Maggie's Farm

OneGuy: And the more you dig into it the more you realize that most of what we believe is preposterous.

The article is just conjecture.

OneGuy: How big is the universe?

In standard cosmology, space itself is a result of the Big Bang expansion, not an explosion within space.

DeGaulle: It's not just that we don't know, Kurt Goedel proved that we can't.

Can't what? Know stuff about the universe? While humans can't know everything with certainty, they can certainly know some things with reasonable certainty. How does Gödel figure into this?

DeGaulle: Surprised you don't know this as you seem to claim to know everything.

We certainly don’t know everything. Indeed, we don’t claim to know anything other than what we can show herein, and even that we are open to learning or correction.

DeGaulle: Goedel's Incompleteness Theorem states that in all mathematical sets of complexity greater than addition and substraction

Tarski showed that real closed fields are complete. Tarski’s axioms of geometry (based on real numbers) are also complete. Oddly enough, while the set of real numbers is larger and encompasses the set of natural numbers, the arithmetic of natural numbers is more complex. Regardless, real numbers and geometry would seem to be a better fit to the natural universe than integer arithmetic.

The larger problem is your assumption that “the physical universe is the largest mathematical set of which we have knowledge”, which is a pretty big assumption. Even if we accept that assumption, incompleteness only applies to certain infinite sets, not what appears to be a finite universe.

Regardless, that seems far removed from knowing about the Big Bang, which, while the knowledge of which is fraught with more prosaic problems, isn’t inherently or logically unknowable.

DeGaulle: Incompleteness applies to all sets of greater complexity than those containing additional or subtractive components.

You ignored the points raised, so we will restate them:

• Incompleteness doesn't apply to a closed real field or to geometry, either of which would seem to be a better fit than natural numbers to represent the universe.
• The universe appears to be finite, not infinite. Theorems of finite sets of discrete elements are necessarily complete.
• You assume the universe is a "mathematical set" rather than the mathematical set being a model of the universe, a fallacy of reification.

DeGaulle: I specifically and systematically addressed all your points.

Don't see where. Let's start with just one. Your claim is that Gödel uncertainty constrains our knowledge of the universe. But if the universe is finite, as it appears to be, then Gödel uncertainty doesn't apply. In a finite set, the validity of every possible theorem can be known.

DeGaulle: The Incompleteness Theorem proved that this knowledge isn't available within any given set of sufficient complexity.

You didn't address even the one point (much less the others). This is easy to determine because 1) You didn't address finite vs. infinite; 2) You didn't address specifics of Gödel incompleteness theorems.

A finite set of natural numbers is not of "sufficient complexity". Every possible theorem of a finite set can be shown to be true or false by exhaustion. For instance, Goldbach's conjecture is unsolved for natural numbers, but is solved for the finite set of natural numbers < 10^18.

DeGaulle: I offer Stephen Hawking's lecture "Godel and the end of physics".

Hawking: "This is very reminiscent of Godel's theorem." In other words, Hawking is making an argument by analogy, not a logically binding argument.

Hawking: "This says that any finite system of axioms is not sufficient to prove every result in mathematics. That's a simplified restatement of Gödel incompleteness, emphasizing that Hawking is making an argument by analogy. As discussed above, many mathematical systems are complete, including real closed fields. Nor does Gödel incompleteness cover finite sets. Nor does any of this mean that the universe is a "mathematical set" of natural numbers. (Wave functions are represented with complex numbers.}

Nor is there any reason to suppose that gravity can't, in principle, be united with the other forces of nature in a physical theory.

Gringo: That statement is definitely stupid, as it was rather hard for Trump to stop a war that began a year after he took office.

The Russo-Ukrainian War started in 2014.

Feel free to ignore the following as it is a bit off-topic.

James4HJ: While Zac has quite come around to praising the USA, but he's at least clear that Russia is the bad guy.

Let's break this into four sections:

Section 1: Why do people love their home countries? Consider the Irish. When the Irish migrated to America in large numbers, they were leaving what Trump would call a "sh!thole" country. The history of Ireland was full of violent conflict between clans, then centuries of occupation. The people of Ireland were dying from starvation by the hundreds of thousands. The immigrants to America were largely poor and uneducated. They lived in crime-infested ghettos. They held to an ancient religion, following a foreign prince wearing a funny looking hat. And they lacked that oh so sweet Anglo-Saxon blood. Yet, the Irish still clung to a dream of Ireland as a heaven on Earth, a place where their ancestors lived and died, and they carried their traditions with them to America. (Today, of course, everyone wants to be Irish on St. Patrick's Day and toast a wee bit of blarney.)

Section 2: America has had a troubled history, from ethnically cleansing the Indians, to chattel slavery, civil war, and a strict system of racial segregation and oppression. Ignoring this is to ignore the very heart of the American story.

Section 3: Despite its shortcomings, or rather because of its continuing struggle to overcome its shortcomings, America has been a beacon to the world. Not only was the United States instrumental in defeating fascism in WWII, but they created a world where every nation would have a say, where America was not the dictator, but the first among equals. Whenever America lived up to those ideals, totalitarians were held at bay. Whenever America failed to live up to its ideals, totalitarians advanced.

Section 4: The world has changed. America will necessarily diminish in influence, the very result of trying to create a more just society for all the world's people. The transition will be fraught with danger and difficulty. The transition will require a deft touch and cooperation between people of good-will. However, no other nation has the incredible resources of America; a highly educated population with a knack for discovery and innovation, a history of entrepreneurship, vast natural resources, and the center of global alliances. America can compete in the modern world, but you don't get to be number one by chanting "We're number one!" and pounding your chest, but by doing the hard work of constant reinvention.

Christopher B: Trump wasn't President then {2014}

No, but the Russo-Ukrainian War was ongoing throughout Trump’s term. If he had a solution for ending the war, he had ample opportunity to do so. As Vindman posted, “What did Trump do during his four years to end the Russia-Ukraine war? Nothing.”

Mark Matis: But nobody is permitted to identify (((THEM))).

Those people.