Category Archives: Science
To start the last week of March Mathness, because it’s a Monday, I’m going to go easy on y’all with some light, easy topics. (Maybe I can lull you into paying attention for the major topic of the month: matrix rotation.)
It has occurred to me that, if I’m talking about math in March, I absolutely must mention one of my all-time favorite mathematical objects, the Mandelbrot. I’ll try to get to that today, but the main topic is a simple something that I ran into while working on my 3D model of the big island of Hawaii.
The question was: How many miles are there per degree of latitude?
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10 Comments | tags: circle of latitude, cosine, Earth, latitude, longitude, Mandelbrot, Maths Town, nautical mile, radius | posted in Math
Last week we celebrated Albert Einstein’s birthday (he turned 140). Now we need another cake so we can celebrate the other March major mathematician’s birthday — Emmy Noether turns 137 today.
To my regret, despite that I frequently invoke her name (she co-starred with Albert in the Special Relativity series), her work in mathematics is pretty far above my head, and I’m simply not qualified to write about it. I can say that her work connects mathematical symmetry with physical conservation laws. She also made significant contributions to abstract algebra.
Just recently, I’ve begun to nibble at the edges of the latter in the form of group theory as a part of studying rotation.
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21 Comments | tags: algebra, cube, Emmy Noether, group theory, mathematics, rotation, square, tesseract | posted in Math
Back at the start of March Mathness I promised the math would be “fun” (really!), but anyone would be forgiven for thinking the previous two posts about Special Relativity weren’t all that much “fun.” (I really enjoy stuff like that, so it’s fun for me, but there’s no question it’s not everyone’s cup of tea.)
Trying to reach for something a bit lighter and potentially more appealing as the promised “fun,” I present, for your dining and dancing pleasure, a trio of number games that anyone can play and which might just tug at the corners of your enjoyment.
We can start with 277777788888899 (and why it’s special).
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4 Comments | tags: 277777788888899, algorithm, calculation, Collatz conjecture, computation, Mandelbrot, mathematics, multiplicative persistence, Numberphile | posted in Math
In the March Mathness post I mentioned that one reason I love March is that it contains the Vernal Equinox, the official astronomical start of Spring. More importantly to me, it means six months of more daylight than darkness, and as much as I’m a night person, I prefer long, sunny days.
Well, today is the day! The equinox happened at 21:58 UTC (two minutes before 5:00 PM locally). What’s better is that, after all the miserable bitter cold and all that snow in February and into March, the weather is indeed finally turning. Deeply embedded in our mythologies is the idea of spring rebirth; New Year’s parties aside, this, today, is the true new year.
And the forecast is for muon showers!
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17 Comments | tags: Albert Einstein, equinox, muon, Special Relativity, spring, spring equinox, tau, vernal equinox | posted in Physics
Speaking of Special Relativity, back when I wrote the SR series, one topic I left along the wayside was the concept of the spacetime interval. It wasn’t necessary for the goals of the series, and there’s only so much one can fit in. (And back then, the diagrams I wanted to make would have been a challenge with the tool I was using.)
But now that we’re basking in the warm, friendly glow of March Mathness and reflecting on Special Relativity anyway, it seems like a good time to loop back and catch up on the spacetime interval, because it’s an important concept in SR.
It concerns what is invariant to all observers when both time and space measurements depend on relative motion.
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7 Comments | tags: Albert Einstein, faster than light, frame of reference, light, light speed, simultaneity, spacetime, Special Relativity, speed of light | posted in Physics
Earlier, in the March Mathness post, I mentioned Albert Einstein was born on March 14th. That’s also Pi Day, which deserved its own pi post (about pizza pi), so old Al had to wait for me to address a topic I’ve needed to address for several months.
To wit: Some guy was wrong on the internet.
That guy was me.
Back in 2015 (also celebrating Einstein’s birthday), I wrote a series of posts exploring Special Relativity. Near the end of the series, writing about FTL radio, I said (assuming an “ansible” existed) I wasn’t convinced it violated causality if the frames of reference were matched.
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13 Comments | tags: Albert Einstein, ansible, causality, causality violation, faster than light, frame of reference, FTL, FTL radio, light, light speed, simultaneity, spacetime, Special Relativity, speed of light | posted in Physics
Happy Pi Day! Order some pizza and use pi to make sure you get the most pie possible! I made a handy chart that may change how you order pizza.
Or not. It’s something I heard about early in the year that caused a minor tweet storm (I’m not on the Twitter, so never saw nothing, which I’m fine with). It centered around how it was often better to order two smaller pizzas than one large one (depending on pricing and assuming your goal is the most pizza possible per peso).
Since pi is involved in this pizza pie probe, I thought it would make a fun topic for Pi Day (not to mention March Mathness).
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15 Comments | tags: normal number, normal sequence, pi, pi day, pizza | posted in Math
Time for math!
I have a special fondness for the month of March. For one thing, it contains the Vernal Equinox — one of my favorite days, because it heralds six months of light. (As a Minnesotan, Spring has much more impact than it did when I lived in Los Angeles.)
March is when the weather elves begin preparing for the April Showers that create May Flowers. It’s when baseball Spring Training is in full swing with the regular season looming (lately, even at the end of the month; this year on the 28th).
It also contains some important birthdays: Albert Einstein (3/14) and Emmy Noether (3/23), to name two, and in their honor I have myriad math posts planned!
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11 Comments | tags: 3Blue1Brown, Albert Einstein, complex numbers, Emmy Noether, mathematics, Mathologer, Numberphile, tesseract | posted in Math
On the one hand, a main theme here is theories of consciousness. On the other hand, it’s been almost eight years blogging, and I’ve covered my views pretty well in numerous posts and comment threads. Our understanding of consciousness currently seems stuck pending new discoveries, either in answering hard questions, or in providing entirely new paths.
A while back I determined to step away from debates (even blogs) that center on topics with no resolution. Religion is a big one, but theories of mind is another. Your view depends on your axioms. Unless (or until) science provides objective answers, everyone is just guessing.
But it’s been three-and-a-half years, and, well,… I have some notes…
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8 Comments | tags: AI, brain, brain mind problem, chaos theory, Cogito ergo sum, computationalism, computer model, computer program, consciousness, human brain, human consciousness, human mind, information theory, Isaac Asimov, mind, stored program computer, Theory of Consciousness, Von Neumann architecture | posted in Computers, Opinion, Science
Folded into the mixed baklava of my 2018, was a special mathematical bit of honey. With the help of some excellent YouTube videos, the light bulb finally went on for me, and I could see quaternions. Judging by online comments I’ve read, I wasn’t alone in the dark.
There does seem a conceptual stumbling block (I tripped, anyway), but once that’s cleared up, quaternions turn out to be pretty easy to use. Which is cool, because they are very useful if you want to rotate some points in 3D space (a need I’m sure many of have experienced over the years).
The stumbling block has to do with quaternions having not one, not two, but three distinct “imaginary” numbers.
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19 Comments | tags: complex numbers, math theory, mathematics, natural numbers, number systems, numbers, octonion, quaternion, real numbers | posted in Math, Sideband
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