General Discussion > Mathematician of the Week

MoTW #7 'Eylan Ayfalulukanä


`Eylan Ayfalulukanä:
'Eylan Ayfalulukanä is this weeks Mathematician of the Week! Seykxel sì nitram! 'Eylan Ayfalulukanä has been paired with James Clerk Maxwell

1. Who are you?
Spoiler- What is your name?
- Where are you from?
- How old are you?
These are just a few intro questions just so we know who you are.My real name is Tim Stoffel, although many folks just call me 'Timba'. I live in Reno, Nevada, in the United States. I am 50 years of age, one of the older folks here on LearnNavi.

2. What brought you to the Mathematics and Statistics board?
SpoilerWere you recommended/invited here by someone? Or did you simply stumble upon it by yourself?I remember the inital discussion about creating this board, and remember first dropping in just after it was created. Although I have not been here a lot, I do check it from time to time, as there is often something interesting posted here.

3. For how long have you liked Math?
SpoilerWhen did you realise that you either enjoyed it or were good at it?I have always enjoyed math to one extent or another. I knew very early on, even as a preschooler, that a scientific or technical career was for me (although I did dream of being a professional football player for several years, until I found that running the scoreboard and videotaping the games (with an open reel VTR, if any of you remember those) was more fun than actually playing.)

4. What subjects/jobs do you do which involve Math? What do you do?
SpoilerTo tell us how you use the knowledge you have!I am a broadcast engineer by trade. This field uses a lot of different kinds of math-- algebra, trigonometry, analytic geometry, complex numbers, even some calculus. As an amateur radio operator, I use much of the same math that I use at work. Astronomy is another favorite hobby, that often involves understanding very large numbers-- and relating these numbers to the public in a meaningful way. I also study a lot of theoretical physics for enjoyment and education, and this uses a bewildering amount of math. I am also involved with zookeeping, which can sometimes involve math when dealing with medicine doses, and portioning out the available food for the day between 18 different animals. Lastly, I enjoy recreational mathematics-- puzzles and games involving math.

5. What Math-related subjects did you take in High School? Or if you are a student, what are you currently studying?
SpoilerState what the course is about and whether or not you enjoy it.I took all the math I could in High School-- Algebra, Trigonometry, analytic geometry, stopping just short of calculus. In place of calculus, I did an independent study program in digital design (which invloved a lot of Boolean algebra), and was one of only three or four students in the school who had access to the school's computer terminal (the personal comuter was just being invented at the time, and I had use of the only TRS80 model 1 in town). Another thing that came from 'skipping calculus' was the ability to work with a college-level professor who was my zoology teacher. All of this High School experience has much more than made up for the decision to 'skip calculus'.

6. What is your favourite number? Why?
SpoilerIs it your lucky number? Date of birth? How did it come to be your favourite number?This is a very good question. I would say that it is 777. That is a number associated with God, Jesus Christ, perfection, and other good things. There is a very interesting numerologic connection between 37, 111, 777 and 888, and this has always been a source of endless fascination for me. Other favorite numbers include pi, the fine structure constant, 3579545 (the analog TV color subcarrier frequency) and 10762238 (the ATSC digital TV symbol rate) (as a challenge, see if you can figure out the relationship between 3579545 and 10762238, keeping in mind that there are 525 lines and 60 fields in an NTSC TV signal, nad that all important integer values in NTSC (except 3579545) are actually those vlaues multiplied by the ratio 1000/1001).

7. Who is your favourite Mathematician/Scientist. Why?
SpoilerHave they motivated you to continue your studies? How have they influenced you? What do they do?There are several, but I think that James Clerk Maxwell stands out as a favorite. He was responsible for describing the electromagnetic nature of light, and what we know today as the electromagnetic spectrum. A great deal of modern physics is based on his work, and the use and manipulation of electromagnetic energy keeps me very gainfully employed!

8. What is your favorite function in math and why?
SpoilerDo you think it's very aesthetic or funny?My favorite mathemeatical function is the Bessel functions. They are used to describe several processes that go on in frequency modulation of an continuous-wave RF carrier. One consequence of Bessel functions is there are certain combinations of frequency and level of a modulating signal that make the carrier disappear, leaving only sidebands. This allows one to very precisely set modulation levels in FM systems. Incidentally, this applies to FM used both in radio, and the FM modulation used in analog videotape recorders. (My best friend Charlie Anderson invented FM modulation for videotape systems way back in 1954!)

9. Three statements about yourself - True or false? - The community has to answer
SpoilerWhatever you want - but at least one of them must be true. Keep the answers secret until the end of your reign.1. I have been in the tunnel of the Large Hadron Collider in France/Switzerland.
2. Math was my weakest acedemic subject in school (gym class was my worst subject overall!).
3. I know Pi to 65 places.

10. Pi or Tau?
SpoilerWhich do you prefer? Why?I would have to say Pi. I have always been fascinated by irrational/transcendtal numbers, but Pi particularly fascinates me. That said, Tau (2pi) comes up far more often in the math I do, as it is an important part of many electronic equations having to do with reactance and waves.

11. Do you prefer to work in degrees or Rads?
SpoilerWhy?For most of what I do, degrees are more appropriate, but I have no trouble at all with radians (see answer 10)(I also appreciate the elegance of how all the trig functions were derived). Most of the computer programming I have done (BASIC and a little C) uses trig functions that only work with radians, so I understand how to easily interconvert between the two. I also seem to remember I recently had to work some problem that used grads. I find overall that trig is the most common higher math that I need to use.

12. Calculatorly or manually?
SpoilerDo you prefer to solve your problem (especially in Calculus) using a calculator or your patience and skill?Calculator, definitely (I also collect scientific calculators). But I do know how do much of what I need to do by hand if need be. I remember one interesting incident that occurred in my high school trig class. Scientific calculators (affordable ones, anyway) were still fairly new in those days. Our teacher wanted us to use trig tables and linear interpolation to get our trig function values. I was one of a small group of students that had access to the school's TI-59 programmable calculators (and evetually had a TI-58 of my own, one of the best gifts I ever got!). I got sick and tired of doing the linear interoplation calculations every time I needed a trig function. So, I wrote a program for the TI-59 that would figure out trig functions by linear interpolation. The teacher was so impressed (and she was one of the best teachers I had in all of High School) that I had gone to all that effort that she finally let me just use the calculator to 'normally' derive trig functions!

13. Joke time!
SpoilerCome up with your best Math joke. No sourcing!There was a physicist, a biologist and a mathemitician that enjoyed having lunch together. One day, they went to their favorite restaurant, and got the booth by the front window. While they were waiting for their food, they were watching a house across the street from the restaurant. As they were watching, two people entered the house. A little later, three people left the house. Commenting on the difference between the number of people who entered and left the house, the physicist said 'The difference must be due to the choice of our frame of reference'. The biologist remarked 'No, you have it all wrong. The people must have reproduced while in the house'. The mathemitician said, 'Wow! You both got it wrong. If exactly one person now enters the house, the house will be empty'.

14. Do you feel the temptation in tests to write your justifications in Na'vi?
SpoilerHave you? If so, when and why?Avatar wasn't even an idea in James Cameron's head the last time I had to write a justification! (The justifications I write now are more along the lines of 'we need this money because.... and the required math is crude ;) ) However, I do find myself writing more and more things in Na'vi. Just today, I labelled a patch panel in both English and Na'vi!

15. Do you like Physics too?
SpoilerIf you don't, get out.sunu nìwotx nang I closely follow the Large Hadron Collider, the LEGO project, our very own Zebra Z pinch machine here in Reno, and many other physics and astrophysics projects. My interest in advanced physics is making me go back and learn a lot of higher math like calculus, linear algebra, tensors, etc. I am not all that good at that kind of math, but I understand it well enough now that I can follow along with understanding in the texts. Working on a University campus gives me access to classes that I will soon be able to take for next to nothing that will strengthen my higher math skills (if linguistics will not crowd them out now!).

16. Real-Life Picture (Optional)
SpoilerWho beest thou?

17. Do you have any other hobbies?
SpoilerNo matter how strange they may be...I think I compensate for my parents, who had no hobbies to speak of! In addition to my paid job as a television engineer, I do enginering work on the side for a number of small Christian radio stations. I just installed some TV translators for the little town of Schurz, Nevada. I was able with their cooperation, to try some new techniques that have given them some of the best TV coverage in the State. My main non-work interest is working with big cats, especially lions and ligers. Besides helping care for these animals at our local zoo, I work to protect people's ability to responsibly keep exotic animals in various non-public settings. Next would be astronomy. A series of unexpected circumstances have landed me in the President's spot in our local club, the Astronomical Society of Nevada. I have my own 8 inch 'scope, as well as group use of the club's 'scopes. (This is going to be a big year for us, with three big astronomical events here in Reno in the next seven months.) I am an amateur radio operator, with the call NS9E. I am not nearly as active as I used to be, as work and the zoo take most of my spare time. I collect old electronic equipment, especially broadcast gear. I just recently got a TV transmitter that I am installing in the collection in my living room. I am an enthusiast of music for the pipe organ, especially the classical repritorie. Reno has a particularly active organ community, and it is great to be an acive part of it. (I do not play, but I understnad the history, physics and technology of the organ very well). Lastly, I spend a lot of time now learning Na'vi and participating with the community here. Besides Na'vi, I am also learning Dothraki and Klingon. So, I really don't have a lot of spare time to do things like eat and sleep ;)

18. This is the story
SpoilerType no more than one sentence. The proceeding Mathematician of the week will then type another sentence continuing the story. A stickied thread can be found showing the story's progress hitherto.After that last 'waking', I really, really hoped that these dreams weren't recursive!

Congrats! It's sad that this board gets so little attention, your post was quite interesting to read.

My guess:

Txantslusam Skxawng:
Congrats 'Eylan Ayfalulukanä, sorry I reacted so late... I am having bad internet at home.... I barely can visits any websites now...

My guess also is F/T/F

`Eylan Ayfalulukanä:
Still trying to find a new MoTW. If you are interested, PM me off-list.

`Eylan Ayfalulukanä:
I guess my time as MoTW has finally come to an end. I have located a worthy (and eager) sucessor who will very shortly take over. So, here are the answers to my N/T questions, along with an explanation (with math) of my question in question 6.

1. Tsleng (I had to get some Na'vi in here somewhere  ;) ) I only wish I could visit the Large Hadron Collider, and get the 'cook's tour'. BTW, just hours ago, they completed the 2011 run of the machine, and they now will be in maintenance mode until February or early March of next year.  The 2011 LHC run exceeded all expecatations!
2. Ngay I struggled to keep a high B average in math in school. But I am really glad I stuck with it. I had straight A's in all the sciences, and high B's in all other academic subjects. I took an F in film study, but only because my film project was a total botch (and now I work in TV!). I hated gym class, as I do not have any athletic prowess at all!
3. tsleng I do know pi to 55 places though.... and I add another five digits every year or so.

Now, the question about the analog TV subcarrier frequency vs the ATSC digital TV symbol rate.

Back in the 1950's, they determined one of the efficient ways to do compatible color TV was to encode the color information onto a subcarrier. The amplitude of this subcarrier determined how bright the color is, and the phase angle of the subcarrier, compared to a reference signal called 'burst', determines hue. The PAL system, used in Europe and many other places, works in a similar manner.

The subcarrier frequency had to be chosen carefully, so its sidebands in baseband video would fall in between the luminance sidebands, which tended to cluster around multiples of the horizontal line rate, which at the time was 15,750 Hz. Bu using a subcarrier frequency that was an odd multiple of half the line rate, this was achieved. In the case of the original NTSC color scheme it was 455/2, or 262.5 times the horizontal line rate. This worked out to 3,583,125 Hz. In the lab, this all worked great.

In the field though, they discovered a disturbing beat between this subcarrier frequency and the sound subcarrier at 4.5 MHz baseband. The fix was to slightly change the sound subcarrier frequency. But then, politics ensued. All the TV repairmen in the US pointed out that this might (they never proved it, though) require every existing TV set in the US to have its sound IF system realigned. So what they did instead, is multiplied the horizontal line rate by a slight offset, equal to just 1000/1001. this gave a new horizontal line rate of  17,734.2657 Hz. This resulted in a field rate of 59.9401 Hz, and a color subcarrier frequency of 3,579,454.454545.... Hz, the subcarrier frequency we have today. Broadcasters yelled and screamed, as they had to purchase very expensive (at the time they had to use tube electronics, now we do it with a single chip) crystal controlled synchronizing generators instead of just using the AC line frequency.

Since these frequencies are all related to each other, they can be derived from each other with digital dividers (broadcasters were using digital electronics long before anyone else except computer folks). And the networks decided that they would use atomic clocks to provide stable signals to their affiliates across the country. This allowed them to have a stable reference for their synchronizing generators. To derive the color subcarrier frequency, they took the 10 MHz standard frequency of their atomic clocks and divided it by 2 to get 5 MHz. Then, 5 MHz*63/88 yielded exactly 3,579545.454545.... Hz For years, you could calibrate your frequency counter by counting the phase-locked color subcarrier in any TV set. (nowdays, due to digital frame synchronizers, and digital transmission, this is no longer true. But many broadcasters, us included, derive our synchronizing signals and carrier frequencies  from a GPS-derived frequency standard, which is very nearly as good as an atomic clock.)

When ATSC digital TV came along, they needed to have some sort of relationship between the analog and digital TV signals to allow digital comb filters to eliminate interference. Plus, this made analog-to-digital conversion easier. So, the digital symbol rate for ATSC was chosen to be 684*analog line rate or 10,762,237.7622 Hz symbols/second. Now, there are two bits transmitted for each symbol, so the data rate is theoretically double this, or  21,5424,475.5245 bits/sec. But there is an overhead here of 188/208 because only 188 bits of the 208 bits in each data packet are used for 'payload' data transmission (the rest are for synchronization and control data). There is also some additional overhead for segment and frame synchronization of the overall RF signal. This amounts to one packet out of every 313 packets. thus, the overall data rate is Fsym*2(312/313)(188/208)= 19,392,658.4598, the oft-quoted data rate of US ATSC digital TV. During actual transmission, a third bit is added to the two bit symbols, so there are actually three bits per symbol during transmission. This third bit is an interesting beast, called a 'trellis code'. It is used to make sure that the transitions between the 8 available levels in the 8VSB transmission system are as distant as practical. This significantly reduces the error rate, and improves the receivability of the signal. This third bit is stripped off before any signal processing is done.

So, this is your math lesson for the day!

Irayo for naming me MoTW!


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