Monthly Archives: November 2013

How Much Does Grad School Cost — Followup

This post follows up on some things people have raised in the lively discussion about my earlier post, How Much Does Grad School Cost? Please start with that post if you’re just joining the discussion now. Thanks!

There’s been a lot of discussion about my earlier post: in the blog comments, on Facebook, by private messages, in person. Much of it is worth sharing or clarifying, so that’s what I’m doing here. To all the folks who commented: thank you for helping shape the discussion.

What does “grad school” mean?

I’m using “grad school” to mean formal education at a degree-granting institution that requires a baccalaureate degree for entrance. I believe this usage is consistent with how most people I know use the term. For me, “grad school” encompasses:

  • Academic doctoral (PhD) programs in any discipline: PhD in history, engineering, physics, sociology, music, literature, Arabic, etc.
  • Professional doctoral programs in any accredited discipline: MD, DO (osteopathy), JD (law), DPT (physical therapy), EdD (education), ND (naturopathy), DC (chiropractic), D.Div. (divinity), DDS (dental surgery), DVM (veterinary medicine), PharmD (pharmacology), PsyD (psychology), etc.
  • Academic masters-level (MA, MS, M.Ed, M.Phil, etc.) programs in any accredited discipline: same list as the PhD programs.
  • Professional masters-level programs in any accredited discipline: MBA (business), MSW (social work), MPH (public health), MHC (mental health counseling), etc.
  • Professional training that grants a degree and license similar in workload to masters-level or doctoral-level work: RPA (registered physician’s assistant), NP (nurse practitioner), RNA (nurse anesthetist), midwives, etc.

One can reasonably argue against inclusion of some of these categories in “grad school”, but given that my point was about the opportunity cost of higher education, these are semantic debates that don’t alter the thrust of the argument.

Is grad school funded for most people?

I’ve learned some things from this discussion: one is that most academic PhD students have some combination of grants, TA-ships, and stipends that means they don’t take on additional student loans for their PhD education and often get some living expenses into the deal.

People disagree about this, though; it appears that PhD funding levels and their effect on surplus depend (to some degree) on:

  • Academic discipline
  • PhD advisor/lab group
  • University (some universities fund better than others)
  • Location (some universities are in expensive cities, while others are more affordable)

A lot of the debate on Facebook centered around PhD-level education in academic disciplines, and I’m prepared to accept the assertion that most people finishing academic PhDs don’t come out with additional debt from them.

However, there are still four other categories of education in my “grad school” list above, and most of them don’t enjoy the same funding status. Although instances do exist of full-ride scholarships or TA-ships for professional doctoral degrees, academic or professional masters-level programs, and professional certifications, they’re not the norm. Most people going into these programs expect to take on new debt from them.

Undergraduate debt can accumulate during grad school

Most student loans offer a deferral during further academic study, but depending on whether they’re subsidized or unsubsidized, the existing loans from undergraduate education may continue compounding during the deferral period. (This isn’t true for federally-subsidized loans, but it is true for direct unsubsidized loans. For more information, and a chart about the maximum borrowing limits for subsidized loans, go here.)

The effect of this can be fairly large; many of my college students talk about coming out of undergrad school with student debt in the range of $40,000 (public university students) to $80,000 or more (private university students). I’m surprised these numbers aren’t higher; Swarthmore (my alma mater) has tuition and fees of $57,870 annually, which would leave a person with $231,480 in debt unless they had scholarships or need-based aid. (From the chart linked above, an undergrad could currently receive a maximum of $23,000 in subsidized loans to cover this, leaving about $200,000 for other loans.)

Let’s suppose a hypothetical private school student (Gina) got scholarships, need-based aid, and subsidized loans to cover half of that, leaving them with $115,740 in unsubsidized loans. We’ll pick a low interest rate and assume that their undergraduate debt is serviced at 3.2% (the lowest interest rate I found in an informal survey of recent graduates; rates ranged from 3.2% up to 8.0%).

Assuming my hypothetical student goes to grad school, gets education deferrals (meaning no repayment required), and doesn’t pay during grad school, that interest still compounds, which leaves Gina owing:

  • After undergraduate: $115,740
  • 1 year grad school: $119,444
  • 2 years grad school: $123,266
  • 3 years grad school: $127,210
  • 4 years grad school: $131,281
  • 5 years grad school: $135,482
  • 6 years grad school: $139,818
  • 7 years grad school: $144,292
  • 8 years grad school: $148,909
  • 9 years grad school: $153,674
  • 10 years grad school: $158,592

Why is this relevant? Because if people take the loan deferment during grad school (which, again in my informal survey, a lot of people do), their debt expands during grad school. That’s part of the opportunity cost.

Some of them pay down their undergraduate debt during grad school, and that’s great. Some of them finish undergraduate education with no debt, and that’s great too. But for a lot of the other people, they didn’t see the effect of debt expansion coming until after they had finished grad school.

Why do you hate education?

I don’t.

Seriously, I love formal education. I loved doing my Masters’ degree, and I’d love to go back and get a PhD because getting to spend six more years studying how people learn sounds awesome. My professors encouraged me to apply, offered connections, offered to hook me up with good departments, everything. Heck, I won a competitive nationwide award for instructional design for which I beat out work by graduate students in PhD programs, and I did it during in the early stages of an MS program. I’d love to go to grad school.

But when I started asking around, nobody could tell me about PhD jobs in my field. The field is growing really fast, but it’s still pretty new, and there aren’t that many tenure-track positions available anywhere. There aren’t many non-academic jobs that require PhDs in instructional design, learning, or the other sub-specializations of my discipline.

As I wrote above, people have basically convinced me that you can do an academic PhD for free and even make some money at it. So why not do the same? Read on.

People are less happy than they seem

My profession is crisis counseling. I run a crisis hotline, I teach crisis counseling practices, and I help a lot of people learn how to be therapeutic listeners.

A side effect of this should be obvious: it’s pretty easy to fall into a conversation with me. Those conversations often turn “serious” pretty quickly, partly because I often ask the hard questions and partly because people seem to know that it’s okay to talk openly about their feelings with me.

I started writing about the cost of graduate school because I spend a lot of time talking about it one-on-one with people who are struggling. A lot of folks are feeling some pretty deep ambivalence and frustration with their decisions to seek graduate education, either because the rewards haven’t been as great as what they were promised or because the costs were higher than they expected.

If you are a quantitative-data-only sort of person, I encourage you to ignore this entire section because I’m not going to name names or share numbers. But if you’re willing to buy into qualitative data collection and trust me as someone who has done crisis counseling and suicide intervention for the last 14 years, read on.

Lots of people in the Facebook comment thread for my last post have talked about how I shouldn’t underrate the happiness, contentment, and satisfaction that comes from graduate education. I apologize if I’ve given the impression that I don’t value those things: I do. But I also talk to a lot of people who’ve done the time, gotten the degree, and haven’t reaped the rewards. Many of the people commenting are ones who’ve hit the jackpot: tenured positions at reputable academic institutions, people working for prestigious tech companies, etc. I am thrilled for those people, but I believe their experience is somewhat unusual. I’ve got some sampling bias because I went to an elite liberal arts institution and tend to be friends with people from similar backgrounds, so that makes up a lot of the discussion base.

In my day job, I work with and teach students from a much broader range of situations: wealthy scions of highly-educated families attending a private university, first-generation college students on HEOP scholarships attending a public university, and lots of folks in between. The experiences these people have are often pretty different from what I heard at Swarthmore, and that difference extends through to graduate schooling. They’re often not getting soft landings, faculty appointments, prestigious jobs, or anything else.

Social curation

A bunch of people have raised the fact that many people with PhDs end up working jobs that don’t fully use their PhDs, whether working on farms or in coffee shops or teaching high school or teaching as adjuncts or consulting part-time, and used it to advance the argument that my economic concerns don’t hold water. Lots of people with Masters’ degrees are working the same kinds of jobs, with the added burden of loans for education. Many of these people, asked if they’re happy with their jobs and their choice to attend graduate school, say “absolutely”.

Many of them also say different things privately. Lots of people talk to me about feeling despair at having to write checks every month for an education that has bought them nothing that pays, and quite a few mention feeling that they have to pretend to feel happy about their current situations because it’s socially awkward to do anything else.

A lot of us get our information about friends from social interactions and social media, and it seems like the social curation effect—people packaging their “highlight reels” and displaying them as normal life—plays into it. It’s uncomfortable in most situations to admit doubt and anxiety into the conversation, so people often don’t. Instead, we make it look like we’re happy, try to keep calm, and carry on.

I think we’re asking the wrong question.

Rather than asking “are you glad that you went to grad school”, I think it’s more relevant to ask “if you had known this would be the result, would you have made the same choice about graduate school?” From what people tell me, a lot of them wouldn’t.

The bottom line

All I’m trying to advocate is a frank appraisal of graduate education’s costs, including long-term and hidden costs, so that people can make their own choices from a position of knowledge.

I believe that when you consider opportunity costs, debt compounding, and other factors, grad school often costs a lot more than people realize up front. This opinion is borne out by the years I’ve spent talking to anxious (and sometimes suicidal) people regretting their educational choices. Whether or not they should, people often don’t see the costs coming.

I’d like to change that. Whether graduate school is “worth it” is a very personal choice, encompassing all sorts of questions about identity, role in the world, desire about how to spend one’s time in life, future job prospects, and more, but on some level it’s still a cost-benefit analysis. Knowing the actual costs and benefits makes that decision easier, not harder.

I also believe that if you see the costs coming and still choose to attend grad school, there are ways to mitigate the costs—provided that you’re aware of the need to think about it. That’s where I hope we can take this conversation.

Finishing the dandelion tincture

When we left the dandelion tincture…

… it was happily macerating in jars, letting the 100 proof vodka (50% alcohol) extract all sorts of goodies from the chopped-up dandelions.  If this sounds unfamiliar, you might want to go back and re-read the post about how I collected dandelions and started the tincture or the one about how to identify dandelions in the wild.

So now, after 4-6 weeks, it’s ready to be finished up.

Preparation

You’ll need:

Bottles ready to be sanitized (c) Hollis Easter
Bottles ready to be sanitized (c) Hollis Easter

Line your strainer with a layer of muslin or cheesecloth. I like to use muslin because I think it filters better, plus it’s cheaper and lasts much longer. Mine started white and is now, after dozens of uses, kind of beige. I like to use a double layer of it, fully lining the strainer.

Next, I put the strainer inside one of those plastic canning funnels sold for working with Mason or Ball jars. This keeps spills and drips to a minimum. Put that whole assembly over a clean, empty Mason jar.

Straining/filtering tools set up (c) Hollis Easter
Straining/filtering tools set up (c) Hollis Easter

Sanitizing

I suspect this step is unnecessary when working with 50% alcohol tinctures, and I was a little haphazard in my sanitizing this time. But, it can’t hurt, and it might help.

Get a pan of water boiling on your stove, with water deep enough to cover your bottles, etc. All of our pots were in use the night I did this, so I used a frying pan. Didn’t have quite enough water in it, which is why I say “a little haphazard”. But never mind.

Bottles being sanitized (c) Hollis Easter
Bottles being sanitized (c) Hollis Easter

Place things in the water, being sure to keep the water at a rolling boil, and leave them in there for a minute or two. Turn them, if necessary, to ensure that the boiling water touches all surfaces. Then use your tongs to remove the bottles, jars, funnels, etc., and place them on a clean surface to dry and cool. It’s important not to touch the surfaces that contact food with your hands from this point onward.

Bottles after being sanitized (c) Hollis Easter
Bottles after being sanitized (c) Hollis Easter

Straining

When you start, your tincture should look something like this:

Tincture ready to be strained (c) Hollis Easter
Tincture ready to be strained (c) Hollis Easter

Mine was slightly cloudy, a yellowish beige color, with a faintly spicy aroma mixed into the evident alcohol fumes. It’s okay to taste the liquid if you like; it should be a little spicy and seriously bitter.

Now our goal it to get all the liquid (menstruum, in herbalist terms) into the jars and get all the solid bits of dandelion (marc) to stay in the muslin. Start by pouring (or spooning, to start) the tincture, dandelion bits and all, into the strainer.

Pouring off the liquid (c) Hollis Easter
Pouring off the liquid (c) Hollis Easter

It’ll go pretty quickly at first, but eventually the muslin filter will start to clog up and the stream of liquid will slow down. That’s when you pour a bunch of the tincture mixture into the strainer, then gather up the corners of the muslin in one hand and squeeeeeeeeeeeeeze the alcohol out of the marc.

Squeezing out the liquid (c) Hollis Easter
Squeezing out the liquid (c) Hollis Easter

Notice that the liquid in the jar, which used to be clear, is now kind of cloudy or milky again. That’s fine. Yes, I really do look like that when I’m squeezing the marc.

Note that the 100-proof vodka in the tincture will also be a fantastic indicator to tell you whether you have any cuts on your hands or fingers. If you already know that you have cuts, you might want to wear gloves to spare your nerves.

Once you’ve squeezed out all the liquid, you’re left with a ball of dried out plant matter.

The leftover marc (c) Hollis Easter
The leftover marc (c) Hollis Easter

Give thanks for the health it’s going to share with you, and then compost it. If you can’t compost it, put it in the trash.

Finishing up

From there, all you have to do is get the tincture into bottles and jars (a fine-neck funnel helps a lot with this, as does an assistant who can keep things from getting knocked over), clean them up, and get them ready for labeling.

You want to avoid having a huge amount of air in the bottles, and you might want to top off the strained tincture with a bit of fresh vodka before starting to fill bottles. Word to the wise: if you’re using dropper bottles, you’ll need to leave more airspace because the dropper will take some of it.

Once they’re all sealed, label them with the contents (“Dandelion whole-herb tincture in 50% alc.”), the length of extraction (“steeped 5 weeks”), the date (“11/15/2013”), and anything else you want to add. Sometimes I add the location where I collected the plants: (“Collected at home, Potsdam NY”).

Store them in a dark location that doesn’t get direct light. If they bubble or hiss when you open them, consider discarding the contents. Otherwise, it seems to last for years.

That’s it! Enjoy your homemade dandelion tincture! If you want to make more, here’s the recipe and the identification guide.

Bottles ready for labeling and storage (c) Hollis Easter
Bottles ready for labeling and storage (c) Hollis Easter

 

 

How Much Does Grad School Cost?

(updated November 16th, 2013. Originally published November 14th, 2013. Follow-up article posted here.)

How much does grad school cost?

More than anyone wants to admit.

There are lots of ways of looking at this question, but I’d like to contribute a view I haven’t seen before: an opportunity cost perspective.

For every year you’re in grad school full time instead of working a job, you’re missing out on the chance to invest toward retirement, houses, or other financial goals. Unless you’re in a graduate program that pays you enough of a stipend that you have some money left over to invest, or you’re working a side job during school, you end up behind.

How far behind?

I decided to focus on one question: assuming that you want to invest some of your money toward retirement, how much does each year of graduate school cost you in the long term? If you want to get the same place—a similar dollar value for retirement at a given age—how much more money do you have to invest annually?

It’s probably obvious that you have to invest proportionally more for each year spent in grad school, but the amount of difference might surprise you.

My point, ultimately, is that grad school is a really expensive choice in ways that are both obvious and subtle. Everyone talks about the crushing load of student debt—paying back what you had to borrow in order to go to grad school—and how hard it can be to find jobs that pay well enough to put a dent in the loans. But most people don’t talk about what happens after that.

When you’re paying back loans, you’re spending present earnings to pay for experiences that happened in the past. But assuming you want to retire in the future, you also need to be making enough more money now that you can make up for the money you couldn’t save during grad school. Depending on how many years you spend in grad school, the amount of extra money you need can be substantial.

How long does grad school take?

Depends on your field. Some fields require Masters’ degrees of 1–3 years in length; some require post-Masters’ certifications that can add another year. Some professional doctorates can take as little as 3 years after college, while some academic disciplines and medical specializations can easily last a full 10 years.

For this discussion, what matters is the number of years a person spends without investing toward retirement.

Surplus

I’d like to introduce a term: surplus. Here we’ll use it to describe the amount of money a person has available for investing once all other bills are paid: taxes, education loans, rent/mortgage, insurance, water, sewer, food, child support, health care, etc.

I’m going to talk about surplus rather than salary levels because people tend to scale up their costs of living as their income increases—and people who go to school longer tend to pay much more per year toward education loans. In terms of what a person is able to invest, surplus seems the best measure.

So, for this discussion, a person who makes $25,000 a year and spends $15,000 is the same as a person who makes $80,000 a year and spends $70,000: both have a surplus of $10,000 annually.

Surplus can change because you alter your income (how much your job pays) or because you change your cost of living (how much you spend on everything). After grad school, assuming you have loans to repay, your cost of living goes way up—meaning that your surplus goes down. To get the surplus back, you either need to economize in other areas of your life (bringing your costs back down) or get a new job (raising your income).

For example: let’s suppose your costs of living are $20,000 a year and you want to put $5,000 a year toward retirement. As long as you can find a job that pays more than $25,000 a year, you’re good. Then you go to grad school for two years, picking up a Masters’ degree that leaves you with $60,000 in debt.

Once you finish, the loan repayments for your MS come to $389 a month, or $4,668 a year. To be in the same place you were before grad school, you either need to cut your other living expenses down to $15,332 or you need to get a job that pays more than $29,668.

Predicting the returns of investments is difficult, but a lot of investors (Warren Buffett among them) agree that 8% annual returns are a pretty solid bet, over time, in the stock market. So we’ll use that 8% return in this discussion, and for the sake of discussion we’ll assume that it includes inflation and capital gains taxation within that 8%.

The scenario

Let’s create some hypothetical people for our discussion. All of them graduated from college with bachelors’ degrees at age 21.

  • Alice got a job with an annual surplus of $1,000. She invests in an IRA and continues doing so until age 65, when she retires.
  • Belle got a job with an annual surplus of $5,000. She invests in an IRA and continues doing so until age 65, when she retires.
  • Clara got a job with an annual surplus of $10,000. She invests in an IRA and a regular investment portfolio and continues doing so until age 65, when she retires.
  • Gina went to grad school. She’s our variable here, and we’ll look at different lengths of time spent in quaternary education. Depending on how many years of schooling Gina goes for, she’s going to need different amounts of surplus to match Alice, Belle, and Clara.

They’re all investing, not just putting that money in a savings account.

How much do they need?

I made a spreadsheet to help keep track of the numbers. You’re welcome to play with it if you like!

At age 65, here’s where things stand with Alice, Belle, and Clara’s retirement accounts:

  • Alice ($1,000 / yr): $386,506
  • Belle ($5,000 / yr): $1,932,528
  • Clara ($10,000 / yr): $3,865,056

So if Gina wants to end up with the same amounts as them (i.e., make graduate school a financially wise decision) she’ll need to contribute larger amounts once she finishes school.

Keeping up with Alice

Here’s how  much Gina has to contribute annually, compared to how many years she spends in graduate school, to keep up with Alice and end up with approximately $386,506 at age 65.

  • 1 year grad school: $1,085
  • 2 years grad school: $1,175
  • 3 years grad school: $1,275
  • 4 years grad school: $1,375
  • 5 years grad school: $1,492
  • 6 years grad school: $1,620
  • 7 years grad school: $1,755
  • 8 years grad school: $1,905
  • 9 years grad school: $2,066
  • 10 years grad school: $2,250

Note that Gina has to have a surplus of these amounts every year, starting as soon as she finishes grad school, or else the numbers go up even more.

These don’t look too bad, especially for the Masters’ degrees. It seems like a solid bet that most people with an MS will be able to get a job that pays at least $275 more, annually, than their previous job paid.

There’s still a concern about the loan repayments, though. If Gina MS has a $5,000 annual loan repayment, that means her new job has to pay $5,275 more than her old one.

Keeping up with Belle

Here’s how  much Gina has to contribute annually, compared to how many years she spends in graduate school, to keep up with Belle and end up with approximately $1,932,528 at age 65.

  • 1 year grad school: $5,420
  • 2 years grad school: $5,870
  • 3 years grad school: $6,355
  • 4 years grad school: $6,885
  • 5 years grad school: $7,465
  • 6 years grad school: $8,090
  • 7 years grad school: $8,772
  • 8 years grad school: $9,520
  • 9 years grad school: $10,330
  • 10 years grad school: $11,215

Note that Gina has to have a surplus of these amounts every year, starting as soon as she finishes grad school, or else the numbers go up even more.

Things start looking a little uglier here. Assuming the same amount of loan repayment for an MS ($4,668 per year), Gina MS now needs a job that pays $6,023 more than her old one, and she needs it as soon as she finishes school. If she’d gone to PhD school, her loan repayments would be higher and she’d need to contribute more because of the opportunity cost, which means that Gina PhD may need a new job, right away, that pays $10,000–$15,000 more than her old one.

Keeping up with Clara

Here’s how  much Gina has to contribute annually, compared to how many years she spends in graduate school, to keep up with Clara and end up with approximately $3,865,056 at age 65.

  • 1 year grad school: $10,830
  • 2 years grad school: $11,730
  • 3 years grad school: $12,710
  • 4 years grad school: $13,770
  • 5 years grad school: $14,925
  • 6 years grad school: $16,180
  • 7 years grad school: $17,555
  • 8 years grad school: $19,040
  • 9 years grad school: $20,660
  • 10 years grad school: $22,430

Note that Gina has to have a surplus of these amounts every year, starting as soon as she finishes grad school, or else the numbers go up even more.

Here’s where things really get unpleasant. If Gina MS wants to be in the same place Clara is, financially, she needs to find a job that pays $7,378 more than her old one. If Gina PhD finishes school in 6 years, her first job needs to pay somewhere around $20,000 more than her old one.

So what?

There are lots of great reasons to go to graduate school. The life of the mind is a wonderful thing, and graduate education opens new doors of thought and of experience that aren’t accessible through any other means.

That said, the job market isn’t what it used to be. Lots of people with advanced degrees are finding it hard to get the work they’re now qualified for—there just aren’t that many tenure-track faculty positions available.

People tend to look at the cost of graduate school in terms of borrowing: how much you’ll have to ask someone else to lend you in order to go to school. This is important, but it leaves out the larger question of lost time.

Assuming you want to retire someday, graduate school comes with a substantial opportunity cost because you lose earnings early in your career when your surplus’s future value is highest because it can compound the longest.

Too long; didn’t read

If you’re thinking of grad school, look at the jobs you think you’ll want to have someday. Find out their salaries, figure out how much your life is likely to cost including loans and everything else at that point, and see how much difference there is between those numbers. That’s your projected surplus.

Take a guess at how old you’ll be when you die, then subtract 65 from it. That’s your years in retirement. Figure out how much money you want to have per year when you retire, and multiply that by your years in retirement. Compare yourself to Alice, Belle, or Clara for this number.

Then look down the list, find the number of years you’ll spend in grad school, and compare your projected surplus to the number on that line. If your projected surplus is higher, you’re good—grad school looks like a solid economic bet for you. If it’s lower, grad school may still be a great choice, but it’s on shakier economic footing.

And remember that these numbers only work if you can make those surplus amounts—and the investments that follow—happen every year, starting as soon as you finish grad school. So you’ve got to find a good job right away. If those good jobs don’t exist, consider skipping grad school and staying in the workforce.

If you found this valuable, please Share it with friends on Facebook or Twitter. Thanks!

Wow! Lots of people wrote comments, both here and on Facebook! I’ve responded to some of them in a follow-up post.

Play faster and better with this 1 weird old trick!

Play faster and better with this 1 weird old trick!

Well, actually it’s a couple of weird old tricks.

Practice.
With intention and careful attention.
Be kind to yourself.

The most important parts:

Practicing with intention is not the same as just playing through the music or working the forms or throwing the ball or whatever you’re practicing. Take a minute before you start and use it to choose some things to notice and work on during this session. Focus your intention on the specific things you’re choosing to practice this time.

Check in periodically to make sure you’re still bringing careful attention to your practice. If you’ve lost focus, that’s fine—just bring yourself back to attention and get back into it.

Be kind to yourself. None of us are perfect at this; that’s why we practice. Learning and improving are unpredictable processes, and progress isn’t linear. Be gentle with yourself on the days when nothing works. Stay at it.

And remember to keep practicing. It’s easy to spend a lot of time researching practice techniques—and there’s nothing wrong with that!—and forget to actually spend any time working on what you learned. Put the time in, with careful attention, focused intention, and a gentle spirit, and you’ll be repaid.

Actually, this is true in many parts of life.

I think most people can make big strides in practicing this on their own, but if you’d like help with it, please ask. I teach private lessons and am happy to offer them over Skype or Google Hangouts to people who don’t live in northern NY. If you’re interested, please get in touch.

Monthly Roundup – September to November 2013

Here’s the quick monthly roundup for what I’ve written over the last few months, organized by subject. I’ve provided links to make it easier to read the articles.

General

Crisis hotlines

Music

Cooking and herbalism

Technology and fun

Triangles and Pyramids: Playing Math!

Triangles and Pyramids

Playing math!

2013-11-10 20.35.50I like playing with math. These days, I don’t need that much math for my daily life–enough to calculate whether I’ve got enough gas to get from A to B, to balance my checkbook, to budget for the training class I’m starting, to figure out expenses on Frost and Fire‘s new album… but I don’t need that much math. I was trained as a computer scientist, but it’s been a while since I’ve done O() analysis on an algorithm or used vector math to build a graphics system.

Math isn’t something I mostly need right now. It’s something I like.

I like thinking about things mathematically, looking for patterns, seeing what I notice, wondering what could explain it. That’s fun stuff.

This evening, I came up with a problem domain for exploring some things about triangles and solids. Jasmine (@jaz_math) and Pete and I spent a couple of hours around the dinner table exploring these questions and bringing various principles from geometry, trigonometry, and calculus to bear on them.

The context

I want to make some little free-standing pyramids that are built with paper. I want to be able to make them by folding a single piece of paper, with only a single piece of tape to hold them together.

Make an isosceles triangle of base b and height l. To start with, I drew one with b = 2 cm and l = 5 cm. Draw it on a sheet of paper, then cut it out. We’ll call this your “source triangle“.

Source triangle
Source triangle

Take a new piece of paper and trace around the source triangle. Then flip the source triangle so it shares one long edge with the previous triangle, and trace it again. Repeat this one more time so you’ve got a drawing with a big shape that sort of curves around a central point, made up of three identical triangles. Cut that shape out. We’ll call this your “net“. Generally, we could call it an n-net where n is the number of triangles it uses.

2013-11-10 20.34.17
Source triangle and 3-net

Fold the net neatly on each of the lines you’ve drawn and then tape the two outside edges together so you’ve got a pyramid that stands on the table. We’ll call this a “pyramid” or a “solid“. If you do it right, it should stand up on its own. You might find it easier to fold the paper over a ruler to get really crisp edges. (Or use the edge of credit card for the full pyramid scheme experience.)

Since it has three sides/triangles, we’ll call it a 3-pyramid or a 3-solid. With more sides, you’d call it an n-solid where n = the number of sides.

Source triangle, 3-pyramid (right) and 4-pyramid (left)
Source triangle, 3-pyramid (right) and 4-pyramid (left)

To help frame the discussion, here are some diagrams and definitions:

Diagrams and labels
Diagrams and labels (click for more detail)
  • n = the number of sides in the solid
  • b = the base length of the source triangle
  • l = the height of the source triangle (perpendicular to base)
  • t = the tallness/height of the pyramid after assembly (measured perpendicular to table)
  • base polygon = the polygon formed on the table by the edges of the pyramid (visible in top view)
  • p = the area of the base polygon

You may find it easier to play with the questions that follow if you make yourself a source triangle, a 3-pyramid, and a 4-pyramid before continuing.

Things to investigate

Maximizing n sides

  • What’s the maximum number of sides (n) that you can use to make an n-pyramid out of a single sheet of paper?
  • Is your answer true for all source triangles? If yes, why? If not, why?

Playing with height: t

  • How does the height of the pyramid change as n increases?
  • Does it follow a pattern?
  • Is that pattern the same for all source triangles?
  • Can you come up with a formula that will accurately predict the height (t) of your n-pyramids?

Playing with area: p

  • How does the area of the base polygon change as n increases?
  • Does it follow a pattern?
  • Is that pattern the same for all source triangles?
  • Can you come up with a formula that will accurately predict the base polygon area (p) of your n-pyramids?
  • Is there a relationship between the area of the original n-net (the flat sheet of paper) and the area of the base polygon p?

Playing with ratios

  • Is there a relationship between t (the pyramid’s height) and p (the base polygon’s area) for a given source triangle? Does it allow you to predict anything as n increases? If so, is it the same for all source triangles?
  • We can describe the relationship between a source triangle’s base and height (b and l) as its aspect ratio. What effect does aspect ratio have on the resulting pyramids?
  • If you made a series of 3-pyramids where you held the source triangle’s height (l) constant but increased the base (b) by 1 cm for each subsequent triangle, what change would you notice in the height of the resulting 3-pyramids (t)? What kind of relationship is it?

Silhouettes

  • If you looked at the pyramid from the side and rotated it so its silhouette was widest, how wide would the silhouette appear at its base? What relationship does the silhouette’s width have with b? Does it depend on n? If so, how?

Onward

We had a lot of fun playing math with these ideas tonight. I hope you have fun too! I’ll post some of the results of our math play later on, but I wanted to let you play with the pyramids on your own first.

These questions are fine for students who’ve had basic geometry, although they’ll have an easier time describing some of the relationships and solving some questions if they’ve had some trigonometry and calculus.

If you have questions, solutions, interesting ideas, things you notice, or things you wonder, please leave a comment!

Try The Honey Badger Diet!

The Honey Badger Diet (c) Hollis Easter
The Honey Badger Diet (c) Hollis Easter

This… is the honey badger (diet)!

You may be surprised to learn that honey badgers do care about some things. They’re actually very sensitive to the size bias and body loathing that are rampant among Mellivora capensis.

Honey badgers receive a lot of negative messaging encouraging them to hate their bodies and feel stupid about their eating choices. For example, hungry honey badgers often have to watch as their food (a scrumptious mouse, for example) is snatched away by humorless, cruel jackals, who take the meal while casting aspersions on the honey badgers. (“Thanks for the mouse, stupid!”)

All this contributes to body dysmorphic disorder among honey badgers, and particularly among youthful badgers, there is a disturbing sociological trend toward binge-and-purge-style disordered eating, as well as a far more insidious result: many honey badgers report that they can’t stop hearing the voices of the other animals making them feel bad for their food choices. They’ve internalized the abuse to the point where it becomes self-perpetuating, and a honey badger may live for decades with the constant fear of being criticized over its eating, its body, or its behaviors around food.

This needs to stop.

The fat shaming and body policing that pervades honey badger society is demonstrably toxic, and even badger cubs less than two years old show awareness of the opinions and judgments others hold about their eating behaviors. Many young honey badgers turn to diets in an attempt to change their bodies to look more acceptable, but these usually fail–initially because the honey badgers get hungry and go looking for sweets and fats like honey and larva; and longer-term because there is no evidence to suggest that most honey badgers, most of the time, can change their metabolisms to carry weight differently.

Toward a solution

What is needed is a radical shift in what constitutes acceptable appearance and societal constructions of health both within honey badger society and, secondarily, within the larger locus of sub-Saharan animal communities.

Toward that end, we propose the Honey Badger Diet as an approach to eating and living well. This represents a sub-section of the larger Honey Badgers At Every Size (HBAES) movement. The Honey Badger Diet is simple, focusing on listening to bodily cues for hunger and satiety, and it also addresses psychological factors that are major problems with most traditional diets.

Step 1: Hunt when you're hungry (c) Hollis Easter
Step 1: Hunt when you’re hungry (c) Hollis Easter
Step 2: Don't give a sh*t. (what people say about you) (c) Hollis Easter
Step 2: Don’t give a sh*t. (what people say about you) (c) Hollis Easter
Repeat as needed (c) Hollis Easter
Repeat as needed (c) Hollis Easter

Discussion

There’s a lot of research suggesting that diets don’t work among humans either. The medical community persists in prescribing diets as a mechanism for achieving weight loss, but there’s a lack of evidence to show that this approach does anything valuable for any but a few unusual humans. Much more commonly, people regain any weight lost, gain a small amount of additional weight, and are subtly changed by the psychological loathing that comes from being ordered to lose weight and subsequently failing.

Health At Every Size (HAES) is about stepping off the scale and focusing on health instead of weight, on pleasurable movement instead of forced gym slogs, and on eating well instead of dieting. It works for humans as well as honey badgers! The Honey Badger Diet is loosely based on some things Linda Bacon wrote, especially this.

I hope they’ll forgive me for framing some HAES concepts using my honey badger fixation.

Be kind to yourself, and to your honey badgers. If people fat-shame you or police your body, emulate the honey badgers and try not to give a sh*t. Ask to see their evidence. And then continue hunting when you’re hungry and not giving a sh*t. Enjoy!

For more honey badgers, see also:

Why You SHOULD Get Chills From That “Homeless Veteran Timelapse Transformation” Video

Man, we loves us some transformations. Makeovers, interventions, whatever you want to call ’em. We love the idea of saviors, too: people who come in and do the transforming/making over/intervening.

This is enshrined on a pretty deep level of our culture, from religious transformers to Home Makeover shows to boot camps to alcoholism interventions to Teach For America to missionaries to Henry Higgins and Eliza Doolittle and on and on. We’ve drunk deep of the idea that it’s a good thing to have folks roaming around and helping others to fix themselves.

I find it somewhat problematic.

Have a look at this video:

Text from the on-screen slides: “Jim Wolf, United States Army Veteran. For decades, Jim has struggled with poverty, homelessness and alcoholism. In September 2013, he volunteered to go through this physical transformation. Since filming, Jim has taken control of his life. He is now scheduled to have his own housing and is attending Alcoholics Anonymous meetings for the first time ever. Donate to Degage Ministries, a non-profit organization, to help transform the lives of other homeless veterans, inside and out.”

Cool, right? A non-profit that exists to help homeless alcoholic veterans get on their feet again is 100% okay in my book.

But I’m frustrated by some of the other themes I see going on in this video. When we start watching, we see Jim, a nice looking guy with long hair, a big beard, a blue nylon jacket, and a cross. In the end, we see Jim, a nice looking guy with short hair, short beard, sharp-looking blazer, nice shirt, good tie, tie bar, and pocket square.

We’re encouraged to see this physical transformation as evidence–an outward and visible sign of an inward and spiritual grace–that Jim has “taken control of his life” and is now on the road to success.

What’s wrong with that?

Appearance as signal

We’re encouraged to see Jim’s situation as filled with problems because of three alleged situations:

  • Jim is poor.
  • Jim is alcoholic.
  • Jim is homeless.

How do we fix those problems? By giving Jim a haircut and sticking him in a nice suit.

Wait, what?

By conflating systemic issues of poverty, substance abuse, and lack of housing with appearance, this video encourages us to use physical appearance as a signaling device to see whether people are “taking control of their lives”, i.e., living in an upright and socially acceptable manner and doing okay or “letting themselves go”, i.e., choosing to live on the street and drink cheap vodka for fun all day.

It is so. not. okay. for us to encourage the idea that appearance is a determiner of worth and that changing how you look will make systemic inequality go away.

This is problematic, and I get it that this is a complicated issue, as lots of people have pointed out. (Read “The Logic of Stupid Poor People” for an excellent look at how important appearance can really be when you’re trying to escape poverty.) That’s not what I’m talking about here: Tressie rightly points out in her article that when you’re poor (and especially when you’re poor and black) you’re playing within a system that is stacked against you, so you take whatever advantages you can get.

But that’s not what’s being celebrated in this video about Jim. We’re not talking about celebrating Jim’s discovery that if he can get someone to give him a suit and a haircut, he’ll be more acceptable and will be the recipient of greater privilege (i.e., free housing, free clothing, free publicity, and praise for going to AA meetings). I don’t think this video is really about Jim all that much.

The (white) savior complex and systems of inequality

We’re encouraged to believe that, if we could just find all the Jims out there, give ’em new suits and a good shave, the problems would go away. Politicians teach us to buy into this idea (remember Mitt Romney’s comments about how he would never be able to convince “those people” to take responsibility for their lives?) and encourage it by pointing out that places like Degage Ministries exist–which sets up the expectation that if people remain homeless/alcoholic/poor, they’re doing it by choice.

I have spent twenty years working on a crisis hotline talking to people in situations like Jim’s, and I resent the hell out of the implication that all of them could have a better life if they just looked nicer. I think most people don’t have the first idea of what it’s really like to be poor, or homeless, or alcoholic.

I said this was all problematic, and I mean that in another way: I’m conflicted because I believe that programs like Degage actually do make a difference and help people. It’s the way that they make a difference, and the way we talk about it, that bothers me.

When we say we’re trying for transformation, what we mean is that we’re trying to help people like Jim, people who don’t fit the system, to change themselves and fit in better. We’re addressing the status quo by trying to fix people who don’t belong.

(Again, I have no problem with people in Jim’s situation trying to claw their way up toward privilege. I have a problem with privileged people like those in the video thinking that haircuts and new suits will effect meaningful and broad societal change.)

Notice the huge hug and gratitude that Jim gives to his (young) (white) saviors at the end of the video? We’re encouraged to give money so that we can rank ourselves with them: goodhearted folks who are making the world better. On some level, this video is about them, and us, in the context of not-yet-fixed poor alcoholics without homes.

We can save Jims all day long and not be done yet; even the Bible says “the poor you will always have with you”. But on some level, and sticking with the Christian imagery since we’re talking about Degage Ministries, isn’t this just giving people fish instead of teaching them to fish?

Ponderings

Why do we accept a system where people like Jim, veterans who’ve served their nation, so often fall into poverty, homelessness, and substance abuse? Why do we create a society that discards them, like so many others, and then refuses to let them sit at the big kids table until they undergo transformations to look like us again?

Why do we have so many homeless alcoholic people in this country? Because we’ve decided that the people are the problem, not the systems of inequality that put them there. While we believe that Jim’s life can be turned around just by some savior coming in, giving him a sweet ‘do and some snappy threads, and getting him on the right path, we won’t ask why we have so many Jims waiting in line after him. If the solutions are obvious and easy, why do we still have so many Jims?

Helping Jim is really important. The starfish story is a good one, and “it matters to this one”. But it’s not enough.

Returning to the appearance as signaling thing for a second. Want to make a difference in the world? Don’t find a homeless person and give his appearance a makeover. Work hard, everywhere you go, to make a world where his appearance doesn’t hurt him. Sit next to people like old-Jim on the subway. Make yourself stop judging people based on their appearance. Focus on what people do, not on what they look like or who you think they are or why you think they need to change. Think about the value structures in society that lead combat veterans to become homeless, and work on changing those.

If Jim wants to get a makeover, fine. But don’t insist that he transform himself into a vision of white corporate acceptability as a condition of having his basic human needs met.

The system is the thing that needs a makeover, and focusing too heavily on transforming Jim distracts us from the larger challenge. Until we fix the system, we’ll have to save every Jim out there. We need to build a system where the Jims don’t need saving.

Leave a comment with your thoughts!

Or share this on Facebook or Reddit or Twitter and start some conversations with it (please be kind to each other).

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Updated 2013-11-19

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Honey Badger Empathy Survey

Honey Badger Empathy Survey (c) Hollis Easter
Honey Badger Empathy Survey (c) Hollis Easter

Survey conducted using Standard Empathy Instrument (Quantitative) version 2.5, n = 577.

In light of the perhaps-surprising results of the initial survey, we attempted to repeat the survey to investigate whether the initial results were anomalous. Regrettably, nearly all the honey badgers had engaged themselves in other activities (seeking honey and larvae, hunting and eating cobras, digging, running backwards in slow motion, etc.) and were unavailable for questioning.

The second survey (n = 12) confirmed the initial results, although several study participants showed worrisome flat affect possibly due to snake venom exposure.