Does the square root of 2 exist?

In a recent OP I looked at a discovery by mathematician Norman Wildberger, who found a general method for generating power series solutions of polynomial equations of any degree. Wildberger has an interesting, extremely unconventional and (in my opinion) flawed philosophy of mathematics, which among other things denies the existence of irrational numbers. Here he explains why √2 doesn’t exist, at least not in the way that mainstream mathematicians thinks it does:

There’s lots to criticize about this, but I’ll save it for the comments.

Wildberger makes waves

Some of you may remember a wild discussion we had at TSZ a couple of years ago, spanning eight months, debating whether “3” and “3.0” refer to the same number and whether measurements can be expressed using real numbers. (Yes, really.) One of the questions that arose during that discussion was on the boundary between pure and applied mathematics, and DNA_Jock referenced the mathematician Norman Wildberger’s opinion on that topic.

Continue reading

Are you smart enough for the Oval Office?

In response to comments questioning his mental stability and cognitive capacity, Donald Trump once tweeted:

Actually throughout my life my two greatest assets have been mental stability and being like really smart…I went from VERY successful businessman to top T.V. Star…….to President of the United States (on my first try). I think that would qualify as not smart but genius….and a very stable genius at that!

Continue reading

A critique of the Trump tariff policy and formula

I’ve decided to take a detailed look at the Trump administration’s tariff policy and the formula they use to set rates, and I figured I might as well make an OP out of it so that others could benefit from my homework. My critique is based on the US Trade Representative’s (USTR’s) explanation of the tariffs, which can be found here:

I’m going to be scathing in my critique because these people are both dishonest and incompetent and deserve to be called out on it.

Continue reading

The problem of evil — for atheists?

The problem of evil is arguably the most difficult philosophical problem facing Christians and other theists who believe in an omniGod — a God who is omniscient, omnipotent, and omnibenevolent. The problem, concisely stated: If God is omnibenevolent, he doesn’t want his creatures to suffer. If he’s omnipotent, he can eradicate evil and suffering from the world. Why, then, doesn’t he do so? Why is there so much evil and suffering?

Atheists have no trouble explaining it. If there’s no God, then there’s no one to prevent evil and suffering. Yet some people insist that the problem of evil is a problem for atheists, too.

Continue reading

Trump’s rambling speeches

An interesting (and scary) New York Times about Trump’s cognitive decline:

Trump’s Speeches, Increasingly Angry and Rambling, Reignite the Question of Age

With the passage of time, the 78-year-old former president’s speeches have grown darker, harsher, longer, angrier, less focused, more profane and increasingly fixated on the past, according to a review of his public appearances over the years.

IMBeggar on divine hiddenness

The previous post (by vjtorley) featured a video by a YouTube Christian apologist, IMBeggar, in which he attempts to defuse the problem of evil. It’s riddled with problems as you can see by reading the OP and the comments.

Out of curiosity, I visited IMBeggar’s YouTube channel and watched some of his other videos. One of them, titled “Why doesn’t God just show Himself?”, tackled the problem of divine hiddenness. It was even worse than the one that addressed the problem of evil. I was surprised to find that I disagreed with every major point.

Continue reading

weirdly, fuel efficiency can be expressed as an area

Yesterday I saw someone joking online about how if you apply dimensional analysis to fuel efficiency, you end up with an area. Why? Because fuel efficiency is expressed (in Canada and Europe, anyway) as liters per 100 kilometers. The liter is a unit of volume, or length3. The kilometer is a unit of length. If you divide length3 by length, you end up with length2, or area. (Similar reasoning applies to American-style fuel efficiency expressed as miles per gallon.) Continue reading

The mystery of celebrity endorsements

In the photo above, you can see the famous basketball player Shaquille O’Neal endorsing Epson printers. He was undoubtedly paid a lot of money for that, because Epson believed that the increase in profits would more than offset the large expenditure. Companies pay big bucks for celebrity endorsements, so they’re obviously convinced that these endorsements are effective. Continue reading

Rationalizing Hell

Detail from The Last Judgement, Jan Van Eyck

Perhaps the most disturbing idea in Christian dogma is the notion of hell — a place of unending torment for the detestable souls who don’t qualify for a blissful eternity with God and the angels in heaven. Who are these horrible people who are condemned to agonizing, eternal punishment? Those who don’t believe in Jesus. That’s it. Merely failing to believe in Jesus means you are one of the loathsome vermin who must suffer forever, with no possibility of a respite, and not even the prospect of a welcome oblivion. Continue reading

ChatGPT narrates TSZ

By now, many of you will have heard of ChatGPT. If you haven’t, be prepared — you’re going to hear a lot about it over the coming weeks and months.

ChatGPT is an artificial intelligence language model with an impressive ability to understand and generate humanlike text, drawing on a vast reservoir of knowledge gleaned from the internet. (It also makes stuff up, which can be a real problem.) It answers queries and can write stories, articles, computer code, and even (bad) poems. I don’t yet understand much about how it works, but when I learn more, I’ll describe it in the comments. Continue reading

Cockatoo intelligence and social learning

We’ve been underestimating birds for far too long. Here’s a great story about how Australian cockatoos have figured out how to open lidded trash bins and how the knowledge has been spreading through local populations via social learning. There are even regional cockatoo cultures which differ in which bin-opening technique the local birds use.

Crafty cockatoos master dumpster diving and teach each other

“Teach each other” is a bit of an exaggeration, but they do learn from each other. Continue reading

More arguments for the soul, examined

In the previous thread I examined (starting here) a couple of Richard Swinburne’s arguments for the soul, pointing out why I think they are flawed.

Because I find this stuff so interesting, I thought I would look for some more pro-soul arguments and open another thread to discuss them. This topic is important to a lot of people, particular those whose religious or spiritual beliefs invoke some concept of a soul or a soul-like entity. Continue reading

Did I lose my mind to science?

That’s the title of a new article at the Patheos website, which describes itself as “the world’s homepage for all religion”. The article is the first in a series by Ted Peters, emeritus professor of theology at Pacific Lutheran Theological Seminary, who understands the threat that materialism (aka physicalism) poses to traditional religious views regarding the self. Continue reading

A Milestone (Millstone?) for Christianity in England and Wales

Results from the decennial census show that for the first time ever, fewer than half of English and Welsh citizens identify as Christian. The decline has been precipitous, as shown by the graph.

It appears that most of the Christians jumping ship end up in the ‘no religion’ category rather than converting to another religion. No data on how many of them still believe in a god or gods, or in a ‘higher power’. Also interesting that if established trends continue, the ‘no religion’ folks will become a majority in the not very distant future.

The graph comes from this BBC article.

Questions for Christians and other theists, part 8: the Trinity

One of the strangest doctrines in all of Christianity is the doctrine of the Trinity. This doctrine holds that there are three divine persons — the Father, the Son, and the Holy Ghost — yet only one deity. Each of the three persons is fully God, and not just a part of God. A famous diagram known as the “Shield of the Trinity” compactly summarizes the idea:


Continue reading