tag:blogger.com,1999:blog-89207959897604283892020-01-24T01:35:57.435-08:00Math Physics BlogUnknownnoreply@blogger.comBlogger273125tag:blogger.com,1999:blog-8920795989760428389.post-35801153847057103782020-01-23T05:55:00.000-08:002020-01-23T05:55:06.265-08:00Learn Algebra in 5 Minutes<font size="4"> <b>Learn Algebra in 5 Minutes</b><br /><br /> Consider this problem, "what number, when added to 5, gives the result 20". <br /><br /> Instead of a sentence, this problem can be written much shorter and clearer as an equation, like this.. <br /><br /> 5+x=20 <br /><br /> where x denotes the number we are trying to find. <br /><br /> Of course, we could also write it as x+5=20 and this is exactly the same equation. Or we could write 20=x+5 which is of course the same thing.<br /><br /> If we manage to find x we say that we've "solved" the equation. Can we solve this equation? Well, we could guess a few numbers for x and try them out. Does x=9 work? Let's see, 5+9=14, so x=9 is not a solution. After a few tries we get the solution, which is x=15.<br /><br /> Guessing a solution is perfectly fine, but it's very time consuming, especially for more complex equations. Of course, we could program a high speed computer to guess solutions and try them out ultra fast until we finally hit on the right solution. And for some very tough equations this is indeed the method used. But this method has one huge flaw.. if it fails to find a solution it does not mean the equation has no solution. That's because even the fastest computer can only make a limited number of tries.. and the actual solution may be something we never get around to trying.<br /><br /> So, coming back to our equation 5+x=20 we should ask if there is a foolproof method that's guaranteed to find the solution. The answer is yes, and it's all about the = sign. Once you truly understand this simple sign solving the equation is easy. <br /><br /> So what does this sign really mean? It means the "object" on the left of the sign is the same exact object as that on the right. They are the same thing.. exactly the same thing. They are the same exact mathematical object but just written in different ways. So there's really only one object!<br /><br /> OK, so our equation says that 5+x is exactly the same object as 20. So, if I do something to 5+x and then I do the same thing to 20 the results will still be equal. Cool. So lets subtract 5 from 5+x to get the result x. Now do the same exact thing to the other side, I'll subtract 5 from 20 to get the result 15. But these two results must be the same, so I can write them as equal to each other, that is x=15. <br /><br /> Bingo, we've solved the equation without any guessing!<br /><br /> Also, I'm not sure if you noticed this, but we just did some basic algebra. Don't let algebra intimidate you, it's just the art of manipulating equations until you get what you want!<br /><br /> Let's look at a slightly more complicated example..<br /><br /> 3*x+2=17<br /><br /> Let's use the same method. First subtract 2 from both sides..<br /><br /> 3*x=17-2=15<br /><br /> Now divide both sides by 3..<br /><br /> x=15/3=5<br /><br /> And that's the solution!<br /><br /> Here's another method I use. It's exactly the same technique as above, but it's faster and easier to handle. Or at least I think so, and I've used it over the years to do massive amounts of algebra!<br /><br /> First move the 2 over to the other side. It was adding, so when it moves over it subtracts, like this..<br /><br /> 3*x=17-2=15<br /><br /> Now move the 3 over. It was multiplying, so when it moves over it divides, like this..<br /><br /> x=15/3=5<br /><br /> This technique is quite general and can be used for any equation. But notice that the order in which you do things is important. For example, you need to get the 2 over to the other side before you can handle the 3.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-68400598705126546702020-01-18T09:27:00.002-08:002020-01-23T06:00:35.916-08:00Contactless Cards change the way you pay<font size="4"> <b>Contactless Cards change the way you pay</b><br /><br /> <div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-wf8-wm_cGRo/XiNNZOTFovI/AAAAAAAAJv4/qG5awvc4kmAqfmPB5gJ8hiPcVFancdhAACLcBGAsYHQ/s1600/nfc-logo.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-wf8-wm_cGRo/XiNNZOTFovI/AAAAAAAAJv4/qG5awvc4kmAqfmPB5gJ8hiPcVFancdhAACLcBGAsYHQ/s200/nfc-logo.png" width="200" height="200" data-original-width="159" data-original-height="159" /></a></div> If your credit/debit card has the NFC symbol then it's a contactless card. <br /><br /> So you can just tap to pay. No swiping. No inserting in a chip reader. Just tap and go. It's super fast. <br /><br /> Of course, the merchant needs an NFC reader. Many do but they don't advertise the fact. <br /><br /> For example, I tapped to pay for a croissant at a bakery in NYC and then for my medications at CVS.<br><br> Oh.. I almost forgot. NFC is Near Field Communication. It's a communication protocol with a range of just a few inches. Perfect for tap and pay.<br><br> <b><a style="text-decoration:underline" target="_blank" href="https://www.amazon.com/?&_encoding=UTF8&tag=abbottsystems-20&linkCode=ur2&linkId=601edc436e035803fc11563a6b43a148&camp=1789&creative=9325">Amazon</a><img src="//ir-na.amazon-adsystem.com/e/ir?t=abbottsystems-20&l=ur2&o=1" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /> </b> Shop Now!<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>Disclosure: As an Amazon Affiliate I earn a small commission when people click on the above links and buy something.<br /><br> Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-23714050352849118942020-01-14T10:27:00.002-08:002020-01-16T11:09:08.947-08:00A Wind Turbine for your Home<font size="4"> <b>A Wind Turbine for your Home</b><br /><br /> First there are commercial wind turbines. These are giant machines, the things you see rotating in the distance on hillsides. <br><br> Vestas has a worldwide installed wind turbine capacity of about 590GW. Siemens has about 100GW of wind turbine capacity in operation. GE rounds out the top three manufacturers with a total installed capacity of 62GW. <br><br> A GW (gigawatt) is a billion watts. It's enough to power about 725,000 homes. <br><br> <b>But what about a wind turbine for your home?</b><br><br> No problem, try a VAWT (vertical axis wind turbine). These things are around 2 feet in diameter and several feet high. Their capacity ranges from 100 watts to about 5 KW. And prices start at just a few hundred dollars.<br><br> Could one of these power your entire house? No, but it could help. The average house needs about 5KW. So if one doesn't do it buy two or three. The wind is free and it doesn't care how many VAWTs you deploy. <br><br> And unlike the sun, the wind is in action overnight. So just connect your VAWT to a high-tech storage battery. Then you have free wind energy even when the wind doesn't blow!<br><br> <b><a style="text-decoration:underline" target="_blank" href="https://www.amazon.com/?&_encoding=UTF8&tag=abbottsystems-20&linkCode=ur2&linkId=601edc436e035803fc11563a6b43a148&camp=1789&creative=9325">Amazon</a><img src="//ir-na.amazon-adsystem.com/e/ir?t=abbottsystems-20&l=ur2&o=1" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /> </b> Shop Now!<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>Disclosure: As an Amazon Affiliate I earn a small commission when people click on the above links and buy something.<br /><br> Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-28383367612871571192020-01-14T09:03:00.002-08:002020-01-14T09:03:17.592-08:00Prime Numbers Explained a Different Way <font size="4"> <b>Prime Numbers Explained a Different Way</b><br><br> Let's consider the positive integers greater than 1, that is 2,3,4,5,.. <br><br> Suppose we are given the first integer and asked to make all other integers using only the multiply operation.<br><br> We soon run into problems because 2*2=4 and we have no way to make 3.<br><br> OK, we just add 3 to our set of given numbers g, so now g={2,3}<br><br> Can we make 4? Yes, 2*2=4<br><br> Can we make 5? No, all our tries fail, so we add 5 to our set of given number g={2,3,5}<br><br> Can we make 6? Yes, 2*3=6<br><br> Can we make 7? No, all our tries fail, so we add 7 to our given numbers g={2,3,5,7}<br><br> Can we make 8? Yes, 2*2*2=8<br><br> Can we make 9? Yes, 3*3=9<br><br> Can we make 10? Yes, 2*5=10<br><br> Can we make 11? No, so we add it to the set g={2,3,5,7,11}<br><br> Can we make 12? Yes, 2*2*3=12<br><br> Can we make 13? No, so add it to the set g={2,3,5,7,11,13}<br><br> Can we make 14? Yes, 2*7=14<br><br> Can we make 15? Yes, 3*5=15<br><br> Can we make 16? Yes, 2*2*2*2=16<br><br> What is the set g that we are generating by this process? It's the set of prime numbers! This is simply another way to explain prime numbers. <br><br> It's a nice demonstration because it shows how prime numbers generate all numbers using only the multiply operation. You can also see that as g gets bigger we can obviously make more numbers from it, so prime numbers become less and less frequent. <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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-34884469768050461592020-01-11T08:22:00.002-08:002020-01-11T08:26:24.603-08:00Australian Fires - The Terrible Numbers<font size="4"> <b>Australian Fires - The Terrible Numbers</b><br /><br /> One billion animals burned. <br><br> Fires are top of the news again today, and finally they are mentioning wildlife. Why is the government not setting up animal rescue centers? Much of the wildlife is unique to Australia. The government should be setting up major centers to preserve species. There seems to be no plan. <br><br> Don't fight the fires, that's a totally lost cause, save the wildlife.<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> Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-29397868829617796942020-01-07T10:18:00.000-08:002020-01-23T06:04:06.695-08:00Wind Turbines - From Hillside to Home<font size="4"> <b>Wind Turbines - From Hillside to Home</b><br /><br /> Vestas has a worldwide installed wind turbine capacity of about 590GW.<br><br> Siemens has about 100GW of wind turbine capacity in operation. <br><br> GE rounds out the top three manufacturers with a total installed capacity of 62GW. <br><br> A GW (gigawatt) is a billion watts. It's enough to power about 725,000 homes. <br><br> These are giant machines, the things you see rotating in the distance on hillsides. What if you want something for your home?<br><br> No problem, try a VAWT (vertical axis wind turbine). These things are around 2 feet in diameter and several feet high. Their capacity ranges from 100 watts to about 5 KW. And prices start at just a few hundred dollars.<br><br> Could one of these power your entire house? No, but it could help. The average house needs about 5KW. So if one doesn't do it buy two or three. The wind is free and it doesn't care how many VAWTs you deploy. <br><br> And unlike the sun, the wind is in action overnight. So just connect your VAWT to a high-tech storage battery. Then you have free wind energy even when the wind doesn't blow!<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> Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-19169142712111199412020-01-05T06:53:00.004-08:002020-01-07T05:31:41.262-08:00The Math of Building Wealth<font size="4"> <b>The Math of Building Wealth</b><br /><br /> A friend of mine is an expert on advanced life insurance policies as a method of building wealth.<br /><br /> I was a bit skeptical so I asked him for numbers based on investing just $1,000 a month starting at age 25.<br /><br /> Here's what he said..<br /><br /> "Starting at age 25, if you were to deposit $1,000 every month, you would start immediately with a $1,060,000 death benefit, and at age 65 you would have roughly $1,200,000 in cash. Your death benefit would have grown to roughly $2,400,000 and you would no longer be required to pay premiums. The policy would continue to grow for the rest of your life, both in cash and death benefit, and with tax benefits."<br /><br /> If you need more details just email Les Himel at <a style="text-decoration:underline" href="mailto:lnhimel@gmail.com">lnhimel@gmail.com</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> Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-88665114887636899122020-01-04T07:42:00.000-08:002020-01-05T06:05:29.223-08:00The Problem with 2020<font size="4"> <b>The Problem with 2020</b><br /><br /> No, not the year itself, but how you write the year on important documents such as checks, invoices and contracts.<br><br> The year 2020 provides scam artists a unique opportunity to forge documents. How?<br /><br /> For example, if you write a check and date it 1/3/20 a scammer could easily change the date to 2017 and then try to cash it as an "old" check. Or a scammer could make an invoice look "old" and unpaid. <br /><br /> The solution is easy. Write the year in full 2020.<br /><br /> Personally I think the year 1/1/2020 - 12/31/2020 will be a great year. But the year 1/1/20 - 12/31/20 not so much.<br /><br /> Oh, and a quick note for my international readers. I'm writing dates in "American", that's month/day/year and not the day/month/year that you use. But the scam avoidance is still the same!<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-3333342043320919382019-12-27T08:01:00.001-08:002019-12-27T08:01:37.149-08:00Physics and the Vacuum<font size="4"> <b>Physics and the Vacuum</b><br /><br /> We live in a causal universe - meaning there’s a maximum finite speed for causality. It’s a fundamental constant of the universe and it’s the same for all observers. It’s by no means obvious that light should travel at this speed. But it does.<br><br> The actual value for the speed of causality is determined by the structure of the “vacuum”. The thing we call the vacuum is complex, with lots happening deep down at the quantum level. Plowing through it is hard work, even for light and gravity waves. And far harder for matter particles.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-21252450309651625662019-12-12T13:12:00.001-08:002019-12-20T05:57:07.359-08:00Boeing 737 Max Saga<font size="4"> <b>Boeing 737 Max Saga</b><br /><br /> Here's my explanation of this terrible tale.<br><br> MCAS is a software patch in the 737 Max flight control computer that tries to compensate for a dangerous aerodynamic instability. The instability came about due to engine choice. <br><br> Boeing used the LEAP-1B engine on the 737 Max. It's a huge diameter bypass engine and it pushed the center of gravity of the aircraft into strange territory. <br><br> Hence the aerodynamic instability. Hence the MCAS software which put pilots into a terrible situation trying figure out what was happening. <br><br> In two cases they could not, and the planes oscillated under MCAS control until they fell out of the sky.<br><br> Many people died.<br><br> Only then was the decision made to ground the plane.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-63223876805578710142019-10-26T09:53:00.003-07:002019-10-26T09:53:28.193-07:00Climate Change and Sea Level<font size="4"> <b>Climate Change and Sea Level</b><br /><br /> The Greenland ice sheet is massive. If it melted sea levels would rise about 23 feet. <br><br> But the Antarctic ice sheet is way bigger. If that sheet melted sea levels would rise about 200 feet and wipe out almost every major city on earth.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-26771508321848968962019-10-23T12:38:00.002-07:002019-10-23T12:45:13.435-07:00Twin Primes Observation<font size="4"> <b>Twin Primes Observation</b><br /><br /> About the distribution of Twin Primes. <br><br> Let p1 be the first prime of a twin prime pair and let p2 be the first prime of the next consecutive twin prime pair. Then, I'm quite surprised how small p2-p1 stays. And when it does increase it will suddenly drop back to a very small number such as 12. <br><br> Anybody have any input on this?<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-6965469930342295592019-10-23T07:13:00.002-07:002019-10-24T08:43:08.068-07:00Einstein's Amazing Luck<font size="4"> <b>Einstein's Amazing Luck</b><br /><br /> Was it amazing luck or was it amazing insight? Whichever it was, at some point Einstein realized..<br><br> At a given point in space it’s impossible to distinguish between the effects of gravity and the effects of acceleration. <br><br> So, when he was trying to generalize Special Relativity to accelerating frames of reference he got an incredible bonus.. gravity suddenly appeared.. and General Relativity became a theory of gravity.<br><br> The rest is history.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-52682413665079859902019-10-22T09:17:00.003-07:002019-12-26T13:56:58.678-08:00Simple and Powerful Diet Secret<font size="4"> <b>Simple and Powerful Diet Secret</b><br /><br /> Read the nutritional label on the package. Or Google the food to read its nutritional label online. Just Google "nutritional label for xxx" where xxx is the name of the food, examples: beans, steak, donuts etc.<br><br> Then.. <br><br> Don't worry too much about calories!<br>Look for high protein. The higher the better.<br>Look for high fiber. The higher the better.<br>Look for low sugar. The lower the better. Zero if possible.<br>Look for low saturated fat. The lower the better. Zero if possible.<br> Simple.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-20167659063204689262019-10-17T09:06:00.002-07:002020-01-14T08:18:04.280-08:00My Favorite Amazon Deals<font size="4"> <b>My Favorite Amazon Deals</b><br /><br /> Here are a few of my favorite Amazon deals..<br><br> <b>AMAZON Business Account</b> Quantity discounts and more. <br><b>CELL PHONES</b> Huge Savings & Huge Selection. <br><b>AMAZON Echo</b> The amazing Alexa voice interface. <br><b>AMAZON Echo Studio </b>Alexa for Music Lovers. <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>Disclosure: As an Amazon Affiliate I earn a small commission when people click these links and buy something.<br /><br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-22499521552694051342019-10-14T07:59:00.003-07:002019-10-14T08:02:29.333-07:00CERN LHC Explained<font size="4"> <b>CERN LHC Explained</b><br /><br /> How did the CERN LHC (Large Hadron Collider) get its name? <br /><br /> Well, it's a large machine, about 27 kilometers in circumference and it collides protons. So it's a large collider. But what about the Hadron in the name? It turns out the proton belongs to a class of particles called Hadrons. The Proton is a Hadron. So we have a Large Hadron Collider.<br /><br /> Why collide protons anyway?<br /><br /> The LHC accelerates two counter-rotating beams of protons. The beam pipes are about 27 kilometers in circumference, and the protons are steered around the machine by powerful superconducting magnets. The two beams intersect at 4 points and this is where the protons collide head-on. The "debris" from the collision is measured to learn about the internal structure of the proton. <br /><br /> It turns out the proton is a complex object. Current theories describe it as composed of three quarks bound together by an incredibly strong force field mediated by particles called gluons. <br /><br /> So colliding protons may result in their constituent quarks colliding and yielding information about quarks. The gluons could also collide and yield more information about the force field within the proton.<br /><br /> The LHC is currently shut down for a major upgrade. But when it's operating this dashboard lets you see the LHC machine status in realtime. Check machine energy, ramps, beam status, machine tests, detector status and more. Plus, see messages from machine operators.<br /><br /> <b><a style="text-decoration:underline" href="http://op-webtools.web.cern.ch/op-webtools/vistar/vistars.php?usr=LHC1">Watch LHC operations in realtime</a></b><br /><br /> It doesn't matter if you're a physicist or simply an interested consumer.. the mystery of the proton is this.. why does nature pack such amazing complexity into such an incredibly small object?<br /><br /> <b>Some interesting LHC stats:</b><br /><br /> Proton are bunched in the LHC beam pipes.<br />There are 2808 bunches in each beam pipe.<br />Each bunch is about 30 cm long and contains approx 10^11 protons.<br />After full acceleration the protons are traveling at 0.999999991 the speed of light.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-19447572332884953422019-10-11T13:03:00.003-07:002019-10-15T08:20:56.114-07:00Amazon Echo and the Elderly<font size="4"> <b>Amazon Echo and the Elderly</b><br><br> My mother-in-law is 94 and she lives alone. Obviously there is much she cannot do. But I setup Amazon Echo for her. And she uses it constantly for..<br><br> -The weather<br>-The time<br>-Switching lights on and off (and dimming them)<br>-Switching the TV on and off (and changing volume)<br>-Placing phone calls<br>-Playing her favorite music<br>-Getting flight status information<br><br> Amazon Echo is an amazing tool for the elderly. I wish this got more publicity.<br><br> Get Amazon Echo. <a style="text-decoration:underline" href="https://amzn.to/33kHBTM">Amazon Echo</a><br><br> TIP: If you're a music lover get the version of the Echo with high fidelity speakers. <a style="text-decoration:underline" href="https://amzn.to/33ty3pF">Amazon Echo Plus for Music Lovers</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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-55566410724993521332019-10-09T13:47:00.000-07:002019-11-29T17:07:36.813-08:00Speed of Light<font size="4"> <b>Speed of Light</b><br><br> If you believe we live in a causal universe then there must be an upper (finite) limit on the speed of causality. Otherwise the universe would not be causal. <br><br>It is by no means obvious that this speed also equals the speed of light. But apparently it does.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-31431727952318344562019-09-19T07:06:00.000-07:002019-09-30T05:37:47.092-07:00Plot Functions with Google Search<font size="4"> <b>Plot Functions with Google Search</b><br><br> The Google Plot Function is powerful, fast and free. It's a great way to teach yourself functions, or to make math homework easier.<br><br> To plot a function just type your request into Google. The format of the request is plot {function}, for example..<br><br> To plot the function f(x)=x^3 just enter plot x^3 into Google. <br><br> Of course, it can handle more complex functions, for example try entering plot 1/(1+x^2)<br><br> Notice the symbols used by the Google Plot function: x^n means raise x to the power n and * is used to denote multiplication.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-59043458934409296572019-09-19T06:37:00.000-07:002019-10-04T11:03:49.037-07:00Gigabit vs Gigabyte<font size="4"> <b>Gigabit vs Gigabyte</b><br><br> The prefix "giga" mean a billion. So a Gigabit is 1 billion bits and a Gigabyte is 1 billion bytes. <br><br> There are 8 bits in a byte. So a Gigabyte is 8x bigger than a Gigabit.<br><br> A Gigabit internet connection is one that can transfer data at the rate of 1 Gigabit per second. A Gigabyte internet connection is 8x faster.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-78951351839255281362019-09-19T06:13:00.000-07:002019-09-19T06:13:27.874-07:00Artificial Gravity<font size="4"> <b>Artificial Gravity</b><br><br> Artificial Gravity is a force that mimics gravity.<br><br> You live on a space station. It's the shape of a giant donut.<br><br> Everything is great, but you and the crew are getting sick of floating around in zero gravity.<br><br> What you need is to generate some "artificial gravity". But how?<br><br> That's easy. Just fire a small booster rocket and spin the space station. You'll be drawn the outside wall of the station which will become your floor. So you can stroll around as usual. And if you drop an object it will fall to the floor. <br><br> So now you have "artificial gravity".<br><br> And if you spin the station at the correct rate you can match the gravity on Earth. <br><br> Spinning is a form of acceleration. But why is that important?<br><br> Because one of the deepest physics insights was Einstein’s observation that, for a small volume of space, the effects of acceleration cannot be distinguished from the effects of gravity. So your “artificial gravity” is not so artificial after all. <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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-87900894946179087262019-09-16T06:59:00.004-07:002019-09-16T06:59:45.665-07:00Giant Magellan Telescope<font size="4"> <b>Giant Magellan Telescope</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-uhgWOsoCv48/XTNP9Tp685I/AAAAAAAAJHY/kSwtN7uEM7cpe8lc0Ecscga84nHDmVJbQCLcBGAs/s1600/telescope-magellan-3.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-uhgWOsoCv48/XTNP9Tp685I/AAAAAAAAJHY/kSwtN7uEM7cpe8lc0Ecscga84nHDmVJbQCLcBGAs/s400/telescope-magellan-3.jpg" width="400" height="137" data-original-width="1024" data-original-height="350" /></a></div>We're going to get a new view of the universe. <br><br> The Giant Magellan Telescope is currently under construction. It will be 10X more powerful than the Hubble Space Telescope. It will be installed on a mountain top in Chile and begin operation in 2027. <br><br> It's a multi-mirror system with 7 primary mirrors and topology adaptive secondary mirrors to eliminate atmospheric distortion.<br><br> <a style="text-decoration:underline" href="https://www.gmto.org">Giant Magellan Telescope</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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-21593022007557322152019-09-16T06:56:00.001-07:002019-09-20T05:31:52.933-07:00Troubleshooting a Gigabit Internet Connection<font size="4"> <b>Troubleshooting a Gigabit Internet Connection</b><br><br> For the longest time I've been using a Verizon Fios 100 Megabit internet connection. <br><br> But Verizon now offers an amazing 1 Gigabit connection. So I upgraded. But when I ran the Verizon speed test I only saw a minor improvement.<br><br> Then it occurred to me. WiFi was the bottleneck. So I hardwired my computer to the router and instantly got the full gigabit 1000/1000 speed. Crazy fast. <br><br> One Gigabit is a truly superb service from Verizon. But this connection is so fast many WiFi routers become a bottleneck. You'll only see the full speed if you hardwire your computer, or if you get a new generation WiFi router that supports gigabit connections.<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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-30757465511000296622019-09-16T06:48:00.000-07:002019-09-16T06:48:03.996-07:00Shannon Entropy Explained <font size="4"> <b>Shannon Entropy Explained</b><br><br> Shannon Entropy (also called Information Entropy) is a concept used in physics and information theory. Here's the scoop..<br><br> Suppose you have a system with n states i.e. whenever you make an observation of the system you find it's always in one of the n possible states.<br><br> Now make a large number of observations of the system, then use them to get the probability pi that if you make an observation the system is in state i. So for every state of the system you have a probability pi.<br><br> Now construct this crazy sum = p1*log(p1) + p2*log(p2) +... + pn*log(pn) where the sum is over all the states of the system.<br><br> If the log is base 2 then (-1)*sum is called the "information entropy" of the system. <br><br> Note that "information entropy" applies to a complete system, not individual states of a system.<br><br> Here's a simple example..<br><br> My system is a penny and a table.<br>I define the system to have 2 states.. penny lying stationary on the table with heads up or with tails up.<br><br> My experiment is to throw the penny and then observe which state results.<br><br> I throw the penny many times and make notes. It lands heads up 1% of the time and tails up 99% of the time (it's a biased penny).<br><br> The crazy sum is 0.01*log(0.01) + 0.99*log(0.99) = 0.01*(-6.643856) + 0.99*(-0.0145) = -0.08079356<br><br> So the information entropy of the system is (-1)*(-0.08079356) = 0.08079356<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> Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-88994057671732990122019-09-16T06:43:00.002-07:002019-09-16T06:43:39.978-07:00Hydrogen Cars Explained<font size="4"> <b>Hydrogen Cars Explained</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 needs 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 gas? 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 gas 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>Unknownnoreply@blogger.com