Supercomputing in Our Daily Life

What happens when you drop a few drops of food color into a cup of clear water? Well, from our life experience, we know that the food color will be eventually mixed with water in the cup and turning the whole cup of water colored. This happens even without us stirring it. This process is called Diffusion. It is a very common physics phenomenon and is the reason that you can wake up and smell the coffee in the morning. What people don't appreciate is how simple it is to model this phenomenon and how widely the model and numerical algorithm apply to other problems in our life, for example, ranking web pages.

In this keynote speech at New Mexico Supercomputing Challenge, I showed that with elementary school math and programming skill, everyone can understand models and computations behind PageRank and Diffusion. The talk was delivered with an on-stage physics experiment, 2 interactive exercises with the audience and challenging questions to the audience for them to think deeper afterward.

Transcript

1. Supercomputing in Our Daily Life From PageRank To Diffusion
4. You shall love each other!!!
8. Alice Bob Chris Dylan Eve
9. 1.000 1.000 1.000 1.000 1.000
10. 1.000 1.000 1.000 1.000 1.000 0.500 0.500 0.500 1.000 0.500 0.500 0.500 0.500
11. 1.000 1.000 1.000 1.000 1.000 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
12. 1.000 1.000 1.000 1.000 1.000 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
13. 1.000 1.000 1.000 1.000 1.000 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
14. 1.000 1.000 1.000 1.000 1.000 0.500 0.500 0.500 0.500 1.000 0.500 0.500 0.500
15. 1.000 1.000 1.000 1.000 1.000 0.500 0.500 0.500 0.500 1.000 0.500 0.500 0.500
16. 0.575 1.000 1.000 1.000 1.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * 0.500 = 0.575
17. 0.575 1.425 1.000 1.000 1.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * (1.000 + 0.500) = 1.425
18. 0.575 1.425 1.000 1.000 1.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * (0.500 + 0.500) = 1.000
19. 0.575 1.425 1.000 1.425 1.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * (1.000 + 0.500) = 1.425
20. 0.575 1.425 1.000 1.425 0.575 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * 0.500 = 0.575
21. 0.575 1.425 1.000 1.425 0.575 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * 0.500 = 0.575
22. 0.575 1.425 1.000 1.425 0.575 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Popularity 0 0.375 0.75 1.125 1.5 Alice Bob Chris Dylan Eve
23. 0.575 1.425 1.000 1.425 0.575 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Popularity 0 0.375 0.75 1.125 1.5 Alice Bob Chris Dylan Eve
24. 0.756 1.064 1.361 1.064 0.756 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Popularity 0 0.375 0.75 1.125 1.5 Alice Bob Chris Dylan Eve
25. 0.756 1.064 1.361 1.064 0.756 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Popularity 0 0.375 0.75 1.125 1.5 Alice Bob Chris Dylan Eve
26. 0.602 1.371 1.054 1.371 0.602 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Popularity 0 0.375 0.75 1.125 1.5 Alice Bob Chris Dylan Eve
27. 0.673 1.229 1.195 1.229 0.673 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * 0.500 = 0.575 Popularity 0 0.375 0.75 1.125 1.5 Alice Bob Chris Dylan Eve
28. Are you sure it is not a Diffusion process?
32. Alice Bob Chris Dylan Eve
33. 0.000 0.000 1.000 0.000 0.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * 0.500 = 0.575
34. 0.000 0.000 1.000 0.000 0.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.15 + 0.85 * 0.500 = 0.575
35. 0.000 0.500 1.000 0.000 0.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.00 + 1.00 * 0.500 = 0.500
36. 0.000 0.500 1.000 0.500 0.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.00 + 1.00 * 0.500 = 0.500
37. 0.000 0.500 0.000 0.500 0.000 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 0.00 + 1.00 * 0.500 = 0.500
38. 0.000 0.500 0.000 0.500 0.000 0.500 0.500 0.250 1.000 1.000 0.500 0.250 0.500 0.00 + 1.00 * 0.500 = 0.500
39. 0.000 0.500 0.000 0.500 0.000 0.500 0.500 0.250 1.000 1.000 0.250 0.250 0.250 0.00 + 1.00 * 0.500 = 0.500
40. 0.250 0.500 0.000 0.500 0.000 0.500 0.500 0.250 1.000 1.000 0.250 0.250 0.250 0.00 + 1.00 * 0.250 = 0.250
41. 0.250 0.500 0.500 0.500 0.000 0.500 0.500 0.250 1.000 1.000 0.250 0.250 0.250 0.00 + 1.00 * (0.250 + 0.250) = 0.500
42. 0.250 0.500 0.500 0.500 0.250 0.500 0.500 0.250 1.000 1.000 0.250 0.250 0.250 0.00 + 1.00 * 0.250 = 0.250
43. 0.250 0.000 0.500 0.000 0.250 0.500 0.500 0.250 1.000 1.000 0.250 0.250 0.250 0.00 + 1.00 * 0.250 = 0.250
44. 0.250 0.000 0.500 0.000 0.250 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Milk 0 0.25 0.5 0.75 1 Alice Bob Chris Dylan Eve
45. 0.250 0.000 0.500 0.000 0.250 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Milk 0 0.25 0.5 0.75 1 Alice Bob Chris Dylan Eve
46. 0.125 0.375 0.000 0.375 0.125 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Milk 0 0.25 0.5 0.75 1 Alice Bob Chris Dylan Eve
47. 0.125 0.375 0.000 0.375 0.125 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Milk 0 0.25 0.5 0.75 1 Alice Bob Chris Dylan Eve
48. 0.250 0.0625 0.375 0.0625 0.250 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Milk 0 0.25 0.5 0.75 1 Alice Bob Chris Dylan Eve
49. 0.200 0.200 0.200 0.200 0.200 0.500 0.500 0.500 1.000 1.000 0.500 0.500 0.500 Milk 0 0.25 0.5 0.75 1 Alice Bob Chris Dylan Eve
50. We are not that much different, after all.
51. They lived happily ever after
52. All models are wrong but some are more useful — George Box