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studying turbulence gave us the first important mathematical insights into the concept of complexity and its relationship to nonlinearity.
Richard Feynman described turbulence as “the most important unsolved problem of classical physics.”
Froude’s number is simply proportional to the velocity squared divided by the length. This ratio plays a central role in all problems involving motion, ranging from speeding bullets and running dinosaurs to flying airplanes and sailing ships.
objects of different sizes moving at different speeds behave in the same way if their Froude numbers have the same value. Thus, by making the length and speed of the model ship have the same Froude number as that of the full-size version, one can determine the dynamical behavior of the full-size ship before building it.
It represents the transition from a primitive trial-and-error, rule-of-thumb approach that served us well for thousands of years toward a more analytic, principled scientific strategy for solving problems and designing modern artifacts ranging from computers and ships to airplanes, buildings, and even companies.
One of the curious unintended consequences of these advances is that almost all automobiles, for example, now look alike because all manufacturers are solving the same equations to optimize similar performance parameters.
a dimensionless quantity: it is a “pure” number that does not change when a different system of units is used to measure it. This scale invariance expresses something absolute about the quantities they represent
Perhaps the most famous dimensionless number is pi (π), the ratio of the circumference of a circle to its diameter.
all of the laws of science must be expressible as relationships between scale-invariant dimensionless quantities,
the intensity of light waves scattered by small particles must decrease with the fourth power of their wavelength.
the shortest wavelengths, corresponding to blue light, dominate.
overall scale of life covers more than thirty orders of magnitude (1030) from the molecules that power metabolism and the genetic code up to ecosystems and cities.
understanding how information processing (“genomics”) integrates with the processing of energy and resources (“metabolics”) to sustain life remains a major challenge.
Understanding more generally the emergence of complexity from simplicity, an essential characteristic of adaptive evolving systems, is one of the founding cornerstones of the new science of complexity.
it is natural to ask if there are “universal laws of life” that are mathematizable so that biology could also be formulated as a predictive, quantitative science much like physics.
it may not be unreasonable to conjecture that the generic coarse-grained behavior of living systems might obey quantifiable universal laws that capture their essential features.
In October 1993 the U.S. Congress with the consent of President Bill Clinton officially canceled the largest scientific project ever conceived after having spent almost $3 billion on its construction.
It would provide critical evidence for testing predictions derived from our theory of the elementary particles, potentially discover new phenomena, and lay the foundations for what was termed a “Grand Unified Theory” of all of the fundamental forces of nature.
one of the major reasons for its collapse was the rise of a climate of negativity toward traditional big science and toward physics in particular.
yes, biology will almost certainly be the predominant science of the twenty-first century, but for it to become truly successful, it will need to embrace some of the quantitative, analytic, predictive culture that has made physics so successful.
We must all die so that the new can blossom, explore, adapt, and evolve.
This apparent general lack of interest by the biological community in aging and mortality beyond a relatively small number of devoted researchers stimulated me to begin pondering these questions.
Consequently, during interludes between grappling with quarks, gluons, dark matter, and string theory, I began to think about death.
the eminent and somewhat eccentric biologist Sir D’Arcy Wentworth Thompson in his classic book On Growth and Form, published in 1917.
biology had remained qualitative, without mathematical foundations or principles, so that it was still just “a science” with a lowercase s. It would only graduate to becoming “Science” when it incorporated mathematizable physical principles.
to understand how something ages and dies, whether an animal, an automobile, a company, or a civilization, one first needs to understand what the processes and mechanisms are that are keeping it alive, and then discern how these become degraded with time.
This line of thinking led me to focus initially on the central role of metabolism in keeping us alive before asking why it can’t continue doing so forever.
Metabolism is the fire of life . . . and food, the fuel of life
despite the naive expectation from natural selection, and despite the extraordinary complexity and diversity of life, and despite the fact that metabolism is perhaps the most complex physical-chemical process in the universe, metabolic rate exhibits an extraordinarily systematic regularity across all organisms.
Kleiber surveyed the metabolic rates for a spectrum of animals
the structures and dynamics being investigated have self-similar properties, which are represented mathematically by simple power laws,
for every four orders of magnitude increase in mass (along the horizontal axis), metabolic rate increases by only three orders of magnitude (along the vertical axis), so the slope of the straight line is ¾, the famous exponent in Kleiber’s law.
This remarkably systematic repetitive behavior is called scale invariance or self-similarity and is a property inherent to power laws.
Elephants are roughly 10,000 times heavier than rats but their metabolic rates are only 1,000 times larger, despite having roughly 10,000 times as many cells to support. Thus, an elephant’s cells operate at about a tenth the rate of a rat’s, resulting in a corresponding decrease in the rates of cellular damage, and consequently to a greater longevity for the elephant,
In addition to metabolic rates, these include quantities such as growth rates, genome lengths, lengths of aortas, tree heights, the amount of cerebral gray matter in the brain, evolutionary rates, and life spans;
There are probably well over fifty such scaling laws and—another big surprise—their corresponding exponents (the analog of the ¾ in Kleiber’s law) are invariably very close to simple multiples of
Particularly fascinating is the emergence of the number four in the guise of the ¼ powers that appear in all of these exponents. It occurs ubiquitously across the entire panoply of life and seems to play a special, fundamental role
a remarkably general universal pattern emerges, strongly suggesting that evolution has been constrained by other general physical principles beyond natural selection.
iso is Greek for “the same,” and metric is derived from metrikos, meaning “measure.” Allometric, on the other hand, is derived from allo, meaning “different,” and refers to the typically more general situation where shapes and morphology change as body size increases and different dimensions scale differently. For example, the radii and lengths of tree trunks, or for that matter the limbs of animals, scale differently from one another as size increases:
At the most fundamental biochemical level metabolic energy is created in semiautonomous molecular units within cells called respiratory complexes
The cycle of releasing energy from the breakup of ATP into ADP and its recycling back from ADP to store energy in ATP forms a continuous loop process much like the charging and recharging of a battery.
every day you typically make about 2 × 1026 ATP molecules—that’s
In other words, each day you produce and recycle the equivalent of your own body weight of ATP!
These little energy generators, the respiratory complexes, are situated on crinkly membranes inside mitochondria
Because muscles require greater access to energy, their cells are densely packed with mitochondria, whereas fat cells have many fewer. So on average each cell in your body may have up to a million of these little engines distributed among its mitochondria
the five hundred or so mitochondria inside each of your cells do not act independently but, like respiratory complexes, have to interact in an integrated coherent fashion
these hundred trillion cells have to be organized into a multitude of subsystems such as your various organs,
And this entire interconnected multilevel dynamic structure has to be sufficiently robust and resilient to continue functioning for up to one hundred years!
Just as organisms are constrained by the integration of the emergent laws operating at the cellular, mitochondrion, and respiratory complex levels, so cities have emerged from, and are constrained by, the underlying emergent dynamics of social interactions.
Revealing, articulating, and understanding these emergent laws that transcend all of life is the great challenge.
