Systemic Action: Make it Mathy!
Yesterday’s comic, The System 333: Full Gadget Ratio has been doing quite well for itself. It made it to the front of Reddit for a hot second, has spread around pretty well on Twitter, etc. However, a bunch of people more mathy than I, thinking I’m secretly trying to be XKCD (hint: XKCD has yet to do a comic about crop marks and bleed), are having some trouble with the equation. Fair, since I spend too much time on the graphic and little on making the equation work. Case in point:
Why take so much time on the graphic only to have such a poorly thought out equation?
I’m not normally one to obsess over others’ comments on the comic, but they have a valid point. Systemics, let’s give this chart an equation to be proud of! Given the variables at hand, help me come up with something better. Use whatever units of measurement you feel appropriate and all the information at hand, and post them here in the comments. I’ll update this chart and give credit where due the best I can. In fact, I’ll be picking at random one of the people who helps in the comments to get a FREE PRINT of this comic from our store, HilariAwesome.com!
UPDATE: It’s been a while, I know. Congrats to Systemic Harris who submitted an awesome entry that will be reflected in the original post, and will also be receiving a print of this comic! Check out the original comic to see the mathy update.
February 3rd, 2010 at 10:07 am
[...] UPDATE-UPDATE: I know what you’re thinking. The equation is crap! Here’s how you can help me fix it! [...]
February 3rd, 2010 at 2:37 pm
(Ross + The System) * internet = AWESOME! Done!
February 3rd, 2010 at 3:12 pm
Sd3 + (T+A)B / W(HU)-N + h
stack the fraction on top of itself
and Sd3 is taking the third derivative of S
accounting for its three dimesions
and you might want to factor in L, the size of a pocket on a pair of Levi's Jeans.
February 3rd, 2010 at 4:38 pm
FGR = hB * U ^ ( [ (S+T) / (WN) ] ( H / A ) )
February 4th, 2010 at 5:42 am
APL GNA STB A BTCH
Add symbols as necessary!
… okay, not really. My maths are limited to making change for up to $100 anymore. Still, it's always more fun when you can read into what the letters are *really* saying. ^_^
February 4th, 2010 at 3:02 pm
from a physics perspective one of the first thing to look at is dimensional analysis — evaluating whether the equation makes sense based on the units of the terms. (for instance, if you were calculating the speed of something in meters/second, it wouldn't make sense to have a mass term (in kilograms) on one side of the equation unless it was divided by another term that also included a measurement of mass, thus removing the kg unit from the equation
S appears to be a volume, so say cm^3
T and B are also apparently volumes
a summation of the volumes would make sense (S+T+B) to maintain the units
A does not have an obvious unit, is it simply a count of adapter cables and power chargers? or can we expand it to be another volumetric measure of the space that those items take up? or is it just a question of the mass of those items?
N is clearly a unitless value, as is U
H is obviously a measurement of time in hours (h)
W is technically a ratio of worry per cost. worry = stress (or pressure) and the SI unit of stress is the Pascal (Pa), which is force/area (kg/(m*s^2))
h and FGR don't have defined units either.
Just from examining this, I would suggest that W is mitigated by both T and B, but B is increased by the inclusion of A and T is made more valuable as U increases, so one part of the equation should probably be:
W / [ (U/T) + (AB)]
This whole term itself should be modified based on the generational age (N) and size (S) of the item, where the higher N, the lower the total FGR, and the larger S vs h, the higher the FGR, so I'd say the final equation would be
FGR = W*S / { (N+h)[ (U/T) + (AB) ] }
There is still some question regarding units, but whatever
February 7th, 2010 at 5:43 am
On the FGR of Mobile Devices:
Clearly, FGR should be a measure of how bulky/inconvenient the object is, amortized over how useful it is. So:
FGR, the base term at first glance should be affine in S,A,B, as these all contribute more or less additively to bulkiness. T is an issue, though for now we can add it in as well. I see lots of people use S*T or some such, which is clearly not right, though my S+T isn't much better. Really, the question is whether S is a volume, or the bulkiest dimension, or maybe, it's the largest face divided by the opposite direction (screen size divided by thickness, say). The question is whether S should be a measure of useful dimensions vs. non-useful dimension, like the latter, or a general matter of how bulky something is to carry around, so a simple volume, or the bulkiest dimension. The interaction w/ T then plays into that. Not sure the best way to handle it. The most accurate would be to break S into the three dimensions and apply T directly, recomputing the volume, but that will complicate the device enormously. So for now we leave it linear.
If a device is twice as useful, it's clearly functionally half as bulky, so divide by U.
Higher H makes it more useful, but how? On the one hand, H should essentially contribute to higher U, as you can't use it if the battery is dead, so will use it more. But only past a point, as if it can do, say, 24 or 48 hours w/out recharge, it's not an inconvenience to recharge every so often. So replacing 1/U by (1 + 1/H)/U is good for bulkiness, as low H decreases effective usefulness a lot, but past a point high H is diminishing returns.
Additionally, though, H plays off against A, as the longer it lasts w/out power the less you need to carry the power adapter around. So perhaps replace the A term by A/H, that is, the bulk of the adaptors is reduced by you maybe not needing to carry them around. Really this should be a threshold effect of some kind, though, where either you are carrying the adaptors around or you aren't, so maybe multiply A by an appropriate shifted Heaviside function of H. Still, the linear approximation is ok for now. And of course, that you rolled chargers & adapters into the same category muddles the issue.
The worry factor increases bulkiness, presumably linearly. But, if newer versions are out, you don't mind it breaking as much because you want to buy the new one. So there should be a W/N factor in there (where obviously we must count N as the number of generations at least as new as this one, to avoid division by 0). Again, though once it is old enough you don't worry at all, but this shouldn't go to 0, so it should be (1+ W/N).
And the constant should definitely be used as a multiplier, to get the units (whatever they are) to come out right.
So maybe:
FGR = (S + T + A/H + B) * (1+1/H)/U * (1 + W/N) * h, or reordered to look a little nicer
FGR = h(1+W/N)(1+1/H)(S+T+A/H+B)/U
August 5th, 2010 at 4:30 am
Really, I don't know why we're considering other options after reading this.