tag:blogger.com,1999:blog-89207959897604283892018-02-24T08:53:42.568-08:00Math PhysicsKen Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comBlogger177125tag:blogger.com,1999:blog-8920795989760428389.post-16122867019395577032018-02-24T08:53:00.001-08:002018-02-24T08:53:42.741-08:00The Problem with General Relativity<font size="4"> <b>The Problem with General Relativity</b><br><br> General Relativity had its 100th birthday in 2015 and it's still the #1 way to describe gravity. But change may be on the horizon.<br><br> The theory is probably the most brilliant physics insight ever produced by a single individual. But it can never be correct at the quantum level and must be replaced or seriously modified.<br><br> Totally new thinking is needed, especially concerning space time coordinates and dimension. <br><br> Sorry Albert.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-15061757161723063462018-02-21T10:46:00.002-08:002018-02-21T10:46:26.387-08:00What is Physics?<font size="4"> <b>What is Physics?</b><br><br> A reality check, food for thought, and perhaps a good topic of discussion..<br><br> Physics is a bunch of procedures that let us predict a small subset of nature with various levels of accuracy. <br><br> That's it. <br><br> There is no truth. <br><br> The so called "Laws" of Physics are not laws, but simply a great name devised by physicists to make their bunch of procedures sound impressive.<br><br> And who said physicists are no good at marketing!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-7063375536974003292018-02-21T10:03:00.002-08:002018-02-21T10:03:18.764-08:00Physics - The Number 3 Strikes Again<font size="4"> <b>Physics - The Number 3 Strikes Again</b><br><br> It seems that Physics likes the number 3 at all levels, from macroscopic down to the quantum level. Consider this.. <br><br> - There are 3 spacial dimensions.<br><br> - The Standard Model has 3 families of fermions.<br><br> - The Color Force has 3 charges, RGB.<br><br> - And we now have the recently discovered "Efimov States" which are bound groups of 3 bosons.<br><br> Coincidence? Maybe. Maybe not.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-45895289042784223422018-02-20T07:20:00.002-08:002018-02-20T09:03:49.514-08:00Information and The Dimension of Space <font size="4"> <b>Information and The Dimension of Space</b><br><br> A simple way to think of the gravitational field of an object is to imagine a fixed number of "lines of force" that radiate from the object evenly into space. The density of the lines at any given point in space represents the strength of the gravitational field at that point. <br><br> With this simple model in mind, we write down Newton's famous formula for the gravitational force f between two masses m and q at a distance r apart..<br><br> f=G*m*q/(r^2)<br><br> G is just a constant which goes by the impressive name "universal gravitational constant", but it's not really interesting. Its value depends on which unit system we're using to measure f, m and r and we can pick a unit system so that G=1, then..<br><br> f=m*q/(r^2)<br><br> We can make q a unit mass, q=1, and imagine we're using q to measure the gravitational field generated by m, so..<br><br> f=m/(r^2)<br><br> This is the essence on Newton's theory of gravitation. But what is this equation really saying? If we think about our lines of force model in a 1-dimensional space and then in a 2-dimensional space we realize that this equation is actually..<br><br> f=m/r^(n-1)<br><br> where n=number of dimensions of the space containing the mass m. <br><br> We can solve this equation for n..<br><br> n=1+(log(m/f)/log(r))<br><br> The expression on the right is an experimentally measurable quantity. But it's the dimension of space! <br><br> Can we push our luck further? Hey, why not..<br><br> In physics we know that the log function shows up in discussions of information entropy. But we've expressed dimension in terms of the log function, so perhaps dimension is derived from the information content of space. Of course, we need to define "information content", but if that could be done we would have a concept more fundamental than dimension. Now that would be a breakthrough!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-63166518240445015682018-02-15T07:18:00.002-08:002018-02-19T10:20:31.211-08:00The Math of Gun Deaths<font size="4"> <b>The Math of Gun Deaths</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-8cARz44Z5d8/WoWoOKZfp1I/AAAAAAAAHrw/8HcruKu5pSogGrxJBLUO8vR7tvaM39CzQCLcBGAs/s1600/guns.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-8cARz44Z5d8/WoWoOKZfp1I/AAAAAAAAHrw/8HcruKu5pSogGrxJBLUO8vR7tvaM39CzQCLcBGAs/s320/guns.jpeg" width="320" height="212" data-original-width="276" data-original-height="183" /></a></div> It happens with depressing frequency in the United States - there's a mass killing and the gun debate jumps to the front. There's much hand waving on both sides for a few days. Then it fades until the next time.<br><br> And there's always a next time.<br><br> So I decided to do some quantitative analysis. Turns out it's hard to understand guns. I'm no slouch at data analysis, but this turned into a mystery..<br><br> I looked at the AR-15, which seems to be the weapon of choice for mass killers. It's available for civilian ownership in many countries. Some make you jump through more hoops than others, but basically if you want one you can get one.<br><br> Then I looked at deaths by guns. The statistics include all types of gun deaths not just mass killings. The numbers are quoted as deaths per 100,000 of population per year. I used the United Kingdom as my baseline.<br><br> United Kingdom 0.23<br><br> United States 10.54<br><br> That makes gun deaths in the United States 4,582% higher than in the United Kingdom.<br><br> Of course, the United States is not the worst. The highest number I found was Honduras at 67.18 and the lowest was South Korea at 0.08<br><br> But still, I think most people identify the United States closely with the United Kingdom. I know I do.<br><br> So the mystery is why gun deaths in the United States are 4,582% higher than in the United Kingdom.<br><br> 4,582% is a massive gap between two close allies.<br><br> Data source: <a style="text-decoration:underline" href="https://en.wikipedia.org/wiki/List_of_countries_by_firearm-related_death_rate">Firearm Death Rates by Country</a><br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-79677874434159688602018-02-07T09:49:00.000-08:002018-02-13T14:24:34.300-08:00Rethinking Black Holes<font size="4"> <b>Rethinking Black Holes</b><br><br> Here's a solution to the "Black Hole Information Paradox" that nobody seems to have considered..<br><br> Hawking Radiation does not exist.<br><br> Reason: Current theories assume the continuum, meaning the position of the event horizon can be specified with infinite accuracy. Suppose this was not the case. Suppose the event horizon was fuzzy. Simply not enough resolution to separate a virtual pair of particles. Then there would be no Hawking radiation.<br><br> And let's not forget, Hawking Radiation has never been experimentally verified.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-65928185691818618752018-02-06T07:50:00.000-08:002018-02-07T09:21:24.038-08:00Borromean Rings<font size="4"> <b>Borromean Rings</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-bBislgvuTo4/WnnOqzLzO8I/AAAAAAAAHqs/Oi2jtvQH9LsFphMBQO8DllrXAJHtsadUgCLcBGAs/s1600/borromean-rings.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-bBislgvuTo4/WnnOqzLzO8I/AAAAAAAAHqs/Oi2jtvQH9LsFphMBQO8DllrXAJHtsadUgCLcBGAs/s320/borromean-rings.jpg" width="320" height="266" data-original-width="220" data-original-height="183" /></a></div> Here's a nice piece of topology.<br><br> Notice that no two rings are linked, yet all 3 rings are linked.<br><br> You could even use this to represent a proton - the rings being the 3 quarks that make up a proton.<br><br> This model even shows the famous "asymptotic freedom" and "confinement" of bound quarks. When the rings are very close together you can move them around as if they were free (asymptotic freedom), but when you try to pull them apart a strong force appears to stop you (confinement).<br><br> Speaking of interesting topology I wonder what would happen if you replaced each ring with a Mobius strip?<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-88986143783173127362018-01-30T05:08:00.004-08:002018-02-01T06:25:01.853-08:00A New Goldbach Conjecture<font size="4"> <b>A New Goldbach Conjecture</b><br><br> The Goldbach Conjecture says.. "every even number greater than two can be written as the sums of 2 primes."<br><br> The Twin Prime Conjecture says.. "there are an infinite number of twin primes." <br><br> Twin primes are two primes separated by just one number. For example: (11,13) are twin primes, so are (1049,1051)<br><br> Neither conjecture has ever been proven or disproven and they remain the holy grail of mathematical research.<br><br> But what if they were connected?<br><br> I did a search of numeric computer tests and found this gem..<br><br> Let a t-prime be a prime that's a member of a twin prime pair. Then..<br><br> "Every even number greater than 4208 is the sum of two t-primes."<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-10060374196074032782018-01-23T14:36:00.003-08:002018-01-30T05:39:33.716-08:00Goldbach Conjecture Revisited<font size="4"> <b>Goldbach Conjecture Revisited</b><br><br> If you could show that the Goldbach Conjecture is "decoupled" from the Axioms of Number Theory then it could never be proved or disproved within Number Theory.<br><br> I wonder if there are ways to check if a mathematical statement is "decoupled" from the Axioms of a system? <br><br> The Goldbach Conjecture is a very simple statement, so surely it must be easy to check if it's decoupled. Methinks not!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-71964719012016604922018-01-13T07:35:00.000-08:002018-02-19T06:22:04.792-08:00The Twin Prime Pair (1049,1051)<font size="4"> <b>The Twin Prime Pair (1049,1051)</b><br><br> Let's write twin primes in binary. <br><br> For example, the twin prime pair (1049,1051)=(10000011001,10000011011). <br><br> Now concatenate the binary bit streams to get 1000001100110000011011=2149403 which is a prime! <br><br> Primes generating primes. Quite amazing. <br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-74216425635130410492018-01-13T05:32:00.000-08:002018-02-16T05:23:46.839-08:00Google Math Tip<font size="4"> <b>Google Math Tip</b><br><br> Need to plot a function? <br><br> Just punch your request into Google to get an instant plot. <br><br> Example: to plot the function f(x)=x^2 just enter plot x^2 into Google. Of course, it can also handle much more complex functions, for example try plot x^3+1/x or try one of my favorites, just enter plot 1/(1+x^2)<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-38097024457981096662018-01-09T15:02:00.000-08:002018-01-10T04:58:12.005-08:00Your chance of winning the Lottery<font size="4"> <b>Your chance of winning the Lottery</b><br><br> We all know the probability is low. But how low? <br><br> Let's take the Powerball, an incredibly popular lottery in the USA. Last week someone won $571 million in the Powerball.<br><br> So what are your chances of winning?<br><br> If your 5 numbers plus the Powerball match the winning six numbers drawn, then you win or share the Grand Prize. If the jackpot is not won in any drawing, the First Prize Pool Money is carried forward and is added to the next Powerball Jackpot.<br><br> Your chance of getting 5 + Powerball - Grand Prize is 1 in 292,201,338<br><br> Powerball offers 9 ways to win, and here are the probabilities..<br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-cLIVzWmuEdw/WlYNfVRYCKI/AAAAAAAAHpY/BPwc9132GhQvjClEVuunRVpoa6h3yIi4gCLcBGAs/s1600/powerball-win-chart.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-cLIVzWmuEdw/WlYNfVRYCKI/AAAAAAAAHpY/BPwc9132GhQvjClEVuunRVpoa6h3yIi4gCLcBGAs/s320/powerball-win-chart.png" width="320" height="258" data-original-width="474" data-original-height="382" /></a></div> So does this mean you should not buy a lottery ticket? If you don't buy your chance of winning is absolutely zero!<br><br> Good luck. <br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-26378366845107116642018-01-05T05:08:00.004-08:002018-01-07T07:22:29.503-08:00Twin Primes - A Surprising Result<font size="4"> <b>Twin Primes - A Surprising Result</b><br><br> Let's write twin primes in binary. For example the prime pair (281,283)=(100011001,100011011). <br><br> Now concatenate the two binary string to get 100011001100011011=144155 which is not a prime. But just reverse the order of concatenation to get 100011011100011001=145177 and this is a prime! <br><br> Here's an even more impressive example.<br><br> The prime pair (1049,1051)=(10000011001,10000011011) then concatenate the binary bit streams to get 1000001100110000011011=2149403 which is a prime! <br><br> Primes generating primes! Quite amazing. Please contact me with your results. <br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-54272094575620980442018-01-04T11:03:00.003-08:002018-01-07T10:25:15.294-08:00Quantum Mechanics Explained Fast <font size="4"> <b>Quantum Mechanics Explained Fast</b><br><br> If I was forced to summarize Quantum Mechanics in one sentence I would say this.. "small objects behave very differently than big objects".<br><br> It sounds like an innocent statement. But it's not. It's a profound discovery of how nature works. <br><br> An example will help..<br><br> Spin is something we're all familiar with. We can make any object spin. And not just a top, spin is used to great effect in many sports such as tennis, baseball and cricket. And of course you could never throw a frisbee without spin.<br><br> We can spin an object at any speed we please, and as soon as it starts spinning it defines an axis about which the spin occurs.<br><br> But that's the spin of a big object, meaning an object we can handle. What about the spin of a really small object such as an electron?<br><br> It turns out the electron spins just like a tiny top - but with two big surprises..<br><br> - What about the speed of spin? <br>The electron spins at a fixed rate that can never be changed. There is no known process that can change the spin rate of the electron. This makes electron spin a fundamental quantity.<br><br> - What about the axis of spin? <br>You can measure the spin along any axis you want and you'll always get the same result, +1/2 or -1/2 (these two values just correspond to the electron spinning clockwise or counter clockwise). So the electron behaves as if it's spinning about every axis at the same time! <br><br> So electron spin is totally different than the spin of a big object such as a top.<br><br> Physicists call the electron a "spin 1/2 particle". And it's not just the electron, all elementary particles have spin except for the recently discovered Higgs boson.<br><br> If you plan to study Quantum Mechanics pay attention to spin. It's a wonderful example of how "small objects behave very differently than big objects".<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-70406396443531952712018-01-04T07:25:00.002-08:002018-02-13T05:55:39.867-08:00Transcendental Numbers - A Simple Definition<font size="4"> <b>Transcendental Numbers - A Simple Definition</b><br><br> Take any number and ask if it can be converted to a rational number by raising it to an positive integer power. If it can we say it's coupled to the integers. If not we say it's decoupled from the integers. <br><br> All rational numbers are coupled by definition. But so are many irrational numbers, for example sqrt(2) is irrational, but (sqrt(2))^2=2. Even many complex numbers are coupled, for example i^2=-1<br><br> So it seems most numbers are coupled to the integers, making integers fundamental. Not true. In fact Cantor showed the opposite is true, most numbers are decoupled from the integers. These are the (still mysterious) transcendental numbers. And the name is good, transcendental numbers "transcend" the integers.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-57490652232893326512018-01-03T04:35:00.000-08:002018-01-05T08:27:08.343-08:00What is a Prime Number?<font size="4"> <b>What is a Prime Number?</b><br><br> Here's a nice simple definition of a prime number..<br><br> Suppose you have a set of objects and I ask you to divide them into subsets of equal size. The key thing here is "equal size".<br><br> This can often be done. But there are some sets where it cannot be done.<br><br> When it cannot be done we call the number of objects in the set a prime number.<br><br> Example: A set of 12 objects can be divided into subsets of equal size (actually, in several different ways), so 12 is not a prime number. A set of 13 objects can never be divided into subsets of equal size so 13 is a prime number.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-30959111761107392342018-01-02T09:44:00.003-08:002018-01-05T08:26:11.330-08:00The Mathematics of Drinking <font size="4"> <b>The Mathematics of Drinking</b><br><br> First we define a fundamental unit - the "standard drink". It's a drink that needs one hour for its alcohol content to be metabolized. In other words it takes one hour to get out of your system.<br><br> Then using this fundamental unit we can measure drinks..<br><br> <b>Liquor (80 Proof - 40% Alcohol by volume)</b><br><br> “Bottle” 750ml = 17 Standard Drinks<br>“Martini” 200ml = 4.5 Standard Drinks<br>“Miniature” 50ml = 1 Standard Drink<br><br> <b>Wine (13% Alcohol by volume)</b><br><br> “Bottle” 750ml = 5.5 Standard Drinks<br>“Big Glass” (10 fluid ounces) = 2 Standard Drinks<br>“Standard Glass” (5 fluid ounces) = 1 Standard Drink<br><br> <b>Beer (5% Alcohol by volume)</b><br><br> “Pint” (16 fluid ounces) = 1.2 Standard Drinks<br>“Bottle” (12 fluid ounces) = 1 Standard Drink<br><br> I think the biggest shock here is the Martini. Wow!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-73762044474969168182018-01-02T08:40:00.000-08:002018-01-05T08:29:10.730-08:00Information and Dimension - Are They Related? <font size="4"> <b>Information and Dimension - Are They Related?</b><br><br> This is an extreme example, but it shows there may be a fundamental relationship between the availability of information and the concept of dimension.<br><br> Sitting on your desk is a sphere. As in mathematics, let's assume an axiom - your sphere is an information void. What's that? It's a closed surface which allows absolutely no knowledge of its interior. The interior of the object is off limits to any form of investigation. Think of its surface as an information barrier that stops any information about the interior from getting out. <br><br> So what properties does your sphere have?<br><br> You can't break it open to look at the interior, that would violate the axiom, so the object must be infinitely strong.<br><br> You can measure its diameter - just use a ruler. You can measure its surface area - just take a small unit square and see how many times you can paste it on the surface.<br><br> What about volume? Be careful, knowing volume means you have information about the interior and that's impossible. Of course you can use the formula volume=(4/3)*pi*r^3 where r is the radius. But this is not a measurement of the interior, so the best you can do is call this volume the "external volume". You have no knowledge of the geometry or topology of the interior, so the "internal volume" could be very different!<br><br> Now, if you can never have any knowledge of the interior you come to a simple conclusion, the object is totally defined by whatever is on its surface. The object certainly looks 3D but can be fully described as if it was 2D. Interesting object! <br><br> Your sphere has no reality inside - just like bubbles in a liquid have no liquid inside. If you own one please handle it carefully!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-64953530035452573542018-01-01T09:22:00.001-08:002018-01-05T08:29:37.997-08:00Prime Cores - The Core of a Prime Number <font size="4"> <b>Prime Cores - The Core of a Prime Number</b><br><br> What's a Prime Core? Take a prime number in binary, then strip off the first and last digits (which, for all primes except 2 are always 1's) then interpret the binary string you have left as an integer, and that's the prime core. <br><br> Example, the prime 79 in binary is 1001111 so its core is 00111 which is 7. So using C to represent the prime core operation, we have C(79)=7. <br><br> Then here's an interesting question: "when is the core of a prime also a prime?"<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-44114308757399705982017-12-29T11:22:00.004-08:002018-01-05T08:28:04.554-08:00The Problem with Blockchain <font size="4"> <b>The Problem with Blockchain</b><br><br> Don't get me wrong. It's clever. The mathematics behind it is very clever. It would make a great PhD thesis. But it's a solution looking for a problem. <br><br> Blockchain is many things to many people. But let's take Bitcoin, the most famous blockchain app.<br><br> A payment method? Really? VISA can process up to 47,000 transactions/second. Bitcoin maxes out at 7 transactions/second. Blockchain is the bottleneck.<br><br> A peer-to-peer system? Really? Nobody cares about peer-to-peer. Most people like a central authority.<br><br> So what is blockchain? It's an example of technology in love with itself. And with no concept of consumer marketing or psychology. <br><br> <a style="text-decoration:underline" href="https://www.tradingview.com/symbols/BTCUSD/">Watch Bitcoin Trading in Realtime</a><br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-23265264122058975902017-12-29T08:43:00.001-08:002018-01-05T08:27:46.021-08:00Quantum Computing Gets Closer <font size="4"> <b>Quantum Computing Gets Closer</b><br><br> Studying computer programming in hopes of getting a great job? <br><br> An experienced programmer looking to boost your career?<br><br> Perhaps the really hot jobs in the future will be in quantum computing.<br><br> It's worth keeping up to speed in this fast developing field, so take some time to learn quantum programming!<br><br> Here's a nice quantum computing tutorial. It teaches you step-by-step how to write a program for these amazing machines.<br><br> <a style="text-decoration:underline" href="https://medium.com/@decodoku/how-to-program-a-quantum-computer-982a9329ed02">How to Program a Quantum Computer</a><br /><br /> Also, IBM is very active in quantum computing. Their main quantum computer research Lab is the Watson Research Center in Yorktown Heights. They have a quantum computer up and running and provide developer tools to let you write and run programs. It's called the "IBM Q experience".<br><br> <a style="text-decoration:underline" href="https://quantumexperience.ng.bluemix.net/qx/experience">IBM Q experience</a><br /><br /> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-40258189690909424172017-12-27T06:14:00.002-08:002018-01-05T08:28:40.521-08:00Hydrogen Cars Explained in 5 Minutes<font size="4"> <b>Hydrogen Cars Explained in 5 Minutes</b><br><br> Hydrogen cars are very different from all other cars (gasoline, battery, hybrid). Here's how they work..<br><br> A hydrogen car is a 100% electric car, but instead of a battery it uses hydrogen fuel cells. These are simple, feed them hydrogen gas and they generate electricity. They are like a battery that never need recharging. There is no combustion, nothing burns, hydrogen gas is simply fed to the fuel cells to produce electricity.<br><br> So where do we get the hydrogen? The cars carry high pressure tanks of hydrogen gas to supply their fuel cells. The tanks get refilled at a hydrogen gas station, and the filling process is very similar to regular gasoline filling. The hydrogen gas station produces its hydrogen on the spot. How? By electrolysis of water.<br><br> Yes, the raw material to generate hydrogen gas is water!<br><br> So, the hydrogen gas station makes hydrogen from water. Cars refill their hydrogen tanks. The hydrogen goes through the car's fuel cells and generates electricity to drive the car. And the exhaust? The car's exhaust is water vapor. There is zero pollution.<br><br> The whole thing is a water to water cycle!<br><br> The range of a hydrogen car is about the same as a gasoline car, and the refueling time is about the same.<br><br> Also, hydrogen is the most abundant element in the universe. So I doubt we'll run out!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-77762936671100578242017-12-23T17:15:00.002-08:002018-01-05T08:34:03.407-08:00Simple Definition of a Prime Number<font size="4"> <b>Simple Definition of a Prime Number</b><br><br> Suppose you have a set of objects and I ask you to divide them into subsets of equal size. The key thing here is "equal size".<br><br> This can often be done. But there are some sets where it cannot be done.<br><br> When it cannot be done we call the number of objects in the set a prime number.<br><br> Example: A set of 12 objects can be divided into subsets of equal size (actually, in several different ways), so 12 is not a prime number. A set of 13 objects can never be divided into subsets of equal size so 13 is a prime number.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-52764589794809142652017-12-23T11:56:00.003-08:002018-02-09T04:45:45.493-08:00Lineland - Math and Physics in 1 Dimension<font size="4"> <b>Lineland - Math and Physics in 1 Dimension</b><br><br> You're a point mass and you live on the x axis. That's your entire world. It's "Lineland". What's your life like?<br><br> First, as regards moving, you only have two directions, forward and backwards. And if you meet another point mass you cannot pass. So you can only know two other masses. You have just two friends maximum!<br><br> You have no reason to count objects beyond two, so you might be slow in developing the concept of integers. Or perhaps you never develop the concept at all. You simply have no need for it.<br><br> What about Physics in Lineland? You're a point mass, so you have mass, let's say m. Another point mass could have a different mass, say M. So at least gravity exists, right? It does, but it has a strange form. Newton's formula for the gravitational force F between two masses m and M is..<br><br> F=G*M*m/(r^2)<br><br> where G is a constant and r is the distance between the two masses.<br><br> The r^2 term is good in a 3D space, but in general it's r^(n-1) where n is the dimension of the space. Putting n=1 for Lineland we get..<br><br> r^(1-1)=r^0=1 so F=G*M*m<br><br> Which means F is independent of distance! Gravity has the same strength no matter how far apart the objects are. So physics in Lineland is very different.<br><br> This is Lineland on the x axis. What if Lineland is the circumference of a circle? That's even more interesting. Would you be aware that Lineland had a "curvature"? What does gravity do now that Lineland is a closed loop? What happens if Lineland is a closed loop that intersects itself at several points? What happens at these intersection points and how do they contribute to gravity? How do things change as the number of point masses in Lineland changes? It turns out that even 1 dimension can be very complex! <br><br> Just think, there's probably a 4 dimensional world somewhere with math teachers looking for a nasty problem to set on an exam. Finally they come up with one, "explain how math would have developed if our world was constrained to just 3 dimensions".<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-75702954711490539092017-12-23T09:07:00.000-08:002018-01-05T08:38:30.207-08:00Bitcoin Trading Explained Fast <font size="4"> <b>Bitcoin Trading Explained Fast</b><br><br> Bitcoin trades 24/7 around the world on many exchanges. So there's no one Bitcoin price and arbitrage opportunities exist.<br><br> If you plan to trade Bitcoins the choice of exchange is very important and should be researched carefully before you open an account. <br><br> <a style="text-decoration:underline" href="https://www.tradingview.com/symbols/BTCUSD/">Watch Bitcoin Trading in Realtime</a><br><br> Here's one of many Bitcoin Exchanges. This one trades Bitcoin in US Dollars, which is called BTCUSD.<br><br> <a style="text-decoration:underline" href="https://www.bitfinex.com">Bitcoin Trading Platform</a><br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.com