Philosophy – Page 2 – Me on the net

Why did he do it?

Why do people become murderers or rapists, or even petty thieves. I mean, sure, sometimes a person could irritate you to the point where a fleeting thought of carnage crosses your mind. But most people would immediately shut down that thought and even be shocked and revolted by it. They certainly wouldn’t act on it.

Surely no one wakes up one morning and thinks “Oh, I’ll become a career criminal,” or “Oh, I’ll violently attack someone today.” It’s easier to explain when the person is immersed in a culture where crime is normal and maybe even expected of one. But there are law abiding people even within the worst of environments, where crime is common.

Embed from Getty Images

Fear of consequences is often used to try to deter people from crime, but in many cases the fear of consequences is not enough to prevent a person committing a crime. Prison may be seen as normal and expected. So called petty criminals may expect to be thrown in to jail many times in their lives and to them it cannot be much of a deterrent.

Of course, one’s better judgement can be nullified by drugs or by alcohol. Many assaults happen when the person who assaults another person is drunk or high on drugs. Other crimes like rape, burglary, and vandalism are also more likely to happen when a person is intoxicated.

Embed from Getty Images

One way that is often suggested to reduce crime is to increase the severity of the punishment, so that fear of consequences is increased. However, this has limited effect only. People still committed murder even when capital punishment was still used. When in a blind rage, if a person is mentally ill, or if the person believes that they can get away with a crime without being caught, then the consequences often do not come under consideration.

In a court of law it is assumed that the person knew that consequences and still continued with their action. In many cases I believe that this is simplistic to say the least. A person sees another person leave a phone or wallet somewhere that the first person can take it from. Often the first person doesn’t think through the consequences of the theft. They don’t even consciously think that they can get away with it. They just react to the item being accessible.

Embed from Getty Images

Also each successful theft reinforces the thief’s feeling that he or she will not be caught, so they do it again. In fact, of course there is a chance that they will be caught each time that they commit the theft, and the more times that they commit the crime, the more likely it is that they will eventually get caught.

If they are likely to get away with the crime nine times out of ten, then if they commit the crime seven times, the chance of them getting caught is better than even. Maybe one way to reduce crime is to teach criminals statistics!

Embed from Getty Images

It seems that the propensity to commit crime is inherent in human beings. It is not related to social standing, as crimes of theft and of fraud are seen to be committed by people of all social standings. The criminals, even those higher up the socioeconomic ladder tend to make the mistake of repeating their crimes, which, as I mentioned above, renders them more likely to be caught.

Of course those lower down the socioeconomic ladder commit simpler crimes like theft and violence often fuelled by alcohol and drugs, and those higher up commit the so-called white collar crimes. A person’s position on the ladder doesn’t seem to bear much relation to whether or not they commit sexually related crimes, and in fact, a person’s higher standing often seems to protect them against being caught – they are able to convince people to look the other way when such a crime is committed, by using their influence or by using their money to buy people off.

Embed from Getty Images

If the propensity for crime is to be found at all levels of society, and the punishment of criminals is relatively ineffective as deterring criminals from committing crime, what is there that we can do about it? In my opinion, not a lot. But nevertheless we need to try, if only to reduce it to the minimum possible.

That is what society, from the beginning up to the present day is trying to do, of course. The consequences of being caught committing a crime don’t stop everyone, but it is likely that they do stop some people. Over harsh penalties from crimes don’t work beyond a certain point, and this has been recognised in societies that have dumped capital punishment.

Embed from Getty Images

We try to keep down crime by locking up those who are caught committing it. Again this has only limited effectiveness as well as, effectively, targeting those at the low end of the socioeconomic ladder. A rich person who is fined for jumping a red light is likely to notice it much less than a poor person. The fines represent a much bigger portion of a poor man’s income than that of a rich man.

The only way to reduce crime to zero is to change the human race. If the genes for criminality and violence were to be bred out of the human race, then we would have no problem with crime. Women would not be raped and funds would not be embezzled. People would not drink drive, and would not bash other people.

However, the genes for criminality might be perilously close to the genes for creativity. Creative individuals are often those who break the rules, who go beyond what is allowed. Creative individuals also tend to be those who are close to the boundary between sanity and insanity. They are the eccentrics among us, the ones who do not fit in.

Maybe we could prevent crime by changing the human race, but we risk creating a society which also has no artists, no eccentrics, and essentially no Leonardo DaVincis, no Isaac Newtons, no Shakespeares, no Albert Einsteins. Society would be the poorer for that.

Embed from Getty Images

Meditation – sort of

English: By kac's meditation — English: By kac’s meditation (Photo credit: Wikipedia)

Meditation brings a lot of contentment to a lot of people, but it is not for me. Oh, I’ve tried it, but I can’t get around a feeling that I’d rather be doing things than sitting there musing on things. Introspection yields practically nothing for me.

That doesn’t mean that I don’t ponder on life, the Universe and all that as anyone who has ever read any of my pondering in this blog and elsewhere will know. In particular I have a fascination for numbers and mathematics. I’ve also wondered about most of the things that occur as topics in philosophy at one time or another.

These musings occur mostly when something triggers them, like a comment in a blog that I’m reading, or the title of the latest book on philosophy. Or even something as mundane as a lotto draw. Or washing up. Any of those can trigger a period of thought about some topic.

In case anyone is wondering, washing up can trigger thoughts about bubbles, or caustic curves, or music when two items of crockery produce a note when they touch during the process. Why, for example does an octave resonate in our minds.

Embed from Getty Images

A note sounds remarkably like a note one octave above it, while sounding different to it. Two notes clash or alternatively resonate, and we call them consonant or dissonant. OK, part of the answer to that one is that if the ratio of the frequencies notes is simple, then the notes are consonant, whereas if the ratio of the frequencies is not simple, the notes are dissonant. However, it is not as simple as that.

Three notes for a chord and things get even more complex, and yet composers seem to intuitively know the rules and complexities and use and even bend them for their own purposes. One composer’s consonance is another composer’s assonance.

Embed from Getty Images

Meditation seems to have benefits for many people, and some organisations have reported benefits from introducing meditation into the workplace. Presumably these benefits outweigh the cost of the time lost in meditation, otherwise it would be of little benefit to the organisation.

That’s the crux of the matter, really. Is the time spent in meditation worth the cost in time taken to meditate? Is it better to spend your time out in the open walking and observing the views, the plants and animals around you, or to stay in one spot and meditating on a flower or whatever? Of course, you can tramp the trails and meditate as some level as you go.

Embed from Getty Images

A form of meditation is introspection, where the person who is meditating tries to examine his or her conscious thoughts or feelings. I’ve tried to do this many times and I find it frustrating. It is easy enough to gauge one’s mood and how one is feeling at a particular time, but I have never ever had a glimpse of any conscious thoughts.

Never have I observed my thoughts when I am thinking about something. For instance, I can imagine that I am staring at something green. I can gain no insight into what it means to be looking at something green. Try it yourself. Close your eyes and imagine a uniform greenness. I would say that you can think of greenness, and you can think of yourself thinking of greenness but you can’t think of yourself thinking of greenness at the same time that you are thinking of greenness.

Embed from Getty Images

Similarly, we can think of ourselves winning the lotto and what we would do with the money, but we can’t, at the same time, think of ourselves thinking of winning the lotto. We can think about our thoughts, but only after we have thought them. We can’t think of the while they are happening.

Out thoughts don’t have to be about real things. There are people, usually mathematicians who try to visualise objects in four dimensions rather than the usual three. Actually, visualising three dimensional objects is hard enough. Try this. Imagine a flexible torus (doughnut shape). Imagine that you make a small puncture in it and pull the edges of the puncture over the torus.

In other words, try to turn it inside out. What shape do you get? The answer turns out to be another torus, but it is not easily visualised. In addition while you can imagine yourself visualising it, you can’t think about yourself visualising it while you are actually doing it. In other words, our consciousnesses seem to be single threaded.

Actually, if you could observe yourself thinking about something, you could presumably observe yourself observing yourself thinking about something, and so on. This would, in theory lead to an infinite layers of you observing yourself.

Embed from Getty Images

Meditation on thoughts or deeds, as I understand it as a non-practitioner, then comes down to a focused concentration on thoughts that have already been thought, as it were, and I guess that meditation could bring one awareness of why one thought those thought or did that deed. This is no doubt beneficial as such meditation could identify things about thoughts and deeds that one could change, perhaps simply by making one aware of why one had those thoughts or did that deed.

For example, if you meditate about what you have done on a particular occasion you might form the conclusion that you should have done something different. When the situation arises next, you will have a considered analysis of what you did before and it may influence you to do something different.

Or you may conclude, during your meditation, that certain events led you into that situation, and you could then avoid those events, thereby avoiding the situation. For instance, you may conclude that rashness is an issue for you and that you should avoid rashness. Tying this to a mantra or key phrase could enable you to avoid rashness, by reminding you of your conclusion and enabling you through the mantra to avoid it. This of course depends on you being able to determine when you are about to do something rash and therefore trigger the mantra and the avoidance.

[I’m not too happy with this post. But let it stand for now. I’ll maybe revisit this later.]

Embed from Getty Images

Oddities

Embed from Getty Images

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?

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

Looking for Inspiration

Embed from Getty Images

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.

Embed from Getty Images

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?

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

Embed from Getty Images

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.

A Visit from the Black Dog

I’m suffering a visit from the Black Dog. I’ve no idea how long it is going to stay. Fortunately for me, it doesn’t incapacitate me, and I doubt that people can detect it by my everyday demeanour.

That, in itself, is a problem. If you look ill, or you sport a bandage or crutches, or you reside in a wheel chair, people can tell at a glance that you are not one hundred per cent fit. That’s not to say that such people do not deserve our sympathy and help. Of course they do. But depression is invisible, unless it render the sufferer unable to function properly.

Much like with IBS sufferers, people cannot see that you are not well, and therefore don’t make allowances for you. This is compounded by the fact that depressed people want to be normal and therefore don’t mention it to people, and suppress, so far as they are able, any external indications of their problems. Outwardly a depressed person may laugh and joke, but, it’s almost a cliché, they are hurting inside. Of course I’m talking about those people who are less seriously affected.

When someone who has depression says that they feel worthless and that life is not worth living or wonders what if it is all worth it, those who they are talking to often nod their understanding. But I’m not sure if they really do understand what it is like to be depressed.

Thomas Nagel once wrote a famous piece on what it is like to be a bat. He argued that it is one thing to imagine what it is like to be a bat, but an entirely different thing to actually experience being a bat. It’s a similar situation to trying to describe a colour to a person who has been blind from birth. The blind person can intellectually understand the concept of colour, in that different coloured objects cause different sensations for a sighted person, but the blind person would not know what it feels like to see colours.

Like the blind man not being able to experience colours, someone who does not suffer from depression is unlikely to be able to understand the experience of depression. They don’t know what it is like to be a person with depression. I believe this to be the case.

On the other hand, maybe suffering from depression is normal, and everyone can experience it. Maybe it’s like grief. Almost everyone is capable of experiencing grief, but a person will not know what it is like to experience grief until they suffer it. Maybe everyone is capable of being depressed, but something external or internal needs to triggers it before they can experience it.

If so, there is hope for depression sufferers that some way may be found to stop an attack of the Black Dog before it appears in your life. Grief, like depression, can be alleviated by medicines, but has to run its course. Grief, like depression, seems endless at the time, but eventually passes.

Trying to operate normally while depressed is a strain. Why chat politely with people when you’d much rather be rolled up in a ball in a cave somewhere? Why bother to explain something that is obvious to you, and apparently causes another person difficulties? This leads to irritation which sometimes manifests as anger. Actually, I’m not sure if heightened irritation is a part of depression or the result of trying to battle through it.

When I’m depressed I hate to be interrupted. When I’m normal, I don’t like to be interrupted, especially if it happens repeatedly, and it may make me a little grumpy. If I’m depressed multiple interruptions to something I’m doing may lead to a minor explosion.

Complex tasks become more challenging during a depressive attack. I’m not sure if depression makes you clumsier, or whether it is the impatience that comes along with it that makes you rush things and therefore bungle them. All I know is that it is harder to do things when depressed. You know you should do them but it all seems pointless. Even if you do do them, you stuff up more than usual.

There is a mental fuzziness which goes along with it. Thinking clearly is harder and remembering things is almost impossible. Words and sentences come harder when I am writing and the Black Dog is around. I look at what I have written and it doesn’t make sense. Well, less sense than it usually does, anyway.

There’s a sort of glimmer of light at the end of the tunnel, in that I know that I will come out of it. I’m not sure medication helps, as although it lifts the mood a little there is still a black cloud at the centre of my existence. I know that sounds overly dramatic, but that is what it seems like in some ways.

Looking at that last paragraph, it doesn’t really get close to what the feeling is for me. That’s the trouble. You can try to communicate feelings and thoughts, but when you look back at what you’ve said, you can see that it misses the essence of the thing. Even talking to another sufferer often ends in a stalemate. One’s subjective experience might be “a smothering cloth” while another’s experience might be “all sharp edges, harsh lights and obstacles everywhere”.

That’s not surprising really. We don’t know what it is like to be a bat, and we don’t know what it is like to be another person. We can only convey a little of our feeling through analogy and metaphor. It is impossible to communicate the essence of a feeling. It is impossible to convey a sense impression.

I don’t know what it feels like to you to experience the colour red, for example, though I expect that it is similar to the way that I experience red. That’s not necessarily true of course. I recall someone trying to convince me that certain Chinese characters conveyed an emotion. Well, not for me, but maybe they did for him.

One thing I’ve never seen mentioned about depression. It’s not a matter of depressed versus not depressed. There are levels of depression, and you don’t just sink down and then, some time later, rise out of it. No, you sink down, rise a little only to sink down again, so you may be almost out of it, only for it to pull you down again. At least, that’s what it seems like to me.

Round it up!

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.

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.

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.

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).

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.

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.

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).

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.

Once a week

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.

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.

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.

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!

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.

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.

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.

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.

Choose! Choose now!

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.

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.

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.

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.

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.

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.

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.

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.

Celebration of Cavewoman

My daughter and I were discussing innovation and inventiveness. Well, actually we weren’t but the subject got mentioned in the context of “what if….”. What if our caveman ancestor had not banged together two rocks and invented fire starting? My opinion was that it was probably our cavewoman ancestor who did it. Our caveman ancestor would probably have banged his thumbs together between the two rocks.

This started me thinking. Inventors are usually man. Rarely, in recent times anyway, is a great inventor a woman. Why is this? Is there really a gender gap in inventiveness?

Thinking back to the caveman and cavewoman days, it is likely that the woman was responsible for the invention of clothing. The caveman was probably happy to chase pigs through the scrub with his dangly bits flopping in the wind, while the cavewoman would be inventing the loin cloth, which the caveman would likely adopt with glee, as it prevented his said dangly bits coming in contact with the gorse and other spiky plants. For the cavewoman there was an advantage that it hid the dangly bits from her view.

Then when the woman in the next cave over, the blonde one with the big … assets, starting wearing that fitting badger skin outfit, cavewomen had invented fashion. Hmm. The charcoal from the newly invented fire really enhanced the under eyes, and the lighter ash really made the cheekbones stand out. Your move, blondie!

And cooking too. Caveman probably dropped his slice of bear loin in the fire and discovered that it tasted great, after you brushed the burnt bits and the ash off. Cavewoman then got a stone, put it on the fire and sizzled her steak on that. With a few grilled veges on the side, for the healthy touch.

Of course when caveman was unsuccessful in bringing home any meat, the family had to subsist on berries and seeds. Crushing the seeds between two rocks probably made them easier to eat and that a short step from grinding them up, which is a small step from mixing them with water and then dropping them on the hot stone. Somehow I don’t imagine the caveman doing that. He’d be too busy describing the ones that got away.

Then when the caveman invited next door over for tea, then something special was required. So wrap the grilled meat pieces in the flat bread, add a few herbs and spices, and hey presto! Instant cuisine. I bet blondie couldn’t even boil an egg. Oh, wait a minute, we haven’t invented boiling things yet.

What if we take that coconut shell and fill it with water and balance it on the fire? Add a few leaves from that bush over there, and we’ve invented tea. A few ground beans from that other bush and we have coffee. Hmm, let’s domesticate a goat, so that we have an assured source of meat, and hey, we can put some of the goat’s milk in the tea.

My semi-serious point is that all these things that were developed in the dim and distant past were likely invented by the women. While the men were out chasing pigs, goats, and badgers and developing weapons and warfare, and all those men things, women stayed in or around the cave inventing, well, home.

When the men came home with pig-on-a-stick, the woman would break down the animal, with a stone knife probably invented by a woman to make it easier, remove the tubes and other gruesome bits, and set it on the fire to cook. She probably accidentally domesticated the dog by feeding it the bits she didn’t want. The cat was always there.

Of course, when you spend your days, sitting on the ground, keeping the fire going, accidentally inventing smoking of meat by hanging it over the fire, the ground begins to get a bit, well, hard. Animals skins help somewhat, but animal skins with dried grass under them were even better! But to keep the grass from leaking out from under the skins, woman had to invent sewing.

Of course, sewing helped the skins look a lot better. Take that blonde girl. What? You bought yours! You invented shopping? Go, girl!!

I’d bet it was a woman who invented agriculture. While man was out chasing deer and tripping over rocks, while he was gathering a paleo diet on the side from bushes and shrubs, woman was at home noticing that some of the seeds gathered last year were sprouting. What if she were to scratch some shallow lines in the ground and plant those sprouting seeds? What is she were to water and weed them and, well, let’s invent a word, cultivate them? Then they wouldn’t have to go so far to find seeds when that idiot man couldn’t find any prey! And if they did grow, she’d save some seed for next year rather than just eat it all.

Then when the cave gets too small for a growing family, it’s the woman who looks around, finds a bigger, better cave, and pays the occupants half an antelope for it. It’s the woman who invents real estate.

It’s the woman who sticks a few palm fronds in cracks in the rock to give them shade from the sun in summer, and who piles up some rocks to block the wind in winter, it’s the woman who diverts the stream away from the living area. Yes, this cave has running water! No need to go down to the stream to drink! It’s the woman who invents home improvement.

Of course, my hypothesis above, that from fire to home improvement, these things were invented by women. The women were, in general, left behind while the men went hunting. The men didn’t have time to invent things, but the women were able to put their minds to work on improving things around the cave, but people give them little credit for it. But when push comes to shove it seems to me that civilisation is the greatest achievement of womankind.

Mental Illness

More and more people are being diagnosed with mental illnesses these days. At least that’t the way it appears. Depression, which I suffer from a little, is rife and almost everyone knows someone who suffers from depression or suffers it themselves.

Schools now have special teachers or teachers’ aides to assist in the management of children with autism and other similar conditions. Sometimes these children cause significant disruption in classrooms and measures to handle this are almost always put into place.

It is unclear whether or not there is a real rise in these conditions. It may be that better diagnosis of these conditions is the cause of the upwards trend in the number of diagnoses of these conditions. Certainly I don’t recall there being a lot of mentally ill people when I was growing up. There were always people who were “different” in some ways, and as a result were often teased or tormented by others of the same age. Hopefully that at least we have left behind us.

Mental illness - blanket man — Mental illness – blanket man

It’s in the lesser mental ailments that I think that we have seen more diagnosis and consequent steep rise. For instance, one hears of the “autism spectrum”. I had erroneously assumed that everyone was on the autism spectrum somewhere with most being on the very low end and that those diagnosed with “autism” were located higher up the spectrum. Reading a few items on the Internet seems to prove me wrong and that there are people on the spectrum and people who aren’t.

When I was young everyone knew of someone whose mother always smelled of alcohol and who had perhaps crashed a car while drunk. Alcoholism was not mentioned as such, so I’m unsure if such a thing was recognised in those days. Alcoholics Anonymous was started in 1935, and I certainly heard of them at some stage when growing up.

Also most families had a creepy uncle who was kept away from the young girls and boys of the family. These days we have “online grooming” and paedophile registers. When I was young scandals were usually dealt with in the family, and steps were taken to avoid situations occurring that led to the scandal. Unfortunately this meant that the scandal was hidden and the victims were often made to feel guilty, when it was not their fault in any way.

With online grooming, the guilty person can be a complete stranger to the child, and this opens a whole new can of worms. Do parents severely restrict a child’s online access and police them every minute that they are online, or do they educate the children about the dangers? Obviously they need to do both. The first strategy mitigates the danger and the second prepares the child for those occasions when the first strategy fails.

When I was young, there was an occasional person who we learnt to avoid. The man on the corner with the fierce dog. The crazy cat lady who constantly talked to herself. The compulsive hoarder who built up a pile of junk in their front yard. These people are still with us, but now they have their own television programmes! They’ve always been with us, and likely always will. They are much more noticeable these days because the television programmes, but I suspect that there aren’t any more of them than there used to be.

I recall one old lady who lived alone. I think that she would, these days, be diagnosed with dementia or Alzheimer’s disease or similar. She would wander the streets in her nightie and her robe and have to be taken back home by someone, usually a neighbour or the police. Now and then one of these confused older people would wander off and get lost sparking full scale searches. This still happens today and sadly, not all such cases are resolved happily.

In some ways the rise of the nuclear family and the relative decline of the extended family may have led to the higher visibility of mental illness in society. The nuclear family, mum, dad, and kids has no room for those who mentally don’t fit in. The extended family however can handle the less mentally stable family members to some extent. Adult children can take turns at looking after granny, or maybe pay for grannies care between them. The cousin who is socially inept or who is slightly autistic can find a niche in an extended family.

This can lead to less visibility of much mental illness as the family is unlikely to mention such problems outside of the family and the ill person may be helped by the familiar and nurturing environment.

Some mental illnesses, however, can’t be handled in this way. The mentally ill person may be violent towards other or to themselves. They may be dangerous to the public, as in the case of the drunk or drugged driver. They may be so out of tune with the world that they need professional help.

In today’s world professional help is often available. In some cases drugs can be effective, as in the case of depression and bipolar disorder. In others there is the possibility of committal to a psychiatric hospital. Such places are generally not nice. The patients are generally gravely ill, and nursers and carers in the hospitals have utmost respect. Often such hospitals are underfunded and can be over crowded. Efforts to make them look better often make then look sad.

In the past, even in some cases in the near past, mental hospitals or asylums were places of horror. The patients often lived in squalor, were strictly restrained and were subjected to horrific “treatments”. Fortunately treatment of mental illnesses has improved significantly over the last hundred years or so. Let’s hope it continues to get better.

Of the two hypotheses as to why the rate of mental illness has increased, I definitely think that the better reporting has been the main cause. That is exacerbated by the reduction in the level at which such problems are reported. Depression would not have considered an illness at one time, for example, and autism is reported more frequently because people are aware of it. I certainly don’t believe that there is more mental illness that when we were young. It’s certainly a lot more visible.