What's most interesting is that you start off with what looks like a math problem, and end up with a completely bizarre human history problem. If I've got this right--and I think I do--this is how it goes:

All math-writing dudes, since basically forever, use implied multiplication (multiplication by juxtaposition). They consider it too obvious to mention. Eventually, but not that long ago (within the last 100-150 years) they debate whether they should make a formalized convention that multiplication (explicit, as opposed to implied) takes precedence over division. This debate is left unresolved, yet in that debate implied multiplication is 100%, still too obvious to mention.

In the 1980s, you get the widespread rollout of calculators to students, which I think hits American schools first. These calculators barf when you try to use implied multiplication, insisting on the consistent use of operators. The next generation of calculators, some have fixed this problem (giving priority to implied multiplication over both division and explicit multiplication, which is up to this point, universally considered correct), some still barf, and some "fixed the glitch" by adhering to strict PEMDAS (which is not correct) and hiding the process, and some use the correct PEJMDAS while adding brackets to your equation, thereby notifying you of how they were treating it.

Somewhere in this mess, a conspiracy of North American teachers, frustrated by these conflicting returns, successfully lobby many calculator-making companies to ditch PEJMDAS (the right one) and only adhere to PEMDAS (the wrong one). Going forward, the majority of calculators (or possibly just the ones sold in America) are PEMDAS. To put it plainly, American teachers bullied calculator companies to only give them calculators that abandon thousands of years of standard notational convention. So now, from this time onward, at least the teachers and the calculators are in agreement. They're wrong, but they're in agreement. Eventually Common Core comes along and exacerbates this problem: All Must Agree, Even in Wrongness.

The American students, taught by this weird Cult of PEMDAS, go on to insist on their ideology. 95% of the world rolls along as they always have, with PEJMDAS, but some notable heavies--such as Google Calculator, which obviously has oversized importance due to widespread availability and usage--continue to spread the cult of PEMDAS.

It's fascinating. A tale of innovation, groupthink, authority, conformity, memetic disease, exceptionalism, midwittery, and dogged insistence.

What's most interesting is that you start off with what looks like a math problem, and end up with a completely bizarre human history problem. If I've got this right--and I think I do--this is how it goes:

All math-writing dudes, since basically forever, use implied multiplication (multiplication by juxtaposition). They consider it too obvious to mention. Eventually, but not that long ago (within the last 100-150 years) they debate whether they should make a formalized convention that multiplication (explicit, as opposed to implied) takes precedence over division. This debate is left unresolved, yet in that debate implied multiplication is 100%, still too obvious to mention.

In the 1980s, you get the widespread rollout of calculators, which I think hits American schools first. These calculators barf when you try to use implied multiplication, insisting on the consistent use of operators. The next generation of calculators, some have fixed this problem (giving priority to implied multiplication over both division and explicit multiplication, which is up to this point, universally considered correct), some still barf, and some "fixed the glitch" by adhering to strict PEMDAS (which is not correct) and hiding the process, and some use the correct PEJMDAS while adding brackets to your equation, thereby notifying you of how they were treating it.

Somewhere in this mess, a conspiracy of North American teachers, frustrated by these conflicting returns, successfully lobby many calculator-making companies to ditch PEJMDAS (the right one) and only adhere to PEMDAS (the wrong one). Going forward, the majority of calculators (or possibly just the ones sold in America) are PEMDAS. To put it plainly, American teachers bullied calculator companies to only give them calculators that abandon thousands of years of standard notational convention. So now, from this time onward, at least the teachers and the calculators are in agreement. They're wrong, but they're in agreement. Eventually Common Core comes along and exacerbates this problem: All Must Agree, Even in Wrongness.

The American students, taught by this weird Cult of PEMDAS, go on to insist on their ideology. 95% of the world rolls along as they always have, with PEJMDAS, but some notable heavies--such as Google Calculator, which obviously has oversized importance due to widespread availability and usage--continue to spread the cult of PEMDAS.

It's fascinating. A tale of innovation, groupthink, authority, conformity, memetic disease, exceptionalism, midwittery, and dogged insistence.

What's most interesting is that you start off with what looks like a math problem, and up with a completely bizarre human history problem. If I've got this right--and I think I do--this is how it goes:

All math-writing dudes, since basically forever, use implied multiplication (multiplication by juxtaposition). They consider it too obvious to mention. Eventually, but not that long ago (within the last 100-150 years) they debate whether they should make a formalized convention that multiplication (explicit, as opposed to implied) takes precedence over division. This debate is left unresolved, yet in that debate implied multiplication is 100%, still too obvious to mention.

In the 1980s, you get the widespread rollout of calculators, which I think hits American schools first. These calculators barf when you try to use implied multiplication, insisting on the consistent use of operators. The next generation of calculators, some have fixed this problem (giving priority to implied multiplication over both division and explicit multiplication, which is up to this point, universally considered correct), some still barf, and some "fixed the glitch" by adhering to strict PEMDAS (which is not correct) and hiding the process, and some use the correct PEJMDAS while adding brackets to your equation, thereby notifying you of how they were treating it.

Somewhere in this mess, a conspiracy of North American teachers, frustrated by these conflicting returns, successfully lobby many calculator-making companies to ditch PEJMDAS (the right one) and only adhere to PEMDAS (the wrong one). Going forward, the majority of calculators (or possibly just the ones sold in America) are PEMDAS. To put it plainly, American teachers bullied calculator companies to only give them calculators that abandon thousands of years of standard notational convention. So now, from this time onward, at least the teachers and the calculators are in agreement. They're wrong, but they're in agreement. Eventually Common Core comes along and exacerbates this problem: All Must Agree, Even in Wrongness.

The American students, taught by this weird Cult of PEMDAS, go on to insist on their ideology. 95% of the world rolls along as they always have, with PEJMDAS, but some notable heavies--such as Google Calculator, which obviously has oversized importance due to widespread availability and usage--continue to spread the cult of PEMDAS.

It's fascinating. A tale of innovation, groupthink, authority, conformity, memetic disease, exceptionalism, midwittery, and dogged insistence.