oQHmK2 j- Abbm2 k

G2ii2`b �M/ LQi2b

k. SmxxH2 oBbm�HBx�iBQMb Q7 "QQH2�M
6Q`KmH�2
1`B+ >QHHQr�v
.PA, RyXjjyR9fBbbMXke9y@8e8kXjXkX?QHHQr�vXR

"�+F;`QmM/

AM i?2 +QKT�`BbQM #2ir22M ?mK�M �M/ +QKTmi�iBQM�H BMi2HHB@
;2M+2- Q7i2M iBK2b i?2 +QKT�`BbQM Bb MQi bi`�B;?i7Q`r�`/ #2@
+�mb2 ?mK�Mb +�M TQbb2bb /QK�BM FMQrH2/;2 BM�++2bbB#H2 iQ
i?2 T`Q;`�K i?2v �`2 +QKT2iBM; rBi?X hQ T`QpB/2 � H2p2H TH�v@
BM; }2H/- Bi Bb ?2HT7mH iQ ?�p2 ?mK�Mb �M/ +QKTmi2`b +QKT2i2
BM � /QK�BM r?2`2 #Qi? bi�`i rBi? 2[m�H /QK�BM FMQrH2/;2-
�M/ i?2 /QK�BM Bb r2HH mM/2`biQQ/X

PM2 bm+? /QK�BM Bb #QQH2�M 7Q`KmH�2X h?2b2 7Q`KmH�2 �`2
b2ib Q7 #QQH2�M p�`B�#H2b i?�i �`2 +QK#BM2/ rBi? i?2 �L.
U!V- P_ U"V- �M/ LPh U¬V HQ;B+�H QT2`�iQ`bX 1�+? #QQH2�M
7Q`KmH� K�Tb iQ � bT2+B}+ i`mi? i�#H2X � i`mi? i�#H2 Bb i?2
`2bmHi Q7 i`vBM; �HH i?2 TQbbB#H2 T2`Kmi�iBQMb Q7 p�Hm2 �bbB;M@
K2Mib �TTHB2/ iQ i?2 7Q`KmH� �M/ i?2 `2bmHiBM; i`mi? p�Hm2b
7`QK i?2 7Q`KmH�X h?2b2 7Q`KmH�2 �`2 r2HH mM/2`biQQ/- �M/
+�M #2 b2H2+i2/ bQ i?2 ?mK�M �M/ �H;Q`Bi?K ?�p2 MQ bT2+B�H
�/p�Mi�;2 Qp2` i?2 Qi?2` BM i2`Kb Q7 /QK�BM FMQrH2/;2- Q`
2p2M i?2 �H;Q`Bi?K ?�b �M �/p�Mi�;2 BM Q`/2` iQ K�F2 i?2
bm++2bb Q7 i?2 ?mK�M 2p2M KQ`2 bB;MB}+�MiX

h?2 `2�bQM r?v i?2 /QK�BM Q7 #QQH2�M 7Q`KmH�2 Bb � ;QQ/
/QK�BM 7Q` +QKT�`BM; ?mK�M �M/ +QKTmi�iBQM�H BMi2HHB;2M+2 Bb
#2+�mb2 i?2`2 �`2 K�Mv T`Q#H2Kb /2�HBM; rBi? i?2b2 7Q`KmH�2
i?�i �`2 LS +QKTH2i2 �M/ ?�`/2`X hrQ bm+? 2t�KTH2b �`2,

RX /2i2`KBMBM; B7 � T�`iB+mH�` 7Q`KmH� +�M 2p�Hm�i2 iQ i`m2-
�M LS +QKTH2i2 T`Q#H2K

kX BMp2`iBM; � i`mi? i�#H2 iQ /2`Bp2 i?2 b?Q`i2bi #QQH2�M 7Q`@
KmH� i?�i `2T`2b2Mib i?2 i�#H2- �M LS ?�`/ T`Q#H2K

A7 ?mK�Mb +�M QmiT2`7Q`K +QKTmi2`b r?2M 7�+2/ rBi? �M LS

+QKTH2i2 T`Q#H2K- i?2M BMbQ7�` �b LS Bb MQi i?2 b�K2 �b S- r2
+�M /2i2`KBM2 i?�i ?mK�Mb �i H2�bi QmiT2`7Q`K /2i2`KBMBbiB+
hm`BM; K�+?BM2b- �M/ +QMb2[m2MiHv ?mK�M BMi2HHB;2M+2 Kmbi
#2 QM i?2 H2p2H Q7 MQM/2i2`KBMBbiB+ hm`BM; K�+?BM2bX

>Qr2p2`- i?2 T`Q#H2K rBi? i?Bb /QK�BM �b 7�` �b ?mK�Mb �`2
+QM+2`M2/ Bb i?�i i`mi? i�#H2b �`2 ?�`/ iQ pBbm�HHv T`Q+2bbX
q2 r�Mi iQ +QK2 mT rBi? � i2bi i?�i ?mK�Mb /QMǶi M22/
� S?. iQ mM/2`bi�M/X aQK2i?BM; pBbm�H Bb B/2�H- �b pBbm�H
`2T`2b2Mi�iBQMb +�M #2 mM/2`biQQ/ #v � ?mK�M rBi? � HQr2`
H2p2H Q7 2tT2`iBb2X AM i?Bb T�T2`- A T`2b2Mi � k. pBbm�HBx�iBQM Q7
#QQH2�M 7Q`KmH�2 i?�i �HHQr ?mK�Mb iQ pBbm�HHv +QKT`2?2M/
i`mi? i�#H2b Q7 mT iQ Rk #QQH2�M p�`B�#H2bX

A #2;BM #v 2tTH�BMBM; ?Qr iQ `2T`2b2Mi #Bibi`BM;b Ub2`B2b Q7 Rb
�M/ ybV rBi? � #QQH2�M 7Q`KmH�2- /m2 iQ i?2 bi`�B;?i7Q`r�`/
Q#b2`p�iBQM i?�i 2p2`v #Bibi`BM; +�M #2 `2T`2b2Mi2/ #v � i`mi?
i�#H2X

"Bibi`BM;b �b "QQH2�M 6Q`KmH�2

"Bibi`BM;b ! +�M #2 2tT`2bb2/ �b HQ;B+ 2tT`2bbBQMb rBi?
#log2 ( |! |)$ #BM�`v p�`B�#H2bX 6Q` 2t�KTH2- rBi? 7Qm` HQ;B+ p�`B@
�#H2b "1-"2-"3- �M/ "4 r2 +�M /2b+`B#2 �HH #Bibi`BM;b Q7 H2M;i?
Re rBi? HQ;B+ 2tT`2bbBQMbX

hQ ;2M2`�i2 � #Bibi`BM; 7`QK � T�`iB+mH�` HQ;B+ 2tT`2bbBQM- r2
2p�Hm�i2 i?2 2tT`2bbBQM 7Q` �HH p�`B�#H2 �bbB;MK2Mib- �M/ Q`/2`
i?2 `2bmHib H2tB+Q;`�T?B+�HHvX

>2`2 Bb �M 2t�KTH2 rBi? k p�`B�#H2b- "1 �M/ "2- �M/ i?2 #QQH2�M
7Q`KmH� "1 " ¬"2X

RX 1p�Hm�i2 i?2 2tT`2bbBQM 7Q` �HH �bbB;MK2MibX

tR tk "1 " ¬"2
y y R
y R y
R y R
R R R

https://dx.doi.org/10.33014/issn.2640-5652.3.2.holloway.1


jy G2ii2`b �M/ LQi2b

kX P`/2` i?2 `2bmHib H2tB+Q;`�T?B+�HHvX
h?2 H2tB+Q;`�T?B+ Q`/2` Q7 i?2 �bbB;MK2Mib Bb,

U�V y y
U#V y R
U+V R y
U/V R R

aQ- i�FBM; i?2 `2bmHib Q7 i?2 #QQH2�M 7Q`KmH� BM i?Bb Q`/2`-
i?2 #Bibi`BM; Bb, R- y- R- RX

A7 r2 BK�;BM2 i?2 �#Qp2 T`Q+2bb �b � ;2M2`�iBM; 7mM+iBQM- r2
+�M H�#2H i?2 ;2M2`�iBM; 7mM+iBQM �b #X A7 r2 �TTHv # iQ �
#QQH2�M 7Q`KmH�- i?2M Bi ;2M2`�i2b i?2 +Q``2bTQM/BM; #Bibi`BM;X
6`QK Qm` T`2pBQmb 2t�KTH2- # ("1 " ¬"2) = 1011X

� 7Qm` p�`B�#H2 2t�KTH2-

# (
("1 ! "2 ! ¬"3)
" ("1 ! "3 ! ¬"4)
" (¬"1 ! ¬"2 ! ¬"3 ! "4)

) = 0001010110010000.

L2ti- A i�HF �#Qmi ?Qr iQ ;2M2`�i2 � #QQH2�M 7Q`KmH� `�M@
/QKHvX h?Bb Bb BKTQ`i�Mi- #2+�mb2 T2` Qm` Q`B;BM�H [m2bi iQ
}M/ � T`Q#H2K /QK�BM iQ +QKT�`2 ?mK�M �M/ +QKTmi2` T2`@
7Q`K�M+2- r2 M22/ � T`Q#H2K /QK�BM i?�i Bb H�`;2` i?�M +�M }i
rBi?BM � T?vbB+�H +QKTmi2`X qBi? Rk #QQH2�M p�`B�#H2b- i?2`2
�`2 2212 TQbbB#H2 mMB[m2 7Q`KmH�2- r?B+? Bb KQ`2 i?�M +�M }i
rBi?BM i?2 T?vbB+�H mMBp2`b2X h?�i #2BM; b�B/- r2 rBHH QMHv
/2�H rBi? � bm#b2i Q7 i?2b2 7Q`KmH�2- bBM+2 KQbi �`2 `�M/QK-
�M/ �`2 MQi mb27mH 7Q` i?2 bQ`i Q7 TmxxH2 i?�i +�M /BbiBM;mBb?
r?2i?2` ?mK�M BMi2HHB;2M+2 i`�Mb+2M/b +QKTmi�iBQM�H BMi2HHB@
;2M+2X

_�M/QKHv a�KTHBM; .BbDmM+iBp2
LQ`K�H 6Q`K U.L6V 6Q`KmH�2

� .L6 7Q`KmH� Bb �M P_ Q7 �L. i2`Kb- bm+? �b ($1 !¬$2) "
(¬$1 ! $2) iQ `2T`2b2Mi $1 % $2X

h?2 TmxxH2b �`2 ;2M2`�i2/ #v `�M/QKHv b�KTHBM; � .L6 7Q`@
KmH� % 7`QK 7Q`KmH�2 rBi? � b2i MmK#2` Q7 p�`B�#H2b &- i2`Kb
'- �M/ K�tBKmK i2`K bBx2 (X h?2 `�M/QK b�KTHBM; Q7 .L6
7Q`KmH�2 Bb +HQb2 iQ mMB7Q`K- rBi? i?2 2t+2TiBQM i?�i 7�Hb2
i2`Kb �`2 }Hi2`2/ QmiX >2`2 Bb ?Qr Bi rQ`FbX

RX h?2 b�KTHBM; T`Q+2bb Bb ;Bp2M i?2 MmK#2` Q7 p�`B�#H2b &-
K�tBKmK HBi2`�Hb T2` i2`K ( �M/ i?2 MmK#2` Q7 i2`Kb 'X

kX 1�+? i2`K Bb `�M/QKHv }HH2/ rBi? HBi2`�HbX

jX � i2`K Bb `2}HH2/ B7 Bib HBi2`�Hb `2bmHi BM � +QMi`�/B+iBQMX

h?2M- � #Bibi`BM; Bb ;2M2`�i2/ 7`QK % mbBM; # ( % )- �b 2tTH�BM2/
2�`HB2`X

LQBb2 +�M #2 �//2/ #v `�M/QKHv ~BTTBM; � +2`i�BM MmK#2` Q7
#Bib )X h?2 2z2+i Q7 �//BM; ) #Bib Q7 MQBb2 Bb iQ BM+`2�b2 i?2
bT�+2 Q7 7Q`KmH�2 #v 2 |! |X

hm`MBM; � "Bibi`BM; AMiQ � SmxxH2

>Qr2p2`- � #Bibi`BM; #v Bib2H7 Bb MQi � TmxxH2 iQ #2 bQHp2/X q2
rQmH/ HBF2 � TmxxH2 rBi? �M 2�bv iQ `2T`2b2Mi bQHmiBQMX PM2
bm+? TmxxH2 Bb iQ }HH BM KBbbBM; #Bib BM i?2 #Bibi`BM;X hQ +`2�i2
i?Bb bQ`i Q7 TmxxH2- � b2i Q7 #Bib * �`2 `2KQp2/ iQ #2 ;m2bb2/X

*QMp2`iBM; i?2 6Q`KmH� iQ k. AK�;2

hQ K�F2 i?2 pBbm�HBx�iBQM 7Q` i?2 ?mK�M- i?2 #Bibi`BM; ;2M2`@
�i2/ #v # ( % ) Bb /BbTH�v2/ �b � k. BK�;2X

h?2 HQ;B+ p�`B�#H2b �`2 bTHBi BMiQ irQ ;`QmTb- �M/ 2�+? ;`QmTǶb
#BM�`v p�Hm2b �`2 +QMp2`i2/ BMiQ BMi2;2`b iQ 7Q`K i?2 +QQ`/B@
M�i2bX

6Q` BMbi�M+2- rBi? 7Qm` p�`B�#H2b r2 ?�p2 irQ ;`QmTb 7Q` i?2
" �M/ + +QQ`/BM�i2bX AX2X " = {$1, $2} �M/ + = {$3, $4}X A7
r2 �bbB;M i?2 p�`B�#H2b �b, $1 = 0, $2 = 1, $3 = 1, $4 = 0- r2
b22 i?�i " �M/ + ;`QmTb +�M `2T`2b2Mi #BM�`v MmK#2`bX AX2X
" = {0, 1} �M/ + = {1, 0}X h?2b2 #BM�`v MmK#2`b �`2 i?2M
+QMp2`i2/ iQ BMi2;2`b- " = 2 �M/ + = 1X

1�+? TQBMi BM i?2 #QQH2�M bT�+2 /2b+`B#2/ #v i?2 7Qm` p�`B�#H2b
?�b �M �bbB;MK2Mi Q7 y Q` R 7`QK % X *QMp2`iBM; i?2 #QQH2�M
bT�+2 iQ � k. ;`�T? �b T`2pBQmbHv /2b+`B#2/- �M/ mbBM; % �b@
bB;MK2Mib iQ }HH BM i?2 ;`�T? r?2`2 y Bb #H�+F �M/ R Bb r?Bi2-
im`Mb i?2 i`mi? i�#H2 BMiQ �M BK�;2X

�b �M 2t�KTH2- b2i % = $2"$3X h?2 HQ;B+ i�#H2 �M/ +QQ`/BM�i2b
�`2 i?2 7QHHQrBM;X



oQHmK2 j- Abbm2 k

k. SmxxH2 oBbm�HBx�iBQMb Q7 "QQH2�M 6Q`KmH�2 jR

$1 $2 t $3 $4 v $2 " $3
y y y y y y y
R y R y y y y
y R k y y y R
R R j y y y R
y y y R y R R
R y R R y R R
y R k R y R R
R R j R y R R
y y y y R k y
R y R y R k y
y R k y R k R
R R j y R k R
y y y R R j R
R y R R R j R
y R k R R j R
R R j R R j R

6B;m`2 R� �M/ 6B;m`2 R# �`2 � `2�HBx�iBQM Q7 i?Bb HQ;B+ i�#H2
+QMp2`i2/ BMiQ � k. BK�;2X AM i?2 H27i T�M2- QM2 #Bi ?�b
#22M `2KQp2/ �M/ `2TH�+2/ rBi? #Hm2- �M/ i?Bb Bb i?2 #Bi iQ #2
;m2bb2/X h?2 `B;?i T�M2 b?Qrb i?2 �Mbr2`X

6B;m`2 k� �M/ 6B;m`2 k# �`2 �MQi?2` TmxxH2 Q7 i?2 b�K2 bBx2-
#mi i?Bb iBK2 rBi? QM2 #Bi Q7 MQBb2 �///2/X h?2 ;2M2`�iBQM
7mM+iBQM 7Q` i?Bb TmxxH2 Bb # ($1 " $2)X

6B;m`2 j�- 6B;m`2 j#- 6B;m`2 9�- �M/ 6B;m`2 9# b?Qr i?2 T`2/B+@
iBQM TmxxH2b ;2M2`�i2/ #v KQ`2 +QKTH2t .L6 7Q`KmH�2- rBi?
�M/ rBi?Qmi MQBb2 �//2/X



jk G2ii2`b �M/ LQi2b

U�V :m2bb i?2 #Hm2 #BiX U#V �Mbr2` iQ TmxxH2X

6B;m`2 R, SmxxH2 rBi? 9 p�`B�#H2bX

U�V :m2bb i?2 #Hm2 #BiX U#V �Mbr2` iQ TmxxH2- MQ MQBb2X

6B;m`2 k, SmxxH2 rBi? 9 p�`B�#H2b �M/ R #Bi Q7 MQBb2X



oQHmK2 j- Abbm2 k

k. SmxxH2 oBbm�HBx�iBQMb Q7 "QQH2�M 6Q`KmH�2 jj

U�V :m2bb i?2 #Hm2 #BibX U#V �Mbr2` iQ TmxxH2X

6B;m`2 j, SmxxH2 rBi? 3 p�`B�#H2bX

U�V :m2bb i?2 #Hm2 #BibX U#V �Mbr2` iQ TmxxH2- MQ MQBb2X

6B;m`2 9, SmxxH2 rBi? 3 p�`B�#H2b �M/ Ry #Bib Q7 MQBb2X


	About This Journal
	The Purpose of the Journal
	Paper Submission Policies
	Other Journal Content

	From the Editors
	Eugenio DarbesioEugenio DarbesioA Corollary of the Conant-Ashby Theorem Applied to Abiogenesis
	Robert SheldonRobert SheldonComets, Water, and Big Bang Nucleosynthesis
	Introduction
	Benefits of a Magnetized Big Bang and Dark Matter Comets
	Consequences of Primordial Comets
	Analysis
	Conclusions
	Acknowledgments

	Robert J Marks IIRobert J Marks IISolution of the Grazing Goat Problem: A Conflict between Beauty and Pragmatism
	Background
	Grazing Goat Problem Solution
	Grazing Goat Problem Inversion
	Final Thought

	Letters and Notes
	Eric Holloway2D Puzzle Visualizations of Boolean Formulae
	Jonathan BartlettThe Products of Hyperreal Series and the Limitations of Cauchy Products
	Tom and Elizabeth SiewertFollowing the Science

	News