How funny is this word? The 'snunkoople' effect

Credit: © flytoskyft11 / Fotolia

 

How do you quantify something as complex and personal as humour? University of Alberta researchers have developed a mathematical method of doing just that -- and it might not be quite as personal as we think.

 

"This really is the first paper that's ever had a quantifiable theory of humour," says U of A psychology professor Chris Westbury, lead author of the recent study. "There's quite a small amount of experimental work that's been done on humour."
"We think that humour is personal, but evolutionary psychologists have talked about humour as being a message-sending device."
The idea for the study was born from earlier research in which test subjects with aphasia were asked to review letter strings and determine whether they were real words or not. Westbury began to notice a trend: participants would laugh when they heard some of the made-up non-words, like snunkoople.
It raised the question -- how can a made-up word be inherently funny?
The snunkoople effect
Westbury hypothesized that the answer lay in the word's entropy -- a mathematical measure of how ordered or predictable it is. Non-words like finglam, with uncommon letter combinations, are lower in entropy than other non-words like clester, which have more probable combinations of letters and therefore higher entropy.
"We did show, for example, that Dr. Seuss -- who makes funny non-words -- made non-words that were predictably lower in entropy. He was intuitively making lower-entropy words when he was making his non-words," says Westbury. "It essentially comes down to the probability of the individual letters. So if you look at a Seuss word like yuzz-a-ma-tuzz and calculate its entropy, you would find it is a low-entropy word because it has improbable letters like Z."
Inspired by the reactions to snunkoople, Westbury set out to determine whether it was possible to predict what words people would find funny, using entropy as a yardstick.
"Humour is not one thing. Once you start thinking about it in terms of probability, then you start to understand how we find so many different things funny."
For the first part of the study, test subjects were asked to compare two non-words and select the option they considered to be more humorous. In the second part, they were shown a single non-word and rated how humorous they found it on a scale from 1 to 100.
"The results show that the bigger the difference in the entropy between the two words, the more likely the subjects were to choose the way we expected them to," says Westbury, noting that the most accurate subject chose correctly 92 per cent of the time. "To be able to predict with that level of accuracy is amazing. You hardly ever get that in psychology, where you get to predict what someone will choose 92 per cent of the time."
People are funny that way
This nearly universal response says a lot about the nature of humour and its role in human evolution. Westbury refers to a well-known 1929 linguistics study by Wolfgang Köhler in which test subjects were presented with two shapes, one spiky and one round, and were asked to identify which was a baluba and which was a takete. Almost all the respondents intuited that takete was the spiky object, suggesting a common mapping between speech sounds and the visual shape of objects.
The reasons for this may be evolutionary. "We think that humour is personal, but evolutionary psychologists have talked about humour as being a message-sending device. So if you laugh, you let someone else know that something is not dangerous," says Westbury.
He uses the example of a person at home believing they see an intruder in their backyard. This person might then laugh when they discover the intruder is simply a cat instead of a cat burglar. "If you laugh, you're sending a message to whomever's around that you thought you saw something dangerous, but it turns out it wasn't dangerous after all. It's adaptive."
Just as expected (or not)
The idea of entropy as a predictor of humour aligns with a 19th-century theory from the German philosopher Arthur Schopenhauer, who proposed that humour is a result of an expectation violation, as opposed to a previously held theory that humour is based simply on improbability. When it comes to humour, expectations can be violated in various ways.
In non-words, expectations are phonological (we expect them to be pronounced a certain way), whereas in puns, the expectations are semantic. "One reason puns are funny is that they violate our expectation that a word has one meaning," says Westbury. Consider the following joke: Why did the golfer wear two sets of pants? Because he got a hole in one. "When you hear the golfer joke, you laugh because you've done something unexpected -- you expect the phrase 'hole in one' to mean something different, and that expectation has been violated."
The study may not be about to change the game for stand-up comedians -- after all, a silly word is hardly the pinnacle of comedy -- but the findings may be useful in commercial applications such as in product naming.
"I would be interested in looking at the relationship between product names and the seriousness of the product," notes Westbury. "For example, people might be averse to buying a funny-named medication for a serious illness -- or it could go the other way around."
Finding a measurable way to predict humour is just the tip of the proverbial iceberg. "One of the things the paper says about humour is that humour is not one thing. Once you start thinking about it in terms of probability, then you start to understand how we find so many different things funny. And the many ways in which things can be funny."

Source:
University of Alberta. "How funny is this word? The 'snunkoople' effect." ScienceDaily. ScienceDaily, 30 November 2015. <www.sciencedaily.com/releases/2015/11/151130131847.htm>.

Quantum physics problem proved unsolvable (Gödel and Turing enter quantum physics)

Source: Planet-science.com

 

A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid -- ICMAT and Technical University of Munich.

 

It is the first major problem in physics for which such a fundamental limitation could be proven. The findings are important because they show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.
A small spectral gap -- the energy needed to transfer an electron from a low-energy state to an excited state -- is the central property of semiconductors. In a similar way, the spectral gap plays an important role for many other materials. When this energy becomes very small, i.e. the spectral gap closes, it becomes possible for the material to transition to a completely different state. An example of this is when a material becomes superconducting.
Mathematically extrapolating from a microscopic description of a material to the bulk solid is considered one of the key tools in the search for materials exhibiting superconductivity at ambient temperatures or other desirable properties. A study, published today in Nature, however, shows crucial limits to this approach. Using sophisticated mathematics, the authors proved that, even with a complete microscopic description of a quantum material, determining whether it has a spectral gap is, in fact, an undecidable question.
"Alan Turing is famous for his role in cracking the Enigma code," said Co-author, Dr Toby Cubitt from UCL Computer Science. "But amongst mathematicians and computer scientists, he is even more famous for proving that certain mathematical questions are `undecidable' -- they are neither true nor false, but are beyond the reach of mathematics. What we've shown is that the spectral gap is one of these undecidable problems. This means a general method to determine whether matter described by quantum mechanics has a spectral gap, or not, cannot exist. Which limits the extent to which we can predict the behaviour of quantum materials, and potentially even fundamental particle physics."
One million dollars to win!
The most famous problem concerning spectral gaps is whether the theory governing the fundamental particles of matter itself -- the standard model of particle physics -- has a spectral gap (the `Yang-Mills mass gap' conjecture). Particle physics experiments such as CERN and numerical calculations on supercomputers suggest that there is a spectral gap. Although there is a $1m prize at stake from the Clay Mathematics Institute for whoever can, no one has yet succeeded in proving this mathematically from the equations of the standard model.
Dr Cubitt added, "It's possible for particular cases of a problem to be solvable even when the general problem is undecidable, so someone may yet win the coveted $1m prize. But our results do raise the prospect that some of these big open problems in theoretical physics could be provably unsolvable."
"We knew about the possibility of problems that are undecidable in principle since the works of Turing and Gödel in the 1930s," added Co-author Professor Michael Wolf from Technical University of Munich. "So far, however, this only concerned the very abstract corners of theoretical computer science and mathematical logic. No one had seriously contemplated this as a possibility right in the heart of theoretical physics before. But our results change this picture. From a more philosophical perspective, they also challenge the reductionists' point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description."
Not all bad news
Co-author, Professor David Pérez-García from Universidad Complutense de Madrid and ICMAT, said: "It's not all bad news, though. The reason this problem is impossible to solve in general is because models at this level exhibit extremely bizarre behaviour that essentially defeats any attempt to analyse them. But this bizarre behaviour also predicts some new and very weird physics that hasn't been seen before. For example, our results show that adding even a single particle to a lump of matter, however large, could in principle dramatically change its properties. New physics like this is often later exploited in technology."
The researchers are now seeing whether their findings extend beyond the artificial mathematical models produced by their calculations to more realistic quantum materials that could be realised in the laboratory.

Source:
University College London. "Quantum physics problem proved unsolvable: Gödel and Turing enter quantum physics." ScienceDaily. ScienceDaily, 9 December 2015. <www.sciencedaily.com/releases/2015/12/151209142727.htm>.

 

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The world's greatest literature reveals multifractals and cascades of consciousness

Sequences of sentence lengths (as measured by number of words) in four literary works representative of various degree of cascading character.

Credit: Source: IFJ PAN

 

 

James Joyce, Julio Cortazar, Marcel Proust, Henryk Sienkiewicz and Umberto Eco. Regardless of the language they were working in, some of the world's greatest writers appear to be, in some respects, constructing fractals. Statistical analysis carried out at the Institute of Nuclear Physics of the Polish Academy of Sciences, however, revealed something even more intriguing. The composition of works from within a particular genre was characterized by the exceptional dynamics of a cascading (avalanche) narrative structure. This type of narrative turns out to be multifractal. That is, fractals of fractals are created.

 

 

As far as many bookworms are concerned, advanced equations and graphs are the last things which would hold their interest, but there's no escape from the math. Physicists from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Cracow, Poland, performed a detailed statistical analysis of more than one hundred famous works of world literature, written in several languages and representing various literary genres. The books, tested for revealing correlations in variations of sentence length, proved to be governed by the dynamics of a cascade. This means that the construction of these books is in fact a fractal. In the case of several works their mathematical complexity proved to be exceptional, comparable to the structure of complex mathematical objects considered to be multifractal. Interestingly, in the analyzed pool of all the works, one genre turned out to be exceptionally multifractal in nature.
Fractals are self-similar mathematical objects: when we begin to expand one fragment or another, what eventually emerges is a structure that resembles the original object. Typical fractals, especially those widely known as the Sierpinski triangle and the Mandelbrot set, are monofractals, meaning that the pace of enlargement in any place of a fractal is the same, linear: if they at some point were rescaled x number of times to reveal a structure similar to the original, the same increase in another place would also reveal a similar structure.
Multifractals are more highly advanced mathematical structures: fractals of fractals. They arise from fractals 'interwoven' with each other in an appropriate manner and in appropriate proportions. Multifractals are not simply the sum of fractals and cannot be divided to return back to their original components, because the way they weave is fractal in nature. The result is that in order to see a structure similar to the original, different portions of a multifractal need to expand at different rates. A multifractal is therefore non-linear in nature.
"Analyses on multiple scales, carried out using fractals, allow us to neatly grasp information on correlations among data at various levels of complexity of tested systems. As a result, they point to the hierarchical organization of phenomena and structures found in nature. So we can expect natural language, which represents a major evolutionary leap of the natural world, to show such correlations as well. Their existence in literary works, however, had not yet been convincingly documented. Meanwhile, it turned out that when you look at these works from the proper perspective, these correlations appear to be not only common, but in some works they take on a particularly sophisticated mathematical complexity," says Prof. Stanislaw Drozdz (IFJ PAN, Cracow University of Technology).
The study involved 113 literary works written in English, French, German, Italian, Polish, Russian and Spanish by such famous figures as Honore de Balzac, Arthur Conan Doyle, Julio Cortazar, Charles Dickens, Fyodor Dostoevsky, Alexandre Dumas, Umberto Eco, George Elliot, Victor Hugo, James Joyce, Thomas Mann, Marcel Proust, Wladyslaw Reymont, William Shakespeare, Henryk Sienkiewicz, JRR Tolkien, Leo Tolstoy and Virginia Woolf, among others. The selected works were no less than 5,000 sentences long, in order to ensure statistical reliability.
To convert the texts to numerical sequences, sentence length was measured by the number of words (an alternative method of counting characters in the sentence turned out to have no major impact on the conclusions). The dependences were then searched for in the data -- beginning with the simplest, i.e. linear. This is the posited question: if a sentence of a given length is x times longer than the sentences of different lengths, is the same aspect ratio preserved when looking at sentences respectively longer or shorter?
"All of the examined works showed self-similarity in terms of organization of the lengths of sentences. Some were more expressive -- here The Ambassadors by Henry James stood out -- while others to far less of an extreme, as in the case of the French seventeenth-century romance Artamene ou le Grand Cyrus. However, correlations were evident, and therefore these texts were the construction of a fractal," comments Dr. Pawel Oswiecimka (IFJ PAN), who also noted that fractality of a literary text will in practice never be as perfect as in the world of mathematics. It is possible to magnify mathematical fractals up to infinity, while the number of sentences in each book is finite, and at a certain stage of scaling there will always be a cut-off in the form of the end of the dataset.
Things took a particularly interesting turn when physicists from the IFJ PAN began tracking non-linear dependence, which in most of the studied works was present to a slight or moderate degree. However, more than a dozen works revealed a very clear multifractal structure, and almost all of these proved to be representative of one genre, that of stream of consciousness. The only exception was the Bible, specifically the Old Testament, which has so far never been associated with this literary genre.
"The absolute record in terms of multifractality turned out to be Finnegan's Wake by James Joyce. The results of our analysis of this text are virtually indistinguishable from ideal, purely mathematical multifractals," says Prof. Drozdz.
The most multifractal works also included A Heartbreaking Work of Staggering Genius by Dave Eggers, Rayuela by Julio Cortazar, The US Trilogy by John Dos Passos, The Waves by Virginia Woolf, 2666 by Roberto Bolano, and Joyce's Ulysses. At the same time a lot of works usually regarded as stream of consciousness turned out to show little correlation to multifractality, as it was hardly noticeable in books such as Atlas Shrugged by Ayn Rand and A la recherche du temps perdu by Marcel Proust.
"It is not entirely clear whether stream of consciousness writing actually reveals the deeper qualities of our consciousness, or rather the imagination of the writers. It is hardly surprising that ascribing a work to a particular genre is, for whatever reason, sometimes subjective. We see, moreover, the possibility of an interesting application of our methodology: it may someday help in a more objective assignment of books to one genre or another," notes Prof. Drozdz.
Multifractal analyses of literary texts carried out by the IFJ PAN have been published in Information Sciences, a journal of computer science. The publication has undergone rigorous verification: given the interdisciplinary nature of the subject, editors immediately appointed up to six reviewers.

Source:
The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences. "The world's greatest literature reveals multifractals and cascades of consciousness." ScienceDaily. ScienceDaily, 21 January 2016. <www.sciencedaily.com/releases/2016/01/160121110913.htm>.

How many ways can you arrange 128 tennis balls? Researchers solve an apparently impossible problem

Tennis balls.Credit: © Hayati Kayhan / Fotolia

 

 

Researchers have solved an apparently overwhelming physics problem involving some truly huge numbers. In summary, the problem asks you to imagine that you have 128 tennis balls, and can arrange them in any way you like. The challenge is to work out how many arrangements are possible and -- according to the research -- the answer is about 10^250, also known as ten unquadragintilliard: a number so big that it exceeds the total number of particles in the universe.

Despite its complexity, this study also provides a working example of how "configurational entropy" might be calculated in granular physics. This basically means the issue of measuring how disordered the particles within a system or structure are. The research provides a model for the sort of maths that would be needed to solve bigger problems still, ranging from predicting avalanches, to creating efficient artificial intelligence systems.
A bewildering physics problem has apparently been solved by researchers, in a study which provides a mathematical basis for understanding issues ranging from predicting the formation of deserts, to making artificial intelligence more efficient.
In research carried out at the University of Cambridge, a team developed a computer program that can answer this mind-bending puzzle: Imagine that you have 128 soft spheres, a bit like tennis balls. You can pack them together in any number of ways. How many different arrangements are possible?
The answer, it turns out, is something like 10250 (1 followed by 250 zeros). The number, also referred to as ten unquadragintilliard, is so huge that it vastly exceeds the total number of particles in the universe.
Far more important than the solution, however, is the fact that the researchers were able to answer the question at all. The method that they came up with can help scientists to calculate something called configurational entropy -- a term used to describe how structurally disordered the particles in a physical system are.
Being able to calculate configurational entropy would, in theory, eventually enable us to answer a host of seemingly impossible problems -- such as predicting the movement of avalanches, or anticipating how the shifting sand dunes in a desert will reshape themselves over time.
These questions belong to a field called granular physics, which deals with the behaviour of materials such as snow, soil or sand. Different versions of the same problem, however, exist in numerous other fields, such as string theory, cosmology, machine learning, and various branches of mathematics. The research shows how questions across all of those disciplines might one day be addressed.
Stefano Martiniani, a Benefactor Scholar at St John's College, University of Cambridge, who carried out the study with colleagues in the Department of Chemistry, explained: "The problem is completely general. Granular materials themselves are the second most processed kind of material in the world after water and even the shape of the surface of the Earth is defined by how they behave."
"Obviously being able to predict how avalanches move or deserts may change is a long, long way off, but one day we would like to be able to solve such problems. This research performs the sort of calculation we would need in order to be able to do that."
At the heart of these problems is the idea of entropy -- a term which describes how disordered the particles in a system are. In physics, a "system" refers to any collection of particles that we want to study, so for example it could mean all the water in a lake, or all the water molecules in a single ice cube.
When a system changes, for example because of a shift in temperature, the arrangement of these particles also changes. For example, if an ice cube is heated until it becomes a pool of water, its molecules become more disordered. Therefore, the ice cube, which has a tighter structure, is said to have lower entropy than the more disordered pool of water.
At a molecular level, where everything is constantly vibrating, it is often possible to observe and measure this quite clearly. In fact, many molecular processes involve a spontaneous increase in entropy until they reach a steady equilibrium.
In granular physics, however, which tends to involve materials large enough to be seen with the naked eye, change does not happen in the same way. A sand dune in the desert will not spontaneously change the arrangement of its particles (the grains of sand). It needs an external factor, like the wind, for this to happen.
This means that while we can predict what will happen in many molecular processes, we cannot easily make equivalent predictions about how systems will behave in granular physics. Doing so would require us to be able to measure changes in the structural disorder of all of the particles in a system -- its configurational entropy.
To do that, however, scientists need to know how many different ways a system can be structured in the first place. The calculations involved in this are so complicated that they have been dismissed as hopeless for any system involving more than about 20 particles. Yet the Cambridge study defied this by carrying out exactly this type of calculation for a system, modelled on a computer, in which the particles were 128 soft spheres, like tennis balls.
"The brute force way of doing this would be to keep changing the system and recording the configurations," Martiniani said. "Unfortunately, it would take many lifetimes before you could record it all. Also, you couldn't store the configurations, because there isn't enough matter in the universe with which to do it."
Instead, the researchers created a solution which involved taking a small sample of all possible configurations and working out the probability of them occurring, or the number of arrangements that would lead to those particular configurations appearing.
Based on these samples, it was possible to extrapolate not only in how many ways the entire system could therefore be arranged, but also how ordered one state was compared with the next -- in other words, its overall configurational entropy.
Martiniani added that the team's problem-solving technique could be used to address all sorts of problems in physics and maths. He himself is, for example, currently carrying out research into machine learning, where one of the problems is knowing how many different ways a system can be wired to process information efficiently.
"Because our indirect approach relies on the observation of a small sample of all possible configurations, the answers it finds are only ever approximate, but the estimate is a very good one," he said. "By answering the problem we are opening up uncharted territory. This methodology could be used anywhere that people are trying to work out how many possible solutions to a problem you can find."
The paper, Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings, is published in the journal, Physical Review E.
Stefano Martiniani is a St John's Benefactor Scholar and Gates Scholar at the University of Cambridge.


Source:
University of Cambridge. "How many ways can you arrange 128 tennis balls? Researchers solve an apparently impossible problem." ScienceDaily. ScienceDaily, 27 January 2016. <www.sciencedaily.com/releases/2016/01/160127053413.htm>.

Students of Krystal Edge College on Excursion

Please give me that word when you have a billion dollar sent into your account....LOL, that was the experience we had on Friday, great time knowing the work of Lister Ross Bower and most importantly the beautiful animals.... Well, I don't like talking much, have a filled day with this.

 

 

 

 

 

 

2016 Cowbellpedia Mathematics Contest is Out

The 2016 edition of the Cowbellpedia Secondary School Mathematics TV Quiz show will work in partnership with the National Examination Council to widen the reach to participants across the country.
Festus Tettey, Head of Marketing Promasidor Nigeria Limited explained at a press conference in Lagos on Tuesday that this year’s competition will be in two stages: Qualifying Written Examination and TV Quiz Show. The stage one examination according to him will be conducted by the National Examination Council NECO on Saturday, March 19, 2016.
The NECO is an examination body in Nigeria that conducts the Senior Secondary Certificate Examination and the General Certificate in Education in June/July and December/January respectively.
NECO was mandated to take over the responsibilities of the National Board of Education Measurement (NBEM) and is headed by a Registrar, appointed by the President under section 9(1) of its establishing Act. Under this year’s arrangement, NECO will turn in its massive structures to participants all over the country.
Tettey added that the stage one of the Mathematics Competition is open to students from 10 – 18 years of age attending full time Secondary Education in both Public and Private Schools in Nigeria. Entry into this competition is FREE.
Each School is required to present their best ten (10) students in Mathematics (five from JSS3 and five from SSS2), irrespective of religion, tribe or state of origin, to enhance their chance of qualifying for the next stage of the competition. According to Tettey, the stage one registration, which is online, involves the following processes:
1. Go to www.cowbellpedia.ng
2. Click on link to register your school
3. Fill the form and submit. Ensure to fill all required fields.
4. An email will be sent to the School and Primary contact email addresses provided when filling the form.
5. Use the link in the email received to verify the email addresses. Both email addresses must be verified before you can login.
6. Once school email address is verified, login to the portal using the school email and password used to register.
7. On successful login, you click on the Add Candidates under Candidate Management.
8. Fill in the candidates’ information on the form, upload the candidate’s picture and click the Save Draft button.
9. You will need to save draft information for 5 candidates before you can submit their registration. If your school is a mixed school, at least 2 of the candidates must be female or you won’t be able to complete the registration.
10. After creating the draft registration for 5 candidates in a category (junior/senior) button will be shown on the page to “Register junior/senior candidates”. Click the button to complete the registration of candidates for that category.
11. A confirmation slip will be generated for you to download and will also be mailed to the School, candidate and parent/guardian email address.
12. Print this confirmation slip and have it stamped and signed by the school principal.
13. The confirmation slip will be required for admitting candidates at the examination venue.

#culled from Marketing Edge