tag:blogger.com,1999:blog-89207959897604283892021-04-18T04:45:28.221-07:00Ken's BlogEclectic posts on Math, Physics, Science and moreUnknownnoreply@blogger.comBlogger317125tag:blogger.com,1999:blog-8920795989760428389.post-42280463716451497192021-04-17T15:59:00.009-07:002021-04-18T04:45:27.160-07:00America - 6 things you need to know<font size="4"> <b>America - 6 things you need to know</b><br><br> 1. Manufacturing. It's long been game over for steel and automobiles. US cities that relied on this are in serious decline.<br><br> 2. Coal Mining. See #1.<br><br> 3. Advanced Physics. This moved to CERN in Switzerland decades ago.<br><br> 4. Medical technology. The US rules.<br><br> 5. Software technology. The US rules.<br><br> 6. Infrastructure. The US is way behind the rest of the world and especially China. Much of the US is still living on 1930s infrastructure. <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-51078696068299343372021-04-11T11:37:00.014-07:002021-04-13T06:00:18.277-07:00US Covid Deaths - April 12, 2021 - With Analysis<font size="4"> <b>US Covid Deaths - April 12, 2021 - With Analysis</b><br><br> The downward trend has stalled and the last couple of days show an uptick. Is this a just blip? The next few days should answer this.<br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-m96xdYSQuKg/YHWUrstdWlI/AAAAAAAAKRw/GeokXEZ1CFcq9QD25LSmRmq6wvknskA4QCLcBGAsYHQ/s652/Screen%2BShot%2B2021-04-13%2Bat%2B8.53.47%2BAM.png" style="display: block; padding: 1em 0; text-align: center; clear: left; float: left;"><img alt="" border="0" width="600" data-original-height="318" data-original-width="652" src="https://1.bp.blogspot.com/-m96xdYSQuKg/YHWUrstdWlI/AAAAAAAAKRw/GeokXEZ1CFcq9QD25LSmRmq6wvknskA4QCLcBGAsYHQ/s600/Screen%2BShot%2B2021-04-13%2Bat%2B8.53.47%2BAM.png"/></a></div> <br><br><br><br><br><br><br><br><br><br><br><br><br><br><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-32332619496740054862021-03-23T09:49:00.004-07:002021-03-23T09:53:16.843-07:00Go to University - Now - Online and FREE<font size="4"> <b>Go to University - Now - Online and FREE</b><br><br> Perfect for Covid or anytime!!! The world's Universities offer about 30,000 online course. And many are FREE.<br><br> Harvard, Stamford, Oxford, Cambridge and many more.<br><br> <a style="text-decoration:underline" href="https://www.classcentral.com/universities">The List</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-73007248421873494142021-03-08T09:52:00.011-08:002021-03-12T11:54:38.715-08:00Was Einstein a Genius?<font size="4"> <b>Was Einstein a Genius?</b><br><br> Yes. But he worked incredibly hard to be a genius. <br><br> He started pondering light when he was just a kid, “if I could run fast enough to catch up with a light beam what would it look like”. This developed into Special Relativity.<br><br> He slogged at General Relativity non-stop for another 10 years before he got it.<br><br> And he completely and totally devoted his life to physics… everything else just an aside. Few people can do this. Few people want to do this. <br><br> Even when he was wrong he was right. I’m thinking about the cosmological constant.<br><br> But in his later years he produced nothing. It was junk. He was at heart a totally classical physicist, and he could never break away from that. But, Einstein being Einstein, perhaps he will turn out to be correct in that also. Never gamble against Einstein.<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-46172005075882725382021-03-04T09:57:00.005-08:002021-03-06T13:25:03.736-08:00What is time?<font size="4"> <b>What is time?</b><br><br> I think it was Feynman who said that a great way to understand something is to look at how it's measured.<br><br> I have a system which can exist in just 2 states and it transitions between them constantly. I'll call this system a "clock" and one transition a "tick".<br><br> Now I have another system that I'm trying to study. It makes just one big transition.<br><br> So while the system makes one big transition how many ticks does my clock make?<br><br> The answer is called time.<br><br> All I'm doing is comparing two systems, the one I'm studying and the one I've designated as a reference system.<br><br> If we take this as our definition of time then such things as "time travel" are difficult to explain. To say the least. <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-31816129476356425892021-03-04T08:31:00.003-08:002021-03-08T10:28:44.574-08:00The Alcohol Drinking Calculator <font size="4"> <b>The Alcohol Drinking Calculator</b><br><br> First we define a fundamental unit - the "Standard Drink". It's any 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. Examples are 1.5 fluid ounces of 80 proof liquor, a 12 fluid ounce bottle of beer, or a 5 fluid ounce glass of wine.<br><br> Using this fundamental unit we can then measure drinks..<br><br> <b>Liquor (80 Proof - 40% Alcohol by volume)</b><br>“Bottle” 750ml = 17 Standard Drinks<br>“Fifth” 200ml = 4.5 Standard Drinks<br>“Miniature” 50ml = 1 Standard Drink<br><br> BTW: A Martini is about 200ml of 80 proof liquor which is 4.5 Standard Drinks and 432 calories.<br><br> <b>Wine (13% Alcohol by volume)</b><br>“Bottle” 750ml = 5.5 Standard Drinks<br>“Big Glass” (10 fluid ounces) = 2 Standard Drinks<br>“Glass” (5 fluid ounces) = 1 Standard Drink<br><br> <b>Beer (5% Alcohol by volume)</b><br>“Bottle” (12 fluid ounces) = 1 Standard Drink<br><br> I think the big surprise here is the Martini. Knock back just 2 Martinis and you've had 9 drinks plus 864 calories. It's going to take 9 hours to get the alcohol out of your system, and a whole lot longer to get the 864 calories off your waist! <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-70989264461132919202021-03-02T11:55:00.024-08:002021-04-11T11:20:15.881-07:00Thai Shrimp Curry <font size="4"> <b>Thai Shrimp Curry</b><br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-wZBhsXhBles/YD6doIY7haI/AAAAAAAAKNw/EwllVSXgvyEImNaFgExI8tAR8-mReezYQCLcBGAsYHQ/s2048/thai-shrimp.jpg" style="display: block; padding: 1em 0; text-align: center; clear: left; float: left;"><img alt="" border="0" height="400" data-original-height="2048" data-original-width="1536" src="https://1.bp.blogspot.com/-wZBhsXhBles/YD6doIY7haI/AAAAAAAAKNw/EwllVSXgvyEImNaFgExI8tAR8-mReezYQCLcBGAsYHQ/s400/thai-shrimp.jpg"/></a></div><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> Chop half an onion. Then peel and chop a chunk of ginger root. Crush a few garlic cloves.<br><br> Using fine olive oil saute them in a casserole. When the onions are tender add a small splash of Thai Red Curry Paste. Stir, and saute for a few seconds to release the flavor of the Curry Paste.<br><br> Now add a small amount of conconut milk and a tablespoon of flour. Boil. Be careful not to let anything burn.<br><br> Now add fresh coriander and basil, chopped to release their flavor. <br><br> Now add a splash of white wine (and/or chicken stock) and a pinch of Paprika and a grind of fresh pepper, and squeze in some lime juice.<br><br> Optional: Slice 1/2 an orange pepper into strips and add. If you're not a fan of orange peppers try chunks of fresh mango.<br><br> Now add the rest of the conconut milk and add a package of frozen peas. Boil. Add water (or chicken stock) if necessary to make sure nothing burns. <br><br> Finally, add the shrimp, boil until the shrimp are cooked and then serve.<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-23391913088554791472021-02-27T07:27:00.008-08:002021-03-04T08:24:46.130-08:00The Rope Problem (and its solution) <font size="4"> <b>The Rope Problem (and its solution)</b><br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-RkYB83cdjHI/YDpkuPpXNdI/AAAAAAAAKNU/Ld6gSE-0GGUHkargM8Vux9HHkEqizsergCLcBGAsYHQ/s2048/rope.jpg" style="display: block; padding: 1em 0; text-align: center; clear: left; float: left;"><img alt="" border="0" height="400" data-original-height="2048" data-original-width="1536" src="https://1.bp.blogspot.com/-RkYB83cdjHI/YDpkuPpXNdI/AAAAAAAAKNU/Ld6gSE-0GGUHkargM8Vux9HHkEqizsergCLcBGAsYHQ/s400/rope.jpg"/></a></div><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> The pic shows a rope of length 80 feet strung between two 50 foot poles.<br><br> At its lowest point the rope is just 10 feet from the ground.<br>What is x, the separation of the poles?<br><br> Solution provided on request.<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-53314159145538896702021-02-19T09:15:00.023-08:002021-02-20T12:59:16.050-08:00A Tiling (Tessilation) Surprise <font size="4"> <b>A Tiling (Tessilation) Surprise</b><br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-KTYV2BHul8k/YC_yJibKi2I/AAAAAAAAKMM/gRPqGko-4You5UxloEpH6NawpiBSc4BKQCLcBGAsYHQ/s720/tiling.jpg" style="display: block; padding: lem; text-align: center; clear: left; float: left;"><img alt="" border="0" width="400" data-original-height="520" data-original-width="720" src="https://1.bp.blogspot.com/-KTYV2BHul8k/YC_yJibKi2I/AAAAAAAAKMM/gRPqGko-4You5UxloEpH6NawpiBSc4BKQCLcBGAsYHQ/s400/tiling.jpg"/></a></div><br><br><br><br><br><br><br><br><br><br><br><br> Tiling, which mathematicians call Tessilation, is the art of covering a flat surface with tiles with no gaps. <br><br> An obvious easy case is to use a square tile. But are there others?<br><br> There are indeed, and some can be quite surprising. Like this one, using a tile in the shape of a convex pentagon. Yes, all the tiles are identical. There is only one shape used here. And the tiling is perfect with no gaps.<br><br> This tiling was only discovered in 2015 using computer searches. So if you plan to tile your bathroom floor, and you want something really rare this is it!<br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-k-czkaH27A8/YDF3wBxqPTI/AAAAAAAAKMk/Voh1VqiUOrcz9h-_6if5tcB6XAvQYGVrACLcBGAsYHQ/s716/convex-pentagon.png" style="display: block; padding: 1em 0; text-align: center; clear: left; float: left;"><img alt="" border="0" width="400" data-original-height="201" data-original-width="716" src="https://1.bp.blogspot.com/-k-czkaH27A8/YDF3wBxqPTI/AAAAAAAAKMk/Voh1VqiUOrcz9h-_6if5tcB6XAvQYGVrACLcBGAsYHQ/s400/convex-pentagon.png"/></a></div><br><br><br><br><br><br><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-12943925661868941862021-02-13T14:03:00.005-08:002021-02-27T14:24:08.784-08:00How the Pfizer and Moderna Vaccines work <font size="4"> <b>How the Pfizer and Moderna Vaccines work</b><br><br> You've probably seen pictures of the Covid Virus with lots of spikes on the surface. These are proteins that let the virus trick a human cell and get inside. Once inside it replicates. When all the copies of the virus leave the human cell, in search of other cells to infect, the human cell is killed. Good for the virus. Bad for the human.<br><br> So the spikes are essential for the virus to operate. The Pfizer and Moderna Vaccines uses this to their advantage. They consist of a snippet of the virus genetic code - the exact snippet that tells how to produce these spikes.<br><br> When the vaccine is injected your cells read the snippet and start manufacturing spikes. This fools your immune system into thinking it's being attacked by the Covid virus. It's not, because the snippet of genetic code is harmless and can only make spikes and not the complete virus. But your immune system is not sure, so it goes ahead and manufactures the antibodies to disable the Covid virus.<br><br> These antibodies remain in your system. So if the real Covid virus comes along they will kill it.<br><br> The vaccine does not kill the virus. It simply preps your immune system to do the job.<br><br> <a style="text-decoration:underline" href="https://ncov2019.live/data">Coronavirus Worldwide Stats</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-31663097525697014732021-01-11T09:24:00.019-08:002021-01-25T12:44:13.928-08:00FreshDirect - Join now and get $50 <font size="4"> <b>FreshDirect - Join now and get $50</b><br><br> I just joined FreshDirect. It's a delivery service for food and wine. The choice is amazing - fresh fruit, vegetables, meat, poulty, seafood, beer and wine.<br><br> And for those who don't want to cook they also offer prepared food and party platters!<br><br> Join now and get $50 off your first order (order must be $99 or more). <br><br> Just click below to join and then use code: FDJAN22 when checking out. <br>Offer EXPIRES Feb 17, 2021<br><br> <b><a style="text-decoration:underline" href="https://www.freshdirect.com/invite/1/abbottsystemsabbottsystems">FreshDirect - Join now and get $50</a></b><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-70272778672144882502021-01-03T06:03:00.026-08:002021-03-04T08:22:19.881-08:00The US, COVID and WW2 <font size="4"> <b>The US, COVID and WW2</b><br><br> US Covid deaths (to date) - 518,000<br>US Deaths in WW2 - 418,500<br>Updated: March 4, 2021<br><br> <b>How the Pfizer and Moderna Vaccines works</b><br><br> You've probably seen pictures of the Covid Virus with lots of spikes on the surface. These are proteins that let the virus trick a human cell and get inside. Once inside it replicates. When all the copies of the virus leave the human cell, in search of other cells to infect, the human cell is killed. OK for the virus. Bad for the human.<br><br> So the spikes are essential for the virus to operate. The Pfizer and Moderna Vaccines uses this to their advantage. They consist of a snippet of the virus genetic code - the exact snippet that tells how to produce these spikes.<br><br> When the vaccine is injected your cells read the snippet and start manufacturing spikes. This fools your immune system into thinking it's being attacked by the Covid virus. It's not, because the snippet of genetic code is harmless and can only make spikes and not the complete virus. But your immune system is not sure, so it goes ahead and manufactures the antibodies to disable the Covid virus.<br><br> These antibodies remain in your system. So if the real Covid virus comes along they will kill it.<br><br> The vaccine does not kill the virus. It simply preps your immune system to do the job.<br><br> <a style="text-decoration:underline" href="https://ncov2019.live/data">Coronavirus Worldwide Stats</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-73245985167233477482020-12-24T08:04:00.022-08:002021-02-13T14:02:27.067-08:00Vaccine 101 - How the Pfizer and Moderna Vaccines work <font size="4"> <b>Vaccine 101 - How the Pfizer and Moderna Vaccines work</b><br><br> You've probably seen pictures of the Covid Virus with lots of spikes on the surface. These are proteins that let the virus trick a human cell and get inside. Once inside it replicates. When all the copies of the virus leave the human cell, in search of other cells to infect, the human cell is killed. OK for the virus. Bad for the human.<br><br> So the spikes are essential for the virus to operate. The Pfizer and Moderna Vaccines uses this to their advantage. They consist of a snippet of the virus genetic code - the exact snippet that tells how to produce these spikes.<br><br> When the vaccine is injected your cells read the snippet and start manufacturing spikes. This fools your immune system into thinking it's being attacked by the Covid virus. It's not, because the snippet of genetic code is harmless and can only make spikes and not the complete virus. But your immune system is not sure, so it goes ahead and manufactures the antibodies to disable the Covid virus.<br><br> These antibodies remain in your system. So if the real Covid virus comes along they will kill it.<br><br> The vaccine does not kill the virus. It simply preps your immune system to do the job.<br><br> <a style="text-decoration:underline" href="https://ncov2019.live/data">Coronavirus Worldwide Stats</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-43544996211193633112020-12-19T09:15:00.007-08:002021-02-19T09:26:54.631-08:00Adding a Duality to The Standard Model<font size="4"> <b>Adding a Duality to The Standard Model</b><br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-CkUQx06DwPY/X941k4vTRQI/AAAAAAAAKHA/gQtZ7zXVDtgd2_IBTj024PvfpZ7lKtIEwCLcBGAsYHQ/s240/standard-model.png" style="display: block; padding: 1em; text-align: center; clear: left; float: left;"><img alt="" border="0" width="400" data-original-height="230" data-original-width="240" src="https://1.bp.blogspot.com/-CkUQx06DwPY/X941k4vTRQI/AAAAAAAAKHA/gQtZ7zXVDtgd2_IBTj024PvfpZ7lKtIEwCLcBGAsYHQ/s400/standard-model.png"/></a></div><br><br> I would like to make a conjecture. It says: every elementary particle in the Standard Model (except the Higgs) of spin s has a dual partner of spin 1/s. <br><br> So the fermions (spin 1/2) in the Standard Model would have spin 2 dual partners and the bosons (spin 1) in the Standard Model would be their own dual.<br><br> Of course, for this to work we need to have at least one spin 2 particle. Maybe many more. So gravity appears automatically. <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-40899949558466306212020-12-12T14:53:00.003-08:002020-12-12T14:57:53.398-08:00Covid Vaccination - The Numbers <font size="4"> <b>Covid Vaccination - The Numbers</b><br><br> I like to estimate systems by doing "back of the envelope" calculations. <br><br> My latest is on vaccinations. <br><br> The US population over 18 years of age is approx 248 million and lets assume 75% get vaccinated (each needs 2 doses) so that's a total of 372 million doses. Now let's suppose the US does this with one giant drive-through with 5,000 lanes!!! It takes 5 mins for one inoculation (including paperwork) and it runs 24/7. <br><br> Then it would take about 8 months to complete vaccinations!!!!!<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-11173385851765704592020-12-10T08:27:00.002-08:002020-12-10T12:07:25.145-08:00Gravity in One Dimension<font size="4"> <b>Gravity in One 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 Gravity in Lineland? <br><br> Consider Newtonian Gravity. 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 Newtonian 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? <br><br> 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? <br><br> How do things change as the number of point masses in Lineland changes? <br><br> It turns out that even one dimension can be very complex! <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-30850825254571912582020-11-30T07:11:00.002-08:002020-11-30T07:11:51.571-08:00Lineland - Life and Physics in 1 Dimension<font size="4"> <b>Lineland - Life 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? <br><br> Consider Newtonian Gravity. 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 Newtonian 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? <br><br> 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? <br><br> How do things change as the number of point masses in Lineland changes? <br><br> It turns out that even 1 dimension can be very complex! <br><br> Just think, there's probably a 4D world somewhere with physics teachers looking for a nasty problem to set on an exam. Finally they come up with one, "explain how physics would have developed if our world was constrained to only 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>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-36828008033284573252020-11-30T06:34:00.003-08:002020-11-30T06:37:47.285-08:00Mathematical Analysis - A Book with a Story<font size="4"> <b>Mathematical Analysis - A Book with a Story</b><br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-XcekR8b6vR0/X8UCxMOPbtI/AAAAAAAAKFs/p5y4p0TzVIEIlGHwmG2xD-LgjSpIV9C0wCLcBGAsYHQ/s2048/math-book-scott.jpg" style="display: block; padding: 1em; text-align: center; clear: left; float: left;"><img alt="" border="0" height="320" data-original-height="2048" data-original-width="1536" src="https://1.bp.blogspot.com/-XcekR8b6vR0/X8UCxMOPbtI/AAAAAAAAKFs/p5y4p0TzVIEIlGHwmG2xD-LgjSpIV9C0wCLcBGAsYHQ/s320/math-book-scott.jpg"/></a></div> When I studied mathematical physics at Sussex University back in 1967-70 one of my math professors was Bernard Scott. <br><br> I remember his lectures well and I bought the course book, "Mathematical Analysis - An Introduction" - which was by him. That was that. <br><br> Then just recently, over 50 years later, I learn that Scott was one of the codebreakers at Bletchley Park during WW2. He broke the Soviet Comintern code in late 1943.<br><br> I still have his book, the very copy I purchased from the university bookstore on Oct 10, 1967.<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-23034236200987744382020-11-13T14:41:00.012-08:002020-11-13T15:04:07.447-08:00Sailing Ships - A Radical New Design <font size="4"> <b>Sailing Ships - A Radical New Design</b><br><br> <div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-SMMt5jwFys8/X68OsXuAtuI/AAAAAAAAKEQ/oj7btzWcL_QyzzuDjc9uIhZDcrD8u1ZowCLcBGAsYHQ/s900/ship-wind-powered.jpg" style="display: block; padding: 1em; text-align: center; clear: left; float: left; margin-right: 1em;"><img alt="" border="0" width="400" data-original-height="506" data-original-width="900" src="https://1.bp.blogspot.com/-SMMt5jwFys8/X68OsXuAtuI/AAAAAAAAKEQ/oj7btzWcL_QyzzuDjc9uIhZDcrD8u1ZowCLcBGAsYHQ/s400/ship-wind-powered.jpg"/></a></div> Blowing in the Wind. A new generation of sailing ship will use giant aerofoils instead of conventional sails. <br><br> The ship will do transatlantic runs in 12 days using 90% less fuel.<br><br> The first one is planned to go into service in 2024. It will be a car transporter with capacity for 7,000 cars.<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-25578569622386168692020-11-12T09:13:00.001-08:002020-11-12T09:13:04.900-08:00Dark Matter - Is Dark Matter Sterile Neutrinos? <font size="4"> <b>Dark Matter - Is Dark Matter Sterile Neutrinos?</b><br><br> Dark matter is still a mystery, but sterile neutrinos may be the answer.<br><br> Let's model the topological aspects of the graviton using a simple paper strip.<br><br> Give it 4 half twists and then join the ends. One half twist correcponds to spin 1/2 so 4 half twists gives spin 2 which matches the graviton.<br><br> But this simple paper strip has a very interesting property. It can "flip" into a double thickness paper strip with just one half twist. That's a spin 1/2 fermion.<br><br> This fermion is oviously neutral and interacts only with the gravitational field, because it's just an "oscillation" of the graviton. All elementary fermions have mass, so it's a good bet this particle has mass. <br><br> The sterile neutrino is like a neutrino, but it's not a neutrino. So it does not violate the 3-generation heirachy of the Standard Model. And things get even better..<br><br> The sterile neutrino is the perfect candidate for dark matter.<br><br> But it will be incredibly difficult to detect. They don't call it dark matter for nothing.<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-2717766017894554002020-11-02T07:53:00.009-08:002020-12-26T14:59:14.083-08:00Sterile Neutrino not a Neutrino? <font size="4"> <b>Sterile Neutrino not a Neutrino?</b><br><br> Sterile neutrinos may be something way more interesting.<br><br> Let's model the topological aspects of the graviton using a simple paper strip.<br><br> Give it 4 half twists and then join the ends. One half twist corresponds to spin 1/2 so 4 half twists gives spin 2 which matches the graviton.<br><br> But this simple paper strip has a very interesting property. It can "flip" into a double thickness paper strip with just one half twist. That's a spin 1/2 fermion.<br><br> This fermion is oviously neutral and interacts only with the gravitational field, because it's just an "oscillation" of the graviton. All elementary fermions have mass, so it's a good bet this particle has mass. <br><br> The sterile neutrino is like a neutrino, but it's not a neutrino. So it does not violate the 3-generation heirachy of the Standard Model. And things get even better..<br><br> The sterile neutrino is the perfect candidate for dark matter!<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-31599583449944846162020-10-08T06:34:00.003-07:002020-10-28T07:20:49.438-07:00Entropy of the Prime Numbers <font size="4"> <b>Entropy of the Prime Numbers</b><br><br> The Prime Number Theorem is one of the most famous theorems in mathematics. It tells us something about the distribution of the prime numbers.<br><br> How many of the first n integers 1,2,3,4,....,n are prime? The Prime Number Theorem says the number of primes is approximately n/log(n) where the log is base e.<br><br> This is not an exact count, n/log(n) is only an approximation, but as n gets bigger the approximation gets better and better.<br><br> Let's use the change of base formula for logarithms to convert this to log base 2. So we get n*log(e)/log(n) where the logs are now base 2. <br><br> The Prime Number Theorem is also a statement about the Shannon Entropy of the primes! Here's how..<br><br> Suppose you have a machine with a big red button. Each time you punch the button the machine responds by displaying an integer in the range 1,2,3,....,n. After much experimentation you discover that the probability of getting integer j is pj. Then physics defines the Shannon Entropy (also called Information Entropy) of this machine as..<br><br> Shannon Entropy=(-1)*sum (pj*log(pj)) for j=1,2,3,...,n and the log is base 2.<br><br> In the special case where all numbers occur with equal probability pj=1/n for all j and we get the famous result for the Shannon Entropy of the machine..<br><br> Shannon Entropy=(-1)*n*(1/n)*log(1/n)=log(n)<br><br> Now imagine this is "distributed" equally across all numbers, so on average an individual integer has log(n)/n entropy.<br><br> If the integers 1,2,3,....,n contain m primes then the Shannon Entropy of the primes is simply m*log(n)/n<br><br> But the prime number theorem says that m=n*log(e)/log(n) approximately. So the approximate Shannon Entropy becomes.. <br><br> Shannon Entropy=m*log(n)/n=log(e)<br><br> and as n approaches infinity this approximation becomes exact. So we can say.. <br><br> "The Shannon Entropy of the Primes is log(e)=1.442695.."<br><br> This statement is equivalent to the prime number theorem. How strange!<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-34148713191882209282020-09-27T09:48:00.003-07:002020-09-27T09:53:39.090-07:00Coronavirus - Stats and Predictions for the US <font size="4"> <b>Coronavirus - Stats and Predictions for the US</b><br><br> The current prediction is for 371,000 US deaths by the end of 2020. But note what happens if mandates are removed - the prediction skyrockets. <br><br> Here's the chart..<br><br> <a style="text-decoration:underline" href="https://covid19.healthdata.org/united-states-of-america?view=daily-deaths&tab=trend">Coronavirus - Stats and Predictions for the US</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-16747446380526468692020-09-26T07:07:00.008-07:002020-09-27T06:00:32.029-07:00Goldbach's Conjecture and Mirror Symmetry<font size="4"> <b>Goldbach's Conjecture and Mirror Symmetry.</b><br><br> Goldbach's Conjecture implies the primes have a limited mirror reflection symmetry. It's easy to see this..<br><br> Let n be any even integer >2. Then consider the sequence 1,2,3,..., (n-1)<br><br> Since n is even (n-1) is odd so the sequence has an integer at the center. Take the right hand side of the sequece and reflect it through the center and then add pairs of numbers. All pairs add to n.<br><br> Godldach's Conjecture implies there must be at least one prime on the right hand side that reflects into a prime on the left hand side.<br><br> That's a limited reflection symmetry for the primes.<br><br> Or to put it another way.. under this reflection operation primes can never totally avoid each other.<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-59055910724916148582020-08-29T06:18:00.001-07:002020-09-26T06:15:42.562-07:00Einstein - The Path to General Relativity<font size="4"> <b>Einstein - The Path to General Relativity</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.com