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September 11th, 2015, 16:29
Originally Posted by Asdraguuhl View Post
But the question that many may ask themselves is….what the hell are they for and how does it help us in any way in everyday life?
It seems to me that this is the wrong question to ask - I wonder how many times new mathematics has preceded and engendered new science.

The great mathematician Paul Erdős used to travel around between his friends with not much more than the price of a cup of coffee in his pocket. He would turn up on their doorstep, announce, "My mind is open," and proceed to stay for several weeks intensely discussing abstract problems while hopped up on amphetamines.

God bless impractical people.
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September 11th, 2015, 16:47
Heard a story about a math professor once who researches new theoretical math concepts that don't have any practical application whatsoever (yet). When asked about it he said something along the lines of "the day there's a real life application of my field of study is the day I lose my job". Right.
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September 11th, 2015, 18:17
Originally Posted by Ripper View Post
It seems to me that this is the wrong question to ask - I wonder how many times new mathematics has preceded and engendered new science.

The great mathematician Paul Erdős used to travel around between his friends with not much more than the price of a cup of coffee in his pocket. He would turn up on their doorstep, announce, "My mind is open," and proceed to stay for several weeks intensely discussing abstract problems while hopped up on amphetamines.

God bless impractical people.
Has anybody on the watch got a finite Erdös number?

pibbur who's Erdös number is larger than the Graham number

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September 11th, 2015, 18:55
Originally Posted by pibbur who View Post
Has anybody on the watch got a finite Erdös number?

pibbur who's Erdös number is larger than the Graham number
Nope. 1/0, or thereabouts.
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September 11th, 2015, 18:59
Originally Posted by Ripper View Post
It seems to me that this is the wrong question to ask - I wonder how many times new mathematics has preceded and engendered new science.

The great mathematician Paul Erdős used to travel around between his friends with not much more than the price of a cup of coffee in his pocket. He would turn up on their doorstep, announce, "My mind is open," and proceed to stay for several weeks intensely discussing abstract problems while hopped up on amphetamines.

God bless impractical people.
It is true that "applicability" doesn't always come immediately….then again, "applicability" is also not guaranteed .

I find the imaginary number i fascinating as it is such a simple idea and at first glance a concept with no practical usefulness yet it has indeed proven to be very important as it is useful to solve differential equations and is also fundamental in Control Theory.

I sometimes wonder what our engineering capabilities would be if we wouldn't have invented these abstract concepts. Of course, this also implies that we aren't able to perform certain engineering/scientific tasks today because we simply haven't come up with the necessary abstract concepts. I really doubt that we have "found" them all .
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September 11th, 2015, 19:05
Interesting stuff:

From the moment in 2013 when paleoanthropologist Lee Berger posted a plea on Facebook, Twitter, and LinkedIn for “tiny and small, specialised cavers and spelunkers with excellent archaeological, palaeontological and excavation skills,” some experts began grumbling that the excavation of a mysterious hominin in the Rising Star Cave in South Africa was more of a media circus than a serious scientific expedition. Daily blogs recorded the dangerous maneuvers of “underground astronauts” who squeezed through a long, narrow chute to drop 30 meters into a fossil-filled cavern, while Berger, who is based at the University of the Witwatersrand in Johannesburg, South Africa, became the “voice from the cave” in radio interviews.
http://news.sciencemag.org/archaeolo…ies-discovered
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September 11th, 2015, 19:19
Originally Posted by Asdraguuhl View Post
I sometimes wonder what our engineering capabilities would be if we wouldn't have invented these abstract concepts. Of course, this also implies that we aren't able to perform certain engineering/scientific tasks today because we simply haven't come up with the necessary abstract concepts. I really doubt that we have "found" them all .
I suspect that's true. Erdős used to joke that he believed in god - but he called him The Supreme Fascist (abbreviated to "The SF"). He said The SF jealously guarded his book of secrets, and he wanted to uncover as many of them as he could before he died.

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September 11th, 2015, 20:29
Originally Posted by Asdraguuhl View Post
I sometimes wonder what our engineering capabilities would be if we wouldn't have invented these abstract concepts. Of course, this also implies that we aren't able to perform certain engineering/scientific tasks today because we simply haven't come up with the necessary abstract concepts. I really doubt that we have "found" them all .
Also in image processing. For instance in obtaining MR images.

BTW, let's not forget this beauty: e^(PI*i)+1=0.

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September 11th, 2015, 22:51
Originally Posted by Ripper View Post
He said The SF jealously guarded his book of secrets, and he wanted to uncover as many of them as he could before he died.
The secrets of Nature are the realm of Physics and I am of the opinion that Mathematics is a pure human invention and as such it doesn't hold any universal truths.

I find it therefore fascinating how this abstract idiom allows us to describe and predict the rules of Nature and manipulate them in our favour.
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September 11th, 2015, 22:54
Originally Posted by pibbur who View Post
BTW, let's not forget this beauty: e^(PI*i)+1=0.
Yes, the wonderful Euler Identity.

I remember posting that same equation on this site….but I don't remember in which thread nor the context in which I posted it.
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September 11th, 2015, 23:02
Originally Posted by Asdraguuhl View Post
The secrets of Nature are the realm of Physics and I am of the opinion that Mathematics is a pure human invention and as such it doesn't hold any universal truths.

I find it therefore fascinating how this abstract idiom allows us to describe and predict the rules of Nature and manipulate them in our favour.
Perhaps mathematics is a purely human contstruct, but I personally suspect that its relationship to nature is such that it is a least a reflection of something more fundamental.
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September 12th, 2015, 09:20
Hyperreal numbers are fun, too.

The opposite of infinity:
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September 16th, 2015, 08:32
The Zipf Mystery
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Default Cat music

September 16th, 2015, 13:25
The University of Wisconsin-Madison shows that while cats ignore humans’ music, they are highly responsive to "music" written especially for them. "We are not actually replicating cat sounds," says lead author Charles Snowdon, an emeritus professor of psychology. "We are trying to create music with a pitch and tempo that appeals to cats." One sample was based on the tempo of purring, the other on the sucking sound made during nursing.
We have developed a theoretical framework that hypothesizes that in order for music to be effective with other species, it must be in the frequency range and with similar tempos to those used in natural communication by each species. […] Younger and older cats were more responsive to cat music than middle-aged acts (cubic trend, r2 = 0.477, P < 0.001). The results suggest novel and more appropriate ways for using music as auditory enrichment for nonhuman animals.

If you'd like to see the effect on your own cat:

Cat music
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September 20th, 2015, 20:19
Quite gruesome : http://www.thehistoryblog.com/archives/34978
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September 30th, 2015, 19:04
Breakthrough rectenna converts light into DC current
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October 1st, 2015, 18:01
Originally Posted by Asdraguuhl View Post
The secrets of Nature are the realm of Physics and I am of the opinion that Mathematics is a pure human invention and as such it doesn't hold any universal truths.

I find it therefore fascinating how this abstract idiom allows us to describe and predict the rules of Nature and manipulate them in our favour.
Originally Posted by Ripper View Post
Perhaps mathematics is a purely human contstruct, but I personally suspect that its relationship to nature is such that it is a least a reflection of something more fundamental.
About that, let me give you my opinion as a physicist:
I also think that mathematics are purely a human construct. I don't believe that people are "discovering" some pre-existing maths, as people may discover rare tropical bugs or fishes. I believe that people are "creating" math, in the same way they created material tools (or clothes, furnitures, etc.) adapted to their environnement.
But I don't think that physics is the science of nature. Physics is the science of models. There is no more universal truth in physics than in maths. There are only suitable approximations in a given context.
The fact that mathematical laws are suitable to describe natural phenomenon seems not like a miracle to me. It happens because the mathematical laws are actually constructed to describe in a simple way (establish a model for) a more complex phenomenon…
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October 1st, 2015, 18:41
But we are left with the question of what has been described as the “unreasonable effectiveness of mathematics”. That is to say, why should mathematics be able to produce such effective models, predictions, and technologies, rather than some other system of thought or representation?

I think that to say physics is the science of models rather than nature is a semantic distinction, when it is models of nature, in this universe, that can be built so successfully using this form of thought.

I wouldn’t necessarily go along with the philosophy that the universe ontologically IS mathematical, but I think it is an aspect of it. Bertrand Russell’s said that “Physics is mathematical not because we know so much about the world but because we know so little; it is only its mathematical properties that we can discover”. I go along with that - but I still think that we can gain some knowledge of the properties of the universe through mathematics.
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October 1st, 2015, 19:29
Well some things in the universe just seem fundamentally mathematic. 1 plus one oranges gives you 2 oranges. Taking away 1 orange gives you 1 orange.
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October 1st, 2015, 20:22
Originally Posted by Luitoine View Post
About that, let me give you my opinion as a physicist:
I also think that mathematics are purely a human construct. I don't believe that people are "discovering" some pre-existing maths, as people may discover rare tropical bugs or fishes. I believe that people are "creating" math, in the same way they created material tools (or clothes, furnitures, etc.) adapted to their environnement.
I fully agree with this.
Originally Posted by Luitoine View Post
But I don't think that physics is the science of nature. Physics is the science of models. There is no more universal truth in physics than in maths. There are only suitable approximations in a given context.
The way I see it, Physics is about observing the Universe and trying to obtain a set of rules/laws that describe said universe as exact as possible.

We are of course limited in both observation and comprehension so it is unlikely that we will ever expose the "truth" of Nature but our intent to do so as best as possible is still there.
Originally Posted by Luitoine View Post
The fact that mathematical laws are suitable to describe natural phenomenon seems not like a miracle to me. It happens because the mathematical laws are actually constructed to describe in a simple way (establish a model for) a more complex phenomenon…
Of course, a 2nd order differential equation to describe a mass-spring system may be quite straightforward without any mistery.

Nevertheless, there are still things that I find fascinating. Take e.g. the imaginary number i that we were talking about. With Euler's formula e^ix = cos(x) + i*sin(x) we relate complex exponentials to oscillations. This gives rise to the Fourier transform where signals in the time domain can be expressed by signals in the frequency domain. It can be extended with the Laplace transform that is very useful to express differential equations as algebraic equations. In Control Theory, working in the s-domain (Laplace Transform) is very common and it impresses me how we can mathematically construct complex dynamical systems by interconnecting simple block diagrams in the s-domain.

Of course, there is a caveat, and that is that it is only applicable to linear systems. I suspect that it is the the "superposition" property of linear systems that allows these mathematical tools to be so effective. In reality, systems tend to be nonlinear so we have to simplify by necessity.

At the university, I had a physics teacher who joked that phycisists would look at nonlinear systems and kept looking until it became a bit more linear and continued looking until it became fully linear so that they could start working .
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