/sci/ - Science & Math

Math is much older than science, so yeah.

The universe doesn't need math.
math needs universe.

>>1050710

> He really believes that math isn't transcendent

>>1050716
prove that math is transcending in hypothetical parallel universe biyotch

>>1050710

Math is part of the universe.

>>1050722
How is math part of the universe?

Math is worth nothing without being applied in science.

>>1050724
fucking idiot

My consciousness doesnt need my body
my body needs my consciousness

>>1050744
>>1050722
Must be trolling

Science develops existing areas of mathematics and also introduces new ones.

Logic doesnt need maths
Maths needs logic

>>1050757
You can be in a comma and your body doesn't need conscience.
Your conscience won't be there if you body's rotted.

Maths is a tool for science, a spanner in the right hands can be very useful but by it's self it is useless

>>1050759
Wrong. Math is pretty much 100% human made. There are no set "rules" in the universe. Things just behave the way they do most of the time. The universe could give fuck all about maths.

>>1050766
^ idiotic

>>1050766
You're confusing me and you're confusing yourself

>>1050771
>has no argument
That anon was right, math is a human construct. We don't discover 1+1=2, we define it to be true.

>>1050766
>There are no set "rules" in the universe
>The universe could give fuck all about maths.

So the universe doesn't have rules but it obeys maths?

>>1050766
>child.

lrn2axioms and set theory

Now go back to the vacuous middle-class highschool where you came from.

>>1050782

>>1050782
^^^ also idiotic

Please prove you conjecture that 1+1=2 is false in the absence of humanity.

>>1050792
The argument is on you to prove it is right without humanity

>>1050785
there are rules in universe and math can represent this rule, universe doesn't follow math, math follows universe. Man I thought mathematicians are suppose to be smart and logical.

If two trees fall down in the forest, and there's no one to hear them fall, how many noises do they make?

>>1050782
So you are saying 1+1 can be not 2? and 1 brick plus 1 brick is not 2 bricks?

>>1050798
Smart and logical doesn't deal well with stupid and illogical

I'm sensing some major samefag in the vicinity.

>>1050803
We define what 1 and 2 are, so 1+1=2 unless you change the definitions.

>>1050766
Yes a human concept to explain reality.

>>1050809
you are talking about symbols for one of something and two of something? you mean we define symbols for one and two of something?

>>1050796
Lol. Why.
I offer that TRUE => TRUE
is a construct that is independent of consciousness. Further, I offer that my opinion on this indisputably carries the weight of opinion. Therefore, the burden of proof is on you to show that TRUE => TRUE is a human construct.

>>1050811
>A human concept to explain evidence subjectively observed and interpreted by humans

Fixed

>>1050814
The numbers 1 and 2 (not just the symbols) don't exist outside of mathematics. We define what 1 and 2 are in relation to one another, thus 1+1=2.

>>1050825
Mathematics exists outside human definition.

>>1050816
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Dumb shit. Think because you've watched a few PBS docs you know what the fuck you are talking about. Math is completely abstract and man-made.

>>1050825
we just take it from universe - we dont define it as somebody want.

>>1050833
What's PBS
PROTIP: Abstract =/=> Manmade

>>1050825
we can define it only in one way - in that way as it goes in universe

>>1050825
How many protons in a helium nucleus. Or are you saying Helium is a human construct?

>>1050816
A=A is at the heart of logic and is true no matter what universe you may be in. Mathematics is just a bunch of definitions we created. It is up to us to make it logical or self consistent but beyond that it is a human creation. If we find an alien civilization they will likely have a few similarities in mathematics but that is only because some of the simplest concepts are universely useful if not universal.

>>1050844
Depends how big the nucleus is

>>1050833
LOL. FUCK LOL. Quoting your source:
"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."

Now GTFO before you embarrass yourself further.

>>1050850
No it doesn't.

>>1050861
Yes it does. It's basic science you fucking inbreed.

>>1050859
That basically says that mathematics is just observation.

Numbers don't exist.

Stop being such a dumb shit. You are a disgrace to humanity.

>>1050859

sounds like a quote from Morris Kline in "Loss of Certainty".

>>1050850
wtf is happening to my /sci/

There has always been a degree of retardedness, and an excess of trolling, often confused between the two. But WTF it this?

>>1050871
You mean symbols for numbers?

>>1050838
You should have been aborted

>>1050874

i think he means quantity a whole. As long as something exists, and that something can be absent, then all of mathematics applies to whatever universe, or environment that we're in.

>>1050877
Apparently you were partially aborted before your daddy changed his mind. Here's another tip. Before there were humans, dinosaurs came in discreet numbers. 1 T-Rex + 1 T-Rex = 2 T-Rex

You are stupid, beyond modern comprehension. There isn't an undergraduate philosophy degree that you could pass with this mindset, let alone anything in the sciences.

>>1050890
>There isn't an undergraduate philosophy degree that you could pass with this mindset, let alone anything in the sciences.
This leads me to believe that you aren't even in college. Now go on, get the fuck out of /sci/. Your baby troll isn't impressing anyone.

>>1050900
but what you can say about dinosaurs?

>>1050900
Okay, you win. Whole numbers are a human concept. (which of course means, aliens won't use them) - I can't be bothered with such blatant anti-logic any more, feel free to have your last attempted dig down vvvvv there

>>1050900

>talks about abortion
>and the childishness of another user

wtfamireading.jpg

The universe does use maths... numbers like pi and phi are universe-created, we've just observed them.

>>1050980
>numbers like pi and phi are universe-created
JESUS CHRIST you mathematicians are fucking useless

>>1050997
>implying a mathematician just made up the value of pi

>>1050890
I disagree, 2+2 = 1

because i have defined it to be so, pic related

math is science

Fixed

>>1051019
FFS. Just 'cos you've shown it's true for apples, does NOT mean it still hold for dinosaurs.

>>1051019

only because the concept that is defined as 1 in mathematics and the concept that is defined as 2 in mathematics have been reversed in your definitions. The symbols 1 and 2 are arbitrary, they must as well be green and blue, or apples and oranges. But the concepts behind them still follow the same rules.

>>1051019
but you just changed SYMBOLS

>>1051021
Sorry, mathematics is not science. It is as much science as Comp. Sci. is for example, it's just a tool.

>>1051054
any science is a tool for something

>>1051037
yes, the concepts behind them, concepts devised by man.

if man is gone, so goes the concept.

Maths is a system devised to explain how the universe works.

>>1050761

Maths IS logic. Mathematics is pure logic in its most refined form.

>>1051102

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

>>1051086
if man is gone concept willnot gone you are liar and troll.

>>1051086

So if all 6 billion some humans are dead...how many dead humans are there? Whether we live or die mathematics continues on being truth.

>>1051146
Oh so the past will still exist even if no one is there to remember it?

and i suppose the universe has intrinsic good and evil as well?

all of these are conceptual, maths is no different.

>>1050694
FUCK YEAH

>>1051102
This is very stupid, axiomatic logic obviously cannot be derived from mathematics, whereas maths can MAYBE be derived from logic (if you follow Frege, Russell-type thinking on this)

If it can, prove that 'P or not P'

>>1051158

Perception doesn't define reality. If all humans died today, the laws of physics wouldn't stop being true. And if mathematics is an extension of pure logic as has been suggested by Bertrand Russel and others, then it is not merely a man made construct.

>>1051158
Reasons to not major in Chem right here...

>>1051167

I never said logic can be derived from maths. I said maths was a refinement of logic, ie it can be derived from logic.

>>1051168
That's as far as you can prove, however. That you exist, and only to yourself. The universe may aswell not exist when your perception ends.

>>1051102
This is backwards - your point is essentially correct, but logic is the most pure, and mathematics follows.

>>1051173
You said "maths IS logic", which is strictly untrue, there's no equivalence relation, mathematics can maybe (I stress maybe) be derived from axiomatic logic, but not the other way around. Logic is as pure as it gets

>>1050694

Science use logic.
Logic is independent from science.

Logic comes from philosophy and, unafortunately, philosophy is NOT welcome here. Therefore...

>>1051190

I meant maths is a part of logic, as in logic is the larger field and mathematics is a smaller field contained within it. I only said it like I did for dramatic effect.

>>1051177
When I said maths is pure logic, I meant that it is the most pure way of expressing logic. I wasn't saying mathematics is more pure.

>>1051155
Truth? maths has no system of verification within itself.
There is no mathamatical formula, no strict logical argument that you can give that will necessitate its truth.

Maths works because of logic, because we have the capacity for logic, we formulated a system using logic to quantify and explain the universe.

>>1051170
fuck yourself, yes i mad.

>>1051206
There are purer ways of expressing logic than mathematics.

>>1051217

Like what?

>>1051206
The most pure way of expressing logic is surely logic?

'ExEy(x=/=y)' and '2' express the same concept but I don't see how the former is less pure

>>1051209
I invite all the high school kids here to review the chemfags rage at the idea that 1+1 still =2, even without humans to conceive such a construct, and use this to assist in choosing their college major.

>>1051231

Logic itself is not a form of expression.

>>1051209
Maths doesn't 'work because of logic', mathematics is just an extension of a very small, well defined set of logical axioms. Mathematical truths just sort of sit there until someone discovers them. So while its not nescessary that mathematic truths will relate to the rest of the universe, it IS true that any proof you discover within mathematics will be true with respect to its own axioms

>>1051226
Strict symbolic logical language, that has no use for abstractions such as 'numbers'.
Godel's proofs for example.

>>1051233
I invite you to prove to me that maths is necessarily true.

if you cant, you have no argument.
its simple.

>>1051241
Wat? Logic is an extremely precise form of expression, far better than the English language in some respects. My guessing is that you just don't know how to express yourself in a logical system?

>>1051250

You mean Godel the mathematician? Just because there are no numbers doesn't mean it's not mathematics.

>>1051233
Not >>1051253, but it really isn't simple, I'm doing an entire module on mathematical logic and even to begin to explain the debate about some of the concepts would go into some outrageously heavy philosophy very quickly.

>>1051253
You're the same faggot with the stack of "quantum chemistry" books who was trying to pass himself off as a qualified scientist yesterday, aren't you.

That's fucking hilarious - you got issues boy. And they're in the realm of psychology, not chemistry or mathematics.

>>1051248
>Maths doesn't 'work because of logic', >mathematics is just an extension of a very small, well defined set of logical axioms

im sure you meant something different from what you typed.
because what you just typed is self contradictory.

>>1051270
Arguably it does - Maths, absent a field (or group, or any QUANTIFIABLE) construct, is no longer maths, it is simple logic.

>>1051250
Symbolic langauge 'has no use' for anything, its just a collection of symbols and rules that you can direct to do certain tasks. The symbols and rules themselves don't care if you use them to represent numbers, and if people (like Godel) find them useful to use in this way then it seems like they ARE useful in a sort of self-proving kind of way

>>1051292
Equally applies to human language

>>1051280
my my angry aint we, getting to that age are you?

>my trip is 3rdyearChemfag
>saying i tried to pass myself off as someone with a degree when a simple look at my trip would say otherwise

HMMMMM

but seriously, cut the ad hom, i gave a simple proposal, dont get all pissy if you realise you're wrong.

>>1051258

I meant expression in the most literal form. I know its a gross over-simplification, but logic is just a very refined form of critical thinking. You still need a means of communicating and expressing the concepts of logic. Logic in and of itself does not "express" itself. I think we're getting too bogged down in semantics now though.

>>1051284
I see what you mean, I meant to take issue with your claim that there is no argument that will necessitate the truth of mathematics, and I took the form of your argument to be:

1. Maths (and by extension, logic) is just a tool we use to explain the universe
2. If we were not around, or did not have the capacity to use logic, we would not use maths to explain the universe
3. Therefore the rules of mathematics are only derivable because of the contingent facts that:
i. We use logic
ii. Maths is predicated on logic
4. Therefore the 'truths' of maths are not nescessary

But I disagree, because the logical rules still stand in relation to each other, even if nothing external

>>1051299
Yes, I think it probably does, but why is that relevant?

>>1050694
the universe has some sort of unconscious inherited knowledge of mathematical language, why ? There isnt a better way to describe the universe without it.

>>1051308
Semantics are important!

I disagree though - we could have two totally different alphabets and still end up communicating the same logical truths to each other. For example, I have seen an 'if... then...' clause written as both c and ->, but because I can run both symbols through a truth table I can express and understand equivalent concepts written in both languages. It is not nescessary for humans to codify the laws of logic in order that they are laws

Though I agree, the concepts of logic do not literally write themselves on a page, but I'm pretty sure (and hopeful) this is not what you meant

>>1051316
hmmm, more along the lines of:

maths is something you either accept or reject, much like logic.

if you accept it, you use it, it works, and things within that system can be true or false, but theres no evidence, logic, reasoning, or whatever to assert that the system itself is true or false.

then you got some people going on to say that the universe follows this exact same system, which we devised mind you, even though its something we accepted to be true.

and of course, this holds true for science or any school built on rationale, how do you know what is "true"? you cant, unless you accept a number of principles/concepts to be true to begin with, and then work from there.

and within that system, there exists "true and false" "right and wrong".

same reason why we say things are "scientifically true" as opposed to "absolutely fucking true"

its built on this philosophical idea of never knowing "truth" because it ultimately comes down to accepting or rejecting a system.

>>1051382
TRUE ∧ TRUE => TRUE
TRUE ∧ FALSE => FALSE

>theres no evidence, logic, reasoning, or whatever to assert that the system itself is true or false.

Please stop. It's beginning to be painful

>>1051445
By all means, do the same for maths as well as logic itself.

go on, should be easy for you amirite?

>>1051445
truth table??? yes I got it

[OR]
A B X
0 0 0
0 1 1
1 0 1
1 1 1

[AND]
A B X
0 0 0
0 1 0
1 0 0
1 1 1

PROFIT!!!

>>1051382
Math is just a list of axioms and theorems built up from those axioms. There is no fuzzy area which requires one to either "accept" or "reject" it. The closest you can get to that is the Axiom of Choice. Please do not pretend to be an expert on mathematics. All of the chemistry students I've seen did not know what the fuck they were doing.

Neither Science or Maths need anything, not each other and not us. We, however, need Maths to *perform* Science (ie. discover shit), whilst there is no requirement for Science in order to *perform* Maths (ie discover shit).

If we're treating OP's artificial, false dichotomy distinction as in any way real, then we can also say that all Maths is completely and utterly irrelevent to everything, since the application of Maths *to* things is Science.

In reality, of course, you can't take the Maths out of Science, since Science is the interpretation of Maths to explain the world, and you can't take the Science out of Maths, since Maths can be interpreted to explain the world.

>>1051382
I approve of this*, I think you might be a little unclear on the role of logic in determining mathematics but that's nothing to be ashamed of - I'm pretty unclear and its my fucking degree. But your basic point is that mathematical and logical systems can only be proven from 'within' the system? Sounds good to me. Have you had a look at Godel's Incompleteness Theorem? Outrageously complicated but gives substantial backup to your point. I can try and explain it if you have the time/energy

*But I think the whole concept of 'truth' is redundant in the first place, so I disagree with you, but that's a little off topic

>>1051467
I already did, long since, upthread.

But you have some weird issue that demands that, while you can accept (T∧F=F) you cannot accept (1+0=1). despite both scenarios being equivalent in terms of (eg) number of axioms. Arguing with you is no different to arguing with any other denialist who refutes what is evident infront of them.

>>1051502
>There is no fuzzy area which requires one to either "accept" or "reject" it

completely right, its that simple, you either accept that maths works and is true and follow its set systems, or you reject maths and do whatever else.

i never mentioned a fuzzy area at all.

similarly, you could accept the notion that only you exist in the world and everything else is a figment of your imagination, or you could accept that there are many people in the world.

there is no way to prove it, you either accept it or reject it.

some people reject it, and to us, those people can sometimes appear to be insane or actually are insane.

>>1051502
>Please do not pretend to be an expert on mathematics. All of the chemistry students I've seen did not know what the fuck they were doing.

you're not the first mathamatician ive met who had the delusion that he had a grander understanding of the universe.
dont worry, it usually dies down after a bit of of self reflection, either that or you go bonkers or win the fields medal.

>>1051519
Wut? 1+0=1 requires a substantial number more axioms than T n T = T

>>1051519
no i agree with the system of maths, im not saying i believe maths to be wrong, im merely saying you cant prove (maths in itself) that its right or true.

in simple terms, you cant use logic to verify logic.
so simply, you either accept or reject logic in the first place, and from that everything else flows.

>>1051506
> I can try and explain it if you have the time/energy

naw, better you save your efforts, im only browsing sci as a break from typing up shitty reports.

good to know im not sounding like a maniac or whatever.

>>1051591
>reject logic

That isn't very... logical...

>>1051580
Depends on what axioms they are. 1+0=1 can be derived from the axiom that 1+0=1, just as T^T=T can be derived from the axiom that T^T=T.

>>1051580
You are overloading the symbols.

>>1051591
>you either accept or reject logic in the first place, and from that everything else flows.

Totally - but you cannot argue from there that logic is inherently 'human' or is not universal.

>>1051619
>but you cannot argue from there that logic is inherently 'human' or is not universal.

logic is a system, so long as you understand it you could be a goldfish for all that matters.

but most importantly you cannot argue that logic is universal, for the same reasons i cannot argue that logic isnt universal.

which is why i really cant see how people can say "the universe adheres to the system of mathamatics that we devised"

>>1051591
*Nearly* right, but there are of course different forms of logic. Godel's Second Incompleteness Theorem says that you can't prove the correctness of a system using a system of equal 'proving power'.

This means that you can't prove system A correct by using system A, but you also can't prove it correct by using anything of equal power, let's say system B, since you could just translate that proof from system B notation into system A notation and have a proof of system A in system A.

By using a more powerful system, say system C, we can't translate the proof into system A, since system A doesn't have the capability of expressing everything that system C does (by the definition of a more powerful system). Of course, we then need a proof of system C using a more powerful system, and so on.

The simple reason we can't prove a system correct in itself is that, if it were wrong then it's perfectly possible for it to give a wrong answer. Thus when asked "are you correct" it is possible for it to give a wrong answer, and thus say "yes". So by proving a system within correct within itself, we haven't actually proved anything.

>>1051659
>>1051619
to clarify "the universe adheres to the system of mathamatics that we devised after we are dead and gone"

>>1051661
...snap.

Godel was probably nut insane in his later years after thinking that up.

>>1051659
Going out on an edge here, and a philosophical one (at best) - but to say that I cannot construct a logical argument using logic that logic is universal (per Godel) does not mean that I cannot construct an argument that such is the case. We may not have formalised, or be able to formalise, some meta-logic that allows us to show logic is universal; but that does NOT imply that the statements (logic is universal) and (logic is not universal) carry the same weight. Indeed, this isn't far off Godel's first theorem - but we both know that asking for a logical proof, is logically futile.

If it wasn't for science then math would not get any funding.

>>1051618
Granted. I assume you meant the more general axiom m+0=m, in which case you need axioms for dealing with the English words 'number', 'zero' and 'successor' ("a number plus zero has no successor", for example, is not an axiom because it isn't well defined)

>>1051770
> to say that I cannot construct a logical argument that X does not mean that I cannot construct an argument that X

I think this proof might be more trivial than you realise, although it was interesting that you approached it the way you did

I cannot construct a logical argument that stealing is wrong, or that 'Harry Potter' is the greatest work of literary fiction since the 'Canterbury Tales', but I can certainly provide an intuative argument for both (one with more force than the other)

>>1051777
I think the mistake you're making is that you're thinking of that line with bits at the end as a representation of the number one, the squashed circle as a representation of the number zero, the cross as a representation of addition and the two horizontal lines as equality of value. That's not at all what I was suggesting. What I was suggesting is that given the axiom:

1+0=1

We can say:

1+0=1

Now, if you want to interpret that via number theory (as the identity condition for addition, for example) then you may wish to back that up with some further axioms and generalisations like you suggest. You are equally justified, however, in interpreting the cross to mean numerical subtraction. You can interpret the vertical stick with bits on as the number five, the cross as numerical division and the squashed circle as the number one as well.

I, however, attached no interpretation to the statement. I merely proved it correct using the axiom I stated.

>>1051837
fucking in this tread your post was already answered!

>>1051837
The point I was making, more involved equating 1 with TRUE, 0 with FALSE etc (not AND with + for obvious reasons, but equivalent complexity) - and moving forward to single digit binary operations. (out of my depth here, but a group where 1+1=0).

>>1051837
OK, your argument is undoubtedly correct, but I'm not sure how far it advances the main thrust of what you're trying to prove, which is that 1+0=1 is axiomatically equivalent to T n F = F.

I think the closest way I can try and make my point is by asking you to consider a sentence like (P n Q), then a sentence like (R -> (P n Q)). Sure, axiomatically they can be stated as just one 'rule', but there seems to be something fundamentally more compound about the second, in that a generalisable rule which would be of some help in a complete system of logic would need three rules to deal with it - one for 'n', one for '->' and one for the rules allowing you to combine them

My point with separating the symbols from their interpretation is that "proof" depends ONLY on the symbols. If we can get from the axioms to the theorem by applying the rules then that's it, proof done, no arguments.

The INTERPRETATION OF THE SYMBOLS is not so clear cut though, since it's just an assumption. We can prove "1+0=1" using many different deductive systems and from many sets of axioms, but it doesn't mean that the number one, added to the number zero gives the number one. That's an interpretation we've given to the symbols.

For simple stuff like 1+0=1 we can confidently declare that it is "obvious", and if our symbol-shifting system gave us "1+0=5" then we would say that the system is wrong. In fact, the system can never be wrong, since we're dealing with proofs. It is still perfectly possible for our INTERPRETATION to be wrong though, which in the case of "1+0=5" meaning the number one being added to the number zero giving the number five is in fact wrong.

For complex examples this becomes very important, since the deductive, symbol-shifting systems are the only way we can 'know' these things: just because the system that gives us "1+0=1" fits our interpretation of it as addition doesn't mean that it is completely equivalent in every case, since the only way to prove such an equivalence is by having a symbol system completely equivalent to the concept with which to compare, which can't be proved without something to compare to, etc.

Thus the theorems and proofs spat out by our symbolic systems can't be known to fit those statements which we interpret them as. The only way to tell whether they match is to use another symbolic system, which just makes another layer of indirection without giving any insight. When things get really complicated and in-depth, there's no way for us to use the "obvious" argument like we can for addition.

>>1051965
But that extrapolates down to T∧F⇒F

>>1051878
Sorry, I wasn't trying to say that the statements 'TRUE AND FALSE is equivalent to FALSE' and 'ONE PLUS ZERO equals ONE' are equivalent, I was just trying to respond to

"1+0=1 requires a substantial number more axioms than T n T = T"

Which is a ridiculous statement since anything can be used as an axiom, including those statements themselves, in which case they can both be proved using one axiom each and thus 'require' the same number of axioms.

>>1051965
I think you're confusing the sense and reference of a symbol in your first paragraph, so I'm not sure the rest follows as comfortably as you think it does

>>1051987
Depends on what your rules and axioms are.

0_0