Do Negative Numbers exist?

Maths is mind bending. It takes 700 pages to prove 1 + 1 = 2. Ultimately maths can’t be proven to be complete, consistent or decidable. (from Veritasium) So is there a discrete point at which it deviates from reality? We’ve all experienced being in the red. My bank statement might read £256. In maths we would assign it a value of -£256, a minus number. I might deposit £300 and happily find myself back in the black. I can’t have minus 3 apples but I can have 3 apples. My feelings in both cases will switch from negative anxiety to positive happiness, but we all know feelings have no place in mathematics. But here they clearly indicate the vectors of positive and negative. So is a minus sign part of a number or a vector associated with it? If it is an associated vector we then only have positive numbers as clean, devoid of any association. ‘-256 =256 x -1’ where -1 is the vector. So are we truly recognising it as such? (I’ve no idea where I’m going with this) In the bank example it’s easy to see the vector change from me owing the bank to the bank owing me, but the apples? I can owe 3 apples having borrowed 3 earlier but however I might want any number of apples for whatever reason I can’t ‘have minus 3 apples’ in the greater scheme of things. The universe doesn’t owe me anything. Does this suggests minus is a human invention only applicable in the human mind? Have we invented it to indicate our difference in feelings from negative anxiety to positive happiness? If minus, the most basic of operators, only exists in the human mind and not in our wider environment can it be deceiving us in our mathematical modelling of it? Can it be a discrete point at which maths deviates from reality?

9/11. 20 Years On. What the President did.

An English class. He hears the news, makes a broadcast and boards Air Force 1. It flies west from South Carolina. On board the phones and TV don’t work well so he’s less well informed than I was at home in the UK. He recalls it with all the alacrity of Homer Simpson, brave, angry, thoughtful, heavy responsibility, we’ll get them. Somewhere over Arizona AF1 turns north. GWB wants to go to Washington, ‘back home I used to be great with a ground to air missile launcher.’ He’s not allowed. After another two hours they land at an air force base in Idaho with a comms bunker. Meanwhile in the Capital there’s so many people in the Whitehouse bunker they run short of oxygen and send out the none essentials. Around 6pm they fly east back to Washington and GWB makes another broadcast. The conspiracy rumour mill begins. The owner of the WTC buildings was facing a humongous loss, half empty, too old and too costly to repair, and too costly to demolish. Israel and the US wanted a reason to go after various Arab states. New York share trading prior to 9/11 showed strong anomalies suggesting prior knowledge. A good few people were phoned and told to stay home that day. Firemen told of hearing a series of thuds (explosions) prior to collapse, and many more. Whatever the truth the Israeli owner of the WTC buildings got a humongous insurance payout, and the US spent 20 years, over 2,000 lives and $2 trillion fighting in Afghanistan. (pop; 39m = $50,000 per person) And now Joe Biden is getting a hard time for drawing a line under this unholy mess. So the actual lessons might well be, 1/ US high rise buildings are susceptible to catastrophic fire collapse, 2/ US government is too top heavy, 3/ and can be outwitted by a small band of dedicated individuals, 4/ wanting a war turns out to be not the same as having one, 5/ a lot of money makes for stupidity, 6/ and spending it on benefits is better than armaments in the long run. But as Homer shows recollection is dangerously prone to misappropriation. There is one good thing. The population of Afghanistan now has a taste for a more civilised society. That just might be stronger than gun toting jihadists.