Text Treatise: Thinking Big, Space Fantasies, and Groping for Infinity

Try to keep up :)

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I've tried to create super-hyper-operators**(see attribution at bottom of article)** to express numbers so large that they're meaningless in this universe, even as expressions of mass, information, energy, power, time, probability, volume etc. 

The  idea is  twofold: 1) to help me fantasize more scientifically accurately aabout imaginary alternate universes and 2) to help me appreciate how big infinity really is.  

You know that 10^10 is 1 with 10 zeroes after it. 10^10,000 would be 1 with 10,000 zeroes after it. 10^100 is known as a Googol. 10^10^100 is 1 with a Googol of zeroes after it, known as a Googolplex. In comparison, 10^10,000 is 10^10^4, so a googolplex would be 10^10^96 times greater. That's assuming that you add the second exponent if you multiply, I'm not sure if you would have to exponentify the numerator to multiply the exponent so as to add the second exponent. Which just shows you even more, how massive the number is.  

But then I tried inventing a new system for showing even larger numbers. 

The next thing I tried to do was create a symbol to represent the next level of hyper operation. I used an up arrow but the keypad doesn't have that. 10x10=10^2. 10x10x10=10^3, and so on, we all know. 10^10=10,000,000,000. 10^10^10= 10^10,000,000,000. A massive number. 1 followed by ten billion zeroes. In contrast, a googol is 1 followed by 100 zeroes. But 1 followed by 10^10 zeroes is still nothing compared to 1 followed by 10^100 zeroes, which is a googolplex. 

Now, 10^10=10>2. 10^10^10 = 10>3. 10^10^10^10 = 10>4.  10>2^2 is a googol (10^100, 10^10^2) and 10>3^2 is a googolplex (10^10^100, 10^10^10^2)

So my next big numeral to invent was 10>100 (or 10>(10^2), not to be confused with 10>10^2. The latter would have 10 "^"s with the 11th position being a ^2; the former would have 100 "^s" -- I'm doing my best to stay consistent with established mathematical symbolism). 

If I wrote 10>10>10 that would not be 10>1 followed by 10 zeroes (10>(10^10) would be that), it would be 10>10 raised to the tenth power successively 10 times, or 10 to the googolplex to the googolplex to the googolplex. MASSIVE, MASSIVE NUMBERS.   And then I pretended that I could comprehend the size of a universe where the average planet was 10>100 km in radius, supposed that I couldn't go any higher, and went to bed mentally exhausted. 

Texting Treatise: Pragmatism is Impossible in an Infinite Universe

"Just came across a tidbit on the traveling atheist that has interesting implications. It's a conditional that applies to anyone who'll say that the universe is infinite in either time or space or both, and for whom morality is defined as doing the greatest good for the greatest number of people. And diminishing suffering. That's actually logically incoherent.

In an infinite universe, there'll be an infinite amount of happiness and an infinite amount of suffering, so nothing you do will have an impact on the total number of either. Consequently, a morality based on the greatest benefit for the greatest number CANNOT BE TRUE if the universe is infinite in any aspect. It is logically contradictory. Therefore, the moral imperative for doing good rather than evil CANNOT just be a pragmatic decision. It must be justified some other way.

'Love logic."

Afterthoughts:

Proof of God: The Argument From Possibility

The Argument From Possibility

                I was recently watching another episode of the traveling atheist (‘Closer To Truth’ with Robert Lawrence Kuhn) and the episode focused solely on the ‘Ontological Argument for God,’ or in other words, the argument from existence. Meaning that some clearly obvious facts about existence are taken and used as the axioms in a logical proof that is intended to demonstrate that God’s existence is necessary.

                Why everyone seems to zero in on Anselm of Canterbury’s “that than which nothing greater can be conceived” thought-experiment as the best representation of the Ontological Argument (or synonymous with it, even), is beyond me. At least one person in the episode (the series is presented through interviews with philosophers, scientists and theologians) made the statement that to take Anselm’s pondering on ‘the greatest conceivable being’ and to hold this up as a proof is to stretch it far beyond what it’s intended to do, even by Anselm himself—and he placed the blame on well-meaning but incorrect theologians in time past. What that interviewee said was that Anselm simply suggested that whatever you conceive of a thing, the actual thing itself is by definition going to be ‘greater’ than the conception of the thing. That seems benign enough, and it’s a satisfactory conclusion to me, who has wondered since first introduced why this is held up as the best that Christian philosophy can do.

Wiki Commons image. Alvin Plantinga.

                The last interviewee of the episode, Alvin Plantinga, also made a similar remark about Anselm, that as stated, the argument doesn’t work. But he had apparently developed an improvement of the argument, which he called “The Argument from Possible Worlds,” or something similar. While I didn’t quite follow his construction of his proof, I immediately understood the summary: he said that as constructed, the proof leads someone to be totally committed to the reality of God’s existence as a necessary fact, provided that he begin with the acknowledgement that it is possible for God to exist. For anyone to believe that God does not exist, they would have to claim that it is impossible for God to exist.

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                This immediately made sense to me, because I’d constructed a similar logical proof before. I don’t believe this is the same proof Plantinga’s developed, and I don’t seek to take credit for his idea, but the thought process is similar, and he did remind me of it. Without further ado, here’s the Argument from Possibility.

The Choice

                Like Plantinga’s Possible Worlds, the proof does not unilaterally demonstrate God’s existence. What it does instead is to show that one must choose between the belief that God’s existence is either a fact, or that it is impossible. To believe that it is possible and yet that it is not actual, is to commit a logical contradiction. It is not possible for God’s existence (1) to be possible, and (2) for God not to exist.

Defining Possibility