The Search for Absolute Zero

There were many great physics breakthroughs in Victorian Britain and a host of pioneering scientists. One of the most famous was born as William Thomson although he is known as Lord Kelvin throughout history. Probably his most famous practical achievement besides his work on hear and energy was helping to build the first transatlantic submarine cable used for the transmission of telegraphs.

Absolute zero is literally the envisioned point at which a material is actually so cold its own particles stop moving. Absolute zero in itself has actually never been achieved, neither in nature nor in the laboratory. Yet researchers have come very close. It really may be impossible to get to absolute zero, and also if we did we might not recognize due to the fact that absolutely no thermometer could determine it.

When we determine the temperature level of anything we are recording the average energy of the particles which make it up. Temperature level suggests precisely how quickly the particles are vibrating or moving around. in a gas or liquid, molecules are actually free to travel in any course, and frequently bounce off one another. So temperature is connected to the mean speed of the particles. Inside a solid, atoms are secured in a latticework structure, really like Meccano held together by electronic bonds. When this becomes hot, the atoms are energetic and agitate around a great deal, like wobbly jello, while sitting in their positions.

The concept was illustrated in several documentaries which were aired originally on the BBC, as part of their Physics season.  I think the programmes are now available on Netflix although I’m unsure of which region it is on.  If you need to switch locales on Netflix you’ll need an account plus a VPN with a residential address. This company provide residential IP addresses – http://www.theninjaproxy.org/security/residential-ip-provider/, although they can be quite expensive.

As you cool down a material, its atoms move much less. Within a gas their speeds drop; in a solid their vibrations are reduced. As the temperature level drops further and further, atoms move less and less. If cooled sufficiently, a material might become so cold that its atoms cease moving absolutely. This hypothetical still point is called absolute zero. The concept of absolute zero was actually identified in the 18th century simply by theorizing a graph of temperature level and energy to zero. Energy rises steadily with temperature level, and the line linking the two quantities can be projected backwards to discover the temperature at which the energy reaches zero: -273.15 degrees Celsius or -459.67 degrees Fahrenheit

In the 19th century, Lord Kelvin contemplated a new Pressure temperature range that commenced at absolute zero.
Kelvin’s scale effectively took the Celsius temperature scale and repositioned it. So, instead of water freezing at O degrees Celsius it does so at 273 kelvins and boils at 373 Kelvins (equivalent to 100 degrees Celsius) Today, the majority of chemists use kelvins to measure temperature.

Further Reading: Useful Article: Match of the Day on iPlayer

The Mathematics of the Drunken Walk

Lectures on statistics are not always the most exciting ones in the world of maths however certain subjects tend to attract students attention.  One of those is of course alcohol, and not in the over indulgence and problematic way where you end up taking a drug like this one called Selincro to combat it’s effects.   It’s actually revolved around a concept called the Drunkard’s Walk a famous mathematical concept.

It can be best explained in a theoretical example about a drunken man who was walking way too close to a cliff for someone in that state.  The idea is that from his starting position a single step forward would send him over the cliff.   He takes completely random steps oblivious to his own safety in any direction.  His probability of taking a step away is 2/3 and of taking a step towards the cliff is 1/3.  The mathematicians problem – what are the drunkards chance of escaping the cliff?

It’s a classic problem but actually touches on some advanced statistical topics. The particular topic is centered around Stochastic Processes which covers these ‘random walk’ issues, the specific name is called a Markov Chain.

Stochastic Process – a random process which explains how a system or process changes over another unit (commonly time).

Random Walk – a path derived from a series of completely random steps in some defined mathematical space.  Our example is the very drunk man tottering on the edge of a cliff.

Markov Chain – a random walk which actually maintains independent events.  That is the next event is not dependent or related to the previous one.  The drunken man has to be so drunk that his position and last action has no bearing on his next step!

The mathematics of this situation is of course all related to probabilities and how likely the man is to survive his reckless behaviour.   The simplest point is the beginning where he is one step away from the edge, the probability of surviving the next step is 2/3 and he has a 1/3 chance of stepping over the edge.

After that of course it get’s more difficult as the man if he survives will be moving away from the cliff edge and buys himself some time.   The easiest way to visualize this situation is to draw a chart of the probabilities with all the possibilities.  This has to include his relative position from the cliff and an assumption about where he ends up and what position is safe!

The problem is actually not that complex but it can seem so purely because there are so many possibilities after the initial even.  The secret is to define the chart with the possibilities and then try and generalize the problem in order to create a formula. This has to include the probability of stepping towards the cliff edge and stepping away

To solve these problems you normally define the expected probability of the event you are trying to measure.  So in this case it would be defining the probability of falling from the cliff – say P1.

Without too much detailed analysis we can get to the formula as follows:

P1 = (1-P) + (p*P2)

Here the variable P2 is the probability of falling from the cliff on a path consisting of 2 steps!

John Welcome

 

Mathematics Key to 4D Printing

Although some of us are just getting our heads around the amazing potential in 3D printing, the next step is already on the horizon.    A leading mathematician has started working on the formulas required to step into an extra dimension!

Three D printing is already revolutionizing all sorts of areas from manufacturing, medicine to science and engineering.  It’s now fairly simple and inexpensive and has the potential to create all sorts of intricate objects quickly and cheaply.   There are printer parts in our machines and indeed people are having printed body replacement parts transplanted into their bodies with great success.

However there is always a next step, and now mathematicians are working on taking us in to the world of 4d printing.  Just to clarify we are talking about the possibility of fabricating objects with a programmable shape over time.  It’s always been theoretically possible however no-one had really starting looking at working through the complexities involved.

This seems to be changing as Professor Pasquale Ciarletta from Milan has just published a paper in ‘Nature Communications’ where he has started working through the numbers about a specific problem with this.  The professor has been focusing on how to control the sudden nucleation of localised furrows in the soft solids produced in 3d printing.

The advantages and possibilities of these developments may not be initially apparent.  However in addition to the advantages to the field of engineering there is huge potential to have the ability to design and print objects which can morph over time.  The paper related the development to the field of development biology as particular interest.  Here we could look at things like tissue morphogenesis and other areas such as issues in the brain or tumour control.

Ciarletta has acknowledged that there are great complexities behind making this work.  There has already been lots of experimental investigation of the issues involved – the physics behind the concept of ‘creasing’ being particularly challenging.  His study proposes a unique mathematical approach to predicting the experimental conditions required to trigger the onset and how creases change over time.  This is the key to being able to control their appearance on a specific scale and ultimately to be able to print them in 4d.

There are parallel advancements being made in the area of 3d printing too.  You can already sit down and watch the football on Match of the Day live like this on a completely 3d printed television set.  It is also now possible to edit specific printed objects after they have been created.  This is achieved by repeatedly changing the colours of 3d printed objects after thy have been printed.

The concept is currently being developed under the name ColorFab and it involves using a specially created 3d printable ink which can actually change colour under certain conditions – primarily after being exposed to UV light.  This of course has a time delay currently estimated at around 20 minutes, however the researchers are hoping to improve on this substantially in further development.

Further Reading: Available on British TV

Deciphering the Fibonacci Sequence

You may have heard the expression, it’s certainly one of the most famous mathematical concepts – show what’s involved with he Fibonacci Sequence?.

The thirteenth Century Italian Leonardo of Pisa, better known from his nickname Fibonacci, was possibly the most gifted Western mathematician of the Middle Ages. Little is known of his life except that he has been this son of a customs official and, as a young child, he traveled to North Africa along with his father. It was here that he first heard about the Arabian mathematics. On his return to Italy, he helped to spread this knowledge through Europe, putting so in motion a rejuvenation in Western mathematics, which had lain largely dormant for centuries throughout the Dark Ages. Especially memorable was that in 1202 he wrote a very influential book called Liber Abaci, wherein he encouraged using the Hindu Arabic numeral system. Here he used the book to describe its lots of advantages for retailers and mathematicians alike across the clumsy system of Ancient Rome numerals then in use in Europe.

Despite its apparent benefits, uptake of this system in Europe was slow, and Arabic numerals were banned within the town of Florence in 1299 on this pretext they were easier to falsify than Ancient Rome numerals. Yet, common sense finally prevailed and the new system has been adopted through Europe by the fifteenth century, making the Ancient Rome system obsolete. The flat bar notation for fractions was initially first utilized in this work. Fibonacci is best known, however, for his debut in Europe of a certain number sequence, that has since become known like Fibonacci Numbers or this Fibonacci Sequence.

There are lots of explanations of this, which although initially sounding quite complicated is actually very simple.  One of the most straightforward ones I’ve heard is to be found on the BBC’s History of Maths programs – you can access this and any other UK TV abroad, from here.

He discovered this sequence – this first recursive numerical sequence known in Europe – although considering a practical problem in this Liber Abaci involving this growth of a hypothetical population of rabbits based about idealized assumptions. He noted that, after every monthly creation, this number of pairs of rabbits increased from 1 to 2 to 3 to 5 to 8 to 13, etc. Soon he also recognized how a sequence progressed by adding this previous two terms, a sequence which could theoretically extend indefinitely.

The arrangement, which had really been known to Indian mathematicians since this sixth Century, has many intriguing mathematical properties, and a lot of this implications and relationships of this sequence weren’t discovered until several hundreds of years after Fibonacci’s death. For example, this sequence regenerates itself in some surprising ways: every 3rd F number is divisible by 2, every 4th F number is divisible by 3, every 5th F number is divisible by 5, every 6th F number is divisible by 8, every 7th F number is divisible by 13, etc.

Additional: – switching Czech IP Address

Great Mathematicians – Euclid

The Mathematics Of Euclid
The Greek Maths legend – Euclid is known throughout history as among the greatest mathematicians and in fact one of his names is the father of geometry. You might not be aware that the standard geometry all people are taught in college is actually called Euclidian Geometry. In Ancient Greece, he worked tirelessly and Euclid accumulated all the knowledge developed in mathematics during that time. From his studies he created his famous work, entitled ‘The Elements’. It is thought that Euclid likely attended Plato’s academy in Athens before moving into Alexandria, in Egypt. In this time, the city had a big library and whats more it even had ready access to papyrus made it the centre for the productions of books. The papyrus is one of the numerous reasons why excellent minds such as Heron of Alexandria and Euclid established themselves in Alexandria and the Nile delta.

Nowadays Euclid, is even more famous and his books and theorems are an essential part of any mathematics education.  You’ll find him studied at every levels from elementary to I last saw a copy in Dublin, in the University College.


Euclid’s Elements consisted of thirteen novels covering a vast body of mathematical expertise, crossing arithmetic, geometry and number theory. The fundamental arrangement of the components starts with Euclid launching axioms. From here he created 465 propositions, progressing from his first recognized principles into the unknown in several of measures, a process he called the Artificial strategy. He looked at mathematics as a whole, but was especially focused on geometry and this specific field formed the foundation of his work. Euclid’s Axioms were based upon 10 statements which could be accepted as mathematical truths. He named these axioms his postulates and split them into two groups of five, these very first set common to all math, the second specific to geometry.

To see some great explanations of these geometric principles search through YouTube or the Open University Maths lessons.  These were recently broadcast on the BBC so you can pick them up on iPlayer – this post shows how to pick up BBC iPlayer from Ireland but it should work from anywhere in the world too.

Many of those postulates appear into be self explanatory into us, but Euclid worked on the principle that no axiom might be accepted without proof. Euclid’s First Group of Postulates – these Common Notions: Things that are equal to these same thing are equal to one another. If equals are added onto equals, the results are equal. If equals are subtracted from equals, these remains are equal. Things which coincide with one another are equal to one another. A straight line can be drawn between any two points.

Any finite straight line can be extended indefinitely in a straight line. For any line segment, it’s potential to draw a circle utilizing the section as these radius and one end point as these centre. If a straight line falling across two other straight lines leads to these sum of these angles on these same side less than two right angles, then these two straight lines. These lines if extended indefinitely, meet on these same side as these side where these angle amounts are less than two right angles.

Euclid felt that anyone who can read and comprehend words could comprehend his notions and postulates but, into make sure, he included 23 definitions of common words, like point and line to ensure that there might be no semantic errors.

Practical Uses of Blockchain Mathematics

To the extent that people consider blockchain technology it’s in combination with the bitcoin. Blockchain is actually a record keeping instrument that is versatile and has uses well beyond that of digital currencies. However Bitcoin’s libertarian mechanic – a validation network without a central authority in office – is not a part of blockchain and might be discarded for government uses of the tool. As a permanent ledger of transactions, blockchain serves as the core component in its bitcoin application. Computers generate them however they still have some serious horsepower required to hash transactions and complete the calculations. Every ten minutes or so, a brand-new block gets added which everybody can see. There isn’t any authority that issues them, Deputy U.S. Chief Technology Officer Ed Felten said.

One of the best explanations I’ve found about blockchain is actually a short video on the BBC website which you can find here – http://www.bbc.co.uk/news/av/business-38932854/what-is-blockchain-and-how-does-it-work. If you’re interested in the more specific subject of digital currency, the financial programmes all now cover the rise of Bitcoin, Ethereum and the other currencies. These are all accessible online however you may have some issues if you’re outside the UK. Using a VPN used to work well to access the BBC but then they started to get blocked, update report here.

Although digital currencies are driving forward the use of blockchain, there are significant developments in other areas too. Agency or A business may use that concept as-is, or it might insert itself. The U.S. Postal Service, for example, has spread the idea of maintaining and producing a Postchain platform. Institutions such as Goldman Sachs are currently researching using blockchain. Felten advised this Information Security and Privacy Advisory Board in June the blockchain could enable contracts that were complicated removing the possibility of human error to be released months or years after establishment.

Travis Hall, a policy analyst in the National Telecommunications and Information Administration, stated government agencies may use blockchain for a slew of instruction activities, such because keeping voter and health care records up-to date, controlling your stresses property titles or monitoring certificates and authentication for Web of Things devices for cybersecurity functions.  There are dangers in this though not withstanding the fact  that many people are able to hide their locations by using devices such as online IP changers just like these.

Since Cryptography underpins the entire series of records, keeping this security of cryptographic keys will be essential if authorities plan to rely on blockchain, Felten stated. Rew Regenscheid, a mathematician at this National Institute of Standards and Technology, stated future cryptographic solutions could offer multiparty digital signatures and privacy enhancements.

Has Someone Actually Solved the Riemann Hypothesis

Sometimes a paper comes along which can breath new life into a subject or problem long thought unsolvable. This year a trio of mathematicians looks like they’ve done just that in offering a new tactic to solve the ‘greatest unsolved problem in mathematics – the Riemann Hypothesis.

This paper has just been published in a maths journal called Physical Review and suggests that the analysis is proven correct then it can also be used to prove the Riemann Hypothesis.

 Prime Numbers
Predicting Prime Numbers

For those whose lives are not centred around mathematics this might sound a little obscure.However for mathematicians it represents fame, success and of course cash.The solution to the Riemann hypothesis is one of the seven Millennium Prize problems which cover the most difficult problems in maths.   For more information on this prize have a look on BBC iPlayer where there was a recent maths documentary, this link shows how to access it from outside the UK.  Every one of these problems comes with a one million dollar prize for a solution.

This hypothesis is names after the German born mathematician Bernhard Riemann.It’s such an important problem because it offers a method to understand the distribution of prime numbers. If a method was found it would completely revolutionise mathematics.Being able to work out how may prime exist in any given situation would make many branches of the science much, much easier.

So where is this solution hidden, well it is suggested it lies in quantum mechanics.

An amazing statement from this paper proposes that quantum mechanics could solve the Riemann Hypothesis. This difficult area of physics usually used to try and make sense of some of the smaller scales in nature.

So what’s in the paper? Well the authors have suggested that the existence of a quantum system of energy corresponds to the proposed conditions in the Riemann Hypothesis.They have also defined a specific variable called the Hamiltonian Operator as the crucial part of this system.

If this all works out then the method effectively reduces the huge problem of the Riemann Hypothesis down to the level of the Hamiltonian Operator. A mythical problem that was almost deemed impossible to solve suddenly becomes much closer.The paper is only in the first stages though and peer review is next which could take some time.

But it certainly has created some excitement for anyone who has even a passing interest in mathematics.

Further Information: BBC News Streaming

Using Baye’s Theorem

Baye’s theorem is usually one of the easiest ways to calculate probabilities as long as you have sufficient information about related conditions. It can be considered a style of understanding the way probability is affected by introducing a new variable or condition. So you need to take care that you fully understand the conditions when using it to calculate probabilities. Keep in mind when using the theorem that the entire probability of all potential x needs to be equal to 1.

The theorem can subsequently be used to find out the level of belief in the hypothesis using the experimental data. When you have ever come across Bayes’ theorem, you likely know it is a mathematical theorem and there is a solution possible. Bayes’ theorem is often used in medical statistics for instance in trials to proves that even if an individual tested positive in a particular scenario. It is certainly now a crucial tool for statisticians and scientists, as well as many people working with probabilities in all sorts of industries. In all of these cases,an understanding of the theorem is an excellent tool for all sorts of statistical work. Bayes’ theorem integrates well with helping to prove or disprove hypothesis, as long as you should consider all the subsequent conditions.

Another area it is used is in the assessment of risk. It is of course a useful way to gain a little insight into possible risks by using Bayes’ to obtain some probability data concerning the event . John Bayes’ was a famous mathematician who published much work particularly in the areas of calculating reverse probability by utilizing conditional probability.

This is the key to understanding this theorem – that you are basically trying to discover the probability that T is true whilst supposing that another piece of evidence is true. Think of a deck of cards which contains 52 individual cards. You can work out the probability easily before a card is drawn however after the calculation is different as there are less cards and of different values. Too bad this type of question isn’t asked in science it’s covered well on the BBC Maths Bytesize site – you’ll need a BBC iPlayer proxy to access from outside the UK.

The difference in the past equation results from the truth of using smart adjustment. When cards are drawn from the pack the maths continually changes as long as they are not replaced or put back. Nonetheless, the fact that it’s possible to describe decision making behaviour with a mathematical function proves that folks utilize some rules or behave irrationally.

Effective evidence is an issue of the level to which an individual’s total evidence for H is dependent upon her opinion about E. Regarding the Bayesian strategy, the proof is more complicated. The simplest way is often to put all these values in a table which can make it simpler to visualize the potential conditional choices.

Additional Reading

Schrödinger’s equation

V limitations of the online browser, partial derivatives aren’t explicitly indicated. The derivation isn’t included within this brief story line. A complete derivation is provided in Lanczos. This very first derivation wasn’t published. It’s always fruitful to search for invariants under transformation. Furthermore, it is crucial that the wave function should have just an individual value at any certain point, as it corresponds to the probability of locating the particle at that point. In this instance the wavefunction could possibly be utilised to predict the relative likelihood (i.e. the probability) of each one of the probable outcomes.

Netflix blocks proxies

A bit of linear algebra is a little price to cover untangling all of this. Liner equations with a couple of variables have an infinite quantity of solutions. The probability of locating changes exactly as the rate of the probability of locating an electron does.  There’s an interesting example featured in the documentary – History of Maths, which is accessible on a few media streaming sites – this should help access from outside the UK – a proxy for Netflix.

The Schrodinger equation takes a number of different forms, based on the physical circumstance. It shows how the quantum wave function changes over time. It’s almost enjoy the equations are attempting to inform you a story. It’s simple to work out this equation. The solution of both of these equations is beyond the reach of this class. This previous equation is in an incredibly significant dimension, hence the solutions aren’t simple to visualize. It is in a very high dimension, so that the solutions are not easy to visualize.

Below it’s a slightly rewritten form. If, on the opposite hand, you assume it’s in a mix of each of the probable states it can be, you are going to be correct.” The wave function is a mix of all the feasible wave functions which exist,” says Martell. In the event the system isn’t conservative, it’s still a constant, but not the complete energy. The waveform analysis procedure is often hard and confusing. You’re not predicted in order to do this transformation. This relationship is called the dispersion relation.

A belief is just one more method of viewing the world. You’re helping confirm your belief, whether or not your belief is true or not. Considering the simple fact that, mathematically speaking, relativity theory and quantum theory are not just distinct from one another, but in addition oppose one another, Dirac’s work could be thought of a fruitful reconciliation between both theories.

Yet Schrodinger’s interpretation couldn’t explain quantum tunnelling. It is simply the conventional Copenhagen Interpretation of the outcomes of them that isn’t right.
Do not forget that low momentum usually means a very long wavelength. In many conditions, an electron will behave as an easy, easy-to-quantify particle. It’s known as the electron. When you look at it in 1 way it seems as a particle. If you differentiate velocity with regard to time, then you’re measuring acceleration. The angle does not seem in Eq. The genuine motion of this completely free particle provides the least average kinetic energy.

Depending on the way that it vibrates determines what type of force you believe you saw. In the current essay, energy is only a constant of the motion, based on specific conditions, but is still quite significant and useful. For an electron travelling through an electric area, as an example, the entire energy is equivalent to the kinetic energy in addition to the possible energy of the area.

Further Reading – Expat UK TV

Understanding Polynomials

Polynomials are categorized into various types. Put simply, as soon as a polynomial is represented in the shape of equation, it is called polynomial equation. They play a critical part in mathematics. Also referred to as factorization, this technique is mostly utilised in simplifying polynomials. You should currently be all set for subtracting polynomials.
There are several different ways of factoring these numbers based on their types and forms. When you bring polynomials, you are just likely to bring the like terms which are categorized according to the amount of terms and the degree. Such numbers are also classified as prime polynomials.

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As a result of how polynomials obey the exact same rules are real numbers we could likewise do the exact same calculation in the fashion of elementary arithmetic, i.e., However many terms a polynomial has, it’s always essential to check for a best common factor (GCF) first. A polynomial is an expression with a power that’s an entire number. Polynomials are employed in a diverse selection of problems where they’re called as polynomial equations. Such polynomials are called reducible polynomial.

The potential things of the trinomial are the binomials which we may make out of these feasible things, taken in each probable order. If that’s the case, you can component out that common component. Inside this expression, there’s a typical element for the initial two terms. A function which consists of polynomial is known as a function. You simply count up how many variables you’ve got the exact same and compose the number before the typical variable part. The maximum value of exponents is known as degree of polynomial. It is also used online to define and protect internet connections for example some use it in VPNs to allow anonymous torrenting as this.

You may prefer the vertical method as you are accustomed to adding numbers vertically. So, since you can imagine, we’ve got a significant number of resulting terms! This time you should bring the numbers together as you’re finding the sum. In the overall form, the quantity of constants, on account of the term of level 0, is always one more than the level of the polynomial. In mathematical provisions, Hamming codes are a category of binary linear codes.

Since the level of the polynomial is the maximum level of all of the terms, Since there’s a single term, this is a monomial. The amount of a polynomial is the maximum level of the terms. It is the degree of the leading term. It is the highest degree of its terms. Since the level of the polynomial is the maximum degree of all of the terms, because there are 3 terms, this is a trinomial. Since it is the highest degree of all the terms, Make sure that you don’t fall into the trap of thinking it is always the degree of the first term. It is the greatest degree of its terms.

Finding out how to factor polynomials doesn’t have to be hard. The theory of polynomials is quite an important and intriguing portion of mathematics. Given 2 people’s ages, there are numerous mathematical relations you are able to calculate utilizing both of these numbers. Similarly the past two terms have a standard aspect. It’s important to not forget to multiply the terms along with the numbers.