About edugovnet.com

Style Change

So far this site has mostly adopted the style of proposition-proof. However, that’s going to change somewhat moving forward. While we might occasionally return to a somewhat systematic development of some of the foundations of mathematics, it probably won’t be the focus. I’m also going to try to use “I” more instead of “we” in my explanations. “We” will mostly refer to “you and I”.

Broader Topic Range

I have some training in math, so I felt comfortable writing about it. However, I’d like to write about other topics that I find interesting as well. Some of them are even fringe areas. In order to help with this, I’ve developed some machinery that’s helped me wade through some of the wilder claims out there.

There are seven main “tiers” of knowledge. These tiers are not absolutes, they simply help me to think and talk about issues without always getting bogged down with whether or not something is “true”. I’m more interested in figuring what’s at least consistent with some of the better understood areas of collective human knowledge. It’s a bit of an epistemological project of mine. I’ve developed these ideas mostly with the help of some LLMs, because most people have better things to do than to spend their time with me talking about bizarre topics.

Some Terminology

Before I get started with the whole tier system, there are a few terms that I should delve into first

Tier System

There’s a lot going on in the table below. It’s explained in more detail below, so you can just skim it for now. You also don’t need to understand all issues mentioned to the right. The main takeaway from that is that there’s more uncertainty even way at the top of the table than is often mentioned. On the other hand, they do get mentioned by those who mention them often. You can find plenty of material about them elsewhere online.

Tier	example	issues
0a	math / logic / CS (theory)	[strong] theories can’t prove consistency, define truth and are incomplete via Tarski/Godel
0b	philosophy / Ethics / Law	Lacks falsifiability, lacks strict methods
1	Hard sciences / Physics / Chemistry / (some) Biology	Initial low entropy problem, other fine-tuning issues, vacuum energy and cosmological constant mismatch, what is dark matter, what is dark energy
2a	Weather forecasting, ecology, botany, oceanography	Softer scientific claims. They tend to be more statistical
2b	Medicine, Psychology, Economics	Softer, Statistical and also have to account for blinding in studies."
3	Persistent Anomalies, e.g. UAPs, Alien Abduction reports, Big Foot, Poltergeists	Data is extremely noisy. Often characterized by persistent accounts from people with all kinds of backgrounds. The accounts are often of such poor quality that the high-quality reports are the exception, not the rule.
4	Accounts involving unwarranted explanations or mechanisms for lower-tier events/observations, e.g. “An extra terrestrial being was flying a UAP.” – the extra terrestrial addition is an unwarranted addition to explain a T3 observation	These have to be subjected to thought experiments. They are extremely messy. They are often at the mercy of whether the right thought experiment has been proposed yet.
5	Claims that violate fairly well-established Tier 0a/1/2 (sometimes 0b) claims	These can range from discredited legal theories to more conspiratorial ones like “The collapse of the WTC can be best explained as a controlled demolition.”
6	Widely rejected claims, e.g. “The earth is flat.”	Sometimes these are so bad that they hardly spread at all and are mostly considered a joke.

The Tier System Explained

Tier 0a

Fields like: Math, Logic, and CS theory are generated through pure thought/computation. This is a bit like the fields of philosophy, ethics, law, and some others. However, unlike those fields, these fields are falsifiable as in

1. some claims are assumed to be true
2. rules are given for reasoning about claims.

Similarly, some claims can be shown, through the rules, to be false.

This is the tier we (you and I) are the most sure about. You might be tempted to think we’re absolutely sure about this stuff. Sometimes that’s how it’s presented, and often that’s how we think about it. However, there are some actual concerns, still. Probably the first issue, which doesn’t get mentioned enough, is error. Flawed proofs that appear to be correct have tricked some of the world’s best minds. Every math department probably gets emailed flawed proofs of results like the Riemann Hypothesis or a proof that P != NP from time to time. It’s a bit more frightening when the flawed proof is by someone within the department itself, and this does happen from time to time.

There’s hope for the future on this and most of the other tiers. For this tier we have been developing tools for formalizing mathematics tools like Lean and others, have been helping mathematicians to validate proofs with computers. Now, the validation is only as good as the setup, but these tools have been set up well, as far as I know. We all know computers aren’t perfect, but we all sense that, when it comes to blindly crunching through calculations and algorithms, we humans just can’t compete. The good news is that math will just become even more certain.

At a more fundamental level, though, mathematicians and logicians like Godel, Tarski, Lob, Turing, and others have shown that

1. The axiom system of ZFC is incomplete.
2. ZFC cannot prove its own consistency.
3. ZFC cannot define its own truth.
4. There’s no algorithm that will decide, after a finite amount of computation, whether a given Turing machine will eventually halt for a specified input.
5. There’s even controversy at the level of Logic. Intuitionists don’t use the excluded middle. I.e. they do not accept that \( p \vee \neg p \) always holds.

1,2, and 3 can all be strengthened, as they apply to weaker theories as well. This means they show up in simpler mathematical theories and are therefore more unavoidable.

Tier 0b

This tier includes fields like: Philosophy, Ethics, Law, and Theology.

Unlike the fields above, these are not [as] falsifiable. As with so many things, the situation can get a bit complicated. For example, in law a legal claim might lose in court and be falsified. So, there are test cases. Also, in ethics, some claims are aligned with current policy and so are more true than other claims that defy accepted policy. Theology claims can, likewise, gain and lose popularity within a religion.

Claims here tend to be valued by their external pragmatic utility - how useful they are to practitioners. For example, fringe theories about how income tax is unconstitutional have repeatedly failed in court. Thus, they aren’t as useful in the real world.

Tier 1

Hard Sciences. These are fields like Physics, Chemistry, and some of the firmer claims of sciences that are considered mostly Tier 2. For example, a claim like, “Many diseases are spread through microscopic infectious agents.” is no longer considered controversial at all. It’s neither a mathematical claim nor a statistical claim, so it doesn’t necessarily obviously fit in Tier 1 or Tier 2. However, it’s such a foundational (almost axiomatic) claim by now, that it’s no longer under serious doubt by practitioners – at all. It doesn’t explain every disease – like autoimmune disorders or many cancers, but it does explain a lot.

Tier 1 represents the claims about the natural world that we have the most certainty about. However, there are still some serious issues with even our most well-established T1 theories/explanations. For example

1. The entropy of the early universe is much lower than experts think it should have been. The physicist Roger Penrose calculated the odds at \(\ \leq 10^{-10^{123}} \).

2. What is dark energy?
3. What is dark energy?
4. There’s a huge disagreement over what the energy density of space should be. The predicted value, using Quantum Field Theory is \( \approx 10^{120} \) times greater than the observed value.
5. What’s the reason for the apparent fine-tuning of the constants of nature.

There might be more issues than the ones provided above. Those are some of the biggest issues that I, as non-practitioner, am aware of. I know that things often look a bit different from within the field, so an expert practitioner of Physics might disagree with some of what I have above. However, from what I can see from the outside, even Tier 1, in which we have the most confidence (about the natural world), still comes with some huge epistemological issues.

On the whole, Tier 1 fields are characterized by making so many successful predictions and having so much consilience with other fields and themselves that anomalies are more the exception than the rule.

Tier 2a

These are softer scientific claims. They might still use mathematical models, but

1. The theoretical footing of the model itself isn’t as solid as it is for Tier 1 claims.
2. The inputs to the models are statistical and hard to pin down exactly. This can happen with population models, climate models, etc…

This tier is for scientific claims that haven’t yet risen to the level of a Tier 1 claim. Keep in mind, as we have alluded to already, that different claims within a field can be categorized into different tiers. Different fields of study have claims that typically lie in different tiers. But, you can think of Tier 2 as a holding tier for claims, until they gain sufficient warrant over time from growing consilience.

This is where newer claims that haven’t been stress tested for consilience with the rest of established Tier 1 claims enough go here. After continued success, a Tier 2 claim will eventually move into Tier 1. On the other hand, if there are issues with reproducing supporting studies, then the claim loses consilience and moves further down into Tier 3 or possibly even into Tier 5 territory.

Tier 2b

This tier is, as the name suggests, quite similar to Tier 2a, except that it has to deal with the expectations of the test subjects. This includes a lot of results in fields like: Economics, Medicine, Psychology, Sociology. The need for blinding or controlling subject bias is the primary differentiator from Tier 2a.

Tier 3

This is the consolidated tier for all persistent claims of anomalies—observations or data that are unexplained by T1/T2 models but do not actively contradict them. The claims are often:

1. Multi-modal (multiple forms of data, e.g., eyewitness and radar).
2. Independent (reported across different people, times, and cultures).
3. Persistent (keep being reported over time).
4. Not controllable, callable, or theoretically cohesive.

This is where everything from Big Foot to the Initial Low Entropy Problem lives. The key differentiator within Tier 3 is the Warrant/Merit of the Underlying Evidence:

• High Warrant (High Merit) Anomalies: These rely on T1-level data. The initial low entropy problem is an example, as it is calculated using highly precise, warranted T1 laws of physics. It’s a gold-standard anomaly, even if its mechanism is T3/unexplained.

• Low Warrant (Low Merit) Anomalies: These rely on T3-level data (anecdotal, noisy, or hard to verify). A UAP sighting is an example.

Tier 3 is where the anomaly itself is housed.

Tier 4

This is the tier for speculative explanations for Tier 3 anomalies. In particular, they are for explanations that introduce mechanisms with lower warrant than what’s currently accepted for Tier 1 or 2 explanations. For example, a UAP is detected somehow – a Tier 3 anomaly. A Tier 4 speculative explanation might be something like, “An ET from another planet/dimension piloted the UAP.” It introduces a mechanism for the UAP appearance that is highly unwarranted given just the data.

My hope is that this will be a useful taxonomy to allow people to separate the bare observation from speculation that often feels natural.

Tier 5

This is the tier for claims that actively contradict Tier 1 and sometimes Tier 2 theories. A good example of this would be a claim like, “The collapse of the World Trade Center on 9/11 is best explained as a controlled demolition.”

As best as I understand it, the collapse of all of the buildings has been shown through computer models to be consistent with the idea that the fires did cause the collapses. On top of that, no evidence has been found in the seismological record that indicates any explosions occurred before the collapse of any of the buildings.

Tier 6

Claims in this tier are solidly at odds with what people understand about how the world works. For example, the claim that, “the earth is flat.” Flies in the face of what most people understand about our world. It lacks so much consilience, that most people treat the claim as a joke. These claims aren’t seriously considered by most people.

Annotations

Tag	Meaning	Applies To
(E)	Empirical	Based on direct observation or experiment
(T)	Theoretical	Derived from established models or equations
(A)	Anecdotal	Based primarily on personal testimony
(M)	Multi-modal	Supported by multiple data types/sensors
(R)	Repeatable	Observed repeatedly or reproducibly
(P)	Practically Testable	Can be tested or verified with reasonable resources
(P-)	Practically Untestable	Requires resources or conditions beyond current technical feasibility (common for cosmological Tier 4 claims, for example)

Three more possible annotations that can be used, but are mostly redundant with the Tier system itself are

Tag	Meaning	Applies To
(C)	Coherent/Consistent	Fits well with existing models – these mostly belong to Tiers 0 - 2
(C-)	Inconsistent/Contradictory	Conflicts with itself, Tier 0a or Tier 1 claims – these mostly belong to Tiers 5 and 6 claims
(S)	Speculative	Extends beyond current evidence – these are mostly Tier 4 claims

Some Considerations

The tier system itself is a Tier 0b framework that aims to assist a user in distinguishing the dynamics of different claims. It’s simply not appropriate to treat every claim like it’s a statement about mathematics. There really is no hope of ever establishing a claim, like “The sky is blue.” in the way that you can establish the claim, “1 + 1 = 2.” They operate very differently. The first can’t be fit into the paradigm of true or false. It’s messier because it refers to “the sky”. A complex thing in nature. The thing itself is complex (what exactly is the sky? Where does it begin and where does it end? etc…). Whereas the second claim is true / false / something else based on precise rules.

The system is an attempt to harmonize some heuristics about knowledge in a way that will find utility among its users. Furthermore, its utility will depend on how its used!

That’s it for this entry. We’ll apply this knowledge tier system to evaluating some fairly fringe theories in upcoming entries.

Thank you for reading!

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