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And then there’s the Quantum Physicists that simply brutaly murders the purity of the mathematician by observing a single particle in two places at once, “proving” that 1+1 does not always equal 2.
In QM, wavefunctions are normalised so that probability can never be larger than one. There is only one particle, it just has a probability of being in a superposition of two states. There aren’t two particles in two states.
Also, you cannot *observe* a single particle in two places, observation of the particle forces it to be in either one state or the other, removing the lid in schrodinger’s massively misunderstood metaphor.
A semester ago I would have argued that Quantum Mechanics is actually pretty mathematically valid, but then my lecturers starting pulling assumptions out of their arses and I gave up.
I am by all means not even an amateur in the subject, but I do find it fascinating.
“…But let’s assume that all the eigenvalues are real, and that we can ensure this by requiring the operator to be Hermitian (which requires us to assume the eigenvectors are normalisable)….”
?? Are you agreeing with me or pointing out that we have to assume the operator to be hermitian? Because without an hermitian operator most of QM doesn’t work, so the solutions without an hermitian operator are generally assumed to be unimportant outside of physics.
Agreeing. “Solutions without an hermitian operator are generally assumed to be unimportant” just sounds like a cop-out for “ooh…this is too difficult otherwise”.
Why can’t we have complex eigenvalues? It’s not like there aren’t systems in classical physics that can have complex-valued properties – aren’t they allowed to count as observables, too?
What’s important is that the observables are orthogonal and span the state space; they can still do that if they’re merely linear without needing them to be Hermitian too.
Suddenly demanding real eigenvalues just sounds like a convention made for the sake of convenience than any physical requirement.
I think you’ve hit the nail on the head there. I guess if we can’t test it there’s no reason to include it in the science.
Most of what i’ve seen in Quantum Mechanics is just iffy assumptions and jiggling round of matrices in order for it to vaguely look like what is happening.
I guess all of physics is that to be fair, it’s just QM is still new-ish.
There are plenty of mathematics where 1 + 1 doesn’t equal two. You’re not even going to phase them with that.
The better argument would have been that math is used by all of the others but only as a tool.
When you see a house you recognize that its pure form is wood and nails – not hammers and saws.
1+1=0 (mod 2)
1+1=10 (binary system)
It’s nothing special for 1+1 not to equal 2.
There is of course a difference in those two examples in that the latter is still the “ordinary” “one plus one equals two”, just in a different notation; while the former is addition in a system which doesn’t have a “two”.
WRONG. If a scientist observes a particle, it’s in one place, not two. The uncertainty principle only applies if a particle is unobserved.
And while you’re at it, go look up “The Observer Effect.”
Maybe it’s not Quantum Physics, but scientists have “observed” a particle in two places simultaneously. I wish I had my sources, the article was quite fascinating.
I wish you had your sources too because i’m pretty sure that revolutionises science.
http://news.nationalgeographic.com/news/2004/08/0818_040818_teleportation.html
Guess it was something like this.
Everyone knows that 1+1 = 10!
Nah, mainly programmers know that.
Actually, the Quantum Physicists floats above the line. And under it.
The picture was probably not wide enaugh, so there was no space for Logic ^^
Math < Logic < Philosophy < Sociology
Boom De Yada Boom De Yada
No. Math contains a system of logical rules within it, but only those rules apply. Next, philosophy is dreaming up stuff, and thinking about could be’s instead of what is. Finally, he didn’t finish the chart. Less pure than psychology is sociology, as it is applied group psychology. After sociology is history, so we can all rag on history.
“could be’s instead of what is” – well the fact is: we don’t know what is – or what isn’t. (The latter is more precise). Its a rather important question of ‘what’ if e.g. PA or ZF is inconsistent, and that is (partially) a philosophical one.
You missed that Sociology was on the chart to the far left. My illustration took it in a complete circle, followed by Boom De Yada, the song for the Discover Channel watching the world revolve. It’s all a matter of perspective.
Philosophy is the quintessence of all ontological disciplines. It’s not just “dreaming up stuff.” It’s been proved that math can never prove its own rules and logics, so that makes philosophy much more pure than that. Funny little experiment: take any article on wikipedia (assuming it’s not down dark because of ACTA), and click the first word-link in the body if the article. Repeat the same step with the article you clicked on. If you don’t run into an infinite loop, you’ll always end up with “philosophy” sooner or later. True story.
ACTA has been around for years and is not causing any threats. All threats are the media overhyping our legitimate concerns about SOPA and PIPA. In the rare event that Wiki goes black to protest it, they have a link on their blackout page that says somethng like “what’s this all about?” which will take you to an in-depth protest page with instructions on how to get around the blackout. The purpose is to get the message heard, and as soon as its heard, they want you to resume havong full access to theor site.
I attempted the experiment that you have listed involving Wikipedia. It does in fact result in either an infinite loop or philosophy for my first few attempts. I am intrigued to see the trend continue. An ironic note on that, my most commonly experienced infinite loop has natural science, science and similar topics as the common interactions.
Taken with how the XKCD comic is set out. History is not applied sociology. At the least not in it’s entirety. You could say history is applied geography, but even then geography isn’t applied sociology either.
which is why im getting a math major.
I see what you did there.
Well, it’s easier for you to become a math major than an English major.
thats an understatement
And what are you getting him/her for?
If you want to be accurate enough to pass your degree, you should have said “I’m majoring in mathematics.”
What? Your critique makes no sense. A “math major” is not a person, it is a major emphasis in a degree program. Sure he could have been more wordy like me or placed a sentence there without any transition like you, but Mr. Chromekreeper had the most succinct and grammatically correct way to state what he wanted to.
thank you, kind sir.
Technically the phrase could be accurate either way. I am both a chemistry major and majoring in chemistry.
Somewhere on the edge of the bell curve is a person who visits Dropping the Science without having read XKCD.
i found out about by reading the SUDO comic on the think geek shirt.
BEST. DESCISION. EVER.
But Mathematicians only can do math, without more specified education, all they can do is calculate. They won’t ever understand the numbers in physics equations. That’s why I’m getting astrophysics major. A practical major.
my brother! i have found you!
A math major is trained to make a mathematical model out of any situation.. it may take longer than someone who is trained in that specific subject who deals every day, but it will get done and it will be much more precise and all factors will be analyzed to a much higher degree.
You young sir, still have much to learn
It’s funny how mathematics is just applied cognitive science. CogSci can’t even be displayed on the diagram, because it is applied everything, and everything applies it.
We would need to know math to do any real scientific work. Math still is on top.
end never forgett, math is no real science, it’s not in our nature like physics or biology. it’s invented by humans
Someone please take a screenshot–no, a photograph of a CRT Monitor with a 1MP Camera–of this and submit it to the failblog. People like this should not be alowed to multiply.
all other science is derived from math.. 1 apple and another apple is 2 apples. Math is defined as the modeling or study of natural phenomenon.
We should send your statement to VD, cause your ignorance makes me sick.
Math is still a Science. He spelled forgett wrong. I don’t know what “end never forgett” even means. And what does this have to do with Vanerial Dissease?
No, he’s right! There are no numbers and formulas in the universe, they are just a human approximation to reality
Yet, we discover rules and axioms in it rather than creating them. This would be like if painters created portraits by wandering through the woods looking for them.
False. The purest science is the sociology of science, since science is a social phenomenon subject to study like any other.
Mathematics Mathematicians.
Curse the forum’s formatting…
Mathematics ≠ Mathematicians
Scientology
Chemistry beats all.
It’s pure enough AND it’s actually useful.
So parabolas, architecture, and basic algebra are NOT useful? Tell that to rocket scientists, or your house.
I’m in bio because I like biology, not because I care about the “purity” of my field of study.
The same can be said of my girlfriend.
Well what is your girlfriend’s opinion of your statement? Does she not have a say in that matter since it pertains to her?
This could be taken multiple ways. Girlfriend in biology, or guy in his girlfriend.
Noone has mentioned the mouseover text for this particular XKCD comic… they mention the quote “Physics is to math as sex is to masturbation.”
And it’s a XKCD comic… when is a XKCD comic *ever* meant to be taken seriously?
… So that’s why I suck at math; I have impurities! I seriously doubt I could use that excuse in my math class though, sadly.
Newton invented calculus to solve physics problems so…
With pencil manufacturers at the tippy top?
Woot, I study the top three.
philosophy, the mother of science, is it pure or or inpure?
I prefer the Queen of Sciences. /sarcasm
Now, onto something pragmatic…
This is an example of reductionism. Math alone couldn’t explain much
My science teacher printed this on a test once. We had to explain it for bonus points.
I don’t see why calling something, “It’s just applied bla bla bla,” is an insult. “Applied” means, “actually put to practical use.” Math might be “pure” but it’s completely useless when it’s just numbers on a page. Unless you APPLY it there’s no point. This science-d*ck-measuring is, quite frankly, beneath scientists, who are supposed to be smart.
It also implies every science except for math is applied, which isn’t true. There are unapplied, pure-theory projects in every single field listed.
I don’t see why calling something, “It’s just applied bla bla bla,” is an insult. “Applied” means, “actually put to practical use.” Math might be “pure” but it’s completely useless when it’s just numbers on a page. Unless you APPLY it there’s no point. This science-penis-measuring is, quite frankly, beneath scientists, who are supposed to be smart.
I don’t see why calling something, “It’s just applied bla bla bla,” is an insult. “Applied” means, “actually put to practical use.” Math might be “pure” but it’s completely useless when it’s just numbers on a page. Unless you APPLY it there’s no point. This science-genitalia-measuring is, quite frankly, beneath scientists, who are supposed to be smart.
WHYFOR AM I GETTING MODDED>
Probably “blah blah,” or it could simply be the length. But all three of them went through. Very rarely do mods remove content from me personally. I can’t speak for everyone else.
Such as this one. It is also awaiting moderation. I am guessing it’s the blah blah.
I like: Psychology is really biology, biology is really chemistry, chemistry is really physics, physics is really math, math is really logic, logic is really philosophy, and philosophy is really psychology.
Or, philosophy is applied metaphysics. XD
Philosophy is not psychology. Philosophy doesn’t use empirical data or theory that defines science as a subject. Sorry, humanities, you’re not welcome here. D:
My friend told me about a professor he had. He asked a girl in the class what her major was. When the girl said “Chemistry” he just sighed and said “What a waste of a perfectly good brain.” By the way, I hate doing math.
HISTORIANS OF THE INTERNET! ATTAAAAAAAAAAAAAAAAAAAACK!
*cough* *reductionism*
Isn’t mathematics just applied logic?