You might die today. You might suffer a stroke, for example. Or, if you venture to the streets, you might be hit by a car. Or if you happen to be outside, you might be hit by a lightning. Or a meteor might strike near enough to you. Or World War III might start with a megaton warhead exploding nearby.
You might, also, if you are single, find your true love today. Or you might be crowned the Supreme Ruler of the Known Universe. Or you might find an important person’s wallet and be able to collect a huge finder’s fee. Or you could find yourself the single winner of a jackpot in the national lottery.
One purpose of the long childhood and adolescence of humans is to allow time for one to be taught and otherwise acquire the necessary skills in the great gamble that we call life. One learns to pay attention to the important things: take care to look both ways before crossing a road, for example. One learns to avoid the really dangerous things, such as touching a hot stove burner with an unprotected hand, or poking inside a live electric socket with an iron nail. Most importantly, one learns to learn, to adapt to new situations.
One learns to emphasize taking into account dangers and opportunities that one regards as likely: for example, when crossing a road, one looks left and right, since those are the directions where one is likely to see approaching vehicles that pose a collision danger. One learns to ignore extremely unlikely dangers: when crossing a road, one does not look up to see if a helicopter is about to land on the road. One also learns to adjust these likelihood estimates based on observations: if there’s a loud noise above, looking up is warranted; there actually might be a helicopter approaching to land.
Most people would not describe making the decision to cross a road as rolling dice, but that’s effectively what it is. Even if one is extremely careful, even if one has looked both left and right, and up for good measure, when one steps on the road and starts walking across it, one exposes oneself to risk. The risk is first that something out of the ordinary happens: a speeding motorcyclist traveling 200 km/h will not be noticed by a pedestrian in a routine safe-to-cross check, and the motorcyclist will not have time to take action to avoid a collision. The risk is also that one’s vigilance might be below par: a pedestrian who always crosses this road at this time of the day, not having encountered any conflicting traffic in the years and years they have taken this road, might not look as carefully as one should. There is also the risk of the extremely unlikely case of an airplane with a total engine failure making a silent forced landing on that road just as one is crossing it (bad news for both the plane and the pedestrian).
The gamble aspect is clearer (but sometimes misunderstood) when a doctor offers a patient the choice between an elective surgery and continuing with noninvasive treatment. Any surgical operation has the risk of death on the operating table; for most elective operations, where the surgeon can screen out high-risk patients, the risk is low, but patients do die in elective surgery all the time. An operation also has the risk of other adverse events, ranging from later death due to, for example, a massive pulmonary embolism, to less drastic ones. Any patient realizes this, and weighs whether the rewards justify the risks. What people sometimes miss is to take account that one is not adding risk but trading risk, for the noninvasive option also carries risk (in some cases even the risk of sudden death at about the time of the surgery would have taken place). However one looks at it, the key point is that one is rolling dice.
There is a philosophical theory that looks at life in this way. The practical knowledge each person carries in their head is modeled as a large table containing an entry for every eventuality that the person can conceive, listing for each the probability of it occurring at this instant, as that person reckons the probability. Each person’s table is different, reflecting differences in life experiences and personality. Each time one makes a new observation about the current situation or takes a decision that changes the situation, the table is instantly updated to match their personal probability for each eventuality in light of the new information or change of circumstances.
The theory requires that the probabilities in the table follow the laws of the formal theory of probability. The theory also says that a person is rational if their table of probabilities never leads them to placing a set of bets that is a sure loser; for example, betting for the equation 2+2=5 (assuming conventional meanings for the symbols in the equation) is a sure loser, while betting for Elvis being alive is not (it’s just very very unlikely). In technical terminology, a set of bets that will surely lose is a Dutch book (I do not know the etymology of that phrase); the theory thus states that rationality means not being vulnerable to a Dutch book.
This theory is, for historical reasons, called Bayesianism (though that term also encompasses other closely related theories); some authors use the more descriptive name of subjective probability. There are three key ideas: first, a probability is always defined in relation to some agent (a person, a computer program, etc), whose history shapes the probability; second, an agent learns by adjusting its probability estimates based on new data; and third, an agent’s actions can be viewed as bets.
Consider any particular moment when an agent receives a new piece of information. The probability the agent has assigned to a particular eventuality just before it receives that information is called its prior probability or just its prior for that eventuality. Conversely, the probability the agent assigns to an eventuality in response to the new information is called its posterior probability or its posterior for that eventuality. There are a number of proposed rules for deriving the posterior from the prior and the nature of the new information; the oldest and best established is based on Thomas Bayes’s Theorem of formal probability theory, which explains the name Bayesianism.
A number of philosophers and scientists of the early 20th Century found the inherent subjectivity of Bayesianism repugnant, and developed several alternative theories, common to all being the idea of the probability of an eventuality being an objective trait of the eventuality, not tied to any particular agent like Bayesianism decrees. Standard statistical inference, as it is taught in most courses of statistics and employed in most statistical studies over the 20th Century and even in this century, is the best known of these alternative theories. All approaches share the same formal theory of probability, but the way they apply it to real-world situations is different. While standard statistics is defensible on its own right, it has been mistaught and misapplied by scientists for nearly a century… but that’s a whole another blog post.
Nevertheless, I find the informal version of Bayesianism that I have described to be a very good rule-of-thumb model of many things. Consider, for example, the question of truth I discussed in my two previous posts (1, 2). Two witnesses may have a totally different view on whether the defendant handled a knife at the scene; this can be viewed as the result of ambiguous information (what each witness actually saw) combining with their personal priors to yield their respective posteriors, which they then offer to the court (no pun intended!). It also neatly explains why people come to different conclusions on such things as the existence of God, the efficacy of homeopathy, and the danger from global climate change; different people have different priors (which is another way of saying that they have different prejudices), and the evidence they have seen is, for many people, not sufficiently impressive to make an appreciable difference to their posteriors. As the saying goes, extraordinary claims require extraordinary evidence… but each person has their own idea of what is extraordinary.
There is, however, some hope. A theorem has been proved saying, in effect, that no matter how divergent the viewpoints of people on some point, sufficient evidence can be imagined to make them all agree. Whether that imagined evidence can, in practice, be found, is another matter.
There is another point to consider, as well. There are eventualities that are fatal. If one’s prior for even one of those eventualities is way too low, one will eventually be killed. On the Internet, we call that earning the Darwin Award; it is the Nature’s way to manage our collective priors.
In my previous post, I discussed why I think there is no such thing as “the” truth, a single truth valid for all intents and purposes. Truth is much more complicated.
Consider the oath administered to a witness at trial. It binds them to “tell the truth, the whole truth, and nothing but the truth” (exact phrasing varies from jurisdiction to jurisdiction), but nobody seriously expects them to tell what actually took place, in a correspondence-theory sense. For one thing, a witness is, of course, restricted by the fact that they are but one person at the scene, and can observe the event from only one place at any one time. Further, a human being is not (with few exceptions) a mere recording machine, able to relay the exact image they saw or the exact sounds they heard; instead, they interpret their observations and store those interpretations (instead of the observations) in their memory, and then relay those interpretations (likely with memory-induced corruption) in speech. Finally, human memory is fallible, and it becomes more unreliable as time moves on, away from the event itself.
Let us imagine a court conducting a criminal trial. This one is a Finnish court, where a witness is always directed to tell what they know of the event in their own words; questions from the lawyers, if any, come later.
THE FIRST WITNESS is a 19-year-old woman, active in the leftist environmentalist movement. Her examination goes as follows:
PROSECUTOR: Are you aware of what event is at issue in this trial?
PROSECUTOR: Please recount in your own words what happened. How did you come to be at the scene, what events did you observe?
WITNESS: Well… We held an anti-nuclear demonstration at the construction site of the new nuclear plant. It was a peaceful event, of course. We carried signs and sang songs. Some troublemakers I had never seen before started throwing stones and perhaps some other things toward the construction site. The police patrol who had been standing nearby ordered us all to leave. My friend Petri went to talk to them, quite peacefully, and suddenly the police started beating him, threw him to the ground, handcuffed him and dragged him to the police van. They did all that to him, without any provocation! All the while the troublemakers continued their activities. That’s all, I think.
PROSECUTOR: By Petri, you mean Petri Suuro, the accused?
PROSECUTOR: Did you see what Petri was doing before the police came to him?
WITNESS: I’m sure he did not do anything justifying their brutality.
PROSECUTOR: Nothing further for the main examination, President.
PRESIDING JUDGE: Anything on behalf of Mr. Suuro? (Advocate shakes head.) All right, any cross examination? Prosecutor?
PROSECUTOR: Thank you, President. (To the witness:) Where was your attention directed to just prior to the police coming to Petri?
WITNESS: I was looking at everything, I believe.
PROSECUTOR: So you saw what the troublemakers were doing, and also what Petri was doing?
WITNESS: Yes, absolutely.
PROSECUTOR: Was Petri standing still, or walking? Did he have anything in his hand, perhaps?
WITNESS: He was standing still, but shouting to the troublemakers. I think his hands were in his pockets; that’s what he usually does with his hands.
PROSECUTOR: Do you know, did Petri carry a knife in pocket?
WITNESS: Absolutely not. He’s a peaceful guy; why would he carry a knife to a demonstration?
PROSECUTOR: You did not see him take a knife out of his pocket?
WITNESS: What knife? He did not have a knife to take out. No, I never saw any knife in his possession.
PROSECUTOR: Nothing further.
PRESIDING JUDGE: On behalf of Mr. Suuro? All, right, let’s end the examination.
THE SECOND WITNESS is a 60-year old man, in charge of the nuclear plant construction site.
PROSECUTOR: You are aware of what events we are discussing today?
WITNESS: Yes, I am.
PROSECUTOR. Please tell us what you know of the events leading to the police arresting Mr. Suuro, sitting there. How did you come to be there at the time, and what did you observe?
WITNESS: Very well. I am a senior manager of the company building the new nuclear plant, and I am in charge of the construction site. We knew, of course, of the planned demonstration; it was fairly well publicized by the demonstrators. We also received information we believed to be somewhat reliable suggesting that the demonstrators intended to set fire to the construction site. I contacted the police and made sure they were present in force. I also attended myself, just in case.
The demonstration started peacefully enough, but soon the demonstrators started throwing rocks and Molotov cocktails through the outer fence. Some did in fact manage to get fires started, and it was difficult for our fire crews to do their job due to the flying rocks. I went to the police to demand action, but they were faster, and were already taking action. My attention was grabbed by shouting near me; it was a young man, I believe Mr. Suuro here, having a loud argument with two police officers. I noticed particularly that Mr. Suuro started to take a knife from his pocket, at which point the officers quite properly restrained him and put him into one of the police vans.
PROSECUTOR: Did you observe the behaviour of Mr. Suuro before the argument with the police?
WITNESS: For me, he was just one of many, and I did not pay him any attention before the argument. I was not even particularly aware of him.
PROSECUTOR: Nothing further.
PRESIDING JUDGE: On behalf of Mr. Suuro?
MR. SUURO’S ATTORNEY: Cross examination only, President.
PRESIDING JUDGE: All right, cross examination, then. Prosecutor?
PROSECUTOR: Nothing, President.
PRESIDING JUDGE: On behalf of Mr. Suuro?
MR. SUURO’S ATTORNEY: Thank you, President. (To the witness:) Did you see the knife well?
WITNESS: I saw it was a knife.
MR. SUURO’S ATTORNEY: What sort of a knife?
WITNESS: A normal kind. Shiny.
MR. SUURO’S ATTORNEY: A butter knife? A puukko? A bread knife?
WITNESS: An average knife. I can’t remember what kind exactly.
MR. SUURO’S ATTORNEY: What was your attention focused on when you saw the knife?
WITNESS: I was looking at Mr. Suuro and the police officers.
MR. SUURO’S ATTORNEY: Not the knife specifically?
WITNESS: I noticed the knife, particularly how it shone.
MR. SUURO’S ATTORNEY: But you were not looking at Mr. Suuro’s hands or pockets when you noticed the knife?
WITNESS: Not specifically. I was looking at the three people involved. But I did see the knife.
MR. SUURO’S ATTORNEY: Apart from the knife, did Mr. Suuro behave aggressively toward the police officers?
WITNESS: He was clearly agitated. Used a loud, angry voice.
MR. SUURO’S ATTORNEY: Just words, no action?
WITNESS: The kife was action. But otherwise no.
MR. SUURO’S ATTORNEY: Do you remember what Mr. Suuro was saying to the officers?
WITNESS: He was, I think, telling them to stop pestering him and go after the real troublemakers.
MR. SUURO’S ATTORNEY: Was Mr. Suuro one of the troublemakers in your estimate?
WITNESS: He made trouble to the officers, and he was one of the demonstrators.
MR. SUURO’S ATTORNEY: Other than the altercation with the police, and his presence at the scene, was he a troublemaker in your estimate? Did you see him throw stones or Molotov’s cocktails, for example?
WITNESS: Not when he was arguing with the officers. Before that I had not paid him any attention,
MR. SUURO’S ATTORNEY: And afterwards he was under arrest. Nothing further, President.
PRESIDING JUDGE: Prosecutor? (Prosecutor shakes head.) All right, this examination is closed.
Mr. Suuro is, in this fictional court case, charged of several offences. Relevant to these two witness examinations are that he allegedly carried a knife illegally in public, and that he attempted an assault of police officers with that knife. Since these are fictional examinations, and I created these two witnesses myself, I can authoritatively say that neither lied. Both complied with the oath they had taken (the local phrasing goes “[...] I shall testify and state the whole truth in this case, without concealing it, adding to it or altering it”). Yet, they tell a completely different story.
The first witness was acquainted with Mr. Suuro and thus had a measure of his character. From her point of view, what happened was an unprovoked attack on a peaceful protestor by the police. This is, of course possible. The second witness reports having seen the knife, but it is possible that he mistook something else for it, or simply imagined it, being undisposed to believing the police taking such action without provocation.
The second witness was predisposed to think ill of Mr. Suuro; not out of personal malice but simply because Mr. Suuro and he were on different sides of a confrontation, and held deeply divergent political views. His account is also plausible; the first witness may not know Mr. Suuro as well as she thinks, and she may not have paid enough attention to him during the demonstration.
It is notable that the first witness does not profess to have seen the absence of a knife; she merely states she knows it was not there. She could be right, of course; she might actually have seen that there was nothing in the pocket, but she only remembers a deep conviction, not the details. She could be wrong, as well; she may have been positioned so that she did not see that pocket and the hand where the knife was, and her strong belief in the absence of the knife, and the haziness of memory by the time of the trial, might make her think she saw its absence.
Now, I deliberately wrote these vingettes to be ambigous; even I do not know who is right. I would have to decide, were I to write a complete story about these fictional events; but for the purposes of this blog post, we do not know.
A court, of course, is obligated to decide the case. Given these two testimonies and no other evidence, it has no choice but to choose who is more believable. If more evidence is presented, it of course may become easier to decide the case. In either case, however, the court does not decide what actually happened. What it decides is whether using the power of the state against Mr. Suuro is warranted given the evidence it has heard. The English translation of the Finnish Code of Judicial Procedure (Chapter 17 Section 2 Paragraph 1) puts it this way:
After having carefully evaluated all the facts that have been presented, the court shall decide what is to be regarded as the truth in the case.
Note that the court is not tasked to determine the truth but what is to be regarded as the truth. What actually took place may be something different. For example, in a criminal case, the standard of reasonable doubt applies: everybody may be convinced that the accused did it (and it even may be that the accused really did do it), but if the court cannot justify to itself why a minority theory must be disregarded as unreasonable, then what is to be regarded as the truth is that the accused did not do it.
We have here already two faces of truth: the truth required of a witness, and the truth required of a court of law. A witness’s truth is that of honesty, not of correspondence to reality. The truth of a court of law is that of justice and of the moderation of the power of the state; again, not of correspondence to reality.
There is at least a third face of truth. When a medical scientist says that a particular treatment is efficacious and safe for the treatment of particular class of patients, they are predicting the future. The scientist’s truth is a best guess derived from studies already performed, and any competent scientist will acknowledge that they might be wrong; there certainly are lots of historical examples of a scientist’s well-backed prediction not corresponding to the reality. Sometimes it is misconduct (but then it’s not well-backed); sometimes it is the application of research methods thought to be correct but later revealed to be faulty; and sometimes it is simply that our research methods, while still considered valid, are not 100 % reliable. But in many many cases, the prediction appears to be correct.
The scientist’s truth is, I think, the most complex. It is partly the same as the witness’s: it is truth of honesty. But it is also something more: the truth of competence, and the truth of expertise. And, like all faces of truth, sometimes it turns out not to correspond with the reality.
I think the best way to see truth is in this way: not as correspondence to reality but as an obligation of a human being. Truth is about honesty, justice, moderation of power, competence, and expertise, mixed as appropriate.
I have been interested in science since before I can remember. I was reading popular science, I believe, before first grade. I was reading some undergraduate textbooks (and the occasional research monograph – not that I understood them) before high school. I did this in order to learn the truth about what the world is. Eventually I learned enough to realize that I wanted to really understand General Relativity. For that, I learned from a book I no longer recall, I needed to learn tensors.
I, therefore, set myself on the project of building my mathematical knowledge base sufficiently far to figure tensors out. By the time I started high school (or rather, its equivalent), I had switched from desiring mathematics as a tool (for understanding Relativity) to taking it as a goal in itself. My goal for the next few years was to learn high school math well enough to be able to study mathematics at university as a major subject. I succeeded.
During the high-school years I also continued reading about physics. My final-year project in my high-school equivalent was an essay (sourced from popular science books) on the history of physics, from the ancients to the early decades of the 20th Century, enough to introduce relativity and quantum mechanics, both at a very vague level (the essay is available on the web in Finnish). I am ashamed to note that I also included a brief section on a “theory” which I was too young and inexperienced then to recognize as total bunk.
At university, I started as a math major, and began also to study physics as a minor subject. Neither lasted, but the latter hit the wall almost immediately. It was by no means the only reason why I quit physics early, but it makes a good story, and it was a major contributor: I was disillusioned. Remember, I was into physics so that I could learn what the world is made of. The first weeks of freshman physics included a short course on the theory of measurement. The teacher gave us the following advice: if your measurements disagree with the theory, discard the measurements. What the hell?
I had understood from my popular-science and undergraduate textbook readings over many years that there is a Scientific Method that delivers truthful results. In broad outline, it starts from a scientist coming up, somehow (we are not told how), with a hypothesis. They would then construct an experiment designed to test this hypothesis. If it fails, the hypothesis fails. If it succeeds, further tests are conducted (also by other scientists). Eventually, a successfully tested hypothesis is inducted into the hall of fame and gets the title of a theory, which means it’s authoritatively considered the truth. I expected to be taught this method, only in further detail and with perhaps some corrections. I did not expect to be told something that directly contradicts the method’s central teaching: if the data and the theory disagree, the theory fails.
Now, of course, my teacher was teaching freshman students to survive their laboratory exercises. What he, instead, taught me was that physics is not a noble science in pursuit of the truth. I have, fortunately, not held fast to that teaching. The lasting lesson I have taken from him, though I’m sure he did not intend it, is that the scientific method is not, in fact, the way science operates. This lesson is, I later learned, well backed by powerful arguments offered by philosophers of science. (I may come back to those philosophical arguments in other posts, but for now, I’ll let them be.)
There are, of course, other sources for my freshman-year disillusionment. Over my teen years I had participated in many discussions over USENET (a very early online discussion network, now mostly obsolete thanks to various web forums and social media). Many of the topics I participated in concerned with the question of truth, particularly whether God or other spiritual beings and realms exist. I very dearly wanted to learn a definite answer I could accept as the truth; I never did. A very common argument used against religious beliefs was Occam’s razor: the idea that if something can be explained without some explanans (such as the existence of God), it should be so explained. Taken as a recipe for reasoning to “the truth”, it seems, however, to be lacking. Simpler explanations are more useful to the engineer, sure, but what a priori grounds there possibly can be for holding that explanatorily unnecessary things do not exist? For surely we can imagine a being that has the power to affect our lives but chooses to not wield it (at least in any way we cannot explain away by other means), and if we can imagine one, what falsifies the theory that one isn’t there?
Many scientists respond to this argument by invoking Karl Popper and his doctrine of falsification. Popper said, if I recall correctly (and I cannot right now be bothered to check), that the line separating a scientific theory from a nonscientific one is that the former can be submitted to an experiment which in principle could show the theory false, and for the latter there is no such experiment that could be imagined; in a word, a scientific theory is, by Popper’s definition, falsifiable. Certainly, my idea of a powerful being who chooses to be invisible is not falsifiable. While there are noteworthy philosophical arguments against Popper’s doctrine, I will not discuss them now. I will merely note that the main point of falsificationism is to say that my question is inappropriate; and therefore, from my 19-years-old perspective, falsificationism itself fails to deliver.
My conclusion at that young age was that science does not care about The Truth; it does not answer the question what is. It seemed to me, instead, that science seeks to answer what works: it seeks to uncover ways we can manipulate the world to satisfy our wants and needs.
My current, more mature conclusion is similar to the falsificationist’s, though not identical. The trouble is with the concept of truth. What is, in fact, truth?
In my teens, I did not have an articulated theory of truth; I took it as granted. I think what I meant by the term is roughly what is called the correspondence theory of truth by philosophers. It has two components. First, that there is a single universe, common to all sensing and thinking beings, that does not depend on anyone’s beliefs. Second, that a theory is true if for each thing the theory posits there is a corresponding thing in the universe possessing all the characteristics that the theory implies such a thing would have and not possessing any characteristics that the theory implies the thing would not have; and if the theory implies the nonexistence of some thing, there is no such thing in the universe. For example, if my theory states that there is a Sun, which shines upon the Earth in such a way that we see its light as a small circle on the sky, it is true if there actually is such a Sun having such a relationship with Earth.
Unfortunately, the correspondence theory must be abandoned. Even if one concedes the first point, the existence of objective reality, the second point proves too difficult. How can I decide the (correspondence-theory) truth of the simple theory “there is a chair that I sit upon as I write this”, a statement I expect any competent theory of truth to evaluate as true? Under the correspondence theory of truth, my theory says (among other things) that there is some single thing having chair-ness and located directly under me. For simplicity, I will assume arguendo that there are eight pieces of wood: four roughly cylindrical pieces placed upright; three placed horizontally between some of the upright ones (physically connected to prevent movement); and one flat horizontal piece placed upon the upright ones, physically connected to them to prevent movement, and located directly below my bottom. I have to assume these things, and cannot take them as established facts, because this same argument I am making applies to them as well, recursively. Now, given the existence and mutual relationships of these eight pieces of wood, how can I tell that there is a real thing they make up that has the chair-ness property, instead of the eight pieces merely cooperating but not making a real whole? This question is essentially, does there exist a whole, separate from its parts but consisting of them? Is there something more to this chair than just the wood it consists of? The fatal blow to the correspondence theory is that this question is empirically unanswerable (so long as we do not develop a way to talk to the chair and ask it point blank whether it has a self).
Scientists do not, I think, generally accept the correspondence theory. A common argument a scientist makes is that a theory is just a model: it does not try to grasp the reality in its entirety. To take a concrete example, most physicists are, I believe, happy to accept Newtonian physics so long as the phenomena under study satisfy certain preconditions so that Newtonian and modern physics do not disagree too much. Yet, it is logically impossible for both theory of Special Relativity and Newtonian physics to describe, in a correspondence theory sense, the same reality: if the theory of Special Relativity is correspondence-theory true, then Newtonian physics cannot be; and vice versa.
If not correspondence theory, then what? Philosophers of science have come up with a lot of answers, but there does not seem to be a consensus. The situation is bad enough that in the behavioural sciences there are competing schools that start with mutually incompatible answers to the question of what “truth” actually means, and end up with whole different ways of doing research. I hope to write in the future other blog posts looking at the various arguments and counterarguments.
For now, it is enough to say that it is naïve to assume that there is a “the” truth. Make no mistake – that does not mean that truth is illusory, or that anybody can claim anything as true and not be wrong. We can at least say that logical contradictions are not true; we may discover other categories of falsehoods, as well. The concept of “truth” is, however, more complicated that it first seems.
And, like physics, we may never be able to develop a unified theory of truth. Perhaps, all we can do is a patchwork, a set of theories of truth, each good for some things and not for others.
Going back to my first year or two at university, I found mathematics soothing, from this perspective. Mathematics, as it was taught to me, eschewed any pretense of correspondence truth; instead, truth in math was, I was taught, entirely based on the internal coherence of the mathematical theory. A theorem was true if it could be proven (using a semi-formal approach common to working mathematicians, which I later learned to be very informal compared to formal logic); sometimes we could prove one true, sometimes we could prove one false (which is to say, its logical negation was true), and sometimes we were not able to do either (which just meant that we don’t know – I could live with that).
I told my favourite math teacher of my issue with physics. He predicted I would have the same reaction in his about-to-start course on logic. I attended that course. I learned, among other things, Alfred Tarski’s definition of truth. It is a linguistic notion of truth, and depends on there being two languages: a metalanguage, in which the study itself is conducted and which is assumed to be known (and unproblematic); and an object language, the language under study and the language whose properties one is interested in. Tarski’s definition of truth is (and I simplify a bit here) to say that a phrase in the object language is assigned meaning based on its proffered translation. For example, if Finnish were the object language and English the metalanguage, the Tarskian definition of truth would contain the following sub-definition: “A ja B” is true in Finnish if and only if C is the translation of A, D is the translation of B, and “C and D” is true in English.
The Tarskian definition struck me initially as problematic. If you look up “ja” in a Finnish–English dictionary, you’ll find it translated as “and”. It now becomes obvious that Tarski’s definition does not add anything to our understanding on Finnish. And, indeed, it is one more link in the chain that says that mathematics is not concerned with correspondence truth. We cannot learn anything about the real world from studying mathematics. But I knew that already, and thus, in the end, Tarskian truth did not shatter my interest in mathematics.
I also learned in that course of Kurt Gödel’s famous incompleteness theorem. It states (and I simplify a lot) that a formal theory that is sufficiently powerful to express all of mathematics cannot prove its own coherence. This was the result my teacher was alluding to earlier, but it did not bother me. I had been taught from the beginning to regard mathematics as an abstract exercise in nonsense, valuable only for its beauty and its ability to satisfy mathematician’s intellectual lusts. What do I care that mathematics cannot prove itself sane?
What I did not then know is the history. You see, up until the late 19th Century, I believe mathematicians to have adhered to a correspondence theory of truth. That is, mathematics was, for them, a way to discover truths about the universe. For example, the number two can be seen as corresponding to the collection of all pairs that exist in the universe. This is why certain numbers, once they had been discovered, were labeled as “imaginary”; the mathematicians who first studied them could not come up with a corresponding thing in the universe for such a number. The numbers were imaginary, not really there, used only because they were convenient intermediate results in some calculations that end up with a real (existing!) number. This is also, I believe, one of the reasons why Georg Cantor’s late 19th Century set theory, which famously proved that infinities come in different sizes, was such a shock. How does one imagine the universe to contain such infinities?
But more devastating were the paradoxes. One consequence of Cantor’s work was that infinities can be compared for size; also, that we can design a new numbering system (called cardinal numbers by set theorists) to describe the various sizes of infinity, such that every size of infinity has a unique cardinal number. Each cardinal number itself was infinite, of the size of that cardinal number. It stands to reason that the collection of all cardinal numbers is itself infinite, and since it contains all cardinal numbers (each being its own size of infinite), it is of a size of infinity that is greater than all other sizes of infinity. Hence, the cardinal number of all infinities is the greatest such number that can exist. But it can be proven that there is no such thing; every cardinal number has cardinal numbers that are greater than it. If one were to imagine that Cantor’s theory of the infinities does describe the reality, that would imply that the universe itself is paradoxical. This Cantor’s paradox isn’t the only one; there are many others discovered about the same time. Something here is not right.
A new branch of mathematics emerged from this, termed metamathematics, whose intent was to study mathematics itself mathematically. The idea was that finite stuff is well understood, and since it corresponds to the reality, we can be sure it is free of paradoxes. Metamathematicians aimed to rebuild the mathematics of the infinite from ground up, using only finite means, to see what of the infinity actually is true and what is an artefact of misuing mathematical tools due to poor understanding of them. This work culminated in two key discoveries of the 1930s: Kurt Gödel’s incompleteness theorem, which basically said that metamathematics cannot vindicate mathematics, and Alan Turing’s result that said that mathematics cannot be automated. Of course, the technique Turing used is his famous Machine, which is one of the great theoretical foundations of computer science.
Fast forward sixty years, to the years when I studied mathematics in university. The people who taught me were taught by the people who had been taught by the people who were subjected to Gödel and Turing’s shocks. By the time I came into the scene, the shock had been absorbed. I was taught to regard mathematics as an intellectual game, of no relevance to reality.
I eventually switched to software engineering, but I always found my greatest interest to be at the intersection of theoretical computer science and software engineering, namely the languages that people use to program computers. In theoretical computer science, the tools are of mathematics, but they are made relevant to reality because we have built concrete things that are mathematics. Mathematics is not relevant to reality because it describes reality, but because it has become reality! And since the abstract work of the computers derive their meaning, Tarski-like, from mathematics, we have no problem with a correspondence theory. Truth is, again, uncomplicated, and it was, for me, for many years.
Until I realized that computers are used by people. In the last couple of years I have been reading up on behavioural research, as it is relevant to my own interest in language design. Again, the question of truth, and especially how we can learn it, becomes muddled.
Forgive me, gentle reader. This blog post has no satisfactory ending. It is partly because there is no completely satisfactory answer that I am aware of. I will be writing more in later posts, I hope; but I cannot promise further clarity to you. What I can promise is to try to show why the issue is so problematic, and perhaps I can also demonstrate why my preferred answer (which I did not discuss in this post) is comfortable, even if not quite satisfactory.
(Please note that this is a blog post, not a scholarly article. It is poorly sourced, I know. I also believe that, apart from recounting my personal experiences, it is not particularly original. Please also note that this is not a good source to cite in school papers, except if the paper is for some strange reason about me.)
All my Ukrainian coworkers, friends, aquaintances, all Ukrainian strangers, my thoughts are with you. You live in interesting times now. I truly hope that all will be well in the end (at least as well as is possible, given all that has already happend).
Ei ole mitään epäselvää: Venäjä on toiminut väärin. Kysymys on, miten se vaikuttaa Suomeen?
Akuutin kriisin aikana, siis juuri nyt, Suomen linja on valtiojohdon – tasavallan presidentin ja valtioneuvoston – käsissä. Heillä on myös paras tieto siitä, mitä oikeasti tapahtuu, sillä heillä on käytössään salaiset tiedustelutiedot, ovat ne kuinka tarkkoja tai summittaisia, sekä tieto muiden valtioiden johdon linjauksista. Heillä on varmasti paremmat tiedot kuin meillä muilla, jotka olemme tiedotusvälineiden (mukaanlukien sosiaalinen media) varassa. Tämän kriisin ratkaisemiseksi tapahtuu varmasti paljon enemmän, kuin lehdistä saamme lukea. Annetaan heille työrauha.
Silti voimme pohtia, mitä tapahtuu, kun akuutti kriisi on päättynyt. Näin suomalaisen kannalta pelottavinta viime viikon tapahtumissa on miettiä, kuinka samankaltaisia Ukraina ja Suomi ovat. Molemmat ovat entisiä Venäjän alusmaita. Molemmilla on yhteinen raja Venäjän kanssa. Jos Venäjä on valmis käymään disinformaatiokampanjaa ja provokaatiokampanjaa Ukrainaa vastaan, miksi se ei tekisi sitä Suomea vastaan?
On yksi keskeinen ero. Ukrainan julkinen hallinto on läpeensä korruptoitunut, valtiontalous on kuralla, demokraattiset käytänteet eivät ole siellä vakiintuneita, ja valtio on ollut sisäpoliittisessa sekasorrossa jo kuukausia. Niissä oloissa Venäjän on ollut helppo tehdä myyräntyötään. Suomen olot ovat toistaiseksi onneksi todella kaukana tästä.
Yhteistä mailla on myös se, että kummallakin on vähemmistön asuttama autonominen alue, johon on liittynyt sotilaallisia paineita. Suomen tapauksessa kyseessä on onneksi ruotsinkielinen Ahvenanmaa maan länsirajalla, toisin kuin Ukrainan venäjänkelinen Krim itärajalla.
Strategisesti tärkeintä Suomelle Ukrainan kohtalon välttämiseksi on huolehtia valtion toimintakyvystä, pitää kaikkien kansanosien (myös vähemmistöjen ja enemmistön) keskinäiset välit sopuisina sekä pitää välit Venäjään kunnossa, silloinkin kun Venäjä tekee pahaa muualla.
Toinen strateginen kysymys on Suomen sotilaallinen puolustuskyky. Olen aiemmin kannattanut asevelvollisuudesta luopumista ja puolueettomuuden säilyttämistä. Näiden kantojeni taustalla on ollut käsitys siitä, että Venäjä käyttäytyy tulevaisuudessakin siten, kuin modernin 2000-luvun valtion tulee käyttäytyä. Viime viikon tapahtumat osoittavat, että tuo premissi ei ole pätevä. Siksi näissä oloissa on mielestäni ensisijaisesti pyrittävä korjaamaan asevelvollisuuden sukupuolisyrjivä rakenne (eli säätää asevelvollisuus koskemaan kaikkia sopivanikäisiä kansalaisia sukupuolesta riippumatta), joskin pidän asevelvollisuudesta luopumista muista syistä toivottavana ratkaisuna, mikäli se on turvallisuuspoliittisesti realistista. Myös tulee vakavasti harkita EU:n sotilaallisen ulottuvuuden kehittämistä aidoksi puolustusliitoksi, johon sisältyy “hyökkäys yhtä kohtaan on hyökkäys kaikkia kohtaan” -periaate. Yksin ei kannata seistä ilkeän naapurin vieressä.
Puolustusliittokeskustelussa isossa roolissa on perinteisesti ollut huoli, että eiväthän suomalaiset joukot vain käytä sotilaallista voimaa maamme rajojen ulkopuolella. Viimeksi vastaava keskustelu käytiin Iceland Air Meet -harjoituksiin liittyen. Itseäni hieman huolettaa puolustusvoimien toimintakyky tositilanteessa pitkän rauhanjakson jälkeen. Ihanko oikeasti sen tulikasteen tulee tapahtua vasta, kun Suomi on all in? On mielestäni perusteltua, että vapaaehtoisista koostuvat yksiköt voisivat osallistua perusteltuihin voimankäyttöoperaatioihin maailmalla, jolloin operaatioiden kulloisenkin päätarkoituksen saavuttamisen lisäksi kehitetään Suomen puolustusvoimien valmiutta.
Nämä päätökset ovat kuitenkin asioita, joihin ei pidä ryhtyä kiireellä. Hoidetaan Ukraina takaisin kuiville, ja mietitään tarkemmin sitten.
Does anybody have a copy of my LLParser.hs that once was available at http://antti-juhani.kaijanaho.fi/tmp/LLParser.hs? It looks like all my copies (except for an early version I used in one of my functional programming lectures) have gone the way of the dodo.
What happens if a pilot, high on alcohol and cocaine, saves his plane and almost all the souls on board after the plane is crippled by a catastrophic equipment failure, one that would have lead to an unsurvivable crash in any other pilot’s hands? This is the question explored in the film Flight directed by Robert Zemeckis and starring Denzel Washington as the pilot in question.
Let’s be clear about this, as the movie has been (in my opinion) badly misrepresented in advertising. It’s not a disaster movie, depicting in lovely detail every scare the crew and passangers go through – the flight and the crash are a short sequence in the early part of the film, and are hardly ever returned to. It’s not a detective story, following the NTSB around as they solve the puzzle. What it is, instead, is the story of the pilot, dealing with the aftermath. It is a morality tale, to be sure, and one that doesn’t paint with subtle strokes.
The mismatch between advertising and movie is nicely underscored by the contrast between advertisements on the screen and the composition of the audience in the screening I attended today, at Finnkino’s Fantasia theatre here in Jyväskylä. There were about twenty people in attendance. All the women present were there with a man; there were some unaccompanied men like myself. The advertisements seemed to be targeted on a woman-rich environment, however.
The movie might pass the Bechdel test, if one is feeling generous. This test requires that a movie should have at least two named female characters that have a conversation about something other than a man. During the flight emergency sequence, the flight attendants do discuss the situation, very briefly, and I think every one of them is named. I don’t think that’s what the test has in mind, though. Other than that, I believe all interactions women have in the film are with one man or another.
The shock of wrong expectations aside, there were some things I really liked about the movie. Nicole (Kelly Reilly), a drug-addict woman looking to get clean who moves in with our alcohol-addict pilot for a while, had some really good sense and did the right thing when it mattered. The story was given a satisfactory ending, something I really doubted could be done as the movie unfolded.
I also like the moral conflict inherent in the setup. The history of aviation has seen many incidents where a pilot heroically saved his plane from a near-crash that he ultimately caused himself. In this movie, there was no such ambiguity as the crash would have happened whoever had piloted the plane; the only question was how bad it would be, and our hero the drug addict dealt with it exceptionally well. The ambiguity is different: the pilot should have been kicked off the controls years before, yet he was the only good choice for this flight, in retrospect.
I don’t regret seeing the film, but I hesitate to recommend it. I’ll call it a draw: 5/10.
Independence day traditions include the televising of two war movies (based on the same book), a military parade and a formal ball.
Let me tell you about the ball. It takes two hours for the host (the President of the Republic) to individually welcome every guest. This is televised and narrated (mostly reciting the guests’ names but also commenting on their attire). Then there’s one hour of televised dances and guest interviews. What happens after the cameras shut down at 10 pm is fodder for the tabloids.
And yes, it has massive ratings. Almost everybody who is not present watches the broadcast.
So there you have it, this is Finland. Happy independence day!
Everybody knows the premise of Iron Sky: as a character in the movie says, it’s “Nazis … from the Moon”. It’s a given that something explosive happens in the movie. Yet, it can carry the story only so far, certainly not the full 93 minutes. Before I saw the film, I worried whether the writers had come up with something good enough to fill the blanks. Suffice to say I’ve seen the movie twice now and expect to go at least once more to the theater.
Yes, there’s lots more than just the high concept. I can’t tell you what it is… spoilers! But I can mention some highlights without giving too much away. There’s a hilarious reenactment of the Youtube hit scene from Downfall. Finland is revealed to be unique in the way it expresses its love of peace. While the President of the United States of America (Stephanie Paul) does look a bit like Sarah Palin, the character is much more believable as POTUS. Oh, and while it’s not a part of the movie, I really like the turn-your-cellphones-off infomercial using characters from Iron Sky. And yes, Iron Sky passes the Bechedel Test.
I can also tell you this: the audience laughed many times, in both occasions; it also was utterly silent in the right moments. (Well, apart from the young man somewhere behind me in the public premiere who found both a nuclear bombing and a spaceship ramming another laugh-out-loud funny.) Iron Sky is a comedy, yes, but it is also deadly serious.
Before I saw Iron Sky the first time, I thought I would be comparing the film to Spaceballs and Galaxy Quest. Now, I don’t find those comparisons very useful any more (but I would rate Iron Sky above Spaceballs, any day). The film I find myself, quite to my surprise, drawn to as the best comparison is Kubrik’s classic Dr Strangelove. While Iron Sky doesn’t match its brilliance, it’s nothing to be ashamed of. After all, Strangelove is one of the best films ever produced.
I give Iron Sky ★★★★☆. Your mileage may, of course, vary.
I sometimes hear it claimed that the practice of charging interest causes an ever-increasing demand for money. The argument goes, since principal plus interest is more than principal alone, money needs to be created (by taking on a new loan) in order to pay back the loan. It is then claimed that this creates a vicious circle of ever-mounting debt. The argument is fallacious and demonstrates a fundamental misunderstanding of the nature of money. If, as is indeed the case, money can be reused, there is no vicious circle. Consider the following gedanken experiment.
Suppose I loan you twelve twenty-euro notes for one year, with principal repayment every month and interest totalling twenty euros due at maturity (that is, at the end of the year).
For simplicity, let’s assume you do nothing with the money, just sit on it. Every month you come to me and give me one of the notes I loaned you.
Assume for simplicity again that I do not do anything with the notes I receive from you, I just sit on them.
At the end of the year, you have one twenty-euro note and an obligation to pay me fourty euros (the last installment of principal, plus the agreed interest). What do you do?
One thing you could do is come to me and ask for a further loan. That could be done, I could give you one of my hoarded twenty euro notes and you could then retire the original debt (albeit with a new twenty-euro debt). But this is not the only option.
Another option is that you mow my lawn a couple of times. The wage we agree on is fourty euros in total (assume for simplicity that there are no taxes etc). You do the work, I give you two of my hoarded twenty-euro notes; you now have six of them, one left from my loan and two that I paid you with. Now you can pay the last installment of the principal and the interest. End result: you are no longer in debt, and you have a twenty-euro note that you can do whatever you want with.
Neither scenario required the creation of new money.
A geek of all trades writes about life, the universe and everything