Scaling: Why Giants Don’t Exist

Scaling: Why Giants Don’t Exist

Michael Fowler, UVa  10/12/06

 

Galileo begins Two New Sciences with the striking observation that if two ships, one large and one small, have identical proportions and are constructed of the same materials, so that one is purely a scaled up version of the other in every respect, nevertheless the larger one will require proportionately more scaffolding and support on launching to prevent its breaking apart under its own weight.  He goes on to point out that similar considerations apply to animals, the larger ones being more vulnerable to stress from their own weight (page 4):

Who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height or a cat from a height of eight or ten cubits will suffer no injury?  … and just as smaller animals are proportionately stronger and more robust than the larger, so also smaller plants are able to stand up better than the larger.  I am certain you both know that an oak two hundred cubits high would not be able to sustain its own branches if they were distributed as in a tree of ordinary size; and that nature cannot produce a horse as large as twenty ordinary horses or a giant ten times taller than an ordinary man unless by miracle or by greatly altering the proportions of his limbs and especially his bones, which would have to be considerably enlarged over the ordinary.

 

For more of the text, click here.

 

To see what Galileo is driving at here, consider a chandelier lighting fixture, with bulbs and shades on a wooden frame suspended from the middle of the ceiling by a thin rope, just sufficient to take its weight (taking the electrical supply wires to have negligible strength for this purpose).  Suppose you like the design of this particular fixture, and would like to make an exactly similar one for a room twice as large in every dimension.  The obvious approach is simply to double the dimensions of all components.  Assuming essentially all the weight is in the wooden frame, its height, length and breadth will all be doubled, so its volume—and hence its weight—will increase eightfold.   Now think about the rope between the chandelier and the ceiling.  The new rope will be eight times bigger than the old rope just as the wooden frame was.  But the weight-bearing capacity of a uniform rope does not depend on its length (unless it is so long that its own weight becomes important, which we take not to be the case here).  How much weight a rope of given material will bear depends on the cross-sectional area of the rope, which is just a count of the number of rope fibers available to carry the weight.  The crucial point is that if the rope has all its dimensions doubled, this cross-sectional area, and hence its weight-carrying capacity, is only increased fourfold.  Therefore, the doubled rope will not be able to hold up the doubled chandelier, the weight of which increased eightfold.  For the chandelier to stay up, it will be necessary to use a new rope which is considerably fatter than that given by just doubling the dimensions of the original rope.

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Why do we believe in electrons, but not in fairies?

Why do we believe in electrons, but not in fairies?

by Benjamin Kuipers

No one has directly observed either electrons or fairies. Both of them are theoretical constructs, useful to explain observations that might be difficult to explain otherwise. The “theory of fairies” can actually explain more things than the “theory of electrons”. So why do we believe in electrons, but not in fairies?

Is the issue a political one, where the “electron” fans got the upper hand in the nineteenth century, so by the twentieth century the “fairy” fans were a scorned and persecuted minority? Or, have we proved for sure that fairies don’t exist?

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The relativity of wrong

The Relativity of Wrong

by Isaac Asimov

I received a letter from a reader the other day. It was handwritten in crabbed penmanship so that it was very difficult to read. Nevertheless, I tried to make it out just in case it might prove to be important.

In the first sentence, he told me he was majoring in English Literature, but felt he needed to teach me science. (I sighed a bit, for I knew very few English Lit majors who are equipped to teach me science, but I am very aware of the vast state of my ignorance and I am prepared to learn as much as I can from anyone, however low on the social scale, so I read on.)

It seemed that in one of my innumerable essays, here and elsewhere, I had expressed a certain gladness at living in a century in which we finally got the basis of the Universe straight.

I didn’t go into detail in the matter, but what I meant was that we now know the basic rules governing the Universe, together with the gravitational interrelationships of its gross components, as shown in the theory of relativity worked out between 1905 and 1916. We also know the basic rules governing the subatomic particles and their interrelationships, since these are very neatly described by the quantum theory worked out between 1900 and 1930. What’s more, we have found that the galaxies and clusters of galaxies are the basic units of the physical Universe, as discovered between 1920 and 1930.

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50 Things we know now that we didn’t know this time last year

50 Things we know now that we didn’t know this time last year

Originally published: 12/28/09, 12:10 PM EDT
By Jeff Houck

If there was an award for best quote of the year, our money would be on Richard Fisher, the director of NASA’s Heliophysics Division.

Fisher was interviewed in October by National Public Radio after NASA scientists discovered a mysterious ribbon of hydrogen around our solar system.

The layer, a sort of protective barrier called the heliosphere, shields us from harmful cosmic radiation. Its existence defies all expectations about what the edge of the solar system might look like.

Fisher’s response: “We thought we knew everything about everything, and it turned out that there were unknown unknowns.”

In other words: We don’t know what we don’t know until we know that we don’t know it.

Life is funny that way. You think you’ve got the world wrapped up in string, only to watch some bit of news come along to unravel your comprehension of how things work.

One thing we did expect: that 2009 would be full of strange and wonderful revelations.

A prediction for 2010? Same thing as this year, only different.

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