Comment of the week

_{Denyse O'Leary

June 6, 2015

Intelligent Design}

Share: Facebook; Twitter; LinkedIn; Flipboard; Print; Email

Science is a method, not a result, nor a being. “Science” doesn’t say anything. With highly politicised topics like this, it is not the data that tells the tale, but rather those flawed humans who may or may not appropriately report the data that tells the tale. There has been enough fraud discovered in academia alone, without systemic bias toward a given result, that to fail to question these results is a major failing on the part of anyone who takes them at face value. – tmosley

Comments

Silver Asiatic:
I didn’t know that the quotient of any two consecutive fibonacci numbers approximates the golden ratio – and the bigger the fibonacci numbers, the closer to the golden ratio: 13/8 = 1.625 55/34 = 1.617647058… 144/89 = 1.61797752 …. 4,181/2,584 = 1.6180340 … Humans discovered this, not invented it.
It was math that was invented by us. We use math to understand relationships. e.g. I can use a man-made invention to measure time, but that doesn't mean I invented time, it means that I invented a clock.Carpathian_{June 10, 2015
June
06
Jun
10
10
2015
09:07 AM
9
09
07
AM
PDT}

Silver Asiatic:
Carpathian Who do you think invented the mathematical concept of >1 ? Do you think there was a time in human history when that concept did not exist?
We have invented every single mathematical concept that exists. Who do you think invented statistics? Do you think it existed before man?Carpathian_{June 10, 2015
June
06
Jun
10
10
2015
09:02 AM
9
09
02
AM
PDT}

Mung:
So math is objective, not subjective?
Math is something we invented and for the most part agree upon. It is not objective in the sense that it exists independent of us. We can use it to understand something "objective" like our Earth or something that doesn't exist, like probability.Carpathian_{June 10, 2015
June
06
Jun
10
10
2015
08:56 AM
8
08
56
AM
PDT}

Carpathian Who do you think invented the mathematical concept of >1 ? Do you think there was a time in human history when that concept did not exist?Silver Asiatic_{June 10, 2015
June
06
Jun
10
10
2015
08:42 AM
8
08
42
AM
PDT}

These graceful spirals are also found everywhere in nature, from the whorls in a nautilus shell to the sweeping arms of galaxies. And they’re related, in turn, to the golden ratio (yet another infinite decimal, 1.61803 …) and the Fibonacci sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …), which neatly describes the arrangement of leaves and petals in plants.
I didn't know that the quotient of any two consecutive fibonacci numbers approximates the golden ratio - and the bigger the fibonacci numbers, the closer to the golden ratio: 13/8 = 1.625 55/34 = 1.617647058... 144/89 = 1.61797752 .... 4,181/2,584 = 1.6180340 ... Humans discovered this, not invented it.Silver Asiatic_{June 10, 2015
June
06
Jun
10
10
2015
08:39 AM
8
08
39
AM
PDT}

Carpathian: Why wouldn’t we expect this since we are describing the same world? So math is objective, not subjective?Mung_{June 10, 2015
June
06
Jun
10
10
2015
08:38 AM
8
08
38
AM
PDT}

kairosfocus:
The attempt tells us quite plainly, that you are resorting to the rhetoric of dismissal because the sheer power and elegant beauty of logical implication applied to structure and quantity in the physical sciences points where you would not go.
I am not dismissing any of the math but I am contesting your implication that math is somehow divine. None of the things you have pointed out lead to an implication of an "intelligent designer" being involved in the creation of the universe. What it shows is that the math "designed" by one mathematician relates to the work of another. Why wouldn't we expect this since we are describing the same world? We as humans, are doing our best to understand the universe, each with a different point of view, and it would come as no surprise that the relationships between our different viewpoints wouldn't somehow show that those mathematical concepts are corroborated by each other. That "mathematical" bigger picture does not point to divinity.Carpathian_{June 10, 2015
June
06
Jun
10
10
2015
08:28 AM
8
08
28
AM
PDT}

Carpathian, I don't see a debate. What I see is you making claims you're unwilling to actually defend. Like your claim that there is non-physical "stuff" going on in the cell or in computer communication. Like your claim that mathematics is a subjective invention, like unicorns and the tooth fairy.Mung_{June 10, 2015
June
06
Jun
10
10
2015
08:25 AM
8
08
25
AM
PDT}

KF,
DS, we have a lot of agreement then.
Yes, definitely. And the Wired article that BA77 posted is very nice (although I notice that they took the step of moving the -1 to the left side, therefore artificially introducing 0 into the equation, which is what I initially complained about in the other thread. :-)daveS_{June 10, 2015
June
06
Jun
10
10
2015
08:13 AM
8
08
13
AM
PDT}

EugeneS:
Mathematics is of course a human invention, an art, a language, a formalism, a study of form (just like any other art). But it’s not all there is to it. It is beautiful and the world is beautiful. The Christian perspective is that the world (and mathematics as a reflection of it) is beautiful for a reason, i.e. because it is a form of Revelation of God, a kind of Scripture.
A statement like this I have no problems with and can easily agree. Math, a tool that we created, can show us things in a way that we may not be able to see without the use of math. But math itself is strictly our own invention and has flaws and limitations that are still being worked on by mathematicians.Carpathian_{June 10, 2015
June
06
Jun
10
10
2015
08:10 AM
8
08
10
AM
PDT}

Mung:
Carpathian, if you don’t actually have any good reasons for what you say just admit it. You won’t be the first to stop by here just to troll. But don’t expect me to feed the trolls.
I find that when I make a serious statement you respond with something that is supposed to be taken as funny. See the following:
Carpathian: Mathematics is the tool that man created to try and understand the universe. Mung: At least you’re not one of those nutcases who thinks that mathematics was invented so a man could count how many wives he had.

Carpathian: We created math and that is why it has limitations in expressing reality. Mung: Thank God you’re not one of those weirdos who thinks that math created us.
If you want to be taken seriously, treat the debate seriously.Carpathian_{June 10, 2015
June
06
Jun
10
10
2015
08:00 AM
8
08
00
AM
PDT}

DS, we have a lot of agreement then. I am not making a design inference argument here but I do hold that this sort of astonishing unity in the midst of diversity is a manifestation of one of the foundational problems in philosophy, the problem of the one and the many. And a surprisingly coherent and intelligible world that is a coherent unified whole in the midst of vast diversity is calling us to ponder as a root of being, unifying mind. Taking Wired's remark uip a notch: wormhole junction. And notice this in the wired article:
Now, maybe you’ve never thought of math equations as “beautiful,” but look at that result: It combines the five most fundamental numbers in math—0, 1, e, i, and ?—in a relation of irreducible simplicity. (Even more astonishing if you slog through the proof, which involves infinite sums, factorials, and fractions nested within fractions within fractions like matryoshka dolls.) And remember, e and ? are infinitely long decimals with seemingly nothing in common; they’re the ultimate jigsaw puzzle pieces. Yet they fit together perfectly—not to a few places, or a hundred, or a million, but all the way to forever. You can take this farther, too. If you write that function above in a more general but still simple form as f(x) = e(zx), where z = (a + bi), what you get is no longer a circle but a logarithmic spiral, combining rotation and growth—now both at the same time! These graceful spirals are also found everywhere in nature, from the whorls in a nautilus shell to the sweeping arms of galaxies. And they’re related, in turn, to the golden ratio (yet another infinite decimal, 1.61803 …) and the Fibonacci sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …), which neatly describes the arrangement of leaves and petals in plants. But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems (you know, sines, secants, and so on) into more tractable algebra—like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digitize music, and it tames all manner of wavy things in quantum mechanics, electronics, and signal processing; without it, computers might not exist.
BTW, infinity is the sixth wormhole line in the junction. Fans of the Honorverse will love that. KFkairosfocus_{June 10, 2015
June
06
Jun
10
10
2015
07:26 AM
7
07
26
AM
PDT}

BA77, I like that wormhole metaphor in the Wired article, though I'd say it is a wormhole junction, which as any sci fi fan will tell you is an econo-strategic pivot. KFkairosfocus_{June 10, 2015
June
06
Jun
10
10
2015
07:17 AM
7
07
17
AM
PDT}

KF,
DS, Have you pondered the significance of such diverse fields of math coming together neatly in one expression that then is a microcosm of entire fields of highest importance?
Of course.
PS: Do us a favour, and discuss a bit on e, i, pi, sin and cos, power series and the expression that ties them all together then the onward links to Laplace, Fourier, Z transforms and differential equations, and explain to us how the unification brought out is trivial and arbitrary, a mere artifact.
I don't believe it's trivial and arbitrary, in fact. I disagree with Carpathian here. I wouldn't be surprised if every sufficiently advanced civilization was aware of Euler's formula.
PPS: This is not a design argument, it is saying that there is reason to believe a good slice of mathematics is deeply embedded in the root of reality, as the logic of structure and quantity worked out. And in that context, it is saying that a good slice of core math seems discovered rather than merely arbitrarily invented, even when that may not at first be apparent.
And I would agree with this. As far as I can tell, a lot of mathematics is discovered rather than invented. If you are not making a design argument here, then I apologize for going off-topic. In the past, you have asked, relating to this formula, "Do we need more of a signature of a rational mind behind reality?", and I was referring to that general line of reasoning.daveS_{June 10, 2015
June
06
Jun
10
10
2015
07:15 AM
7
07
15
AM
PDT}

God by the Numbers - Connecting the constants Excerpt: The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: e^pi*i. This number is equal to -1, so when the formula is written e^pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e^pi*i+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.",,, The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.,,, Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe.,,, The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God. http://www.christianitytoday.com/ct/2006/march/26.44.html?start=3 (of note; Euler's Number (equation) is more properly called Euler's Identity in math circles.) Euler's identity - Mathematical beauty Excerpt: Euler’s identity is often cited as an example of deep mathematical beauty.[3] Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:[4] The number 0, the additive identity. The number 1, the multiplicative identity. The number pi, which is ubiquitous in the geometry of Euclidean space and analytical mathematics (pi = 3.14159265…) The number e, the base of natural logarithms, which occurs widely in mathematical analysis (e = 2.718281828…). The number i, the imaginary unit of the complex numbers, a field of numbers that contains the roots of all polynomials (that are not constants), and whose study leads to deeper insights into many areas of algebra and calculus. (Both pi and e are transcendental numbers.) Furthermore, the equation is given in the form of an expression set equal to zero, which is common practice in several areas of mathematics. Stanford University mathematics professor Keith Devlin has said, “like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence”.[5] And Paul Nahin, a professor emeritus at the University of New Hampshire, who has written a book dedicated to Euler’s formula and its applications in Fourier analysis, describes Euler’s identity as being “of exquisite beauty”.[6] The mathematics writer Constance Reid has opined that Euler’s identity is “the most famous formula in all mathematics”.[7] And Benjamin Peirce, a noted American 19th-century philosopher, mathematician, and professor at Harvard University, after proving Euler’s identity during a lecture, stated that the identity “is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth”.[8] A poll of readers conducted by The Mathematical Intelligencer in 1990 named Euler’s identity as the “most beautiful theorem in mathematics”.[9] In another poll of readers that was conducted by Physics World in 2004, Euler’s identity tied with Maxwell’s equations (of electromagnetism) as the “greatest equation ever”.[10] per wikipedia The Most Beautiful Equation of Math: Euler’s Identity http://www.science4all.org/le-nguyen-hoang/eulers-identity/
The following is interesting. Euler's formula (the most famous of all formulas), is graphed out as a right handed spiral
The Baffling and Beautiful Wormhole Between Branches of Math http://www.wired.com/2014/11/eulers-identity/ picture http://www.wired.com/wp-content/uploads/2014/10/5d_euler_f.jpg gif of Euler's http://www.songho.ca/math/euler/files/euler_ex01.gif The following images show the graph of the complex exponential function, e^{ix}, by plotting the Taylor series of e^{ix} in the 3D complex space (a helix) http://www.songho.ca/math/euler/euler.html
What is interesting to the fact that Euler's graphs as a right handed spiral is that DNA is also a right handed spiral. In the following article, Adam Rutherford takes exception to the many incorrect examples of left handed DNA spirals he finds on the internet and even at many reputable institutions:
DNA's twist to the right is not to be meddled with, so let's lose the lefties - Adam Rutherford - 30 April 2013 http://www.theguardian.com/science/blog/2013/apr/30/dna-twist-to-right Correct DNA spiral - image http://images.wisegeek.com/dna-close-up.jpg
Of related interest, here is an interesting quote from Euler himself:
A DEFENSE OF THE (Divine) REVELATION AGAINST THE OBJECTIONS OF FREETHINKERS, BY MR. EULER Excerpt: "The freethinkers (atheists) have yet to produce any objections that have not long been refuted most thoroughly. But since they are not motivated by the love of truth, and since they have an entirely different point of view, we should not be surprised that the best refutations count for nothing and that the weakest and most ridiculous reasoning, which has so often been shown to be baseless, is continuously repeated. If these people maintained the slightest rigor, the slightest taste for the truth, it would be quite easy to steer them away from their errors; but their tendency towards stubbornness makes this completely impossible." http://www.math.dartmouth.edu/~euler/docs/translations/E092trans.pdf
of note: Leonard Euler is considered one of the greatest mathematicians ever and was also un-apologetically Christian his entire life.bornagain77_{June 10, 2015
June
06
Jun
10
10
2015
06:48 AM
6
06
48
AM
PDT}

DS, Have you pondered the significance of such diverse fields of math coming together neatly in one expression that then is a microcosm of entire fields of highest importance? I still remember the shock at a student astronomy club when an upper 6th former scratched out the derivation and its conclusion. It stunned me then, and it strikes me now, especially having gone on to use the onward things that flow from its context - for years, I lived more in the complex frequency domain than in the time domain. KF PS: Do us a favour, and discuss a bit on e, i, pi, sin and cos, power series and the expression that ties them all together then the onward links to Laplace, Fourier, Z transforms and differential equations, and explain to us how the unification brought out is trivial and arbitrary, a mere artifact. PPS: This is not a design argument, it is saying that there is reason to believe a good slice of mathematics is deeply embedded in the root of reality, as the logic of structure and quantity worked out. And in that context, it is saying that a good slice of core math seems discovered rather than merely arbitrarily invented, even when that may not at first be apparent.kairosfocus_{June 10, 2015
June
06
Jun
10
10
2015
06:42 AM
6
06
42
AM
PDT}

KF,
DS, If there were substantial disagreement, that would be one thing, but what I am seeing is things as insubstantial as “C – A = B” and this used to drive dismissal. The broad context of the Euler Identity is on the table, that needs to be spoken to. KF
The problem I see is that there isn't much substance to these Euler Identity arguments to begin with. At least with "information" based approaches, there is the possibility of setting up a statistical model and performing a hypothesis test. In contrast, all we have here is a list of "connections", with no way of quantifying the likelihood of such. It's just an extraordinarily weak argument.daveS_{June 10, 2015
June
06
Jun
10
10
2015
06:09 AM
6
06
09
AM
PDT}

I'm currently reading "The Fabulous Fibonacci Numbers" Posamentier and Lehmann. It's a very enjoyable insight into the beauty in the world - obviously and strong evidence of design.Silver Asiatic_{June 10, 2015
June
06
Jun
10
10
2015
05:02 AM
5
05
02
AM
PDT}

DS, If there were substantial disagreement, that would be one thing, but what I am seeing is things as insubstantial as "C - A = B" and this used to drive dismissal. The broad context of the Euler Identity is on the table, that needs to be spoken to. KFkairosfocus_{June 10, 2015
June
06
Jun
10
10
2015
03:30 AM
3
03
30
AM
PDT}

Don't mind Carpathian. He spouts things like "A + B = C" and "C – A = B" at us expecting us to accept them as objective truth while saying they are the products of his subjective internal brain states [or wherever he thinks he invented them].Mung_{June 9, 2015
June
06
Jun
9
09
2015
05:45 PM
5
05
45
PM
PDT}

What is astonishing in this seemingly deep connection between math and beauty is the fact that the 'argument from beauty’ is a Theistic argument. It is certainly not a atheistic materialist argument:
Aesthetic Arguments for the Existence of God: Excerpt: Beauty,,, can be appreciated only by the mind. This would be impossible, if this `idea’ of beauty were not found in the mind in a more perfect form. http://www.quodlibet.net/articles/williams-aesthetic.shtml
Of related interest to the theistic 'argument from beauty', in the following article, though somewhat technical, it is almost comical to read how every approach, in which the materialists tried to reduce the subjective sense of beauty to a mere material mechanism, was thwarted.
Beauty Evades the Clutches of Materialism – March 27, 2013 http://www.evolutionnews.org/2013/03/beauty_evades_t070321.html
But where this ‘sense of beauty’ in mathematics, that apparently has been so fruitful for science, breaks down is with string theory and m-theory:
The part of the book (‘The Trouble With Physics’) I found most interesting was the part which tells how the string theorists were scammed by Nature (or Mathematics). Of course, Smolin doesn’t put it exactly like this, but imagine the following conversation.——— String theorists: We’ve got the Standard Model, and it works great, but it doesn’t include gravity, and it doesn’t explain lots of other stuff, like why all the elementary particles have the masses they do. We need a new, broader theory. Nature: Here’s a great new theory I can sell you. It combines quantum field theory and gravity, and there’s only one adjustable parameter in it, so all you have to do is find the right value of that parameter, and the Standard Model will pop right out. String theorists: We’ll take it. String theorists (some time later): Wait a minute, Nature, our new theory won’t fit into our driveway. String theory has ten dimensions, and our driveway only has four. Nature: I can sell you a Calabi-Yau manifold. These are really neat gadgets, and they’ll fold up string theory into four dimensions, no problem. String theorists: We’ll take one of those as well, please. Nature: Happy to help. String theorists (some time later): Wait a minute, Nature, there’s too many different ways to fold our Calabi-Yao manifold up. And it keeps trying to come unfolded. And string theory is only compatible with a negative cosmological constant, and we own a positive one. Nature: No problem. Just let me tie this Calabi-Yao manifold up with some strings and branes, and maybe a little duct tape, and you’ll be all set. String theorists: But our beautiful new theory is so ugly now! Nature: Ah! But the Anthropic Principle says that all the best theories are ugly. String theorists: It does? Nature: It does. And once you make it the fashion to be ugly, you’ll ensure that other theories will never beat you in beauty contests. String theorists: Hooray! Hooray! Look at our beautiful new theory. ———- Okay, I’ve taken a few liberties here. But according to Smolin’s book, string theory did start out looking like a very promising theory. And, like a scam, as it looks less and less promising, it’s hard to resist the temptation to throw good money (or research) after bad in the hope of getting something back for your effort. http://www.amazon.com/review/R2H7GVX4BUQQ68/ A Capella Science – Bohemian Gravity! – video https://www.youtube.com/watch?v=2rjbtsX7twc
But if we rightly let agent causality, i.e. God, back into our mathematical descriptions of the universe, as the Christian founders of modern science themselves held to be behind the mathematical laws of the universe, then the most beautiful solution imaginable pops out for us as a solution to the 'theory of everything'. Namely, Christ's triumph over death, through God's love for fallen man, provides an empirically backed reconciliation of Quantum Mechanics and General Relativity into the much sought after 'theory of everything':
,,,the resurrection of Christ from death provides a empirically backed reconciliation of Quantum Mechanics/Special Relativity, (Quantum Electrodynamics), and General Relativity into the much sought after ‘theory of everything’: https://uncommondescent.com/intelligent-design/mathematician-planck-data-disappoints-multiverse-claims/#comment-548426
Verse and Music:
Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross. Empty (Empty Cross Empty Tomb) with Dan Haseltine Matt Hammitt http://www.godtube.com/watch/?v=F22MCCNU
bornagain77_{June 9, 2015
June
06
Jun
9
09
2015
04:43 PM
4
04
43
PM
PDT}

To add to what EugeneS and Axel have stated, it is said that the best mathematical theories, that are later confirmed empirically to be true, were born out of the mathematician's 'sense of beauty'. Paul Dirac is said to have mathematically discovered the ‘anti-electron’, before it was empirically confirmed, solely through his mathematical ‘sense of beauty’:
Graham Farmelo on Paul Dirac and Mathematical Beauty - video (28:12 minute mark - prediction of the 'anti-electron') https://www.youtube.com/watch?v=YfYon2WdR40
As the preceding video highlighted, Paul Dirac was rather adamant that beauty was integral to finding truth through math:
‘it is more important to have beauty in one’s equations than to have them fit experiment’ Paul Dirac
Albert Eisteins was also a big fan of beauty in math. Einstein stated:
Truth not equal to Beauty - Philip Ball – May 2014 Excerpt: ‘the only physical theories that we are willing to accept are the beautiful ones’ http://aeon.co/magazine/philosophy/beauty-is-truth-theres-a-false-equation/
As well, In January 1933, the Belgian mathematician and Catholic priest Georges Lemaitre traveled with Albert Einstein to California for a series of seminars. After the Belgian detailed his Big Bang theory, Einstein stood up applauded, and said,
“This is the most beautiful and satisfactory explanation of creation to which I have ever listened.”
Alex Vilenkin, who mathematically proved that all inflationary universes must have had a beginning, commenting on Euler's Identity, stated,,,
"It appears that the Creator shares the mathematicians sense of beauty" Alex Vilenkin - Many Worlds in One: (page 201) http://books.google.com/books?id=9nRGwQnvGx0C&pg=PA201
As well, Richard Feynman called Euler’s Identity a ‘jewel’:
“Richard Feynman was a huge fan and called it a "jewel".” http://www.sciencedump.com/content/world%E2%80%99s-most-beautiful-equations
‘Mathematical beauty’ even had a guiding hand in the discovery of the Amplituhedron:
The Amplituhedron (mathematical beauty - 21:12 minute mark) - Nima Arkani-Hamed, Professor of Physics, Institute for Advanced Study in Princeton, N.J. - video https://www.youtube.com/watch?v=By27M9ommJc#t=1272
Paul Dirac, when pressed for a definition of mathematical beauty, reacted as such:
Dirac threw up his hands. Mathematical beauty, he said, ‘cannot be defined any more than beauty in art can be defined’ – though he added that it was something ‘people who study mathematics usually have no difficulty in appreciating’. http://aeon.co/magazine/philosophy/beauty-is-truth-theres-a-false-equation/
And indeed, just as Dirac held, it is found when mathematicians are shown equations such as Euler's identity or the Pythagorean identity the same area of the brain used to appreciate fine art or music lights up:
Mathematics: Why the brain sees maths as beauty – Feb. 12, 2014 Excerpt: Mathematicians were shown "ugly" and "beautiful" equations while in a brain scanner at University College London. The same emotional brain centres used to appreciate art were being activated by "beautiful" maths.,,, One of the researchers, Prof Semir Zeki, told the BBC: "A large number of areas of the brain are involved when viewing equations, but when one looks at a formula rated as beautiful it activates the emotional brain - the medial orbito-frontal cortex - like looking at a great painting or listening to a piece of music." http://www.bbc.com/news/science-environment-26151062
For any math geeks who may be reading this, here is some fine art for you guys to appreciate:
(Eight of) The world’s most beautiful equations http://www.sciencedump.com/content/world%E2%80%99s-most-beautiful-equations
bornagain77_{June 9, 2015
June
06
Jun
9
09
2015
04:41 PM
4
04
41
PM
PDT}

Thank you Eugene. What an interesting quote. The old 'elegance', aesthetic criterion, Einstein claimed to favour in selecting his hypotheses. That does tell its own story, and I believe may chime with what I was going to write, before I read your post, i.e. that I believe I was right the first time: I do think maths is unique and languages are not akin at the same existential 'a priori' level (if that doesn't sound like double-dutch or tautology). Mathematics is an 'a priori', divine creation/design. Languages are more evocative of Michelangelo's remark about seeing the statue in the block of stone, and just chipping off the rest. The subject or model of the sculpture is the primordial reality, but if not of a naturalist, representational nature offers, the imagination of the sculptor boundless possibilities, whereas the converse is true of maths. It's God's way or the highway! It is, itself, the primordial reality upon which material designs and creations may be based, and not an open-ended trove at the whim of the mathematician. It is - ironically - set in stone, so to speak! Hence its value, in the eye of the philatelist, even above the rarest British colonial stamp, Lord Kelvin, if you are listening from on high. Doesn't sound as if Dirac would have made much of a 'naive realist' partisan of scientism, does it, poor soul? You know who those hypersceptics (usually, I suspect, secondary-school children) remind me of? Old Polonius in Hamlet, with his constant carping adages.Axel_{June 9, 2015
June
06
Jun
9
09
2015
02:10 PM
2
02
10
PM
PDT}

Apparently Carpathian is a dualist and is not an empiricist. One wonders why he acts like an ID critic.Mung_{June 9, 2015
June
06
Jun
9
09
2015
01:56 PM
1
01
56
PM
PDT}

Axel, An interesting point. Anyway, just bumped into another quote about the beauty of mathematics:
"A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data." Paul A.M.Dirac.
EugeneS_{June 9, 2015
June
06
Jun
9
09
2015
01:27 PM
1
01
27
PM
PDT}

KF,
The attempt tells us quite plainly, that you are resorting to the rhetoric of dismissal because the sheer power and elegant beauty of logical implication applied to structure and quantity in the physical sciences points where you would not go.
Or, perhaps s/he believes otherwise. Simply disagreeing with you is not necessarily "resorting to the rhetoric of dismissal".daveS_{June 9, 2015
June
06
Jun
9
09
2015
12:36 PM
12
12
36
PM
PDT}

EugeneS, personally, (for what it's worth), I would be more inclined to describe mathematics as a discovery, and not just like any other art. Of course, discovery in a general sense can cover an awful lot of the most banal functions... such as discovering, as tots (however unconsciously,) that we can perform certain actions, such as walking and talking. But in science, imo, it's raised a notch, and in maths, another notch; the apex, and a unique kind of discovery. I suppose languages are akin to it, in that they realise a conceptual potential.Axel_{June 9, 2015
June
06
Jun
9
09
2015
12:11 PM
12
12
11
PM
PDT}

Carpathian, if you don't actually have any good reasons for what you say just admit it. You won't be the first to stop by here just to troll. But don't expect me to feed the trolls.Mung_{June 9, 2015
June
06
Jun
9
09
2015
12:00 PM
12
12
00
PM
PDT}

Carpathian, Did you notice that I took time to highlight a very particular facet of Mathematics and to point to its connexions onwards, highlighting that certain core aspects show a powerful pattern? I am not speaking to all of math, but to key aspects of it. To try to counter an equation that brings together the 5 most important numbers and the three most important operations from domains as separate as geometry of circles (pi), quadratic equations (i), logarithms and their relation to Y = 1/x --> e, power series, triangles and trigonometry [sin, cos in power series form], Taylor series, and then onwards Fourier and Laplace transforms as well as the linked Z transforms, the complex frequency and transient domain, differential equations and more, by putting up a trivial and empty expression that in effect says equals are equals is a red herring and strawman fallacy. The attempt tells us quite plainly, that you are resorting to the rhetoric of dismissal because the sheer power and elegant beauty of logical implication applied to structure and quantity in the physical sciences points where you would not go. You have implied much that you would not, and also have revealed something of a cramped mindset that should give pause. An intelligible, supremely rational world. One that is astonishingly pervaded by Mathematical linkages and relationships. What best explains that? Oh, maybe that is the problem. Plato, in The Laws, Bk X . . . his cosmological inference:
Ath. . . . when one thing changes another, and that another, of such will there be any primary changing element? How can a thing which is moved by another ever be the beginning of change? Impossible. But when the self-moved changes other, and that again other, and thus thousands upon tens of thousands of bodies are set in motion, must not the beginning of all this motion be the change of the self-moving principle? . . . . self-motion being the origin of all motions, and the first which arises among things at rest as well as among things in motion, is the eldest and mightiest principle of change, and that which is changed by another and yet moves other is second. [[ . . . .] Ath. If we were to see this power existing in any earthy, watery, or fiery substance, simple or compound-how should we describe it? Cle. You mean to ask whether we should call such a self-moving power life? Ath. I do. Cle. Certainly we should. Ath. And when we see soul in anything, must we not do the same-must we not admit that this is life? [[ . . . . ] Cle. You mean to say that the essence which is defined as the self-moved is the same with that which has the name soul? Ath. Yes; and if this is true, do we still maintain that there is anything wanting in the proof that the soul is the first origin and moving power of all that is, or has become, or will be, and their contraries, when she has been clearly shown to be the source of change and motion in all things? Cle. Certainly not; the soul as being the source of motion, has been most satisfactorily shown to be the oldest of all things. Ath. And is not that motion which is produced in another, by reason of another, but never has any self-moving power at all, being in truth the change of an inanimate body, to be reckoned second, or by any lower number which you may prefer? Cle. Exactly. Ath. Then we are right, and speak the most perfect and absolute truth, when we say that the soul is prior to the body, and that the body is second and comes afterwards, and is born to obey the soul, which is the ruler? [[ . . . . ] Ath. If, my friend, we say that the whole path and movement of heaven, and of all that is therein, is by nature akin to the movement and revolution and calculation of mind, and proceeds by kindred laws, then, as is plain, we must say that the best soul takes care of the world and guides it along the good path. [[Plato here explicitly sets up an inference to design (by a good soul) from the intelligible order of the cosmos.]
Pardon, but I must suggest, you lift your head up from looking at your feet and see what is there all around you. KFkairosfocus_{June 9, 2015
June
06
Jun
9
09
2015
12:00 PM
12
12
00
PM
PDT}

Mathematics is of course a human invention, an art, a language, a formalism, a study of form (just like any other art). But it's not all there is to it. It is beautiful and the world is beautiful. The Christian perspective is that the world (and mathematics as a reflection of it) is beautiful for a reason, i.e. because it is a form of Revelation of God, a kind of Scripture.EugeneS_{June 9, 2015
June
06
Jun
9
09
2015
11:55 AM
11
11
55
AM
PDT}

Prev 1 2 3 4 5 6 7 Next

You must be logged in to post a comment.

Leave a Reply