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11/30/10 01:15 am - the calculus of clean, part 1

How bad you smell is a monotonically increasing function of the time since your last shower. Therefore, to minimize the integral from t to t + a of your stench, where t is the time since your last shower and a is the time you spend awake, you should minimize t.

(Alternatively, you could minimize a...)

8/1/10 01:29 am - Why machined stuff is expensive

(alternatively, 'why machining takes so damn long')

To produce a block of a specified size, follow these 22 simple steps:

1. Cut the stock somewhat oversize with a bandsaw.
2. Get parallels of the appropriate height and put them in the vise.
3. Clamp the part in the vise on top of the parallels. If you are an idiot or too cheap for a good vise, whack it with a deadblow hammer a few times.
4. Face off the top.
5. Remove the part, clean the parallels and the vise, flip the part over, and clamp it again.
6. Face off the top.
7. Measure the thickness.
8. Mill the dimension to size.
9. Remove the part, clean the parallels and the vise, turn the part 90 degrees, and clamp it again.
10. Face off the top.
11. Remove the part, clean the parallels and the vise, flip the over, and clamp it again.
12. Face off the top.
13. Measure the thickness.
14. Mill the dimension to size.
15. Remove the part, clean the parallels and the vise, turn the part 90 degrees so one of the remaining unfaced sides is facing up, and clamp it again. Remember which pair of faces the part was held by.
16. Face off the top.
17. Remove the part, clean the parallels and the vise, flip the part over and rotate it 90 degrees so it is now being held by the other pair of faces, and clamp it again.
18. Face off the top.
20. Face off the top.
21. Measure the thickness.
22. Mill the dimension to size.

Total time: 40+ minutes. All just to get a dimensioned block.

More precision means more time: more accurate measurements with better measuring tools (such as a micrometer instead of a caliper) are slower, performing more measurements for better accuracy means more steps, etc. Side milling the last two faces is discouraged because 1) the endmill will deflect and 2) the tram of the vise will affect the squareness of the sides.

This is why part of being a good machinist is knowing the acceptable tolerances. Sometimes good enough is good enough. Fortunately, the inverse is true of precision as well: less precision means less time. There are plenty of quick and dirty measurement/placement techniques that would get any real machinist fired, but if nobody cares about the difference in the end, saving time is very valuable.

11/20/09 03:38 am - 100%?

A friend of mine recently asked why people bother saying things like 'this is important, do your best', when everyone really should be doing their best anyway.

I want to make it perfectly clear that 'doing your best' all the time is Bad from a number of perspectives. On the surface, it seems fine. Who wants to produce something that is not their best work?

When necessary, people can push themselves past their physical limits. Adrenaline rushes have been known to increase strength dramatically, even to superhuman levels, for a short time. You can 'precharge' muscle groups for a more coordinated, rapid, or powerful action. The same applies to mental limits of concentration and thought. You can definitely work harder than usual or focus on a difficult problem to produce superior results.

The problem with pushing the limits is that the limits are not just some arbitrary line drawn in the sand. They represent what a person is physically capable of over time. Pushing them means you need time to recover afterwards.

This brings us back to the original point - why is it bad to put 100% effort into everything? Simple. It leaves you with no 'go' to expend extra effort when it is necessary. Running continuously at the limit increases wear and tear on the body, just as it does for other mechanical systems. If you concentrate very hard on everything, you are likely to be worn out when the situation demands more. Life is dynamic, and running at a constant redline means you waste effort on the unimportant tasks and have none left for the important ones.

In short, it is no good to push yourself when there is no need. When you claim to put 100% (or '110%') effort into everything, it means your 100% threshold is very low, you are inefficient and need to work harder to compensate, you cannot deal with unusually adverse situations, or you do not know your limits and when to apply your effort. It definitely means something to me when someone tells me that something will require extra effort. If it does not to you, then you are probably doing something wrong.

This absolutely does not mean to apply the minimum effort to everything. Consider the trade-offs between effort and quality of result, and go the extra mile when you feel you can or when the outcome will be substantially better for it.

11/19/09 04:12 am - Chemical energy

(This is along the lines of the 'electronics are fast' post.)

Intuitively, what people think of as 'a lot' of kinetic energy is orders of magnitude away from what one might consider 'a lot' of chemical energy. Consider the following:

When you think of something that has a lot of kinetic energy, you might think of a car speeding down the highway or maybe an artillery shell. Both of them clearly contain 'a lot' of energy, since they can do plenty of damage if they smash into something.

Cars are driven by internal combustion engines. The engine converts chemical potential energy into heat by burning fuel, then rather inefficiently converts that into mechanical kinetic energy. This energy drives the car. All of the potential energy of the car came from the gasoline powering it. At a rough estimate, about 10% of the energy in the gasoline ends up moving the car forwards. And you can accelerate to highway speeds quite a few times before you burn even one gallon of gas.

This leads us to the conclusion that gas contains a colossal amount of energy. Well it definitely does; the truth is that one-tenth of the energy in just half a cup of gasoline has about the same energy as a car going 65mph. It is about 400kJ of energy.

It turns out that an artillery shell typically contains more kinetic energy. For example, consider the British 3.7cm AA gun, which fired a 12.7kg shell at 792m/s measured at the muzzle. This translates to almost 4MJ of kinetic energy: ten times that of the aforementioned car, and about that of half a cup of gasoline.

To be fair, the lesson to be learned from this is probably that gasoline contains an extreme amount of energy compared to most other things; at 44MJ/kg, it has ten times the energy density per mass of TNT.

EDIT: See the comments for more interesting discussions about electrical surge energy.

10/3/09 08:40 am - "Let's not do x because x sucks"

...is perfectly legitimate reasoning. Nobody wants to deal with something that sucks.

The counterpart to this is "let's not do x because we suck". This commonly used and absolutely invalid reasoning leads only to failure. Allow me to elaborate.

People claim that the Itanium tanked because it was too hard to write a compiler for. Well, it was, but consider the implications of this reasoning. If a good compiler had been developed for this architecture, maybe we would have unlocked untold amounts of processing power. Maybe this would have driven development of new commodity processors that would have outperformed what we have now by leaps and bounds. Maybe we could have finally ditched x86 and all of its cruft.

But no, people were too lazy to put in a fixed, if large, amount of work to do essentially unbounded good later on. This is the essence of "let's not do x because we suck".

Now in reality Itanium had other shortcomings, such as sucking, and nobody really knows if we missed out on major improvements in processor technology. But there are other areas where this pattern is more obvious, and the people involved in bringing a new technology to market should by no means ditch an idea unless the idea is unsound.

Come on guys, you can do better than that.

8/16/09 01:28 pm - Merge made by octopus.


That is absolutely the most amusing message ever produced by any command-line utility.

Supposedly, git 'octopus merge' supports up to 16 branches. Maybe it should print more numerically accurate messages?

Merge made by triapus.
Merge made by quadrupus.
Merge made by quintapus.
Merge made by hexadecapus.

8/14/09 03:10 pm - Zucchini

I dislike a lot of foods, but I can usually understand how some people like them. Zucchini has me puzzled, though. It tastes bad enough to make me gag, and bad enough such that I could not imagine anyone enjoying it. People who claim to like it say it tastes much better when cooked with something flavorful. Any time I eat something of this sort, the taste of zucchini shows through; but if all you want to do is mask the flavor, why not use a less repulsive base?

Maybe it is just me (if zucchini is akin to en.wikipedia.org/wiki/Phenylthiocarbamide). What does zucchini taste like if not vomit-inducing?

7/18/09 08:34 am - Electronics are fast

This is a revelation I had some time ago.

So consider a CPU running at a typical 3GHz. Three billion cycles per second. Not extraordinary these days. That sure sounds pretty fast, but how fast is it really?

Now consider an object moving at 10km/s. This is certainly very fast by any human standards (objects in low earth orbit hurtle along at 7-8km/s).

Now think about what these two objects do in one microsecond. The fast-moving object moves a total of 10 millimeters, a rather unimpressive distance. In the meantime, though, the CPU completes three thousand cycles.

I used to worry about jitter and delay with electronic measurements of projectiles. Well, it turns out that there are much more important things to worry about than microseconds of lag or whatnot unless you are making precision measurements or making an implosion-type nuclear bomb. Electronics operate on an entirely different time scale from the vast majority of mechanical things.

7/15/09 11:20 pm - Four dimensions is worse than you think

Four-dimensional space (i.e. four space dimensions, not spacetime) is sort of weird to picture. Mostly it is easiest to think about the relation between four- and three-dimensional space as analogous to the relation between three- and two-dimensional space. If one were to intersect a four-dimensional hypersphere with a 'slice' of three-dimensional space, the intersection would be a sphere, much as an ordinary sphere would intersect a plane in a circle. And so on. If you think about it for a while and see enough projections of four-dimensional shapes, eventually you get it.

Now consider this: in three dimensions, three-dimensional shapes are 'always' visible in that you can see them from any angle. It does not matter how you turn a three-dimensional shape; its cross-section always has a nonzero area. Two-dimensional shapes are 'usually' visible, in that from every angle except edge-on the shape has a nonzero section when projected onto, say, your retina. One-dimensional shapes (lines and line segments) project to something of zero area and are thus 'never' visible.

If we extend this analogy down to two dimensions, we get that two-dimensional objects are always visible since it is always seen from edge-on (living on a plane gives you a one-dimensional view of the world, just as space gives you a two-dimensional view). One-dimensional shapes are usually visible, since from every angle except end-on, the projected image has nonzero 'area'. Zero-dimensional objects (points) project to points and are thus never visible.

If we generalize this to 'in n dimensions, n-dimensional objects are always visible, (n-1)-dimensional objects are usually visible, and (n-2)-dimensional objects are never visible', then in four dimensions we get that four-dimensional objects are always visible, three-dimensional ones are usually visible (ok...) and two-dimensional objects are never visible. What the hell.

I suspect it is possible to reconcile with this but the idea is substantially harder to understand than other concepts relating to four-dimensional space.

EDIT: I forgot to mention that this generalization may not actually be legitimate. It makes enough sense that it is reasonable, but little enough sense that it is intuitively preposterous.
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