This is part of the Toronto visit series.

“Do you have change for $5?”
“I can only give you one loonie and two lizes”
“What?”
Dumps coins on counter.
“Oh…”

(Canada has no bills under $5 and circulates the $1 and $2 coins.)

Before playing with Canadian money, I had thought that a $2 denomination, whether coin or bill, would be a great idea. But the problem I encountered here was that I was just unable to get very many $1 coins when the $2 coin was also widely circulating. This makes sense, because each transaction at most ends up giving you one additional $1 coin if done optimally. But if you had to always pay odd dollar-amount fees like the $3 streetcar fares, then you need many $1 coins which you don’t have. Compare this to the US system, where you get lots of $1 bills from daily transactions — up to four $1 bills in a transaction ($0-$4 in change). It surprised me that the latter situation is more flexible, because I did not take into account the dynamic effects that repeated transactions have.

Perhaps the intellectual impetus behind a $2 denomination is based on the idea of binary denominations, namely $1, $2, $4, $8, etc., which seems intuitively “nice” for efficiency. It’s hard to think why this should be desired now, it just seemed obvious. Perhaps in such a system the fewest coins/bills need to be carried to ensure all transaction amounts within a range are possible. Or perhaps the fewest coins/bills change hands on average over transaction amounts distributed a certain way (exponentially decreasing frequency as amounts go up?). Yet this system may not work so well, because though it is great for one transaction, you always need a complete set to make it work for the next transactions. The more critical element is net wallet change.

In fact you want this wallet distribution to be, in some rough sense, stable. At worst it should be invariant, and at best, surplus producing. What I mean is illustrated by this:

transaction amount: wallet change
$1: -1 $1
$2: +3 $1, -1 $5
$3: +2 $1, -1 $5
$4: +1 $1, -1 $5
$5: -1 $5

Why pay with $5 for a $2 fee rather than two $1? Well, we assumed that both payment and change-making use the “lazy algorithm” seen in real life: it’s the choice requiring the fewest coins/bills (and among those, the lowest denomination ones). Note that there is an asymmetry since the payer doesn’t have to make exact change but the cashier must settle with exact change.

If all transactions were integer amounts between $1 and $5, and we have an endless supply of $5 (let’s say that’s what the ATM gives), then some transaction amount distribution would make the wallet distribution invariant (as far as it concerns denominations under $5). For example, this (*):

transaction amount: frequency
$1: 17
$2: 3
$3: 3
$4: 2
$5: 1

On the other hand, a flat distribution would give a net surplus of +1 $1 per transaction. Either case would be fine. But in Canada with the $2 coin, the tabulation is different:

transaction amount: wallet change
$1: -1 $1
$2: -1 $2
$3: +1 $2, -1 $5
$4: +1 $1, -1 $5
$5: -1 $5

With the same transaction amount distribution as (*), we would end up with -3 $1 per transaction, a severe deficit. And unlike any other denomination, $1 is a necessity (it’s an atom). I’m not saying this transaction amount distribution is right, but whatever it be, the existence of $2 totally changes the wallet situation and in this case made things worse.

In the US, the existing denominations are kind of close to binary, except there is a magnitude gap between $1 and $5 ($2 bills do exist but rarely circulate), which seemed like a fault. But considering what happened in Canada, maybe this is a blessing in disguise.

obviously referring to a dating site — currently it’s restricted to MIT and Harvard students. This one tries on an idea that I’ve heard discussed numerous times in different contexts, but apparently nobody went and did it in all these years. Instead of running a matching algorithm, it asks third parties (i.e. matchmakers) as well as the interested parties themselves to suggest matches. The thing that is supposed to keep this low-risk is anonymity: a match isn’t revealed until the two primary parties involved mutually accept or their lists intersect.

As with all things that involve anonymity, this asks for trollish and antisocial behavior. I’ve already registered three aliases on moira for exactly this purpose — ok, ok, so they’ve suppressed that antic after people raised concerns, though these and other ramifications should have perhaps been worked through a bit more carefully pre-launch.

The spam potential remains. A matchmaker’s identity isn’t revealed unless both people accept her suggestion, so pranks and insults can be conducted to an extent. One way around this may be grafting social graph data onto the system for collaborative filtering (if they manage to obtain such data…). And if they do, perhaps the suggestions of more closely related people should weigh more, along with those of successful matchmakers. Perhaps there should even be more weight if multiple matchmakers concur. This is extremely intriguing, because eliminating spam is equivalent to predicting who is a likely match, and collaborative filtering for this problem is an unexplored direction.

The more fundamental question is why such a site is even necessary.

Ostensibly, there is a gain over the serial nature of asking in person, due to the ability to make more informative decisions by using data you don’t have or cannot socially obtain in the open. If anonymity compels people to provide more preference information into the system than they would otherwise do, then everybody is better off. This is the positive aspect.

Nevertheless, if we wanted to use full information, why not run a global algorithm? If humans had no feelings, they could just make a list ranking whom they liked in order, and let a computer take care of allocation, almost like housing assignments. But alas, despite the rationality and efficiency of this obvious method, real humans appreciate neither the results nor the implications of it. Nobody likes to ponder the idea of not being #1. So something like nchoosetwo is a compromise, and hides the negative aspect of knowing too much: hurt feelings. But now the site becomes very dangerous. Under the cover of anonymity, the site is collecting ranking information about people from every action on the site. One particular situation in which an explicit rank order is elicited is where there are multiple matches. By your choice, you reveal to the system that “A is better than B.” Is this something the site should know? Not to mention that proposing matches in parallel, when combined with side information from the subsequently unfolding real world, also leaks preference information to an anonymous matchmaker. Those are much more dangerous information than who your Facebook friends are…

So far though, this site has embarrassingly few features. When you have a mutual match, all it does is to print:

Mutual crush! How about a date?

Tellingly, you can’t remove this.

Turns out there is.

No surprise to medical students, I’m sure, but interesting to me.

Among other things, the umbilical vein passes through the navel on its way to the liver. After birth, the outside part of the umbilical cord falls off, of course, but the inside part stays, and turns into this “round ligament of the liver,” and continues to hang around.

Climate engineering may happen but it seems like the energies available to control the weather/climate is not nearly enough (not even the same magnitude) to make this a stable plant. Frankly it seems like a bad idea at this stage of technological development. On the other hand, it is a valid point to say that the climate is already being engineered anyway (more and more) just by the very fact that we take input and commit output to the system. It doesn’t much matter that we still don’t know what we’ve been doing.

In this sense, I think the entire argument about whether global warming is happening or not or is the model believable or not or is it actually global cooling is beside the point. The actual effect doesn’t matter as much as the fact that we’re engineering any system beyond our capability to understand it, much less to control it. One day there may be a way to engineer the climate in a controllable, stable fashion. Before that, it is prudent to be paranoid about the inputs driving the system unless there is proof that said inputs do not drive one of the unstable modes of the system.

Kendall goes on to question the utility of free speech as understood by Mill and lists a number of arguments based on practicality and human nature against the idea of an “open society” actually working as Mill intended, all of which are probably valid but ultimately unsatisfying. However, one extended philosophical point stood out:

Third, Mill denies the existence … not only of a public truth [my note: for the purpose of lubricating free debate], but of any truth whatever… whenever and wherever men disagree about a teaching, a doctrine, an opinion, an idea, we have no way of knowing which party is correct; the man (or group) who moves to silence a teaching on the ground that it is incorrect attributes to himself a kind of knowledge (Mill says an “infallibility”) that no one is ever entitled to claim short of (if then) the very case where the question is sure not to arise — that is, where there is unanimity, and so no temptation to silence to begin with.”

….

The proposition that all opinions are equally — and hence infinitely — valuable, said to be the unavoidable inference from the proposition that all opinions are equal, is only one — and perhaps the less likely — of two possible inferences, the other being: all opinions are equally — and hence infinitely — without value, so what difference does it make if one, particularly one not our own, gets suppressed? This we may fairly call the central paradox of the theory of freedom of speech. In order to practice tolerance on behalf of the pursuit of truth, you have first to value and believe in not merely the pursuit of truth but Truth itself, with all its accumulated riches to date. The all-questions-are-open-questions society cannot do that; it cannot, therefore, practice tolerance towards those who disagree with it. It must persecute — and so, on its very own showing, arrest the pursuit of truth.

There is something interesting here, although first the wrong parts must be excised. For one, I don’t like the infinitely valuable or infinitely without value sentence. That’s stupid. The only conclusion is obviously just what the original says, that all opinions are equally valuable, so as long as the value is positive, then at least some argument can be made to not suppress them. As a side note, I’m not even sure that Mill says all opinions are equal or whether just all opinions have positive (but possibly unequal) value. Kendall’s scaling relationship between the value of an opinion and how much it should not be suppressed may not be Mill’s idea at all. Either way, we can treat the phrase equality of opinions as either what it says or as positive valuation of opinions, and read it as equal treatment of opinions.

Now then the good part. The meta-tolerance paradox itself is a bit contrived (even if it does come up almost daily) since once the “no truth” hammer is found, it can hit pretty much anything. But, it caused me to think of a related and much more relevant paradox. It isn’t about believing in the Truth a priori. It is about believing that there is some truth to be found — that the pursuit has an end, that there is a purpose to the debate. Otherwise free speech for that purpose would have no point, either. Now, if the purpose is to seek convergence from open debate, then there is certainly nothing to guarantee that the process of debate will ever converge (setting aside what it converges to) — not because there is not a truth. But even worse is if every opinion is to be equally valuable for all time, for it prohibits convergence! For convergence to happen, by definition, some opinions will need to be reduced and others bolstered, perhaps on account of reason. The only way out of this is to say opinions are equal only initially. Unfortunately, society has no time origin. Even if it did, we are way past time 0 and hence must be in a state biased toward certain possibilities of truth and therefore inequality of various opinions. Therefore, it is the inequality of opinions on the way to convergence to truth — the ostensible goal of free speech — that strikes down the non-suppression of some speech on the grounds that all opinions are equal. This is the central paradox of Mill’s thesis that I see.

I guess the point is that non-suppression must be based on something less absolute than what Mill says, as it is in practice.

First, this watch seems pretty interesting. It is based on the idea that if you’re never going to get enough hours of sleep a night anyway, then you are best to get a full number of sleep cycles, rather than a fractional one. So it tracks your sleep cycle and wakes you up when you’re most awake.

This reminds me of my general annoyance with the whole concept of sleep and the inefficiency it causes. Sleep has got to be one of the worst vestigial devices still left in humans, although not as bad as the appendix.

Years ago, I came across a blog in which the person was trying out the concept of polyphasic sleep, which is basically napping frequently for short periods each time. The idea was to save total amount of time slept, I guess, or to make sleep more efficient. I guess it worked out well enough to cause a whole bunch of fanatical people to try it.

Admittedly, that was a bit out there, but there were some other good advice based on what this person tried. One of the more useful was on how to wake up on time and how to shift sleep schedule around.

Basically you should only go to bed when you’re tired and want to sleep. Otherwise, you just won’t fall asleep and the time is wasted. What that means is it’s quite easy to push your sleep schedule later. Pulling your sleep schedule earlier is much harder since we’ve established that you can’t go to bed earlier. But it can be done by controlling the other end, by forcing yourself to wake up at the desired time. That is hard to do. But it has to be done. The idea is by the next day you will be tired earlier and will go to bed earlier. Actually the first day after deprived sleep is not that bad, so what is needed is simply a little bit of discipline in waking up.

So that brings us to waking up on time. The advice I remember, and that I have verified, is you must train yourself like a beast to have a Pavlovian wake up routine. Hear the alarm, and you must get up and do something that absolutely prevents yourself from falling asleep again and do the same thing every day. Snooze buttons just don’t work, because that allows you to fall back to sleep, and then you’ll be trained in that routine of automatically falling back to sleep when you hear the alarm, which is totally the wrong thing. Once the routine is established, it will be very easy to keep it because no cognitive process or will power is involved. It is simply an automatic response. Do this for long enough and you will wake up at exactly the right time even before the alarm sounds.

The difficulty is to establish this automatic response in the first place, especially if one is already trained in some god-awful snooze button routine. The trick is to change the stimulus — a different alarm sound, a different alarm position, a different alarm dynamic, a different sleep position — basically anything that is different. But it has to be a novel configuration for which one is not already conditioned in. Then one must try very hard in the first few days not to get conditioned into sleeping through that. Then it will work pretty well. Routine is the key. It is much easier to keep the same conditioned routine every day than is to disrupt it in the middle, with something one is previously too well conditioned in.

One of the more interesting corollaries is if you are lax and generally not careful about this process, you can condition yourself to do crazy things “in sleep”, akin to sleep-walking, all in the name of turning off the alarm. The brain is a strange object.

A lot of work these days goes into novel human-computer interfaces (think coffee table displays, networked whiteboards, etc.) and gestures (think various touch responses like multi-touch zooming), but in my opinion (and metaphor), these work are like lightly scratching the skin when there is a deep deep itch.

The deep itch is a totally multi-input environment. I don’t mean multiple non-interacting or minimally interacting users on the same machine. I don’t even mean multiple users who interact only when it is obvious to do so, like during conferencing, or when the game players are in one area of the map. These are all fundamentally still single input environments, because each user owns a static token, be it the single identity in a conference, the single drawing pen on the virtual whiteboard, or the same virtual character in a game!

Why not be bolder? Suppose two people are working on a desktop, whether locally or via a network connection. Why not have two mouse cursors and two possible focuses? It works like this: any place that cursor X clicks receives focus for all of cursor X’s associated inputs (perhaps keyboard X). Each user gets a set of inputs, then they can be working on separate windows, or even separate parts of the same window. They can both see what is going on with the both of them so they can really collaborate. Change two users to some other number and the same applies. None of this VNC-like fighting cursor crap. Let each user have multiple sets of inputs and still the same applies. See, now you can really multitask with two hands and feet if you want rather than glorified time sharing — lots more possibilities here than boring gestures! It’s how the real world works anyway. Besides, if processes can share a processor, users can certainly share a virtual interface and all of its objects and resources.

It seems like all — and I do mean all — interfaces existing and under development suffer from some kind of designer brain freeze where each user is assumed tied to a single and static virtual token in the interface, simply due to the coincidence that the user is tied to a single and static physical input set. That’s stupid. If you could have 10 hands rather than 2, wouldn’t you rather have 10 hands? Well, in the virtual interface, you can and should. And if your 10 hands can all work, and your friend’s 10 hands can work, you should be able to work together so you have 20 hands in total. Swap hands, too.

This is so obvious, I don’t even understand why it hasn’t been done 10 or 15 years ago…

Utilization of divergent integrals and a new symbolism in contact and crack analysis
VI Fabrikant
Prisoner #167932D, Archambault Jail, Ste-Anne-des-Plaines, Quebec, Canada J0N 1H0

Correspondence: Email: valery_fabrikant@hotmail.com

Received for publication 15 June 2006. Revision received 1 December 2006.

Abstract
The main potential function, used for the complete solution of the contact and crack problems for elliptical domains, is presentable as an integral of an expression comprising a logarithm of a distance between two points. These integrals were considered to be impossible to compute, though various derivatives of these integrals were computed in the past. The new symbolism, introduced here, combined with utilization of divergent integrals, allows us to compute these integrals exactly and in a closed form. It also introduces a dramatic simplification in the final expressions and restores some mathematical symmetry and elegance.

You can look up this guy on Wikipedia.

Let’s see, it all started with somebody wondering if you can get a letter back from the postal service once it has been mailed, but before it has been delivered. Maybe you changed your mind about sending the letter, for example. I still don’t know the answer, but I’m guessing if there is no return address on it, forget it. If there is a return address, however, it ought to be possible, right? The sender will get the letter back normally in the case that it is undeliverable, so the sender is essentially a secondary recipient. What does the postal service do with undeliverable mail that has no return address anyway? Shred it? Anyway, this doens’t seem like a satisfactory conclusion in any case, that the return address should play an unrelated role in the mail interception problem.

Which brings me to the second topic. If we abstract away the implementation details and take the return address to be a bona fide secondary delivery address, then we can do some unexpected things, for example,

• What if put the destination address in the return address position and put a bad address in the destination address? The mail still gets delivered…
• But wait, undeliverable mail is only one of many conditions for returned mail. Insufficient postage is another. So don’t even bother putting a stamp on there…
• Now, sometimes, the postal service delivers the mail anyway, so for recoverability, swap the return and destination addresses; this way, you at least get the mail back if USPS is too nice.
• Even better, for automatic redundancy, put the destination address in both the return address and destination address positions, so no matter what, the postal service delivers the mail.

Wow, I like this already (“this” being the idea, not actually doing it). If Wikipedia is to be believed, the blatant scam in the last scheme is actually legal and works. But I’ve also heard the postal service sometimes delivers with insufficient postage but bills the recipient for postage due mail.

The few times I messed up with first-class postage raises, I’ve got mail back with insufficient postage. Which makes me wonder about the the price of first-class postage. In 1993, it was $0.29. Today (2006) it is $0.39. That’s pretty much in the inflationary range. With the proposed hike to $0.42 next year, there is also this new thing:

The post office is planning a ”forever” stamp for letters, good no matter how many times postal rates increase. That means people could say goodbye to those annoying 2- or 3-cent stamps that have to be added to letters every time rates go up. The idea for the special stamps, which would be sold at the same price as other first-class stamps, was included in proposals announced yesterday that would also raise stamp prices 3 cents — to 42 cents — next year.

That’s nice, you can buy floating-value stamps. The comments that follow in the link are even more interesting…(*) I’ve never seriously thought of postage stamps as a money instrument before. Of course you can buy them on ebay and sometimes stores for a discount (never understood where the discount comes from… value of liquidity?), but those are not as explicit as the derivative market that may result from the trading of “forever” stamps just before and after a rate hike. Can you imagine the run on “forever” stamps before a rate hike by arbitragers and eBay hawkers? Will there be a ration or what? Or as somebody in the comments suggested, they really shouldn’t be sold for X months prior to a rate hike (X depending on interest rates and percentage of hike). Let’s see how this pans out. I still send first-class mail, after all, even without the interest in derivatives.

Actually, when I first read about “forever” stamps, I was confused, because I’ve seen non-denominated stamps before that just say “First Class USA” and I had wondered whether they acted like “forever” stamps. I’ve just assumed they had whatever value they were purchased at. Of course this is correct – they are distributed right after a rate hike before stamps with the newly approved price is printed, and are worth the price at the time of purchase. But it must get confusing, if not for the postman then certainly for me… recently there has been a plethora of flag designs… I can’t remember which is which. Well, here are some that I recall seeing fairly often and recall wondering about their values:

$0.05	$0.10	$0.10	$0.25
$0.29	$0.32	$0.32	$0.33
$0.34	$0.37	$0.39	$0.41

More of them here. All right, that’s it.

(*) There is some mention in the comments about some arbitraging scheme of postages denominated in different currencies. This is a nice idea that actually has some applications in online forums, and will be discussed in another post.