May 14th, 2013
by Max Andrews
When we think of infinity we usually think of the usual two categorical distinctions: a potential infinite and an actual infinite. A potential infinite suggests that infinity is only an idea or a concept but doesn’t actually exist in the Platonic sense or in the physical sense. In any set, one may always be added. An actual infinite is the notion that there exists such a set, Platonic or physical, whichis infinite. A potential infinity may be symbolized by a lemniscate: ∞. An actual infinite can be depicted by the aleph-null or aleph-nought: ℵ0 (The Hebrew letter aleph with a subscript zero).
First, let’s have a brief refresher on set theory. A set is any collection of things or numbers that belong to a well-defined category. In a set notation, this would be written as {2, 3, 5, 7, 11} being the first five prime numbers, which is a finite set of things. Let’s simply signify this set as S. There is a proper subset (SS) of S. There are members in S that are not in SS, but no member of SS that is not in S.
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Posted in Logic, Mathematics, Metaphysics | No Comments »
April 27th, 2013
by Max Andrews
The fundamental question raised by these postulates of special relativity is how different coordinate systems (reference frames) are related, i.e., how one transforms between them. (x, y, z, t) denotes the coordinates of some event in frame S, what are the coordinates (x’, y’, z’, t’) in the frame S’ moving at the velocity v relative to S? But first, a clarification on proper time and coordinate time:
Proper time is time measured between events by use of a single clock, where these events occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a shorter proper time between two events than a non-accelerated (inertial) clock between the same events.
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Posted in Physics, Science | No Comments »
December 10th, 2012
by Max Andrews
Hey Max,
I guess since I requested the Q&A section, I’ll start it off!
I recently had a conversation with an atheist in which I walked him through the Kalam Cosmological Argument. This inevitably led into a conversation about what criteria a “first cause” must meet. It was difficult for me to explain, and for him to understand how God exists as a necessary being, or out of His own nature.
The atheist resorted to a version of ”Flying Spaghetti Monster” argumentation, in which he said, “How do we know that the first cause wasn’t a giant pink unicorn, or that two universes didn’t just mate and form ours?”. For obvious reasons, his argument is absurd. But what’s the best way to explain the concept of the first cause, and why it couldn’t be a “giant pink unicorn”?
Thanks a lot,
Richie Worrell (USA)
Richie,
I’m always amazed at some of the philosophical lunacy some atheists come up with. The mockery of using phrases like “flying spaghetti monster” or a “giant pink unicorn” weren’t originally developed in response to the kalam. They were developed in response to intelligent design suggesting the designer could be a spaghetti monster. I recall Dawkins using it several times and it has gained popularity in response to the ontological argument.
Nonetheless, let’s accept his flying pasta, pink unicorn, and sexual universes for the sake of discussion. Let’s recap the the kalam argument:
- Whatever begins to exist has a cause of its existence.
- The universe began to exist.
- Therefore, the universe has a cause of its existence.
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Posted in Apologetics, Arguments for the Existence of God, Kalam, Q & A | 7 Comments »
October 8th, 2012
by Max Andrews
When considered in the range possible explanans for the origin of information in the universe/multiverse the options must meet the conditions of causal efficacy and specificity. The first condition states that origin of information must be causal. Information does not arbitrarily pop in and out of existence but requires a source. The second condition states that the origin must sufficiently explain the specificity in information and must provide more than mere Shannon information.
Consider a computer as an example for information relay (a phenomenal entity). The computer is and can be used as a channel, it can be a receiver, and it can be a source of information. However, to say that the information in the computer no longer needs an explanation for its origin would suffer the problem of information displacement. What begs the question is from where did the information in the computer come? The answer would inevitably become a software engineer or a programmer. Undirected material processes have not demonstrated the capacity to generate significant amounts of specified information. Information can be changed via materialistic means. The computer can change the initial coding from the programmer and introduce noise on the sending and receiving ends.
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Posted in Multiverse | 7 Comments »
August 27th, 2012
by Max Andrews
In our experience, intentions get actualized any number of ways[1]: A sculptor by chiseling at stone, musicians by writing notes, engineers by drawing up blueprints. In general, all actualizations of intentions can be realized in language. Precise enough sets of instructions in a natural language can tell the sculptor how to form the statue, musician how to record the notes, and engineer how to draw up blueprints.
Why should an act of speech be God’s mode of creation? Language is the universal medium for actualizing intentions. The language that proceeds from God’s mouth in the act of creation is the divine Logos (Jn. 1.1-5). In the act of creation God the Father speaks the divine Logos in the power of the Holy Spirit. The divine Logos is not just language in the ordinary sense (utterances that convey information), but the very ground and possibility of language. Words need power to accomplish their end and God’s Word has that power (Is. 55.11).
Given that we are made in God’s image, the Trinitarian structure of creation is reflected in human speech.
“The word [goes] out of the mouth of God in such a manner that it likewise ‘[goes] out of the mouth’ of men; for God does not speak openly from heaven, but employs men as his instruments, that by their agency he may make known his will.”[2]
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Posted in Christianity, Mathematics | 2 Comments »
June 26th, 2012
by Max Andrews
Whenever probability is being considered there must be some type of relevant or total background information (usually depicted as k). The immediate objection when applying a probability rule or calculus to the fine-tuning of the universe in a multiverse scenario would be to say that this is universe is not an appropriate random sampling. In other words, if we know of [at least] only one universe with these values the random sample size is precisely 1; thus, no random sample can be used to assess the probability of certain values of physics in the argument. In statistics a random sample drawn must have the same chance of being sampled as all the other samples. Since we know of only one universe we do not know what the range of values for the constants and physics could be. Additionally, since we don’t know how narrow or broad these ranges could be there’s no way of drawing out any probability based argument for fine-tuning. However, we can know what other universes would be like if the values were different. If our natural laws have counterfactuals that are in any way incoherent then this is an appropriate sampling. Also, to make this objection and advocate that we just so happen to live in a life permitting universe in the multiverse then this objection cannot be made since the claim that we happen to life in a life-permitting one amongst countless others suggest we can know what the other samplings are.
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Posted in Cosmology, Mathematics, Philosophy of Science | 1 Comment »
April 18th, 2012
by Max Andrews
Information theory is the branch of probability theory that deals with uncertainty, accuracy, and information content in the transmission of messages. It can be applied to any system of communication (electric signals, fiber optic pulses, speech, etc.). Random signals, known as noise, are often added to a message during the transmission process, altering the signal received from that sent. Information theory is used to work out the probability that a particular signal received is the same as the signal sent. In transmitting a sequence of numbers, their sum might also be transmitted so that the receiver will know that there is an error when the sum does not correspond to the rest of the message. The sum itself gives no extra information, simply a confirmation. The statistics of choosing a message out of all possible messages (letters like the alphabet or binary digits for example) determines the amount of information contained in it. Information is measured in bits (binary digits). If one out of two possible signals are sent then the information content is one bit. A choice of one out of four possible signals contains more information although the signal itself might be the same.
For more information see John Daintith and John Clark’s The Facts on File Dictionary of Mathematics (New York: Market Book House, 1999), 97.
Posted in Mathematics | No Comments »
April 18th, 2012
by Max Andrews
A method of proving mathematical theorems, used particularly for series sums. For example, it is possible to show that the series 1 + 2 + 3 + 4 + … has a sum of n terms of n(n + 1)/2. Firest one must show that if it is true for n terms it must also be true for (n + 1) terms. According to the formula
Sn = n(n + 1)/2
if the formula is correct, the sum of (n +1) terms is obtained by adding (n +1) terms is obtained by adding (n + 1) to this
Sn+1 = n(n + 1)/2 + (n +1)
Sn+1 = n(n + 1)(n + 2)/2
This agrees with the result obtained by replacing n in the general formula by (n + 1), i.e.:
Sn+1 = n(n + 1)(n + 1 + 1)/2
Sn+1 = n(n + 1)(n + 2)/2
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Posted in Logic, Mathematics | No Comments »
February 15th, 2012
by Max Andrews
Posted in Cosmology, Science, Science and Religion | 2 Comments »
February 8th, 2012
by Max Andrews
The Word of the Week is: Multiverse
Definition: The term to designate the existence of many worlds or universes. Contrary to just one world, a uni-verse, there are many worlds, a multi-verse.
More about the term: The multiverse is not monolithic but it is modeled after the contemporary understanding of an inflationary model of the beginning of this universe suggesting a plurality of worlds. Max Tegmark has championed the most prominent versions of the multiverse.[1] There are four levels of the multiverse.
- Level One: The level one is, for the most part, more space beyond the observable universe. So, theoretically, if we were to go to the “edge” of the universe there would be more space. Having this model as a version of the multiverse may be misleading because there is still only one volume, landscape, or system involved. A generic prediction of cosmological inflation is an infinite space, which contains Hubble volumes (what we see in our universe) realizing in all conditions—including an identical copy of each of us about 10^10^29 meters away.[2]
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Posted in Cosmology, Philosophy | 2 Comments »
The Language of God
by Max AndrewsIn our experience, intentions get actualized any number of ways[1]: A sculptor by chiseling at stone, musicians by writing notes, engineers by drawing up blueprints. In general, all actualizations of intentions can be realized in language. Precise enough sets of instructions in a natural language can tell the sculptor how to form the statue, musician how to record the notes, and engineer how to draw up blueprints.
Why should an act of speech be God’s mode of creation? Language is the universal medium for actualizing intentions. The language that proceeds from God’s mouth in the act of creation is the divine Logos (Jn. 1.1-5). In the act of creation God the Father speaks the divine Logos in the power of the Holy Spirit. The divine Logos is not just language in the ordinary sense (utterances that convey information), but the very ground and possibility of language. Words need power to accomplish their end and God’s Word has that power (Is. 55.11).
Given that we are made in God’s image, the Trinitarian structure of creation is reflected in human speech.
Posted in Christianity, Mathematics | 2 Comments »