I had intended to write about our country's approaching death loop, but then Google's AI helped me find a more troubling topic: Google's AI “summaries”

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“I’m not sure you’re authorized to know that”

So, I started a post about this: the House Minority leader’s stated intention to go after Trump donors when he and his associates regain control of either the House, the Senate, or both:

Hakeem Jeffries Vows to Criminalize White House Ballroom Donors

“More likely this is part of what Donald Trump has been doing since day one of his presidency,” Jeffries claimed, “running the largest pay-to-play scheme in the history of the country and probably soliciting, uh, donations from people who’ve got business, uh, before the United States government.”

Jeffries went on to promise that the matter “will” be investigated, insisting, “All of this will have to be uncovered. It will. And these people are gonna be held accountable, uh, no matter how long it takes.”

He closed with a thinly veiled threat aimed at Trump’s supporters and donors: “That’s gonna be the reality of the situation, and that’s our warning to all of these people participating, uh, in this scheming to manipulate taxpayer dollars and, of course, to destroy the people’s house. The White House, uh, belongs to the American people. It doesn’t belong to Donald Trump.”

I’d thought to bring up similar threats made by Jeffries last week to pursue not only White House ballroom donors, but anyone who’d “collaborated” or cooperated with Trump during his administrations. I’d seen videos of Jeffries saying that, but couldn’t lay my hands on an example immediately, so I turned to Google’s new, enhanced search feature. Imagine my surpise to learn that, according to Google, it never happened:

AI Overview

Based on recent public statements, there is no evidence that House Democratic Leader Hakeem Jeffries said, "When Democrats retake power, we’re going to seek prosecutorial vengeance"

. The statement is a fabricated quote. In fact, Jeffries has publicly criticized the use of the justice system for political retribution. 

Well. I knew I’d seen him make that exact threat, so I dug deeper, without the assistance of Google’s censors, and here’s what those guardians of knowledge deny exists:

Here’s the full video of Jeffries vowing to take vengeance. Begin at 2:25

And here’s the danger of the new AI research tool: very, very few Google AI users go beyond what that company’s algorithms tell them is a true and accurate answer to their question, even when, as seen here, that summary is neither. Non-political questions seem to yield objective results* , but political issues not so much, yet most questioners are content to rely on what Google’s far-left programmers feed them, and don’t check the original source materials.

Pew Research Confirms Google AI Overviews Is Eroding Web Ecosystem

Research shows only 1% of users click a link in AI summaries. It also confirms that Reddit, Wikipedia, and YouTube are the most cited.

According to the research findings:

Users End Their Browsing Session

“Google users are more likely to end their browsing session entirely after visiting a search page with an AI summary than on pages without a summary.

This happened on 26% of pages with an AI summary, compared with 16% of pages with only traditional search results.”

Users Refrain From Clicking On Traditional Search Links

It also says that users tended to not click on a traditional search result when faced with an AI summary:

“Users who encountered an AI summary clicked on a traditional search result link in 8% of all visits. Those who did not encounter an AI summary clicked on a search result nearly twice as often (15% of visits).”

Only 1% Click Citation Links In AI Summaries

Users who see an AI summary overwhelmingly do not click the citations to the websites that the AI summary links to.

The report shows:

“Google users who encountered an AI summary also rarely clicked on a link in the summary itself. This occurred in just 1% of all visits to pages with such a summary.”

*Here’s an example of what would seem to be a useful, objective answer to a run of the mill inquiry. I know nothing about the physics involved, though, so it’s possible that the answer is entirely wrong; nevertheless, I’m willing to trust it, but unfortunately, most users are extending that trust to everything Google’s AI search engine produces, which spells trouble.

These are results for what's the mathematical explanation for how something like a garden hose can wrap itself into a knot?

AI Overview

A garden hose wraps itself into a knot due to the interplay of entropy, statistical mechanics, and topology

. The mathematical explanation is that random movements will almost always lead a flexible, agitated string toward one of the vast number of tangled configurations, rather than the single, perfectly untangled state. 

The principle of entropy

In physics, the second law of thermodynamics states that the entropy (or randomness) of a closed system will naturally increase over time. A straight, untangled hose is a state of very low entropy, as it has a high degree of order. In contrast, there are countless ways for that hose to be tangled, representing a state of high entropy. 

  • Statistical probability: Any time the hose is moved, shaken, or jostled, the universe is simply choosing one of the available configurations. Because the number of tangled states is exponentially larger than the number of untangled states, a random motion almost guarantees a move toward a more disordered state.

  • A simple analogy: Imagine a box filled with puzzle pieces. There is only one way for the puzzle to be perfectly assembled, but an enormous number of ways for the pieces to be in a jumbled mess. If you shake the box, it is far more likely that the pieces will settle into a messy state than a completed one.

Mathematical knot theory

Knot theory is a branch of topology that classifies and studies the properties of mathematical knots. While mathematical knots are closed loops (unlike a hose with ends), the principles help explain the entanglement process of flexible objects. 

  • Invariants: Mathematicians use concepts like "crossing numbers" and "polynomial invariants" to classify and distinguish between different knots. Experiments with agitated strings have found that the longer and more flexible a string is, the more complex the knots that form.

  • Reidemeister moves: Knot theory describes how a knot can be transformed, or untangled, using a series of three basic moves called Reidemeister moves. However, these transformations are often difficult to apply in the real world, which is why a tangled cord is so hard to quickly untangle. 

Physical and mechanical factors

The mathematical probabilities are amplified by the physical characteristics of the hose and the actions performed on it.

  • Length and flexibility: Research has confirmed that longer and more flexible strings are far more likely to become knotted. A short, stiff object simply doesn't have enough length or the freedom of movement to form a coil or a loop that a free end can pass through.

  • The tumbling mechanism: The process of a hose wrapping itself up usually begins with a loose, random coiling motion. One free end can then "braid" its way through a loop created by another part of the hose, initiating the first crossing.

  • Kinks versus true knots: It is important to distinguish between a temporary kink and a stable topological knot. A kink is a local, folded-over section that can be unbent, but it can also be the first step in forming a stable knot. The stiff, non-elastic nature of many hoses, combined with a "memory" of a coiled shape, makes them especially prone to kinking.

  • Improper coiling: The way a hose is stored also affects tangling. When you coil a hose by pulling the end off a fixed reel or hook, it introduces a twist with every loop. This added torsional energy increases the likelihood of a more complex entanglement. 

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