Breakdown of Scale Invariance – Hilarity Ensues

By cjohnson | March 1, 2006 2:51 am

So it is that time of year. On Sunday, the Academy Awards (Oscars) take place, but that’s not what I’m talking about. It is the days immediately after…..

In the days (or week?) after the Oscars, a number of glossy Hollywood gossip magazines (Us Weekly, People, and In Touch, for example) will do specials on the various dresses, (or ballgowns, etc,) worn by many of the stars who attended. Why do I care about this? Because they do something really silly in these presentations. They’ll have several pages of the pictures of the outfits, but they rescale all the women to be the same height! It only works properly if you see them side by side in the magazine, not on the web, so you have to look at the printed results to see how funny it is.

I noticed this by chance (no, don’t ask….) a few years ago and now I look forward to it every year because it’s just plain ridiculous, and the results are often funny. Why? Well, take someone like Christina Ricci, at 5 ft 1 in, and rescale** her photo so that she is the same height as Uma Thurman, who is 6 ft tall. What do you get? Well, the proportions are wrong….. Ricci will probably have a huge head compared to Thurman, etc, etc. I don’t know why, but every year I like seeing the results of this little game. (This has nothing to do with making fun of people’s heights, but everything to do with a magazine trying to acheive uniformity by rescaling in this way. I’d love to know which editor was responsible for that brilliant idea, which seems to be copied a lot now.)

Stop by a magazine stand and have a flick through for a quick laugh.

Oh…. while I’m at it, I’ll go for a bit of science of scaling: Here’s a random bit of writing, by George Johnson in 1999, about scaling laws in biology: (Link.)


[Update: **Of course, who ever did that would be a “Ricci Scaler”, :-) A cheap joke for the possible amusement of a relatively small community trained in differential geometry.]

  • Kristin

    I like to talk about scaling properties of food. Once we went over to dinner at the home of a couple of fellow physics graduate students, where they had painstakingly prepared a stack of crepes to serve to the large crowd. Each had to be reheated individually, and it was quite a task. I remember commenting that the crepes were wonderful, but tiramisu scales much better for a crowd. Ditto for lasagna, pizza, moussaka…

  • http://http::/ Daryl McCullough

    I’m not sure if this interesting or original or nontrivial, but it occurs to me that all violations of scale invariance are ultimately due to quantum mechanics. The equations of classical mechanics—Newton’s laws of motion, Newtonian gravity, laws of electrodynamics—have no preferred scale. If there were no quantum effects, then we could perfectly well have a planet that was exactly like the Earth, except that everything was scaled up (or down) by a factor of 100.

  • Elliot

    So Daryl does that mean we could have a 600 foot tall Uma Thurman?

  • http://http::/ Daryl McCullough


    Well, Uma’s scale is mostly due to the Bohr radius, r = h-bar^2/(m e^2), where m is the mass of the electron, and e is the charge of the electron. So we could get a version of Uma that was about 1 cm tall by just replacing all her electrons by muons (207 times the mass, so 1/207th the Bohr radius). Frankly, I can’t think of a practical way to get a 600 foot tall Uma.

  • citrine

    I have a copy of an article that appeared in the Scientific American a while back. It’s a discussion of why toast falls butter side dowwn. The argument basically boils down to the values of the physical constants of the universe and surmises that even in a hypothetical planet supporting human-like life forms 8’tall, toast would fall butter side down.

    I’ve often thought about “pet maintenance scaling laws”. If keeping one cat requires w amount of work, how much work is required for the care and upkeep of n cats? Remember that having more than one cat presumably requires resolving cat fights and that n!/2 types of pairwise interactions are possible between n objects.

  • Ken Muldrew

    In biology scaling is due to the way that lengths, surface areas and volumes scale. Most chemical reactions occur on surfaces but the stuff has to diffuse (or be transported) through volumes. Similarly loads come from mass (volume) but have to be transmitted along linear rigid pieces and across surfaces. Simple mechanics is sufficient.

    Do you suppose the normalization is a result of the MSM’s penchant for “balance” in reporting?

  • http://http::/ Daryl McCullough


    Yes, I understand that limits on scale can be understood without quantum mechanics given parameters such as the strength of materials, but those parameters in turn are determined by quantum effects. Specifically, consider heat dissipation: Heat production inside an organism is roughly proportional to its mass, which is roughly proportional to the cube of its linear size. Heat dissipation is roughly proportional to the square of its linear size. Therefore, without a design change (more efficient way to dissipate waste heat), we have a limit to how large a particular organism can be:

    Heat dissipation rate >= heat production rate
    K1 * L^2 >= K2 * L^3

  • http://http::/ Daryl McCullough

    Whoops, somehow my post got chopped off.

    My point was that if heat dissipation is roughly K1 * L^2, and heat production is roughly K2 * L^3, then L is limited to be less than or equal to K1/K2. However, the numbers K1 and K2 are ultimately determined by quantum-mechanical effects.

  • Ken Muldrew

    Your specific example is exactly what I was getting at (e.g. sail-fins in dinosaurs are thought to have been organs for increasing the surface area for heat dissipation for an otherwise large, squat beast that would get too hot if it moved much). I don’t see where qm enters the picture except for the limit where qm is the underlying basis of mechanics. It would be like saying that hydrogen bonding is due to qm (and of course it is), so having liquid water on the planet is due to qm, therefore life depends on qm. It’s true, but just saying that life depends on liquid water is perfectly satisfying on its own; just as scaling can be understood as the way that (classical and statistical) mechanics scale with added dimensions.

  • Clifford

    Ken…. #6, maybe that is the reason… maybe there was pressure from agents? Maybe it is all part of the well-known urge to make all women’s bodies conform to some uniform standard in the fashion world.

    Ken, Daryl, citrine :- On the scaling and physics issues mentioned by many…Yes, transport and diffusion are key processes which produce interesting limitations on scaling… surface area is so important, for example, as is surface tension, in fact…. you don’t get really huge pond-skaters……

    It is a wonderful intersection of physics, chemistry and biology.

    Kristin…. As to the logistics of cooking… yes! I agree that’s really interesting too…. and often frustrating…. transport and diffusion play a role there too (just keeping eveything hot when preparing lots of dishes…or lots of versions of the same dish…..but limited by not scaling up the over, stove, utensils…….) Oh…. scaling is on my mind a lot when having a dinner party……indeed.

    citrine… do you think cats would scale better or worse than dogs? Maybe the n! gets enhanced or suppressed by the different personality tendencies? I can’t decide… On the one hand, maybe after a bit of a tussle, most of the cats would just go off into dark corners and under furniture and hide there, looking out at what’s going on from a safe vantage point…. but on the other hand they might just all fight endlessly….. but I feel the latter is more likely for dogs…… but then I’m biased a bit…..


  • spyder

    there is more to that fashion layout than just scaling:
    for example one of the companies with which we contract for our summer rock-n- roll tours is cubepasses, who scale down and retouch posters and band photos to use as laminates, backstage ID, tour all access passes and the like. They shrink, contort, cut, and highlight, even putting in various backgrounds for different venues. Pretty elegant work actually, but (and there is a but) it represents only virtual presentation; there is little that could be manifest factually in consensual reality.

    the below link is for a photo retouch service that evidences just how much scaling is available to the graphic artist in remaking fashion for publication.

    and as an example of the controversy itself. Who is real??

  • Clifford

    Hmmm… bit annoyed with myself… I just realized I missed the opportunity to sneak in the pun “Ricci Scaler” into the post. Drat! drat! drat!.


    (Ok…I can’t resist… a small update…..)

  • LambchopofGod

    Regarding that update….I’m scared to ask what a “cummunity” is……hope Christina won’t get tenser if she reads that.

  • Clifford

    thanks for the roundabout spelling correction!



  • citrine


    Curiosity provoked me into googling Nina Ricci. The second hit for her is the Nordstrom dept store website. It’s kind of ironic that these names appear in two worlds usually thought as being disparate – GR and in the world of high fashion.

    If someone sells Mary Kay to earn support herself while devoting most of her time to Relativistic Astrophysics would she be a Cosmologist and a Cosmetologist? (I used the female pronoun as a convenience; it’s not meant to exclude people of any gender.)

  • Clifford

    Maybe she/he gets to be both!

    Like being an optician and an optometrist at the same time?

    Or maybe better would be someone who has a MD, but is also trained as a medical physicist….. They would be a Physician and a Physicist….


  • Chris W.

    Back to scaling: What about the role of gravity? Arbitrary scale-up of buildings and living organisms runs into problems on its account.

    Rough summary:

    – Scale-down runs up against the atomic structure of matter and its non-classical behavior at that scale.

    – scale-up runs up against the ever-mounting effects of gravity and inertia, as compared with the growth of strength of materials. Consider trying to spin a very big flywheel, with the same proportions and composition of a smaller one, at the same angular velocity as the smaller one. A classic consequence of special relativity is that the rigidity of so-called rigid bodies is limited; otherwise some parts of them could be forced to exceed the speed of light relative to other parts. (Recall in this context that the strength of materials originates in the atomic and quantum structure of matter.)

    Of course this actually has little to do with the aesthetics of same-scale visual comparisons of Christina Ricci and Uma Thurman (or, say, Charlize Theron or Queen Latifah) in evening gowns.

  • ThePolynomial

    If you rescaled Uma, would the process be Thurman-dynamics? And if they think Ms. Becall’s too tall, would that be Lauren’s contraction? God these are stretches (ha, stretches…)

  • Plato

    By ones very own nature “fluidity esteemed” might have been dressed according to some “emotive measure,” while recognizing, it is also fully dressed and wrapped in the intellectual one? :)

    Tricky minds here.

  • Clifford

    ThePolynomial: – LOL!! I see there are others as bad as me…..

    Oops…. we’re on the wrong thread here….shouldn’t we be on the Bad Physics Jokes thread from a few weeks ago?


  • I, Robot

    While it does exist yet in literal form,

    From the Future to the Notebook

    signs of new life emerge as images photonically flicker in the new logic forming apparatus

    I had a dream….:)


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