basics
rallain | September 3, 2008**pre reqs:** *none*
Often I will do some type of analysis that I think is quite cool. But there is a problem. I keep having to make a choice. Either go into all the little details, or skip over them. My goal for this blog is to make each post such that someone could learn some physics, but I also don't want it to go too long. So, instead of continually describing different aspects of basic physics - I will just do it once. Then, when there is a future post using those ideas, I can just refer to this post. Get it?
Fine. On with the first idea - kinematics. Kinematics typically means…
sporte | August 15, 2008Vaccines work by stimulating the immune system to respond to a specific thing. Most of the vaccines we use are designed to prime the immune system so that it's ready to fight off some kind of disease, like whooping cough, polio, or influenza. Some vaccines can have more specialized functions, like stimulating the body to attack cancer cells, kill rogue autoimmune cells, or prevent pregnancy. We'll look at what they do in later posts, for now, let's look at the kinds of things that can be used as vaccines.
It's an amazing assortment. Even more amazing is that these items don't all work in…
goodmath | May 30, 2008 One thing that I've been getting a lot of requests about is the ongoing
mortgage mess in the US. I wrote a bit about it a while ago, explaining
what was going on. But since then, I've gotten a lot of people asking
me to explain various things about how mortgages work, and what kinds
of trouble people have gotten into.
Mortgage Basics
The basic idea of a mortgage is very simple. You want to buy a house, but you don't have enough money to buy it up front. So you borrow money to pay for it. A
mortgage is a loan that provides you with money to purchase a house, using the
house itself as the…
sporte | May 29, 2008RFLP is an acronym that stands for "Restriction Fragment Length Polymorphism." That's quite a mouthful and once you've said this phrase a few times, you realize why we use the initials instead.
I know a Restriction Fragment Length Polymorphism sounds like something that must be impossibly complicated to understand, but if we take the name apart, it's really not so bad.
Let's start with most familiar one of the four words and work from there. My guess is that for many of you, that word is "length." When we talk about length in this context, we are talking about the length of a piece of…
sporte | April 4, 2008This morning I had a banana genome, an orange genome, two chicken genomes (haploid, of course), and some fried pig genome, on the side. Later today, I will consume genomes from different kinds of green plants and perhaps even a cow or fish genome. I probably drank a bit of coffee DNA too, but didn't consume a complete coffee genome since my grinder isn't that powerful and much of the DNA would be trapped inside the ground up beans.
Of course, microbes have genomes, too. But I do my best to cook those first.
So, what is a genome? Is it a chromosome? Is it one of those DNA fragments or…
sporte | February 16, 2008I love the way you show me secret things.
All I do is type: Select * from name_of_a_table
And you share everything with me.
Without you, my vision is obscured, and all I see is the display on the page.
In fact, this was the push that finally made me decide to learn SQL.
In our bacterial metagenomics experiment, I realized that my students could use FinchTV to enter their blast results into our iFinch database.
That was cool, but with the web interface, we could only view one result at a time.
On the other hand, if we use the right SQL query in the iFinch query window, we can see…
goodmath | November 14, 2007 I haven't written a basics post in a while, because for the most part, that well has run dry, but once
in a while, one still pops up. I got an email recently asking about proofs by contradiction and
counterexamples, and I thought that would be a great subject for a post. The email was really
someone trying to get me to do their homework for them, which I'm not going to do - but I can
explain the ideas, and the relationships and differences between them.
Proof by contradiction, also known as "reductio ad absurdum", is one of the most beautiful proof
techniques in math. In my experience,…
sporte | September 5, 2007If you've read any of the many stories lately about Craig Venter or Jim Watson's genome, you've probably seen a "SNP" appear somewhere. (If you haven't read any of the stories, CNN has one here, and my fellow bloggers have posted several here, here, here, here, here, and here.)
You may be wondering, and rightly so: just what is a SNP?
Never fear, hopefully this post will answer some of those questions.
tags: DNA sequencing, DNA , SNPs, genetic testing
SNP stands for Single Nucleotide Polymorphism. That's a mouthful. It means some people, will have one base at a certain position, in a…
goodmath | May 7, 2007 This is something that came up in some of the comments on the recent "nimbers" post, and I thought it was worth promoting to the front, and getting up under an easy-to-find title in the "basics" series.
In a lot of discussions in all different areas of math, you encounter talk about sets and classes, and you'll find people worried about whether they're talking about sets or classes. What's the difference? I mentioned this once before, but it's buried in a discussion of the concept of "meta", which is why I thought it was worth moving it to its own top-level post: if you don't know the…
goodmath | April 16, 2007 I've used the term innumeracy fairly often on this blog, and I've had a few people write to ask me what it means. It's also, I think, a very important idea.
Innumeracy is math what illiteracy is to reading. It's the fundamental lack of ability to understand or use numbers or math. And like illiteracy, true innumeracy is relatively rare, but there are huge numbers of people who, while having some minimal understanding of number and arithmetic, are functionally innumerate: they are not capable of anything but the most trivial arithmetic; and how anything more complicated than simple basic…
goodmath | April 7, 2007 For the basics, I wrote a bunch of stuff about sorting. It seems worth taking a moment
to talk about something related: binary search. Binary search is one of the most important
and fundamental algorithms, and it shows up in sorts of places.
It also has the amazing property that despite being simple and ubiquitous, it's virtually
always written wrong. There's a bit of subtlety in implementing it correctly, and virtually
everyone manages to put off-by-one indexing errors into their implementations. (Including me; last time I implemented a binary search, the first version included one of the…
sporte | March 31, 2007Science labs are not for all people.
I've always enjoyed teaching lab courses, so some of you might find it strange that I agree with some of the comments from Steve Gimbel and fellow Sb'ers on the questionable benefits of laboratory courses in introductory physics. But you see, I wasn't very impressed with the undergraduate physics labs that I took either. And with a little reminiscing, it's pretty easy to pick out example labs where the kindest description is "time-waster."
This wasn't true of all my lab courses. My biochemistry and microbiology lab courses were phenomenal, and, it's…
goodmath | March 22, 2007 This came up in a question in the post where I started to talk about π-calculus, but I thought it was an interesting enough topic to promote it up to a top-level post. If you listen to anyone talking about computers or software, there are three worlds you'll constantly hear: parallel, concurrent, and distributed. At first glance, it sounds like they mean the same thing, but in fact, they're three different things, and the differences are important.
The connection between them is that they're all terms that describe systems made up of computers and software that are doing more than one…
goodmath | March 14, 2007 Today's bit of basics is inspired by that bastion of shitheaded ignorance, Dr. Michael Egnor. In part of his latest screed (a podcast with Casey Luskin of the Discovery Institute), Egnor discusses antibiotic resistance, and along the way, asserts that the theory of evolution has no relevance to antibiotic resistance, because what evolution says about the subject is just
a tautology. (I'm deliberately not linking to the podcast; I will not help increase the hit-count that DI will use to promote it's agenda of willful ignorance.)
So what is a tautology?
A tautology is a logical statement…
goodmath | March 13, 2007I've been getting so many requests for "basics" posts that I'm having trouble keeping up! There are so many basic things in math that non-mathematicians are confused about. I'm doing my best to keep up: if you've requested a "basics" topic and I haven't gotten around to it, rest assured, I'm doing my best, and I will get to it eventually!
One of the things that multiple people have written to be about is confusion about what a mathematician means by a theory; and what the difference is between a theory and a theorem?
Math folks do use the term "theory" in a very different way than most…
goodmath | March 12, 2007 I've received a request from a long-time reader to write a basics post on modal logics. In particular, what is a modal logic, and why did Gödel believe that a proof for the existence of God was more compelling in modal logic than in standard predicate logic.
The first part is the easy one. Modal logics are logics that assign values to statements that go beyond "This statement is true" or "This statement is false". Modal logics add the concepts of possibility and necessity. Modal logic allows statements like "It is necessary for X to be true", "It is possible for X to be true", etc.
The…
goodmath | March 11, 2007 In math and computer science, we have a tendency to talk about "going meta". It's actually a
pretty simple idea, which tends to crop up in other places, as well. It's also one of my favorite concepts - the idea of going meta is just plain cool. (Not to mention useful. There's a running joke among computer scientists that the solution to any problem is to add a level of indirection - which is programmer-speak for going meta on constructs inside of a programming language. Object-orientation is, in some sense, just an example of how to go meta on procedures. Haskell type-classes are an…
goodmath | March 7, 2007 Today's basics topic was suggested to me by reading a crackpot rant sent to me by a reader. I'll deal with said crackpot in a different post when I have time. But in the meantime, let's take a look at axioms.
What is an axiom?
If you want to do any kind of formal or logical reasoning, or any kind of inference, you need to start with some set of known facts. There is simply no way of performing inference starting from absolutely no knowledge. Axioms are the set of known facts that are accepted as
basic primitive unproven facts: all proofs are ultimately built upon the inference rules of…
goodmath | March 1, 2007 One thing that I frequently touch on casually as I'm writing this blog is the distinction between continuous mathematics, and discrete mathematics. As people who've been watching some of my mistakes in the topology posts can attest, I'm much more comfortable with discrete math than continuous.
The distinction is a very important one. Continuous mathematics is, roughly speaking, math based on the continuous number line, or the real numbers. The defining quality of it is that given any two numbers, you can always find another number between them - in fact, you can always find an infinite set…
goodmath | February 28, 2007 Multiple people have written to me, after seeing yesterday's
href="http://scienceblogs.com/goodmath/2007/02/basics_algorithm_1.php">algorithms basics post, asking me to say more about sorting algorithms. I have to say that it's not my favorite topic - sorting is one of those old bugaboos that you can't avoid, but which gets really dull after a while. But there is a kernel of interest to it - sorting can be used to demonstrate a lot of interesting ideas about
computational complexity.
In that vein, let's start with a little bit of complexity. There's actually a trick based on Kolmogorov/…