MD, PhD, MAE, FMedSci, FRCP, FRCPEd.

dementia

Recent statements concerning US pharmaceutical pricing have drawn renewed attention to an entirely new horizon in mathematics. The method, associated with remarks by Donald Trump and repeated by several of his sycophants, departs from standard arithmetic in a manner that is rhetorically vigorous but mathematically ridiculous.

Percentage change is defined relative to a single, clearly specified baseline. A decrease from $600 to $100 is therefore calculated as (600-100)/600×100 = 83.3%. In other words, the price falls by 83.3% relative to the original $600 price. This is the method used in economics, finance, accounting, retail pricing, and presumably even by the secondary-school mathematics teachers who attempted to educate Trump.

However, the new alternative math proceeds differently. It implicitly combines two distinct operations: first, the increase from $100 to $600, correctly described as a 500% rise when measured against the initial $100; and second, the subsequent decrease from $600 back to $100. Rather than evaluating this decrease against the higher price, however, the method appears to retain the earlier, lower baseline, thereby generating a claim of a “600% saving.” The arithmetic equivalent of moving the goalposts and then declaring victory by an even larger margin.

Within standard mathematics, this shift in baseline is not permissible. Percentage changes are inherently asymmetric because they depend entirely on the reference point selected. The same absolute difference – in this case, $500 –  produces different percentage values depending on whether it is measured relative to $100 or $600. This is not a technical loophole but the entire point of percentages.

The problem with this approach becomes clearer if one follows it to its logical conclusion. Under standard arithmetic, a 100% price reduction means the price has fallen all the way to zero: a $100 product reduced by 100% costs nothing. A reduction greater than 100% would therefore produce a negative price, meaning the seller would have to pay the customer to accept the product. If one claims that a fall from $600 to $100 represents a 600% decrease, the numbers cease to correspond to any coherent pricing system. The calculation implies that prices can fall not merely to zero, but to values several times smaller than zero.

The attraction of the Trump method is easy to understand. By selecting whichever baseline produces the largest possible percentage, the resulting figure acquires an air of spectacular achievement. It transforms an already substantial price reduction into something approaching numerical performance art.

Trump’s alternative arithmetic therefore succeeds in generating impressively large numbers by abandoning the one feature percentages require most: consistency. The result is as unsound as most things about Trump. Yet it seems rhetorically effective – particularly with “low IQ people”, as Trump likes to call his followers.

In other words, by cherry-picking the baseline for maximum impact, the Trump method turns an already solid 83% cut into a sensational “600% savings”. It sacrifices precision for hype – effective populism perhaps, poor math for sure!

None of this would be worth mentioning, of course, if it were the only incident where Trump misleads his public. Sadly, he is telling multiple and often much more consequential untruths on a daily basis.

George Washington: “The foolish and wicked practice of profane cursing and swearing… is a vice so mean and low, without any temptation, that every man of sense and character detests and despises it.”

Spencer W. Kimball: “Profanity is the effort of a feeble brain to express itself forcibly.”

William W. Purkey: “Profaneness is a brutal vice. He who indulges in it is no gentleman.”

John H. Groberg: “Stay out of the gutter in your conversation. Foul talk defiles the man who speaks it.”

 

Apart from anything else, the thing that nobody could have possibly missed when observing US politics is Trump’s increasingly primitive vulgarity. Here is a short list of notable quotes that I found [there are surely many more]:

  • September 2005: “I don’t even wait. And when you’re a star, they let you do it. You can do anything. Grab ’em by the pussy. You can do anything.” (In a private conversation with Billy Bush on an “Access Hollywood” bus).
  • August 7, 2015: “You could see there was blood coming out of her eyes, blood coming out of her wherever.” (Referring to Megyn Kelly after a primary debate).
  • November 12, 2015: “I would bomb the hell out of them. I’d blow up every single inch; there would be nothing left.” (Regarding ISIS during a campaign rally in Fort Dodge, Iowa).
  • November 13, 2015: “ISIS is making a tremendous amount of money because of the oil that they took. They have some in Syria, they have some in Iraq. I would knock the hell out of them, but I’d bomb the shit out of them.” (At a rally in Beaumont, Texas).
  • September 22, 2017: “Wouldn’t you love to see one of these NFL owners, when somebody disrespects our flag, to say, ‘Get that son of a bitch off the field right now. Out! He’s fired. He’s fired!’” (At a rally in Huntsville, Alabama, referring to NFL players kneeling during the national anthem).
  • January 11, 2018: “Why are we having all these people from shithole countries come here?” (During a bipartisan meeting on immigration, referring to Haiti, El Salvador, and African nations).
  • Early 2024 (Reported July 2025): “With Putin I said, ‘If you go into Ukraine, I’m going to bomb the shit out of Moscow. I’m telling you I have no choice.'” (At a private fundraiser, recounting a past warning he claimed to have given to Vladimir Putin).
  • June 24, 2025: “We basically have two countries that have been fighting so long and so hard that they don’t know what the fuck they’re doing.” (To reporters at the White House before boarding Marine One, referring to the conflict between Iran and Israel).
  • November 14, 2025: “Quiet, piggy.” (To Bloomberg’s Catherine Lucey on Air Force One when she asked about the Epstein files).
  • May 22, 2025: “You are a terrible reporter. No. 1, you don’t have what it takes to be a reporter. You are not smart enough… And you are a disgrace. No more questions from you.” (To NBC’s Peter Alexander in the Oval Office).
  • November 18, 2025: “They’re all guilty. Every one of them. We’re going to get them. These people are scum, they’re absolute scum.” (Referring to the “Deep State” and political investigators during a televised address).
  • November 26, 2025: “The writer of the story, Katie Rogers… is a third-rate reporter who is ugly, both inside and out.” (Posted to Truth Social regarding a New York Times article about his health).
  • February 5, 2026: “I had to win it. I needed it for my own ego… Beating these lunatics was incredible.” (Recalling the 2024 election during a prayer breakfast event).
  • April 5, 2026: “Tuesday will be Power Plant Day, and Bridge Day, all wrapped up in one, in Iran. There will be nothing like it!!! Open the Fuckin’ Strait, you crazy bastards, or you’ll be living in Hell — JUST WATCH! Praise be to Allah.” (Posted to Truth Social as an ultimatum regarding the Iranian blockade of the Strait of Hormuz).
  • April 6, 2026: “I’m telling you, I’m being fucking straight with you—we aren’t playing games anymore. They open it or we level it. It’s very simple.” (In a follow-up clarification to reporters regarding his social media post and the Tuesday deadline).

This sort of language from a US persident is unprescedendted and it impacts significantly on the quality of the political (and other) discourse across the globe. But it also begs a worrying question: Is Trump’s increasingly aggressive and profane rhetoric a sign of his cognitive decline? The shift from his earlier “Trumpisms” to the stark, expletive-laden ultimatums of 2026 – such as the “Open the Fuckin’ Strait” post – suggests to me a breakdown in impulse control that is a hallmark of deteriorating executive function.

As Trump pivots from policy debate to raw vitriol, labelling opponents as “scum” and “crazy bastards,” the language appears less like strategic provocation and resembles the ramblings of a man losing his grip on reality. Political figures across the spectrum have characterized these outbursts as the ravings of a dangerous and mentally unstable person, sparking louder and louder calls for the 25th Amendment.

This prospective cohort study investigated associations of coffee and tea intake with dementia risk and cognitive function. It included female participants from the Nurses’ Health Study (NHS; n = 86 606 with data from 1980-2023) and male participants from the Health Professionals Follow-up Study (HPFS; n = 45 215 with data from 1986-2023) who did not have cancer, Parkinson disease, or dementia at study entry (baseline) in the US.

The primary exposures were intakes of caffeinated coffee, decaffeinated coffee, and tea. Dietary intake was collected every 2 to 4 years using validated food frequency questionnaires. The primary outcome was dementia, which was identified via death records and physician diagnoses. The secondary outcomes included subjective cognitive decline assessed by a questionnaire-based score (range, 0-7; higher scores indicate greater perceived decline; cases defined as those with a score ≥3) and objective cognitive function assessed only in the NHS cohort using telephone-based neuropsychological tests such as the Telephone Interview for Cognitive Status (TICS) score (range, 0-41) and a measure of global cognition (a standardized mean z score for all 6 administered cognitive tests).

Among 131 821 participants (mean age at baseline, 46.2 [SD, 7.2] years in the NHS cohort and 53.8 [SD, 9.7] years in the HPFS cohort; 65.7% were female) during up to 43 years of follow-up (median, 36.8 years; IQR, 28-42 years), there were 11 033 cases of incident dementia. After adjusting for potential confounders and pooling results across cohorts, higher caffeinated coffee intake was significantly associated with lower dementia risk (141 vs 330 cases per 100 000 person-years comparing the fourth [highest] quartile of consumption with the first [lowest] quartile; hazard ratio, 0.82 [95% CI, 0.76 to 0.89]) and lower prevalence of subjective cognitive decline (7.8% vs 9.5%, respectively; prevalence ratio, 0.85 [95% CI, 0.78 to 0.93]). In the NHS cohort, higher caffeinated coffee intake was also associated with better objective cognitive performance. Compared with participants in the lowest quartile, those in the highest quartile had a higher mean TICS score (mean difference, 0.11 [95% CI, 0.01 to 0.21]) and a higher mean global cognition score (mean difference, 0.02 [95% CI, −0.01 to 0.04]); however, the association with global cognition was not statistically significant (P = .06). Higher intake of tea showed similar associations with these cognitive outcomes, whereas decaffeinated coffee intake was not associated with lower dementia risk or better cognitive performance. A dose-response analysis showed nonlinear inverse associations of caffeinated coffee and tea intake levels with dementia risk and subjective cognitive decline. The most pronounced associated differences were observed with intake of approximately 2 to 3 cups per day of caffeinated coffee or 1 to 2 cups per day of tea.

The authors concluded that “greater consumption of caffeinated coffee and tea was associated with lower risk of dementia and modestly better cognitive function, with the most pronounced association at moderate intake levels”.

Prior to this new study, observational evidence from prospective cohort studies and meta-analyses had already suggested that moderate coffee and tea consumption—typically 1–5 caffeinated cups per day—was associated with a modestly lower risk of dementia and slower cognitive decline, often with J- or U-shaped dose responses favoring moderate intake. Yet, findings had been inconsistent across cohorts – stronger for tea in some Asian studies, mixed for coffee, and varying by sex or vascular risk factors. Caffeine was hypothesized to protect via adenosine antagonism and amyloid reduction, while polyphenols offered antioxidant and vascular benefits. The limitations of this body of evidence included confounding by lifestyle, self-reported exposures, reverse causation, and lack of randomized trials confirming causality. The new study seems to settle at least some of the uncertainties and makes a causal link more likely. 
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