Okay, there will be a test after you read this post.  Here we go.  Do you know these people?

  • Beyoncé
  • Jennifer Lopez
  • Mariah Cary
  • Lady Gaga
  • Ariana Grande
  • Katy Perry
  • Miley Cyrus
  • Karen Uhlenbeck

Don’t feel bad.  I didn’t know either.  This is Karen Uhlenbeck—the mathematician we do not know.  For some unknown reason we all (even me) know the “pop” stars by name; who their significant other or others are, their children, their latest hit single, who they recently “dumped”, where they vacationed, etc. etc.  We know this. I would propose the lady whose picture shown below has contributed more to “human kind” that all the individuals listed above.  Then again, that’s just me.

For the first time, one of the top prizes in mathematics has been given to a woman.  I find this hard to believe because we all know that “girls” can’t do math.  Your mamas told you that and you remembered it.  (I suppose Dr. Uhlenbeck mom was doing her nails and forgot to mention that to her.)

This past Tuesday, the Norwegian Academy of Science and Letters announced it has awarded this year’s Abel Prize — an award modeled on the Nobel Prizes — to Karen Uhlenbeck, an emeritus professor at the University of Texas at Austin. The award cites “the fundamental impact of her work on analysis, geometry and mathematical physics.”   Uhlenbeck won for her foundational work in geometric analysis, which combines the technical power of analysis—a branch of math that extends and generalizes calculus—with the more conceptual areas of geometry and topology. She is the first woman to receive the prize since the award of six (6) million Norwegian kroner (approximately $700,000) was first given in 2003.

One of Dr. Uhlenbeck’s advances in essence described the complex shapes of soap films not in a bubble bath but in abstract, high-dimensional curved spaces. In later work, she helped put a rigorous mathematical underpinning to techniques widely used by physicists in quantum field theory to describe fundamental interactions between particles and forces. (How many think Beyoncé could do that?)

In the process, she helped pioneer a field known as geometric analysis, and she developed techniques now commonly used by many mathematicians. As a matter of fact, she invented the field.

“She did things nobody thought about doing,” said Sun-Yung Alice Chang, a mathematician at Princeton University who served on the five-member prize committee, “and after she did, she laid the foundations for that branch of mathematics.”

An example of objects studied in geometric analysis is a minimal surface. Analogous to a geodesic, a curve that minimizes path length, a minimal surface minimizes area; think of a soap film, a minimal surface that minimizes energy. Analysis focuses on the differential equations governing variations of surface area, whereas geometry and topology focus on the minimal surface representing a solution to the equations. Geometric analysis weaves together both approaches, resulting in new insights.

The field did not exist when Uhlenbeck began graduate school in the mid-1960s, but tantalizing results linking analysis and topology had begun to emerge. In the early 1980s, Uhlenbeck and her collaborators did ground-breaking work in minimal surfaces. They showed how to deal with singular points, that is, points where the minimal surface is no longer smooth or where the solution to the equations is not defined. They proved that there are only finitely many singular points and showed how to study them by expanding them into “bubbles.” As a technique, bubbling made a deep impact and is now a standard tool.

Born in 1942 to an engineer and an artist, Uhlenbeck is a mountain-loving hiker who learned to surf at the age of forty (40). As a child she was a voracious reader and “was interested in everything,” she said in an interview last year with Celebratio.org. “I was always tense, wanting to know what was going on and asking questions.”

She initially majored in physics as an undergraduate at the University of Michigan. But her impatience with lab work and a growing love for math led her to switch majors. She nevertheless retained a lifelong passion for physics, and centered much of her research on problems from that field.  In physics, a gauge theory is a kind of field theory, formulated in the language of the geometry of fiber bundles; the simplest example is electromagnetism. One of the most important gauge theories from the 20th century is Yang-Mills theory, which underlies the standard model of elementary particle physics. Uhlenbeck and other mathematicians began to realize that the Yang-Mills equations have deep connections to problems in geometry and topology. By the early 1980s, she laid the analytic foundations for mathematical investigation of the Yang-Mills equations.

Dr. Uhlenbeck, who lives in Princeton, N.J., learned that she won the prize on Sunday morning.

“When I came out of church, I noticed that I had a text message from Alice Chang that said, Would I please accept a call from Norway?” Dr. Uhlenbeck said. “When I got home, I called Norway back and they told me.”

Who said women can’t do math?

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COMPUTER SIMULATION

January 20, 2019


More and more engineers, systems analysist, biochemists, city planners, medical practitioners, individuals in entertainment fields are moving towards computer simulation.  Let’s take a quick look at simulation then we will discover several examples of how very powerful this technology can be.

WHAT IS COMPUTER SIMULATION?

Simulation modelling is an excellent tool for analyzing and optimizing dynamic processes. Specifically, when mathematical optimization of complex systems becomes infeasible, and when conducting experiments within real systems is too expensive, time consuming, or dangerous, simulation becomes a powerful tool. The aim of simulation is to support objective decision making by means of dynamic analysis, to enable managers to safely plan their operations, and to save costs.

A computer simulation or a computer model is a computer program that attempts to simulate an abstract model of a particular system. … Computer simulations build on and are useful adjuncts to purely mathematical models in science, technology and entertainment.

Computer simulations have become a useful part of mathematical modelling of many natural systems in physics, chemistry and biology, human systems in economics, psychology, and social science and in the process of engineering new technology, to gain insight into the operation of those systems. They are also widely used in the entertainment fields.

Traditionally, the formal modeling of systems has been possible using mathematical models, which attempts to find analytical solutions to problems enabling the prediction of behavior of the system from a set of parameters and initial conditions.  The word prediction is a very important word in the overall process. One very critical part of the predictive process is designating the parameters properly.  Not only the upper and lower specifications but parameters that define intermediate processes.

The reliability and the trust people put in computer simulations depends on the validity of the simulation model.  The degree of trust is directly related to the software itself and the reputation of the company producing the software. There will considerably more in this course regarding vendors providing software to companies wishing to simulate processes and solve complex problems.

Computer simulations find use in the study of dynamic behavior in an environment that may be difficult or dangerous to implement in real life. Say, a nuclear blast may be represented with a mathematical model that takes into consideration various elements such as velocity, heat and radioactive emissions. Additionally, one may implement changes to the equation by changing certain other variables, like the amount of fissionable material used in the blast.  Another application involves predictive efforts relative to weather systems.  Mathematics involving these determinations are significantly complex and usually involve a branch of math called “chaos theory”.

Simulations largely help in determining behaviors when individual components of a system are altered. Simulations can also be used in engineering to determine potential effects, such as that of river systems for the construction of dams.  Some companies call these behaviors “what-if” scenarios because they allow the engineer or scientist to apply differing parameters to discern cause-effect interaction.

One great advantage a computer simulation has over a mathematical model is allowing a visual representation of events and time line. You can actually see the action and chain of events with simulation and investigate the parameters for acceptance.  You can examine the limits of acceptability using simulation.   All components and assemblies have upper and lower specification limits a and must perform within those limits.

Computer simulation is the discipline of designing a model of an actual or theoretical physical system, executing the model on a digital computer, and analyzing the execution output. Simulation embodies the principle of “learning by doing” — to learn about the system we must first build a model of some sort and then operate the model. The use of simulation is an activity that is as natural as a child who role plays. Children understand the world around them by simulating (with toys and figurines) most of their interactions with other people, animals and objects. As adults, we lose some of this childlike behavior but recapture it later on through computer simulation. To understand reality and all of its complexity, we must build artificial objects and dynamically act out roles with them. Computer simulation is the electronic equivalent of this type of role playing and it serves to drive synthetic environments and virtual worlds. Within the overall task of simulation, there are three primary sub-fields: model design, model execution and model analysis.

REAL-WORLD SIMULATION:

The following examples are taken from computer screen representing real-world situations and/or problems that need solutions.  As mentioned earlier, “what-ifs” may be realized by animating the computer model providing cause-effect and responses to desired inputs. Let’s take a look.

A great host of mechanical and structural problems may be solved by using computer simulation. The example above shows how the diameter of two matching holes may be affected by applying heat to the bracket

 

The Newtonian and non-Newtonian flow of fluids, i.e. liquids and gases, has always been a subject of concern within piping systems.  Flow related to pressure and temperature may be approximated by simulation.

 

The Newtonian and non-Newtonian flow of fluids, i.e. liquids and gases, has always been a subject of concern within piping systems.  Flow related to pressure and temperature may be approximated by simulation.

Electromagnetics is an extremely complex field. The digital above strives to show how a magnetic field reacts to applied voltage.

Chemical engineers are very concerned with reaction time when chemicals are mixed.  One example might be the ignition time when an oxidizer comes in contact with fuel.

Acoustics or how sound propagates through a physical device or structure.

The transfer of heat from a colder surface to a warmer surface has always come into question. Simulation programs are extremely valuable in visualizing this transfer.

 

Equation-based modeling can be simulated showing how a structure, in this case a metal plate, can be affected when forces are applied.

In addition to computer simulation, we have AR or augmented reality and VR virtual reality.  Those subjects are fascinating but will require another post for another day.  Hope you enjoy this one.

 

 

DEEP LEARNING

December 10, 2017


If you read technical literature with some hope of keeping up with the latest trends in technology, you find words and phrases such as AI (Artificial Intelligence) and DL (Deep Learning). They seem to be used interchangeability but facts deny that premise.  Let’s look.

Deep learning ( also known as deep structured learning or hierarchical learning) is part of a broader family of machine-learning methods based on learning data representations, as opposed to task-specific algorithms. (NOTE: The key words here are MACHINE-LEARNING). The ability of computers to learn can be supervised, semi-supervised or unsupervised.  The prospect of developing learning mechanisms and software to control machine mechanisms is frightening to many but definitely very interesting to most.  Deep learning is a subfield of machine learning concerned with algorithms inspired by structure and function of the brain called artificial neural networks.  Machine-learning is a method by which human neural networks are duplicated by physical hardware: i.e. computers and computer programming.  Never in the history of our species has a degree of success been possible–only now. Only with the advent of very powerful computers and programs capable of handling “big data” has this been possible.

With massive amounts of computational power, machines can now recognize objects and translate speech in real time. Artificial intelligence is finally getting smart.  The basic idea—that software can simulate the neocortex’s large array of neurons in an artificial “neural network”—is decades old, and it has led to as many disappointments as breakthroughs.  Because of improvements in mathematical formulas and increasingly powerful computers, computer scientists can now model many more layers of virtual neurons than ever before. Deep learning is a class of machine learning algorithms that accomplish the following:

With massive amounts of computational power, machines can now recognize objects and translate speech in real time. Artificial intelligence is finally getting smart.  The basic idea—that software can simulate the neocortex’s large array of neurons in an artificial “neural network”—is decades old, and it has led to as many disappointments as breakthroughs.  Because of improvements in mathematical formulas and increasingly powerful computers, computer scientists can now model many more layers of virtual neurons than ever before. Deep learning is a class of machine learning algorithms that accomplish the following:

  • Use a cascade of multiple layers of nonlinear processingunits for feature extraction and transformation. Each successive layer uses the output from the previous layer as input.
  • Learn in supervised(e.g., classification) and/or unsupervised (e.g., pattern analysis) manners.
  • Learn multiple levels of representations that correspond to different levels of abstraction; the levels form a hierarchy of concepts.
  • Use some form of gradient descentfor training via backpropagation.

Layers that have been used in deep learning include hidden layers of an artificial neural network and sets of propositional formulas.  They may also include latent variables organized layer-wise in deep generative models such as the nodes in Deep Belief Networks and Deep Boltzmann Machines.

ARTIFICIAL NEURAL NETWORKS:

Artificial neural networks (ANNs) or connectionist systems are computing systems inspired by the biological neural networks that constitute animal brains. Such systems learn (progressively improve their ability) to do tasks by considering examples, generally without task-specific programming. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as “cat” or “no cat” and using the analytic results to identify cats in other images. They have found most use in applications difficult to express with a traditional computer algorithm using rule-based programming.

An ANN is based on a collection of connected units called artificial neurons, (analogous to axons in a biological brain). Each connection (synapse) between neurons can transmit a signal to another neuron. The receiving (postsynaptic) neuron can process the signal(s) and then signal downstream neurons connected to it. Neurons may have state, generally represented by real numbers, typically between 0 and 1. Neurons and synapses may also have a weight that varies as learning proceeds, which can increase or decrease the strength of the signal that it sends downstream.

Typically, neurons are organized in layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first (input), to the last (output) layer, possibly after traversing the layers multiple times.

The original goal of the neural network approach was to solve problems in the same way that a human brain would. Over time, attention focused on matching specific mental abilities, leading to deviations from biology such as backpropagation, or passing information in the reverse direction and adjusting the network to reflect that information.

Neural networks have been used on a variety of tasks, including computer vision, speech recognitionmachine translationsocial network filtering, playing board and video games and medical diagnosis.

As of 2017, neural networks typically have a few thousand to a few million units and millions of connections. Despite this number being several orders of magnitude less than the number of neurons on a human brain, these networks can perform many tasks at a level beyond that of humans (e.g., recognizing faces, playing “Go”).

APPLICATIONS:

Just what applications could take advantage of “deep learning?”

IMAGE RECOGNITION:

A common evaluation set for image classification is the MNIST database data set. MNIST is composed of handwritten digits and includes 60,000 training examples and 10,000 test examples. As with TIMIT, its small size allows multiple configurations to be tested. A comprehensive list of results on this set is available.

Deep learning-based image recognition has become “superhuman”, producing more accurate results than human contestants. This first occurred in 2011.

Deep learning-trained vehicles now interpret 360° camera views.   Another example is Facial Dysmorphology Novel Analysis (FDNA) used to analyze cases of human malformation connected to a large database of genetic syndromes.

The i-Phone X uses, I am told, uses facial recognition as one method of insuring safety and a potential hacker’s ultimate failure to unlock the phone.

VISUAL ART PROCESSING:

Closely related to the progress that has been made in image recognition is the increasing application of deep learning techniques to various visual art tasks. DNNs have proven themselves capable, for example, of a) identifying the style period of a given painting, b) “capturing” the style of a given painting and applying it in a visually pleasing manner to an arbitrary photograph, and c) generating striking imagery based on random visual input fields.

NATURAL LANGUAGE PROCESSING:

Neural networks have been used for implementing language models since the early 2000s.  LSTM helped to improve machine translation and language modeling.  Other key techniques in this field are negative sampling  and word embedding. Word embedding, such as word2vec, can be thought of as a representational layer in a deep-learning architecture that transforms an atomic word into a positional representation of the word relative to other words in the dataset; the position is represented as a point in a vector space. Using word embedding as an RNN input layer allows the network to parse sentences and phrases using an effective compositional vector grammar. A compositional vector grammar can be thought of as probabilistic context free grammar (PCFG) implemented by an RNN.   Recursive auto-encoders built atop word embeddings can assess sentence similarity and detect paraphrasing.  Deep neural architectures provide the best results for constituency parsing,  sentiment analysis,  information retrieval,  spoken language understanding,  machine translation, contextual entity linking, writing style recognition and others.

Google Translate (GT) uses a large end-to-end long short-term memory network.   GNMT uses an example-based machine translation method in which the system “learns from millions of examples.  It translates “whole sentences at a time, rather than pieces. Google Translate supports over one hundred languages.   The network encodes the “semantics of the sentence rather than simply memorizing phrase-to-phrase translations”.  GT can translate directly from one language to another, rather than using English as an intermediate.

DRUG DISCOVERY AND TOXICOLOGY:

A large percentage of candidate drugs fail to win regulatory approval. These failures are caused by insufficient efficacy (on-target effect), undesired interactions (off-target effects), or unanticipated toxic effects.  Research has explored use of deep learning to predict biomolecular target, off-target and toxic effects of environmental chemicals in nutrients, household products and drugs.

AtomNet is a deep learning system for structure-based rational drug design.   AtomNet was used to predict novel candidate biomolecules for disease targets such as the Ebola virus and multiple sclerosis.

CUSTOMER RELATIONS MANAGEMENT:

Deep reinforcement learning has been used to approximate the value of possible direct marketing actions, defined in terms of RFM variables. The estimated value function was shown to have a natural interpretation as customer lifetime value.

RECOMMENDATION SYSTEMS:

Recommendation systems have used deep learning to extract meaningful features for a latent factor model for content-based music recommendations.  Multiview deep learning has been applied for learning user preferences from multiple domains.  The model uses a hybrid collaborative and content-based approach and enhances recommendations in multiple tasks.

BIOINFORMATICS:

An autoencoder ANN was used in bioinformatics, to predict gene ontology annotations and gene-function relationships.

In medical informatics, deep learning was used to predict sleep quality based on data from wearables and predictions of health complications from electronic health record data.

MOBILE ADVERTISING:

Finding the appropriate mobile audience for mobile advertising is always challenging since there are many data points that need to be considered and assimilated before a target segment can be created and used in ad serving by any ad server. Deep learning has been used to interpret large, many-dimensioned advertising datasets. Many data points are collected during the request/serve/click internet advertising cycle. This information can form the basis of machine learning to improve ad selection.

ADVANTAGES AND DISADVANTAGES:

ADVANTAGES:

  • Has best-in-class performance on problems that significantly outperforms other solutions in multiple domains. This includes speech, language, vision, playing games like Go etc. This isn’t by a little bit, but by a significant amount.
  • Reduces the need for feature engineering, one of the most time-consuming parts of machine learning practice.
  • Is an architecture that can be adapted to new problems relatively easily (e.g. Vision, time series, language etc. using techniques like convolutional neural networks, recurrent neural networks, long short-term memory etc.

DISADVANTAGES:

  • Requires a large amount of data — if you only have thousands of examples, deep learning is unlikely to outperform other approaches.
  • Is extremely computationally expensive to train. The most complex models take weeks to train using hundreds of machines equipped with expensive GPUs.
  • Do not have much in the way of strong theoretical foundation. This leads to the next disadvantage.
  • Determining the topology/flavor/training method/hyperparameters for deep learning is a black art with no theory to guide you.
  • What is learned is not easy to comprehend. Other classifiers (e.g. decision trees, logistic regression etc.) make it much easier to understand what’s going on.

SUMMARY:

Whether we like it or not, deep learning will continue to develop.  As equipment and the ability to capture and store huge amounts of data continue, the machine-learning process will only improve.  There will come a time when we will see a “rise of the machines”.  Let’s just hope humans have the ability to control those machines.

BITCOIN

December 9, 2017


I have been hearing a great deal about Bitcoin lately specifically on the early-morning television business channels. I am not too sure what this is all about so I thought I would take a look.    First, an “official” definition.

Bitcoin is a cryptocurrency and worldwide payment system. It is the first decentralized digital currency, as the system works without a central bank or single administrator. … Bitcoin was invented by an unknown person or group of people under the name Satoshi Nakamoto and released as open-source software in 2009.

The “unknown” part really disturbs me as well as the “cryptocurrency” aspects, but let’s continue.  Do you remember the Star Trek episodes in which someone asks, ‘how much does it cost and the answer is _______ credits’?  This is specifically what Bitcoin does, it is digital currency. No one controls Bitcoin; they aren’t printed, like dollars or euros – they’re produced by people, and increasingly businesses, running computers all around the world, using software that solves mathematical problems. A Bitcoin looks as follows-if you acquire a physical object representing“coin”.

Bitcoin transactions are completed when a “block” is added to the blockchain database that underpins the currency however, this can be a laborious process.  Segwit2x proposes moving bitcoin’s transaction data outside of the block and on to a parallel track to allow more transactions to take place. The changes happened in November and it remains to be seen if those changes will have a positive or negative impact on the price of bitcoin in the long term.

It’s been an incredible 2017 for bitcoin growth, with its value quadrupling in the past six months, surpassing the value of an ounce of gold for the first time. It means if you invested £2,000 five years ago, you would be a millionaire today.

You cannot “churn out” an unlimited number of Bitcoin. The bitcoin protocol – the rules that make bitcoin work – say that only twenty-one (21) million bitcoins can ever be created by miners. However, these coins can be divided into smaller parts (the smallest divisible amount is one hundred millionth of a bitcoin and is called a ‘Satoshi’, after the founder of bitcoin).

Conventional currency has been based on gold or silver. Theoretically, you knew that if you handed over a dollar at the bank, you could get some gold back (although this didn’t actually work in practice). But bitcoin isn’t based on gold; it’s based on mathematics. To me this is absolutely fascinating.  Around the world, people are using software programs that follow a mathematical formula to produce bitcoins. The mathematical formula is freely available, so that anyone can check it. The software is also open source, meaning that anyone can look at it to make sure that it does what it is supposed to.

SPECIFIC CHARACTERISTICS:

  1. It’s decentralized

The bitcoin network isn’t controlled by one central authority. Every machine that mines bitcoin and processes transactions makes up a part of the network, and the machines work together. That means that, in theory, one central authority can’t tinker with monetary policy and cause a meltdown – or simply decide to take people’s bitcoins away from them, as the Central European Bank decided to do in Cyprus in early 2013. And if some part of the network goes offline for some reason, the money keeps on flowing.

  1. It’s easy to set up

Conventional banks make you jump through hoops simply to open a bank account. Setting up merchant accounts for payment is another Kafkaesque task, beset by bureaucracy. However, you can set up a bitcoin address in seconds, no questions asked, and with no fees payable.

  1. It’s anonymous

Well, kind of. Users can hold multiple bitcoin addresses, and they aren’t linked to names, addresses, or other personally identifying information.

  1. It’s completely transparent

Bitcoin stores details of every single transaction that ever happened in the network in a huge version of a general ledger, called the blockchain. The blockchain tells all. If you have a publicly used bitcoin address, anyone can tell how many bitcoins are stored at that address. They just don’t know that it’s yours. There are measures that people can take to make their activities opaquer on the bitcoin network, though, such as not using the same bitcoin addresses consistently, and not transferring lots of bitcoin to a single address.

  1. Transaction fees are miniscule

Your bank may charge you a £10 fee for international transfers. Bitcoin doesn’t.

  1. It’s fast

You can send money anywhere and it will arrive minutes later, as soon as the bitcoin network processes the payment.

  1. It’s non-reputable

When your bitcoins are sent, there’s no getting them back, unless the recipient returns them to you. They’re gone forever.

WHERE TO BUY AND SELL

I definitely recommend you do your homework before buying Bitcoin because the value is roller coaster in nature, but given below are several exchanges in which Bitcoin can be purchased or sold.  Good luck.

CONSLUSIONS:

Is Bitcoin a bubble? It’s a natural question to ask—especially after Bitcoin’s price shot up from $12,000 to $15,000 this past week.

Brent Goldfarb is a business professor at the University of Maryland, and William Deringer is a historian at MIT. Both have done research on the history and economics of bubbles, and they talked to Ars by phone this week as Bitcoin continues its surge.

Both academics saw clear parallels between the bubbles they’ve studied and Bitcoin’s current rally. Bubbles tend to be driven either by new technologies (like railroads in 1840s Britain or the Internet in the 1990s) or by new financial innovations (like the financial engineering that produced the 2008 financial crisis). Bitcoin, of course, is both a new technology and a major financial innovation.

“A lot of bubbles historically involve some kind of new financial technology the effects of which people can’t really predict,” Deringer told Ars. “These new financial innovations create enthusiasm at a speed that is greater than people are able to reckon with all the consequences.”

Neither scholar wanted to predict when the current Bitcoin boom would end. But Goldfarb argued that we’re seeing classic signs that often occur near the end of a bubble. The end of a bubble, he told us, often comes with “a high amount of volatility and a lot of excitement.”

Goldfarb expects that in the coming months we’ll see more “stories about people who got fabulously wealthy on bitcoin.” That, in turn, could draw in more and more novice investors looking to get in on the action. From there, some triggering event will start a panic that will lead to a market crash.

“Uncertainty of valuation is often a huge issue in bubbles,” Deringer told Ars. Unlike a stock or bond, Bitcoin pays no interest or dividends, making it hard to figure out how much the currency ought to be worth. “It is hard to pinpoint exactly what the fundamentals of Bitcoin are,” Deringer said.

That uncertainty has allowed Bitcoin’s value to soar a 1,000-fold over the last five years. But it could also make the market vulnerable to crashes if investors start to lose confidence.

I would say travel at your own risk.

 


Two years ago, I wrote a post about THE universal language.  Can you guess what language that is?  Well, there are approximately six thousand-five hundred (6,500) spoken languages in the world today.  However, approximately two thousand (2,000) of those languages have fewer than one thousand (1,000) speakers. The most popular language in the world is Mandarin Chinese. There are 1,213,000,000 people in the world speaking Mandarin. The following list will indicate the top ten (10) languages spoken.

  • FRENCH: Number of speakers: 129 million
  • MALAY-INDONESIAN: Number of speakers: 159 million
  • PORTUGUESE: Number of speakers: 191 million
  • BENGALI: Number of speakers: 211 million
  • ARABIC:     Number of speakers: 246 million
  • RUSSIAN:  Number of speakers: 277 million
  • SPANISH:     Number of speakers: 392 million
  • HINDSTANI:     Number of speakers: 497 million
  • ENGLISH: Number of speakers: 508 million
  • MANDARIN:      Number of speakers: 1 billion+

An old-world language tree looks something like the following:

old-world-language-tree

As you can see, language is very very complicated– but fascinating.

With this being the case, how on Earth could there be one UNIVERSAL language and what is it?  MATHEMATICS is a language recognized and used by all people on our very small “blue dot”.  I know this sounds very strange but that definitely is the case.  So—do we celebrate accomplished mathematicians and if so how?  YES, starting with the INTERNATIONAL MATHEMATICAL OLYMPAID (IM0) for pre-college.  Let’s take a look.

IMO:

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 100 countries from 5 continents. The IMO Advisory Board ensures that the competition takes place each year and that each host country observes the regulations and traditions of the IMO.   The IMO Foundation is a charity which supports the IMO. The IMO Foundation website is the public face of the IMO. This is a particularly valuable resource for people who are not necessarily mathematical specialists, but who want to understand the International Mathematical Olympiad.

The symbol for the IMO is given below.

symbol

ORIGIN:

The International Mathematical Olympiad (IMO) is an annual six-problem mathematical Olympiad for pre-college students, and is the oldest of the International Science Olympiads.   Please note the phrase pre-college, although almost all of the students taking the test are high school age.  This is due to the questions being asked.  The first IMO was held in Romania in 1959. It has since been held annually, except for 1980. Approximately one hundred (100) countries send teams of up to six students, plus one team leader, one deputy leader, and observers to the Olympiad.

The content ranges from extremely difficult algebra and pre-calculus problems to problems involving branches of mathematics not conventionally covered at school nor university level,  These are  such problems as projective and complex geometryfunctional equations and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems, even if the solutions require a great deal more knowledge. Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity.

The selection process differs by country, but it often consists of a series of tests which admit fewer students at each progressing test. Awards are given to approximately the top-scoring fifty percent (50%) of the individual contestants. Teams are not officially recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more than individual scores.  Contestants must be under the age of twenty (20) and must not be registered at any tertiary institution. Subject to these conditions, an individual may participate any number of times in the IMO.

SCORING AND FORMAT:

The examination consists of six problems. Each problem is worth seven points, so the maximum total score is forty-two (42) points. No calculators are allowed. The examination is held over two consecutive days; each day the contestants have four-and-a-half hours to solve three problems. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometrynumber theoryalgebra, and combinatorics. They require no knowledge of higher mathematics such as calculus and analysis, and solutions are often short and elementary. However, they are usually disguised so as to make the solutions difficult. Prominently featured are algebraic inequalitiescomplex numbers, and construction-oriented geometrical problems, though in recent years the latter has not been as popular as before.

Each participating country, other than the host country, may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury which is responsible for all the formal decisions relating to the contest, starting with selecting the six problems from the shortlist. The Jury aims to order the problems so that the order in increasing difficulty is Q1, Q4, Q2, Q5, Q3 and Q6. As the leaders know the problems in advance of the contestants, they are kept strictly separated and observed.

Each country’s marks are agreed between that country’s leader and deputy leader and coordinators provided by the host country (the leader of the team whose country submitted the problem in the case of the marks of the host country), subject to the decisions of the chief coordinator and ultimately a jury if any disputes cannot be resolved.

RECENT AND FUTURE IMOS:

The two-day event is truly global in nature with the following locations having been selected.

The only countries to have their entire team score perfectly in the IMO were the United States in 1994 (they were coached by Paul Zeitz); and Luxembourg, whose one-member team had a perfect score in 1981. The US’s success earned a mention in TIME Magazine. Hungary won IMO 1975 in an unorthodox way when none of the eight team members received a gold medal (five silver, three bronze). Second place team East Germany also did not have a single gold medal winner (four silver, four bronze).

The top 10 countries with the best all-time results are as follows:

countries

CONSLUSIONS:

I think a competition such as this is one of the best events sponsored because it gives recognition to those who excel within a specific discipline.  After all, we have the Oscars, the Grammys, the People’s Choice Awards, the Country Music Awards. Pro Bowl, Super Bowl.  Why not celebrate the talents of those around the world who “march to the beat of a different drummer”?  Just a thought.


I want us to consider a “what-if” scenario.  You are thirty-two years old, out of school, and have finally landed a job you really enjoy AND you are actually making money at that job. You have your expenses covered with “traveling money” left over for a little fun.  You recently discovered the possibility that Social Security (SS), when you are ready to retire, will be greatly reduced if not completely eliminated. You MUST start saving for retirement and consider SS to be the icing on the cake if available at all.  QUESTION: Where do you start?  As you investigate the stock markets you find stocks seem to be the best possibility for future income.  Stocks, bonds, “T” bills, etc. all are possibilities but stocks are at the top of the list.

People pay plenty of money for consulting giants to help them figure out which technology trends are fads and which will stick. You could go that route, or get the same thing from the McKinsey Global Institute’s in-house think-tank for the cost of a new book. No Ordinary Disruption: The Four Global Forces Breaking All the Trends, was written by McKinsey directors Richard Dobbs, James Manyika, and Jonathan Woetzel, and offers insight into which developments will have the greatest impact on the business world in coming decades. If you chose stocks, you definitely want to look at technology sectors AND consider companies contributing products to those sectors.  The following list from that book may help.  Let’s take a look.

Below, we’re recapping their list of the “Disruptive Dozen”—the technologies the group believes have the greatest potential to remake today’s business landscape.

Batteries

energy-storage

The book’s authors predict that the price of lithium-ion battery packs could fall by a third in the next 10 years, which will have a big impact on not only electric cars, but renewable energy storage. There will be major repercussions for the transportation, power generation, and the oil and gas industries as batteries grow cheaper and more efficient.  Battery technology will remain with us and will contribute to ever-increasing product offerings as time goes by.  Companies supplying this market sector will only increase in importance.

Genomics

genomics

As super computers make the enormously complicated process of genetic analysis much simpler, the authors foresee a world in which “genomic-based diagnoses and treatments will extend patients’ lives by between six months and two years in 2025.” Sequencing systems could eventually become so commonplace that doctors will have them on their desktops.  This is a rapidly growing field and one that has and will save lives.

Material Science

advanced-materials

The ability to manipulate existing materials on a molecular level has already enabled advances in products like sunglasses, bike frames, and medical equipment. Scientists have greater control than ever over nanomaterials in a variety of substances, and their understanding is growing. Health concerns recently prompted Dunkin’ Donuts to remove nanomaterials from their food. But certain advanced nanomaterials show promise for improving health, and even treating cancer. Coming soon: materials that are self-healing, self-cleaning, and that remember their original shape even if they’re bent.

Self-Driving or Autonomous Automobiles

self-driving-vehicles

Autonomous cars are coming, and fast. By 2025, the “driverless revolution” could already be “well underway,” the authors write. All the more so if laws and regulations in the U.S. can adapt to keep up. Case in point: Some BMW cars already park themselves. You will not catch me in a self-driving automobile unless the FED and the auto maker can assure me they are safe.  Continuous effort is being expended to do just that.  These driverless automobiles are coming and we all may just as well get used to it.

Alternate Energy Solutions

reneuable-energy

Wind and solar have never really been competitive with fossil fuels, but McKinsey predicts that status quo will change thanks to technology that enables wider use and better energy storage. In the last decade, the cost of solar energy has already fallen by a factor of 10, and the International Energy Agency predicts that the sun could surpass fossil fuels to become the world’s largest source of electricity by 2050.  I might include with wind and solar, methane recovery from landfills, biodiesel, compressed natural gas, and other environmentally friendly alternatives.

Robotic Systems

advanced-robotics

The robots are coming! “Sales of industrial robots grew by 170% in just two years between 2009 and 2011,” the authors write, adding that the industry’s annual revenues are expected to exceed $40 billion by 2020. As robots get cheaper, more dexterous, and safer to use, they’ll continue to grow as an appealing substitute for human labor in fields like manufacturing, maintenance, cleaning, and surgery.

3-D Printing

3-d-printing

Much-hyped additive manufacturing has yet to replace traditional manufacturing technologies, but that could change as systems get cheaper and smarter. “In the future, 3D printing could redefine the sale and distribution of physical goods,” the authors say. Think buying an electric blueprint of a shoe, then going home and printing it out. The book notes that “the manufacturing process will ‘democratize’ as consumers and entrepreneurs start to print their own products.”

Mobile Devices

mobile-internet

The explosion of mobile apps has dramatically changed our personal experiences (goodbye hookup bars, hello Tinder), as well as our professional lives. More than two thirds of people on earth have access to a mobile phone, and another two or three billion people are likely to gain access over the coming decade. The result: internet-related expenditures outpace even agriculture and energy, and will only continue to grow.

Artificial Intelligence

automation-of-knowledge

It’s not just manufacturing jobs that will be largely replaced by robots and 3D printers. Dobbs, Manyika, and Woetzel report that by 2025, computers could do the work of 140 million knowledge workers. If Watson can win at “Jeopardy!” there’s nothing stopping computers from excelling at other knowledge work, ranging from legal discovery to sports coverage.

 

The Internet of Things (IoT)

iot

Right now, 99% of physical objects are unconnected to the “internet of things.” It won’t last. Going forward, more products and tools will be controlled via the internet, the McKinsey directors say, and all kinds of data will be generated as a result. Expect sensors to collect information on the health of machinery, the structural integrity of bridges, and even the temperatures in ovens.

Cloud Technology

cloud-technology

The growth of cloud technology will change just how much small businesses and startups can accomplish. Small companies will get “IT capabilities and back-office services that were previously available only to larger firms—and cheaply, too,” the authors write. “Indeed, large companies in almost every field are vulnerable, as start-ups become better equipped, more competitive, and able to reach customers and users everywhere.”

Oil Production

advanced-oil-technology

The International Energy Agency predicts the U.S. will be the world’s largest producer of oil by 2020, thanks to advances in fracking and other technologies, which improved to the point where removing oil from hard-to-reach spots finally made economic sense. McKinsey directors expect increasing ease of fuel extraction to further shift global markets.  This was a real surprise to me but our country has abundant oil supplies and we are already fairly self-sufficient.

Big Data

big-data

There is an ever-increasing accumulation of data from all sources.  At no time in our global history has there been a greater thirst for information.  We count and measure everything now days with the recent election being one example of that very fact.  Those who can control and manage big data are definitely ahead of the game.

CONCLUSION:  It’s a brave new world and a world that accommodates educated individuals.  STAY IN SCHOOL.  Get ready for what’s coming.  The world as we know it will continue to change with greater opportunities as time advances.  Be there.  Also, I would recommend investing in those technology sectors that feed the changes.  I personally don’t think a young investor will go wrong.

THE ACCOUNTANT

October 23, 2016


My wife and I love to go to the movies.  When I say go, I mean GO.  We don’t download movies at home; we don’t subscribe to Netflix, Starz, HBO, HULU, etc.   We like to make our movie watching an event.  (OK, we are weird.)  I can barely remember one bad movie in my lifetime—something like David Letterman meets Godzilla.  We love movies.  You get the picture.

I generally do not write about movies because everyone has his or her own taste. I am the furthest thing from an experienced movie critic.   My thought is—if you like it, it’s good.  There is one movie we have seen lately I definitely can recommend—THE ACCOUNTANT.  Let’s look at several specifics to start with.

CAST: 

WRITER:  Bill Dubuque

DIRECTOR:  Gavin O’Conner

STUDIO:  Warner Brothers

RUNNING TIME: 128 Minutes

Christian Wolff is a mathematical genius who works as a forensic accountant at ZZZ Accounting in Plainfield, Illinois.  His primary responsibility is tracking insider financial deceptions for numerous criminal enterprises brokered to him by a mysterious figure known as “The Voice”.  The “Voice” contacts him by phone which is really spooky when initially encountered in the movie. As a child, Christian was diagnosed with autism and offered an opportunity to live at Harbor Neuroscience Institute in New Hampshire. Although Christian had bonded with Justine, the mute daughter of the institute’s director, his father, a decorated military officer, declined, believing that Christian should overcome the hardships inherent in his condition rather than expect the world to accommodate to them. The pressure of raising a special needs child drove Christian’s mother to abandon him and his younger brother, Braxton, who were left in their father’s care.  The movie indicates the family moved thirty-four (34) times in seventeen (17) years.  Each move was to introduce new experiences to Christian and his older brother Braxton with hopes of preparing both for adult life.

I don’t know if you are familiar with autism but several symptoms are as follows:

  1. Not speak as well as his or her peers?
  2. Have poor eye contact?
  3. Not respond selectively to his or her name?
  4. Act as if he or she is in his or her own world?
  5. Seem to “tune others out?”
  6. Not have a social smile?
  7. Seem unable to tell you what he or she wants, preferring to lead you by the hand or get desired objects on his or her own, even at risk of danger?
  8. Have difficulty following simple commands?
  9. Show you things without bringing them to you?
  10. Not point to interesting objects to direct your attention to objects or events of interest?
  11. Have unusually long and severe temper tantrums?
  12. Have repetitive, odd, or stereotypic behaviors?
  13. Show an unusual attachment to inanimate objects, especially hard ones (e.g., flashlight or a chain vs. teddy bear or blanket)?
  14. Prefer to play alone?
  15. Demonstrate an inability to play with toys in the typical way?
  16. Not engage in pretend play (if older than age 2)?

Ben Affleck absolutely nails many of the traits and characteristics of an autistic adult although due to his father’s persistence with training Christian on how to overcome his difficulties, he is highly functional as a mathematician.  Affleck, in my opinion, will be nominated for an Oscar for this one.  His work is just that good.

The plot is anything but cookbook.  There are many twists and turns and the ending is really surprising.  You cannot guess as to how this one turns out. Many movies today are more of the same but The Accountant is quite the exception.  I’m not going to spoil it for you by divulging more of the plot but the entire movie is action-filled with a cast that certainly works very well together. It’s one of those movies complicated enough to see twice or even three times, each time discovering something you have missed previously.

I can definitely recommend this one to you.  Take a look.

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