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For those of you who are knew around here (or those of you with poor memories), I am by training, a mathematician.

Today, you get a mathematics fashion mathematics lesson from 3stylelife, and it directly relates to the transformation from business to casual, and more importantly, the transformation back. The math-phobic readers need not worry; I’ll be gentle.

In mathematics, a function, operation, mapping, doohickey, is called invertible if there exists another function, operation, mapping, or doohickey that exactly undoes the results of the original function, op…you get it.

The concept translates pretty simply to fashion. An invertible action is any one that can (easily) be undone. Why do we care? Take the situation in Business Awesome video. I needed to transform from a (relatively) formal business image to a casual one in a short time.

But, what if I needed to transform back to a business setting quickly (or unexpectedly) as well? Let’s look at the changes I made (in mathspeak, the functions I applied to my outfit):

  • I removed my tie.
    This is reversed easily enough; I’ll I have to do is retie the tie. At worst that’ll take me 25 minutes.
    Verdict: Invertible
  • I unbuttoned and untucked my shirt.
    Again, no big deal; a couple flicks of the fingers and the buttons are redone, hiding the casual v-neck shirt along with it. Tucking the shirt in isn’t much harder.
    Verdict: Invertible
  • I reversed my belt.
    This one’s even more of a no-brainer. They should call them invertible belts.
    Verdict: Invertible
  • I changed my shoes.
    This isn’t as obvious. Shoes are easy to take off (even if I did forget how to tie shoes between the ages of 5 and 10, the velcro years) and put back on. However, I changed my shoes in the car. If I happened to be walking downtown when a business situation, it would have been rather difficult to change shoes (given that I’m not the accomplished wizard I wish I were). Yet still, in most instances I would have enough notice to make this…
    Verdict: Invertible
  • I put on a bracelet.
    Heck, the thing undid itself a few times during the day.
    Verdict: Invertible
  • I chalked my pants
    Well damn. This would be the one highly non-invertible thing I did. While chalk comes out of clothes very, very easily in the wash (trust me, it comes out 100%; it just dissolves in the water), it does not easily rub off. In fact, trying to brush chalk off of fabric just smears it (ruining the image) and pushes it into the fibers (making it harder to remove). It doesn’t behave like a blackboard, where the chalk actually prefers to stick to your hands.
    Verdict: NOT Invertible

As I’ve said; I’m all about versatility, change, and freedom. Invertible actions (like most of the ones described above) keep your options open at all times, and that’s a good thing. Non-invertible actions are often spectacular, but you have to be careful not to paint (or chalk) yourself into a corner.

This doesn’t just apply to picking out clothes but modifying or designing clothes. I’ve drawn designs on blank t-shirts with sharpie markers before. The result is really cool; but that blank shirt option is pretty much gone forever. On the other hand, I’ve used shipping tape to make designs on shirts before (the lack of a link indicates that I should write a post about that…), and that was completely removable. I’m not saying on option is better than the other; you just need to be aware of what you’re doing (like so much in fashion).

P.S.: read the Wikipedia article on Invertibility to see just how complicated mathematicians can make a simple concept. Welcome to my world.

While working on designs, I play around constantly with different artistic and mathematical algorithms, to explore their design possibilities. Much of the time, the stuff I find out is cool, but not what I’m (currently) looking to use in anything for production.

I’ve been looking for a way to put that material to good use; and the obvious solution is you. I can put out some mini-tutorials, and maybe someone out there will find a cool application for it (if you do, let me know!).

The first incarnation of this is a quick description of how to create a “trippy” or heavily patterned Pac-Man shape. The images I’m including here were created using GIMP (an open source image manipulation program), but all the steps should be accessible for all major image editing programs (MS paint excluded).

The process is actually fairly simple, and relies on a mathematical transformation: conversion from rectangular to polar coordinates. In broad terms; this transformation takes a rectangular image and maps it to a circle, as you’ll see in the images.

The first step is to create a patterned design (of your choice) that fills a rectangular canvas fully from top to bottom, but only covers three-fourths of the screen horizontally, as shown below (for more pictures of the pattern, and how it was developed, check out these photos on Flickr):

Why three-fourths? Because our friend Pac-Man is three-fourths of a circle (with an eye). The transformation from a rectangular to a circular image will convert the empty rectangle into an empty “pizza slice” or wedge that will provide the classic Pac-Man shape.

The most likely roadblock you could face is getting the Pac-Man to face the right direction. While it may be feasible to simply rotate the final design, if you have other design elements (or aren’t using layers), this may be difficult. Best to get the transformation right the first time.

To perform the Polar Coordinate transformation (don’t worry, you won’t have to bust out your graph paper and scientific calculator), you’ll likely want to look under the “Filters” category. This is an actual menu heading in GIMP (the full path is Filters -> Distorts -> Polar Coordinates), but may be a little deeper in other programs. Some programs even have plug-ins for this feature.

This will bring up a window with some options for the Polar Coordinate transformation. The pertinent one is called Offset Angle. This determines the angular position on the circle for where the design will begin (and be mapped counter/clockwise around the circle). Click the preview box to view the changes as you alter the value. As shown in this picture; Pac-Man doesn’t exactly look like he’s doing very well:

By adjusting the offset angle to 240 degrees, I rotate the transformation before applying it, getting the image I’m looking for:

The final result is as follows: a cool effect that doesn’t require too much pain to develop. I’ll keep looking for the perfect way to use it; y’all do the same!

-Barry

A brief piece of instructive, creative nonfiction, detailing how I got a great deal on this car in 3 hours despite no preparation or research.

It was already Friday afternoon. Late Friday afternoon, and since work started at 8 AM on Monday, I had approximately 22 business hours left to buy my first car.

Time is the one thing your (newly) local car salesman doesn’t want you to have. Debt, a record, a love for the color red? No problem, anything but time. In a business where competition is high, customer loyalty is almost nonexistent, and price is merely a cloudy impression, comparison shopping is the devil. With time, you can pit companies against each other, like this (scroll down to the section “Negotiate mercilessly with dealers”). But to win this game, you usually need time. I had none.

Time wasn’t the only thing I didn’t have. Experience and credit were nonexistant (thanks to a small college town and a household where plastic is a class 4 hazardous material, respectively). My mental state was quite degraded, a result of having just driven 11 hours through the middle of the night, including a stop at a surprisingly disappointing Denny’s near Busch Gardens.

All I thought I had was that I’d read an article about an author who’d gone undercover as a used car salesman. As I thought back to that computer screen text, the answers formed quickly in my head. My mind wasn’t up to doing the textbook plan of action (and as I said, time was not on my side), but I was just punchy enough to try something a little more unconventional. It was time for a little magic.

- – - – -

The two biggest weapons a car salesman has are intimidation and deception.

Examples of Intimidation

  • Tall men with deep vows and slicked back golden hair.
  • Back-room financial discussions with closed doors and no windows.
  • Drawn out processes increasing your time investment.
  • Speech after speech about one-time offers and deals that end when you leave the room.
  • Leaving you alone in the room after you’ve rejected an offer.

Examples of Deception

  • Any time the words “special deal” are mentioned.
  • Changing finance details between the sales floor and the finance room.
  • Fake computer displays that “notify” you that no bank will provide you credit.
  • The four-square sales method (from the aforementioned article).
  • The “good cop/bad cop” routine.

My only chance was to turn the tables, with a little intimidation and deception of my own. The result? I’m the proud owner of a brand new 2009 Toyota Yaris, negotiated over just 3 hours at $2500 under asking price with an 8.9% interest rate. All this for someone with zero credit and $40,000 in student loan debt.

You can do it too.

Treat the sales room like a deposition.

Anything you say can aid will be used against you during the sale. Starting work on Monday? Oh, you better seal a deal tonight, even if it is a high interest, right? Have some medical bills you’re behind on? Hmm, we’ll have to increase your costs; taking you on is a credit risk! But we’ll sell you a car anyway…

Treat every word with care; volunteer no extraneous information. If you have something incriminating, don’t be afraid to hide it (when legal). Obviously, you can’t lie about your credit score. You can lie about how long you have to make your decision, or how much your great aunt is planning to give you to help out with the down payment. You absolutely can lie about how interested you are in a particular vehicle. Counter deception with deception.

Role Reversal

In the standard interaction, you, the buyer need or very much want a new car, and the dealership is trying to get you to buy one for the highest price possible. They have enormous leverage because you have to buy and they’ll (maybe not in today’s economy) be quite fine if they don’t sell.

While it’s not possible to be in complete control, you can reverse the roles to give you a great deal (sic) more power. To do this, you must convince the dealer that a new car is not a necessity. Perhaps you have a perfectly working (albeit old) car already. Perhaps you found a great used car at that Carmax down the street. Perhaps that’s just going to be your story. Make it clear you’ll buy now only if it’s worth your while; nothing bad will happen if you don’t.

Suddenly, the dealership is lowering the price and revealing “special” programs to create a sale where one might not have previously existed. Even better, they know that every dealership you visit is doing the same thing. That’s a position of advantage, of leverage.

I did it with my own good cop/bad cop play. My parents were in Charleston with me to help me move in, so instead of having the standard interaction develop in which the kid falls in love with a flashy car while the parents try to talk him out of it, we teamed up for a different appearance.

Always be leaving.

We all wanted the Yaris. There can be no denying that. But three eager beavers are more dangerous than one. Thus, we agreed, my parents would be excited about the Yaris, pushing me to buy, while I remained the inexplicable 21-year-old stick in the mud who would be content with that boring, reliable used car (and waffles for breakfast everyday).

The saying in sales is “Always Be Closing.” Car dealers do it well; they are always pushing you to accept the current deal. Every step of negotiation you dismiss is another pay cut for them. The equivalent statement for prospective car buyers is “always be leaving.” Treat every offer as unacceptable, irritating.

My parents helped by letting me be unimpressed to a level that would have forced any salesman to give up on my, had I been alone. If you keep claiming that you’re going to leave, eventually they’re going to agree that it’s a good idea. The power of a third party (a roommate, a significant other, a parent, an attorney) keeping you in the game for the dealer is surprisingly powerful.

A Rabbit in the Back Room

As Denny Crane of Boston Legal would say, the secret to life is to always be able to pull a rabbit out of your hat.

Everything I’d done could have fallen apart if I hadn’t had one last trick up my sleeve, and this is a sure winner. A final rabbit; the last move, the winning move. I had gotten what I wanted in the sales room; $2500 under asking price and at 8.9% interest loan. Unfortunately, every deal you get on the floor can be whisked away in the financial dungeon, if you let it.

The salesman will never blame the dealership. Likely candidates are banks (who “for some reason” can’t approve that level of credit), government and laws, or arcane corporate rules. Or you, but only if the guy is a complete rookie. Regardless, Mr. Finance is giving the best deal his little heart can find, even if its $40 more per month, for 3 more months than you were told!

Never, ever, believe what he says is preventing you from getting the deal the sales person told you. They’ve already crunched the numbers; they can’t be uncrunched. Mr. Finance is trained to use his perceived authenticity and the mystery of mathematics to get you to accept a worse deal than what the dealer is willing to give you.

Now, the saleswoman on the floor quoted me $255 at 8.9% interest. Mr. Finance’s opener? $296 at 10%. Here comes Peter Cottontail…

It turns out that there are only 4 variables that determine the total cost of a vehicle; the principal (that pretty (or scary) number on the sticker), interest rate, down payment, and the length of contract/number of payments. If you know a bit of algebra/calculus, you can come up with a formula for how much you’ll pay over time (and in the process, your monthly payment).

You should have seen the look on Mr. Finance’s face when I wrote down that formula right in front of him. Then I calculated exactly how much he was trying to overcharge me. How’s that for an intimidating little rabbit?


By the way, here is that formula, for your personal use (and hopeful intimidation):

C = (P-D)(1+R/12)^(12T)

To use this formula, plug in the principal for P, the down payment for D, the rate for R, and the number of years in the contract for T. Don’t worry about knowing the math behind it (though if you’re interested, feel free to ask), it’s all a show anyway.

He had no response. It appeared that I knew more about financing than he did (deception at its finest). How could he compete with that? Thirty minutes, and little resistance later, I had my first car.
Glad to see my math degree start paying off in the real world.

Today, I came across a really nice 3-in-1 “dress” which looks like a cuffed-button down, layered cardigan and skirt. Thanks to the bloggers at Omiru for getting it on my radar! Here’s look at the piece:

I think it’s a nice garment (though, personally, I don’t think I could pull it off as well as the oddly shiny mannequins). What the people at Omiru found remarkable (rightfully so) was the price: $36.

What a great deal! $36 for what is essentially a skirt, cardigan, and button down?! How is this possible? It’s an amazing deal, right?

Sort of.

This is where the cool hand of mathematics comes to rain on your parade. 36 bucks is indeed a very flashy, low price for three pieces.

But wait. It’s not actually three pieces, it just looks like that. So how much value is lost when we can’t use the pieces in other outfits? Let’s run some numbers.

Conservatively (read: you can probably find these things cheaper), let’s assume you can get the following prices:

Cuffed Button-down: $35
Cardigan: $40
Skirt: $25

This would mean that recreating this one particular design would cost $100 (277% of our original price). Terrible deal, right?

Sort of. Remember that these pieces are then available to use in other outfits as well, which adds to the value they provide you. Unfortunately, it’s hard to quantify this. Instead, let’s consider the long-term strategy; buying multiple button-downs, cardigans, and skirts:

3 x Button-down = 3 x $35 = $105
2 x Cardigan = 2 x $40 = $80
2 x Skirt = 2 x $25 = $50

Total: $235.

Total number of outfits: 3 x 2 x 2 = 12.

Cost per outfit = $19.58 (about 54% of our original cost).

Even if we assume that some of the combinations just won’t work (perhaps we bought a strongly patterned button down, or an unusually colored cardigan), the better value comes from combining individual pieces. Let’s say only two-thirds of our resulting outfits “work”:

Total number of outfits: (2/3) x 3 x 2 x 2 = 8

Cost per outfit = $29.38 (about 82% of our original cost).

And this doesn’t even account for the added value these pieces have in being mixed with the other garments we already own!

Conclusions:

If you already have an extensive wardrobe, purchasing a combination piece, like the $36 dress above, can be a nice addition; it’s not particularly expensive, even if it’s not necessarily the best value. But don’t think you’re getting an incredible deal, you’re not, because a lot of the value has been removed.

However, if you’re building a wardrobe (new or old), get the most for your money! Purchasing individual pieces gives you a significantly better return for your money (in terms of available outfits), and will also let you use your own creativity a bit more in designing what you wear. A win-win situation in my book!

-III

The strange attractor is a very interesting piece of mathematics (specifically chaos theory). In simple terms, if a physical process is governed by a strange attractor, than some measurable (position, velocity, etc.) changes in a seemingly random fashion, but bound by a set of constraints.

The trajectory is always new, and does not repeat itself, but remains within some extrema. This can be seen clearly in this photo of a Lorenz Attractor.

There is a powerful analogy to the world of fashion here, related to the difference between elementary and interpretive design. So much of design and fashion follows the pattern of a strange attractor, in that the basic structures remain unchanged, and simple, interpretive changes sustain the illusion of progress and change. Changing colors, hemlines, pocketing and detailing.

It’s rare that change in fashion adds a new degree of freedom, a completely new set of trajectories to explore and fill. Why? It’s risky, dangerous, probably bad for business. But once someone opens the door, we all rush in and consume the new possibilities. Our trajectories immediately begin to inhabit the new space. Think of the power you can wield if you break the new ground? Think of the change you can create, the progress you can be responsible for.

-III