Cashing in the Cash

I can’t remember the last time I used cash. In fact, I actively avoid it. I don’t want crumpled grubby bits of paper in my pockets and heavy pocket wrecking pieces of metal weighing me down. When you have a pocket full of cash, you have a pocketful of inconvenience.

You have to keep track of how much you have, whether it is enough to pay for what you need and you have to periodically top up your supply from inconvenient locations at inconvenient times. I have no idea why people still use cash, I really don’t.

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We got a cheque the other day. Yes, a real cheque with words and numbers written on it. A piece of paper worth a not inconsiderable amount of money. So we tried to pay it into my wife’s bank account. Oh no, sorry, this cheque is made out to both of you. You can’t put it into the bank account belonging to a single person.

So, we fortunately had a joint account, albeit with a different bank, so we took the valuable piece of paper to the second bank. It is not my purpose here to protest, complain or whinge about customer service, so I will merely say that it wasn’t a fun experience. Firstly we had to travel to the location of the second bank, who had, for very good reasons which I find acceptable, just closed our local branch. Secondly we had to deal with a ‘real person’, and actually living and breathing human being.

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Now, I’ve got no problem with real persons. As long as they keep their distance, I will keep mine, and I grudgingly admit that sometimes you have to deal with a real person. But I shouldn’t have to deal with a real person just to deposit a cheque into a bank account, surely?

OK, most cheques can be deposited into your account via a hole in the wall ATM, I know, and this cheque was slightly different. It was a cheque from the UK being paid into a local account so currency conversion had to be done.

I’ve paid local cheques into local accounts in the past, and the process was much the same. The only difference was that we had to sign a piece of paper, extruded from a machine on the real person’s desktop, to agree to refund the money, should the cheque not be honoured by the UK bank.

There are other ways of transferring funds between local banks and the UK, of course, which don’t involve pieces of paper travelling the world, of course. We maintain a bank account in the UK, and it is relatively simple to transfer money from that account to one of our local accounts electronically with having to once deal with a real person.

We could, of course, get people to use electronic means to transfer money from their UK accounts to our UK accounts, but some people, for whatever reason, prefer to send pieces of paper. Probably they are either think that electronic transfers are complex and challenging, which of course they aren’t, or they prefer to send something at least a little tangible.

What kicked off this train of thoughts? It was one of a number of articles by finance industry players which were dismissive or antagonistic towards BitCoin. I bought $200 worth of BitCoin in November 2013, and if I still had it now it would be worth around $4200. Rumour has it that it will rise a lot more. Other rumours are that it is a bubble which will soon burst.

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One of the accusations levelled against BitCoin is that there is no single entity behind it and if the bubble burst, people will be hurt and no one will be held responsible. Well, is that any different from a fiat currency or a commodity currency? A fiat currency is one whose value depends on the support of a government diktat, while a commodity currency has a value that is related to the value of a commodity such as gold.

In the case of a fiat currency, it is effectively the government saying “You can buy things with the dollar things”. So you take along pieces of paper, or these days more likely a bit of plastic, and get back a tin of beans, plus some heavy metal circular things if you use the paper, and feel (relatively) happy.

The government doesn’t do much more than guaranteeing “this is a dollar” and printing pieces of paper with that message, and similar for metal coins, but the number of coins and paper in circulation aren’t anywhere near to, say, the number of dollars in the government’s budget. The majority of dollars only exist as a number in an account somewhere, usually with a bank.

In the case of a commodity based currency, such as that based on gold, a government agrees to supply a given but variable amount of gold for a currency on demand. Of course no one ever demands gold for their dollars or whatever. Why gold? Because there were originally coins made out of gold and gold was relatively more valuable than silver or bronze.

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This has meant that the metal gold is these days worth much more than its relative abundance would imply. In spite of gold rushes gold is a fairly common metal that is fairly useless for anything except decorative candlesticks and similar.

BitCoin is often represented as being different from either of these two types of currency. It doesn’t have a central authority to say “this is a BitCoin”, and no one is going to give you a hunk of metal for it, unless they actually want to buy the metal to make candlesticks.

But BitCoin is not really that different from the other two types of currency. Both of the above types of currency are just numbers in an account of some relatively reliable organisation like a bank or other organisation, just as the BitCoins in my wallet are just numbers in the bitchain.

The difference is that because no one owns the bitchain, that all sorts of dodgy dealings are possible and people like drug dealers and cartels and so on are adopting BitCoin and other so called cryptocurrencies.

However it is no use trying to ban such currencies. That particular genie can’t be forced back into the bottle. Any attempt to regulate cryptocurrencies will simply lead to them going underground.

Oddities

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Humans and not very good at calculating odds and how probabilities work. For instance, if we are tossing coins and we get six heads in a row, the probability of getting yet another head is still fifty-fifty. Yet people feel that after a series of heads that it is more likely that more tails than heads will turn up for a while, so that the ratio of heads to tails returns to the expected one to one ratio.

But the expected ratio of heads to tails for all subsequent tests is one to one. It’s as if a new set of tests is being started, and so any lead that has already built up is, in all probability, not going to be reduced.

This seems odd. If we have done one thousand trials and have turned up 550 heads to 450 tails, the ratio of heads to tails is about 0.818 and the ratio of heads to the number of tests is 0.55. Surely more tests will take the ratios closer to the expected values of 1.0 and 0.5? Surely that means that there will be more tails than heads in the future?

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Well, the answer to both questions is no, of course. The ratios for the whole test may move closer to 1.0 and 0.5, but equally, they may move further away. In the extreme case, there may never be a tail again. Or all the rest of the throws may result in tails.

Interestingly, if the subsequent tests produce a series of heads and tails, the difference between the number of heads and tails stays at around 100, but the ratio of tails to heads for the whole test slowly creeps closer to 1.0 and the ratio of heads to the total number of tests closes in on 0.5 as more and more trials are done. By the time we reach two million tests, the two numbers are not very far from the expected values, being 0.9999 and 0.5000 respectively.

So, if you think to yourself, as you buy a lotto ticket “Well I must eventually win, if I keep buying the tickets”, it doesn’t work like that. You could buy a lotto ticket forever, literally, and never ever win. Sorry.

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Lotto and sweepstakes are, I believe, a different type of gambling from other forms, such as betting on horses or poker and other gambling card games. Lotto, sweepstakes and raffles involve no element of skill, and the gambler’s only involvement is buying the ticket. Betting on horses or cards involves skill to some extent, and that skill comes down to things like working out the probabilities of a particular card coming up and the probabilities of other players having certain cards in their hands.

Both types of gambling encourage the gambler to gamble more. If a gambler doesn’t win on the Lotto he or she might say to his or herself “Better luck next time.” Of course, luck does not exist, but probabilities do, and this is a mild form of the Gambler’s Fallacy described above. Nevertheless, people do win and the winners appear on television for us all to see and emulate.

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There’s two sorts of strategy for winning the Lotto. First there’s the “always use the same numbers” strategy, and then there’s the “random numbers” strategy. If you always use the same numbers, goes the theory, then eventually there must be a match. That’s wrong of course, since the number combination may not appear before the end of the universe.

The random number strategy argues that there is no pattern to results so it is silly to expect a particular pattern to eventuate. This strategy acknowledges the random nature of the draw, but doesn’t give the gambler any advantage over any other strategy, even the same numbers strategy. It is certainly easier to buy a randomly generated ticket than to fill in a form to purchase the same numbers every time.

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Some people experience a run of luck. They might have three things happen to them, so go and buy a lotto ticket while their luck holds. Then is they win they attribute it to their lucky streak. It’s all nonsense of course. They conveniently forget the many, many times that they bought a ticket because of a lucky streak, only for the ticket to be a loser.

The proceeds from the sales of lotto tickets don’t normally all go to holders of winning tickets. Firstly the operators of the system need to recoup their costs. It’s not cheap to own and operate those fancy machines with the tumbling balls and it also costs to employ the people to check that the machines are fair.

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If one of the balls is dented, will that affect the probability of that ball being selected? Maybe, just a little, but the draw should be fair so those providing the lotto equipment spend a large amount of effort to ensure that they are fair, and the costs of that effort must come out of the prize funds.

Secondly, the state or maybe the lotto organisation itself will often withhold part of the lotto sales takings for local or national causes, such as cancer research, or societal things, like the fight against teen suicide. The money for humanitarian causes is deducted from the prize funds.

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One of the humanitarian causes is often the fight against problem gambling. It’s ironic and somewhat appropriate that funds from gambling are used to combat problem gambling. It seems that some people get such a thrill from gambling that they use all their, then borrow or steal from others to continue to gamble.

They invoke the Gambler’s Fallacy. They suggest that their luck must change sooner or later. It doesn’t have to, and may never change, but they continue to spend money on their gambling. They also don’t take account of the fact that they might win, eventually, by sheer chance, but it is unlikely that their winnings will cover what they have already gambled away. They have a tendency to believe that one big win will sort things out for them. It won’t of course.

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So, the only true fact about Lotto and similar draw is that you have to be in to win. But just because you are in doesn’t mean that you will win. You probably won’t. The best way to treat Lotto and other similar games is that you are donating to a good cause and you might, but probably won’t get something back. So, I’m off to buy a lotto ticket. I might win thirty million dollars, but I won’t cry if I don’t.

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Looking for Inspiration

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I suppose that everyone has seen the so-called “Inspirational Quotes“. If you haven’t, it is unlikely that you have been using the Internet a lot! Inspirational Quotes are short sentences, usually totally devoid of context that, supposedly, provide guidance or inspiration for those who need it. Usually the quotation is in large font applied over the top of a sunset, or a couple hand in hand, or a cute puppy or other animal.

Since the quotation is usually without context, the reader is free to apply it however he or she wants. You can apply it to your own situation, whatever that might be. A large portion of the quotes exhort the reader to just get up and do it, whatever it might be. The idea is that one should take one’s chance and go for it.

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This is all well and good if the advice is appropriate. The original writer has no way of knowing this. Someone might take the message as a sign to get out of a situation where they are safe and comfortable and to take risks. Unfortunately, if this turns out to be a mistake, there is usually no way back.

Many of the inspirational quotations have a religious slant to them.  Søren Kierkegaard reportedly said “Now, with God’s help, I shall become myself.” It’s easy to make fun of inspirational quotes, both religious and secular, such as the foregoing. After, if he wasn’t himself when he made the quotation, what was he? It is so devoid of context that one can’t help asking oneself what one is supposed to do to become oneself?

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Can the quotations be dangerous? I suppose that if one is depressed or suicidal it would be unfortunate to come across a quotation that said, basically, “just do it,” but it is unlikely that a simple quotation like that would actually incite suicide.

I suspect that most of the inspirational quotations are pretty benign. People look at them and are momentarily uplifted or cheered up by then, but then just carry on with their lives. The quotations may help them cope with a difficult situation or help them be happy in the situation that they find themselves in. I doubt that the motivation goes deep enough to completely change their lives, but I don’t know if anyone has ever checked or studied the phenomenon.

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After I started thinking about inspirational quotations, I wondered who it is who writes the things. Someone must spend a lot of time either extracting them from online books and pages and maybe they even type them up from paper books! In many cases they then paste the text onto pretty pictures of all sorts of things. Sunsets seem to be a favourite.

Then I discovered the on-line generators for these things. Some of them just allow you to type in whatever you like, but some of them will generate the whole thing for you. One that I’ve played with a bit is InspiroBot, which produces quotations using some sort of algorithm, and calls itself an Artificial Intelligence. It produces image/quote combinations which range from ones which seem sense free to those that seem like they mean something.

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I was wondering how the meme arose, then I though back to the times when computers were just entering the workplace. Way back when printers could only print letters and numbers people would draw something using just letters and numbers. If you went up close you could see the letters and numbers but from a distance the different densities of the letters looked like a image of something, so people covered whole walls with, say, a picture of an astronaut, or a pinup.

When printers could print images these were replaced with smaller pictures of astronauts or pinups or someone’s kids. Then someone somewhere decided to inspire their staff with a poster or picture with an inspiring caption. Naturally spoof and satires of these soon appeared, and also people started putting up quotations that had inspired them, and spoofs and satires of those also appeared.

Nowadays of course, the whole thing has moved to “social media”. People spot a quotation which appeals to them and post it on Facebook. This quite often means that you might see the same “inspirational posting” several times, as other people share it with their friends which might include you!

I’m intrigued by the programs that produce the quotations by algorithmic means. Since they produce only a short sentence, there’s more chance that you can see sense in the result, than there would be if the algorithm produced a whole article or something. I’ve found one site where an algorithm produces a small article on each refresh, and the results seem to me to be a bit odd when I try to make sense of them.

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It reminds me of a famous hoax perpetrated by Alan Sokal on the unwary editors of an academic journal. Sokal wrote an article which was composed of buzzwords and references to Post Modern writers, since he believed that all that was required of an article to get it published was the buzzwords and the gratuitous references to Post Modern writers.

He succeeded in getting it published, which ironically gives the article meaning of exactly the sort that he was ridiculing. While it had no meaning in the context of an academic article, it was an unfavourable commentary on the meanings and lack of rigour espoused by the Post Modern movement. If you are interested in producing your own Sokal-type article, there is a web site called “The Post Modern Essay generator, which will do it for you.

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So, are all, or the majority of inspirational quotations generated by an algorithm or do people create them and post them themselves? I think that most are created by people. At least the quotes are, but the actual postings may not be. The quotes seem to, in most cases, almost make sense, but they don’t always seem to match with the pictures. I’d guess that people are using a generator but posting their quotes, whether gleaned from elsewhere or created by themselves, and the picture is more or less random and may not match the quotation.

Round it up!

Circle of Life
Circle of Life

Quite often a visit to Wikipedia starts of a train of thought that might end up as a post here, and often I forget the reason that I was visiting Wikipedia in the first place. However in this case I remember what sparked my latest trip to Wikipedia.

I was looking at the total number of posts that I have made and it turns out that I have posted 256. This is post number 257, which is a prime number incidentally. To many people 256 is not a particular interesting number but to those who program or have an interest in computers or related topics, it is a round number.

US 256
US 256

A round number, to a non-mathematician is a number with one or more zeroes at the end of it. In the numbering system with base 10, in other words what most people would considered to be the normal numbering system, 1000 would be considered to be a round number. In many cases 100 would also be a round number and sometimes 10 would be as well.

In the decimal system, which is another name for the normal numbering system, the number 110 would probably not usually be considered a round number. However, if we consider numbers like 109, 111, 108 and 112, then 110 is a round number relative to those numbers. Rounding is a fairly arbitrary thing in real life, usually.

We come across round numbers, or at least rounded numbers in the supermarket on a daily basis, if we still use cash. Personally I don’t. I recall when the one cent and two cent coins were introduced people were appalled that the supermarkets would round their bills to the nearest convenient five cents.

5 lirot
5 lirot

 

So a person would go to a supermarket and their purchases would total to, say, $37.04. The cashier would request payment of $37.05. Shock! Horror! The supermarket is stealing $0.01 off me! They must be making millions from all these $0.01 roundings. In fact, of course, the retailer is also rounding some amounts down too, so if the bill was $37.01 the customer would be asked to pay only $37.00. So the customer and the supermarket, over a large number of transactions, would end up even.

Then of course the 5 cents coins were removed and this added an extra dilemma. What if the total bill was $37.05? Should the customer’s bill be rounded to $37.00 or to $37.10? This is a real dilemma because, if the amount is rounded up, then the supermarket pockets five cents in one ten cases, and if it is rounded down the supermarket loses five cents in one in ten cases. If the supermarket a thousand customers in a day, one hundred of them will pay five cents more than the nominal amount on their bill, meaning that the supermarket makes a mere five dollars.

Big Money
Big Money

The emotional reaction of the customer, though, is a different thing. He or she may feel ripped off by this rounding process and say so, loudly and insistently. Not surprisingly most supermarkets and other retailers choose to round such bills down. Of course, all the issues go away if you don’t use cash, but instead use some kind of plastic to pay for your groceries, as most people do these days.

There are degrees of roundness. In one context the number 110 would be considered round, if you are rounding to the nearest multiple of ten. If you are rounding to the nearest multiple of one hundred, then 110 is not a round number, or, in other words a rounded number. If we are rounding to the nearest multiple of three, then 110 is not a rounded number but 111 is (111 is 37 multiplied by 3).

Binary Backdrop
Binary Backdrop

Real numbers can be rounded too. Generally, but not always, this is done to eliminate and small errors in measurement. You might be certain that the number you are reading off the meter is between 3.1 and 3.2, and it seems to be 3.17 or so, so you write that down. You take more measurements and then write them all down.

Then you use that number in a calculation and come up with a result which, straight out of the calculator, has an absurd number of decimal places. Suppose, he said, picking a number out of the air, the result is 47.2378. You might to choose to truncate the number to 47.23, but the result would be closer to the number that you calculated if you choose to round it 47.24.

Currency Symbols
Currency Symbols

A quick and easy way to round a real number is to add half of the order of the smallest digit that you want to keep and then truncate the number. For the example number the order of the smallest digit is 0.01 and half of that is 0.005. Adding this to 47.2378 gives 47.2428, and truncating that leaves 47.24. Bingo!

Another way of dealing with uncertain real numbers such as results from experiments is to calculate an error bound on the number and carrying that through to the calculated result. This is more complex but yields more confidence in the results than mere rounding can.

Tube
Tube

To get back to my 256th post. Why did I say that this is a round number in some ways? Well, if instead of using base 10 (decimal), I change to using base 16 (hexadecimal) the number 256 (base 10) becomes 100 (base 16), and those trailing zeroes mean that I can claim that it is a round number.

Similarly, if I choose to use base 2 (binary), 256 (base 10) becomes 100000000 (base 2). That is a really round number. But if I use base 8 (octal), 256 (base 10) becomes 400 (base 8). It’s still a round number but not as round as the binary and hexadecimal versions are, because it start with the digit 4. As a round number its a bit beige.

It’s interesting (well it is interesting to me!) that there are no real numbers in a computer. Even the floating point numbers that computers manipulate all the time are not real numbers. They are approximations of real number stored in a special way (which I’m not going to into).

General Double Precision Float
General Double Precision Float

So when a computer divides seven by three, a lot of complex conversions between representations of these numbers goes on, a complex division process takes place and the result is not the real number 2.333333…. but an approximation, stored in the computer as a floating point number which only approximate, while still being actually quite accurate.

One third
One third

 

Once a week

English: Lunar libration. see below for more d...
English: Lunar libration. see below for more descriptions Français : Librations de la lune. Voir une description détaillée en dessous. (Photo credit: Wikipedia)

I’ve been pondering the topic of ‘the week‘. Not the ‘topic of the week’. The week, as in seven days. It’s an unusual number to use as a unit for a length of time, as it is a prime number of days, and this makes using fractions of a week a bit tricky. Half a week is 3 and a half days long, so it’s not usual to, for instance, agree to meet someone in ‘half a week’.

No, we say ‘See you in three days’, or four days. We might say ‘this paint will take 2 and a half days to fully dry’, but this is a bit odd. We’d usually say something like ‘this paint will take between 2 and 3 days to fully dry’. We usually treat days as ‘atomic’ when counting days. The number of days is usually an integer, although we could break days down and use fractions or real numbers with them.

Unusual Calendar
Unusual calendar. 12 months 9 days in week

The fact that the number of days in a week is a prime integer also makes converting from weeks to days and days to week interesting. Quick, how many days in seventeen weeks? The answer is 119. How many weeks is 237 days?  The answer is 33 with six days left over. It’s not easy.

Four weeks is 28 days, which is approximately a lunar cycle. It is also very approximately one month. There are approximately thirteen 28 days period in a year, assuming a 365 days year which is approximately correct. This is probably why some calendars have thirteen months.

Lunar eclipse
Lunar eclipse

The lunar cycle is around 29 and a half days, whereas the month defined as one twelfth of a year is around 30 and a half days. Nothing fits! The month is based on the lunar cycle, and the ancients noticed that that the twelve lunar cycles is 354 days which was close to the 365 and a bit days that comprise a year.

So, they decided to make it fit. They divided the year into 12 months, which left them with bits of days just lying around. This was obviously untidy so they scrunched up the bits into one days and tagged them onto the various months more or less at random. The final left over bit that they ended up with they ignored.

Monthly bus pass
Monthly bus pass

That’s how we ended up with mnemonic rhyme “30 days hath September, April, June and November…” with that horrible line that doesn’t scan. That’s rather appropriate really, as the reason that the rhyme is needed is because the days don’t fit properly into the months. It’s an uneven rhyme for an uneven scheme.

The ancients ignored the odd bit of a day that was left over until someone noticed that the year was still sliding out of synchronisation with the seasons. So they added or took away a day or two here and there in special, short or long years. Problem solved.

Leap year 1908
Leap year 1908

Well sort of. They ended up with a super complex list of rules for working out how many days there are in a month, where to fit extra days into the calendar, and when to fit them in. Horror!

Finally scientists decide to cut through all this confusion and define a second by using an atomic clock. Providing you don’t accelerate the clock to a significant fraction of the speed of light and keep it at absolute zero. Easy!

First atomic clock
First atomic clock

Again, sort of. The standard second times sixty give a standard minute. The standard minute times sixty gives the standard hour. The standard hour times twenty four gives the standard day and the standard day times seven gives the standard week. Yay, you might say.

Unfortunately the actual day and therefore the actual week is not exactly equal to the standard day or week. It would be quite legitimate to claim “Wow, this is a long week, it’s 0.608111.. standard seconds longer than a standard week”. But don’t expect much sympathy.

Leap second 2016
Leap second 2016

Seven days is actually a pretty reasonable length to a week. We divide it into “the weekend” and “the rest of the week”. If it was a couple of days longer, it would be a long time between weekends. We’d probably be tempted to add an extra day to each weekend, or maybe alternate weekends…. But now we’re getting complicated again.

If the week was shorter, we’d probably get less work done. If the week was five days and we still had a two day weekend then time available for work would be about 17% less. Of course five day working weeks are fairly recent in historical terms, but I’m not going to work out the numbers for a 6/7 working week and a 4/5 working week.

Aztech Sun Stone Replica
Aztech Sun Stone Replica

Speaking of work, and assuming that most people would not work unless they have to, we have developed various coping strategies. We count the days to the weekend. “Only three more days to the weekend.” Tomorrow is Thursday and that means only one more day to the weekend.”

We designate Wednesday as “Hump Day”, since it is the middle of the week and if we reach Hump Day before having a breakdown or perhaps killing someone, that’s a win. There’s only half the week to go and we’ve broken its back.

We celebrate Fridays, often with a quick drink, then shoot off to enjoy the weekend. We come in on Mondays, faced with five more days of toil. On Tuesdays, we’ve at least knocked off one day, but it’s still a bit beige. Wednesday is Hump Day and we’re halfway there! When Thursday comes we’re almost there, and Friday is relatively easy. It’s practically the weekend, when we block out the thought of Monday all together if we can.

TGIF - switch off
TGIF – switch off

The week has a sibling called the “fortnight”. Two weeks, as a chunk. At one time the fortnight was usually reserved for a summer holiday. A fortnight at the beach or the bach. Time away with the kids. Idyllic golden weather by the sea. Of course, we only remember the good times, and forget the bad ones, but still it would be summer, it would be fairly warm, and the weather is usually better in the summer.

Weeks are the medium sized sections of our lives, often used to split up the humdrum from the pleasant parts of our lives. We should appreciate our weeks, no matter how many standard seconds long they are.

Girl on a swing
Girl on a swing

Choose! Choose now!

Fractal tree
Fractal tree

Life throws many choices in our way. One view of the world is that it is like a many branched pathway, with our every day choices causing us to thread a particular path though this maze of branches, to reach the ever growing tip of the tree of events that is our past.

The future is yet to come into being but we can see dimly into it, and we use this limited view to inform our choices. The view into the future is like a mist. Things appear dimly for a while only to fade and be hidden from view. Sometime in the future is the instant of our demise. We know it’s coming but we do not usually know how and when.

Misty Morning
Misty Morning

We try to compensate for our inadequate view of the future by trying to cater for all possibilities, and one way we do this is by making a will, to prescribe how we would like our things, our assets, to be distributed when we are dead.

Some people try to predict the future. Some people gamble, on horses or whatever, trying to guess the winner of a race. There are two sorts of such people, those who estimate the odds and then build in as much of a safety margin as they can. These are usually the ones who run the books, while the other sort take a more optimistic view and gamble that the bookmakers are wrong. The first group is generally happy to make small profits while the second group want high returns. Generally the first group does a lot better than the second group over a reasonably long time frame.

Bookmakers at Higham
Bookmakers at Higham

The interesting thing about choice is that it is a discrete thing. We choose from one or more possibilities and the number of those possibilities is an integer. Often it is a choice between option one or option two. Pretty obviously it isn’t option one point five.

If we have two possibilities, call them A and B, then the probability of A occurring might be thirty percent. This means that the probability of B happening is seventy percent. The two must always add up to one hundred per cent.

Choice of paths
Choice of paths

So there is a mapping here between discrete events and continuous probabilities. Between integers and real numbers. One way of looking at this is that “event A” is a sort of label to the part of the probability curve that represents the event. Or it could be considered that the probability of the event is an attribute of the event.

It could be that when a choice is made and the probability of making that is more probably than making the other choice then that it is similar to making a choice of road. One road is wide and one is narrow. The width of the road could be related to the probability of making that choice.

Choice of routes to Pinnacle Hill
Choice of routes to Pinnacle Hill

The width of the road or the probability of the choice may well be subjective of course. I might choose to vote for one political party because I have always voted for that party. The probability of me voting for that party is high. The probability of my voting for another party would be quite low. However for someone who is the supporter of another party, the road widths are the other way around.

Is it true that when I vote for the party that I usually vote for that I exercise a choice? Only in a weak way. Merely doing things the way that one has always done is just taking the easy way and involve little choice. The reason for taking the easy choice may be because one has always done it that way and there is no reason to change. Habit, in other words.

A or B?
A or B?

Most choices we make are similar. We have a set of in-built innate or learned reactions to most situations, so that we don’t have to trouble to make a choice. If you make a choice, if you drill down far enough you will find that there are always reasons for a choice that you make. Your father always voted for the party, so you do out of loyalty and shared beliefs.

Every choice, when you examine it, seems to just melt away into a mass of knee jerk reactions and beliefs. When you examine choices you find that there was in fact no other way that we were likely to choose and free choice doesn’t really exist.

Spoilt for Choice
Spoilt for Choice

We have all been to a fast food restaurant only to find that the person before us is unable to make up their mind. This is probably because they do not have strong preferences so that they don’t have any reason to choose one dish over the other, or they dislike all the dishes equally.

If we put people in a situation where they have no reason to prefer one course of action over another and we force them to make a choice, they will often think up ludicrous reasons for making the choice that they finally make.

Reason Why lobby card
Reason Why lobby card

For instance on game shows where they have to make a selection from a multiple choice question in a limited amount of time, quite often they will say something like “I haven’t pressed B in a while”, or “I guessed A last time and it worked out for me so I did it again”, even something like “It’s my boyfriends favourite colour.” It’s hard to know if they really used that reasoning or whether they are justifying their choice after the event.

Another way to cause people to make a random choice is to try and remove all distractions. I can envisage an experiment where people are placed in a room with a screen and two buttons. They are then told by a message on the screen to press the correct button within ten seconds and a count down starts. Since they have no knowledge of which is the correct button they will be forced to choose any button to press or to let the timeout expire. Then they will asked why they chose that particular button. The results of such a test would be interesting.

Random Walk Trace
Random Walk Trace