There are a number of books based on the recent work by psychologists and experimental philosophers which look at the way ordinary people argue and make inferences. It's not a pretty sight. Michael Philips' book is as good as any of them (I've read a few) and if you don't know about Confirmation Bias, Anchoring, the Familiarity Heuristic or just how low the standards for science journalists are, then it is well worth the read.
However, there's one thing Philips and the others miss. People don't hold silly beliefs because they can't think straight. No. They don't think straight so they can hold silly beliefs. And people hold silly beliefs because it helps them define themselves, blocks out unwelcome facts and justifies their choice of goals and ambitions. Christian. Accountant. LISP programmer. Liverpool supporter and Oakland Raiders fan. Such people believe certain things to be true and have devout hopes that other things will be. Having a personal and intellectual identity that is not based on a core set of beliefs is right up there with triple-lutzes and the ability to speak six languages as requiring years of study, practice and the right genes in the first place.
If that seems hard to believe, then think about what it's like at work. The fact-free management strategies; the products launched without the slightest testing; the endless spin from HR, IR and PR; the need to go along to get along; the group-think; the staggering hypocrisy of the "corporate values". The opposite of science, said Lewis Wolpert, isn't art, it's politics. Policies must be seen to be right until their sponsoring Minister is relieved of her post, when the outgoing Minister's fact-free policies are replaced by the incoming Minister's fact-free policies. Everyone knows it's nonsense, but since everyone's jobs depends on it, everyone has to behave as if it's all true. This is known as "denial" in the trade, and that everyone knows they are professing twaddle only makes the denial more vehement and the peer-pressure more intense.
The spin and nonsense that pours out of politicians, bureaucrats, PR firms and corporate PR is not caused by an inability to apply deductive logic. It is a way of jamming the lines of communication, so that nothing of any significance can be transmitted. While the newspapers, bloggers and pundits are discussing the latest distraction or blatant codswallop, they cannot be laying out the facts - which would be far more damaging.
As for the more technical fallacies of reasoning explained in these books, there is no way that a GP or Health Service bureaucrat is ever going to understand that if the false negative rate of a test is nine times the prevalence of the disease, the chance that a positive reading means that you actually have the disease is only ten per cent. Because if they did, they would realise that testing for low-prevalence diseases is going to be very expensive if accurate and stigmatise way more people than it would save if cheap.
And if that paragraph meant nothing to you, or you didn't understand the calculation, then read Philips' book. Carefully.
Monday, 5 April 2010
Friday, 2 April 2010
Moving to the Cloud
I have taken my first tentative steps to using the Cloud. In other words, I'm slowly transferring my computer life from a housebound computer to servers situated God knows where but that I can access from anywhere at anytime. I read about Dropbox in Rands' blog about his favourite development tools and wondered about using it for on-line backup of the few files I really need to keep. I'd set up a Gmail account a while ago and had played about with setting up iGoogle, but not really got much further than making it a fancy personal portal. Reading a review of an Android phone, it seemed that Google had advanced since I'd last looked at it. So I went back to take a look.
It took me a while of experimenting to get the hang of it, but I've made the jump. Google co-ordinates with Windows and Mac, which is useful since I have a MacBook Pro and a Windows 7 Asus netbook. As always, before you do this at home, take backups of your Address Book / Contacts / Calendar / Mail.
I set up Gmail to collect the mail from all my other accounts, and my computers' mail clients to collect mail from Gmail. Two things here: 1) Make sure you leave the original on the server when your mail client downloads; 2) set up a rule to copy the messages from your Inbox to a local folder on your machine. Otherwise when you delete or archive the original in the Gmail Inbox, you'll lose the copies on your machine next time it synchronises. Don't forget to change the account you're sending the mail from to your Gmail account. After a while people will update their contacts and you can close down the other e-mail accounts. Don't do that, however, until you have contacted all the recruitment agents you have ever talked to and updated the contact details on LinkedIn, Monster and any other site you are on.
I set up Gmail contacts - use the Google Contact Manager gadget in Gmail - with all my contacts and then synced the Mac Address Book to it. Finally I set up a Google Calendar and an account for it in iCal. So Google is acting as the central server for my mail, contacts and calendar. Again: I use the Google account in iCal to make appointments in the future, when an appointment is done, I move it from the Google calendar to a local one. So I have a record of what I've done on the Mac, but not on Google. I did this because the Google Calendar functionality for recurring events isn't quite as smart as iCal and I nearly lost the records of one recurring event by doing so.
I set up Dropbox on the Mac and Asus. Henceforth any documents I want to work on from multiple locations have to be stored in the Dropbox directory. And you must close the file you're working on before it will update from your PC to the cloud copy at Dropbox, ready to be downloaded to your other machine. Dropbox handles conflicts sensibly, so you won't lose stuff if you work on the document on two machines but for some reason don't update the copy on one of them first.
There's more involved than you might think, but it's less complicated than it sounds. The reward is that all your computers are using the same data and sync to your cloud server. There's still more tweaks to learn, but it feels good. And because I've set up an amazing iGoogle, I can go anywhere, log on and have my life in front of me just like that.
However, the To-Do and Notes are in my Moleskin cahier notebook and that's where it's staying. As one acquaintance said when I jotted something down "Wow, that's real old-school". It's also way, way, faster than trying to type it on your iPhone or even on your computer.
Happy Easter
It took me a while of experimenting to get the hang of it, but I've made the jump. Google co-ordinates with Windows and Mac, which is useful since I have a MacBook Pro and a Windows 7 Asus netbook. As always, before you do this at home, take backups of your Address Book / Contacts / Calendar / Mail.
I set up Gmail to collect the mail from all my other accounts, and my computers' mail clients to collect mail from Gmail. Two things here: 1) Make sure you leave the original on the server when your mail client downloads; 2) set up a rule to copy the messages from your Inbox to a local folder on your machine. Otherwise when you delete or archive the original in the Gmail Inbox, you'll lose the copies on your machine next time it synchronises. Don't forget to change the account you're sending the mail from to your Gmail account. After a while people will update their contacts and you can close down the other e-mail accounts. Don't do that, however, until you have contacted all the recruitment agents you have ever talked to and updated the contact details on LinkedIn, Monster and any other site you are on.
I set up Gmail contacts - use the Google Contact Manager gadget in Gmail - with all my contacts and then synced the Mac Address Book to it. Finally I set up a Google Calendar and an account for it in iCal. So Google is acting as the central server for my mail, contacts and calendar. Again: I use the Google account in iCal to make appointments in the future, when an appointment is done, I move it from the Google calendar to a local one. So I have a record of what I've done on the Mac, but not on Google. I did this because the Google Calendar functionality for recurring events isn't quite as smart as iCal and I nearly lost the records of one recurring event by doing so.
I set up Dropbox on the Mac and Asus. Henceforth any documents I want to work on from multiple locations have to be stored in the Dropbox directory. And you must close the file you're working on before it will update from your PC to the cloud copy at Dropbox, ready to be downloaded to your other machine. Dropbox handles conflicts sensibly, so you won't lose stuff if you work on the document on two machines but for some reason don't update the copy on one of them first.
There's more involved than you might think, but it's less complicated than it sounds. The reward is that all your computers are using the same data and sync to your cloud server. There's still more tweaks to learn, but it feels good. And because I've set up an amazing iGoogle, I can go anywhere, log on and have my life in front of me just like that.
However, the To-Do and Notes are in my Moleskin cahier notebook and that's where it's staying. As one acquaintance said when I jotted something down "Wow, that's real old-school". It's also way, way, faster than trying to type it on your iPhone or even on your computer.
Happy Easter
Labels:
Diary
Wednesday, 31 March 2010
Tech Moves
This is going to be a very subjective post. No careful thought here. This weather sucks! It's as cold as bloody February and we're coming up to the Easter weekend. At least I have a Columba from Lina Stores in Soho to keep me going, plus three Rivette movies I found in Fopp to keep up the cultural quotient.
Finally I upgraded my mobile phone. And not to an iPhone either. Far too many people on the Chav Express (the Waterloo to Reading train) are playing games, looking at photos, and maybe listening to music - not mobile blogging, sending literate texts and looking at interesting web sites. iPhones are toys that cost £40-odd a month.
I settled on the Sony Ericsson C510 - free with a 300 minute £15 24-month contract from Vodafone and I may go for the £5 Internet, which along with the Orange £5 broadband brings my costs to £25 a month. The C510 plays really well with Snow Leopard - get the downloads of Media Sync here and of the iSync drivers here - and they work just great. I have an 8GB memory card and a special adapter for the phone to a 3.5mm jack plug (from Carphone Warehouse) so I can use my Bose noise-cancellers. The media player is sharp and clear with decent bass - for a portable media player. The camera isn't quite up to my Canon A590 IS, but it's way better than I need for this blog. Oh, and as a phone it's a step up from my trusty Motorola V220. I think the iPod Mini from the mid-Oughties is about to be retired.
The other side of that acquisition is the Asus 1005P netbook. Windows 7 Starter 1GB RAM, 160GB HDD, 10-inch screen, 90% laptop-sized keyboard. It makes my 15-inch MacBook Pro look positively hefty. I downloaded Open Office, Firefox and Thunderbird and have been up and running for the past week or so. I am not going to use Office 2007 and have you ever known anyone actually use Microsoft Works? It's a nice little machine to use. It's not a Macbook Air, but it does cost about £270 against the Air's £1,200 or so.
The only thing left is a colour printer. It has to do photo-quality and be networked - wireless will do. Haven't settled on one yet, but I'll get there. Maybe.
Finally I upgraded my mobile phone. And not to an iPhone either. Far too many people on the Chav Express (the Waterloo to Reading train) are playing games, looking at photos, and maybe listening to music - not mobile blogging, sending literate texts and looking at interesting web sites. iPhones are toys that cost £40-odd a month.
I settled on the Sony Ericsson C510 - free with a 300 minute £15 24-month contract from Vodafone and I may go for the £5 Internet, which along with the Orange £5 broadband brings my costs to £25 a month. The C510 plays really well with Snow Leopard - get the downloads of Media Sync here and of the iSync drivers here - and they work just great. I have an 8GB memory card and a special adapter for the phone to a 3.5mm jack plug (from Carphone Warehouse) so I can use my Bose noise-cancellers. The media player is sharp and clear with decent bass - for a portable media player. The camera isn't quite up to my Canon A590 IS, but it's way better than I need for this blog. Oh, and as a phone it's a step up from my trusty Motorola V220. I think the iPod Mini from the mid-Oughties is about to be retired.
The other side of that acquisition is the Asus 1005P netbook. Windows 7 Starter 1GB RAM, 160GB HDD, 10-inch screen, 90% laptop-sized keyboard. It makes my 15-inch MacBook Pro look positively hefty. I downloaded Open Office, Firefox and Thunderbird and have been up and running for the past week or so. I am not going to use Office 2007 and have you ever known anyone actually use Microsoft Works? It's a nice little machine to use. It's not a Macbook Air, but it does cost about £270 against the Air's £1,200 or so.
The only thing left is a colour printer. It has to do photo-quality and be networked - wireless will do. Haven't settled on one yet, but I'll get there. Maybe.
Labels:
Diary
Monday, 29 March 2010
Another Meaningless Feedback Exercise
Recently one of the team sent round a request for feedback about internal communications and how we could make our new office a great place to work. This hit a nerve and I sent this back...
I know this exercise is about posters round the office and stuff like that, but I'm going to hi-jack to get serious for a moment.
Comms in a large company is about management "delivering a message" to the staff. Whether we hear it or agree with it is irrelevant: the job is done when the words are spoken. We're a publicly-quoted company and Stock Exchange regulations mean that management can only tell is what they have already told the Stock Exchange. Unless it is has no market significance. I like (our senior manager's) weekly note, but the rest of the printed comms and the articles on the Intranet are internal PR and describe a world where everything is good and the sun always shines. Not the company I work in.
Can we make this a great place to work? Not when so many other people seem to be busy making it frustrating and irritating to work here. In the short time since the takeover, the bureaucracy has run completely out of control. I am far from the only person who feels this way. Here are just some of the irritations:
I have 10 passwords for internal systems from logging on to my laptop to making travel bookings. I could get more but simply don’t use the additional systems. The existing systems have out-dated organisation charts, names and job titles. Every time we want to use a new system, we have to tell it our details.
We have managers who have been in post for six months and more and are still not registered with the bureaucracy for their relevant sign-offs.
The data security measures come across as distrust. We are not the enemy, hackers and and organised criminal are, but we are treated as if we are going to steal and misuse data at every opportunity. The security is also at times farcical: we sat through a DVD about data security that told us to shred newspapers! We had internal comms written by someone who didn't know the very important difference between deleting and shredding a file. When I asked why the company had introduced lock-down on its computers, the answer was that most of the staff could not be trusted to use their computers sensibly.
We have an IT support desk that doesn’t know what software it supports. We have restrictions on the size of e-mail attachments but no company-wide way of sending large files to each other. We have no collaboration software – which you can get for free from Google Docs!
We have no documentation for the databases we use – even the Group Data specialists say they would talk to the person with product knowledge to find out which tables are the “good” ones. We have no official support from Group Data.
We have an integration process so out of touch with the business it was going to implement an unworkable solution to providing Brand information – until we found out by chance and raised hell. That's just one example and I have no doubt I will find others as I get more involved. Never forget that the grand plan dismisses the people now, but integrates the systems in two years' time. There is no world in which that is a sensible decision.
The Balanced Scorecard process took a senior manager two hours to complete, of which thirty minutes was spent on a helpline. He asked us to bear with it and fill in the forms. How about that he said that we were not to waste our time on it until HR made it useable? It shouldn't be as unthinkable as it sounds.
How many hours are wasted by all this? How many managers have decided that their job is simply to engage with the bureaucracy and have given up trying to do any productive work? How much goodwill does the company lose and how much morale does it damage?
These details add up to a feeling that won't go away because someone puts cookies out every day.
What it feels like to work here is that we achieve what we do despite the organisation, not because of it; it feels like we are here for the benefit of the “support” functions, not that they are here to support us; it feels like the organisation sacrifices productivity and morale for the appearance of compliance and it feels like we are not trusted. Above all it feels like any request to change anything will be denied because there are no resources, and any complaint will be spun right back as if it's a good thing. This is why the majority say they do not think that management will do anything about the results of the staff survey.
Could this be a great place to work? Let's get real - this will never be Google. Could this be a better place to work? Start by fixing the air conditioning before it gets to June and we're all sweltering. Get my managers the sign-offs they need so we don't have to keep going to other managers for signatures. Get us an official Group Data support person / mentor for six months so we can learn all we need to. And while I'm having dreams - make our procurement intranet as easy to use as Amazon. As for decoration? In my dreams we have a budget for some decent art - the Contemporary Arts Society can help there (hell, the guys at the Seven Dials Club did a good enough job) - otherwise I would prefer bare walls to point-of-sale posters.
I know this exercise is about posters round the office and stuff like that, but I'm going to hi-jack to get serious for a moment.
Comms in a large company is about management "delivering a message" to the staff. Whether we hear it or agree with it is irrelevant: the job is done when the words are spoken. We're a publicly-quoted company and Stock Exchange regulations mean that management can only tell is what they have already told the Stock Exchange. Unless it is has no market significance. I like (our senior manager's) weekly note, but the rest of the printed comms and the articles on the Intranet are internal PR and describe a world where everything is good and the sun always shines. Not the company I work in.
Can we make this a great place to work? Not when so many other people seem to be busy making it frustrating and irritating to work here. In the short time since the takeover, the bureaucracy has run completely out of control. I am far from the only person who feels this way. Here are just some of the irritations:
I have 10 passwords for internal systems from logging on to my laptop to making travel bookings. I could get more but simply don’t use the additional systems. The existing systems have out-dated organisation charts, names and job titles. Every time we want to use a new system, we have to tell it our details.
We have managers who have been in post for six months and more and are still not registered with the bureaucracy for their relevant sign-offs.
The data security measures come across as distrust. We are not the enemy, hackers and and organised criminal are, but we are treated as if we are going to steal and misuse data at every opportunity. The security is also at times farcical: we sat through a DVD about data security that told us to shred newspapers! We had internal comms written by someone who didn't know the very important difference between deleting and shredding a file. When I asked why the company had introduced lock-down on its computers, the answer was that most of the staff could not be trusted to use their computers sensibly.
We have an IT support desk that doesn’t know what software it supports. We have restrictions on the size of e-mail attachments but no company-wide way of sending large files to each other. We have no collaboration software – which you can get for free from Google Docs!
We have no documentation for the databases we use – even the Group Data specialists say they would talk to the person with product knowledge to find out which tables are the “good” ones. We have no official support from Group Data.
We have an integration process so out of touch with the business it was going to implement an unworkable solution to providing Brand information – until we found out by chance and raised hell. That's just one example and I have no doubt I will find others as I get more involved. Never forget that the grand plan dismisses the people now, but integrates the systems in two years' time. There is no world in which that is a sensible decision.
The Balanced Scorecard process took a senior manager two hours to complete, of which thirty minutes was spent on a helpline. He asked us to bear with it and fill in the forms. How about that he said that we were not to waste our time on it until HR made it useable? It shouldn't be as unthinkable as it sounds.
How many hours are wasted by all this? How many managers have decided that their job is simply to engage with the bureaucracy and have given up trying to do any productive work? How much goodwill does the company lose and how much morale does it damage?
These details add up to a feeling that won't go away because someone puts cookies out every day.
What it feels like to work here is that we achieve what we do despite the organisation, not because of it; it feels like we are here for the benefit of the “support” functions, not that they are here to support us; it feels like the organisation sacrifices productivity and morale for the appearance of compliance and it feels like we are not trusted. Above all it feels like any request to change anything will be denied because there are no resources, and any complaint will be spun right back as if it's a good thing. This is why the majority say they do not think that management will do anything about the results of the staff survey.
Could this be a great place to work? Let's get real - this will never be Google. Could this be a better place to work? Start by fixing the air conditioning before it gets to June and we're all sweltering. Get my managers the sign-offs they need so we don't have to keep going to other managers for signatures. Get us an official Group Data support person / mentor for six months so we can learn all we need to. And while I'm having dreams - make our procurement intranet as easy to use as Amazon. As for decoration? In my dreams we have a budget for some decent art - the Contemporary Arts Society can help there (hell, the guys at the Seven Dials Club did a good enough job) - otherwise I would prefer bare walls to point-of-sale posters.
Labels:
Day Job
Friday, 26 March 2010
Views From the Sixth Floor - Shaftesbury Avenue
Recently my part of The Bank's business moved up to the sixth floor. This has some rather good views over the West End. We're not going to be there for long - maybe another nine months - so I'm going to be snapping away whenever the light is good enough.
This little street behind an Odeon cinema looks a lot better in this photograph than it does from ground level...
And this is a view into an upper floor studio or store at Central St Martin's...
And who can resist - well, I can't - the sight of cranes silhouetted against an evening sky?
They moved into the space before they had a LAN wired in, so for about six weeks they were using ordinary BT broadband and VPN. For the first three weeks, they were using wireless to get to the broadband and even the colouring-in people noticed it was slow. Now we're all wired up and our Cisco VoIP phones are back on-line. So they're going to move the seats around again. Which really is moving deckchairs on the Titanic of morale they've made for themselves.
This little street behind an Odeon cinema looks a lot better in this photograph than it does from ground level...
And this is a view into an upper floor studio or store at Central St Martin's...
And who can resist - well, I can't - the sight of cranes silhouetted against an evening sky?
They moved into the space before they had a LAN wired in, so for about six weeks they were using ordinary BT broadband and VPN. For the first three weeks, they were using wireless to get to the broadband and even the colouring-in people noticed it was slow. Now we're all wired up and our Cisco VoIP phones are back on-line. So they're going to move the seats around again. Which really is moving deckchairs on the Titanic of morale they've made for themselves.
Wednesday, 24 March 2010
My Brush With Algebraic Geometry
Sometime back in the mid-Ougties I decided that I would try to learn some Algebraic Geometry. I did what anyone would do: I bought Hartshorne's Algebraic Geometry and Eisenbud's Commutative Algebra from Amazon and started reading. Some many months later, when I realised I had no idea what "divisors" really were, I ran across a simple explanation in Shaferavtich's book and bought that. Apparently many people have problems learning from Hartshorne's comprehensive but very abstract book. (A divisor, by the way, is a generalisation to higher dimensions of the idea of the roots of a polynomial.)
Why algebraic geometry? Isn't algebra one thing and geometry another. Well, here's how it works. Descartes taught us how to take a curve and describe it with an equation such as y = 3x+4. This can be written in the form f(x,y) = 0 (y - 3x+4 = 0 in the example). In other words, a curve or a finite set of points is the solution to an equation: it's the set of points (x,y) such that f(x,y) = 0. Now let's take the ring of real-valued functions of two variables with real coefficients, R(x,y), and consider the ideal (f) generated by f(x,y). Factor R(x,y) by the ideal (f) to get the quotient ring R(x,y)/(f). Each one of these steps generates an unique object, so we can take a curve and associate it with a quotient ring. We can also associate the curve with a field of rational functions by looking at all the real-valued rational functions defined everywhere on the curve: this is the function field. It turns out that (roughly) the curves are equivalent if their function fields are isomorphic. So we can learn a lot about curves from these algebraic objects. But notice how quickly it went from something you did in school to something you can do an entire Maths degree and still avoid (commutative algebra).
The subject is cluttered with a lot of what's known in the trade as "machinery", which is one of those terms that mathematicians get and is difficult to explain. "Machinery" is needed for a number of things: one is using equivalence classes to mod out issues with specific co-ordinate representations of spaces or functions; another is to ensure that local representations of a part of a space or function are "glued together" in a coherent way; and yet another is representing a space or object by a set of ideals or filters. The first piece of real machinery most mathematics undergraduates come across is a differentiable manifold or a fibre bundle.
The abstract spaces of algebraic geometry, called schemes, use all the machinery ever devised and then some more. A scheme is a locally ringed space such that every point has an open neighbourhood that is isomorphic to the spectrum of some ring. A locally ringed space is a topological space with a gadget called a sheaf that assigns a ring of functions (think of them as polynomials) to each open set. The spectrum of a ring is its set of prime ideals with the Zariski topology and a sheaf of rings defined in a manner so horrible not even Shaferavitch could simplify what's on page 70 of Hartshorne. When I first tried getting to grips with the definition I thought of schemes as like manifolds made up of locally patched Stone spaces (very "sort of"). As an example, the spectrum of the integers consists of: a) ideals generated by the prime numbers, b) co-finite subsets of the (ideals generated by the) primes and c) a set of polynomials which don't have a particular prime as a zero.
It's very good for stretching the brain. But in the end, I'm a logician and just not that interested in curves and numbers and other such things. I found Goldblatt's Topoi: Categorical Analysis of Logic recently and am reading that almost for light relief. It uses categories called topoi to construct alternative models of set theory. Toposes were invented by Grothendieck to solve problems arising in algebraic geometry. Hence my interest: toposes are used in mathematical logic and set theory to do all sorts of clever things, and second because algebraic geometry doesn't fit with the conventional foundational / axiomatic approach to mathematics. I will go on dipping into the books, but there are some things you really do need to study full-time, and algebraic geometry is one of them.
Modern algebraic geometry is not about conics and envelopes of curves and anything else you may recognise from A-levels. In the same way that Georg Cantor had to develop the theory of infinite sets to cope with zeros of Fourier series, Alexander Grothendieck developed vast swathes of category theory to cope with problems in algebraic geometry and frame it in a general setting. Of this approach, its high priest, Robin Hartshorne, says: "the person who works with schemes has to carry a considerable load of technical baggage... sheaves, abelian categories, cohomology, spectral sequences and so forth". Not to mention a hefty lump of commutative algebra.
Why algebraic geometry? Isn't algebra one thing and geometry another. Well, here's how it works. Descartes taught us how to take a curve and describe it with an equation such as y = 3x+4. This can be written in the form f(x,y) = 0 (y - 3x+4 = 0 in the example). In other words, a curve or a finite set of points is the solution to an equation: it's the set of points (x,y) such that f(x,y) = 0. Now let's take the ring of real-valued functions of two variables with real coefficients, R(x,y), and consider the ideal (f) generated by f(x,y). Factor R(x,y) by the ideal (f) to get the quotient ring R(x,y)/(f). Each one of these steps generates an unique object, so we can take a curve and associate it with a quotient ring. We can also associate the curve with a field of rational functions by looking at all the real-valued rational functions defined everywhere on the curve: this is the function field. It turns out that (roughly) the curves are equivalent if their function fields are isomorphic. So we can learn a lot about curves from these algebraic objects. But notice how quickly it went from something you did in school to something you can do an entire Maths degree and still avoid (commutative algebra).
The subject is cluttered with a lot of what's known in the trade as "machinery", which is one of those terms that mathematicians get and is difficult to explain. "Machinery" is needed for a number of things: one is using equivalence classes to mod out issues with specific co-ordinate representations of spaces or functions; another is to ensure that local representations of a part of a space or function are "glued together" in a coherent way; and yet another is representing a space or object by a set of ideals or filters. The first piece of real machinery most mathematics undergraduates come across is a differentiable manifold or a fibre bundle.
The abstract spaces of algebraic geometry, called schemes, use all the machinery ever devised and then some more. A scheme is a locally ringed space such that every point has an open neighbourhood that is isomorphic to the spectrum of some ring. A locally ringed space is a topological space with a gadget called a sheaf that assigns a ring of functions (think of them as polynomials) to each open set. The spectrum of a ring is its set of prime ideals with the Zariski topology and a sheaf of rings defined in a manner so horrible not even Shaferavitch could simplify what's on page 70 of Hartshorne. When I first tried getting to grips with the definition I thought of schemes as like manifolds made up of locally patched Stone spaces (very "sort of"). As an example, the spectrum of the integers consists of: a) ideals generated by the prime numbers, b) co-finite subsets of the (ideals generated by the) primes and c) a set of polynomials which don't have a particular prime as a zero.
It's very good for stretching the brain. But in the end, I'm a logician and just not that interested in curves and numbers and other such things. I found Goldblatt's Topoi: Categorical Analysis of Logic recently and am reading that almost for light relief. It uses categories called topoi to construct alternative models of set theory. Toposes were invented by Grothendieck to solve problems arising in algebraic geometry. Hence my interest: toposes are used in mathematical logic and set theory to do all sorts of clever things, and second because algebraic geometry doesn't fit with the conventional foundational / axiomatic approach to mathematics. I will go on dipping into the books, but there are some things you really do need to study full-time, and algebraic geometry is one of them.
Labels:
philosophy
Monday, 22 March 2010
What's Your Myers-Briggs Type?
Someone at work mentioned that they had done a Myers-Briggs and been pronounced an ISTJ. They weren't sure they really liked it, but from what I know of them it was as accurate as any of these things can be. This made me look again and I decided I'm almost the opposite: an ESFP. That means I get energy from dealing with people or other stimuli, focus on details and facts, put personal and social criteria above "objective" ones, and prefer not to commit to an early decision but leave my options open for as long as possible.
How does this square with the fact that sometimes I will be very glad when a meeting gets cancelled so I can concentrate on some piece of programming or analysis? Isn't that very introverted? Extroversion, in the psychological sense, isn't about people, it's about your need for external stimulation (which back when these psychologists were getting going and there was no TV, You Tube or iPods, pretty much meant people). An introvert is scared of being overwhelmed, an extrovert is scared of being bored. Anyway, we can't like everyone and some people or situations with people in them are just not simpatico, so it's not about people, it's about the kind of people. If most people aren't your kind of people, you're not going to be seen around people much - but that doesn't mean you're not an extravert. It just means you are in a minority.
As for the details bit, well, that's me. Life is not a big picture, it's a mass of details, but of course what I know with experience is that implementation without strategy is blind, but strategy without implementation is empty. Where I work, we have neither.
As for the criteria, yes, I put personal factors first (is this what we want to be doing? how does it make me look? what are the other people we don't want to be confused with doing? how will it be taken?) but only because, again, experience tells me that you have to do the numbers first. The numbers tell me what to reject - too expensive, not profitable enough, takes too long, won't fit through the door, insurance is impossible - but not what to accept. It's the personal stuff that tells me what to accept after all the duff stuff has been rejected.
As for not committing? Put that down to the influence of the Rat in my Chinese horoscope. We Rats have to have an escape plan - and anyone with an out before they go in is not committing. My main decision criterion is: how much will this cost to reverse / undo / paint over / do another way? If the answer is, not much, then I'll go ahead with a decision. If the answer is, a whole lot, I will usually decide we have to do it another way, one that we can back out from. Anything with low entry barriers and huge exit costs is going to get a very wide berth from me - hence my never even thinking of marriage. I could no more consider marriage than a sailor could spit into the wind. So I leave as much undecided as possible, partly to give Fate and Lady Luck as many opportunities as possible, and partly because I prefer the process the French call engragement - whereby one eventually does something without ever actually having decided to do it. (I'm sure that word exists - I read it somewhere, but I've never seen it since.)
However, I bet that if I actually answered the questions (which I just did here) I would need to pay attention to the words. One of the questions is: after prolonged socialising, do I feel the need to get away for some peace? You might say yes if you've seen me on occasion, but you would be missing the fact that I was "socialising" with people or in a situation I didn't want to be with or in right from the start: I was being dutiful. Under those circumstances anyone would want to get away asap - and if I had somewhere with people to go afterwards, I would, but I don't, so it looks like I'm getting some peace and quiet.
I might be an ESPF but I very often live the life of an ISTJ. There's nothing that says the way you're living is how you want to be living, and looking at how you do live may be no guide to who you are. It's just a guide to the compromises you made.
How does this square with the fact that sometimes I will be very glad when a meeting gets cancelled so I can concentrate on some piece of programming or analysis? Isn't that very introverted? Extroversion, in the psychological sense, isn't about people, it's about your need for external stimulation (which back when these psychologists were getting going and there was no TV, You Tube or iPods, pretty much meant people). An introvert is scared of being overwhelmed, an extrovert is scared of being bored. Anyway, we can't like everyone and some people or situations with people in them are just not simpatico, so it's not about people, it's about the kind of people. If most people aren't your kind of people, you're not going to be seen around people much - but that doesn't mean you're not an extravert. It just means you are in a minority.
As for the details bit, well, that's me. Life is not a big picture, it's a mass of details, but of course what I know with experience is that implementation without strategy is blind, but strategy without implementation is empty. Where I work, we have neither.
As for the criteria, yes, I put personal factors first (is this what we want to be doing? how does it make me look? what are the other people we don't want to be confused with doing? how will it be taken?) but only because, again, experience tells me that you have to do the numbers first. The numbers tell me what to reject - too expensive, not profitable enough, takes too long, won't fit through the door, insurance is impossible - but not what to accept. It's the personal stuff that tells me what to accept after all the duff stuff has been rejected.
As for not committing? Put that down to the influence of the Rat in my Chinese horoscope. We Rats have to have an escape plan - and anyone with an out before they go in is not committing. My main decision criterion is: how much will this cost to reverse / undo / paint over / do another way? If the answer is, not much, then I'll go ahead with a decision. If the answer is, a whole lot, I will usually decide we have to do it another way, one that we can back out from. Anything with low entry barriers and huge exit costs is going to get a very wide berth from me - hence my never even thinking of marriage. I could no more consider marriage than a sailor could spit into the wind. So I leave as much undecided as possible, partly to give Fate and Lady Luck as many opportunities as possible, and partly because I prefer the process the French call engragement - whereby one eventually does something without ever actually having decided to do it. (I'm sure that word exists - I read it somewhere, but I've never seen it since.)
However, I bet that if I actually answered the questions (which I just did here) I would need to pay attention to the words. One of the questions is: after prolonged socialising, do I feel the need to get away for some peace? You might say yes if you've seen me on occasion, but you would be missing the fact that I was "socialising" with people or in a situation I didn't want to be with or in right from the start: I was being dutiful. Under those circumstances anyone would want to get away asap - and if I had somewhere with people to go afterwards, I would, but I don't, so it looks like I'm getting some peace and quiet.
I might be an ESPF but I very often live the life of an ISTJ. There's nothing that says the way you're living is how you want to be living, and looking at how you do live may be no guide to who you are. It's just a guide to the compromises you made.
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