Trevis Litherland’s Post

A good reminder for those whose natural impulse is analysis: Describing is not Explaining. Continue reading below on the complexity and power of Causality.... https://lnkd.in/gEUW8xkP

The attention mechanism isn't a collection of gears and pulleys but a collection of matrices and mathematical operations. Using the attention mechanism, a model can focus on what it finds most useful to aid its next prediction. For example, if we want a model to fill in the missing part of this sentence: "I need _______ to spread on my bread," the model would pay attention to two words: "spread" and "bread" to fill in the missing word. By paying attention to these words, it would understand that what should be in the missing space is a word that represents something edible and spreadable. With this intuition in mind, it would be able to guess with a high probability that the word should be "butter" because it fits these criteria.

Solving the nonsymmetric stochastic inverse eigenvalue problem? Well, talk about setting things in motion.¹ That's German; and Greek to me, Newton. To paraphrase Stefano Palminteri here, how does understanding sentences that mix Italian, French and English square with the stochastic parrot hypothesis?² 𝘓𝘦𝘨𝘨𝘪 𝘲𝘶𝘦𝘴𝘵𝘰, 𝘱𝘭𝘦𝘶𝘳𝘦𝘳 and go scrub.³ Ha-ha, hallucination with and without psychosis! See here for that which was to be demonstrated (𝘲𝘶𝘰𝘥 𝘦𝘳𝘢𝘵 𝘥𝘦𝘮𝘰𝘯𝘴𝘵𝘳𝘢𝘯𝘥𝘶𝘮) and was quite easily done (QED).⁴ So, go to pot! You're not putting bugs or getting germs in my field.⁵ 💋 Al It is now Tuesday, 4 June 2024, 11:38:55Z. ¹ https://lnkd.in/enMpe_-i; https://lnkd.in/ewzFhn3Q ² https://lnkd.in/eFWszzAc ³ https://lnkd.in/eHgA4KKv ⁴ https://lnkd.in/eKiFvr-9 ⁵ https://lnkd.in/eQVFGWnp Credit: the image was accessed at https://lnkd.in/er_uwEK6.

https://lnkd.in/g4BidNXQ I was reading this research article last night about threshold graphs, shifted complexes, and graphical complexes written and published by Caroline Klivans. See I read this article to understand another research article of topological combinatorics for vertex simplicial complexes written and published by Dr. Anton Dochtermann. I am still a little fuzzy on what I read but I noticed certain patterns in a threshold graph and what shows that a vertex has a face and non-face on each point and edge that connects the simplexes. There are some detailed proofs for each theorem in the Klivans article and the definition and propositions of threshold graphs and simplexes is what I found interesting. #combinatorics #thresholdgraphs #graphtheory #learning #researcharticles

I honestly think this horsw•√π÷ is best reserved for new principles with less concensus on how they work. That being said, I will clarify both by which axioms of mathematics and by which axioms of logic (a) I foundationally operate — "get to know this sailorly-swearin', ostensible cognitive trainwreck of an author who might just be humanity's one-last-shot in a very Parker-and-Stone-grained reference frame on r reality, and (b) I was operating for the sake of my proof, and tend to operate as I delve into proof as I envision a mathematician wants to see logical statements laid out before him or her. Maybe a sweeping introduction regarding probability, DESPITE the obvious success of my deductive process (I'm sorry; since I fixed that case 1 debacle, has anything been jumping to your mind as "oooo he's not gonna be able to to fix to address this the nuanced little exception to that claim...?" Nah, didn't *think* so. I know they're gonna come at me from every angle, are sharpening their protractors as we speak. I'm going to give them a nice pincushion in which to release their anger that isn't me or the success of my proof to go big. It's what the problem needed. My sort of logic tree shape preference. It still grows by the same set of rules, even if it maybe sways banyan per axiom of choice, every once in a while. https://lnkd.in/gn_DAWs6

We sometimes have a very loose interpretation of the word "is". Unhelpfully so. Call me old fashioned but "is" to my mind entails something happening now. Things that people imagine will happen in a few years, are not - at least to sticks-in-the-mud like me, an "is". People imagine many things. Often they have been imagining the same thing for many, many years past if we care to look, always for a few years in the future. So we need, I think, to be careful to differentiate what is in the imagination, from what is actually an "is". We should also understand that a memorandum of understanding, or MOU, is fundamentally about things that are in the imagination. That is not to denigrate their value or usefulness. The imagination is after all a powerful place. Those things that "are" always begin with imagination at some point. So MOU's are a legitimate process between parties for thinking about those things ahead of time. Ahead of time being the key phrase. They are not yet an "is". They might become one, but they aren't yet. More importantly, there is no guarantee they will. Things of imagination have a high attrition rate. We all like a bit of optimism every now and again, and in that per se there is no crime. But in deploying it let's be careful to understand what is already an "is" and what isn't. And for a free tip on the side, where numbers of an "is" are given and compared with an imagined, watch the units quoted. With a microscope. If the units are not the same, inspect - and think - doubly carefully.

Cognitive Load Theory Revisited https://buff.ly/4eOUpXt

Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern. However, the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …  called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation ζ(s) = 0 lie on a certain vertical straight line. This has been checked for the first 10,000,000,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.

In a complex adaptive system there is no linear causality... Forecasting and backcasting both assume a degree of predictable relationship between cause and effect; so in complexity, we focus on ‘side casting’, casting around in the present to discover opportunities https://lnkd.in/d98ErfDj

Junk Theorems And Junk Theories = I will begin this post with: Junk Theorem and then give an example of: Junk Theory = Here is an example of a Junk Theorem: Divisibility Test by 63 For example, 1071 is divisible by 63. Here is how this Junk Theorem works: Since 63 is the product of 9 and 7 - we first test divisibility by 9 and then by 7. Divisibility by 9 is easy - just add all the digits: 1 + 0 + 7 + 1 = 9 If the sun is divisible by 9 then the number is divisible by 9. To test divisibility by 7, do this: 1) Remove the last digit: remove 1 from 1071 leaving 107. Then subtract twice of the last digit from the remaining number: 107 - 2 = 105. If this number is divisible by 7 then the original number is divisible by 7. You can repeat with 105: 105 remove 5 = 10 10 - 2*5 = 0 So 105 is divisible by 7. That means 1071 was divisible by 7. That means 1071 was divisible by 9 x 7 = 63 One key insight is you can apply Junk Theorem recursively. For example consider: 7281906345771111 - if you add the dights it comes to 63, add them again it comes to 9 ... so the original number 7281906345771111 is divisible by 9. You can do the same for divisibility by 7. = Let me now claim this: THE THEOREM OF DIVISIBILITY BY 63 IS A JUNK THEOREM!! You are stunned at this point. You say: this seems to be a beautiful theorem - how can this be a Junk Theorem?? Here is the issue: This theorem is valid for decimal representation of a Number. We demonstrated divisibility of 1071 by 63 - assuming the Decimal Representation (also known as base 10 representation). The theorem is not a: Theorem about Number The theorem is a: Theorem about base 10 representation of a Number This Junk Theorem (test of divisibility by 63) is not valid in other based like base 5 representation of a Number. You can verify this fact yourself. Do the calculation by hand - it is a good exercise. This is a stunning revelation: Number (Theorem holds in any base representation) vs Representation of Number (Theorem holds in a particular base representation) In other words: Theorems on Number (Genuine) vs Theorems on Number Representation (Junk) Clear?? = Now that I have explained Junk Theorem, let me give an example of a Junk Theory: Numerology (known before the 20th century as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in words and names. When numerology is applied to a person's name, it is a form of onomancy. It is often associated with astrology and other divinatory arts. You are not satisfied, you demand one more example. That's also easy, thank God: Agile The whole point of Agile is to talk about Agile. Agile is about representation of agile in Jira or Asana or Miro boards. All these talk about Agile doesn't make you actually agile. Agile is an exemplary Junk Theory. Satisfied now? Debashis