Wealthy patron to support artist/scientist/writer. Said patron will provide for all of my (few) worldly and (not so few) intellectual needs. In return I will undertake bizarre projects designed to delight, enlighten, and sometimes confuse. I can also add “color” to formal gatherings and tutor your kids in (mad) science. Please include a photo of my new living quarters and workshop space.
Doing the monthly cleaning of the comments for this blog. You may notice that there are almost none. Most of the ones that I get are trying to sell me something. But then there’s always that one… So I write about science things. And every time I do, I get a comment saying that I’m going to hell, that the only truth is in the Bible, that kind of thing. Okay, guy. This post is for you.
Science is not really the sort of thing that requires belief. But admittedly, the basis of science is. So here’s what I believe (in no particular order):
- There is an objective reality. I’m not saying that I live there, or that anyone lives there, just that there is such a thing. We can agree that the sky is blue, that the sun comes up in the morning, that the moon hangs in the sky, things like that.
- That aforementioned objective reality can be described. Yep, we use metaphor to do it. The moon is round and usually kinda silvery looking. And make no mistakes, the language of mathematics and logic are, themselves, metaphor. An equation is a statement saying that this thing behaves like this in these circumstances.
- The rules of logic are valid in this objective reality that I believe in. Once we agree on what the words “bright” and “dim” mean, we can also agree that the sun is not “bright” and “dim” at the same time.
There are things that I know to be true because I have witnessed them. I’ve seen (with my own eyes) the curvature of the earth from a research airplane flying at 60,000 feet. Yep, it really is round, and the sky is pretty dark up there. I’ve performed experiments that show both light and matter as being a particle and a wave. I’ve seen the glow of a nuclear reactor — yep, radioactivity is real. So I do have a lot of personal experience from which to draw upon, all of which corroborates the modern ideas of physics. I can say with confidence that I also believe my own experience.
And that’s about it. If you are going to try to tell me that you “don’t believe in science”, that’s fine. Just let me know where you think that scientific thought went wrong. Was it all good up to Aristotle? Up to Newton and Copernicus? If your worldview does not include Einstein, can you tell me how it is that GPS works (because Einstein’s general theory of relativity is integral to that)?
It’s also cool if you think that the world is only 4000 (or however many) years old and that all of the so-called “scientific evidence” was placed by god in order to test faith. But please, let me know how that helps solve a problem. Not because I want to ridicule your beliefs, but because I really want to know.
So I have this fun idea. It’s something that can be done for about $10K or so, but I’m having a hard time with one particular aspect of it. Allow me to explain…
Imagine that you have two velocipedes (yes, they have to be velocipedes for… reasons) and you mount them side-by-side and about three feet apart with tubing. In between, you hang a lightweight, but comfortable chair. Perhaps something like a lawn chair. Using the same tubing, you mount four electric motors around the outside in a quadrocopter arrangement, complete with propellers. Electric motors are becoming quite efficient, and you can find some on the order of one HP per pound at reasonable prices.
So far, you have a person-sized, velocipede, steampunk quadrocopter. Which is great, but would be way too heavy to actually lift off. Which is why you need a 30′ helium balloon. This would be attached to the rest via the same tubing and a kevlar fiber net over the top. Internal to the balloon is an electric compressor such that the balloon can be dynamically deflated and inflated. So it can provide just enough lift that the quad motors can lift it the rest of the way. But since they’ll be relying in part on ground-effect, the system is tuned such that you can only get about 10′ high.
I have it all laid out in my head, and trust me, it’s awesome! But now for the hard part. How much trouble would I get in to for this? Technically, it’s a “manned, un-tethered, gas balloon” according to their regulations. But since the balloon is not providing the lift (just weight-offset), it’s also technically an ultralight. But since it relies on ground-effect, it’s also a hovercraft and outside of the FAA’s purview.
So my guess is that the FAA won’t be able to decide between laughing at me and having me shot. Any thoughts?
There is so much that I do that I would want to write about. Much of the work that I do would make for some fantastic conference or journal articles. And some it would’ve even made a great master’s or doctorate’s thesis. BUT… the reality of the situation is that I am almost constantly under some non-disclosure agreement or other. Not that the work I do is terribly secretive. There’s no national security issue (usually) and no chance of any disclosure actually hurting whatever company I’m working for.
But the knee-jerk reaction nowadays is to hide everything that everyone does, all the time. Just in case. As though my obscure bit of network queuing code would sink the company were it ever revealed. From the standpoint of furthering the art, this is not a wise policy. From the standpoint of furthering my career, it’s damned annoying.
As always, XKCD said it best…
I am a scientist (if you know me at all, you’re saying “duh” right about now) but I am not a science cheerleader. By this I mean that I do not try to uphold the ivory tower at all costs. Primarily because, if we start to do this, then we are no longer doing science. That said, let me shed some light on a glaring problem with the way that science is done nowadays.
Most institutions are “publish or perish” in fact if not outright stated. This means that, as a working scientist, you are regularly expected to publish your results. This part, I’m actually okay with, in principle at least. Putting things in to the public domain is a good thing. But now for the two not-so-good things (there are more than two, but I’ll only talk about these today).
First, most journals do not put their content in to the public domain. You have to pay (and pay through the nose) in order to see it. This is not conducive to good science. Mind you, there are attempts to mitigate this. There’s the physics pre-print archive covering physics, the public library of open science with bioscience-related content, and most journals now have a free content section. There are even (illegal) torrent sites and aggregators dedicated to swiping content from closed journals and sharing with the world (nope, I won’t provide a link for those). So this is slowly getting a bit better.
Second, and much more importantly, failure is not an option when it comes to publication. With very few exceptions, only successful experiments and proven theorems are accepted for publication. This is so absolutely wrong that it almost defies logic. Science would be far more transparent and progress much more rapidly (and more importantly, honestly) if null results could be published. Again, this is slowing starting to change. Recently there have been attempts to rectify this to a degree. the Journal of Negative Results is one such attempt, though it limits itself to the biosciences.
Clearly these two factors are a huge hindrance to the reasonable progression of scientific research. I myself have been stymied in the past, needing to see a particular set of results, but being unwilling or unable to pay the exorbitant journal access fees. Additionally, I could have been save a lot of trouble had null results been published. But that’s now how scientific publishing works. And so I (and countless others) have wasted a significant amount of time following paths that could have easily been avoided, if only access were more open and honest failures held in equal esteem to successes.
I’ll end it here, though I’ll pick this up again shortly. And if you’d like to read more, here’s a better written article:
I’ve had pretty much enough of two aspects of the science v. art arguments. The first argument is that they have been, are now, and forever shall be, at odds with each other. Bullshit. Those who make such arguments tend to have no knowledge of either science or art. I am a scientist who dabbles in a variety of artistic endeavors. My girlfriend and my best friend are both artists who are very scientifically-minded. There are no differences in our philosophical outlooks. More on this in a moment.
The next common aspect of the argument is that science and art need each other: science to improve the quality of art, and art to enable visualization of science. Well, yeah, maybe. But that misses the point. At least those who put forth that argument are not perpetuating some mythical war between the two.
Here’s how it really is, folks: They are the very same thing!
We are puny humans with very small minds and a very limited capacity to describe and define the universe. Reality around us is so much grander than we can ever know, let alone describe. To paraphrase Oliver Sacks, not only do we not live in reality, we’ve never even visited the place. And so, in an attempt to capture its beauty, we create metaphor.
Science does so by using a variety of descriptive languages (various mathematical systems, and words as precisely defined as the language allows). But science goes in knowing full well that all of these constructs are nothing more than metaphor for something that may never be fully understood, except in limited context.
Art does so by using a variety of descriptive languages (visual symbols, forms, musical notes, and words as the language allows). But art goes in knowing full well that all of these constructs are nothing more than metaphor for something that may never fully captured, except in limited aspect.
Both rely on the same tools and insights and reasoning; indeed, the very same parts of the soul. Because in all cases, the sciartist is attempting to express an aspect of the universe that they see, in order to better understand it, and maybe even present it to a wider audience.
So enough of the arguments. Science is art. Art is science. Both are nothing but metaphor for the vast, the sublime, the beautiful, and the unknowable. End of rant.
It has been said that, during the first atomic bomb test, Enrico Fermi wanted a quick estimate of the energy of the blast. So, as the shock wave hit, he tossed a handful of paper scraps in to the air and watched how far they were carried. He estimated that the energy was about ten kilotons – remarkably close to the measured value of twenty.
Whether this actually happened or not, is a subject for historians to debate, but it makes for a good story nonetheless. And it serves to illustrate how a quick and dirty estimate can aid in decision making. In science classrooms around the world, these sorts of approximation problems are used to teach “science thinking” without getting bogged down in math. And, like all good science tools, it’s partly a matter of convenience and partly a matter of laziness. Some approximation exercises that I remember from my own schooling:
- How fast would you have to stir your coffee in order to make it boil?
- How many gas stations are there in the United States?
- If everyone in China faced west and sneezed at the same time, how would the earth’s rotation change?
- How fast would you have to drive a car through a hard rain in order to meet a wall of water?
With these types of problems, it isn’t the answer that is interesting but how one arrives at it. And once you get the hang of this you can get a surprising level of accuracy, particularly if you know which way to fudge the numbers. Of course, there are a few tricks to this kind of “Fermi estimate”. Trick number one, don’t care too much about what the answer actually is. If you’re attached to an outcome, you may subconsciously pick numbers that steer toward it.
Trick two, go fast the first time around and then fix it later. The first pass-through is just to get the process right. In subsequent estimations, you can try to get better numbers or to include things that you hadn’t previously thought of.
Trick three, round to the nearest whatever. Some numbers are easier to work with than others. You can work with powers of ten just by moving the decimal point. Computer engineers and programmers know the powers of two better than their own phone numbers. Once you get a feel for how numbers themselves work, then calculation becomes a snap. And because you don’t care about the end number, you can feel free to round off a bit.
Here’s an interesting example…
One morning, I was driving up to a nowhere spot in central California to meet with a client. Radio coverage was essentially non-existent and so I ended up listening to someone on AM talk radio. This someone made the claim that if global warming is man-made, it’s probably from everyone running their air conditioners. Let’s look at this claim and construct a very simple model.
There are approximately four hundred million people in the US right now (and we’re going to ignore Alaska – they probably don’t do too much air conditioning). We’ll assume that each and every person has a five thousand square foot home, five thousand square foot office, and ninety thousand square feet representing their share of communal space (public buildings, malls, etc.). So every man, woman, and child has their very own air-conditioned area of one hundred-thousand square feet. Further, we shall assume that their ceilings are ten feet high, giving each person a million cubic feet of air-conditioned bliss. Four hundred trillion cubic feet in total (notice all of the powers of ten that I’m using).
How cold do they like it? Let’s further assume that every person in the US is currently trying to fight one hundred degree weather and cool their space down to seventy degrees. If air conditioners were one hundred percent efficient (spoiler: they are not) then we’d have to warm a like mass of air by thirty degrees. For our initial model, we’ll assume that air conditioners are only twenty percent efficient (probably they’re a bit better than this, but this is closer to the truth) and so we will have to warm five times that volume (five is almost as easy to use as two and ten).
So, in our hypothetical model, we’re warming up two quadrillion cubic feet of air by thirty degrees. That’s a lot of air. Let’s convert to cubic miles, for sake of readability:
(2,000,000,000,000,000) / (5280 x 5280 x 5280)
So about thirteen thousand cubic miles – a much more manageable number.
How much air is there in the continental United States? According to Wiki, there are about three million square miles of surface area. The atmosphere extends upward to about sixty miles, but most of the action takes place within three miles of the surface, so let’s just use that and approximate that there are about ten million cubic miles of air.
Divide the one in to the other, and the air-conditioned-warmed air represents only one tenth of a percent (note that I’m doing a lot of rounding here) of the volume of air in the United States. All of our air conditioning would warm that mass by three one-hundredths of a degree.
But (and this is a big “but”), our model assumes that all cooling and all air is evenly distributed all over the country by the same amount, everywhere. This simply isn’t true. Additionally, it isn’t true that every person has that much cooled volume. And finally, it isn’t true that every person in the country requires cooling by thirty degrees, all at once. Cities like Phoenix may require more cooling all in one spot; and places like Seattle may not require any. So we can see some ways to begin to refine our model.
I’m not going to argue that air conditioning causes or doesn’t cause warming. It may actually have a measurable (though tiny) effect in some places. The point of this exercise is to show both the power and the peril of making a casual model.
My homework assignment to you: play with this (either on paper or in your head)! See if you can think of ways to refine it. See if you can think of wrenches to throw in to the works. See if you can find some better numbers to use. Feel free to cheat and use the internet if you get lazy (but please give it a go, first).
Well, not so much. You see, from a mathematical standpoint, the term “infinity” is defined as being the size of the set of integers. So is it possible to have something bigger than this? Yepers, and it is best illustrated by trying to map one thing to another.
By “mapping” you can think of placing marbles into an egg carton, one per slot. If you’ve marbles left over, then the number of marbles is larger than the number of slots. So let’s start off with an infinitely long egg carton, each slot numbered 1, 2, 3, etc. Now well take an infinite number of marbles, with the same numbers on them. None left over, obviously.
Suppose we’ve twice as many marbles, this time labeled 1, 2, 3, etc.; and then -1, -2, -3, etc. We’ll even throw in an extra marble labeled zero. Is this the same size? Yes it is, because you can alternate marbles. First put the zeroth marble into slot one, then the number one marble into slot two, then the negative one marble into three, the two marble into four, the negative two marble into five, and so on. You never run out of marbles, of course, but you never run out of slots either. And the important point: for any specific marble, you know exactly which numbered slot it goes into. So the set of all integers (positive, negative and zero) is the same size as the set of all positive integers.
Let’s throw a curve: all rational numbers. For those of you whose math escapes you, a rational number can be expressed as the ratio of two integers. In other words, any particular rational number x can be expressed as ( a / b ) in which a and b are both (non-zero) integers. So how big is the set of rational numbers? It turns out that it’s still the same size of infinity. Here’s how:
Let’s make a table of all possible a’s and b’s:
The grid is infinite in both the a and b directions as it contains all positive and negative integers along those axes. So how do we map this onto the line of positive integers? Just start in the “middle” (pick a point, any point) and spiral out. Yep, it sounds like cheating, but again, you can compute where any marble on the a-b grid would be placed into the infinite egg carton.
So again, the set of all rational numbers is the same size as the set of all positive integers — regular ol’ infinity. So how about something larger than infinity? Next we’ll try the set of all irrational numbers.
Again, in case you’ve forgotten, an irrational number is one that cannot be described as the ratio of two integers. Things like pi and e (base of the natural logarithm) and the square root of two are decimal numbers that never end and never repeat. So it would take an infinite number of integers (regular infinity) just to represent each one. And guess what? In between every rational number, there are an infinite number of irrational numbers. If you take pi as an example, you could change any one of its infinite digits and come up with an entirely different number.
So guess what? We just ran out of slots in our egg carton. Since we can change any one or all of the digits in any particular irrational number (even an infinite number of them) to get a new number; and since there are an infinite number of irrational numbers, even between each rational number; we have waaay too few slots in our infinite egg carton.
The size of the set of all irrational numbers is the first transinfinite number, aleph-one (aleph-zero is another term for regular infinity). We can even get bigger than this, defining in similar ways aleph-two, aleph-three, etc, even on to aleph-infinity.
So there you go: a quick and dirty (and honestly, not terribly rigorous) introduction on numbers that are actually larger than infinity. To summarize (again, not very rigorously): infinity plus infinity equals infinity (all positive and all negative integers); infinity times infinity also equals infinity (all rational numbers); but infinity to the power of infinity is bigger (all irrational numbers).