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. 

Personal Life Update: Discipline

I'm thrilled to pieces over the fact that for three days running, I have gotten up before sunrise and run at least one mile. My fastest time was on the first day, (7.35/mi.) whereas yesterday and today (8.45), I've done worse, probably because of soreness and tiredness from the sudden restart of a routine that I haven't trained myself to do in a very long time. If I can keep up the consistency, then I should be able to improve by leaps and bounds over the coming week or two, and after that, it'll keep getting easier.

I'm really strongly motivated to once and for all get back to my high-school habit of running every single day. I have stellar cardiovascular health as of now (120/70 blood pressure and 64 bpm resting HR), but my pulmonary and muscular endurance is embarrassing. I shouldn't be out of breath after one mile, when I could run 3 miles straight at a minute's faster pace at the age of 17 and not be as winded. I'm not running for Calorie loss, as I've noticed it's become popular to do: increasing and decreasing your speed to keep your body from becoming more energy efficient, so you burn more fat. No, I'm running to build up my long-distance endurance. I want to be able to run 15 miles at a 6:30-minute-mile average clip and feel relaxed and rejuvenated at the end. I once had that. After incorporating situps into my daily routine, I almost never experienced abdominal cramps again, and I have never had chronic pain in my knees or ankles or shins.

I want to experience that again. And the physical benefits will of a certainty accompany the exercise, because a 6-mile run will burn 500+ Calories without having to gimmick your muscles into utilizing glycogen stores, as the heady modern technical body-sculpting think-tanks now recommend.

I have a suspicion that my idle time outside of work is given to me in this period of my life to allow me to work hard at becoming a better man: to train in matters of fiscal responsibility, time management, physical fitness, practical theology, developing a disciplined routine, and accomplishing the task of "completing" this blog so that I will have no concern that I "missed something" by the time I become de facto disqualified from writing as a single man.

So there's four big areas in which I'm striving to apply and strengthen discipline:

• In a daily routine, to ensure that I go to bed early enough to be able to wake before sunrise.
• In a fitness regimen, to become outwardly the man a wife deserves, and for many more reasons.
• In career searching, to minimize the time spent in a rut, living at home.
• In writing, to deny the time outside of work to be wasted, so that my sojourn in economic dependence can not be said to have been a wasted period of my life. To complete the purpose of the blog, so that I can mentally move on to the next phase of my life's adventure.

And it's a daily choice to work at it. So far, I've made it 3 steps without stumbling. I'm encouraged by the thought of what I can accomplish with my hands (and feet! :) ) over a longer period of time, if I do not grow weary in being diligent with the time I'm given.

Time, after all, is a gift from God. Rather than see it as a curse (loneliness, prolonged debt), I will see it as a blessing (time to improve myself in other areas, and to reach out through this medium to glorify Him in the intervening time).

~ Rak Chazak

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

Treatise: Time Well Wasted

Treatise: Time Well Wasted

       If I told you that I’d wasted my time, after talking to you or spending a lot of time with you etc etc then it wouldn’t necessarily be an insult. A waste of time says nothing about the means by which the time was wasted. Time can either be spent well or spent poorly. This has to do with what you did with your time. And time is either wasted or not wasted. Wasting has to do with what you didn’t do with your time. Your time was wasted if you had something important to do that you didn’t do, because of whatever you did instead. And what you did instead could have been productive just as easily as it could have been unproductive. Therefore, it is quite possible to waste your time well. I have often done this in the past, and so I consider time spent talking to people and building relationships, when I could be studying something or working on an ongoing project, to be time well wasted. 

        Let me tell you how I came to have this opinion. When I was saved/’reignited’ (God knows the difference) in the Spring of 2010, I was drawn into a continual process of “self-learning,” self simply by virtue of the fact that I alone sat at my computer and followed the indications of my curiosity (which, like the conscience, is one way that I believe God’s Holy Spirit works through us to guide us to truth. In my experience, resolving a question has many times led to the discovery of a profound Biblical doctrine, scientific factoid, historical account, or mode of reasoning that has benefited me as a growing believer, and so I try to pray that God will manipulate my subconscious mind to lead me to think His thoughts after Him, so that I can “follow ‘my’ instincts,” knowing that they are His leading). I would spend several hours a day clicking links and reading extensive articles on websites such as Answers in Genesis, Christian-ThinkTank, Tektonics, TrueOrigin, ApologeticsPress, and later GotQuestions, Answering-Islam, and others. I discovered many sites after a time, but these were the key ones in the beginning, by which I learned vast amounts of apologetics and wrestled through the initial phase of wanting to verify to remove the chance of doubt returning. I believe I spent over 100 hours between mid-March and late May, absorbing and processing huge stores of Biblical information. A full half of those were consumed in the mid-period by a thorough analysis of “errors” in the Bible, to be able to consciously confidently accept that the Bible is inerrant. 

       The consequence of spending all this time researching Biblical Christianity was that I wasted the remaining time that I had not already wasted by oversleeping, playing video games, arguing on discussion forums, eating, watching movies online, etc, so that there was very little time to study, and my grades consequently suffered. Time wasted, but was it not well spent? Can time be any better spent than worshiping God, reading His Word, learning about Him and the world that He created, and in turn sharing it with others? I don’t think so. But can you nevertheless spend so much time simply learning about God that the other aspects of a life pleasing to Him, such as communion with other Christians, witnessing to the Lost, and the godly aspects of a life of personal responsibility, involving personal growth and academic, professional and civic success (by God’s standards) – that these aspects atrophy? Of course. And I believe that I began to do that then, and continued it without exercising the self-control I needed until about Summer 2012. 

       I’ve been getting better even since, and am now ‘taking a break’ (comparatively speaking) from all the reading I’ve done online, and am focusing more intensively on my professional development, and with having fellowship with other Christians. But looking back, I conclude that I wouldn’t have gotten to this point of spiritual maturity that I’m at now, if I hadn’t put in the long hours over the past three years to study and learn from those older, wiser, more knowledgeable and experienced than I. So was it time well spent? Absolutely. Therefore I consider it time well wasted. It was only ‘wasted’ in the sense that there were other things I could have been doing at that time, which suffered from neglect. But it was time well spent because I’ve now become highly prepared for future trials of faith and whatever ministry God has planned for my adult life. I feel nothing if not ready…confident. Now I can turn my energies toward things I’d semi-left behind in the meantime, and not worry about there being any loose ends. 

        I think that Satan and his workmen like to use the opposite method of Genesis 50:20 and attempt to use what God has intended for good and pervert it for evil. God can never be fooled this way—but we can, if we’re not careful. Is doing something good a good thing? Self-evidently so, yes. But can a good thing be done in a wrong way? You bet. For me, studying the Word and ‘loving God with my mind,’ as the Greatest Commandment reads in part, was my “good,” and neglecting to exercise self-discipline with respect to prioritizing my time between things with deadlines and things without was my “bad way” in which I did it. The question is, where should the line be drawn between continuing to do a particular good, and stopping it lest you do it to the exclusion of other goods? Everyone must decide for themselves on a case by case basis. If you must waste time, waste it well. But it is better not to waste it at all. 

~ Rak Chazak

Journal Entry: Thoughts About Being Bad At Keeping Track of Time and Numbers

I keep a typed Journal on my computer, and I've been keeping track of a few countdowns and "countups," such as the number of days since my birthday, and one of these countdowns is until a particularly unusual astronomical phenomenon, which I'll address in a future post (take note, if you google it, I am not of the opinion that it's a date that predicts the Rapture or Second Coming--the latter would be impossible, anyway, because we would be in the midst of the Tribulation, and that's patently not the case). Here's what I wrestled with one day.

Monday, July 8

Countdown 2 is numbering the days remaining until September 23^rd, 2014. But I’ve been notoriously bad at keeping countdowns before, or countups for that matter, if you look at my [previous Journal] entries where I was trying to keep track of how many of the 180 days in the school year had passed. I was off by double digits by the end. So these counts I have are partly an experiment to see if I can keep track of time accurately and consistently.  I’m going to attempt to lay out my reasoning below so that it’ll be possible to check my process at some point in the future.

Okay, here’s my check on Countdown 2: Apparently I’ve been counting down to September 13. Here’s what I did. I counted the rest of the days in July, not including the 8^th, and all the days in August. Then I counted 22 days in September, thus not including the 23^rd. That gives me 23, 31 and 22, respectively, which add up to 76. The days from July 9^th through next July 8^th, inclusive, are 365 days, and so for the next year (2016 is the next leap year). The total of all this comes to 806. Subtracting 10 days gives 796 days until September 13, not inclusive. So even with meticulous attention, I can still have an error of one or two days after only a little more than a half year, as you can see. This irks me. I should note that the counts on the back inside folder page of (Volume 10) were done prior to the recount I’m doing right now. This way, anyone reading after can adjust for my errors. It would make so much more sense to me if the number I had was higher than the one I just got, because then I could justify it by saying that I was counting inclusively with either today’s date or the final date. But alas, the error is the opposite, and so I can’t find any other conclusion than that I have made a counting error at some point when I wasn’t going day-by-day. How frustrating! For a guy who isn’t stupid, to be this poor with numbers, it’s immensely irritating to consistently make mistakes of the simplest sort – forgetting a number here or there, or a minus sign, or misplacing a decimal. This is the ironic reason why I was bad at calculus. Not because the logic was difficult, but because I would make minute numerical errors that would completely throw off the answer, and it would be impossible to find out where the mistake was without a monumental waste of time that wasn’t guaranteed to even be fruitful. Logic isn’t hard for me to keep track off, it’s the quantifying of things that aren’t distinguishable (one ‘3’ is the same as any other ‘3’). I’m not the sort of person who can discover a new mathematical equation, or program a computer. I have a certain level of respect for those who can and do, although I’m reserved, because I recognize that they’re not fundamentally more intelligent than me (some are, quite a few, however, are not), just as I am not fundamentally more intelligent than someone whose expertise lies in law or economics whereas mine is in the life sciences – the thing to be aware of is that our brains work differently, and our minds think differently. Some people’s ‘way’ of thinking is simply better suited for highly numerical things, like accounting, cyber security, or teaching hyper-advanced Calculus to PhD candidates. Then there are those who are good with people, not numbers, and still others whose mindset (meant here in the same way as the word “skill-set”) makes them better able to be self-sufficient than others. There is a certain level of intelligence possessed by those who can build their own house, repair their own cars, farm their own land and hunt their own food, that is far too often overlooked by those who have been blessed by those who do these things for us, allowing our minds to think about things beyond what’s necessary to secure our immediate survival. My exasperating failure to keep track of numbers without an aid is a small blessing to me that reminds me to be humble in how I view myself, and to be appreciative and respectful of others who do the things that I can’t. My understanding of how intelligence works, moreover, prevents me from being overmuch impressed with someone’s performance to the point of being blinded to their fallibility as a human being. Just because someone’s an accountant, doesn’t mean he knows how to best improve the economy. Just because someone’s a psychiatrist, doesn’t mean they know how to talk to people. Just because someone’s a neuroseurgon, doesn’t mean he can tell you whether mind is all brain or if there’s a soul. Just because someone’s a biologist, doesn’t mean he can tell you how life begins. Just because someone’s smart, in other words, doesn’t mean that their knowledge is real knowledge, or that they can apply what they know wisely. Even smart people can make dumb decisions. So my wisdom to you is to be wary. No one can require you to listen to them as if they have a handle on the truth themselves, because no matter how much they know or think they know, there is ALWAYS someone better than them. Someone who knows more, and who can think about the same things without making mistakes. My voyage of thought has taught me this much.  

After posting this, now that I'm connected to the internet, I checked with a google search and found that my original end-date of September 13 was in fact the partial solar eclipse I was thinking of. I confused it with the final total lunar eclipse of that year, which is the 23rd. Alas, this serves to demonstrate why I lose track of dates so easily. But at least now I have the time remaining until both, accurate to the day. :P

~ Rak Chazak