Althouse: "It is true that everything we can see now, out to 13.8 billion years of light-travel time, was once the size of a grapefruit, buzzing with hideous energies..."

May 12, 2016

"It is true that everything we can see now, out to 13.8 billion years of light-travel time, was once the size of a grapefruit, buzzing with hideous energies..."

"... but that grapefruit was already part of an infinite ensemble with no edge, except one made up of time. When we look out, we look into the past, the farther we look, the more deeply into the past we see. At the center is the present. Alas there is no direction in which we can look to see the future — except perhaps into our own hearts and dreams. All we know is right now."

From "Don’t Let Them Tell You You’re Not at the Center of the Universe."

64 comments:

buwaya said...: Now that does no good at all. People will start putting on airs.; 5/12/16, 6:54 PM
Hagar said...: When asked "What is time?" Einstein answered "It is that which we measure with a clock."; 5/12/16, 6:56 PM
traditionalguy said...: Many, many moons from now the tides will cease to come in and to go out at same the border of the ocean. Then Time will have outlasted God's promise that the motion He started and that He restrains and will never cease.; 5/12/16, 7:11 PM
Sprezzatura said...: http://bloggingheads.tv/videos/3036; 5/12/16, 7:16 PM
Paul Snively said...: I still think that the rate at which time passes not being a constant is Einstein's—and science's generally—most astonishing discovery. On a job I had some years back, at which I worked with folks who were deeply involved in unmanned space flights at JPL, I greatly enjoyed talking with them about the ins and outs of writing software for these craft that had to take the relativistic change in the rate at which time passed on the craft into account. Good times.; 5/12/16, 7:21 PM
rhhardin said...: Science for women.; 5/12/16, 7:26 PM
Paul Snively said...: BTW, not that it makes any practical difference, but the article gets the light cone exactly backwards: the light cone originates in a point (the Big Bang), and, being light, spreads out in all directions thereafter. So in relativity, we talk about "the visible universe," i.e. the universe that we are able to see because light within it has had enough time to get to the observer, who must be within its light cone. The description that "your lover doesn't have quite identical information to you" is, perhaps, solipsistically poetic, but wrong.; 5/12/16, 7:27 PM
rhhardin said...: Lies expand at the speed of light. The truth takes longer.; 5/12/16, 7:33 PM
rhhardin said...: At night you lose your light cone and have to rely on touch.; 5/12/16, 7:34 PM
Kalli Davis said...: The nonsensical sentence that made me stop reading:

"It is true that everything we can see now, out to 13.8 billion years of light-travel time, was once the size of a grapefruit, buzzing with hideous energies, but that grapefruit was already part of an infinite ensemble with no edge, except one made up of time."

So the universe was infinite, but the size of a grapefruit, with no edge; yet had an edge.; 5/12/16, 7:45 PM
Paddy O said...: Those who don't know the past are doomed to repeat it. So the future is relative to the amount of historical ignorance. In which case the best way for us to know our future is to see what happened in the past, at which point the future changes because we know the past and are no longer doomed to repeat it.; 5/12/16, 7:45 PM
Paul Snively said...: Brian A David: So the universe was infinite, but the size of a grapefruit, with no edge; yet had an edge.

It's a surprisingly inartful article, but it's not nonsense. There was a time, very shortly after the Big Bang, when the universe was approximately the size of a grapefruit. But it doesn't make sense to talk about "before the Big Bang" (in time) or "outside the universe" (in space), because the Big Bang is when spacetime came into being. One of many weird things about the universe is that it is expanding. I don't mean "galaxies etc. are getting farther apart in space." I mean "spacetime itself is expanding." This is the cause of the "red shift" in astronomy, the fact that we observe the CMBR (Cosmological Microwave Background Radiation) hanging in there at about three degrees Kelvin in every direction, etc.

So the problem isn't that the article is talking nonsense; it's that General Relativity sounds like nonsense.; 5/12/16, 7:55 PM
James Pawlak said...: And God said, “Let there be light,” and there was light. 4 God saw that the light was good, and he separated the light from the darkness. 5 God called the light “day,” and the darkness he called “night.” And there was evening, and there was morning—the first day.; 5/12/16, 7:59 PM
CWJ said...: This is the best damned thing I've read in years. When I combine it with Pope Benedict's musings upon eternity, (in the words of Jordan Baker) it all makes sense.
Wow.; 5/12/16, 8:00 PM
CWJ said...: Thank you Althouse. I never would have found this otherwise.; 5/12/16, 8:01 PM
chickelit said...: Sir Isaac Newton did some rough calculations and reckoned that matter of the universe could fit in a nutshell. Whence the saying "In A Nutshell." The known universe was much smaller then which explains his underestimation.; 5/12/16, 8:20 PM
Quaestor said...: ...Einstein’s relativity teaches us that the center of the universe is everywhere and nowhere.

Don't let anyone tell you you're the center of the universe, because you're really nowhere. Frame of reference is everything.

And God said, “Let there be light,” yaddah, yaddah...

Which is no better, and certainly less interesting than:

Verily at the first Chaos came to be, but next wide-bosomed Earth, the ever-sure foundations of all the deathless ones who hold the peaks of snowy Olympus, and dim Tartarus in the depth of the wide-pathed Gaia, and Eros, fairest among the deathless gods, who unnerves the limbs and overcomes the mind and wise counsels of all gods and all men within them. From Chaos came forth Erebus and black Night; but of Night were born Aether and Day, whom she conceived and bare from union in love with Erebus. And Earth first bore starry Heaven, equal to herself, to cover her on every side, and to be an ever-sure abiding-place for the blessed gods. And she brought forth long Hills, graceful haunts of the goddess-Nymphs who dwell amongst the glens of the hills. She bore also the fruitless deep with his raging swell, Pontus, without sweet union of love. But afterwards she lay with Heaven and bore deep-swirling Oceanus, Coeus and Crius and Hyperion and Iapetus, Theia and Rhea, Themis and Mnemosyne and gold-crowned Phoebe and lovely Tethys. After them was born Cronos the wily, youngest and most terrible of her children, and he hated his lusty sire. — Theogony of Hesiod

Gaia, at least, was one sexy bitch — gettin' it on with all them Titanic cats. Whereas Jahweh was reduced to doing card tricks he learned in 7th grade study hall.

Prepubescent boys are being crucified in Syria because Allah, Yahweh's even more demented kid brother, told somebody who likes to quote Scripture to do it. 2000 or more years of holy wars and inquisitions have bled us near to death... Haven't we finally had enough of this ancient of days crap? Can't reasonable people just admit that the Bronze Age, like Elvis, has left the fucking building?; 5/12/16, 8:35 PM
Quaestor said...: GUILDENSTERN Prison, my lord?

HAMLET Denmark’s a prison.

ROSENCRANTZ Then is the world one.

HAMLET A goodly one, in which there are many confines, wards, and dungeons, Denmark being one o' th' worst.

ROSENCRANTZ We think not so, my lord.

HAMLET Why, then, ’tis none to you, for there is nothing either good or bad, but thinking makes it so. To me it is a prison.

ROSENCRANTZ Why then, your ambition makes it one. 'Tis too narrow for your mind.

HAMLET O God, I could be bounded in a nutshell and count myself a king of infinite space, were it not that I have bad dreams.

GUILDENSTERN Which dreams indeed are ambition, for the very substance of the ambitious is merely the shadow of a dream.

HAMLET A dream itself is but a shadow.

ROSENCRANTZ Truly, and I hold ambition of so airy and light a quality that it is but a shadow’s shadow.

HAMLET Then are our beggars bodies, and our monarchs and outstretched heroes the beggars' shadows. Shall we to th' court? For by my fay, I cannot reason.; 5/12/16, 8:43 PM
David said...: It is true that everything we can see now, out to 13.8 billion years of light-travel time, was once the size of a grapefruit, buzzing with hideous energies, but that grapefruit was already part of an infinite ensemble with no edge, except one made up of time.

That's how it appears to us from our point of observation but the probability is that more much more is observable if you know where to look, or where to be when you are looking.; 5/12/16, 8:49 PM
traditionalguy said...: I take it the posited enigma has nothing to do with Astrology, but the amount of pure conjecture and untested guess work about seeing light waves that originate from some unknown source thirteen billion years ago, that is unlikely to even be there anymore, makes Astrology seem to be a rational science by comparison.

It's time to listen to Bryson's A Short History of Nearly Everything again. That book tells us how certain men were about everything until the next discovery came along in all the fields of human knowledge we call science.; 5/12/16, 8:49 PM
Quayle said...: "buzzing with hideous energies"

But if you don't drive an electric car, you're going to cause this entire system to overflow with heat energy. Now that's science for you!

(Don't look now but our global warming arrogantists have a significant digit problem in their calculation.); 5/12/16, 9:03 PM
n.n said...: Yeah, the secular faith is a more plausible creation, and the pro-choice religion reconciles moral and natural imperatives. When was the last time that a cult sacrificed and cannibalized several million human lives annually? For wealth, pleasure, leisure, and a green lawn? As virginal sacrifices?

I think that even Islam plays second string to the secular faith and pro-choice religion of progressive liberalism.

Anyway, science was a philosophy constrained to a limited frame of reference and deduction, not inference and liberal doses of assertions. Today, neither time nor space can constrain people's imaginations nor conflation of the logical domains. It's no wonder that people believe in spontaneous conception and receive their religious/moral instruction from gods in the twilight zone who are notoriously selective or unprincipled.; 5/12/16, 9:05 PM
Obadiah said...: > Can't reasonable people just admit that the Bronze Age, like Elvis, has left the fucking building?

No. Many reasonable people are wholly unsatisfied by the shallow explanations offered by science. Sure, you can "explain" events by telling a story about how this particle bumped that one, and this "random" event triggered an avalanche of other random events, leading to the cause and effect we can see. But seen from some distance, all those random events sure look orchestrated and planned. All of the finely-tuned parameters of the universe suggest that someone put us here. Science grandly reveals the laws, but refuses to admit that there is a lawgiver. Elitist scientists may mock the beliefs of ordinary folk, but I would say that lots of ordinary folks are more in touch with reality. They know bullshit when they see it.; 5/12/16, 9:24 PM
William R. Hamblen said...: H. P. Lovecraft wrote this, "Hideous energies"?; 5/12/16, 9:56 PM
Nichevo said...: This comment has been removed by a blog administrator.; 5/12/16, 10:00 PM
Nichevo said...: This comment has been removed by a blog administrator.; 5/12/16, 10:03 PM
M Jordan said...: Here's the thing I never could get: how can the universe be expanding? Into what? Empty space? How's that different than universe space? I can understand stars and planets moving outward from some primal center, but they're moving into space, right? I mean, what the hell is space anyway?; 5/12/16, 10:21 PM
mtrobertslaw said...: Time rests entirely on memory. Without memory, we would have no concept of something called "the past", and without that concept, there is no time.; 5/12/16, 10:23 PM
Paul said...: But those Romulan Warbirds are still out there! Cloaked, of course.; 5/12/16, 10:38 PM
J. Farmer said...: "Time rests entirely on memory."

Language, too, I would say. I have a complicated intellectual relationship with Noam Chomsky's work (the political work, that is; I'm unqualified to judge the linguistic). Nonetheless, I think his central premise regarding the common human biological root for language is true (regardless of what one thinks of Chomsky's political opinions, we should all be eternally grateful for the part he played in demolishing the useless behaviorists). Memory is certainly crucial, but it is the capacity to verbally communicate and "pass down" memories that is truly transformative.

p.s. for all the limitations of an empiricist/materialist world view, knowledge by divine revelation does not seem to me to be a very useful alternative.; 5/12/16, 10:49 PM
Original Mike said...: "I can understand stars and planets moving outward from some primal center, but they're moving into space, right?"

No.

"I mean, what the hell is space anyway?"

A reasonable question, but whatever it is, it is not expanding into itself.; 5/12/16, 10:50 PM
chickelit said...: M Jordan asked: I mean, what the hell is space anyway?

Einstein answered: "Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning."; 5/12/16, 10:54 PM
J. Farmer said...: Looks to me like most people do not (and cannot) understand physics (myself included) to a significant degree. Basic premises and concepts, sure. Beyond that, forget about it. Physics is written in the language of mathematics, and most people struggle with estimating sales tax or proper tipping, never mind algebra or calculus.; 5/12/16, 11:19 PM
M Jordan said...: Blogger chickelit said..Einstein answered: "Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning."

Physical objects are not in space? What's that mean? They sure seem like they're in space. Of course, if space is simply nothing, then physical objects, being something, aren't in space ... I guess.

I appreciate the complex, contradictory world the quantum physics guys explained to us, but they sure haven't explained it very well. Humans may not naturally understand the essence of time and space, but I do think we get both of them in a simple but true way. Space is where, time is when.; 5/12/16, 11:32 PM
JackWayne said...: Any statement that starts off "It is true..." about a theory is just nonsense.; 5/12/16, 11:56 PM
Alex said...: What I don't understand is if you believe in Big Bang theory, by what mechanism is space itself expanding? Think about it - it's a weird theory with no real evidence. I think the steady-state universe is more likely.; 5/12/16, 11:56 PM
Alex said...: M Jordan said...
Here's the thing I never could get: how can the universe be expanding? Into what? Empty space? How's that different than universe space? I can understand stars and planets moving outward from some primal center, but they're moving into space, right? I mean, what the hell is space anyway?

If you look at our 3-D space from a 4th dimension, it's all flat. That's what Einstein theorized anyways. Gravity is simply the opposing force from space itself reacting against objects. Sounds weird and frankly I don't think it's true.; 5/12/16, 11:58 PM
Gideon7 said...: The end of the universe will be just as spectacular as the Big Bang. It's called the Big Rip. You will literally see the galaxies dissolving one by one, then the stars, then the planets, then the Earth itself, then you.

It's basically the Big Bang running backwards and outwards, faster and faster, on smaller and smaller scales. It will happen 16+ billion years from now.

If you could travel in a near-FTL spacecraft you really could go to Douglas Adams' Restaurant at the End of the Universe and watch it all go foom while drinking champagne.; 5/13/16, 12:14 AM
chickelit said...: M Jordan asked: Physical objects are not in space? What's that mean? They sure seem like they're in space.

Does it look like objects are in space or does it look like there's space between objects?; 5/13/16, 12:26 AM
Paul Snively said...: What I don't understand is if you believe in Big Bang theory, by what mechanism is space itself expanding? Think about it - it's a weird theory with no real evidence. I think the steady-state universe is more likely.

Actually, General Relativity has enormous experimental support, and steady-state theories have been completely debunked at this point.; 5/13/16, 12:26 AM
Paul Snively said...: Alex: If you look at our 3-D space from a 4th dimension, it's all flat. That's what Einstein theorized anyways. Gravity is simply the opposing force from space itself reacting against objects. Sounds weird and frankly I don't think it's true.

That's not quite right: in General Relativity, it's accepted that spacetime is actually curved (technically, the geometry of General Relativity is "non-Euclidean." Specificially, it's Riemannian), and gravity is, indeed, the curvature of spacetime caused by mass. This, again, has experimental support.

tl;dr anytime anyone wants to bet against General Relativity, I'll take that bet.; 5/13/16, 12:36 AM
cubanbob said...: I'm still baffled at what was the triggering event of the Big Bang. Why didn't it happen earlier or later? And what was there an instant prior to the initial point? I have a difficult time conceptualizing what Paul Snively said about the universe expanding into time instead of space-I see no practical distinction since the universe is expanding and that expansion has to occupy something and the something has to exist even if just for instant prior to it being filled up. It's turtles all the way down.

Let's get back to Donald Trump and Hillary Clinton, no neurons will be overly taxed discussing that topic.; 5/13/16, 12:54 AM
Lewis Wetzel said...: "It is true that everything we can see now, out to 13.8 billion years of light-travel time, was once the size of a grapefruit, buzzing with hideous energies..."
The size of a grapefruit? Compared to what? There was nothing else. It was as big as the universe. And its energies weren't hideous. There was nothing that could have conceived of anything as hideous. All that exists is now, it's not like there is a past or future that we can ever experience (when we experience the future, it will be now).
It bothers me when people confuse features of thought or language with a external, non-experienced reality. It is confusing the signifier and the signified.
If you find a fossil form of an amphibian with fins, you haven't found a fish evolving to a land animal, you've found a rock that filled in the space left by a decaying animal that was complete unto itself, it was not 'becoming' anything.; 5/13/16, 3:15 AM
Chris N said...: Time and space are the very concepts being manipulated within these equations, and by definition, VERY hard to visualize, but the equations so far, as far as has been observed, accurately explain all known experience.

Spacetime then curves in a Riemannian way; and light can be observed to 'bend' around stars like our sun and of course any object with mass (Arthur Eddington first went off the coast of Africa to the shadow the moon cast upon the Earth, to test this out....where the stars should be vs where they are...).

I recommend George Smoot's book on the COBE experiments (cosmic background radiation from the Big Bang) as a decent read for other laypeople

Math can be hard because it often seems a compendium of very smart guys' equations, often in different notations, often with steep learning curves.

Still not entirely convinced 'Alex' isn't some kind of program/machine learning trollbot.; 5/13/16, 3:33 AM
Chris N said...: George Smoot's 'Wrinkles In Time.' Maybe he embellished his role a bit, but for a good story about pretty interesting science, I'd recommend it.; 5/13/16, 3:46 AM
Lewis Wetzel said...: Time and space are the very concepts being manipulated within these equations . . .
There ya' go! Time and space are concepts.; 5/13/16, 4:04 AM
rhhardin said...: Those who don't know the future are doomed to repeat it.; 5/13/16, 4:57 AM
rhhardin said...: Before the big bang, all subjects were in the objective case and verbs were non-finite.; 5/13/16, 4:58 AM
Jaq said...: You can choose not to believe the big bang theory, it just makes it really hard to make any predictions about the future of the universe that are at all likely to be borne out by observation, on the other hand, what difference does it make at this point?; 5/13/16, 5:22 AM
Jaq said...: I mean, what the hell is space anyway?

Well, there is the concept of space as in three dimensional distance, and conceptual spacetime that each of us carries around in our head of adding the forth dimension of time moving in a single direction of course, but these are a simplification of our universe that work well enough for us to hit a moving animal with a flying spear, for example. It's just a useful conceit. The problem with these concepts is not that they are not useful, and close enough to land a man on the moon, for example, it's that they are not useful once we get to conditions that are far outside of human experience.

Personally I think that the "true" laws of the universe may well be outside of our grasp as thinkers. The universe is not bound by the plausible. Still, we can knit our thinking closer to it with advanced math that very few understand and find properties and effects that we can exploit to make really cool weapons.; 5/13/16, 5:50 AM
sinz52 said...: cubanbob asks: "I'm still baffled at what was the triggering event of the Big Bang. Why didn't it happen earlier or later?"

There is no earlier!

The Big Bang created "the arrow of time" along with everything else. Time isn't independent, but part of our universe.

Asking "What happened earlier" is like asking "What's 10 miles north of the North Pole?"

Anyway, modern cosmic inflationary theory suggests that our universe is just one of zillions in the cosmos. The whole thing just runs by itself.; 5/13/16, 5:56 AM
sinz52 said...: Paul Snivley said: "tl;dr anytime anyone wants to bet against General Relativity, I'll take that bet."

Actually, there were a number of alternative theories to Einstein's theory. The most well-known was the Brans-Dicke theory, in which the gravitational constant is replaced by a variable that can vary.

And General Relativity cannot be the whole answer, because it contradicts some aspects of quantum mechanics. There must be SOME even more general theory--a unified field theory--of which both General Relativity and quantum mechanics are special cases.; 5/13/16, 5:59 AM
Ignorance is Bliss said...: I see this article was placed in the Science section. That had me fooled for a little while, into thinking it might be, you know, science. Then I saw that it was dated April 1st.

Well played, New York Times, well played!; 5/13/16, 6:04 AM
tim maguire said...: The title reminds me of an old observation: If the universe is infinite, then every point within it is the center. Especially me.; 5/13/16, 6:27 AM
Robert Cook said...: "Personally I think that the 'true' laws of the universe may well be outside of our grasp as thinkers. The universe is not bound by the plausible."

J.B.S. Haldane, a British biologist and geneticist, said, in 1927, "...my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose."; 5/13/16, 6:56 AM
Robert Cook said...: "I'm still baffled at what was the triggering event of the Big Bang. Why didn't it happen earlier or later?"

Who says it didn't happen earlier, or won't happen later...many times? Aside from the notion there are countless other universes co-existing "now," there is also the notion of the Big Bang being followed later by a Big Crunch, the collapse of the universe into nothingness,(followed by another Big Bang, creating a new universe, followed by another Big Crunch, followed by another Big Bang...on into infinity.)

This, by the way, is very similar to the Hindu notion of existence. From Wikipedia:

"According to Hindu philosophy, the universe (or multiverse) never came to be at some particular point, but always has been, always will be, but is perpetually in flux. Space and time are of cyclical nature. This universe is simply the current one, which is in flux and constantly changing, when it finally ceases to manifest, a new one will arise. An interesting parallel to these ideas can be found in the ekpyrotic model of the universe. This concept is also accepted by Buddhist Dharma.

"The birth of the universe (Brahma) is followed by the life of the universe (Vishnu) and the destruction of the universe (Shankar) Or (Mahesh)."; 5/13/16, 7:04 AM
Robert Cook said...: "All of the finely-tuned parameters of the universe suggest that someone put us here."

Not in the least.

Who? How? Why?; 5/13/16, 7:11 AM
Chris N said...: ***I meant other lay people like me.

I still take it Robert Cook, while offering some insight on the arts and sciences also still believes in ideological principles which purport to undercut and explain the arts and sciences.

The particular animus against religious doctrine, for socialists, tends to be an obvious sticking point because religious doctrine directly contradicts what Socialists come to believe. Their minds and hearts, and beliefs, tend to become invested in a theory of history of what will be possible (the perfect, good society here on Earth and perfectible Man). Thus anything threatening this vision must be eradicated: The Afterlife, all-too-human behaviors (for much religious moral thinking got dragged along and weaponized against religion) Heaven, local gods or God, raw Platonic idealism etc.

These ideological principles and the Marxist theory of history are ultimately untestable and unscientific, and the faith and hope Socialists place in them...beyond reason.

It's kind of a zombie religion; an old dried beehive in the walls, a few of the rooms still buzzing even now.; 5/13/16, 8:43 AM
Chris N said...: ***I still expect, but won't quite predict, the NY Times editorial board to ideologically resemble that of the Guardian.

These things happen, and true believers, offering little of value but failed doctrine, go where the money, laws, education, hospitals and any other shared pot of money and common purpose are.; 5/13/16, 8:52 AM
Robert Cook said...: "I still take it Robert Cook, while offering some insight on the arts and sciences also still believes in ideological principles which purport to undercut and explain the arts and sciences."

Huh?; 5/13/16, 9:04 AM
Paul Snively said...: sinz52: And General Relativity cannot be the whole answer, because it contradicts some aspects of quantum mechanics.

It's far safer to say quantum mechanics (at least in its most popular, Copenhagen interpretation formulation) can't be the whole answer, for a few reasons, a couple of which are 1) it doesn't account for gravity at all, and 2) it doesn't offer deterministic conclusions, only probabilities, even though the central equation in it—Schrödinger's equation—is entirely deterministic, and in fact adds only a single term to the Hamilton-Jacobi equation, the most generally applicable formulation of classical mechanics.

tl;dr Quantum mechanics has been selling woo-woo unphysical mysticism since Bohr and Heisenberg rammed their dualist philosophy down the physics community's collective throats at the 5th Solvay Conference in 1927, which is why you have outright flights into fantasy like string theory and brane theory today. Someday perhaps physics will wake up, shake this nonsense off, and decide to be a science again. In the meantime...

There must be SOME even more general theory--a unified field theory--of which both General Relativity and quantum mechanics are special cases.

Maybe, but not necessarily: it's at least as possible that someone will decide two key things: 1) to take the existing mathematics of quantum mechanics seriously (as is done, e.g. by Everett and those following him), and 2) take a long, hard look at the mathematical underpinnings of both quantum mechanics and General Relativity with an eye toward weeding out processes that are overwhelmingly likely to result in exactly the singularities we encounter in attempting to combine the equations. In other words, there's obviously no physical problem—the universe has no difficulty with both quantum mechanics and General Relativity being true. There's a mathematical problem with saying, on one hand, "the large-scale structure of spacetime follows this form of smoothly continuous mathematics" and "the small-scale structure of spacetime consists of an infinite number of infinitely-small points." One approach to addressing this consists of reformulating General Relativity as the kind of so-called "gauge theory" that is used in the context of quantum mechanics. This paper take a good running start in that direction, using a form of "Geometric Calculus" that's derived from some brilliant, but nearly lost, mathematics discovered by William Kingdon Clifford, itself based on prior work by Gunter Grassman and William Rowan Hamilton, in the late 19th century.

In other words, we got ahead of ourselves a bit at the end of the 19th and beginning of the 20th centuries, thinking we had improved mathematical thinking with Cantor's set theory and the Bourbaki reformulation of foundations in those terms. It seems pretty clear now that we're paying the price for that, and the most promising research today involves revisiting the mathematics of the 19th century.; 5/13/16, 9:52 AM
Lewis Wetzel said...: Robert Cook wrote:
"Who? How? Why?"
God, God's spirit moving on the face of the waters, and love.; 5/13/16, 11:36 AM
Jim S. said...: In my experience, people always equate the center of the universe with importance. So when they hear that premodern people thought the earth was at the center of the universe (based on Aristotle and Ptolemy, incidentally, not the Bible), they assume that the premoderns thought we were the most important things in the universe. But any perusal of their cosmology shows the opposite: the center was actually the bottom of the universe. The closer you were to the center, the less important, the less esteemed you were. Think about it: what did they think was at the center of the earth? Hell, the outer darkness, the place where one was removed from God's awareness. Moreover, at least according to Dante, Satan was at the center of hell and thus of the earth and thus of the universe. This is why Arthur Lovejoy said the premodern cosmology wasn't geocentric; it was diabolocentric.; 5/13/16, 1:32 PM
Michael McNeil said...: When asked “What is time?” Einstein answered “It is that which we measure with a clock.”

No he didn't.; 5/14/16, 7:50 AM