everybody is egotistical enough to think that it is their chosen field of study is the best and purest and awesome-est field there is, and that us plebeians should just shut up and be in awe of them. Historians do it, teachers do it, scientists do it, mathematicians do it, engineers do it, manual laborers do it, politicians do it, everybody does it.

They're all wrong, of course. But noone will admit it.

Philosophers suspect that all disciplines have the capacity to be regarded as best/purest/awsomest - if one is prepared to take a broad enough veiwpoint.

[Slawbug]

Wowzers. Dantius made a post that I strongly agree with.

[Student of Trinity]

Originally Posted By: waterplant

Philosophers suspect that all disciplines have the capacity to be regarded as best/purest/awsomest - if one is prepared to take a broad enough veiwpoint.

Originally Posted By: W.S. Gilbert

If everyone is somebody, then no-one's anybody.

Originally Posted By: W.V.O. Quine

There is no first philosophy.

[Slawbug]

CONSIGN IT THEN TO THE FLAMES: FOR IT CAN CONTAIN NOTHING BUT--

[Lilith]

w.v.owns

[Dantius]

And here I was thinking that Slarty had given up spam...

[The Mystic]

Originally Posted By: Student of Trinity

Math is a very small subset of history.

All the math that will ever be presented or studied will be expressed as thoughts by someone or something. Those thoughts are events, a very small subset of the events in all of history.

So, if we could only have perfect knowledge of history, we would know all of math.

Assuming, of course, that the ancients knew everything there is to know about math.

[MissSea]

Originally Posted By: Math is not a wizened llama.

... abstract constructs of language with no basis in any real language.

It sounds to me like you just provided a rather concise definition of emotion. How do you describe happy? Or sad? What does hate mean to you? Those are all abstract constructs. Linguistics seeks to quantify these constructs, even if it lacks the the formula of how to arrive at such an undefined limit (apologies for the pathetic math analogy -- I barely survived my freshman college Calc class).

And, my dear Alorael, though as you stated, math describes all things, math can also BE described by many, many things. For just as language can be descriptive of an object, so can the way the language is constructed be descriptive of the creator.

Go with me here: for example, the pythagorean theorem (one of the only things I remember from geometry) states the a squared plus b squared equals c squared. Pythagoras was not only a man of science, but by all accounts, he was deeply spiritual. Perhaps in his studies, he deducted that a (the science) plus b (the spirit) joined to explain c (all things). Two sides that reach the same path. Just a theory, but it shows how history, language and psychology all pulled together to explain the universe in a very deductive way.

Of course, I could be totally off. I did use Wikipedia to look up Pythagoras ...

-MissSea

[Randomizer]

Originally Posted By: The Mystic

Originally Posted By: Student of Trinity

Math is a very small subset of history.

All the math that will ever be presented or studied will be expressed as thoughts by someone or something. Those thoughts are events, a very small subset of the events in all of history.

So, if we could only have perfect knowledge of history, we would know all of math.

Assuming, of course, that the ancients knew everything there is to know about math.

But history is always being written so eventually everything in math will be found in history.

Still I wouldn't mind consigning New Math to the flames.
For those of you that didn't have to learn it during the 60's then see Tom Lehrer's New Math

[Slawbug]

Originally Posted By: MissSea

How do you describe happy? Or sad? What does hate mean to you? Those are all abstract constructs.

Are they really? They aren't physical objects, but they are objectively identifiable human experiences. Are experiences abstract constructs?

Quote:

Linguistics seeks to quantify these constructs, even if it lacks the the formula of how to arrive at such an undefined limit...

Not really. Well, at rare times I suppose, but that's kind of like saying "math seeks to calculate the value of irrational numbers to more and more decimal places." While technically accurate, that is a tiny and unrepresentative part of what math as a discipline seeks. Likewise here. Linguistics is not about mapping out specific semantic domains with increasing precision -- that's a goal more often pursued by prescriptivist language teachers.

[MissSea]

Originally Posted By: CRISIS on INFINITE SLARTIES

Originally Posted By: MissSea

How do you describe happy? Or sad? What does hate mean to you? Those are all abstract constructs.

Are they really? They aren't physical objects, but they are objectively identifiable human experiences. Are experiences abstract constructs?

I think activities can be described objectively. We went here, we did this, etc. The emotions you feel aren't absolutes, though. What registers as a reaction of happy to one person, may not appear in another. The emotions themselves aren't definable, which is why language struggles to describe them. It's a constant pursuit to write that one phrase that describes everything one is feeling.

Originally Posted By: CRISIS on INFINITE SLARTIES

Originally Posted By: MissSea

Linguistics seeks to quantify these constructs, even if it lacks the the formula of how to arrive at such an undefined limit...

Not really. Well, at rare times I suppose, but that's kind of like saying "math seeks to calculate the value of irrational numbers to more and more decimal places." While technically accurate, that is a tiny and unrepresentative part of what math as a discipline seeks. Likewise here. Linguistics is not about mapping out specific semantic domains with increasing precision -- that's a goal more often pursued by prescriptivist language teachers.

Yes, but the flip side of prescriptivism is descriptivism -- linguists who are trying to determine <i>why</i> we use the language we do. And couldn't you say that understanding is the same as quantifying emotion?

For example, many teachers (especially in middle schools) have "dead word graveyards" on their walls -- words that aren't particularly descriptive, and thus deserve to be buried and not used. An example is "great". A prescriptivist teacher might ask, "What does that word mean, really? Could you find another word that may better describe what emotion you'd like to convey?" On the other hand, a descriptivist teacher might ask, "Why did you choose the word in the first place? Is it deliberate? Are you trying to convey some emotion by using it?"

(See: Misunderstood teenager being stopped by Mom on her way upstairs after a particularly grueling day of Calculus. Says Mom: "We're going to have family game night." Says daughter, voice dripping with disdain: "Great.")

As an aside, personally, I don't ascribe to any words being considered "bad". I think words are devoid of morality. Some can evince strong emotion, though. But society applies that morality.

And watch out bashing prescriptivist language teachers -- don't you need to learn the rules before you then break them? How else can rebellion and revolution take place unless a recognized set of rules is first applied and then broken?

- MissSea

[Student of Trinity]

Originally Posted By: The Mystic

Assuming, of course, that the ancients knew everything there is to know about math.

Originally Posted By: Randomizer

But history is always being written so eventually everything in math will be found in history.

Originally Posted By: William Faulkner

The past isn't dead. It isn't even past.

@Slarty:

Oh give me a Hume,
With his skeptical gloom,
And his fears that he doesn't exist.
How seldom is heard
Anything so absurd;
Was he mad, or just thoroughly pissed?

CHORUS:
Hume, Hume is so strange!
He's a positive negativist.
His thinking was blurred,
If it even occurred,
And he probably doesn't exist.


(As a matter of fact I myself admire Hume a lot. (You can't help admiring someone who can out-consume Schopenhauer and Hegel.) It's only the Muse of Parody that seems to hate him.)

[Slawbug]

Yes, I remember that one SoT -- it was inspired

 

Originally Posted By: MissSea

Yes, but the flip side of prescriptivism is descriptivism -- linguists who are trying to determine <i>why</i> we use the language we do. And couldn't you say that understanding is the same as quantifying emotion?

No, I wouldn't. Quantification implies changing the form of something -- perhaps cosmetically or perhaps through significant truncation -- to make it numerical. Looking at it functionally, you get an output that is totally different from what you put in. Understanding does too, but it produces a complex cognitive structure rather than a number. They are totally, totally different processes, whether applied to emotion or anything else.

 

Also, that's not what descriptivism is -- it has nothing to do with asking why we use particular linguistic forms. I know you won't like this link, but it's a reasonable description:

http://en.wikipedia.org/wiki/Descriptive_linguistics

 

Quote:

And watch out bashing prescriptivist language teachers -- don't you need to learn the rules before you then break them? How else can rebellion and revolution take place unless a recognized set of rules is first applied and then broken?

Prescriptivist teaching *can* be a good way to learn the rules. The problem is that it is invested in maintaining the same set of rules, but actual language use changes over time, often slowly but sometimes fairly suddenly. If you are a prescriptivist, you think that your rules are correct and the vernacular is wrong, whereas a descriptivist viewpoint always places the vernacular first. For a simple example, which one of these is "correct"?

 

(1) Who did you go to the prom with?

(2) Whom did you go to the prom with?

 

The descriptivist answer is 1 and the prescriptivist answer is 2. (Some prescriptivists might go further and assert that you can't split prepositions and objects in English, although that has never actually been the case.) Typically, pronouns have case in English that must match their use. However, over the last century this has eroded in some circumstances, including when an accusative pronoun from a later prepositional phrase begins a sentence. That's actual use. That's actual, current, English grammar. But it's not what English grammar has been standardized as in the past. Which do you prefer? *shrug*

[Lilith]

the sad thing is this is still better than how the thread started out

[Lilith]

hey so slarty are you ever going to finish that deathmatch thing or can i at least annoy you enough about it that you kill everyone like you did with the other one

[The Mystic]

Originally Posted By: Randomizer

But history is always being written so eventually everything in math will be found in history.

Well, I'm not holding my breath until the day we know everything (which, of course, will never happen).

Originally Posted By: Lilith

hey so slarty are you ever going to finish that deathmatch thing or can i at least annoy you enough about it that you kill everyone like you did with the other one

I thought the deathmatch was finished.

[Slawbug]

He's talking about the Video Game Stunt Double Deathmatch Tourney. But it will take a few more years of neglect before that one is as behind as the original Deathmatch!

[Student of Trinity]

That Slarty. He's even fallen behind in his neglecting.

[Lilith]

Originally Posted By: CRISIS on INFINITE SLARTIES

He's talking about the Video Game Stunt Double Deathmatch Tourney.

she

[Zalatar2]

I'm kindof lost. Okay. so Lilith is a 'she', X has been almost totally forgotten here, there's a bunch of awesome mathematical and linguistic discussion, and idk what is going on, so I think we should bring this back into ow ow ow

 

I'm ow trying to ow pull this threaow ow ow back on track.

 

ow

ow

ow

my arm

ow

My mentaow arm is being pulled owut of it's socket

ow

 

Okay. Phew. Back on track.

 

X. I think that X should be found SOMEWHERE, if not in this game. Maybe in this game in an easter egg or something?

 

*rubs mental arm*

 

Back off track.

I didn't even bother to read all 8 pages, I only read 1,2 and 8. So, I know that the people of this forum are even more awesome than I already thought you people were : you like math! (I think)

 

Back ow on track.

 

"I can't shake him!"

"Stay on target."

"I can't shake him!"

"Stay on target."

"AAAAAAA-"

 

Back on track.

 

PLEASE STAY ON TRAXCK.

[Dantius]

Originally Posted By: Zalatar2

I'm kindof lost. Okay. so Lilith is a 'she', X has been almost totally forgotten here, there's a bunch of awesome mathematical and linguistic discussion, and idk what is going on, so I think we should bring this back into ow ow ow

I'm ow trying to ow pull this threaow ow ow back on track.

ow
ow
ow
my arm
ow
My mentaow arm is being pulled owut of it's socket
ow

Okay. Phew. Back on track.

X. I think that X should be found SOMEWHERE, if not in this game. Maybe in this game in an easter egg or something?

*rubs mental arm*

Back off track.
I didn't even bother to read all 8 pages, I only read 1,2 and 8. So, I know that the people of this forum are even more awesome than I already thought you people were : you like math! (I think)

Back ow on track.

"I can't shake him!"
"Stay on target."
"I can't shake him!"
"Stay on target."
"AAAAAAA-"

Back on track.

PLEASE STAY ON TRAXCK.

What.

[The Mystic]

Originally Posted By: CRISIS on INFINITE SLARTIES

He's talking about the Video Game Stunt Double Deathmatch Tourney. But it will take a few more years of neglect before that one is as behind as the original Deathmatch!

I see....I must've forgotten about that one. I guess my memory needs a serious upgrade.

[Alorael at Large]

Originally Posted By: MissSea

Originally Posted By: Math is not a wizened llama.

... abstract constructs of language with no basis in any real language.

It sounds to me like you just provided a rather concise definition of emotion. How do you describe happy? Or sad? What does hate mean to you? Those are all abstract constructs. Linguistics seeks to quantify these constructs, even if it lacks the the formula of how to arrive at such an undefined limit (apologies for the pathetic math analogy -- I barely survived my freshman college Calc class).

Okay... but what I meant is constructs of language. Like artificial, constructed languages, but often lacking a full language because the point is to illustrate a point or consider a possibility rather than to actually communicate. And linguistics isn't in the business of quantifying emotions anyway.

In any case, I don't think I get it. People describe "happy" and "sad" all the time. It's meaningful and communicative to talk about them. What's the problem?

Quote:

And, my dear Alorael, though as you stated, math describes all things, math can also BE described by many, many things. For just as language can be descriptive of an object, so can the way the language is constructed be descriptive of the creator.

Go with me here: for example, the pythagorean theorem (one of the only things I remember from geometry) states the a squared plus b squared equals c squared. Pythagoras was not only a man of science, but by all accounts, he was deeply spiritual. Perhaps in his studies, he deducted that a (the science) plus b (the spirit) joined to explain c (all things). Two sides that reach the same path. Just a theory, but it shows how history, language and psychology all pulled together to explain the universe in a very deductive way.

Pythogoras's role in proving the Pythagorean theorem is irrelevant. The theorem is true, and it would be true regardless of who first articulated it, or why, or even how.

You can use math to create equations to describe Newtonian mechanics, or even relativity and quantum dynamics. Physical reality is, in a significant sense, dictated by the math. You can use equations to describe cellular processes or the spread of alleles in a population or the virulence of a disease. Life, too, is dictated by math. Economists try to describe very complex behaviors and market forces with math; that tends to be descriptive rather than true in the physical sense, but it's still trying to fit reality to a mathematical model.

You cannot use anything else to derive math. You can write a lot about it, but in the end math isn't dependent on descriptions, or history, or real-life implications. Math is, and mathematicians don't create new math so much as they discover new ways to manipulate mathematical concepts or prove one theorem true and another false. It's a platonic discipline.

—Alorael, who considers prescriptivists helpful for the maintenance of a cohesive and, sometimes, elegant language. Descriptivists, however, are necessary to keep the official language from diverging completely from the language actually used to communicate. Both have their roles.

[Randomizer]

Originally Posted By: Student of Trinity

That Slarty. He's even fallen behind in his neglecting.

Procrastination is more than a lifestyle choice, it's a whole way of life.

[Zalatar2]

I repeat. Please. Stay. On. Traget.

 

I misspelled traget on purpose, so as to catch your eye.

Target!

Now if you weren't caught by the traget now you've been caught by the target being spelled correctly.

 

Is it possible to misspell X?

 

XD

 

XD

 

XD

 

XD

 

(XD on XD which is for the XD)

 

Anyways, I think that X should just be in an easter egg. Probably not part of the actual plot line. Maybe if someone were crazy or stupid enough (or both, like me) to make a thingymajigger of avernum/exile that continues X's story.

Or maybe it could just be called X's story.

[Lilith]

Originally Posted By: Zalatar2

I repeat. Please. Stay. On. Traget.

I misspelled traget on purpose, so as to catch your eye.
Target!
Now if you weren't caught by the traget now you've been caught by the target being spelled correctly.

Is it possible to misspell X?

XD

XD

XD

XD

(XD on XD which is for the XD)

Anyways, I think that X should just be in an easter egg. Probably not part of the actual plot line. Maybe if someone were crazy or stupid enough (or both, like me) to make a thingymajigger of avernum/exile that continues X's story.
Or maybe it could just be called X's story.

in mainstream economic theory, value derives from scarcity

please make your posts more valuable

[Alorael at Large]

More helpfully, I'm not sure what track you're so insistent on. Threads can change topic like any conversation, and that's perfectly okay. Not even the original poster gets to police the thread.

 

—Alorael, who will consider any more long rants against the discussion taking place spam. Please don't spam.

[Student of Trinity]

Posts in the state of nature are nasty, brutish, and short.

 

Ah, there I go again, naively idealizing the state of nature.

[Zalatar2]

Oh, well, sorry then.

I didn't know that threads were supposed to do that.

I guess this is sortof like one of X's experiments then.

I feel like such a noob now... i'ma go cry.

[Goldengirl]

Originally Posted By: Student of Trinity

Posts in the state of nature are nasty, brutish, and short.

Ah, there I go again, naively idealizing the state of nature.

Are you attempting to say that natural posts are short? I'd contend that...

Oops.

[MissSea]

Originally Posted By: Mastery and Mischief

In any case, I don't think I get it. People describe "happy" and "sad" all the time. It's meaningful and communicative to talk about them. What's the problem?

Okay, now I'm confused. I may have to go back and check the original post here, but I thought we were discussing how math is the only discipline unable to be defined by anything else. My original comment was indicating that though people can describe happy and sad, there are infinite ways to describe it. Therefore to be able to quantify emotion is something with which language struggles, just as math struggles to define things occurring or existing in the universe.

Originally Posted By: Mastery and Mischief

Math is, and mathematicians don't create new math so much as they discover new ways to manipulate mathematical concepts or prove one theorem true and another false. It's a platonic discipline.

Hmm. What I glean from your comment is that all math already exists in the world, while language is something that's constantly evolving, therefore math cannot be described by other disciplines because it already exists. But I think that's a short-sighted view of both disciplines. Just because a language dies doesn't mean its roots aren't found in other languages.

And it seems to be making math very insular. Why do mathematicians seek to discover anything in the first place? What is the point? Knowledge? Pride? Societal betterment? I don't for a second think that math isn't affected by other disciplines. And that it is affected by other disciplines also means that it can be described by them.

-MissSea

[Student of Trinity]

Every discipline is special in some way, and no discipline is totally isolated from all others. But math really is unique, because it's so entirely abstract. Other disciplines all have some arbitrary elements. A rose by any other name would smell as sweet; as far as we can tell, electrons could just as well have been a tad heavier or lighter than they are; the Battle of Hastings could have been fought in 1067, for all the difference it would really have made.

 

Math, though, is different. Math is what's left when you take away everything that's arbitrary. Math is what has to be just so, and couldn't be otherwise.

[Slawbug]

Originally Posted By: Student of Trinity

But math really is unique, because it's so entirely abstract. Other disciplines all have some arbitrary elements... Math, though, is different. Math is what's left when you take away everything that's arbitrary. Math is what has to be just so, and couldn't be otherwise.

This is an assertion that sounds nice, but there's no substance to it (at least not any that's been explained). Why does the fact that math is entirely abstract make it any less arbitrary than (for example) language? Yes, numbers and operations follow patterns and rules of logic, but so do (for example) languages. What makes the patterns and rules of logic used in math so totally devoid of arbitrariness?

Or to put it more briefly: Why couldn't math be otherwise?

[Alorael at Large]

Originally Posted By: MissSea

Okay, now I'm confused. I may have to go back and check the original post here, but I thought we were discussing how math is the only discipline unable to be defined by anything else. My original comment was indicating that though people can describe happy and sad, there are infinite ways to describe it. Therefore to be able to quantify emotion is something with which language struggles, just as math struggles to define things occurring or existing in the universe.

Quantification of emotion is something with which I think everything struggles. Quantitative psychology and neuroscience are struggling the most fruitfully, but we don't actually understand emotion all that well. That said, while we can't quantify, we can describe just fine.

Math doesn't struggle to describe things existing in the universe. It doesn't describe things, although it can be used to model things. Math deals with math.

Quote:

Hmm. What I glean from your comment is that all math already exists in the world, while language is something that's constantly evolving, therefore math cannot be described by other disciplines because it already exists. But I think that's a short-sighted view of both disciplines. Just because a language dies doesn't mean its roots aren't found in other languages.

That's not at all what I'm saying. Math doesn't really exist at all. Math is descriptions of logical truths. The truths are true whether or not they have been discovered, articulated, and rigorously proven or not. These truths can only be described by math because that's what math is: descriptions and codifications of the logical progression from axioms to theorems.

Languages have really nothing to do with it. You can also describe ancient Roman history, which isn't changing, but that doesn't make history any more an abstract and fixed discipline.

Quote:

And it seems to be making math very insular. Why do mathematicians seek to discover anything in the first place? What is the point? Knowledge? Pride? Societal betterment? I don't for a second think that math isn't affected by other disciplines. And that it is affected by other disciplines also means that it can be described by them.

Flippantly, because mathematicians, like other academics, must publish or perish. Really, I think it's because those who are drawn to academic math are those who want to work out new theorems. It's knowledge, and pride, and sometimes the hope that new mathematical insights will be helpful to society (although uses for new math almost always follow new math by decades or more).

Originally Posted By: Slarty

This is an assertion that sounds nice, but there's no substance to it (at least not any that's been explained). Why does the fact that math is entirely abstract make it any less arbitrary than (for example) language? Yes, numbers and operations follow patterns and rules of logic, but so do (for example) languages. What makes the patterns and rules of logic used in math so totally devoid of arbitrariness?

Or to put it more briefly: Why couldn't math be otherwise?

We can think about what a universe would be like if Planck's constant were much larger, or if Rome had survived until the present day, or if roses were all green. It may be, in some sense, possible for the deductions of math to be wrong, but not in this universe. And I don't just mean this physical universe; even with all the constants changed and matter rearranged, 2=3, the angles of a triangle add up to 180º, and a^n + b^n != c^n for n > 2. These are, in a sense, arbitrary truths, but they are true. Languages generally follow some reasonable pattern, but you can alter the vocabulary or syntax and still get a coherent language.

I've been saying it over and over, but it doesn't seem to be working. I'll say it again, though: math is the only discipline that is entirely deductive. It can't be otherwise because logic dictates that it is how it is. Nothing else is so rigidly defined by truths that not only are not otherwise but that cannot conceivably be otherwise.

—Alorael, who thinks SoT's brief explanation is the closest to what he's been driving at in this discussion.

[Slawbug]

I agree that abstraction and deductiveness are different about math. I just don't see how that makes it less arbitrary. Deductions have to start with something to deduct from -- there must be a First Cause, if you will -- and whatever that is, is just as arbitrary for math as a set of scientific or historical observations are.

[wz. As]

The arbitrariness lies somewhere else. With history or linguistics or biology, you could say that the arbitrariness appears when you look at the world. The laws of the universe are fixed, but what happened in 1066 or which word we use to refer to a rose or which proteins take apart DNA are arbitrary in that the world might have happened differently. In math, the arbitrariness comes in setting up the rules of the game (contrast this with the fixed laws of nature), but once you have done that, everything that comes after necessarily follows from the rules you started with.

 

Alorael, it's interesting that you cite angles of a triangle adding up to 180 degrees as an example of the non-arbitrariness of math. There are models of geometry — spherical geometry, hyperbolic geometry — where the angles of a triangle add up to greater than or less than 180 degrees, respectively. Of course, once you define what your model is, every truth that follows is a necessary truth.

[Alorael at Large]

And you've just given my response to Slarty: the axioms are arbitrary, but the theorems built upon them are not. They're set as soon as the axioms are chosen. (In the case of triangles, you're choosing your version of the parallel postulate: given a line and a point, how many lines parallel to the first line pass through the point? Postulate zero lines, one line, or more lines and you'll get elliptic, Euclidian, and hyperbolic geometry.)

 

In other disciplines, you don't get to pick your axioms. They're the ones reality deals you. In math, you can pick any axioms you want. Some of them don't let you go very far, and some are so alien to anything you can actually experience that it's difficult to see any reason to work with them. (Want to postulate 2=3? Good luck going anywhere!) But you can do it, and you still have math.

 

—Alorael, who considered not using the 180º triangle example. In fact, there are many non-Euclidian geometries that disagree. But that's the basic fact taught in geometry classes, and it seems like a reasonable place to start. Call it a centrifugal force of math: fictitious, but a useful shorthand.

[Slawbug]

I agree with all of this, and this is really what I was trying to say, too: there are arbitrary elements to math, even if they are different ones from the arbitrary elements in most disciplines.

[Pathos]

I clicked the first page.

 

Then I clicked the last page.

 

Now I'm just lost.

[Dikiyoba]

It is called topic drift. It happens.

 

Dikiyoba.

[Alorael at Large]

Originally Posted By: CRISIS on INFINITE SLARTIES

Deductions have to start with something to deduct from -- there must be a First Cause, if you will -- and whatever that is, is just as arbitrary for math as a set of scientific or historical observations are.

Except with observations, your deductions start with the arbitrary (or inductive) truths you're given. In math, you can start with whatever you want. The axioms aren't arbitrary; your choices are. If you make different choices, you get different theorems out of the mix. The real difference is that math doesn't care which axioms you're working with. Your math is just as valid with any set of axioms. Less useful or less publishable, maybe, but no less true.

Start doing scientific work based on data that goes counter to what's observed or analyzing history that isn't part of any record and you're on solid crackpot ground.

—Alorael, who finds the difference to be meaningful and significant. The elements are arbitrary in different senses. In math, axioms are arbitrary because they are based on random choice (although not really random). In other fields, the starting principles are arbitrary because they aren't chosen at all; they're the hand reality has dealt.

[Student of Trinity]

Math is not the conclusions, and it's not the arbitrary premises, either. It's the fact that the conclusions follow from the premises. And that's not arbitrary at all.