[Independant Discovery] The Pattern in the Sums of Digits of Perfect Squares

I remember sitting in algebra 1 class. In 8th grade, students hadn't been separated out much by ability and so my merciful teacher, Mrs. Parker, was kind enough to overlook the lack of attention paid her by some of us. Those who could afford to let our minds wonder were usually doing something quite nerdy, anyway. My friend, Brilliant Beautiful Beth, and I (take a moment to realize this was a different day and age) passed back and forth better and better (and oftentimes quite entertaining) designs for explosives. My boyfriend, Outstanding Oakland, sat at the back of BBB's row with a compass and a straight edge, sure he could find a method of forming a perfect triangle with only those tools. This is the part where a fraction of polymath readers think, "yeah, that was middle school," and another fraction think, "are these people from the same planet as me?" I assure you, everyone who has abilities in one thing certainly makes up for it by a lack somewhere else...Did anyone ever see me play basketball?

One day, I was playing with perfect squares. I wrote them down:
1, 4, 9, 16, 25, 36, 49, 64, 81...

Something popped out at me, for some reason:
One number was 9
One number was 36, and 3+6=9
One number was 81, and 8+1=9

I thought maybe this was a pattern, so I pulled back focus and looked at the short list again. I noticed that the last digits were:
1, 4, 9, 6, 5, 6, 9, 4, 1
It is a palindrome! (A word a had recently learned at quiz bowl, thank you Mrs. Hughes)
It turns out that I was identifying the diagonal of the Vedic Square.

I wondered what would happen if I continued it:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, (oh, a zero- that was exciting) 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 361…

The final digits went 1 4 9 6 5 6 9 4 1 0 1 4 9 6 5 6 9 4 1 0. I realized that 1 wasn’t the first perfect square- zero was, and so I grouped them: 0 (1496) 5 (6941) 0.

I went back to my original list of perfect squares, and in looking over it, half-heartedly added the digits in each number together (81:8+1=9, 64:6+4=10:1+0=0, etc), and another pattern began to emerge:

1 4 9 7 7 9 4 1 9 1 4 9 7 7 9 4 1 1 1 4 9 7 7 9 4 1 9

(1 4 9 7)-(7 9 4 1) 9 (1 4 9 7)-(7 9 4 1) 1 (1 4 9 7)-(7 9 4 1) 9

Beyond this point, I think displaying more lists of typed numbers will increasingly loose meaning, but you can get the idea by looking at the picture.

This was the first year my school had computers that went on the internet for us. (Yes, I'm that old) I didn't know how to talk about these things, let alone search for them. I showed this to my teacher, who in all fairness, didn't really pay attention. Turn about, of course, is fair play. Magnificent Mum smiled and told me that she loved me and that I was very smart. Otherwise, I set my little discovery aside. Once I got to college, though, it occurred to me to do a web search. Google (the new search engine that trumped yahoo/gopher/askjeeves) gave me two links when I searched it, both of which looked more like programming code than anything I knew how to understand.

Today, I decided to make a blog post, since I already had a scan of the thing that I had written neatly during some general requirement course in college. I re-googled, using the first full iteration of the pattern from the final column in the picture (1 4 9 7 7 9 4 1 9 1 4 9 7 7 9 4 1), and found only two websites that had it in any form: 

Some 2012 Forum Discussion
(btw- LOVE these people! In another life I hope to work for the Lone Gunmen)

A Mathematics Discussion Forum
(love these people, too, hence the totally unnecessary minor in applied mathematics)

Anyway, I figured Polymath Voyage is my bully pulpit, so I thought I'd share. :)

[Sport-Like Activities] Intro to Backpacking Class

In short: I recommend this class for any newbie.

I recently took a free Intro to Backpacking seminar at my local REI. It was packed full of information. The presenter had probably never done it before, as evidenced by the fact that nearly all the tips that weren't off the stock REI power point began with, "And, well, I guess that's it about that. Oh- but- wow, also sometimes..blah-blah-blah..so maybe do that too." Also, it ran roughly an hour over time, but despite the rough presentation, the guy really seemed to know what he was talking about and I (being a total novice) think that I learned a lot. Personally, I'm not sure that I'll ever go backpacking, but I've already applied some of what I've learned to other activities like biking. I've included a rough overview below.

Basic Considerations

• Learn rules of public lands and wilderness area
• Do an overnight practice with gear before a multi day trip
• Avoid game trails- they look like abandoned trails
• Use camp stove instead of campfire
• Talk to a ranger
• Check water availability- can bring filtration system and steripen
• Wilderness and back country use permit if area requires
• Extra batteries steripen, lamp, gps
• 3 season tent
• Down bag compacts better - synthetic handles water better

Essentials

• Clothing Layers
• Long Underware
• Winter cap even in summer
• Rain layers
• Wind resistant shell-primaloft insulation
• Base - polar tech type
• Water
• Food
• 1st aid
• Pocket knife
• Storm proof matches
• Map and Compass - gps can fail
• Head lamp (better led and hands free long life) or flashlight
• Sunglasses and screen
• Emergency Blanket and space blanket
• TP
• Whistle or signal mirror
• 100ft of cord - bear bag, rain fly, spear with knife for fishing

Mainstays: Packs, Bags, and Tents

• Packs
• External Frame
• Older, cheaper moderately heavy loads
• Feels like carrying the load
• Internal Frame
• Load is more balanced, feels like wearing the load
• More freedom and balance
• Size
• Usual 4k-5k cubic inches
• 4-6 pounds (ultra lites <3, loose comfort
• S,M,L - iliac crest to c7 vertebrae, torso length
• Gregory and deuter packs fit women best
• # in pack name is liter size
• How to pack
• Bag in bottom (gear helps compress) stuff/compression sack if necessary
• Water is heavy, so against your back
• Break up tent- poles in outside side pocket
• Tent on top- 1st thing to unpack
• Bags
• Types
• Down (better)- more compact-able, lasts longer, pricier Higher fill number, more compressable, higher weight, smaller feathers
• Synthetic - supposedly does better when wet, but pretty much screwed when it gets wet no matter what.
• Pad
• Open Cell Pad - more comfortable and compact-able
• Closed Cell - warmer, lighter
• R-value - resistance -additive
• Tents
• Up mesh, down weight
• Hoop/Tunnel is lighter
• Tarp- no flors or bug screens
• Bug tents - no rain fly
• Choose a tent ~4 lbs
• 1/2 dome rei old mountain man said good in rain, snow, hail
• Aluminum poles are better than fiberglass

Other Items

• Stove
• Propane - lower altitude
• @ Altitude, international whisperlight - white gas, unleaded - gas- alcohol
• MSR pocket rocket
• Clothes
• Not cotton
• Smart wool best for hiking
• Liners to re-use socks
• Lightweight marmot rain jacket
• Light gloves and balaclava
• Lightweight hiking footwear (gortex)
• Food, Water, Cooking
• Platapus to haul water
• 1L pot for cooking
• 1 bowl, spoon, cup
• Camp suds
• Move dehydrated meals to ziplocs from foil
• Extra batteries
• Pack-towels

Precautions

• 1st Aid Wilderness October
• Trekking poles
• Bears not known to attack groups of 4 or more

Books: Ultralight backpacker and Lighten up

Local Areas:
Beginners: Laurel HIghlands Trail, Racoon Creek State Park
Next: Forbes Park, Quebec Natural Run, Dolly Sods
Advanced: Black forest

Organizations:
Venture Outdoors
WPA Orienteering club
Keystone hiking club
Sierra club

[Video Review] The Beautiful Truth

Unfocused, Generalizing, and Post Hoc Ergo Propter Hoc

A guy in Alaska thought he'd make a documentary, but he wasn't sure what to make it about.  He liked natural stuff and had heard of the Gerson Treatment of diet to combat cancer.  He decided to use his son as a story-telling device (which he doesn't do very well), and filmed some conspiracy nuts that had lost their jobs experts talking about alternative thoughts on... well... all sorts of barely related stuff.  They do, however, manage to demonize the AMA, ADA, FDA, American Cancer Society, Big Pharma, Medical Researchers, ConAgra, Monsanto, vaccines, doctors, dentists, and Nazi's all with one big brush while intermittently infomercialling for the Gerson therapy.

Some issues tackeled are:

• The dangers of fluoride in our drinking water.
  (This is the part where it is pointed out fluoride-scientist-Hodge worked on the A-bomb and that the Nazi's also put fluoride in drinking water)
• The dangers of dental fillings and their associated mercury
• How non-organic and cooked foods have different "energy patterns"
  (This is the part where they show images that demonstrate nothing in particular.)
• Genetically Modified Food dangers
• Difficulty in the casket-making business in dealing with larger bodies.
  (No joke.)

You can see basically the whole thing here.

[Teaching Excellence] Study Skill Tips

Many of my students seem to become really frustrated when they spend a great deal of time studying, but don't get anything out of it.  I asked what they do to study, and it turns out that they have some well-intentioned, but mis-guided ideas about how to study.  Since I've been in school for just about ever, I put together how I've studied to get the most out of my efforts.

Memorizing
This is important in things like Biology.

1. Class Notes
   Organize Take your notes, and rewrite them-organizing them.
   Condense Take your re-written notes, and condense them.  In the condensed form, put a key word or phrase instead a paragraph or list if you already know the information well.  Try abbreviations.  Try anything that works for you to get it into a more manageable amount of information.
   Review your condensed notes, close your eyes, and recite or re-draw/write the info page by page
   Review Sheets Use your condensed notes to make a very condensed version (no more than 4 pages) that you can review easily.
2. Reading the TextTake Notes You already take lecture notes, so you know how best to organize them so you can review them easily. (Some like bullet points, some like paragraphs, some rely on pictures, etc)  Be sure to note any terms or concepts you do not know that aren’t explained in the text to look up and fill in.     (These are extra great if you are not selling back your text and can take them right in the book margins and white spaces!  I also like to highlight related ideas in the same color, then the next idea in a new one.)
   Start with the Introduction If there is one, this is usually where you can find context for what you are studying.
   Read the Section Headings and skim pictures This will give you an idea of the story your chapter is trying to tell you.
   Read the Summary This usually tries to tie the details together and can make mentally organizing as you read a bit easier.   If there isn’t a full chapter summary, sometimes there are section summaries (usually italicized) or section subtitles that will accomplish the same goal.
   Read the Questions This will give you a hint as to what is most important in the chapter.
   Start reading Now you can read the chapter.
   Stop reading Every time a complete thought has been made, look back over it and the notes to make sure you understand.  Look at the previous paragraphs, the next paragraphs, and the section title to orient the information.
   Pictures Carefully study the pictures as they are referred to in the text.  This is vital in biology, as many concepts are incomplete without understanding the accompanying diagrams.
   New Questions As you move from one thought to another, try to think of a question that might be asked about each.  Write that down along with the answer.
   Note Management Follow the same procedure for your book notes as for the class notes.
3. Review
   Plan to meet About 10 minutes before class starts, talk over the chapter with a study group. This will force you to review, listen to, and talk about the information.

Problem-Solving
This is important in things like Math.

1. Class Notes
   Organize Break your notes down by section and concept. Complete the process for each concept before moving on to the next one.
   Theory Copy the theory notes: The definitions and derivations.  Repeat derivation copying (try to not look at the previous copy) until you can do it by heart.  You do not need to understand it fully yet.
   Examples Copy the examples, one by one.  Repeat copying as before. 
   Compare By the end of the section, you should be able to identify the analogous steps between the theory notes and the examples.
2. Reading the Text
   Read Read through the text for the section.  This will help you identify exceptions and other key points about the process.
   Problems (with solutions) Work out problems that have solutions available.
   Problems (with answers) Work out problems that have answers available.
   Problems Work out additional problems for practice.
3. Review
   Practice for Speed Practice problems you have already completed for speed.  On a test, this is what will really help you out!

[Healthy Life] Purees

I fully believe that the best way to get good nutrition is to pick vegetables out of your ground/greenhouse/whatever (assuming it is toxin-free), rinse, and consume.  Ideally, each one would be grown in conditions most conducive to reaching their full nutritional potential.  In a perfect world, the plethora of vegetables, beans, legumes, and fruit on our dinner plates would be both appetizing and satisfying.

But that is not real.  My mum's home cooking was of the McDonald's, Pizza Hut, Kraft Mac 'n Cheese oeuvre and my husband's diet when I met him was composed of chicken nuggets, Doritos, and yet more of the cheesy blue box.  I've been working on improving this, but I have to confess:  I don't like peppers, carrots, celery, asparagus, cauliflower, and all their little friends, though I do pretend most of the time to try to fool myself into eating them.

We do have some veggies with our dinners, but it is just a side, and I have a usual rotation that I use with The Mister- green beans, peas, broccoli, and carrots.  In anything with a red sauce, I hide spinach, which my Aunt Marcie taught me.  She also taught me that I can use applesauce instead of oil when baking. I use brown sugar or molasses instead of white sugar, so that along with the sweetness (and calories) comes at least a little nutritional value.  I add a little pepper or lemon juice to almost everything savory I make, because science suggests that they increase bio-availability (they help your body absorb the nutrients that you ingest).  I cook with olive oil (the good stuff that burns when you take a shot) in place of other oils, butter or margarine.  I keep a refrigerated tub of the stuff for spreading.  You get the picture- I try to make our food as healthy as possible.  Despite this effort, we still probably have higher proportions of meat, carbs, starches, and cheese than we should and not enough of the vitamin-packed vegetables.  The Mister and I aren't that many years off from having kids, so I've been thinking about how to address this, and get us into good habits before little and impressionable people happen.

Enter my friend, Cassandra.  A couple of years ago, she and I were talking about cooking and she told me about Deceptively Delicious and the Sneaky Chef books. The main theme behind these books is to make purees of fruits and veggies, and include them in our regular cooking.  The directions say to make them ahead of time and freeze them.  This sounded great, but when I froze some, I found that I had to thaw the whole thing to get a little out each time.  Not good, as freeze-thaw cycles degrade the good stuff.



Okay, so aliquots it is.  Storage dishes left me lacking when it came to left-overs and took up too much space in my little freezer.  Next came the ziplocs, but wow was that wasteful.  Also, they froze into amorphous blobs that made it difficult to stack and to store other things around them. 

Enter my friend, Stacy.  Stacy has a son, and is a particularly awesome parent, who made her own baby food.  This involved a lot of puree-ing.  I remember her saying that she'd freeze them in her silicon muffin pans, and that it would be the right serving size.  Soooo....

I stole that.

 So we'll see how it goes. 

[Quotation] Study of the Classics

"Hayden and Mozart never studied the classics.  They couldn't.  They invented them."
- Sam Seaborn

[Graduate School] Stolz Rotation

I just completed a rotation in the Stolz Lab.  I did some really neat things there.  I'm not going to blog about techniques or results, but there were a few more general things that I took from this experience that I think are worth sharing. 

Being a leader in your field isn't all that fun.  Solutions that you need are not available for purchase and must be made from scratch each time.  Equipment isn't designed for what you need, so jerry-rigging or modifying mal-adapted machines is often necessary.  Every stride you make is questioned by all those lagging behind you. 

Working in an over-crowded lab cramps my style.  I need my own space- even if it is small- to organize my things and create a lean space with all my post-its and colored pens. I like to think through my experiments at my desk and in my notebook before moving forward. I like to read and study with my notes and primary literature and texts and laptop all accessible. For some this isn't important, but for me it turns out it is.

Life is amazing.  Bacteria can use arsenic instead of phosphorus to build it's DNA.  Others can use arsenic as a terminal electron source in photosynthesis (instead of water).  These little bugs support the Ian Malcom principle of "Life finds a way," demonstrating the versatility of living systems. They live in crazy environments.

Finally, I must bring up that Dr. Stolz is pretty amazing.  He had a Nature publication before finishing graduate school, he has had one since, and he has had two recent Science papers.  He's had projects backed by all the usual suspects, but additionally by groups like the Department of Energy and NASA.  He taught me at the bench, was always happy to make time for my questions, and was flexible with direction when students interest or needs led to a new path.

[Elements of Success] Biotech Seminar

It was billed as a resume session, but it was way better than that.  We met with two people from a smaller biotech company and one from a large company.  From the smaller company we had a business guy and a research guy.  From the larger company was a lady who started out in academia, moved into marketing, and is now in sales.

Notes about the Biotech Industry

• Scale economies have to be achieved when they can be.
• Marketing is very scalable because everything must be marketed.
• Development is moderately scalable.
• Discovery is not scalable.
• In 2011 many drug patents expire.
• Big pharma can't fix their discovery machine, so they turn to smaller ones.
• Small to medium sized companies are where new stuff comes from.  Large companies contract with the smaller ones.

Careers in Biotechnology

• Look at internship programs.
• PhD’s can do a post-doc in industry.
• To get a job, networking (especially at meetings) is vital.
• Technical training (B.S.) is a prerequisite even for business positions.
• Cross-functional collaboration is key in small-medium sized companies.

Finding a Biotech Job

• Try to get past HR with contacts.  You must have a significant portion of the minimum requirements. 
• At some larger companies, a computer algorithm looks for key words in your resume/cv, so tailor them to match the job description. 
• The cover letter is very important. 
• The objective is what you can bring to the company. 
• “I want to bring my expertise to the company to help them meet their objectives.” 
• If working with a recruiter- meet them in person. (Big in Boston and San Francisco)

 

An Interview in Biotech

Expect:
30-60 minutess long
There should be ~5 relaxed intro, but no personal questions or off-limits topics.
Core assessment
-Objectives and resume
-Questions to identify behavioral characteristics
It should end with a wrap-up.

General:
Research the people who are interviewing you and get background on the company.
Behavioral- good communication during the interview is important to demonstrate skills.
Make good eye contact (A post on this is to follow)
Don't ramble.  Be succinct without being abrupt.
Interviewee should talk 80% of the time.
Ask some questions to balance the conversation.
Don't answer questions with questions.
If you don't know: "I'm sorry, I can't answer that, can I get back to you?"
Business attire of course- better overdressed than under.

Specifics:
Background-Why are you interested in this company?
Legal- They can't ask about married, kids, nationality, etc.  You can bring up your own info like this if you want.

Provide examples of situations when you
-made extraordinary efforts to meet a deadline.
-took responsibility.
-made key decisions.
-were flexible, adaptive, and handled hurdles.
-were given an assignment with little direction.

Demonstrate that you
-are not sensitive to criticism.
-take initiative.
-are forward thinking.
-are strategic.
-have good business acumen.
-can motivate the team.
-can deal with issues.
-have leadership/followership.
-are a team player.
-prioritize 1-Customer, 2-Company, 3-Team, 4-Self.

Demonstrate
-what you have brought to a presentation or talk.
-what you have brought to your team.

I must say that there was one note I had that I didn't understand at all.  Please clarify if you know what it means:
"Know what the end goal is and predicted measures"