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(Dartmouth College)   The day science said "fark it, it's all miracles"   (dartmouth.edu) divider line 77
    More: Interesting, philosophy of science, Newton's law, applied mathematicses, old quantum theory, actual world, imaginary, theorems, classical mechanics  
•       •       •

4510 clicks; posted to Geek » on 18 Feb 2014 at 11:48 AM (1 year ago)   |  Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»



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2014-02-18 11:53:45 AM  
www.theroundtableonline.com
 
2014-02-18 12:05:16 PM  
tl;dr
 
2014-02-18 12:11:01 PM  
s2.quickmeme.com
 
2014-02-18 12:16:30 PM  

2chris2: tl;dr


Math works, making things line up to formulae we don't understand the causal relationship with.  This can make science based on these formulae seem arcane and mysterious instead of informative.   Empiricism can fall on the wayside as we focus more on mathematical beauty in a way that could be considered magical thinking, if it weren't so damn useful.
 
2014-02-18 12:23:47 PM  
I love science and knowledge, but I'm not reading all of that.

Someone do the thread a solid and give us the Cole's Notes version.
 
2014-02-18 12:24:06 PM  

ikanreed: 2chris2: tl;dr

Math works, making things line up to formulae we don't understand the causal relationship with.  This can make science based on these formulae seem arcane and mysterious instead of informative.   Empiricism can fall on the wayside as we focus more on mathematical beauty in a way that could be considered magical thinking, if it weren't so damn useful.


Isn't optimizing for mathematical beauty simply another way of invoking Occam's Razor?
 
2014-02-18 12:26:39 PM  

2chris2: tl;dr


Cliff Notes Wikipedia.

// some string theorists think his argument justifies what they are doing.
 
2014-02-18 01:05:13 PM  

ikanreed: Math works, making things line up to formulae we don't understand the causal relationship with. This can make science based on these formulae seem arcane and mysterious instead of informative. Empiricism can fall on the wayside as we focus more on mathematical beauty in a way that could be considered magical thinking, if it weren't so damn useful.


It's not magical thinking. What's really happening is we're coming to that barrier between how the Universe actually works, and how we think it works as interpreted through our models and observations.

The Universe is under no obligation to validate the way we describe it using things like logic, math or physics, and the realization that even our best tools of observation might be totally inadequate at explaining the big picture is quite unsettling.
 
2014-02-18 01:06:56 PM  
A paragraph should be a discrete thought with a beginning, middle and end. Its purpose is to convey a piece of information to the reader in a digestible bite. Look at this abomination:

Somebody once said that philosophy is the misuse of a terminology which was invented just for this purpose. [2 This statement is quoted here from W. Dubislav's Die Philosophie der Mathematik in der Gegenwart (Berlin: Junker and Dunnhaupt Verlag, 1932), p. 1.] In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms. Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world, the same does not seem to be true of the more advanced concepts, in particular the concepts which play such an important role in physics. Thus, the rules for operations with pairs of numbers are obviously designed to give the same results as the operations with fractions which we first learned without reference to "pairs of numbers." The rules for the operations with sequences, that is, with irrational numbers, still belong to the category of rules which were determined so as to reproduce rules for the operations with quantities which were already known to us. Most more advanced mathematical concepts, such as complex numbers, algebras, linear operators, Borel setsãand this list could be continued almost indefinitelyãwere so devised that they are apt subjects on which the mathematician can demonstrate his ingenuity and sense of formal beauty. In fact, the definition of these concepts, with a realization that interesting and ingenious considerations could be applied to them, is the first demonstration of the ingeniousness of the mathematician who defines them. The depth of thought which goes into the formulation of the mathematical concepts is later justified by the skill with which these concepts are used. The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.[3 M. Polanyi, in his Personal Knowledge (Chicago: University of Chicago Press, 1958), says: "All these difficulties are but consequences of our refusal to see that mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting" (p 188).]

...It isn't just poorly written, it's a vicious assault on the English language. It is offensive just to look at. If you held it up in front of a grammar teacher they would flee like a vampire confronted with a garlic-soaked crucifix.
 
2014-02-18 01:09:29 PM  

SpectroBoy: Isn't optimizing for mathematical beauty simply another way of invoking Occam's Razor?


Once you get into the math of Occam's Razor, pretty much.

And the effectiveness of mathematics in the natural sciences becomes quite reasonable, once you consider how hard the alternative of avoiding any correspondence to any mathematics. (Infinity gives a lot of room for corresponding to things.)
 
2014-02-18 01:12:11 PM  

Gunther: Its purpose is to convey a piece of information to the reader in a digestible bite.


The opening with "philosophy is the misuse of a terminology which was invented just for this purpose" didn't give you warning that the philosopher writing the paragraph has other ideas about the purpose of writing?
 
2014-02-18 01:27:34 PM  

abb3w: SpectroBoy: Isn't optimizing for mathematical beauty simply another way of invoking Occam's Razor?

Once you get into the math of Occam's Razor, pretty much.

And the effectiveness of mathematics in the natural sciences becomes quite reasonable, once you consider how hard the alternative of avoiding any correspondence to any mathematics. (Infinity gives a lot of room for corresponding to things.)


go further
reality is beautifully described by math

the EM equations are simplicity
e=mc2
inverse square laws

the list goes on and on


not understanding how science works doesnt mean that science doesnt work
 
2014-02-18 01:45:07 PM  
So, you mean that wizards are really really awesome mathematicians?.

Also...

31.media.tumblr.com

www.vilcek.com
 
2014-02-18 01:47:21 PM  
Aliens:  Sweet little world you have here.  How did you sort it?

Humans:  We used mathematics

Aliens:  Math? Hrm.  We tried that once, didn't pan out.
 
2014-02-18 01:49:51 PM  

BafflerMeal: Aliens:  Sweet little world you have here.  How did you sort it?

Humans:  We used mathematics

Aliens:  Math? Hrm.  We tried that once, didn't pan out.


Why would aliens talk to meat?.
 
2014-02-18 01:52:23 PM  

CygnusDarius: BafflerMeal: Aliens:  Sweet little world you have here.  How did you sort it?

Humans:  We used mathematics

Aliens:  Math? Hrm.  We tried that once, didn't pan out.

Why would aliens talk to meat?.


The flapping holes are quite attractive.
 
2014-02-18 01:53:50 PM  
0.999... ≠  1
 
2014-02-18 01:53:57 PM  

Gunther: However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.[3 M. Polanyi, in his Personal Knowledge (Chicago: University of Chicago Press, 1958), says: "All these difficulties are but consequences of our refusal to see that mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting" (p 188).]

...It isn't just poorly written, it's a vicious assault on the English language. It is offensive just to look at. If you held it up in front of a grammar teacher they would flee like a vampire confronted with a garlic-soaked crucifix.

Agreed, but it is fun in a beat poet rhythm, you know a wine soaked bespeckled maths grad student riffing at the typewriter.
 
2014-02-18 01:57:35 PM  

BafflerMeal: The flapping holes are quite attractive.


That's an excellent name for a girl band.
 
2014-02-18 02:04:31 PM  

Eddie Adams from Torrance: BafflerMeal: The flapping holes are quite attractive.

That's an excellent name for a girl band.


Or a GILF S&M porn.
 
2014-02-18 02:05:49 PM  

I drunk what: 0.999... ≠  1


ummmmmmmmmmmmmmmmmmmmmm
for almost all uses of  .9 repeating ....

and then I found these ...
1) 
1/9 = 0.111... 
9 x (1/9) = 9 x (0.111...) --- Multiply 9 to both sides 
9 x (1/9) is 1 
9 x (0.111...) is 0.999... 
1 = 0.999... 

2) 
Let x = 0.999... 
10x = 9.999... --- Subtract an x from both sides 
9x = 9.0 (since x=.999...) 
x=1 (however, we started with x = 0.999...) 

3) 
1/3 = 0.333... 
2/3 = 0.666... 
3/3 = 0.999... 
(3/3 is also 1)
 
2014-02-18 02:09:08 PM  

CygnusDarius: So, you mean that wizards are really really awesome mathematicians?.


HP Lovecraft did it, read 'Dreams in the Witch-House'.
 
2014-02-18 02:10:06 PM  
This line of thought has been around for a long long time.  It was also the subject of my thesis in philosophy (as a dual physics-philosophy student).  This little piece contributes nothing original and doesn't even seem to acknowledge the historical thought on it.

The thing that annoys me about this particular thesis, though, is that it misses the whole point: the unreasonable effectiveness of math in the sciences is the same phenomenon as the much wider unreasonable effectiveness of language in all communication.  Our world of perception appears to be patterned.  We can pattern recognize.  Correlation between perceptions appears to be sufficient for all communication, prediction, etc.  Getting lost on math is entirely the wrong generality here.
 
2014-02-18 02:13:53 PM  

I drunk what: 0.999... ≠  1


Oh jeez. Another one of these threads. Thanks, dude.
 
2014-02-18 02:18:39 PM  

Ishkur: ikanreed: Math works, making things line up to formulae we don't understand the causal relationship with. This can make science based on these formulae seem arcane and mysterious instead of informative. Empiricism can fall on the wayside as we focus more on mathematical beauty in a way that could be considered magical thinking, if it weren't so damn useful.

It's not magical thinking. What's really happening is we're coming to that barrier between how the Universe actually works, and how we think it works as interpreted through our models and observations.

The Universe is under no obligation to validate the way we describe it using things like logic, math or physics, and the realization that even our best tools of observation might be totally inadequate at explaining the big picture is quite unsettling.


yeah.

was going to comment on something similar.  math is nothing more than a truth preserving system.  in other words, it is a logically valid system.  however, that makes no determination of its soundness... to address soundness, you're in another branch of philosophy.

fortunately, we don't require soundness in science.  we only desire predictability.  so, instead of testing for soundness, we test for repeatability.  once it's repeatable enough, we run with the application until something better comes along.

for science, truth is not at issue.  that's a philosopher's game, and a losing game at that, because no one ever proved this world had to be logical.
 
2014-02-18 02:33:53 PM  

namatad: 1/9 = 0.111...
9 x (1/9) = 9 x (0.111...) --- Multiply 9 to both sides
9 x (1/9) is 1
9 x (0.111...) is 0.999...
1 = 0.999...


so then 1 + 1 = 0.999... + 0.999... ? which is 1.999...8?

i thought 1 + 1 = 2 ?!?!?  i'm so confused

math iz hard

would it help if i use a calculator...?
 
2014-02-18 02:45:31 PM  

pute kisses like a man: no one ever proved this world had to be logical.


Or even exist, in any real sense.
 
2014-02-18 02:46:37 PM  

Ishkur: The Universe is under no obligation to validate the way we describe it using things like logic, math or physics, and the realization that even our best tools of observation might be totally inadequate at explaining the big picture is quite unsettling.


Or the universe just may change upon being observed so the nature of it is difficult to define without a large enough scope of time.
 
2014-02-18 02:48:16 PM  

I drunk what: so then 1 + 1 = 0.999... + 0.999... ? which is 1.999...8?


.999... + .999... = 1.999...

As it's a repeating decimal, it doesn't end in an 8. Ever.
 
2014-02-18 02:51:01 PM  

ex0du5: This little piece contributes nothing original and doesn't even seem to acknowledge the historical thought on it.


"This little piece" was published in 1960. I would hope that by 2014 it isn't that original anymore, as it has become some of the historical thought on the subject.
 
2014-02-18 02:52:00 PM  

Kome: As it's a repeating decimal, it doesn't end in an 8. Ever.


what is 9 + 9 = ?
 
2014-02-18 02:54:10 PM  
I'm not about to read that hideous tl; dr abortion... but I'm wondering if someone can enlighten me on this:

I understand that fractal mathematics is a very useful tool in describing and emulating complex systems in the natural world. I get that.

I also understand that, fundamentally, it is based on numbers that are imaginary. Numbers that, like i, are purely hypothetical constructs; that have absolutely no meaningful analog in our experiential world. The real world.

So, natural systems and order are understandable and reproducible by unnatural means with no basis in reality. How?

Is this mere coincidence? Or evidence of design? Or is it something else that I'm not getting?

I'll hang up and listen for the answer...
 
2014-02-18 02:56:14 PM  

I drunk what: Kome: As it's a repeating decimal, it doesn't end in an 8. Ever.

what is 9 + 9 = ?


Neither of those are repeating decimals. Hey, wanna play cards? Because at least as long as you're going to threadjack, might as well break out the classics.
 
2014-02-18 02:57:38 PM  

harleyquinnical: Or the universe just may change upon being observed so the nature of it is difficult to define without a large enough scope of time.


Uniformitarianism IS a presupposition, after all.

It makes science uncomfortable to admit that.
 
2014-02-18 02:59:16 PM  

ex0du5: This line of thought has been around for a long long time.  It was also the subject of my thesis in philosophy (as a dual physics-philosophy student).  This little piece contributes nothing original and doesn't even seem to acknowledge the historical thought on it.

The thing that annoys me about this particular thesis, though, is that it misses the whole point: the unreasonable effectiveness of math in the sciences is the same phenomenon as the much wider unreasonable effectiveness of language in all communication.  Our world of perception appears to be patterned.  We can pattern recognize.  Correlation between perceptions appears to be sufficient for all communication, prediction, etc.  Getting lost on math is entirely the wrong generality here.


nice points


Kome: I drunk what: so then 1 + 1 = 0.999... + 0.999... ? which is 1.999...8?

.999... + .999... = 1.999...

As it's a repeating decimal, it doesn't end in an 8. Ever.


THIS
 
2014-02-18 03:18:49 PM  

Ishkur: harleyquinnical: Or the universe just may change upon being observed so the nature of it is difficult to define without a large enough scope of time.

Uniformitarianism IS a presupposition, after all.

It makes science uncomfortable to admit that.


Then again, maybe there are two Universes to be thinking about here: the physical (encompassing all things that matter and are of matter), and the philosophical (asking the bigger questions of 'why?', 'why not?' and possibly 'why me?'  It doesn't seem reasonable to me to see something for what it is and prescribe how it should act, especially if it has been around longer than we have.  Sociologically and psychologically, doing so leads to disobedience...maybe I'm just applying things incorrectly.

www.explainxkcd.com
 
2014-02-18 03:21:30 PM  

Mr_Fabulous: Numbers that, like i, are purely hypothetical constructs; that have absolutely no meaningful analog in our experiential world.


Numbers are used to measure things. If you are comparing two signals over time, i measures that they are 90° out of phase while -1 measures 180° out of phase and 1 measures completely in phase.
 
2014-02-18 03:26:06 PM  

harleyquinnical: Then again, maybe there are two Universes to be thinking about here: the physical (encompassing all things that matter and are of matter), and the philosophical (asking the bigger questions of 'why?'


"Why?" is probably not the right question to ask because

1) You cannot technically prove why and
2) It is assuming telos in the answer.

"Why" automatically presumes purpose and intent. This is wrong. Some things (in fact, probably all things though there is no way of knowing this for sure) have no purpose. "Why" is a malformed question analogous to dividing by zero and is not interesting to rational inquiry. You can keep asking "Why?" to every question until you get to root level knowledge and then one more "Why?" takes you beyond human comprehension and understanding. It is, ultimately, unanswerable and unsolvable. We will never know "why". No science ever uses the word "why" -- the better question is "how".

Just because we can't answer why doesn't mean we can't know anything.
 
2014-02-18 03:30:30 PM  

Kome: ex0du5: This little piece contributes nothing original and doesn't even seem to acknowledge the historical thought on it.

"This little piece" was published in 1960. I would hope that by 2014 it isn't that original anymore, as it has become some of the historical thought on the subject.


But it really wasn't original then.  You have to understand that the problem of order is not fifty years old. It is millennia old, and philosophers have been throwing out their thoughts on it since ancient history.  Even the point that language and mathematics are the same thing was known by the end of the eighteenth century with the formalization of logic, and the concept of symbols, information, and syntax being the root of our description of a patterned reality was being openly discussed before Shannon had rigorised information theory.  Wittgenstein and Quine were discussing correlation as the root of these in the early 20th century.  The Vienna club and much of the whole Lvov-Warsaw school of logic was built around this discussion.  Carnap, Tarski, etc. wrote seminal papers on this.

This little piece shows no understanding of that.
 
2014-02-18 03:49:02 PM  

harleyquinnical: Ishkur: harleyquinnical: Or the universe just may change upon being observed so the nature of it is difficult to define without a large enough scope of time.

Uniformitarianism IS a presupposition, after all.

It makes science uncomfortable to admit that.

Then again, maybe there are two Universes to be thinking about here: the physical (encompassing all things that matter and are of matter), and the philosophical (asking the bigger questions of 'why?', 'why not?' and possibly 'why me?'  It doesn't seem reasonable to me to see something for what it is and prescribe how it should act, especially if it has been around longer than we have.  Sociologically and psychologically, doing so leads to disobedience...maybe I'm just applying things incorrectly.

[www.explainxkcd.com image 740x308]


and math is just a part of philosophy.
 
2014-02-18 03:55:54 PM  

harleyquinnical: Ishkur: harleyquinnical: Or the universe just may change upon being observed so the nature of it is difficult to define without a large enough scope of time.

Uniformitarianism IS a presupposition, after all.

It makes science uncomfortable to admit that.

Then again, maybe there are two Universes to be thinking about here: the physical (encompassing all things that matter and are of matter), and the philosophical (asking the bigger questions of 'why?', 'why not?' and possibly 'why me?'  It doesn't seem reasonable to me to see something for what it is and prescribe how it should act, especially if it has been around longer than we have.  Sociologically and psychologically, doing so leads to disobedience...maybe I'm just applying things incorrectly.

[www.explainxkcd.com image 740x308]


sociology deals in probabilities, so its measures and predictions are more in ranges, rather than in pin point accuracies. doesnt make some of it less of a science, just a more vague one.

economics on the other hand is almost worthless at predicting. when was the last time economics accurately predicted anything?

psychology gets interesting, esp when you talk about pharmacological aspects.
now we are talking about applying probabilities to samples of one.
On average, people react this way. You dont. Something might be wrong. LOL
Which doesnt detract from the usefulness of therapy, esp things like behavior modification.
people can modify their behavior, some therapy assists with that, etc etc etc

/back to tensors
 
2014-02-18 03:59:16 PM  
Yeah.... but what if we are all just brains in jars!?!?!?!


Mannnnnnnnnnnn

What if . . . .
 
2014-02-18 04:06:54 PM  

Ishkur: I love science and knowledge, but I'm not reading all of that.

Someone do the thread a solid and give us the Cole's Notes version.


Time cube
 
2014-02-18 04:09:52 PM  

Ishkur: harleyquinnical: Then again, maybe there are two Universes to be thinking about here: the physical (encompassing all things that matter and are of matter), and the philosophical (asking the bigger questions of 'why?'

"Why?" is probably not the right question to ask because

1) You cannot technically prove why and
2) It is assuming telos in the answer.

"Why" automatically presumes purpose and intent. This is wrong. Some things (in fact, probably all things though there is no way of knowing this for sure) have no purpose. "Why" is a malformed question analogous to dividing by zero and is not interesting to rational inquiry. You can keep asking "Why?" to every question until you get to root level knowledge and then one more "Why?" takes you beyond human comprehension and understanding. It is, ultimately, unanswerable and unsolvable. We will never know "why". No science ever uses the word "why" -- the better question is "how".

Just because we can't answer why doesn't mean we can't know anything.


Y is a crooked letter that can't be made straight
 
2014-02-18 05:37:51 PM  

Kome: Neither of those are repeating decimals.


1.  that isn't an answer to the question you were asked.

2.  o noes, i guess you win, no wait

what is 9.000... + 9.000... = ?

lelz

Kome: Hey, wanna play cards?


well since you're not so good at elementary math, perhaps you'd like to take a crack at some elementary logic...?

here ya go :)

notreligious.typepad.com

take your time, no rush...

if you'd like to poll the audience or phone a friend feel free.  or perhaps you'd like to give you a 50/50 and take away two of the wrong answers...?

namatad: THIS


... is incorrect.  Good jorb lad u get a trophy
 
2014-02-18 05:54:29 PM  

I drunk what: Kome: Neither of those are repeating decimals.

1.  that isn't an answer to the question you were asked.

2.  o noes, i guess you win, no wait

what is 9.000... + 9.000... = ?

lelz

Kome: Hey, wanna play cards?

well since you're not so good at elementary math, perhaps you'd like to take a crack at some elementary logic...?

here ya go :)

[notreligious.typepad.com image 367x177]

take your time, no rush...

if you'd like to poll the audience or phone a friend feel free.  or perhaps you'd like to give you a 50/50 and take away two of the wrong answers...?

namatad: THIS

... is incorrect.  Good jorb lad u get a trophy


both cards? All the cards? An infinte number of all the cards?
 
2014-02-18 05:57:20 PM  
Ah-HA!  NONE OF THE CARDS!  Because then all things remain true
 
2014-02-18 06:03:30 PM  

Mjeck: both cards?


yes

Mjeck: All the cards?


sometimes

Mjeck: An infinte number of all the cards?


only if you asked for permission

Mjeck: Ah-HA!  NONE OF THE CARDS!  Because then all things remain true


is everything true, eris?
 
2014-02-18 06:14:31 PM  
I drunk what:
well since you're not so good at elementary math, perhaps you'd like to take a crack at some elementary logic...?

here ya go :)

[notreligious.typepad.com image 367x177]

take your time, no rush...

if you'd like to poll the audience or phone a friend feel free.  or perhaps you'd like to give you a 50/50 and take away two of the wrong answers...?


Bah.  Turning over any of them is a test of the idea.   Not necessarily a conclusive test though.

/Ditto for all subsets, except the empty set which is a member of all sets
 
2014-02-18 06:20:25 PM  

I drunk what: or perhaps you'd like to give you a 50/50


hmmm, or maybe we can do that??

you, you utes!
 
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