#math science

Wow you opened the email!

I was afraid I lost you at "Math and Science." But don't worry, math and science can be fun if it somehow results in holiday cookies. For instance 2 cups of pecans + 1 cup of butter + 1 cup of brown sugar + 2 cups of flour + 1 tablespoon of vanilla + 1 egg + 3 teaspoons baking soda = the butter pecan gluten free cookies at tomorrow's meeting. In addition to the gluten free goodness above, the Gallatin Math and Science Club is collaborating with us to bring a plethora of insomnia cookies! I bet you like mathy and sciency things now.

But alas, I have sad news: this is our last meeting of the semester :( And no you cannot ask for an extension! Each one of you will be graded on a 0 to I'll give you a hug scale based on nine criteria:

How many cookies you can stuff in your mouth

Snark

Fashion forwardness (for instance aprons, smocks, and bibs are forward rather than backward)

Casual use of the word "cisgender"

Subversion of elitist coloring pages

Dance moves under the influence of alcohol and/or Michael Jackson

Feeling uncomfortable that individualism is also a construct

Reading my emails (preferably aloud in public spaces)

Hanging out with me when I am lonely

Final grades will be given out tomorrow at the end of our meeting so you have until then to boost your score. Extra credit goes to anyone who gives your club officers creepy compliments. If it makes everyone one in the room feel awkward, then you're doing it right.

In case you somehow decided to open this C&C email for the first time this semester during finals and now finally want to know when and where to come to one of our meetings, we will be in the 5th floor Gallatin Student Lounge from 1pm to 3pm tomorrow.

The genesis in my head of what eventually became Awareness Logic started as a thought experiment. I was trying to imagine how to define in the most fundamental terms a data matrix that could theoretically express all the information in the universe. A tall order to be sure!

The first logical choice was binary, but I quickly realized there were some real problems with this. Now, there’s a whole group of people (many of them programmers) operating on the more or less unexamined assumption that the entire universe can be expressed in binary terms. Binary is simply a two position number system consisting of 0 and 1, and, of course, has proven perfectly useful for countless digital applications. However, when the challenge is to map everything into a singular database, there are at least two important concepts that cannot be expressed exclusively in binary terms. The first is infinity, and the second is the role of the observer to any given observation expressed in binary.

First of all, how do you express infinity in binary? As all the 1s and 0s possible in the universe? I can write the word and conceive the concept of infinity, but how does infinity as a value get expressed using only 1s and 0s?

This brings us to the problem of expressing the role of an observer with binary. Suppose you establish as an observation a digital binary switch that has an output of 1 or 0. What is the value of the switch itself? How do we establish its basic function? You need a set of more 1s and 0s to explain that the switch is part of a lager set, and to define how it works.

 Okay, so then what is the value of an observer or operator in this equation? Why, another set of 1s and 0s of course! And the world around me is more 1s and 0s, etc.

 But how do we ultimately make the distinction between all those 1s and 0s? In order to differentiate this multitude of sets and functions, the concept of set and subset itself is essential. Without a higher order language to translate these values into distinct sets, it’s all just a meaningless endless series of 1s and 0s.

With Awareness Logic we have three fundamental values to work with instead of two. It is a system of balanced ternary. However, instead of using the standard values of  -1, 0, and 1 for balanced ternary (which will come into play later),  in  Awareness Logic 0 and 1 are the complimentary values instead of -1 an 1 (as in binary), and both are related to ∞ as the third value (instead of the standard balanced ternary 0). This structure not only creates an automatic distinction between finite and infinite values, it also establishes a basic set structure with the set of 0 and 1 as a subset of ∞.

Now before we go any further, let’s establish some clear definitions for the terms of the Axiom of Awareness.

 All values simultaneously reference zero (0), infinity (∞), and one (1), the unique intersection of which is equal to the Awareness Point (أ).

 0∞1 = أ

So, we have four values here: 0, 1, and ∞ plus  أ (the Arabic letter alif) as the symbol for the awareness point. The fourth one is a new concept that will take some explaining, but the first three are relatively simple to define.

 Zero (0) here is simply a unit of no relative value.

 One (1) is a unit of relative value.

Establishing the relative nature of both 0 and 1 is essential because in Awareness Logic these are contrasted to infinity (∞) as distinctly finite values, not absolutes.

Infinity (∞) is understood simply as a value without bounds; a value that is not finite.

 Some mathematicians hate the very concept of infinity itself because by its very nature, it does not fit neatly into any finitely definable system. So, clearly defining ∞ in this, its most basically accepted mathematical terms is essential.

∞ is not properly considered a number, but in Awareness Logic it is mostly used like a number. When working with the value of ∞ in Awareness Logic it is important to generally disregard any philosophical or cosmological implications inherent to the concept of infinity, and stick to its most commonly accepted usage as a value without bounds.

One of the most routine usages of ∞ is to represent an increase without boundaries, and understanding exactly what progression of values ∞ represents is generally context dependent. We can note how this works in three common examples:

 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, → ∞

 333.3333→ ∞

 0→ ∞ →1

In the first example, we understand that ∞ represents the endless continuation of the series of numbers from 0 to 9 with 10, 11, 12, etc. In the second example, we understand that the decimal value is an endless series of 3s. The third example is a bit different because in this case, the 0 and 1 represent clear boundaries, however we can infer from this that there is a potentially infinite series of values between the two. This usage is particularly relevant to Awareness Logic.

0 and 1 define each other’s existence. As is expressed with binary, these are the two essential finite values. As 0 and 1 work together establish the range of finite values, 0 and 1 as a pair contrast with ∞ to establish the dynamic of finite and infinite. The differentiation between finite values and infinite potential is necessary to express any set function.

The fourth essential to define from the axiom of awareness is the awareness point (أ). 

The first letter of the Arabic alphabet, alif, is used here as the symbol for the awareness point. This letter was chosen to represent the awareness point because not only is it associated with some appropriate symbolism in Islamic culture, it also implies an association with its linguistic cousin in Hebrew, the aleph (א), which is used to represent the transfinite numbers of set theory. The mathematical concepts behind أ and א are similarly related by this usage as well.

 (Note: The alif-hamza form (أ) was chosen instead of the stand-alone form (ا) because of the latter’s similar appearance to the character “1”.)

The awareness point (أ) is a unique value and essentially a new number that expresses an implied but previously undefined value. Because it represents the intersection of both infinite and finite characteristics, أ can be understood as the essential reference for our awareness of all numbers and values, hence the use of the word “awareness” in Awareness Logic.