http://chrissaffran.com/equations daily 0.75 2014-06-16 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402943012219-G3B556X89P0DQY9P0B8B/Endnote2.png equations https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402943012219-G3B556X89P0DQY9P0B8B/Endnote2.png equations https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402943223195-S4608JVXGL1E7FKJJEA0/Endnote2a.png equations http://chrissaffran.com/updates daily 0.75 2014-07-24 http://chrissaffran.com/updates/2014/7/19/share-your-thoughts-information monthly 0.5 2019-01-11 http://chrissaffran.com/updates/2014/7/19/update-alpha monthly 0.5 2014-07-20 http://chrissaffran.com/gravity-and-evolution-references daily 0.75 2014-06-18 http://chrissaffran.com/contact daily 0.75 2023-07-27 http://chrissaffran.com/delta daily 0.75 2015-08-11 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1439255426892-S4KKVV46LIP0E29Z9MAW/image-asset.png Gravity and Evolution, Part Two Figure 1. Schematic depicting relationships between points at the surface of the earth, h₁ and h₂, and the corresponding normal vectors, DM1 and DM2, intercept points at the magnetosphere, z₁ and z₂, and solar wind forces p₁ and p₂. Given that the magnetosphere is shaped by the distribution of solar wind forces giving rise to solar wind dynamic pressure, we see that the magnitude of any p determines the magnitude of any DM. Moreover fluctuations in p must give rise to fluctuations in DM. Therefore we can expect that there exists some neighborhood, H₁, around a given point h₁, for which the magnitude of DM1 fluctuates nearly uniformly given a given some distribution of forces around z₁. We can also see that area of H₁ depends in part upon the pressure gradient around z₁, and so the DM1 uniformity cannot extend to some distant neighborhood, H₂, feeling the effects of a pressure gradient around p₂, and where p₂ ≉ p₁. Note too that there exist intrinsic regional affects on the magnitude of DM and how it varies in response to fluctuations in p, which arise from the incident angle θ, and so this contributes to the determination of the area and shape of any H. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402641519072-4BHL5TVL1OAWFTM0RZ8K/Equation1-2 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642209756-GCC2FPBWOWGQFU3OWI0V/Equation3-4-5 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642302904-73ABTOPV2L5B45JAAN6Y/Equation6-7 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642443203-FZPOF4AYFFF4PJ6B9SOD/Equation8-9 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642510247-XZI2R53SESYND2QAG0QV/Equation10 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642541266-00P0EAOTV5X9EHQ4U0JU/Equation11 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642609330-WWXX4G1JHV2JKCMPNBUG/Equation12-13 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642634530-TR9FAO8GNCIWJ19ICL91/Equation14 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642657348-Q2CZ3F84VQC2M73OXLKZ/Equation15 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642696369-VRUCZC7AEUDJ6X6KDZ7Z/Equation16 Gravity and Evolution, Part Two https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402642743908-TE18KNS6NQP01MBWMYCN/Equation17 Gravity and Evolution, Part Two http://chrissaffran.com/a-letter-to-a-man-holding-two-books daily 0.75 2025-08-16 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403122625179-6GHFDIXYMURHSOQJDI1U/uncert.jpg A Letter to a Man Holding Two Books https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403122632959-H26W65DDCWUW4M1E5YEL/Jarre.jpg A Letter to a Man Holding Two Books - Alfred Jarry Frenchman and ’Pataphysician https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403122637617-GMDE4FJB8ZSAMX80G5H2/pat.jpg A Letter to a Man Holding Two Books http://chrissaffran.com/thesis daily 0.75 2015-09-10 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1441864508461-NBV7S63WCB2D63DYNSD2/Figure+1.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403038320473-APQJ3JAW3IPBYETM95W0/Figure2.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403038079955-A21XF0FPJ80H8NC2B1AA/Figure3a.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403038083886-5Y13DFDSU3T6R1JL42X9/Figure3b.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403067786887-UIGGKVZOVZNDE44JSRLN/Equation1.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403068102887-MQKCMOOIJ4BX45W5HZQB/Equatio2-3-4.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403068375995-66SFNL37W189R4RAVUQX/Equation5.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403068481211-PQFIL4UK9YE88E0UFBDU/Equation6.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403037695547-N9VI7VKMX8LMCQ9FGIOB/Figure4a.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403037701347-OMW8XOF2ZEIZ28A738U0/Figure4b.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403037705351-XZ0DMVKYDDUM7C3NNFNP/Figure4c.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403037710436-4R28L2J517722UHSS301/Figure4d.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403037714465-I5ZGF0PY5FGZ73KL3EA4/Figure4e.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403039022724-F3A0YCFH7B9IX8JUK8I9/Table1.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403039447577-RSP0MCQSVJVWTTSPP93I/Figure5.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403040041947-MI24U9AV31JF65KYVWDS/Figure6a.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403040045067-DNP176UTW3EFWIF8VWNH/Figure6b.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403107274226-8KODZKW2UB73FR11MAYA/Equation7.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403095421366-PJ3B05NMDTKV7SN3SLHH/Equation8.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041562772-0SCMVVDIYXZ0VXVT32VG/Figure7a.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041567739-LCKGWQHAN2GXC1TSSC3Q/Figure7b-c.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041573512-NP4USVQGEBYSEMMG1YAP/Figure7d.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041702632-KEF3AOZNA7JLNJJ8622J/Figure7e.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041593446-GMC5QL1L4PDRLBGQ7HO4/Figure7f-g.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041757866-MYH04MS2GI7EE2VC4AAG/Figure8a.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041764155-PWZW25AC11V9PYDXG5K4/Figure8b.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041769547-7AJZ7O6WR5Z23RTO8SRQ/Figure8c.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041774438-EKBIHGOBW0WLK75W7OY0/Figure8d.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041781342-7OE7HV3WD403UYG64HQ4/Figure8e.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041786304-EJH12Y5TE562AJWS3CRW/Figure8f.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403041790032-247XL14P5J89AZUVOM4F/Figure8g.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403096784640-I2IMDUTO277ISQ0WEK31/Equation9.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403097104594-77LOGFDL15RI7H5G3JIU/Equation10.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403097140631-P00YPAJWHUIQYHVD0GIJ/Equation11.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403097170784-JYO0L6T6VIMSPJ179MD6/Equation12.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403042444787-PPI8WBYW9RY4GWQN8HJI/Figure9a.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403042449031-OFGMB2QMTZUEMI26P3WZ/Figure9b.png A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ http://chrissaffran.com/prose daily 0.75 2025-08-16 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1402524402478-791WJ5HLDTA1H6KMINVG/vintage.jpg Prose Circa 1995, working on a early draft of The Courier, a feature screenplay that ultimately landed me a job as an in-house writer at Inklein Entertainment, NYC. http://chrissaffran.com/specificity daily 0.75 2023-10-24 http://chrissaffran.com/gravity-and-evolution daily 0.75 2025-08-16 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403029643711-4WCMEPTRKU33FRXOC9WN/Equation1.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403029708458-OKLFXDQYCEU3WKZLR7ZG/Equation2-3.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403029767774-JHWIETB0BYWX1UAXQ84A/Equation4.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1401956726076-BXXVXU7CZE0NQZX9V2KE/image-asset.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403029907453-KBTSMMAIW41B5XWS9R8A/Equation5.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403029939040-HR9RJNVUG5OZK70OA1FM/Equation6-7.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030025011-1DT7281QH0P1L4KHCXOV/Equation8.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030119692-NFZBVOQO06Q3CHDSZF5I/Equation9-10.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030152356-F81E641WR3XMG47XTTS4/Equation11.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030211907-XDGYIAJMEXGGN640PLGY/Equation12.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030246865-0GWBDLLZDIVBRIPUK3LT/Equation13.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403113861365-7I7BE5EKE09H5CO791UK/image-asset.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030290868-K3I9L38Q9YLIMEQP1H9Z/Equation14-15.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030339981-4UE8V0TRJVBVPG886CG1/Equation16-17-18.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030360806-0O21Z2BQ9SZAZ1VS7S7R/Equation19.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030403706-RP2EYNZ6RWUDFZBEJDLP/Equation20.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030453084-KKJ2HJ0KSA0H1OHFID4J/Equation21.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030479375-AIYH03HQPDIVJW25U5D8/Equation22-23.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030498639-OMPQGY2POODQAXP7U4G5/Equation24.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030547201-EY41K7Z63I79IIEHDCNY/Equation25.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030611161-Q9OHZ59LQSPLX10XCVAR/Equation26.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030661704-1AUVMV4VWK3LPBURTLTG/Equation27-28.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030691387-UQ1OZL08PKTQQ08TGJX2/Equation29.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403019789810-L3Y8Z9U9UCNPDD8BCV5I/image-asset.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030746152-SH20AD6VOWJ3HQ8JM3ME/Equation30.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403021786368-SO6OV95VRN80R78PBQUB/image-asset.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403030880768-DAWW8MUNPIDLMSTZMQF6/Equation31-32.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031065385-0OE5DAPAVKAOZHED9EDC/Equation33-34.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031138037-U57KTQYMR2BG82ARFZ2J/Equation35-36.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031175197-4F0EJ5A4ERISTZZNJS4S/Equation37-38-39.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031240268-YT6ZHRXIAE1B8APB9JZC/Equation40.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031318093-XC9AC8B8QEYWH3U8ZP8U/Equation41.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031387046-LFQ6RKAGZ7TXDWSGQCK7/Equation42.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031440498-8HPCL4X95KRL2HUNLTIZ/Equation43.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031528441-PS5OSCG1JH8LH6879V2G/Equation44-45.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031612981-CVO6QVKD98CMYMDZCOPW/Equation46-47.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031664828-FY5N3946IR6SH26NHGI5/Equation48.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031703457-CGX4PLVMSUEOZMALJESM/Equation49.png Gravity and Evolution, Part One https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403031754018-2UR7VJ03PUPK6AYCBS6S/Equation50.png Gravity and Evolution, Part One http://chrissaffran.com/brownian-rachets daily 0.75 2021-07-20 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403152174050-QRVSPDKP1Y5YI0QUXYXR/Equation1.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403152930347-FYXLIVWJYR3EW0OG24NH/Equation2.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403153545635-8EZOF9SWIOGOHJC9D74P/Figure1.png Brownian Rachets Nagayama, K., et. al. Heterogeneous response of traction force at focal adhesions of vascular smooth muscle cells subjected to macroscopic stretch on a micropillar substrate, Journal of Biomechanics. http://dx.doi.org/10.1016/j.jbiomech.2011.07.023. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403154366184-DKANSO4XRMOSEBEMNQ8Y/image-asset.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403154489859-AFBVRXJMHS9564GBIWDA/image-asset.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403154614791-M1GTE5NYWL95ZA3B1ZW6/Equation5.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403154707733-VFF2BD2MRR4STJRBSYVC/Equation6.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403154906641-EN9RRMO9V1LXS26ON634/Equation7.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1439432389408-REYX1P5HV2GN8674SZT4/image-asset.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403154983972-UN846HVZCAW2Q7FJSY2C/image-asset.png Brownian Rachets https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403155097378-NWN7B9YVLKWFX921GSHB/Figure2.png Brownian Rachets Nagayama, K., et. al. Heterogeneous response of traction force at focal adhesions of vascular smooth muscle cells subjected to macroscopic stretch on a micropillar substrate, Journal of Biomechanics. http://dx.doi.org/10.1016/j.jbiomech.2011.07.023. http://chrissaffran.com/brownian-ratchet-references daily 0.75 2014-06-19 http://chrissaffran.com/philosophy daily 0.75 2019-08-13 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403162538262-L2QT2YAEEDSZ388KKX8G/Equation1.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403162678115-64949YX02HQ73LYX4GHL/image-asset.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403162708175-FABFR8IMC75JBXUML61R/Equation3.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403162788567-C3UASMP6FW9CT38BAVZY/Equation4.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403162944398-PN5XGMP5O7YNCFWGML5A/Equation5.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405963746476-XO52B1VBW1REG026TFU6/Equation6.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405621480744-W4F8DJIQB29SNF9TQEGY/Equation7-8.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403163951398-2SLX8ZHHX72KWVHW4H42/Equation9.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403164067470-0446XBBL6F86AKIQ6QYR/Equation10-11 Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1406041070557-LUVKZAH4GL50PSZTI4MY/Equation12-13.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405459301860-ZDR5J3IPSVABBQWM6JLB/Equation14.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1404763043619-EGYSFF3JBDE4QJIP7BWB/Equation15.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1404763323038-VNR7JU3EN8X9PHXGZCM3/Equation16.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405459666413-T5NLVX9FCK37JCIASE4Q/Equation17 Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403462671816-LSACD1561IM396577IWJ/Equation18.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403462748534-VQVSA5SD8IPG3EVBQPWD/Equation19.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403462797609-XNF5CT6K258RXL0A2ZEC/Equation20.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403650850498-HO1SMK8PNJYWAYRTYUD5/Equation21.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403463638861-4UNWMQWA9FQNT1XUQFAT/Equation22.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405459866778-99GXLAR23WGHVT3WPKRL/Equation23 Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1404576281481-P368D88WCRNDWF8VM730/Equation24.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1404576342851-6GZ3CEQL3PHEQBF6WH4G/Equation25 Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407077934397-WD7Z6K74QBDSUPARU5QD/Figure1a.png Philosophy - Figure 1a https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407077934274-01UCDU4OA0VT99XWT3JX/Figure1b.png Philosophy - Figure 1b https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407077935893-SEM05XY989SRV6HGG0B8/Figure1c.png Philosophy - Figure 1c https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407077941094-Y7W3QOEYLS4EGZXWIEIO/Figure1d.png Philosophy - Figure 1d Sensor construct adrift in sea of Type A particles. The sensor is only binary in the abstract, since evaluation to 1 is constant and perpetual. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407077941796-95W67MNHH5MUQUZU57VW/Figure1e.png Philosophy - Figure 1e Introduction of the Type B particle causes a break in the continuous evaluation to 1, thus giving existential context to the evaluation. Now the sensor is meaningfully binary: it evaluates to 1 or 0. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405373423492-ZXFUTYVQ6DFNT68EKVXH/Equation26.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405373800300-IX10CDL3SYAWA1IOQ2YF/Equation27.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405373990078-JE3Z0G0ZRJ2PCI1BR9BU/Equation28.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405375120533-S1W2C2GEZ95MCMST2Y5J/Equation29-30.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405461358491-6SYFOZQ0VVQABZ7RRQ4K/Equation31.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1405459999300-DTW1CYVFZAK86QDYRX4Y/Equation31-32.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1406035870315-TDR38XPQEECP50K4AKS5/Equation34.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1406035940027-TPDA76RNW7NAU5HRK1EF/Equation35.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1406035964295-MMFOUZT7B443KVP8LVTR/Equation36.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024153856-B18LQKH54JH7O5KTLNEY/FIgure2a.png Philosophy - Figure 2a Figures a through f depict the described interacting bowling balls ungrouped with their relevant lateral velocity and kinetic energy. Transverse molecular velocity is ignored here as we have chosen a LOI at the elemental amalgam point of the bowling balls—i.e., each bowling ball constitutes an element. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024154125-CC9PF50DLC124GSHZ6KG/FIgure2b.png Philosophy - Figure 2b Note that the lateral velocity of all the bowling balls is all zero. Since they all have mass this might appear at first glance to be a violation of conservation of momentum. However at a lower LOI we observe that, on a molecular scale, the momentum of the molecules of ball 1 are indeed transferred to those of ball two, only in the form of a compression wave which moves through ball 2 at the speed of sound in a bowling ball. Not all of this molecular velocity is lateral, it radiate throughout ball 2 with both lateral and transverse velocity. That said, the transverse components of the molecular velocities sum to zero and lateral velocity of the bowling ball as an element is halted. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024155721-X9DV22CXGT78XL8K5RRL/FIgure2c.png Philosophy - Figure 2c The compression wave continues through ball 2 and into ball 3, transferring kinetic energy. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024155913-KVCCHU8SR3FDLOSYV8JS/FIgure2d.png Philosophy - Figure 2d As the compression moves through ball 3 into ball 4, the kinetic energy is transferred once more. In this case, however, ball 4 also acquires velocity almost equal⁹ to that originally possessed by ball 1, as in a Nweton's cradle. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024160146-HJQ5AHS3S75C9JZCL2PV/FIgure2e.png Philosophy - Figure 2e Here we have added ball 5, which is not in direct contact with ball 4. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024158516-MPKDWIQZHKCZ4NQGE06M/FIgure2f.png Philosophy - Figure 2f Ball 4 translates its kinetic energy and lateral velocity to ball 5. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407162530580-G2IGVY3ES3K1E2NTRKEP/FIgure2g.png Philosophy - Figure 2g Figures g through l depict the bowling balls collected into various simple and complex formal systems, with the systems and their components labeled. Here ball1, (the exhiform) with nonzero lateral velocity and kinetic energy approaches balls 2, 3, and 4 (collectively, the obsiform), which have zero lateral velocity and kinetic energy. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407162530716-CMSEC871918MF7GLYQS3/FIgure2h.png Philosophy - Figure 2h Ball 1 transfers kinetic energy to ball 2 of the obsiform in a simple interaction that can be viewed as an independent subformal system. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407162533293-9MRURZT4HO8QC3ZVXBC1/FIgure2i.png Philosophy - Figure 2i A second simple interaction transfers the kinetic energy to ball 3. Note that this can also be viewed as the terminal step in a mediated interaction between balls 1 and 3, where ball 2 is the mediator. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407162532014-ROEPVEZX1GT454EN8SDD/FIgure2j.png Philosophy - Figure 2j Another simple interaction between balls 3 and 4 transfer the kinetic energy from the former to the latter. This however can also be viewed as a complex interaction: one, for example, between balls 1 and 4, mediated by balls 2 and 3. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407162533392-1U4MFZRC5OUFMK3IPUU2/FIgure2k.png Philosophy - Figure 2k Adding a 5th ball, which we can arbitrarily assign to an encompassing metasystem as an obsiform, we can view the entire initial system an exhiform with which the encompassing metasystem is simply interacting. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407162534482-70EJLV3LPEI62JT6QP0W/FIgure2l.png Philosophy - Figure 2l We can, however just as easily view the metasystem as complex, choosing, for example, to view balls 1, 2, and 3 as the exhiform and ball 4 as the mediator. Moreover, we can view ball 1 as the exhiform and balls 2, 3, and 4 as the mediator (not shown). https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024437197-ELD0QWD2SF87A7FERQNN/Figure3.png Philosophy Figure 3 Simple diagram of a transmission event. Some arbitrary form or collection of forms undergo a transformation such that the result is form B, thereby generating a transmission signal. This originates at some position at a time zero—the transmission moment. Form A cannot observe this transformation at time zero, and so B does not (yet) exist with respect to A. At some short time later, (moments indicated by the second lowest red and green dots), the transmission front has expanded outward as a function of time (vertical axis), however A is still outside the transmission cone, and so B is still unobserved by A, and therefore still nonexistent. Then at some later time (moments indicated by the second highest red and green dots) the transmission front reaches A, producing an observation moment in which A is transformed, and with the result that B now exists with respect to A. Note the similarity to a light cone, which is, in fact, a type of transmission cone: one in which light constitutes the mediating signal. Note however transmissions cones have the ability to incorporate "holes," a property not strictly exhibited by light cones. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024572116-AYMF8X1M8G3XNIJ6P56B/Figure4a.png Philosophy - Figure 4a A massive fast-moving object on a collision course with the Sun, traveling along a trajectory such that the Sun blocks the Earth's view of it. This creates a transmission shadow within the transmission cone of the Sun's light interacting with the massive fast moving object in which the earth is situated. Therefore, nothing on the Earth has any interaction with the massive fast-moving object, and so it does not (yet) exist with respect to the earth. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024571788-8QY5NUQVRXS0Z57T77W4/Figure4b.png Philosophy - Figure 4b As the object draws closer to the Sun it's path is curved by the Sun's gravity, such that the Earth remains in its transmission shadow. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024577867-M0WN0ZUREH22NC2J3MWD/Figure4c.png Philosophy - Figure 4c The massive fast-moving object impacts the sun, causing a new transmission signal emanating from the Sun itself—i.e., the sun has been transformed, and this transformation is observable by the Earth by means of an interaction mediated by a burst of solar radiation. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024575843-HU527ME8GBVKE96CG3LU/Figure4d.png Philosophy - Figure 4d As the transmission signal expands outward at the speed of light, the transmission front and transmission cone are more easily recognizable. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024585074-8ZZP2PGZ64Y6ZYK4NPRZ/Figure4e.png Philosophy - Figure 4e Even 8 minutes after the interaction between the massive fast-moving object and the Sun, the transmission front has not yet reached the Earth, and so there is no effect of the event on the Earth or anything on it. Therefore the massive fast-moving object is still completely undetectable by the Earth in any way, and so the object still does not (yet) exist with respect to the Earth. It does, however, exist with respect to the Sun. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407024586743-3KMWZXEXT7XMNOK3VQ1V/Figure4f.png Philosophy - Figure 4f The transmission front reaches the Earth, and instantly the Earth observes the collision. In this way the massive fast-moving object is finally observed by the Earth (albeit, still not visually), and so the object now materializes into existence with respect to the Earth. https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407177951126-Q3G6XZ3JLL0XOZ8U8WYT/Equation37.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1408215694685-6KMODGUTBZ3FVS6P481K/Equation38.png Philosophy https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1407179431341-QSN7PLQOI4GAE7U6T17I/Equation39.png Philosophy http://chrissaffran.com/home daily 1.0 2023-07-27 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1401913207977-E8KBOZ6NXDB3LJIUJH8P/Chris_Saffran.png Home "Cause and effect, means and ends, seed and fruit, cannot be severed; for the effect already blooms in the cause, the end pre-exists in the means, the fruit in the seed." –Emerson http://chrissaffran.com/about daily 0.75 2026-02-23 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1565815193986-F49FH84W97HIFQ0KSIFV/Medscape_ih_190726_christian_saffran_lab_work_690x485.jpg About Me - Medscape article Med Student Recalls Being Kidnapped and Thrown Into a Trunk by Leslie Kane August 13, 2019 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1565814560671-T3E3TDP9OIXXXZVQ7USZ/Cornell_Chris_7262016.jpg About Me - Cornell Alumni Magazine article Early Detection - Former undercover cop Christian Saffran applies his investigative skills toward earning an MD-PhD by Beth Saulnier May/June 2017 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1492668384217-28Y050G9A9RT92FEIO3J/IMG_0644.JPG About Me - New York Times article Ex-Detective’s New Assignment: Investigating the Science of the Brain by Jim Dwyer August 16, 2016 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1492668111298-34SZACFDOL3WBQO3MZCS/IMG_0648.JPG About Me - Cornell Chronicle article At 45, ex-detective shifts investigation skills to medicine by Timothy Malcolm August 17, 2016 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1492667677120-0HPFPUTC21ZLF7L51BY4/IMG_0647.JPG About Me - ABC News interview Former NYPD officer becoming doctor, all despite a learning disability Interview by Kemberly Richardson Aired August 31, 2016 http://chrissaffran.com/science daily 0.75 2025-08-16 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/077bcfd7-f7b7-4e74-bab9-13e79ad2366d/Untitled.png Scientific Research and Writing - Make it stand out Alignment of FAN1 MIP-box docking predictions with the MLH1 MIP-interacting site in the presence of MLH3, PMS2, and MLH1. http://chrissaffran.com/a-discourse-on-ten-essential-musical-works daily 0.75 2023-10-24 https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403125951319-LSJ7IMUU61V1ZEV5R61M/Equation1.png A Discourse on Ten Essential Musical Works https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403126220271-IYRV1AFC2F3QUJMMSPC6/Equation2.png A Discourse on Ten Essential Musical Works https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403126249682-R14K4U115HFX9HLQZ4OT/Figure1.png A Discourse on Ten Essential Musical Works https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403126805500-JEW6OKLIQE1A9JGBV4FH/image-asset.png A Discourse on Ten Essential Musical Works https://images.squarespace-cdn.com/content/v1/538f7b50e4b0009f317c3819/1403127003002-EPZREUFBNB4J2WXT31W8/image-asset.png A Discourse on Ten Essential Musical Works http://chrissaffran.com/thesis-references daily 0.75 2014-06-18