“Human beings are not the perfectly rational creatures they would be if they strove for truth and consistency at all times. Nevertheless, if we can be motivated by a desire to eliminate inconsistency in our beliefs and actions, reason is no mere slave. We may use reason to enable us to satisfy our needs, but reason then develops its own motivating force”
Peter Singer (1981). The Expanding Circle: Ethics and Sociobiology, p. 143
Gendler, T. S. (2011). On the epistemic costs of implicit bias. Philosophical studies, 156(1), 33-63.
The craving for a drink in real dipsomaniacs, or for opium or chloral in those subjugated, is of a strength of which normal persons can form no conception. ‘Were a keg of rum in one corner of a room and were a cannon constantly discharging balls between me and it, I could not refrain from passing before that cannon in order to get the rum’; ‘If a bottle of brandy stood at one hand and the pit of hell yawned at the other, and I were convinced that I should be pushed in as sure as I took one glass, I could not refrain’: such statements abound in dipsomaniacs’ mouths.
William James, Principles of Psychology (New York: Henry Holt and Company, 1890), p. 543. Via Laurence. Thanks Laurence!
As users become more familiar with an environment they situate themselves more profoundly. We believe that insights concerning the way agents become closely coupled with their environments have yet to be fully exploited in interface design
Hollan, J., Hutchins, E., & Kirsh, D. (2000). Distributed cognition: toward a new foundation for human-computer interaction research. ACM Transactions on Computer-Human Interaction (TOCHI), 7(2), 174-196.
Ed Yong has some excellent guidelines for scientists on giving comments to journalists, but I wanted to add a single piece of advice, one which will help whether you are talking to Ed or to less scrupulous journalists:
“Don’t be afraid to tell the journalist what the story is”
By this I mean you are allowed to not answer the question. This feels weird, since it violates conversational and academic rules, but the thing the journalist should be interested in is the real story. The questions just exist to get to that (which is why Ed says he often asks pretty vague questions). If you think the journalist is asking the wrong question, don’t answer it – tell them what the right question is.
If you restrict yourself to answering the wrong questions, the risk for everyone is that the (mistaken) framing stays in place, just with a few qualifications from you. For example, if the journalist is researching a study which says “fabulous brain training method boosts IQ” your comments that the study has flaws, or is a provisional result only, will lead to the headline “fabulous brain training method boosts IQ”. Or, if you are lucky, “fabulous brain training method might boost IQ”. And down in paragraph 4 will be some quote from you warning people not to get carried away.
Far better would be to give the journalist an alternative story, rather than some doubts. Tell them “no brain training method you can pay for works any better than free methods which are available to everyone”. Or “the brain is a machine which runs on blood, the best thing for your brain is physical exercise, not brain training”. This is news people can use. If you really disagree with a study, offering an alternative narrative is your best chance of that study being put in the correct context. “You don’t beat owt with nowt”, as they say.
This is what – I think – Ed is getting at when he says he wants the context from scientists, the “something interesting that I couldn’t have predicted”.
Further reading: George Lakoff “Don’t Think of an Elephant!: Know Your Values and Frame the Debate” (an actual book, so no hyperlink!)
Link: Ed Yong: “A Guide for Scientists on Giving Comments to Journalists“
I’ve been trying to think of documentaries on cognitive science topics. This is what I’ve got so far. Can you help?
And, an honourable mention for
There’s a hoo-har in psychology right now about replication. Spurred on by some high profile fraud cases, awareness of the structural biases surrounding publication and perennial rumblings about statistical malpractice, many are asking if the effects reported in the literature are real. There are some laudable projects aimed at improving best practice in science – journals of null results, pre-registration for experiments, the Center for Open Science (see previous link), but it occurs to me that all of this ignores an important bit of context. At the risk of stating the obvious: you need to build in support for replications only to the extent that these do not happen as part of normal practice.
Cumulative science inherently supports replication. For most of science, what counts on news is based on what has been done before – not just in an abstract theoretical sense, but in the sense that it relies on those results being true to make the experiments work. Since I’m a psychologist, and my greatest expertise is in my own work, I’ll give you an example from this recent paper. It’s a study of action learning, but we use a stimulus control technique from colour psychophysics (and by ‘we’, I really mean Martin, who did all the hard stuff). As part of preparing the experiment we replicated some results using stimuli of this type. Only because this work had been done (thanks Petroc!) could we design our experiment; and if this work didn’t replicate, we would have found out in the course of preparing for our study of action learning. Previously in my career I’ve had occasion to do direct replications, and I’ve almost always found the effect reported. I haven’t agreed with the interpretation of why the effect happens, or I’ve found that my beliefs about the effect from just reading the literature were wrong, but the effect has been there.
It is important that replication is possible, but I’ve been bemused that there has been such a noise about creating space for additional formal replications. It makes me wonder what people believe about psychology. If a field was one where news was made by collecting isolated interesting phenomena, then I there would be more need for structures to support formal replication. Should I take the reverse lesson from this – the extent to which people call for structures to support formal replication is evidence of the lack of cumulative science in psychology?
The rhetoric of wonder is all about encouraging participation. But this infantilising power dynamic is not conducive to confident involvement or critical inquiry.
Righteously snarky CiF, Prof Brian Cox: physicist or priest? Many popular scientists are atheist, so why are they so happy to use the misty-eyed language of religion? by
Eliane Glaser
I screwed up. My latest column for BBC Future is about why cyclists enrage motorists. My argument is that cyclists offend the ‘moral order’ of the roads, evoking in motorists a feeling of outrage over perceived rule breaking.
Unfortunately, I included some loose words in my article that implied things I don’t believe and wasn’t arguing. Exhibit A:
Then along comes a cyclist, who seems to believe that the rules aren’t made for them, especially the ones that hop onto the pavement, run red lights, or go the wrong way down one-way streets.
This wrongly suggests both that I think the typical cyclists breaks the law (they don’t), and/or that motorists are enraged by cyclists’ law breaking. This is not the case, rather I am arguing that motorists are engaged by cyclists’ perceived rule breaking, where I mean rule in the sense of ‘convention’. Cyclists habitually, legally, and sensibly break conventions of car-driving such as waiting in queued traffic, moving at the speed limit or not under-taking.
Exhibit A has now been changed in the article to the more pleasing:
Then along come cyclists, innocently following what they see are the rules of the road, but doing things that drivers aren’t allowed to: overtaking queues of cars, moving at well below the speed limit or undertaking on the inside.
So, my bad and apologies for this. I should have been a lot clearer than I was. I’m just grateful that a few people understood what I was getting at (if you read the whole article I hope the correct interpretation is supported by the rest of the phrasing I use). The amount and vehemence of feedback has been quite surprising. Lots of people thought I was a frustrated driver who hated cyclists. In fact, the bike is my main form of transport. I’ve ridden nearly every day for over ten years (and been hit by a car once). For this article I was trying not to sound like the self-righteous cycling proto-fascist I feel like sometimes. I obviously succeeded. Perhaps too well.
Other people thought I was claiming that this was the only factor affecting road-user’s attitudes. I don’t think this. Obviously selective memory (for bad cyclists or drivers), in- group/out-group effects and the asymmetry in vulnerability all play a role. I did write a version of the article which laid out the conceptual space a bit clearer, but I decided it was boring to read, and really I wanted to talk about evolutionary game theory and make a novel – and, I thought, interesting – claim.
I sometimes think I should get “Telling the truth, just not the whole truth” translated into Latin so I can use it as the motto for the column. Each one I write someone comes back to me with something I missed out. If I tried to be comprehensive I’d end up with a textbook, instead of a 800 word magazine column. I don’t want to write textbooks, so I’m reasonably happy with leaving things out, but I do worry that there is a line you cross when telling some of the truth amounts to a deception or distortion of the whole truth. I’m trying, each time, not to cross that line. Feedback on how to manage this is welcome.
There were many other comments of all shades. You can ‘enjoy’ some of them on the BBC Future facebook page here. If you did leave a comment on email/facebook/twitter I’m sorry I couldn’t respond to all of them. I hope this post clarifies things a bit.
Work for 6 years. The 7th, go alone or among strangers, so the memory of your friends does not hinder you from being what you have become
Either Vinay, or via Vinay
I have not failed. I’ve just found 10,000 ways that won’t work.
Thomas Edison, attib.
So, previously on this blog (here, and here) I was playing around with the bootstrap as a way of testing if two samples are drawn from a different underlying distribution, by simulating samples with known differences and throwing different tests at the samples. The problem was that I was using the wrong bootstrap test. Tim was kind enough to look at what I’d done and point out that I should have concatenated my two sets of numbers and the pulled two samples from that set, calculated the mean difference and then used that statistic to constructed a probability distribution function against which I could compare my measured statistic (ie the difference of means) to perform a hypothesis test (viz. ‘what are the chances that I could have got this difference of means if the two distributions are not different?’). For people who prefer to think in code, the corrected bootstrap is at the end of this post.
Using the correct bootstrap method, this is what you get:
So what you can see is that, basically, the bootstrap is little improvement over the t-test. Perhaps a marginal amount. As Cosma pointed out, the ex-gaussian / reaction time distributions I’m using look pretty normal at lower sample sizes, so it isn’t too surprising that the t-test is robust. Using the median rather than the mean damages the sensitivity of the bootstrap (contra my previous, erroneous, results). My intuition is that the mean, as a statistic, is influenced by the whole distribution in a way the median isn’t, so it a better summary statistic (statisticians, you can tell me if this makes sense). The mean test is far more sensitive, but, as discussed previously, this is because it has an unacceptably high false alarm rate which is insufficiently penalised by d-prime.
Update: Cosma’s notes on the bootstrap are here and recommened if you want the fundamentals and are already degree-level comfortable with statistical theory.
Corrected boostrap function:
function H=bootstrap(s1,s2,samples,alpha,method)
difference=mean(s2)-mean(s1);
for i=1:samples
sstar=[s1 s2];
boot1=sstar(ceil(rand(1,length(s1))*length(sstar)));
boot2=sstar(ceil(rand(1,length(s2))*length(sstar)));
if method==1
a(i)=mean(boot1)-mean(boot2);
else
a(i)=median(boot1)-median(boot2);
end
end
CI=prctile(a,[100*alpha/2,100*(1-alpha/2)]);
H = CI(1)>difference | CI(2)
“The story of the origins of capitalism, then, is not the story of the gradual destruction of traditional communities by the impersonal power of the market. It is, rather, the story of how an economy of credit was converted into an economy of interest; of the gradual transformation of moral networks by the intrusion of the impersonal—and often vindictive—power of the state.” (p.332)
Our attitude to debt is a symptom of this erosion of social economies by currency economies. Mutually agreed, honour, credit is replaced by state-backed, economic credit. Loans which inexorably grow due to interest are enforced by brutal laws against debtors. This is the context for the rapacity of European colonialists – they were driven on by the tyranny of interest.
“All this helps explain why the church had been so uncompromising in its attitude toward usury. It was not just a philosophical question; it was a matter of moral rivalry. Money always has the potential to become a moral imperative unto itself. Allow it to expand and it can quickly become a morality so imperative that all others seem frivolous in comparison. For the debtor, the world is reduced to a collection of potential dangers, potential tools, and potential merchandise. Even human relations become a matter of cost-benefit calculation. Clearly, this is the way the conquistadors viewed the worlds they set out to conquer” (p. 319)
It is the secret scandal of capitalism that at no point has it been organized primarily around free labor. The conquest of the Americas began with mass enslavement, then gradually settled into various forms of debt peonage, African slavery, and “indentured service” (p.350)
This is a scandal not just because the system occasionally goes haywire, as it did in the Putumayo, but because it plays havoc with our most cherished assumptions about what capitalism really is—particularly that, in its basic nature, capitalism has something to do with freedom. For the capitalists, this means the freedom of the marketplace. For most workers, it means free labor. Marxists have questioned whether wage labor is ultimately free in any sense (since someone with nothing to sell but his or her body cannot in any sense be considered a genuinely free agent), but they still tend to assume that free wage labor is the basis of capitalism.
Our dominant image of the origins of capitalism continues to be the English workingman toiling in the factories of the industrial revolution, and this image can be traced forward to Silicon Valley, with a straight line in between. All those millions of slaves and serfs and coolies and debt peons disappear, or if we must speak of them, we write them off as temporary bumps along the road. Like sweatshops, this is assumed to be a stage that industrializing nations had to pass through, just as it is still assumed that all those millions of debt peons and contract laborers and sweatshop workers who still exist, often in the same places, will surely live to see their children become regular wage laborers with health insurance and pensions, and their children, doctors and lawyers and entrepreneurs.”(p351)
With this framing, Graeber repaints Adam Smith’s economic account – “It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.” etc – as a purely moral account, a utopia utterly unlike the actual economic conditions Smith lived in.
To understand the history of capitalism, however, we have to begin by realizing that the picture we have in our heads, of workers who dutifully punch the clock at 8:00 a.m. and receive regular remuneration every Friday, on the basis of a temporary contract that either party is free to break off at any time, began as a utopian vision, was only gradually put into effect even in England and North America, and has never, at any point, been the main way of organising the production for the market, ever, anywhere.
This is actually why Smith’s work is so important. He created the vision of an imaginary world almost entirely free of debt and credit, and therefore, free of guilt and sin; a world where men and women were free to simply calculate their interests in full knowledge that everything had been prearranged by God to ensure that it will serve the greater good. (p.354).
For some critical commentary see here: http://onthespiral.com/review-reactions-debt-first-years, the Crooked Timber seminar (ht Alex)
Update 30/12/12. There’s an important point about rights being conceptualised as property, which Gemma summarises well:
Our freedom is defined as a right, which we own, as opposed to Graeber’s view that rights are actually obligations on others (e.g. our right to free speech is actually others obligations to allow my free speech). Rights have been defined in this way to justify debt-peonage or even slavery – if we own our rights, like property, then we are free to give them away or even sell them (p206).
Update: This post used an incorrect implementation of the bootstrap, so the conclusions don’t hold. See this correction
Mike suggested that I alter the variance of the underlying distibutions. This makes total sense, since it matches what we are usually trying to do in psychological research – detect a small difference in a lot of noise. So I made the underlying distibutions look a lot like reaction time distributions, with a 30ms difference between them. The code is
t0=200;
s1=t0+25*(randn(1,m)+exp(randn(1,m)));
s2=t0+25*(randn(1,m)+exp(randn(1,m)))+d;
Where m is the sample size, and d is either 0 or 30. For a very large sample, the distributions look like this:
After a discussion with Jim I looked at the hit rate and false alarm rate separately. For the simple comparison of means, the false alarm rate stays around 0.5 (as you’d predict). For the other tests it drops to about 0.05. The simple comparison of means is so sensitive to a true difference, however, that the dprime can still be superior to that of the other tests. Which suggests dprime is not a good summary statistic to me, rather than that we should do testing simply by comparing the sample means.
So I rerun the procedure I described before, but with higher variance on the underlying samples.
The results are very similar. The bootstrap using the mean as the test statistic is worse than the t-test. The bootstrap using the median is clear superior. This surprises me. I had been told that the bootstrap was superior for nonparametric distributions. In this case it seems as if using the mean as a test statistic eliminates the potential superiority of bootstrapping.
This is still a work in progress, so I will investigate further and may have to update this conclusion as the story evolves.
David Graeber traces a line from Roman property law, through Cartesian dualism and Hobbes’ state of nature, to the foundational myth of the free market:
At this point we can finally see what’s really at stake in our peculiar habit of defining ourselves simultaneously as master and slave, reduplicating the most brutal aspects of the ancient household in our very concept of ourselves, as masters of our freedoms, or as owners of our very selves. It is the only way that we can imagine ourselves as completely isolated beings. There is a direct line from the new Roman conception of liberty – not as the ability to form mutual relationships with others, but as the kind of absolute power of “use and abuse” over the conquered chattel who make up the bulk of a wealthy Roman man’s household – to the strange fantasies of liberal philosophers like Hobbes, Locke, and Smith, about the origins of human society in some collection of thirty- or forty-year-old males who seem to have sprung from the earth fully formed, then have to decide whether to kill each other or begin to swap beaver pelts.
David Graeber (2011) ‘Debt: The First 5000 years’, p209-210.
Graeber uses an anthropologist’s view of history to argue that markets are brought into existence by the state, and particularly by an expansionist military state which wishes to force all social actors to be intermediaries in the war machine. By obliging everyone to accept state currency a state-coinage-slavery complex is created. This dynamic drives the creation of slaves, which are, by definition, people ripped from all social context. The collision of market economies with social economies (which are about interaction as much as obtaining goods) creates a moral dilemma which we can trace written in the texts of all the ancient religions (you’ll have to read the book for details). The dominant modes of human relation in historical time have been three: exchange, hierarchy and communism (not in the Marxist sense). The dominion of the exchange mode, and its perversion into being primarily market exchange, reduces the primacy of the other modes in the models of liberal/market thinkers, and so our conception of our selves (individually and politically) is contaminated by contradictory notions of debt and ownership (again, you’ll have to read the book). Ultimately this finds expression in a vision of ourselves as separate from our own bodies, and in the foundational myth of economics in which we markets come into being de novo among an asocial but equal status collection of isolates who can begin to trade to satisfy their wants.
It’s an extremely rich book, which is also very disorganised in its arguments. I’m still digesting what I’ve read so this is a poor summary. Most importantly for me, and separate from the specifics of the argument, the anthropological and historical material does the job of expanding our conception of what we and our society could be.
Pro-tip: on the final pages (p384-387) Graeber offers his own summary of the thesis of the book.
Update: This post used an incorrect implementation of the bootstrap, so the conclusions don’t hold. See this correction
This surprised me. I decided to try out bootstrapping as a method of testing if two sets of numbers are drawn from different distributions. I did this by generating sets of numbers of size m from two ex-gaussian distributions which are identical except for a fixed difference, d
s1=randn(1,m)+exp(randn(1,m));
s2=randn(1,m)+exp(randn(1,m))+d;
All code is matlab. Sorry about that.
Then, for each pair of numbers I apply a series of different tests for if the distributions are different.
1. Standard t-test (0.05 significance level)
2. Is the mean(s1)
4. Bootstrapping using the median as the test statistic (0.05 significance level)
I used Ione Fine’s pages on bootstrapping as a guide. The bootstrapping code is:
function H=bootstrap(s1,s2,samples,alpha,method)
for i=1:samples
boot1=s1(ceil(rand(1,length(s1))*length(s1)));
boot2=s2(ceil(rand(1,length(s2))*length(s2)));
if method==1
a(i)=mean(boot1)-mean(boot2);
else
a(i)=median(boot1)-median(boot2);
end
end
CI=prctile(a,[100*alpha/2,100*(1-alpha/2)]);
H = CI(1)>0 | CI(2)<0;
I do that 5000 times for each difference, d, and each sample size, m. Then I take the average answer from each test (where 1 is 'conclude there distributions are different' and 0 is 'don't conclude the distributions are different'). For the case where d > 0 this gives you a hit rate, the likelihood that the test will tell you there is a difference when there is a difference. For d = 0.5 you get a difference that most of the tests can detect the majority of the time as long as the sample is more than 50. For the case where d = 0, you can calculate the false alarm rate for each test (at each sample size).
From these you can calculate d-prime as a standard index of sensitivity and plot the result. Sttest, Smean, Sbootstrap and Sbootstrap2 are matrices which hold the likelihood of the four tests giving a positive answer for each sample size (columns) for two differences, 0 and 0.5 (the rows):
figure(1);clf
plot(measures,norminv(Sttest(2,:))-norminv(Sttest(1,:),0,1),'k')
hold on
plot(measures,norminv(Smean(2,:))-norminv(Smean(1,:)),'r')
%plot(measures,norminv(Smedian(2,:))-norminv(Smedian(1,:)),'c--')
plot(measures,norminv(Sbootstrap(2,:))-norminv(Sbootstrap(1,:)),'m')
plot(measures,norminv(Sbootstrap2(2,:))-norminv(Sbootstrap2(1,:)),'g')
xlabel('Sample size')
ylabel('sensitivity - d prime')
legend('T-test','mean','bstrap-mean','bstrap-median')
Here is the result (click for larger):
What surprised me was:
Update 28/11/12
-Fixed an inconsequential bug in the dprime calculation
-Closer inspection shows that the simple mean case gives a ~50% false alarm rate, but the high sensitivity offsets this. Suggests dprime isn't a wise summary statistic?
I have made myself a new website for my day job. I used wordpress, and it was fantastically convenient. I’m also pretty happy with how it looks. Feedback welcome.
This has been in my email signature for the last year or so.
If you email me, please say your full name, level and, if relevant, which course(s) you are referring to. Although you know what “the lecture” or “the coursework” refers to, I may not. If you refer to an article, book or a webpage, please give the full reference and/or URL so that I know what you are talking about. Similarly, if you include a citation (surname, date) in a piece of writing, please include the full reference (in APA style) at the end.
It is important that you leave the University of Sheffield in the habit of writing formally to people. I may not be bothered by you not including an introduction to your email, or by you not signing it, but many people you write to will be. You should also make an effort to capitalise, punctuate and spell correctly in your email. Again, although I may not judge you negatively if you fail to do this, many people will, so you should practice the habit of taking care over these things when you write.
If you are a PSY241 student, please read this before emailing me
http://psy241.group.shef.ac.uk/psy241wiki/index.php/FAQ
If you need a response by a particular time, it helps if you mention this in the email. If you have an urgent query (i.e. requires a response within 48 hours) email is not appropriate. Please call instead.
I do not read my email over the weekend, or after 5pm.
Answers to most of the questions I get asked are readily available, either in the Undergraduate Handbook or on the Departmental or University webpages. If you write to me with a question like this I will probably write back and ask you where you have looked already for the information. If you want to avoid this, please say in your email how you tried searching for the information you required before emailing me.
If we make an appointment to meet you must turn up on time. If you are late I may not be able to begin a meeting with you because it will infringe on other commitments. If you are unable to make an appointment, or are going to be late, please call to let me know, so that I am able to do other things with my time and am not waiting around like a lemon.
Finally, congratulations on reading this far. Here’s some good advice: “The way to get a first class mark is to answer a specific question by making arguments about theories and supporting those arguments with evidence”. Even if you aren’t aiming for a first class mark, you can still avoid getting a lower mark than you should by ensuring that you answer the question. We cannot give you marks for providing correct information which does not answer the question.
Bonus advice for 2012: If you want to get answers from busy people, ask simple direct questions. “Is today’s lecture at 12 o’clock?” is better than “When are the lectures?”, and may be more in line with what you really want to know anyway. Both of these options are better than something like “What do I need to know about the course?” which is so poorly specified that you are unlikely to get a swift and helpful answer.
Consciousness is a fascinating but elusive phenomenon; it is impossible to specify what it is, what it does, or why it evolved. Nothing worth reading has been written on it.
Stuart Sutherland, in The International Dictionary of Psychology entry on Consciousness
In Science in Action, Bruno Latour talks of the birth of the modern science of geology, triumphed by Charles Lyell. He discusses Lyell’s attempt to professionalise and win respect for geology, and the need to find funds to support research in the new discipline. One solution to the need for funds it to appeal directly to the public, in Lyell’s case by writing a book that the landed gentry might read and so be convinced to donate to the cause of Geology:
If geology is successful in reshaping the earth’s history, size, composition and age, by the same token, it is also extremely shocking and unusual. You start the book in a world created by God’s will 6000 years ago, and you end it with a few poor Englishmen lost in the eons of time, preceded by hundreds of Floods and hundreds of thousands of different species. The shock might be so violent that the whole of England would be up in arms against geologists, bringing the whole discipline into disrepute. On the other hand, if Lyell softens the blow too much, then the book is not about new facts, but is a careful compromise between commonsense and the geologists’ opinion. This negotiation is all the more difficult if the new discipline runs not only against the Church’s teachings but also against Lyell’s own beliefs, as is the case with the advent of humanity into earth history which Lyell preferred to keep recent and miraculous despite his other theories. How is it possible to say simultaneously that it is useful for everyone, but runs against everyone’s beliefs? How is it possible to convince the gentry and at the same time to destroy the authority of common sense? How is it possible to assert that it is morally necessary to develop geology while agonising in private in the meantime on the position of humanity in Nature?
(p.149)
Replace 19th century geology with ‘cognitive sciences’, and gentry with ‘public’, and the essential tension is still there. The new brain science seeks attention and kudos, and in doing this must reach an uncomfortable accommodation with the ‘authority of common sense’. Psychologists and neuroscientists want to be heard in the public domain, but they will get so much more attention if they flatter received wisdom rather than attempt to overturn strongly held intuitions about human freedom, reasoning and morality.
Life shrinks or expands in proportion to one’s courage.
Anaïs Nin, volume 3 of her diaries (apparently)
There are no solutions here – it’s about what problems you choose to address on an ongoing basis
Rob Riordan, via @AlecPatton
I hear new news every day, and those ordinary rumours of war, plagues, fires, inundations, thefts, murders, massacres, meteors, comets, spectrums, prodigies, apparitions, of towns taken, cities besieged in France, Germany, Turkey, Persia, Poland, &c., daily musters and preparations, and such like, which these tempestuous times afford, battles fought, so many men slain, monomachies, shipwrecks, piracies, and sea-fights, peace, leagues, stratagems, and fresh alarms. A vast confusion of vows, wishes, actions, edicts, petitions, lawsuits, pleas, laws, proclamations, complaints, grievances, are daily brought to our ears. New books every day, pamphlets, currantoes, stories, whole catalogues of volumes of all sorts, new paradoxes, opinions, schisms, heresies, controversies in philosophy, religion, &c. Now come tidings of weddings, maskings, mummeries, entertainments, jubilees, embassies, tilts and tournaments, trophies, triumphs, revels, sports, plays: then again, as in a new shifted scene, treasons, cheating tricks, robberies, enormous villanies in all kinds, funerals, burials, deaths of Princes, new discoveries, expeditions; now comical then tragical matters. To-day we hear of new Lords and officers created, to-morrow of some great men deposed, and then again of fresh honours conferred; one is let loose, another imprisoned; one purchaseth, another breaketh: he thrives, his neighbour turns bankrupt; now plenty, then again dearth and famine; one runs, another rides, wrangles, laughs, weeps &c. Thus I daily hear, and such like, both private and publick news. Amidst the gallantry and misery of the world: jollity, pride, perplexities and cares, simplicity and villany; subtlety, knavery, candour and integrity, mutually mixed and offering themselves, I rub on in a strictly private life.
Robert Burton (1577-1640), The Anatomy of Melancholy (p.19)
Matt is making a drawing machine. A robot which will live on a wall and plot out paths which are an algorithmic solution to the artistic seeds that Matt feeds it. I’m helping Matt, but we’re stuck with a bit of the maths.
Due to artistic and practical constraints, this is how the robot will work: there will be two motors, top left and top right, from which a ‘pen’ is suspended. Our problem is about how to change the length of the chains from which the pen is suspended to draw a straight line between two points. I’ve done a diagram to make this easier to explain. The crudely drawn black circles are the two motors. There is a small blue circle (a start point), and the two chains in green (with lengths l1 and r1 respectively. The target endpoint is show as a red cross, with the chains shown in purple (with lengths l2 and r2 respectively (obviously there are only ever two chains, one right and one left, not four).
Calculating the length of the chains at the start and the end is fairly trivial. The problem is at what rate to turn the motors to lengthen or draw in the chains to get between the start and the end points drawing a straight line. For artistic reasons it is absolutely essential that the line drawn between two points is straight.
I had a go at solving this. You can have a look at this python code (incidentally, my first ever python script!). The problem is, my solution makes curved lines, like this (points along the path shown as blue dots)
The chains need to be tightened by some amount during travel to stop a curve being described, but I know enough maths to know that I don’t have a hope of solving this one. Can you help?
Style is knowing who you are, what you want to say, and not giving a damn.
Gore Vidal, I’m told
I have no explanation for my own vile ambitions. Confronted with your pus, I could not stop to examine my direction, whether or not I was aimed at a star. As I limped down the street every window broadcast a command: Change! Purify! Experiment! Cauterize! Reverse! Burn! Preserve! Teach! Believe me, Edith, I had to act, and act fast. That was my nature. Call me Dr. Frankenstein with a deadline. I seemed to wake up in the middle of a car accident, limbs strewn everywhere, detached voices screaming for comfort, severed fingers pointing homeward, all the debris withering like sliced cheese out of Cellophane – and all I had in the wrecked world was a needle and thread, so I got down on my knees, I pulled pieces out of the mess and I started to stitch them together. I had an idea of what a man should look like, but it kept changing. I couldn’t devote a lifetime to discovering the ideal physique. All I heard was pain, all I saw was mutilation. My needle going so madly, sometimes I found I’d run the thread right through my own flesh and I was joined to one of my own grotesque creations – I’d rip us apart – and then I heard my own voice howling with the others, and I knew that I was also truly part of the disaster. But I also realized that I was not the only one on my knees sewing frantically. There were others like me, making the same monstrous mistakes, driven by the same impure urgency, stitching themselves into the ruined heap, painfully extracting themselves
F., in Leonard Cohen’s Beautiful Losers (1966), p.175