Babbage ’ s letter to Tennyson

1. Babbage’s letter to Tennyson On "The Vision of Sin"Babbage wrote, “In your otherwise beautiful poem, one verse reads, Every moment dies a man, Every moment one is born.  ... If this were true, the population of the world would be at a standstill. In truth, the rate of birth is slightly in excess of that of death. I would suggest [that the next version of your poem should read]: Every moment dies a man, Every moment 1 1/16 is born. Strictly speaking, the actual figure is so long I cannot get it into a line, but I believe the figure 1 1/16 will be sufficiently accurate for poetry.” http://en.wikipedia.org/wiki/Charles_Babbage

2. Radians 1.5 ? 0.5 What does ? = What theory is this based on? Is there anything aesthetic about this? Could things be different?

3. Radians V Degrees • d/dx (sin x) ≈0.017453292cosx (if the angles add up to 360 degrees) • d/dx (sin x) = cos x (if the angles add up to 3.14) So is there beauty in the language of mathematics? Consider examples from your own studies?

4. Math as denoted in different “languages” • Just as the decimal system goes by 1, 10, 100, 1000, 10000, etc • the Maya vigesimal system goes 1, 20,400, 8000, 160000 • Numbers in the Maya system can be written vertically or horizontally.

5. On the basis that • = 1 see if you can express the Mayan number 168,421 vertically.

6. What level of mathematics do you believe could be achieved? • The Caracol building in Chichén Itza, Mexico is thought by many to be a Mayan observatory. • able to calculate the length of the year to be 365.242 • Mayan astronomers found that 149 lunar months lasted 4400 days. This gives 29.5302 days as the length of the lunar month. At Palenque in Tabasco they calculated that 81 lunar months lasted 2392 days. This gives 29.5308 days as the length of the lunar month. The modern value is 29.53059 days. • How can this be, since academics hold that the Mayan system was not used to calculate division and multiplication? What are the implications for knowledge in mathematics and history, or even for that matter, Fermat’s last theorem? (data gathered from below site) http://www.13moon.com/ABOUT%20THE%20MAYA.htm

7. Axiom becomes Theorem A B How do we know that A=B? Do the proof, what do we need to be certain of?

8. Axioms Euclid’s Axioms: 1. It shall be possible to draw a straight line joining any two points. 2. A straight line may be extended without limit in either direction. 3. It shall be possible to draw a circle with a given center and through a given point. 4. All right angles are equal to each other. 5. There is just one straight line through a given point which is parallel to a given line.* How might point 5 be wrong? Clue: Quantum physics disputes axiom 5.

9. Reimann’s Geometry • Sum of angles of a triangle = 270 degrees So where do truth and certainty fit into all of this? Can we argue that mathematics or its language is anyway intuitive?

10. Reimann’s Geometry Changed Euclid’s 5th axiom Given a line and a point P not on 1, there are no lines in the plane of P that pass through P and do not meet 1 Meant that first and second axioms also had to be changed This was applied to a ground breaking new theory in the C20th for instance in Einstein’s Theory of Relativity and Schwarzschild’s work on Black Holes