New Scientist vs. William Lane Craig on infinity explanations

_{Denyse O'Leary

March 25, 2016

Cosmology, Mathematics, News}

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Not to start up the infinity battle again (okay, maybe we are … ), from New Scientist:

Explanimator: Does infinity exist in the real world?

…

Some mathematicians are trying to rebuild the foundations of mathematics without the infinite. But if there is a biggest number, what would happen when you add one to it? The solution could be thinking of numbers as a cycle rather than a linear series, some sort of loop where you revert back to the beginning. It’s a little strange, but then so is infinity. More.

The reader who forwarded the tip comments, “Compared to William Lane Craig’s lectures, this article seems shallow and infantile.”

Here’s Craig. Readers can decide:

See also: Durston and Craig on an infinite temporal past

and

Infinity at Starbucks: Starring Laszlo Bencze and Art Battson

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Comments

mapou: sqrt(-1) is, of course, nonsense Here's one for Mapou since I can't tell if (s)he's serious or not about complex numbers. If there is no reality in the use of i, what is the method for obtaining sin(1.0) to say 50 places, and what are the underlying mathematical structures in this? And if a person does this in a Far Eastern country does it work out identically as to doing it in the West? Or in the Third World? (angle in rads). But maybe Mapou's is turning the discussion into a joke, intentionally - if not their contribution is a good joke.groovamos_{March 25, 2016
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I see. Well, in that case I won't ask any more questions.Aleta_{March 25, 2016
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So how do you explain that there are mathematical formulations that use i = sqrt(-1) to model the real world, and for which the models are extremely accurate?
I don't believe it. For the same reason that I don't believe a lot of other crap that are handed down to us from elitists. It's crap. I don't believe in gravitational waves, black holes, Big Bang, wormholes, accelerated expansion and spacetime either, for examples. It's all crap.Mapou_{March 25, 2016
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So how do you explain that there are mathematical formulations that use i = sqrt(-1) to model the real world, and for which the models are extremely accurate?Aleta_{March 25, 2016
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By the way, I am so confident that distance is an abstract perceptual illusion that I predict the following. In the foreseeable future, when our knowledge will have increased and physicists finally wake up from their stupor, we will develop technologies that will allow us to travel instantly from anywhere to anywhere without going through the intervening positions.Mapou_{March 25, 2016
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Aleta:
So, mapou, if only particles exists, does math exist when we speak it or write it, as sounds and written symbols are made of particles?
In my opinion, symbols are abstract entities and exist only in a different realm that our consciousness has access to. They do not exist in the physical world. However, infinity does not exist anywhere, not even in the abstract realm. It's nonsense. Otherwise, our spirits would sense it directly.
Second question: Does something like i = sqrt(-1) have absolutely no meaning even if we use it in formulas which successfully model how certain things in the real world work?
sqrt(-1) is, of course, nonsense. It's nonsense even in the abstract world of our conscious thoughts. Otherwise, we would sense it directly. When you write i, it could be any variable that represents any other number. So you can manipulate it in equations just like any number variable (e.g., x, y, z, etc.). But insisting that it represents the square root of -1 is nonsense since it contradicts the accepted definition of multiplication and numbers. Again, just my opinion.Mapou_{March 25, 2016
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Aleta:
Two questions: 1. So is there any mathematics at all? What am I doing when I write that (3 + 2i)^2 = 5 + 12i? Is this just meaningless?
No, not meaningless. Just nonexistent.
2. In your opinion, mapou, what does/b> exist?
In the physical universe, only particles, their properties and their interactions exist. Everything else is abstract or BS. But there is a complementary-opposite realm (it's all Yin and Yang) in which there are no interactions. In that realm, things just are and can neither be created nor destroyed. This is the realm of the entities that give us consciousness among many other things. Just my opinion.Mapou_{March 25, 2016
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So, mapou, if only particles exists, does math exist when we speak it or write it, as sounds and written symbols are made of particles? Second question: Does something like i = sqrt(-1) have absolutely no meaning even if we use it in formulas which successfully model how certain things in the real world work?Aleta_{March 25, 2016
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mike1962 @1, I agree. However, even if you knew the total number of particles in the universe (the universe is certainly finite), the number itself would still be abstract and nonexistent. Only the particles exist, IMO.Mapou_{March 25, 2016
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Two questions: 1. So is there any mathematics at all? What am I doing when I write that (3 + 2i)^2 = 5 + 12i? Is this just meaningless? 2. In your opinion, mapou, what does/b> exist?Aleta_{March 25, 2016
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What exactly does it mean for a mathematical concept to exist in the real world?
Neither Euclidean nor non-Euclidean geometry exists since they both embrace infinity.Mapou_{March 25, 2016
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Even numbers are abstract and non-existent. So what can one say about infinity? Again, I will wear Immanuel Kant's hat to make a point. If a number exists, where is it? If infinity exists, where is it? If distance exists, where is it? If time exists, where is it? If space exists, where is it? If spacetime exists, where is it? If a unicorn exists, where is it? And so on. I was going to add gravitational waves (spacetime ripples) to the list but I'm getting off topic already.Mapou_{March 25, 2016
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Do imaginary numbers exist in the real world? Do non-Euclidean two dimensional spaces exist in the real world? Do quaternions exist in the real world? How about pi? How about a perfect circle? What exactly does it mean for a mathematical concept to exist in the real world?Aleta_{March 25, 2016
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Should our mathematics be limited by the capacity of the physical or material universe?
It cannot be otherwise. I mean, do we exist in the real world in which we calculate in? Or do we exist in an imaginary (fictitious) parallel mathematical universe?Mapou_{March 25, 2016
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Does infinity exist in the real world?
No, but what other world is there? Did mathematicians or materialists invent a parallel universe where infinity exists while I was not looking?Mapou_{March 25, 2016
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Question:
Should our mathematics be limited by the capacity of the physical or material universe?
Answer: NoAleta_{March 25, 2016
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Correction: If the universe has the capacity to store 10^122 bits, I guess that means any number between 0 and 2^(10^122) - 1 (inclusive) could be represented. The rest of my comment stands, I believe.daveS_{March 25, 2016
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mike1962,
The universe only has so many bits of information. The largest number is limited by that.
Do you know what the approximate magnitude of this number would be? Edited: I think the first video answers my question by estimating the maximum information the universe could store as 10^122 bits. But numbers much larger than that arise in mathematics, and of course mathematicians deal with infinite cardinal and ordinal numbers all the time. Should our mathematics be limited by the capacity of the physical or material universe?daveS_{March 25, 2016
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Question: "Does infinity exist in the real world?" Answer: NoAleta_{March 25, 2016
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But if there is a biggest number, what would happen when you add one to it? You can't. That's why it's the biggest. The universe would not accommodate it. You will have reached the end of the universe's resources. Just like any computer. The trap is peoples' intuition leads them to believe there is no limit. But there is a limit. The universe only has so many bits of information. The largest number is limited by that.mike1962_{March 25, 2016
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