A user-friendly and accessible text offering comprehensive coverage of the new PTLLS Award for trainee teachers in the Lifelong Learning Sector.
This is the third revised and updated edition of Preparing to Teach in the Lifelong Learning Sector, aimed at people new to teaching who need a good basic introduction to all the key aspects at an appropriate level. It is easy to read, with plenty of practical activities and examples throughout.
To earn a Preparing to Teach in the Lifelong Learning Sector designation, a Certificate in Teaching in the Lifelong Learning Sector, a Diploma in Teaching in the Lifelong Learning Sector, or a Post-Graduate Certificate in Education requires a careful study of theory and practice. Whether you're interested in the PTLLS, CTLLS, DTLLS or PGCE designation, you'll get help preparing assignments and evaluating your progress with this resource. Assignments are focused to cover the full teacher training course with the following modules; -Preparing, Planning, and Developing Effective Teaching, Learning and Assessment; -Personal Development and Professional Practice; -Theories and Practice of Teaching and Learning; -Personal Development and Professional Practice; -Evaluating the Learner Experience; -Access, Progression, and Achievement. Throughout, the author argues that people are not born to teach-they are trained to teach.
This accessible book comprehensively covers the new assessment requirements for Preparing to Teach in the Lifelong Learning Sector (PTLLS). This updated edition includes: -practical interactive activities for readers -roles, responsibilities and relationships -inclusive learning and teaching approaches -learning and development for individuals and groups -principles and practice of assessment The book will be helpful to unqualified teachers, and to anyone embarking on a PGCE or Certificate in Education programme in PCE. The book also provides knowledge for Learning and Development units. You can also access additional web resources at www.sagepub.co.uk/francisandgould Moving to the New Award? New edition mapped to the new Level 3 Award in Education and Training available! Achieving Your Award in Education and Training - request an inspection copy!
Following the success of her previous Practical Teaching guide, Linda Wilson has written the ultimate handbook for the student teacher wishing to pursue the next stage of training in the Lifelong Learning Sector. Practical Teaching: A Guide to PTLLS and DTLLS is the perfect companion for those studying or teaching the PTLLS (Preparing to Teach in the Lifelong Learning Sector) and DTLLS (Diploma of Teaching in the Lifelong Learning Sector) qualifications. Drawing on years of experience in the field, Linda Wilson takes readers through all aspects of teaching and learning; from the initial interviews and inductions through the learning process, to assessment and finally reflection, offering helpful and workable tips for success along the way.This book is directly mapped to the units and learning outcomes of the PTLLS and DTLLS qualifications, and supplies practical ideas for teaching in an easy-to-read style. Essential theory is introduced on a need-to-know basis, and is set in the context of its application within the classroom.
This volume examines key areas in post-compulsory education through topical discussion, practical exercises, theory, reading, analysis, information, and examples of student work.


When I started in on this project, I was a complete electronics newbie. I had no memory of holding a soldering iron. (Though as soon as that rosin core got hot, I recognized the smell. I'm pretty sure I must have soldered as a kid or in a past life or something.) I made...a number of mistakes as I built my first keyboard, but in the end I have a fully working keyboard. I'm attempting to recount, from memory, everything I did. Especially everything I did wrong. If you know what you're doing, you probably laughed or cried a fair bit as you read part 1 of this writeup. If you don't know what you're doing, it's my hope that this writeup shows you just how easy it is to build something that you might otherwise consider out of reach.
As I finished off Part 1 yesterday, I'd just managed to get the matrix on the left hand side of the keyboard wired up. From there, I wired up some temporary leads to the rows and columns on the left side. I used adapted breadboard wires from Adafruit. These have the advantage of plugging directly into the pins on the Teensy++ microcontroller. If I was working from a PCB, this wouldn't be necessary, but, since I didn't have a PCB to work from I was doing this freehand.
Once I got the rows and columns connected to the Teensy, I found some bad solder joints. I used the solder sucker to undo my bad joints and redid them.
Even once I'd debugged the bad solder joints, I was still seeing...weird behavior. Some areas of the keyboard weren't generating keystrokes. My first assumption was that I just had a few bad solder joints in a row. So I redid them. That didn't really help. Sometimes, it changed the failures a bit, but it didn't actually fix things. "I know what this is! I must have toasted some of the diodes by shorting or melting them during some of my ham-fisted soldering." So I replaced the diodes. Nope.
I unplugged the keyboard from the Teensy and started poking around with the multimeter. I couldn't find anything wrong at all. I went back and tested the "bad" diodes with the multimeter (like I should have done in the first place). They were all fine.
I plugged the left hand back into the Teensy. A different region of the keyboard was now misbehaving. Finally, I realized that certain leads from the matrix to the Teensy were misbehaving when they were plugged in next to each other. What was going on is likely obvious to anyone who understands electricity. My assumption is *mumble* *mumble* interference *mumble* shoddy wiring *mumble*. Rejiggering the wires made the problem go away. Not exactly a shining example of root cause analysis, I know.
At this point, it was time to try to wire the two halves of the keyboard together. I just needed to find a 13 wire cable.
Yes. 13 wires. On my wiring of the ErgoDox shells, I have 5 rows of up to 8 columns.
Normal keyboards are typically wired in something like a 6x18 matrix. Because the ErgoDox is a split layout, it's effectively wired as two separate mini-keyboards. The "real" ErgoDox design sticks an IO Expander on one of the hands' PCB so it can be connected to the other one by an 1/8 inch headphone-style cable. That's slightly more advanced than I'm capable of at this point, so I went for the hacky solution - just back-hauling the entire matrix from the left hand over to the right hand side where the Teensy lives.
There was just one small problem. Finding a 13 wire cable.
An 8 connector cable is no problem. Easy to find. You can even go up a bit from there. But try as I might, I couldn't find a reasonable cable with enough wires for me. Then I hit upon an idea.
So I pulled out my wire cutters and *snip*, I had a 13+ connector cable that I could solder to both sides of my keyboard.
I connected both halves of my keyboard to the Teensy and plugged the Teensy into my desktop machine. I hit some keys on the right hand. Everything looked fine. I hit some keys on the left side. And...nothing. Nothing at all.
It turns out that HDMI cables are made of twisted pairs of various gauges of wires. That fail for this application in exactly the same way as my own twisted rats' nest of cabling did.
In the end, I took some of the jumper wire I got from Adafruit and just used it as a ribbon cable. I tried chaining it, so I could have a 20" cable rather than an 8" cable, but things started misbehaving.
I threaded the jumper cable from the left hand to the right and got it connected to the Teensy. What I had at this point wasn't ideal, but it did work.
It was time for final assembly. That sounded so nice. "final". Ha ha ha. No. At a guess, I ended up taking the keyboard shell apart and putting it back together about 20 times after this point.
So, I grabbed the back halves of the keyboard shell and carefully aligned them on top of the front halves. I grabbed some screws I had lying about and....they didn't fit. The screw heads were just a little bit too big to fit in the screw holes printed into the back shell of the ErgoDox.
In Part 1, I described the SLS (Selective Laser Sintering) process Shapeways used to 3D print my keyboard shell. What I ended up with is just white plastic -- It's fairly easy to customize. In this case, I started my customization by picking up my Leatherman and starting to carve out the edges of the screw holes one at a time. This technique was good enough to get the right hand side of the keyboard fully put together. During my initial final assembly, I managed to over-tighten one of the screws causing the plastic on the bottom side of the case to snap, leaving me down one screw hole. Thankfully, Dox (and/or his co-conspirators) nicely over-provisioned the keyboard shell with screws. Being down one screw isn't a significant hardship.
I flipped the keyboard over and connected it up to my desktop and started testing each of the keys....and found that I had a few new key failures. I unscrewed all the screws I'd just managed to tighten and set to work with the multimeter and soldering iron. Mostly, it seems I managed to stress the solder joints connecting the column wires to the keyswitches. A little bit of work with the solder sucker and soldering iron and I was ready for reassembly. I managed to repeat this process a few times. I'm now...rather better at freehand solder joints than I was when I started this project. None of this would have been an issue with a PCB to mount my keyswitches in.
Now that the right hand was behaving, I was ready to screw the left side together. My screws still didn't fit in the holes I needed to sink them into. The correct solution would have been to wait until the next morning and walk down to the hardware store and buy properly sized screws. As you can tell from what I've already written, I haven't exactly done everything...correctly.
Rather than whittle out the screw holes on the left side, I hit upon a technique that seemed to work for me, but is probably quite dangerous and prone to catastrophe. Kids, don't try this at home until and unless an expert weighs in and says I'm just being overly dramatic.
The shell of my keyboard is made from plastic. Sure, it's not injection-molded like most plastic you'll find in a commercial product, but it has most of the properties of regular plastic. I already described how it snaps when it's subjected to too much stress. It also melts when it gets hot. Perhaps you see where I'm going?
I carefully aligned the back shell of the left hand on top of the front shell. I picked up one of my slightly-too-big screws. I placed the screw in the hole I wanted to secure. It did not seat itself properly because the screw head had a larger diameter than the hole I intended it to fill. I turned the temperature of my soldering iron way up. (As I said in the previous paragraph: Kids, don't try this at home.) I rested the tip of the soldering iron on the screw I hoped to sink. I applied a small amount of pressure with the soldering iron. As it became warm, the screw began to sink into the plastic. As it became warm, the plastic began to emit a noxious odor. When the screw appeared to be properly seated, I removed the soldering iron. This seemed to work quite well and I used the same technique for the remainder of the screws.
I think I mentioned earlier that the way one uploads new firmware to the Teensy is by tapping a little black reset button.
That button drops the Teensy into upload mode so you can blow new firmware into its tiny little brain. When you're using a Teensy on a breadboard, this is nice and easy. You can use a finger or a small screwdriver or a tweezer or just about anything to tap that little black button. When it's sealed away inside your keyboard, it's a little bit harder to press. I really, really, really didn't want to have to disassemble my keyboard every time I wanted to reprogram it. So I took advantage of one of the properties of plastic I've already written about. I did something that would probably get me kicked out of electronics class, especially if it's not done in a well ventilated area.
One should never plunge one's soldering iron into plastic. One should never then hold one's soldering iron inside a piece of plastic and slowly melt out a groove of plastic. When one is finished doing things one should never do, one should carefully clean one's soldering iron while it's still hot.
That completed, I could now easily tap the Teensy's reset button with the keyboard fully assembled.
Time to switch to the production firmware!
I carefully tapped each key on my keyboard. Finally, every key registered. Each key only registered once. I was ready to switch the Humble Hacker firmware from "matrix discovery mode" to keyboard mode. That way, rather than each key telling me its coordinates in the matrix, it would instead, you know, generate a keystroke. I'm told this is a desirable property in a keyboard.
I realize I should step back a bit and describe the firmware build environment, at least a little bit.
Getting the keyboard firmware built was fairly straightforward, though it did involve a bit of cobbling things together. The Humble Hacker firmware seemed to be the most flexible option for "new keyboard, new matrix" (as opposed to "upgrade an old keyboard"), though there were a number of other options available. At some point, the author broke apart a single "keyboard" repository into a set of repositories - "firmware", "hardware", "remapper" and "kspec". I actually had the most luck following the instructions from the "keyboard" repository which is marked as "DEAD".
In addition to the Humble Hacker source, I needed to install the Teensy Loader in order to blow firmware into the Teensy.
To build that firmware, I needed a crosscompiler toolchain. The last time I needed a cross-compiler toolchain, I had to commit unspeakable acts involving multiple bootstrapping builds of gcc, insane sets of shell scripts and a summoning grid. It was bad enough that I ended up just installing a compiler on a Nokia N800 and building things there.
Thankfully, things are easier these days.
I downloaded an installable cross-compiler toolchain. It took about 10 minutes. No lurking horrors needed to be placated with the offering of a child-to-be-born. No contracts in blood. No bootstrap compiler. Not even a shell script.
I recall a little bit of futzing around to try to get the kspec tool to build from the Humble Hacker repository. In the end I just used a prebuilt version.
So, back to the keyboard build-out.
I turned off the "matrix discovery mode" in the humble hacker firmware. I did the bare minimum I needed to get the "Q" key to print a "Q" on screen. I rebuilt the firmware, tapped the little black button on the Teensy with a screwdriver and flashed the new firmware.
Ready for glory, I tapped "Q" and...nothing.
I reflashed the firmware and tried again. Nothing.
I turned matrix discovery mode back on. Everything was great.
I opened up the source to the Humble Hacker firmware and started reading code. Apparently, it's more common to wire your diodes on the columns, rather than the rows.
At this point, I was pretty good at rewiring the keyboard. I was also pretty sick of rewiring the keyboard. But there was an easier way.
My "Q" registered just fine.
I filled in more of the kspec matrix.
The Humble Hacker firmware has support for multiple (toggleable) keyboard layers. You can do just about anything you want. Native Dvorak keyboard? No problem. Native Colemak keyboard? Sure thing. Design your own. You can do that if you want. You can't reprogram the keyboard without installing a firmware update, but there's no reason you couldn't write firmware that could do that.
Knowing (hoping) that I would eventually have a keyboard I needed to type on, I had ordered a set of keycaps from WASD Keyboards earlier in the year. I'd ordered, basically, "one keyboard" of keys.
I set about placing the right keycaps on the right keys. Just click em in place, right? Not so much. If you look at most modern keyboards (other than laptop or ultra-thin keyboards), you'll see that the keys have a pleasing sculpted shape. Each row has its own shape.
The ErgoDox shape isn't exactly the same as your typical desktop keyboard. Nor does it have all the same keys. It needs a couple weird-shaped vertical keys and a whole slew of slightly-wider-than-normal keys. Once I got a full set of keys on the keyboard, it felt...weird. The shapes just didn't fit.
Now, where have I seen this layout before?
I hadn't payed incredibly close attention to the layout of the ErgoDox - It had some properties I really cared about (like keys aligned in columns and clusters of keys designed to be pressed with your thumbs). Past that, it was just the first thing that looked even vaguely plausible.
Once I actually thought about it, I realized where I'd seen a layout like that before. It was, in fact, glaringly obvious. I just hadn't realized how glaringly obvious it was.
It just so happened that I had an old, dead Kinesis lying around. (Everybody does, right?) I harvested its keycaps and started pulling the keys I'd bought from WASD off of the ErgoDox. As I did so, I managed to yank one of the keyswitches up. After a small detour to the soldering station, I was back in business. (While I had the keyboard open, I locked down most of the keys by painting the edges of the keyswitches with superglue.)I was rather more careful as I pulled the remaining keycaps. I'd been using my fingers for the first few.
I spent Thanksgiving in northern Virginia with family. I'd brought along my new keyboard. TSA at Logan were....curious about my keyboard. And surprised I don't work at MIT. But totally comfortable with weird hardware with lots of bad solder joints.
Shortly after getting to Virginia, I noticed that my "A" key was frequently generating two "A" characters each time I tapped it. I wasn't 100% sure what was wrong, but based on past experience, I was willing to go with my gut. I would have been willing to bet money that it was a bad solder joint.
My father-in-law was quite accommodating and I soon found myself at the kitchen table warming up his soldering rig.
Five minutes later, I had an A key that generated only a single "A".
How do I know how long this took, you ask? I spent a number of years in consulting and am careful to run a timer for everything I do so I can charge appropriately. No, wait. That's not it. I've never been much good at time accounting. I didn't think very hard about how long it was taking me to build my first keyboard. I didn't really want to think very hard about it. I sort of wish I didn't know how long it took. But I do.
Remember how, back in Part 1, I said that as I sat down for my first soldering experiment I started the pilot of Community on Hulu? Well, as I was futzing with the firmware, I ran out of Community to watch. That'd be 71 half-hour episodes. To have _something_ on as I was finishing up, I put on the pilot of Modern Family. I...did not enjoy that and will not be repeating the mistake.
Yes. It's not quite my ideal keyboard or keyboard layout and is different enough than everything I've ever spent time typing on that I'm still getting somewhat fatigued using it for more than a short period if time, but I'm getting better.
It's nicely portable. I quite like being able to fold it in half and tuck it away for transport.
I know how it works. A friend commented that this is one keyboard I'd hate to spill something into. Thinking about it, I realized that I'm actually less worried about something bad happening to this keyboard. I'm confident that, given minimal (and fairly ubiquitous) tools I could repair it without too much effort.
Where am I headed next?


text:
How to Prevent the Next Heartbleed
dwheeler.com
All Horses Are the Same Color
·December 4, 2021
eperdew
I started to write out what is happening here more formally, but I think it was not very elucidating. No matter what, the problem is that the proof of the inductive step is wrong. The problem is (as mentioned in the article), that for sets of size two, your inductive hypothesis is not sufficient to prove that h1 and h2 are the same color.
Saying it's the base case that's wrong is a little weird. In general your base case can be vacuously true without any issue. However, if it is (and your goal is non-vacuously true for something), then your inductive step will require a branch in it. One side of the branch in your proof will look like a proof of a base case.
I have maybe a skewed view on this from using Coq.
amitkgupta84
You're 100% correct. I would be more unequivocal -- saying that the problem is the base case isn't just a little weird, it is incorrect. Your analysis nails it.
diffeomorphism
Disagree. The induction step works perfectly fine for n>=2. In particular, if you can give me the base case "any two horses have the same color", then this proof works and all horses have the same color.
The problem is that the base case is n=2, but the student checked n=0 and n=1.
The base case is not n=2, it's clearly stated as n=1 in the proof.
The inductive step works fine if you introduce the premise n>=2. It is not valid to introduce that premise. The inductive step is therefore wrong.
The proof in the post is saying the base case is P(1) and the inductive case is that for all n, P(n) => P(n+1)
"P(1)" is true. "For all n, P(n) => P(n+1)" is false. The inductive step is wrong
A completely different proof not present in this post could be:
Base case: P(1) and P(2) Inductive case: for all n > 1, P(n) => P(n+1)
In that completely different proof, the inductive step would be correct and the base case would be wrong. That proof is not in the original post.
wisty
No, the induction step works for n>=3. The induction step fails for n=2.
For n=2, you can't prove h1 is the same colour as h2, because you don't have a h3 to compare it to.
mcphage
Their inductive step is perfectly valid. However, requires a group of horses with one removed to still have a horse remaining. Using N=1 is an incorrect base case. Had they proved the N=2 base case, their entire argument would work.
Of course, you can't prove the N=2 base case, so that's why the argument uses the wrong base case.
The inductive step introduces a premise that "requires a group of horses with one removed to still have a horse remaining." It is not valid to introduce this premise. The inductive step is not valid.
dsizzle
The "vacuously true" part seems unnecessary (and weirdly subjective). The N=1 base case requires considering N=2 when you apply the inductive step and that fails.
The example I'm about to give is overkill, but I'm trying to make my point very carefully.
Suppose you want to prove something for integers >= 2. E.g., suppose you want to prove for all n >= 2, n is positive. The statement you're trying to prove for a given n is actually
P(n) := n >= 2 -> n is positive
Let's prove it by induction.
P(0) is 0 >= 2 -> 0 is positive. P(0) is vacuously true, because 0 < 2.
Suppose P(n). We want to show P(n + 1). Our goal is
n + 1 >= 2 -> n + 1 is positive. Let's break this into the cases n >= 2 and n < 2.
For n >= 2, we assume P(n) and have the LHS of the implies. This gives us n is positive. Say by definition or by a lemma that n positive -> n + 1 is positive, and we handle this branch.
For n < 2, the inductive hypothesis tells us nothing. Assume the LHS of our goal, i.e. n + 1 >= 2. We want to prove n + 1 is positive. Well 2 is positive and therefore n + 1 is positive by transitivity.
This is what I mean by the base case not being special. E.g., in Coq, induction over the natural numbers always starts at 0. When you think about doing induction starting at another number, you're transforming your goal to include something of the form n >= m -> P(n).
Ericson2314
Pre formal methods, sophists spin false proofs like this example. Post formal methods, sophists spin false propositions.
sidedishes
I don't understand why it's more or less weird to say the base case is wrong vs. the inductive case is wrong. If H(n) is 'all sets of horses of size n contain horses of the same colour', the linked argument seems like
H(1) is true
H(n) => H(n+1) (with a sleight of hand that it's only for n >= 2)
It seems to me like changing either the argument to assert H(2) is true, or the scope of the second statement to include n = 1, would be enough. It seems the fault of both statements equally to not fit with the other, so why is it weirder to say the base case is wrong?
You just said it. The base case is true. The inductive case is wrong. You called it true "with sleight of hand", but that's more of a poetic statement; mathematically it's simply wrong.
One could write a completely different proof where the base case(s) cover n=1,2 and the inductive step is as in the post. In such a proof, the base case would be wrong and the inductive step would be correct. But that's a different proof, not the one in the post.
Dylan16807
> You just said it. The base case is true. The inductive case is wrong.
Not really. H(1) is true. H(2) is false. But either one could be your base case.
The inductive step could be true or false, again depending on what you call your base case.
poetically
I don't think this is correct. The main argument uses a very specific inductive invariant of applying transitivity of equality to a non-empty set. The argument doesn't apply in the base cases because it is vacuously true so the minimal base case is actually a set with 3 horses because that is the only case where transitivity of equality can be used non-trivially.
dwohnitmok
> The argument doesn't apply in the base cases
No I'm still with eperdew on this. You don't apply an inductive argument to base cases, so that statement doesn't really make sense. From a pedagogical point of view, I think it is very important to drive home the point that there is nothing special about your choice of base case, other than that it affects the argument in your inductive step, otherwise it's too easy to make the choice of base case seem "magical."
In fact I'd go further. Whenever you have an error in an inductive argument, it is always in the inductive step and never the base case, since you can always choose whatever base case you want (you might just find it makes your inductive step impossible to prove, so if you do prove something, you've made a logical error in your inductive step).
At worst, an "error" in choice of base case leads to a proof that cannot be completed, not an erroneous proof.
EDIT: "it is always in the inductive step and never the base case" except of course if you've somehow made an error in the initial proof of the base case, but that is distinct from choosing the "wrong" base case.
EDIT 2: I just understood what you meant by "apply," (doesn't fulfill the preconditions of the inductive step, vs I thought you meant relevant to proving the base case) sure that's a reasonable way of looking at it too, but again I'm very wary of saying that it's the wrong base case that leads to proving a falsehood as I lay out elsewhere.
shkkmo
> you might just find it makes your inductive step impossible to prove, so if you do prove something, you've made a logical error in your inductive step
The inductive step should be proven completely independently of proving a base case. Indeed, if the inductive step is proven correctly you see that it is limited in scope to n>1.
You can then use any base case you can prove where n>1. Let's say you pick a base case of one trillion. Easy enough to show thay every set of one trillion horses is the same color (since no such sets can exist). You can then easily use induction to show that every set larger than one trillion horses is also the same color!
So really, both base and induction were wrong in different ways but if the induction had been proven correctly, the inapplicable base case would have been clear.
So what would say is the error in the inductive step here?
dan-robertson
I think that is a complicated way to look at things. The error is that the argument assumes that for a, b being elements of H, the sets H - {a} and H - {b} meet. This is true for |H|>2 but the first induction case is for |H|=2, where the assumption is obviously false. But when you read the induction case you may think of n as being large and so not notice the error.
Yes, this is what I said in another comment.
fnord123
Why is the base case 3? H(1) contains one colour of horse. H(2) when removing one horse contains one colour of horse.
The problem afaics is that there is a supposition that we are talking about sets of horses with the same colour. So if you "suppose for all sets of n horses, every horse in the set has the same color" then you can prove that horses in that set have the same colour. If P then P.
GhettoComputers
Is Godel's theorem what you're referring to? https://plato.stanford.edu/entries/goedel-incompleteness/
Yes, I also think it has nothing to do with base case and general case, there is just a flaw in the argument. When arguing that h2 also is brown one assumes wrongly that there are other elements in the reduced set left.
phkahler
The problem is the second line:
"Now suppose for all sets of n horses, every horse in the set has the same color."
There is no justification for that. They then go on to talk about removing a horse from such a set, but we've already lost.
nnoitra
It's part of the inductive proof process. Assuming that it holds for n you need to show that it implies that it holds for n + 1 as well.
>> It's part of the inductive proof process. Assuming that it holds for n you need to show that it implies that it holds for n + 1 as well.
No. That's wrong. They assert it up front (that it is true for any n horses) and then go on to use it in the proof for n+1. The only time it's OK to assert your claim up front is if you're trying to prove it false by contradiction.
For an inductive proof, you must prove that if it holds for one case (n=1 here) it also holds for the next case. The base case is important and is proven (or obviously) true. A set of n is not the base case here, and they assert something about it without proof.
EDIT: Nope, my dumb. The wording is odd, but for induction we show that it is true for n=X (X is the base case and is 1 in this example). the inductive step is to show that being true for n implies being true for n+1 which is what they did here.
That isn't really a problem, just poorly worded (like a number of sentences in the article.) This is a pretty standard step of an inductive that should read more like: Given that n is some positive integer where every set of n horses has the same color...then you try to prove that holds true for n+1 as well.
The actual problem in that proof is setting up the proofs of the inductive rule. There is an implicit assumption/condition that n+1 >= 3 that is not acknowledged.
If you acknowledge that condition, then it becomes quite clear that you can only prove a base case for n = 1 and only prove an induction rule for n >= 2 .
throwvirtever
I feel like I'm too ignorant of mathematics to be confused by this "proof".
When you set out to prove "for any set of n horses, every horse in that set has the same color" and you then "suppose for all sets of n horses, every horse in the set has the same color" as a first step, you're messing with a tautology, aren't you? I mean if you've supposed that it's true for all, it's definitely true for any, right?
What am I missing that makes the problem subtle and interesting, rather than just blatantly circular from the start?
mannerheim
The inductive step assumes the hypothesis is true for n, and proves it for the n+1 case. The overall proof is then for all positive integers, n.
There are two steps of an inductive proof
one is proving the inductive rule that: p(n) implies p(n+1)
the other is proving that there exists some number i for which p(i) is true. This, combined with the proof of the inductive rule, allows you to prove that p(n) is true for all n >= i.
ajuc
It's not circular, because you aren't using the assumption A in the final proof, you are just using the implication A(N) => A(N+1) in the final proof.
the final proof is:
A(1) is true
A(N) implies A(N+1)
means that
A(N) is true for all N >= 1
the assumption that A is true for N was just used as a condition in the implication
If A(N) is false in general - you would realize that despite assuming it - because the implication or the base case couldn't be proven.
indianboy42
Isn't that just how proof by induction works? You assume the hypothesis is true for n and prove it for n+1
ahartmetz
But you don't go from n-1 to n. You'd have to start at the infinite horses case where the conjecture must be true for, well, who knows what reason. Intuitively, "Consider the conjecture proven. If we reduce the difficulty, it's still proven" just seems obviously wrong.
smohare
That's not the issue at all, since the base case of n=1 is established trivially and so the quoted statement is merely the inductive hypothesis. But the inductive argument relies on n>2 to invoke transitivity on a non-empty intersection necessitating a separate justification for n=2.
This post is basically a paraphrase of a well-known example, which has its own Wikipedia page https://en.m.wikipedia.org/wiki/All_horses_are_the_same_colo...
I think the fallacy is explained better there tbh.
I also think it's confusing to say one isn't the base case. When you apply the inductive step there you hit N=2, and indeed the step fails because there's no overlap.
tux3
This is indeed much clearer than the OP's version. In this one, the transitivity is obvious, because the article clearly explains that you may take out any horse from n + 1 and note that the remaining n have the same color, then do that observation again with another one, and use the horses that never left the group as a transitive link.
I agree this is much more worth looking at.
wruza
(wiki) Thus in any group of horses, all horses must be the same color.
Yes, iff n horses have the same color. I fail to see any paradox here (and in subj tfa too) and why induction is of any importance to it. We worked it all out of a restricting assumption which wasn't contradicted, but that's it. It doesn't tell us anything about all other cases, e.g. when n horses do not have the same color.
Can someone please explain what I'm missing here?
The inductive step allows you to stipulate what seems like a strong assumption, in this case that all horses in sets of size N have the same color. I think you're reacting to that seeming like it's the problem, because at first that seems like where the "cheating" is occuring: you can obviously have a set of horses that aren't all the same color.
But actually that's part the power of the inductive step: you do have the freedom to choose whatever assumptions you want. The question is whether it's true for N+1, for all N. In this case, it's not: the inductive step fails. But there's nothing flawed with the starting premise per se (aside from it being intuitively obvious that it will never work). The interest here is that it seems you can get further than you should be able to, and it's a little tricky to figure out where the logic falls apart.
What you're missing is that "n horses have the same color" is true for n=1. So therefore we should be able to invoke the induction to bigger and bigger numbers.
If the induction actually was valid for 1->2, we'd have a hell of a problem.
Now I think I understand the subtlety, thanks! The induction part is important here because we start from n=1 (where the assumption is not as obviously questionable as for n in general, because it's coincidentally/degeneratively true in relation to our reasoning) and then the "base error" allows us to generalize into a bigger mistake.
lambdatronics
Yeah, it's phrased weird. In the inductive step, what you want to do is prove that "if all sets of horses with size n have the same color, then all sets of horses with size n+1 have the same color." In order to prove that, you start with the assumption that all sets of horses with size n have the same color. They're not actually assuming it's true for all n right away, they're just assuming that they've gotten it for some n.
GolDDranks
"Now suppose for all sets of n horses, every horse in the set has the same color"
This sounds so obviously false to me, that I initially thought that he must have meant "now suppose for all sets of n horses such that every horse in the set has the same color". I.e. take all sets of n horses and then filter them to only get the uniformly colored sets.
But he doesn't mean that, it is meant as the induction step:
"Now suppose a world where for all _possible_ sets of n horses, it turns out that every horse in the set _necessarily_ has the same color."
In my mind, the article is a bit poorly worded, but then again, maybe it makes sense for mathematicians.
crdrost
I'm not sure any wording helps, because the reason it strikes us so poorly is that it's such an implausible idea.
It might help to make it more concrete, to say "assume that we've proven this for say n = 3, all sets of three horses have the same color. Then I can prove it's true for n+1, because my set {Auris, Brunellus, Camper, Diego} of four horses is the union of two overlapping 3-sets, {Auris, Brunellus, Camper} and {Brunellus, Camper, Diego}. By the transitive property, Diego must have the same color as Auris and the result holds. But obviously this works not just for 3 going to 4, but also 4 going to 5... Any set of size n+1 is made up of two overlapping sets of size n."
Maybe also someone can then intuit that the wool is being pulled over their eyes in this step?
That is the same sentence just abbreviated and using standard words. Nobody says "suppose a world where", you just say "suppose that". Also, you just say "if ..., then ...", not "suppose if ..., then it necessarily turns out that ...".
> In my mind, the article is a bit poorly worded, but then again, maybe it makes sense for mathematicians.
That is the point. This example is given to first year students to show them why you need to be careful in your proofs and why properly wording/formulating statements is important.
wombatpm
There are variations of this style of proof the shows all horses have an infinite number of legs, since horses must have an even number of legs to stand, yet they have two legs in back and forelegs in front, giving them six legs which is an odd number of legs for a horse. The only number that is even and odd is infinity, hence horses have an infinite number of legs.
There is also lemma that since Alexander the Great rode a Black horse, he did not exist, but if he did exist he would have an infinite number of arms and legs
pinerd3
This is clever, but I wouldn't call it a variation on this style of proof — the OP was an example of a somewhat-subtle logic error, while this is just two instances of wordplay (forelegs ⇔ four legs; six legs being an 'odd' number of legs for a horse).
The joke is funny though
I don't understand. How is that six legs? How is that an odd number? Am I missing a joke?
erulabs
Yes, it's an English language joke:
Two legs in back, and "forelegs" in front (four-legs). 2 + 4 = 6, which is a peculiar (aka odd) number of legs for a horse to have. Thus horses have both odd and even number of legs, meaning horses have infinite legs.
pfdietz
Actually, the argument was that Alexander the Great had an infinite number of arms. You see, in a famous battle he was forewarned. And as we all know, forewarned is four armed. The rest of the argument is similar.
Holy moly did I miss the joke
I'm a complete native and fluent English speaker for 30+ years.
Thank you for the explanation - I know others here may need it but, and in all kindness, I'm lmaoing over here being explained this joke like a toddler.
forelegs means "front legs", but also sounds like "four legs". "odd number" means "strange number", and also "number not divisible by 2".
james_in_the_uk
Six legs on a horse would be very odd indeed
The situation could be much worse.
https://www.penny-arcade.com/comic/2008/05/26/the-unhorse
allannienhuis
fourlegs
charcircuit
infinity is typically not defined to be even or odd.
georgeoliver
Wow, I guess I should have studied logic!
Can someone explain in English how the author goes from "[now] suppose for all sets of n horses, every horse in the set has the same color" to 'proving' anything?
amalcon
Though incorrect, this is meant to be an example of proof by induction. Proof by induction is (to simplify a little) where you prove that any number N+1 will have a given property as long as N has that property. You can use this same rule twice to prove that N+2 has this property, and so on.
Finally, you prove that any arbitrary number (say, 1) has the property in another way, and you've proven that property for all N greater than or equal to 1.
The error in the proof is explained in the linked page, but basically the problem is that the proof that N implies N+1 doesn't actually work for all N, and particularly it doesn't let us go from 1 to 2.
joppy
This is standard induction: let P(n) be some statement about the number n. If you can establish that P(n) implies P(n+1) for all n >= 1, and that P(1) is true, then P must be true for every positive integer. You can find many examples by googling for "induction proof".
The problem in the proof is that the inductive step P(n) implies P(n+1) only holds for n >= 3, and so the fact that P(1) is true does not imply anything for the larger integers.
didibus
Okay, but my issue and I think the one of the OP is that even for n >= 3 how did they prove that all horses are the same color for n >= 3?
It's not proven in a vacuum: it's proven under the assumption that it's true for N-1. E.g. if we assume that all groups of 2 horses are the same color, we can prove that all groups of 3 horses are by labelling them A, B, C. A and B are the same color because they are a group of 2; B and C are the same color because they are also a group of 2; A and C are the same color transitively (or because they are also a group of 2). Therefore A, B, and C are the same color. This step is logically sound, and you can do this for any N greater than three.
The problem is that this fails when tried for N=2, because then each sub-group can have only one horse in it. We already know that each horse is the same color as itself, so we don't actually reveal any new information by doing this. Since it doesn't work for N=2, the base assumption used for the N=3 case is incorrect.
dack
Yeah this is why I'm confused as well. I don't follow how if we assume n are the same color, that it implies anything about n+1. It sounds like the article is saying that the N+1 logic makes sense for n > 2, but I don't see how it does.
jpmoral
The idea is that if it holds for n = 3 then it holds for n > 3. The way to show that it holds for n = 3 is to show that it holds for n = 2, which it doesn't.
bonaldi
This is quite tricky to do, because it's almost a sleight of hand and expressing it in English is like watching the trick from behind the magician - you can obviously see the wrongness.
But: if you skip a pair of horses (which is how the trick is done/the error introduced) it might be:
Assume any group of 3 horses are the same colour. Can we show that adding another horse will result in a group of horses that are all the same colour?
Well yes: take your new group of 4 horses, and extract 1. (h1). Three horses remain and they must by definition be the same colour. Put h1 back and extract a different horse (h2). Now three remain and must by definition be the same colour as each other.
But when h2 was out, h1 was part of a group that was all the same colour. And when h1 was out, h2 was part of a group that was all the same colour. Therefore they must all be the same colour. It doesn't matter how many different horses you find and bring to your initial group of 3, the rules will mean the resulting group of 4 is always the same colour. And so it is true for a group of 4 horses.
By the same reasoning, it must then be true for a group of 5, and so on up to all horses.
So all horses are the same colour, so long as the first assumption (that any group of 3 horses must be the same colour) holds.
The trick/error is jumping from "a group of 1 horses must all be the same colour" to "a group of 3 horses must be the same colour" which is an easy jump to miss if you go from "1" to "n", instead of "1" to "3".
(The logic doesn't work for a pair of horses, because once h1 is taken out there are no other horses left that h2 must be the same colour as.)
marcodiego
This is called proof by induction. There is an intuitive path to understand it: Consider the set of the natural numbers; it contains 0 (zero) and for any K which belongs to this set, its successor (K + 1) also does. It is clear that if a property if valid for 0 and, in the case it is valid for a K which is not 0 implies it is also valid for K + 1, then such property is valid for all natural numbers.
TylerE
He does't. Read the last paragraph:
This false proof highlights the danger of neglecting the base case of an inductive argument. Here the true base case was not n=1, but rather n=2. Since the base case is false, we should have prudently stopped our argument there before embarrassing ourselves.
This brings up an interesting problem with inductive arguments I've never thought of: how does one prove a base case is a sufficient starting point for induction? In the horse example, we know there can be groups of multi-colored horses so our intuition guides us to a counter example, but it seems like a detail like that could easily be overlooked for something more complicated.
You have to find the minimal case where the inductive invariant is valid. In this case when the horses are separated into two groups, A and B, the assumption is that their intersection is non-empty (A ∩ B ≠ ∅). Because only in the case where the intersection is non-empty can we apply transitivity of equality to conclude that their union (A ⋃ B) satisfies what we are trying to prove. But as the article argues this fails for a very simple counter-example where A and B are non-empty but their intersection is empty.
auggierose
Sorry, this answer is confusing. The base case just needs to have the property you want to prove. The induction step does all of the heavy lifting to go from n to n+1. In this case, the induction step fails, because it cannot go from 1 to 2. Simple as that.
Edit: I removed the wrong. It's just confusing.
Where exactly is my error?
Any example is a base case that is sufficient for starting an inductive truth, as long as it is covered in your inductive rule.
The actual error is is a logic error in the proof of the inductive rules that takes a logical step that only holds for n>=2 but doesn't acknowledge that condition. If that logical step is done properly and the condition made explicit, it is clear that a base case of n=1 won't prove anything with that inductive rule that only applies to n>=2.
You don't have to. See my top level comment. In short, you have to strengthen your goal in order to have a strong enough inductive hypothesis to prove anything. E.g., instead of "picking a base case" that's sufficient, you work the base case into the goal, like n >= 2 -> P(n). Then you do the base case as part of a branch in the inductive step, without using your inductive hypothesis.
You can't, you just make assumptions with imperfect information. https://plato.stanford.edu/entries/goedel-incompleteness/
k_bx
> In particular, h_1 is brown. But when we removed h_1, we got that all the remaining horses had the same color as h_2. So h_2 must also be brown. Hence, all horses in H are brown.
This is an error. h1 and h2 don't have to be the same by any previous conclusions. If you have two horses, white and brown, it's true to say if we remove one or another that "all horses that are left are same colour", but they by no means need to be of same colour between themselves.
ineedasername
Reminds me of "everything has a 50/50 chance".
Because for any event or proposition it will either happen or not happen, two possible states. And you figure probabilities from the canonical fair coin and come up with two states & a 50/50 chance of either one coming up. So the proposition "A giant meteor will hit the Earth tomorrow" will either happen or not happen, so there's a 50/50 chance of a global extinction event tomorrow.
fallingfrog
Hmm, I think there is a more basic error here. If you remove an element from your set of n + 1 horses, you get different sets of n horses depending on which one you take out. Here's where the mistake is:
"Consider any set H of n+1 horses. We may pick a horse at random, h_1 in H, and remove it from the set, getting a set of n horses. By the inductive hypothesis, all of the n remaining horses are the same color.
On the other hand, if we remove a different horse h_2 in H, we again get a set of n horses which are all the same color. Let us call this color "brown," just to give it a name. In particular, h_1 is brown. But when we removed h_1, we got that all the remaining horses had the same color as h_2. So h_2 must also be brown. Hence, all horses in H are brown."
Nope, when you removed h1, and when you removed h2, by assumption you got two sets of uniform color, but you never proved they had the same uniform color as one another. The ambiguity lies in the English phrase "same color" which can be interpreted in two different ways. It could mean "uniform color within the set of n horses" or "uniform across every set of n horses".
Edit: You seem to have deleted the part I was responding to. Here's a new response:
> Nope, when you removed h1, and when you removed h2, by assumption you got two sets of uniform color, but you never proved they had the same uniform color as one another.
This part of the proof happens sneakily here:
>> But when we removed h_1, we got that all the remaining horses had the same color as h_2.
The sneaky part is 'all the remaining horses' which does allow you to prove they're all the same color if the number of "remaining horses" is > 0.
This is where the inductive step sneaks in the n>=2 assumption.
> The base case is the former but the inductive step appears to be assuming the latter
The inductive step doesn't make that assumption. What it does do is assume that n>=2. The step basically says: from a set s1 of n+1 horses, remove horse h1 (this assumes n>=0). This gives you a set s2 of n horses, and we already know that all sets of n horses have horses of one color. Now take the original set of n+1 horses and remove a different horse (h1<>h2 assumes n>=1), leaving a set s2 of n horses, which we again already know are all same color. Now assume that there is yet another horse h3 (h1<>h2<>h3 assumes n>=2) that is in the original set s1. Since h3 is in s2 with h1 and in s3 with h2, h3 is the same color as h1 and h2. Since h3 is any arbitrary member of s1 besides h1 and h2 we know that all members of s1 are the same color.
Thus the inductive rule is indeed valid for every n≥2. If you can ever prove that every pair from a horse population has the same color you have also shown that every size of sets of horses from that population will also all have the same color.
SamBam
Consider if it were true that, for any set of 3 horses, they were all the same color (within the set of three).
This would mean it would be impossible to have a set of 3 brown horses and a white horse hanging around.
Why? Because if you added the white horse to the group and removed another horse, then you wouldn't have a group of three of the same color. So this would contradict our assumption.
So, if our assumption at top is true, it can only be true if all horses are the same color.
That's all that the original proof is saying, only stated slightly differently. It's saying that the only way the hypothesis could be true for N is if it's also true for N + 1.
vecter
You can conclude that H - {h1} and H - {h2} share the same color with each other because (assuming n >= 2), there will be a third horse h3 in both those sets. Therefore by transitivity, these two sets must have the same color.
This is implied and not explicitly stated, so it could be clarified.
mstade
This reminds me of another story involving horses and, while not quite as formal as this, at least involved some creative (or humorous at least) argumentation.
A while back in Sweden some fella started a movement which argued that horses are in fact a fruit that does not exist. It became a quite popular meme and the founder was even interviewed on national television. (Yes, really.) When asked how a horse could possibly be a fruit that doesn't exist, he likened them to dragons. See, dragons are a kind of lizard, but they're also just a figment of our imagination and so therefore can not possibly exist. Horses are the same except they're a fruit, and they don't exist. He presented this argument with a straight face in the middle of a riding school with horses in the background, leaving the interviewer dumbfounded. It was a glorious and hilarious moment in Swedish television history.
Unrelated to inductive reasoning, but a fascinating fact is that humans are naturally dark skinned (native Europeans used to have blue eyes and dark skin), some humans today have melanin mutations that cause them to be lighter, and chimpanzees are all white: they are just covered in black hair.
BeFlatXIII
Related to skin pigmentations, a "white" horse with a black nose is, in fact, a fully greyed-out horse. True white horses have pink noses and are much rarer.
I think a better explanation would be that the induction step missed an edge case: To claim that H/h1 and H/h2 are the same color, we need the two sets to overlap by at least one horse. This actually works perfectly for all but n=2...

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* Ymca
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The Ocean County YMCA's Crochet Club hosts first-ever Made With Love event at The HOPE Center
The Ocean County YMCA partners with national nonprofit to provide warmth for those in need this winter.
By: Ocean County YMCA
The Y hosts Made With Love event.
TOMS RIVER, N.J. - Jan. 13, 2021 - PRLog -- The Ocean County YMCA has proven once again that it is more than just a gym and swim center. Through the years, the Y has continuously responded to various needs in order to serve the community. That call has not changed in the New Year, in fact, it is stronger than ever as members of the Y's Crochet Club hosted its first-ever Made With Love event at The HOPE Center in Toms River on January 6. This initiative was made possible through the efforts of Warm Up America! – a national nonprofit based out of Dallas that spearheads the annual initiative.
"Made with Love has been going strong for seven years now here in Dallas," said Jenny Bessonette, Executive Director of Warm Up America! "We are so thankful for our national volunteers who generously host their own Made With Love events across the country."
Andrea Amante, Crochet Club Program Coordinator at the Ocean County YMCA says she is continuously humbled and amazed by the generosity and tenacity of the women in the crochet club. "When the Y, and the world at large, shutdown in March, they quickly adjusted to meeting via Zoom rather than put our activities on hold," she said.
When Amante suggested joining the Made With Love initiative with the goal of crocheting 1,000 items, the club got to work. "Not only did they tirelessly crochet projects, but they spread the word about our project far and wide," she added. "As a result, the Ocean County YMCA Crochet Club was able to donate over 1,600 warm winter items to those in need in our community!"
Volunteers at The HOPE Center will distribute 850 items to families and individuals throughout the winter. The remaining 750 gifts of warmth have already been donated to local Code Blue Warming Centers and to a senior center. "Throughout the pandemic, these women have continued to meet virtually and work on various other projects," said Peter T. Rosario, President & CEO of the Ocean County YMCA.
Another important social initiative taken on during the pandemic was "CLICK for Babies: Crochet a Cap, Help Save an Infant", which was organized by the National Center on Shaken Baby Syndrome. "Ladies in our Crochet Club crocheted caps in all shades of purple that were distributed to new parents, along with a video and booklet about Shaken Baby Syndrome," said Rosario.
The group also participated in the "Hooked on Crochet" initiative during Dr. Martin Luther King Week of Service by crocheting nests for the millions of displaced and injured birds being rescued and rehabilitated as a result of wildfires in Australia.
"We hope and pray that these projects not only provide physical warmth to those who receive them, but also spiritual and emotional support knowing that each one of these projects was handmade for them with love and kindness by their fellow neighbors," said Rosario. "This is what the YMCA is all about – strengthening the foundations of community."
To learn more about Ocean County YMCA or to make a donation, visit ocymca.org.
About WARM UP AMERICA!
Started in a small Wisconsin town with neighbors knitting and crocheting afghans for people in need, Warm Up America! is a charity that has warmed people's lives since 1991. Founder Evie Rosen came up with the idea of having volunteers knit or crochet small sections and then others join them together to make a full afghan, which quickly caught on. Thanks to the generosity of knitters and crocheters around the country, today Warm Up America! distributes warm blankets, hats and other items to tens of thousands of people in need.
About The Hope Center
The HOPE Center is a 501(c)(3) non-profit organization initiated by the Clergy Association of Greater Toms River. Its mission is to provide support, resources, referrals, food to clients as they work to overcome a current life crisis. To learn more, visit houseofhopeocean.org.
About the Ocean County YMCA
At the Y, we take immense pride in our work to strengthen communities and help all of us be our best selves. We provide a place to play, to learn, to be healthy, and to give back. We believe that everyone, no matter who they are or where they are from, deserves the opportunity to reach their full potential. Everything the Y does is in service of making sure people and communities thrive. The Ocean County YMCA in Toms River features the following onsite amenities: 6,800 sq. ft. functional wellness arena, cardiovascular center, 12 lane competitive size pool with access to adult and family locker rooms, and child watch room. To learn more, visit ocymca.org.
https://ocymca.org/ocean-county-ymca-hosts-made-with-love...
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text:
Melun, Île-de-France
Paris and Environs Sketchbook
Turner Bequest CCLVII 77 a
With the sketchbook turned horizontally, Turner filled much of this page with cursory sketches of the architecture of the riverside town of Melun, located some twenty-eight miles south-east of central Paris on the banks of the Seine. The medieval Église Saint-Aspais is featured on the left-hand edge of the page. Turner made several sketches of Melun in the present volume, a list of which is provided in the sketchbook Introduction. For the watercolour of the town which Turner worked up with a view to engraved reproduction around this time, see Tate D24690 (Turner Bequest CCLIX 125). This led to an illustration in the 1835 volume of Turner's Annual Tour: Wanderings by the Loire and Seine (1833–5; later reissued as Rivers of France); see Tate impression T04725.
John Chu
bridges and viaducts(4,130)
bridge(3,996)
features(8,906)
tower(2,977)
townscapes / man-made features(21,691)
townscape(3,313)
river(7,970)
places(41,542)
cities, towns, villages (non-UK)(13,330)
Melun(15)
countries and continents(17,513)
France(3,518)
Joseph Mallord William Turner Melun, Île-de-France
Joseph Mallord William Turner Provins, Île-de-France
Joseph Mallord William Turner Saint-Germain-en-Laye, Île-de-France
Joseph Mallord William Turner Corbeil-Essonnes, Île-de-France
Joseph Mallord William Turner Vincennes, Île-de-France
Joseph Mallord William Turner ?Saint-Cloud, Île-de-France
Joseph Mallord William Turner Charenton-le-Pont, Île-de-France
Joseph Mallord William Turner Saint-Cloud, Île-de-France


text:
Petxenegs o Patzinaks (llatí: Расinасае, Romanès: pecenegi, armeni: badzinag, Búlgar/Rus: petxenegui (Печенеги), grec: Patzinaki/Petsenegi (Πατζινάκοι/Πετσενέγοι) o menys freqüent Πατζινακίται, hongarès: Besenyő, turc antic (suposat): *Beçenek, Turc: Peçenekler) foren una horda túrquica semi-nòmada de les estepes de l'Àsia Central que parlaven la llengua petxeneg, inclosa al grup de les llengües turqueses. Van formar part del kanat dels Turcs Occidentals (vers 560-700) i després foren expulsats pels karluks cap al baix Sirdarià i la mar d'Aral i van establir com a terres de pastura les situades entre l'Ural (Yayiq) i el Volga (Itil).

Etimologia
El seu nom és incert i s'ha proposat com a etimologia bajanak o bajinak que vol dir 'per aliança', és a dir una tribu o clan format per aliança. Al  els xinesos esmenten els Pei-ju identificats com els petxenegs per Pelliot, però també amb els Sui-shu i els alans. Un document tibetà del segle VIII esmenta els Be-ča-nag i els Hor (oghuz) a la regió del Sirdarià. Estarien aliats amb els Kangar (probablement els kengeres de Transcaucàsia o Àsia central.

Llengua
Mahmud al-Kashgari, un home de lletres del  especialitzat en dialectes turcs, va argumentar que la llengua parlada pels petxenegs era una variant dels modismes cuman i oghuz. Va suggerir que les influències estrangeres sobre els petxenegs van donar lloc a diferències fonètiques entre la seva llengua i l'idioma parlat per altres pobles turcs. Anna Comnè també va afirmar que els petxenegs i els cumans compartien una llengua comuna. Encara que la pròpia llengua petxenega es va extingir fa segles, els noms de les «províncies» petxenegues documentades per Constantí Porfirogènit demostren que els petxenegs parlaven una llengua turca. Es creu que els petxenegs pertanyien a la branca oghuz de la família turca, però la seva llengua està poc documentada i, per tant, és difícil de classificar.

Història

Orígens
Entre el 889 i el 893 foren expulsats de les seves terres pels turcs oghuz, karluks i kimaks i van entrar a territoris dels khàzars, als que probablement abans pagaven tribut (o els en van pagar llavors), però que posteriorment els van refusar; llavors es van dirigir més a l'oest i es van establir a un país que van anomenar Lebèdia (que era el nom dels seus caps) al nord de la mar d'Azov, on fins llavors vivien els magiars. Segons Constantí Porfirogènit parlaven la mateixa llengua que els cumans o qiptxaqs però Mahmud al-Kashgharí els associa més aviat amb els búlgars, parlant un turc especial amb els finals amputats Van continuar avançant cap a l'oest i van arrabassar als magiars el país anomenat Atelkuzu (la part occidental de l'estepa russa entre el Dnièper i el baix Danubi. Vers el 900 portaven una vida nòmada entre la desembocadura del Dnièper i la del Danubi.

Simeó I de Bulgària (893-927) els va utilitzar per combatre els magiars, aliats romans d'Orient (894-895). El 915 estaven en relacions amb els russos, eren aliats de Bizanci, i atacaven els búlgars. El 920 s'enfrontaven als russos. El 934 es van aliar als hongaresos per envair l'Imperi Romà d'Orient per Tràcia; el 944 el príncep rus Igor va baixar fins a Constantinoble i va tenir el suport dels petxenegs, però aquestes accions foren puntuals. El 972 van caure en una emboscada fatal del sobirà rus Sviatoslav. Les relacions amb els russos encara van empitjorar sota el regnat de Wladimir (978-1015), la qual cosa els va dur a la guerra (988-1006 o 1007).

El 1026 van passar el Danubi però foren rebutjats per Constantí Diògenes; el 1036 Iaroslav I de Kíev els va infligir una greu derrota que, junt ama la seva aliança amb els cumans i oghuz, va comportar que fossin foragitats de l'estepa russa i que fossin obligats a dirigir les seves ambicions cap a territori romà d'Orient; així el 1051, pressionats pels oghuz, van envair l'Imperi; el 1060 els russos van derrotar els oghuz occidentals i poc després els cumans entraven a l'estepa pòntica, i altre cop van ser empesos i van haver d'envair territori de Bizanci 1064 per Tràcia, arribant fins a les portes de Constantinoble; els romans d'Orient els utilitzaven com a mercenaris però amb el perill que aquest turcs d'Europa no guardessin fidelitat a l'emperador quan lluitessin contra els turcs a l'Àsia Menor, com efectivament va passar el 1071 en vespres de la Batalla de Manazkert, quan els mercenaris petxenegs van abandonar les tropes imperials i es van passar a Alp Arslan, el sultà seljúcida.

El 1087 els petxenegs van atacar altre cop l'Imperi entrant a Tràcia fins a Koulé (entre Enos i Constantinoble) on foren finalment rebutjats; el seu kan, Tzelgu, va morir. Aleix I Comnè els va perseguir i fou derrotat a Dristra (Silístria) la tardor del 1087, i els imperials es van salvar per l'arribada d'un altra horda turca, els cumans o kiptxak (polovtzes dels russos) sorgits de l'estepa russa al darrere dels petxenegs, als que van derrotar a la vora del Danubi.

Quan els cumans o kiptxak van retornar a l'estepa russa els petxenegs van tornar a l'atac (1088-1089) i van arribar fins a Ipsala, al sud d'Adrianòpolis, on Aleix Comnè va haver de comprar la pau. El 1090 es van aliar als seljúcides d'Àsia Menor per atacar Constantinoble per la vall del Maritza, d'Adrianòpolis a Enos, mentre la flota dels seljúcides, amb base a Esmirna, atacava les costes, i des de Nicea, l'exèrcit seljúcida amenaçava Nicomèdia. Els petxenegs van passar l'hivern a Lülé Burgàs, davant de les línies romanes d'Orient que s'havien retirat fins a Txorlu; Aleix va cridar altre cop els cumans o kiptxak que, dirigits per Togortak i Maniak, van tornar de Rússia i van sorprendre els petxenegs per la rereguarda; el 29 d'abril del 1091 els romans d'Orient i kiptxak units van derrotar decisivament els petxenegs a Levúnion. Els petxenegs foren delmats i molts es van unir als cumans o van passar a ser mercenaris per a Bizanci, per a Rússia (on foren anomenats Caputxes Negres o Černii Koblutsi) o per al rei d'Hongria. Els que van sobreviure com a lliures es van retirar a Valàquia i encara van fer un nou intent, una generació després, el 1121, limitada a Bulgària, però foren sorpresos i massacrats per l'emperador Joan Comnè la primavera del 1122.

En les cròniques del  de Mahmud Kashgari Divânü Lugâti't-Türk, el nom de Beçenek rep dos significats. El primer es refereix a "una nació turca que viu als voltants del país de Rum", on "Rum" s'utilitzava entre els turcs per referir-se a l'Imperi Romà d'Orient. La segona definició de Kashgari era la d'una branca de turcs Oghuz i descrivia els Oghuz com un llinatge de 22 branques, sent la 19 l'anomenada Beçenek. Max Vasmer deriva el nom de la paraula turca "cunyat, parent" (Bacanak en Turc actual).

Sigui quin sigui l'origen, els petxenegs apareixen tan sols a les fonts escrites de la història als segles  i , com a habitants de la regió de les valls inferiors del Volga, el Don i les muntanyes dels Urals. Entre els segles  i  controlaven les estepes del sud-est d'Euràsia i la Península de Crimea. Encara que van representar un poder regional important a la zona, com moltes altres tribus nòmades el seu concepte d'estat no va anar més enllà que la d'efectuar atacs i pillatges ocasionals als pobles veïns i de llogar-se com a mercenaris a altres estats i pobles.

Si hem de fer cas a les fonts de Constantí Porfirogènit, escrites el 950, Patzinakia, el regne petxeneg, arribava a l'oest fins al riu Siret (i fins i tot a la franja oriental dels Carpats), i es trobava a quatre dies de marxa de "Tourkias" (segurament l'actual Hongria).

De les fonts armènies
A les cròniques armènies de Mateu d'Edessa els petxenegs són anomenats un parell de vegades. La primera menció és al capítol 75, on es diu que l'any 499 del calendari armeni, que correspon als anys 1050-51 del calendari gregorià) el poble Badzinag va atacar diversos estats de Roma, p. ex. al territori romà d'Orient. La segona menció es fa al capítol 103, que tracta de la batalla de Manazkert. En aquest capítol es diu que els aliats de Roma, els Padzunak i els Uz (branques dels turcs Oghuz) van canviar de bàndol durant la batalla i van començar a lluitar contra les tropes de l'Imperi Romà d'Orient, (al costat dels turcs Seljúcides). En el capítol 132è es descriu una guerra entre Roma i els Padzinags que segueix amb la derrota de les tropes romanes d'Orient, i un setge fracassat contra Constantinoble pels Padzinags. En aquest capítol, els Patzinags es descriuen com una exèrcit d'arquers. En el capítol 299, el príncep armeni, Vasil, que lluitava a l'exèrcit romà d'Orient, va enviar una expedició de Padzinags (que habitaven la ciutat de Misis, prop de l'actual Adana, molt lluny de les terres que habitaven els petxenegs) a l'ajuda dels cristians.

Aliança amb l'Imperi Romà d'Orient
Al , els romans d'Orient van aliar-se amb els petxenegs, utilitzant-los per defensar-los d'altres tribus més perilloses com les tribus eslaves i els magiars. Es tracta d'una antiga estratègia romana de dividir i vèncer que va ser continuada durant la fase medieval utilitzant les enemistats tribals.

Els Uz, un altre poble turc de les estepes, van ser expulsats pels petxenegs de la seva terra; degut a això van efectuar pillatges i atacs per aconseguir aliments i altres béns. Una aliança dels oghuz, kimaks i karluks també va pressionar els petxenegs, però un altre grup, els samànides, derrotaren aquesta aliança. Pressionats cap a l'oest pels khàzars i els cumans el 889, els petxenegs igualment van empènyer els magiars a l'oest del Dnièper el 892.

El 894, els búlgars entraren en guerra contra l'Imperi Romà d'Orient. A principis del 895, l'emperador Lleó VI el Savi va emanar l'ajuda dels magiars, que van enviar un exèrcit sota el comandament de Levente a l'interior de Bulgària. Levente va liderar una campanya excel·lent i va envair el cor de Bulgària, mentre que l'exèrcit romà d'Orient va envair Bulgària des del sud. Atrapat en la pinça dels magiars i els romans d'Orient, el tsar Simeó I va adonar-se que no podia lluitar en dos fronts, i ràpidament va concloure un armistici amb l'Imperi Romà d'Orient.

El tsar Simeó va utilitzar els petxenegs per defensar-se dels magiars. Els petxenegs van ser tan efectius que fins i tot van expulsar els magiars de les estepes pòntiques empenyent-los a l'oest del baix Danubi, fins a la planúria de la Pannònia, on més tard fundarien el regne d'Hongria.

Decadència
Des del , els petxenegs van iniciar una relació inestable amb el Principat de Kíev. Durant més de dos segles van efectuar pillatges i atacs a les terres eslaves, que a vegades van esdevenir guerres a gran escala (com la guerra del 920 d'Ígor de Kíev recollida a les cròniques), però també van crear-se algunes aliances temporals (p. ex. el 943 en la campanya de Igor contra els romans d'Orient). El 968, els petxenegs atacaren i assetjaren la ciutat de Kíev.

Alguns petxenegs acompanyaren el príncep de Kíev Sviatoslav I en la seva campanya contra Bizanci el 970-971, encara que els petxenegs van matar el príncep de Kíev en una emboscada el 972, i d'acord amb les cròniques, el Kan petxeneg Kurya va fer una tassa amb la seva calavera; una costum tradicional dels nòmades de les estepes. La balança de les lluites entre els eslaus i els petxenegs va canviar durant el regne de Vladímir I de Kíev (990-995), qui va fundar la ciutat de Pereiàslav en el lloc de la victoria sobre els petxenegs, però va seguir amb la derrota dels petxenegs durant el regnat de Iaroslav I de Kíev (1037). Poc després, els petxenegs van ser reemplaçats de les estepes pòntiques per un altre poble nòmada turc els cumans o Polovtesos.

Després de segles de lluites contra tots els seus veïns: L'Imperi Romà d'Orient, Bulgària, el principat de Kíev, Khazària i els magiarss. Els petxenegs van ser exterminats com a força independent a la Batalla de Levúnion per un exèrcit combinat de romans d'Orient i cumans sota el comandament de l'emperador Aleix I Comnè el 1091. Atacats un altre cop el 1094 pels cumans, molts petxenegs van ser assassinats o assimilats. Van ser una altra vegada derrotats pels romans d'Orient a la batalla de Beroe el 1122, al territori de l'actual Bulgària. Durant algun temps, comunitats significatives de petxenegs romangueren encara a Hongria, però finalment van deixar de distingir-se com a poble per ser finalment assimilats pels seus veïns—búlgars, magiars i Gagaús. Durant el  va haver a Hongria un cert renaixement de gent que addicionava al seu nom el nom de petxeneg. Gran part dels petxenegs vivien a la regió de Tolna. Abu-Hàmid al-Gharnatí a finals del  es referia a petxenegs que habitaven a Hongria. Altres van sobreviure amb grups de tribus nòmades de pastors de les terres altes dels Balcans com a Yörüks i finalment van adoptar l'islam.

Costums
 Incineraven als morts
 N'hi havia que portaven barba i altres que no
 Vestien túniques curtes
 Des de finals del  es van fer cristians (vers 988-991), però el 1009-1010 per influència d'un fakih captiu molts es van fer musulmans.

Kans dels petxenegs
 Kurya c. 970
 Metiga c. 980
 Kuchug c. 990

Referències

Bibliografia
 Pálóczi-Horváth, A. (1989). Petxenegs, Cumans, Iasians: Gents de les estepes a l'Hongria medieval. Hereditas. Budapest: Kultúra [distributor].
 Pritsak, O. (1976). The Pečenegs: un cas de transformació econòmica i social. Lisse, Netherlands: The Peter de Ridder Press.

Enllaços externs

 www.patzinakia.ro
 Crònica Primera
 Dels petxenegs

Grups turquesos
Rus de Kíev

redpajama_set_name: RedPajamaWikipedia


It is undisputed: SF6 is an excellent quenching and insulating gas that has been used in the energy sector worldwide for more than 50 years. The energy related development in the high and extra high voltage range would have been impossible without the use of SF6 with its excellent dielectric stability and good electric arc quenching properties.
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Today is the first day of the summer clothing season. It's 60º in New York, and 52º in Paris, where I wish I was today. I'll bet the Chestnut buds are about to pop. It's sweater weather (a tan cashmere Martin Margiela V-neck) and I'm wearing white-and-brown saddle shoes. My assistant Michael showed up for work in off-white-and-brown saddles today. I know we were both shod for summer, because today is the first business day of the year where white is traditionally considered right. It's one of those nice old fogey rules that I like to keep up, the same as taking my hat off in an elevator or walking on the curb side of a lady.
Nobody loves rules like an anarchist, which I consider myself in theory. To a real anarchist, laws are unnecessary because good manners should be enough to deter improper actions. Usury is tacky. Assault is undignified. Identity theft is simply not done. I know I'm an idealistic dreamer in this, but I have every confidence that some day humanity will be guided by cultural principles, not legal codes.
To me the rules of dress are simply proven principles, like the Golden Section or the Fibonacci number. I don't say you can't wear white shoes before Memorial Day; but I tend not to. And in my own personal code, because of global warming, I have moved the official white shoe day forward to Major League Baseball's opening day, and extended the white shoe season through the World Series.
Correct shoes during baseball season.
My white dinner jacket has finally been located. (I couldn't find it the other day when I wanted to show it to some guests. It was in the basement, thank the insect god unharmed by the moths, carpet beetles, and other vermin that frequent that dicey space.) The seersucker is ready to go, although it will not be premiered on a sub-80º day, as are the linen and madras.
Let's think about linen for a moment. There is no good reason why linen should be worn only in the warmest months. In our time of global warming, linen should be worn much more often. For one thing it is a much more environmentally-friendly fabric than cotton, which is one of the most problematic crops in the world. (For enlightenment on the problem of cotton I highly recommend watching the documentary The World of Monsanto.) Linen is not only Earth-friendly, it is also longlasting and superior in strength. I have a great old Issey Miyake linen suit that is heavy enough for October and I have no compunction about wearing it then.
The natty art dealer Barry Friedman in a proper linen jacket.
White suits or suits in the ice-cream hue range are traditionally for summer, although NBA coaches seem entirely unaware of the convention. And of course Tom Wolfe has made winter white a dandy's splendor, and women have made it an institution—so there's no reason men can't wear white of a certain weight in outerwear. It has a long and honorable tradition among "Alpine troops," and my wife has a wonderful Jean-Paul Gaultier toggle coat that I would wear if it were my size.
The author in a white cotton Ralph Lauren blazer and Hermes sailor shirt with hat designer Stephen Jones, in Stephen Jones hat.
Anyway, the last week or so has seen me storing away the overcoats, the cold weather gear, and my heaviest suits (the 13- to 14-ounce Savile Row numbers conceived in their best no-central-heating tradition), and pulling out the Bermudas, the polos, and the patterned trousers. And suddenly here's a whole new selection of duds that I haven't seen or thought about since last September or so. The seasonal transition is interesting because it's a natural moment for wardrobe appraisal and analysis, not to mention taking stock of one's figure. Are you ready for the pool, the links, the clay and grass courts? Are you ready for lolling, basking, and shade-sitting? Are you ready for the seasonal plumage display of an expanded visual spectrum in line with the floral splendor of the botanical world? Are you?
With my madras and linen pressed, I feel rather ready. But every season one notices a few areas that could use reinforcement, improvement, or elaboration. I believe in buying substantial wardrobe additions when I'm flush, but shopping seasonally even when on a budget, believing that you can stick with the same basics, suits, blazers, trousers, etc., by refreshing them with new shirts, ties, and socks. And so I'll be out there over the next week looking for ties that say "this summer," some new polos, and socks.
I'll be out looking for white socks to wear with my white shoes. And I don't mean tube socks. I mean white hose. It's something every well-dressed man should own. I've found good white socks at a good price at Barneys New York, on and off, and have also found good quality thin white socks at Uniqlo. In fact I may head over there right now. And after years of trading barbs on the issue I may go over to the position of GQ "style czar" Adam Rapoport on shorty socks. I have been mocking these for years, suggesting that the men's sub-anklets should feature the same pom-poms one sees on some of the ladies' equivalents, but after several seasons of observing these socks in foursomes I have developed a tolerance that, combined with my own tan line, has shifted my position. So where do you buy yours, Adam?
Of course, for a lot of my friends summer means no socks at all till September. I am not one of the perpetually bare-ankled crowd, as my large Irish feet tend to perspire, but I do find tanned bare ankles okay. But they have to be tanned first. So I'm working on them weekends.
What will I buy this season? I'm always on the lookout for good tees wherever I go. A.P.C., Agnes B., Margiela, Supreme. As for tailoring, I have my old two-button light blue pincord suit in the pile of clothes to be donated to charity. I'm sure it will still look good on someone, but I need a hipper cut. I'm guessing that I bought this at Brooks Brothers ten years ago—as I recall I was on a break from a commercial and I went into the store with Kate Moss. They are cheap to begin with and this one was on sale. I may have paid about a hundred bucks for it. Kate wanted a pincord suit too, but they only had them in boys and they couldn't fit her. Anyway, I need a slimmer suit.
Brooks still offers pin cord, and they've modernized the silhouette with slim lapels and flat-fronts, but at $598 they're not the steal they once were. The GQ boys seem to favor the Uniqlo whipcord suit and I don't blame them. They're sharp and absurdly inexpensive. Sold separately, I think the jacket is $79.50 and the trousers $39.50. You almost can't afford not to buy one.
hi glenn, will you talk on the blog about what happened at interview? im actually really disappointed. i liked the new direction the mag had taken. im thinking especially of an interview you did with richard prince, and an old republished chat between jasper johns and rauschenberg. i guess now it's going back to teri hatcher covers?
Graphic Tee's are in and INDIE PEACE shirts are a great item to have during the Summer and also for the Fall! Check out www.indiepeace.com for more information.
ah, Glenn, great tip on the Uniqlo whipcord.
This time of year I enjoy cutting the legs off my banana republic flat front chinos; voila, broken-in weekend shorts!


Virginia's Working Families Deserve Paid Family and Medical Leave. Now.
Balancing work and family obligations is hard and definitely keeps us busy! We wake up early, get our kids off to school and arrive at work, ready to work hard.


text:
Cosplayers will strut their stuff at The Rand Show later this month
Later this month the annual Rand Show expo is set to take place at the Johannesburg Expo Centre.
As you might be aware, this year The Rand Show will play host to a Fortnite tournament but if gaming isn't your thing there is another geeky contest taking place.
From 20th – 21st April and 27th – 28th April, The Rand Show will play host to a number of cosplay contests. The contests will be facilitated by The Dark Carnival.
"The Rand Show is proud to introduce its first annual Cosplay Competition. The competitions have been structured to appeal to beginners and pros alike and are guaranteed to be loads of fun and an experience never to be forgotten, for both participants and spectators," Kasoa Jabrzemski of The Dark Carnival said in a statement.
So how can you take part?
Firstly, you'll need to head to the Gaming & Entertainment Pavilion which costs an additional R20 on top of the cost for admission to The Rand Show.
The Cosplay Masquerade is described as an informal contest where cosplayers aged six years an up are welcome to learn and talk with other cosplayers.
For cosplayers looking to take competition a bit more seriously, the Cosplay Competition will be held on 27th and 28th April and there are three divisions for the contest. Something to note is that ahead of the contest you will be pre-judged and you will have to perform a skit on-stage.
The Newcomer division is for new and casual cosplayers and there will be three age groups.
13- 15 years
The intermediate division is named Like a Boss and experienced cosplayers are not allowed to enter this particular contest. This competition is for cosplayers with some experience aged 16 years and older.
The big competition is Beast Mode and is purely for experienced cosplayers. This competition is for cosplayers ages 16 and up. The Beast Mode contest will also have a R30 000 grand prize for the winner.
To enter these competitions you'll need to head to this website to register your participation before 7th April. You won't have to submit a photo for the entry.
For more information about The Rand Show's gaming focus for 2019, be sure to head to the official event website.
Oh, and for those wondering, the header image is a cosplayer who attended rAge 2018.
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Brendyn Lotz
Brendyn Lotz writes news, reviews, and opinion pieces for Hypertext. His interests include SMEs, innovation on the African continent, cybersecurity, blockchain, games, geek culture and YouTube.
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New Zealand Engineering News (NZEN) has been the industry's journal of record since 1969. Every month it keeps its 37,810 readers in New Zealand abreast of the latest news, products and processes in an increasingly automated and diverse engineering industry. With design and manufacturing driven by CAD/CAM and robotics support, we make sure our readers are kept up to the minute with technical articles and case studies from New Zealand and overseas to provide models for development.The magazine prides itself on its editorial and content independence but recognises the importance of hands-on editorial input from engineering companies and support services. Advertisers in the company's special features sections are entitled to receive professionally written or edited articles tailored to their needs but providing added value to readers.Every month, well marked sections of the magazine and the online edition will contain valuable insights into related areas such as training and safety programmes, recycling options and the increasing use of plastics and composites to maintain product strength and lose weight.The latest from the backbone of the engineering sectors like welding and CNC machinery are not left out in a rush to new ideas. The latest techniques and products around for steel and metals fabrication, foundry operations and materials and mechanical handling are well covered.In response to trade demand, NZEN introduces, this year, a dedicated section each month on management, banking and finance, recruitment and a monthly section on clean technologies, including preventative maintenance and waste management. All this provided by a team of professional journalists in all major centres around the country.
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text:
Category: The Thermals
The Thermals – Fuckin A
ARTIST: The Thermals
TITLE: Fuckin A
SINGLES: How We Know
OTHER SONGS YOU MAY KNOW: Um..doubtful
LINEUP: Hutch Harris, Kathy Foster, Jordan Hudson
WHAT'S IT ALL ABOUT: The Thermals move into being a real band, and their fury lit up the Pacific Northwest.
SOME WORDS, PHRASES AND CLAUSES ABOUT THIS RECORD: It's hard to believe that Hutch Harris and Kathy Foster were folkies before the Thermals, but they were. Now that Harris, Foster, and Jordan Hudson became the Thermals after Harris recoded and album under that name, there's no 'folk' here, unless it's the punk rock for the people as the new 'folk'.
Harris' guitar screams and howls, much like his vocals on many tracks. Foster's bass is in the Laura Balance mode, distortion and volume and working in lockstep with drums. There's definitely passion and fire here.
It's under 30 minutes long, but it doesn't seem like a rip-off. Harris' vocals and lyrics point to the anger the youth felt about the world in the mid-2000's. A leap forward and worthy of your catalog.
NOTES & MINUTIAE: This was recorded in four days, in a studio (unlike their debut)
GRADE A-: The Thermals were a hidden gem of the 2000's, and this record truly started them toward toward their glory days.
The Thermals – More Parts per Million
TITLE: More Parts per Million
OTHER SONGS YOU MAY KNOW: Not outside of KEXP, probably
LINEUP: Hutch Harris.
WHAT'S IT ALL ABOUT: Basically a solo album for Hutch Harris, who did everything himself. Kathy Foster, his former folkie duo partner, would soon join as he put together a real band.
SOME WORDS, PHRASES AND CLAUSES ABOUT THIS RECORD: It's a cheap album, all done by Hutch Harris, and costing less than $100 to record. It is a bit rough around the edges, but it does sound like the Thermals.
Harris changed directions from his old band with Kathy Foster, who soon joined Harris on stage with Jordan Hudson, writing in a alternative / punk rock style with some earnest vocals.
This is another record where the songs whir and blur together, and it's hard to pick out a standout cut. It's all OK, and Harris and company would improve as they matured as a band.
NOTES & MINUTIAE: The folk due was Hutch & Kathy – which sounds like an SNL skit.
GRADE: C+: I can't say it's great, but it's decent enough in parts. It just all is kind of the same, really.


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Watch Snow White and the Huntsman
"The Fairytale is Over"
Snow White and the Huntsman is a fantasy film that was released in 2012. The movie is based on the fairy tale Snow White. However the movie is an altered version of the fairy tale and is actually a bit of an action adventure film as well. The movie was directed by Rupert Sanders and written by Even Daugherty, John Lee Hancock and Hossein Amini. Another thing to note is that this is Bob Hoskins' last movie as he is now retiring from acting.
As far as the plot and storyline goes, the movie begins as Snow White is born and immediately appointed as the heiress to the throne currently held by King Magnus and Queen Eleanor. Snow White is their daughter as a result. One day the Dark Army invades the kingdom and threatens it. However, King Magnus' forces defeat them and he rescues a very beautiful woman known as Ravenna. Since Magnus' wife is dead he decides to marry Ravenna. However on their wedding night she kills him and takes over the throne. Shortly after she takes over the throne, Ravenna decides to capture Snow White and lock her up in the north tower of the castle since she is a threat to Ravenna. During her reign, Ravenna she rules with absolute authority and regularly sucks the life out of people to maintain her youthful appearance. After consulting with the mirror on the wall, she learns that in order to preserve her youth and maintain her rule she must kill Snow White. Ravenna then orders her to be brought to her but the plan fails as Snow White escapes into the wilderness. The Huntsman is ordered by the Queen to capture her. However he believes that Ravenna will betray him so he helps Snow White learn how to fight and eventually eliminate Ravenna. Eventually Snow White returns to the castle and defeats Ravenna. In the end she takes over the kingdom and peace is restored.
The movie Snow White and the Huntsman got average reviews among some critics. They believed that some key aspects of the movie were mediocre and could have been better such as the acting and the script. However some of the more renowned critics believed that the movie was very good and brought a whole new exciting theme to the movie. With its pacing, action sequences and dark tone, the movie was regarded as a very solid one. It was also quite popular among the audience and viewers believed that it was a fine movie in its own right.
Adventure, Fantasy, Drama
| 2012 | | 6.1/10 | 57/100
Kristen Stewart, Chris Hemsworth, Charlize Theron, Sam Claflin
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Watch Snow White and the Huntsman Trailer
Official Trailer (HD) Kristen Stewart, Charlize Theron|1:52
Watch Snow White and the Huntsman Online - Watch online anytime: Stream, Download, Buy, Rent
Snow White and the Huntsman is available to watch and stream, download, buy, rent on demand at FuboTV, TNT, FlixFling VOD, Google Play, Amazon, Vudu, iTunes, YouTube VOD online.
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This listing is for FEATHERS ONLY - Vase and other accessories pictured are not included. **SOLD PER 1/4LB***BESTSELLER : OP9 - Bulk Ostrich Feathers 4-8"
OP9 Ostrich Feather Drabs will range in size from 4-8" inches long and are available in a variety of colors for all of your projects. OP9LB Ostrich Drabs have wispy hair-like feathers coming out from a stiff center quill (between 1-2 inches long) and will range 2-4 inches wide. These feathers come from the body of the ostrich. Purchasing Ostrich Feathers by the pound are subject to a 10% variance in quality and size.
Image details : Made with only 12 OP9 Ostrich Drabs 4-8"
All Custom Fees or Duty Taxes associated with the international purchase of Peacock, Pheasant, Ostrich or Partridge Feathers are the responsibility of the buyer and are Non-Refundable. In rare circumstances, Customs or Immigration can seize items and/ or can cause a delay in delivery. Our products are made with natural materials; therefore each item will have unique differences and variances.
Some handmade items or parts have been manufactured by our partners in China. THIS LISTING IS FOR FEATHERS ONLY - VASE AND OR ACCESSORIES NOT INCLUDED.


Category: B.Kamins. Tags: B. Kamins, concentrate, Soothing.
This breakthrough Soothing Skin formula soothes sensitive and problematic complexions. The preparation blends easily to cosmetically neutralize and reduce the appearance of blotchiness. Bisabolol helps to restore smoothness while cooling the skin.
Aqua (Water/Eau), Bio-Maple Compound (Maple Isolate)(Acer Saccharum), Ethylhexyl Methoxycinnamate, PEG-8, Cetyl Alcohol, Coco-Caprylate/Caprate, Squalane, Carbomer, Stearic Acid, Cyclomethicone, PEG/PPG-18/18 Dimethicone, Ceteareth-12, Polysorbate 80, Tocopheryl Acetate, retinyl palmitate, bisabolol, sodium hydroxide, phenooxyethanol, capylyl glycol, sorbic acid, Blue 1 (CI 42090), Yellow 5 (CI 19140), Yellow 6 (CI 15985).
Apply Soothing Skin concentrate to affected areas, avoiding eye area, after cleansing. Also may be reapplied throughout the day as needed.
Morning: Follow with Booster Blue Moisturizer SPF 15.
Night: Follow with Night Cream.
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