May 7, 2015 at 1:04 am #21065
The cell has been compared to many things, from “a complex chemical refinery” (by the
physicist James Trefil) to “a vast, teeming metropolis” (the biochemist Guy Brown). A cell is both of those things and neither. It is like a refinery in that it is devoted to chemical activity on a grand scale, and like a metropolis in that it is crowded and busy and filled with interactions that seem confused and random but clearly have some system to them. But it is a much more nightmarish place than any city or factory that you have ever seen. To begin with there is no up or down inside the cell (gravity doesn’t meaningfully apply at the cellular scale), and not an atom’s width of space is unused. There is activity every where and a ceaseless thrum of electrical energy. You may not feel terribly electrical, but you are. The food we eat and the oxygen we breathe are combined in the cells into electricity. The reason we don’t give each other massive shocks or scorch the sofa when we sit is that it is all happening on a tiny scale: a mere 0.1 volts traveling distances measured in nanometers. However, scale that up and it would translate as a jolt of twenty million volts per meter, about the same as the charge carried by the main body of a thunderstorm.
Whatever their size or shape, nearly all your cells are built to fundamentally the same plan: they have an outer casing or membrane, a nucleus wherein resides the necessary genetic information to keep you going, and a busy space between the two called the cytoplasm. The membrane is not, as most of us imagine it, a durable, rubbery casing, something that you would need a sharp pin to prick. Rather, it is made up of a type of fatty material known as a lipid, which has the approximate consistency “of a light grade of machine oil,” to quote Sherwin B. Nuland. If that seems surprisingly insubstantial, bear in mind that at the microscopic level things behave differently. To anything on a molecular scale water becomes a kind of heavy-duty gel, and a lipid is like iron.
If you could visit a cell, you wouldn’t like it. Blown up to a scale at which atoms were about the size of peas, a cell itself would be a sphere roughly half a mile across, and supported by a complex framework of girders called the cytoskeleton. Within it, millions upon millions of objects—some the size of basketballs, others the size of cars—would whiz about like bullets. There wouldn’t be a place you could stand without being pummeled and ripped thousands of times every second from every direction. Even for its full-time occupants the inside of a cell is a hazardous place. Each strand of DNA is on average attacked or damaged once every 8.4 seconds—ten thousand times in a day—by chemicals and other agents that whack into or carelessly slice through it, and each of these wounds must be swiftly stitched up if the cell is not to perish.
The proteins are especially lively, spinning, pulsating, and flying into each other up to a billion times a second. Enzymes, themselves a type of protein, dash everywhere, performing up to a thousand tasks a second. Like greatly speeded up worker ants, they busily build and rebuild molecules, hauling a piece off this one, adding a piece to that one. Some monitor passing proteins and mark with a chemical those that are irreparably damaged or flawed. Once so selected, the doomed proteins proceed to a structure called a proteasome, where they are stripped down and their components used to build new proteins. Some types of protein exist for less than half an hour; others survive for weeks. But all lead existences that are inconceivably frenzied. As de Duve notes, “The molecular world must necessarily remain entirely beyond the powers of our imagination owing to the incredible speed with which things happen in it.”May 7, 2015 at 6:21 am #21068
Keith Devlin: free online course in mathematical thinking, sep-nov 2015May 7, 2015 at 10:33 am #21070
Courage, pilgrim! Here’s a visual metaphor. Imagine a graph with real numbers on the horizontal axis and, well, imaginary ones on the vertical. Now, remember the exponential function, f(x) = ex, from high school math? Ordinarily it graphs as an upward swooping curve—the very paradigm of progress. But put i in there, Euler showed, and eix instead traces a circle around the origin—an endless wheel of samsara intercepting reality at –1 and +1. Add another axis for time and it’s a helix winding into the future; viewed from the side, that helix is an oscillating sine wave.
That’s the essence of Euler’s alchemy: By venturing off the real number line into this empyrean dimension, he showed that disruptive, exponential change (the land of e) reduces to infinite repetition (π). You might think you’re getting ahead in the world, but from this astral perch you’re just running laps.May 7, 2015 at 2:26 pm #21071
That’s very interesting. I didn’t know that before.
Pity he spoiled it with the stupid line about crop circles at the end…
Obviously, there’s something very deep going on there. I wonder what it is.
I don’t buy the ‘real numbers’ v. ‘imaginary numbers’.
Imo, all numbers are imaginary numbers.
That itself is a fascinating philosophical topic, of course.May 7, 2015 at 9:36 pm #21080
Yes. A beautiful, strange equation. Here is the proof:
(I cannot post the embed code and change the video size as before. Now I must post the youtube link and cannot minimize the video. It’s too large, always :-()May 7, 2015 at 10:06 pm #21082
More brain gymnasticMay 9, 2015 at 2:30 am #21123
(I cannot post the embed code and change the video size as before. Now I must post the youtube link and cannot minimize the video. It’s too large, always :-()
If you go to SHARE, then EMBED, then SHOW MORE, YouTube will give you a choice of sizes to display.
However, it would be better if the right hand margin here would be further to the right, and allow a larger size. But it cannot be, because of the widget that displays the archive and all that crap. But YOU are the one who made that happen. There is no need for the archive to display on this Forum page is there, when it is on the Home page.
It would be better if the video resized automatically to fit the page.
I have had all these things sorted, before, but then when WordPress or bbPress do an upgrade, changes happen, and I am weary of all the messing about that it takes to fix the glitches.May 21, 2015 at 10:35 am #21252
Most of our oceans arrived from elsewhere. Around the same time as the deluge was raining down on the surface of the Earth, the inner planets of our Solar System were pummelled by comets and asteroids that were rich in alien water. The evidence for these events, known collectively as the Late Heavy Bombardment, are carved into the surface of the Moon.
No-one knows how many objects hit the Earth and how much water they brought. But this period of intense bombardment lasted from 4.5 billion to 3.8 billion years ago and, by the end of it, the Earth had all of its oceans.
Exactly where these comets and asteroids came from is uncertain. One way to work it out is to examine the relative proportions of heavy water in comets and asteroids that come from different parts of the Solar System. Heavy water contains deuterium, a form of hydrogen that contains a neutron as well as a proton in its nucleus.May 23, 2015 at 1:48 am #21260
String theory… Euler, again…
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