I want to start by pointing out that Timothy Gowers is not some internet SJW loon. He’s a mathematician, professor, and Fields Medal winner. Even though nothing is expressed here, based on Timothy’s past tweets trying to appease the 2+2=5 crowd, there is an implication. He may be suggesting integer + integer = rational number, but when I see 4.00, I see someone bring precision into the mix.
Update: Gowers did clarify this poll with a series of incoherent and unrelated thought tweets (22 of them) that hint at precision, integer vs real numbers, and various math games. As expected, instead of any clarity, there was more disintegrated confusion. He did clarify that he’s not a Platonist in math (good), but views himself from the formal theory – which means math is merely a numbers game detached from reality and something to play around with.
What is the ‘Precision’ Attack?
The precision argument summed up goes as follows: 2 is only really something in the abstract, once you bring it down to the real world (2 of something), there will always be a range of precision that results in 2 not being 2. For example, if you have a 2×4, which is a 2″x4″ piece of wood – what are the dimensions? Well, it’s 2″ by 4″. Increase the precision, it’s 2.0″ by 4.0″. Increase it again, you may end up with 2.0362″ x 4.0197″. From this, they try to bring out the idea that numbers, in a sense, are fluid. When one speaks of 2, they’re not talking about 2… like a real hard 2, they’re talking about something like 2.
It’s not that they’re asking you to declare 2+2=5; it would honestly be too hard for people. What they’re asking of you is to declare that 2+2≠4 (2+2 doesn’t equal 4) and this is the true goal of these people.
Abstract Numbers Allow for the Infinite
Numbers, as a system, were built in such a way to allow one to go beyond the perceivable bounds of the real world need at a specific timeframe. There was a time when counting didn’t see the need to go past of a few hundred thousand. The idea of needing more than a million was viewed as silly because a normal city only had 50,000 and population was the highest conceivable thing to count. Even though counting didn’t conceive a need of going past a certain threshold of numbers, numbers were still constructed to allow for one to expand it, if needed. As science progressed, we found the need for more numbers. Speaking about DNA cells, we are into the quadrillions.
The same is true of precision. Numbers can go as far as one needs in precision. There was a time, where the most complicated things people did was make buildings, a precision of millimeters was as far as needed. Microprocessors are working with the precision much more intense like nanometers.
The range of numbers and precision is based on the context of what one is doing. If one is building a deck, a 2.0″ x 4.0″ board is what is used. It is of no consequence if it is really 2.01″ x 4.02″ or 2.000000000000″ x 4.000000000000″. The same is true of counting humans. I am 1 human. I’m not 1.0 human. I’m not 0.91 human if I’m missing a hand, nor am I 0.9999999 human if I just cut my fingernails short.
Precision, in the real world, isn’t an infinite range of possibilities. No matter how hard one tries, there will never be 0.999999999999999999999999999 human.
The Takeaway and The Motive
While writing this article, I found the real motive to become clear. Even though the argument that a 2×4 with more precision would be 2.0015″ is conceivably a real thing, why isn’t the same thing plausible with a human? (as in a 1.00000001 human?). The takeaway is that this isn’t about math, but the concepts that math is applied to. This includes humans, 2x4s, and units of measurement. It’s about people’s conceptual faculties.
The reason a human isn’t 1.000 is that it doesn’t matter to the concept of a human. There’s just a human and there’s not human. You’re not more quantity of a human if you’re overweight, nor are you less quantity of a human if you’re below 170lbs. The same is true of a 2×4 board. Even though one could take the precision to some infinite range, it’s not part of the concept beyond the range of the 2×4 concept. This is why 2.0″ precision with regards to a 2×4 is right and 2.0″ precision with regards to a microprocessor is wrong.
When one is expanding the precision outside the range of the concept, they’re deconstructing the concept with the inevitable goal of destroying it. This is what it’s all about.