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MATH AND LOVE ARE PRETTY SIMILAR

Math	Love
1 Understand the problem	1 Understand the problem
2 Identify potential techniques	2 Identify potential partners
3 Choose the best one	3 Choose the best one
4 Implement and check answer	4 Implement and check answer

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PREFACE: THERE ARE 4 (OR MORE?) PERMUTATIONS TO “BOY SEEKS GIRL”. FOR SIMPLICITY, I WILL JUST DISCUSS #1. THE MATH IS THE SAME WITH # 2-4. �PLEASE EXCUSE THE BLATANT SEXISM.�

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2: IDENTIFY POTENTIAL PARTNERS WITH�THE GOLDEN RATIO, Φ

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DaVinci’s Salvadore Mundi; the Parthenon

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MEET JADE

2019

Would you rate her an 8 or 9? A 6 or 7?

How you can be sure?

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MEASURE JADE

2019

Face length, face width, dist bet eyes, nose width, mouth width, lips to chin, ear length.

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JADE, MATHEMATICALLY

2019

Six Φ Measurements
Face length / width
Mouth width / interocular
Mouth width / nose width
Lips to chin / interocular
Lips to chin / nose width
Ear length / nose width
Average

Ratio
1.433
1.125
1.184
1.200
1.263
1.526
1.289

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A FEW CELEBRITIES

2019

Six Φ Measurements
Barbie
Scarlett Johansson
Taylor Swift
Lupita Nyong’o
Ryan Gosling
Brad Pitt
JT (Your speaker)

% Dev from Φ
-0.3%
-2.5%
-2.9%
-3.3%
-3.4%
-3.9%
-9.7%

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Φ RATIO OF NON-CELEB FACE MEASUREMENTS vs �SURVEY RATINGS, r = .47

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PLASTIC SURGEONS & MAKEUP ARTISTS KNOW Φ

2019

Anastasia Soare patented eyebrow stencils with (SP-HP)/(HP-EP) = Φ. (Phi brows!)

SP=inner starting pt, HP=high pt, EP=end pt

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JADE’s PHI BROWS

2019

(SP-HP)/(HP-EP) = 1.621 ≈ Φ. Also with near Φ eyebrows is Julianna Margulies The Good Wife.

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3: CHOOSING THE BEST PARTNER: Barbara Bush: “I married the first man I ever kissed.” OPTIMAL?

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CHOOSING THE BEST ONE:

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1. You are at a singles bar with a large number of available, attractive single women.

2. You want to maximize your chance of walking out the door with the best woman, however you decide best; but they are all attractive.

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CHOOSING THE BEST ONE, CONTINUED:

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3. You need to chat with a woman to determine your preference.

4. You chat in random order, one at a time.

5. After chatting, you must make a decision. If you decide yes, she accepts, and you are done. If you decide no, she is gone forever, and you chat with the next woman.

What is your optimal strategy? You want to maximize your chance of walking out the door with the best woman.

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OPTIMAL STRATEGY: �LOOK, THEN LEAP

2019

If you select first person, you get the best 1/n of the time.

If you select the last person, you get the best 1/n of the time.

Optimal Strategy: Look, Then Leap. Look at the first r-1, then leap at the next applicant who is better than everyone you have seen so far.

But which value of r-1 ?

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LOOK AT THE FIRST 37%; CHOOSE NONE; THEN CHOOSE THE NEXT WOMAN BETTER THAN EVERYONE �YOU HAVE SEEN SO FAR

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EXAMPLE: Let n=5. �37% * 5 = 2 (rounded). �∴ LOOK AT 2, THEN LEAP.

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Assume true preference is 1<2<3<4<5; 1=best.

Case 1: Interview #3, then #4, then #2; leap at #2, because 2 < min{3,4}; but #2 is not the best.

Case 2: Interview #5, then #1, then #2, then #3, then #4; now you must leap at #4, but #4 is not the best.

Test all 5! permutations. This strategy selects the best 43.33% of time.

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REJECT 1^st r-1, THEN TAKE BEST

2019

# Applicants	Take Best After r-1 =	Prob. of Getting Best
3	1	50%
4	1	45.83%
5	2	43.33%
10	3	39.87%
50	18	37.43%
100	37	37.10%
∞	37%	1/e

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This strategy also works with applicants over a lifetime. If your dating life expectancy is uniform from age 18 to 40, then 37% *(40-18) + 18 ≈ 26.1 is the age to leap.

This problem is called The Secretary (hiring) Problem in the literature, but also applies to looking for a parking space, an apartment, selling a house, etc. Widely discussed, including modifying assumptions.

2019

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LOVE IS IRRATIONAL

We used irrational numbers Φ and e.

More irrationals from Heart parametric equations:

x = 16(sin(t))³

y = 13cos(t) – 5 cos(2t) – 2 cos(3t) – cos(4t)

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WELL, I DID NOT USE THE 37% RULE …�

2019

References:

Christian, B. and Griffiths, T. (2016). Algorithms to live by. Henry Holt and Company. New York.

Ferguson, T. (1989). Who solved the secretary problem? Statistical Science 4 (3). 282-289.

Fry, H. (2015). The mathematics of love. Simon & Schuster, Inc. New York.

Gilbert, J. and Mosteller, F. (1966). Recognizing the maximum of a sequence. Journal of the American Statistical Association. 61(313). 35-73.

Meisner, G. (2018). The golden ratio: the divine beauty of mathematics. Race Point Publishing.

Schmid, K., Marx, D., Samal, A. (2008). Computation of a face attractiveness index based on neoclassical canons, symmetry, and golden ratios. CSE Journal Articles. 92. 2710-2717.

Soare, A. Method of shaping eyebrows. (2015). US Patent No. 9210989 B2. https://patentimages.storage.googleapis.com/4e/91/e9/aa1c58792972cc/US9210989.pdf

References:

Christian, B. and Griffiths, T. (2016). Algorithms to live by. Henry Holt and Company. New York.

Ferguson, T. (1989). Who solved the secretary problem? Statistical Science 4 (3). 282-289.

Fry, H. (2015). The mathematics of love. Simon & Schuster, Inc. New York.

Gilbert, J. and Mosteller, F. (1966). Recognizing the maximum of a sequence. Journal of the American Statistical Association. 61(313). 35-73.

Meisner, G. (2018). The golden ratio: the divine beauty of mathematics. Race Point Publishing.

Schmid, K., Marx, D., Samal, A. (2008). Computation of a face attractiveness index based on neoclassical canons, symmetry, and golden ratios. CSE Journal Articles. 92. 2710-2717.

Soare, A. Method of shaping eyebrows. (2015). US Patent No. 9210989 B2. https://patentimages.storage.googleapis.com/4e/91/e9/aa1c58792972cc/US9210989.pdf