Lissafi na Analog da Wakilci: Bincike na Falsafa

Teburin Abubuwan Ciki

1. Gabatarwa

Kamar agogo da rikodin sauti, lissafi yana zuwa cikin nau'ikan dijital da analog. Idan aka kwatanta da lissafin dijital, an yi watsi da lissafin analog a cikin wallafe-wallafen falsafa, wanda ya haifar da fahimtar kuskure game da yanayinsa da iyawarsa. Ra'ayin da aka karɓa cewa lissafin analog yana da mahimmanci game da ci gaba ba daidai ba ne a zahiri, kamar yadda bincike mai zurfi na tarihin misalan kwamfutocin analog marasa ci gaba ya nuna.

Wannan takarda tana haɓaka cikakkiyar lissafi na lissafin analog dangane da wani nau'in wakilcin analog na musamman wanda ya ƙunshi duka aiwatarwa masu ci gaba da na daban-daban. Fahimtar lissafin analog yana da mahimmanci don cikakkiyar fahimtar falsafar lissafi gabaɗaya kuma yana da muhimman tasiri ga bayanan lissafi a kimiyyar kwakwalwa ta zamani da kimiyyar fahimi.

2. Kwamfutocin Analog

Wannan sashe yana bincika nau'ikan kwamfutocin analog daban-daban daga ƙarni na 20, yana nuna bambancin hanyoyin lissafin analog.

2.1 Kwamfutocin Analog na Injina

Kwamfutocin analog na injina suna amfani da abubuwan jiki kamar gears, levers, da cams don yin lissafi. Misalai sun haɗa da na'urar bincike daban-daban da Vannevar Bush ya haɓaka a MIT, wanda zai iya warware hadaddun lissafin bambance-bambance ta hanyar haɗin kai na injina.

2.2 Kwamfutocin Analog na Lantarki

Kwamfutocin analog na lantarki suna amfani da masu ƙara aiki, masu tsayayya, da masu ƙarfi don ƙirar ayyukan lissafi. An yi amfani da waɗannan tsare-tsare sosai don kwaikwayon ainihin lokaci na tsarin jiki a aikin injiniya da aikace-aikacen kimiyya.

2.3 Abubuwan Analog Marasa Ci Gaba

Sabanin ra'ayin da aka karɓa, yawancin kwamfutocin analog sun haɗa da abubuwan da ba su ci gaba ba. Misalai sun haɗa da kwamfutocin analog na tushen relay da tsarin da ke amfani da masu ƙarfin dijital, suna nuna cewa rashin ci gaba yana dacewa da lissafin analog.

3. Me Ya Sa Lissafin Analog Ya Zama 'Analog' da 'Lissafi'

Wannan sashe yana haɓaka tsarin ka'idar asali don fahimtar lissafin analog.

3.1 Analog a matsayin Ci Gaba

Ra'ayin gargajiya yana daidaita lissafin analog da ci gaba, amma wannan ya kasa yin la'akari da misalan tarihi na lissafin analog na daban-daban. Ci gaba ba dole ba ne kuma bai isa ba don lissafin analog.

3.2 Analog a matsayin Haɗin Kai

Lissafin Lewis-Maley ya ba da shawarar cewa wakilcin analog ya ƙunshi haɗin kai na tsari tsakanin wakiltar da kaddarorin da aka wakilta. Wannan hanya tana ɗaukar duka aiwatarwa masu ci gaba da na daban-daban.

3.3 Me Ya Sa Ya Zama 'Analog'

Lissafin analog da gaske ya ƙunshi wakilcin analog, inda jihohin lissafi ke ɗauke da alaƙar analog na tsari ga abin da suke wakilta, ba tare da la'akari da ko waɗannan alaƙun suna ci gaba ko daban-daban ba.

3.4 Me Ya Sa Ya Zama 'Lissafi'

Lissafi ya ƙunshi sarrafa wakilci bisa tsari bisa ga dokoki. Lissafin analog yana gamsar da wannan ma'anar ta hanyar alaƙar wakilci na halayya da dokokin canji.

4. Tambayoyi da Ƙin yarda

Wannan sashe yana magance ƙalubalen da za a iya fuskawa ga lissafin da aka gabatar.

4.1 Ashe Wadannan Ba Kwamfutocin Gauraya Ba Ne?

Kasancewar abubuwa daban-daban a cikin kwamfutocin analog ba lallai ba ne su sanya su zama tsarin gauraya. Yawancin tsarin analog kawai suna haɗa abubuwan daban-daban yayin da suke kiyaye alaƙar wakilcin analog.

4.2 Ashe Wannan Daidai Lissafi Ne?

Tsarin da suka cika ma'auni na sarrafa wakilci na tsari sun cancanci zama tsarin lissafi, ba tare da la'akari da cikakkun bayanai na aiwatarwa ba.

4.3 Lissafin Lewis-Maley Yana Da Matsala

Duk da cewa lissafin Lewis-Maley yana da iyakoki, yana ba da tsarin da ya fi dacewa don fahimtar lissafin analog fiye da hanyoyin tushen ci gaba.

5. Tunani na Karshe

Fahimtar lissafin analog yana da mahimmanci ga cikakkiyar lissafin falsafar lissafi kuma yana da muhimman tasiri ga bayanan lissafi a kimiyyar fahimi da kimiyyar kwakwalwa. Lissafin tushen wakilcin da aka haɓaka a nan yana ba da madaidaicin siffanta lissafin analog fiye da ra'ayin tushen ci gaba na gargajiya.

6. Bincike na Asali

Takardar Maley ta wakilci gagarumar gudummawa ga falsafar lissafi ta hanyar ƙalubalantar daidaitawar lissafin analog da ci gaba na daɗe. Bincikensa ya nuna cewa bambanci na asali tsakanin lissafin analog da dijital ba ya cikin ci gaba da bambanci, amma a cikin yanayin wakilci. Wannan hasashe ya yi daidai da sabon aiki a kimiyyar lissafin kwakwalwa, kamar bincike daga Aikin Blue Brain, wanda ke nuna cewa lissafin jijiyoyi sau da yawa yana amfani da dabarun analog-dijital gauraye waɗanda ba su dace da rukunan gargajiya ba.

Lissafin tushen wakilcin da Maley ya haɓaka yana da muhimman tasiri ga fahimtar lissafin halitta. Kamar yadda aka lura a cikin bincike daga Cibiyar Kimiyyar Kwakwalwa ta Allen, tsarin jijiyoyi sau da yawa yana amfani da wakilcin analog don sarrafa azanci yayin amfani da ƙarin wakilci daban-daban don sarrafa alama. Wannan hanya ta gauraya tana ƙalubalantar tsarin fahimi na dijital kawai kuma tana nuna cewa cikakkiyar fahimtar lissafin jijiyoyi yana buƙatar lissafin duka bangarorin analog da dijital.

Sukar Maley na ra'ayin ci gaba yayi daidai da abubuwan da suka faru a cikin kwamfutocin analog na zamani, musamman a aikin injiniyan neuromorphic. Bincike daga cibiyoyi kamar ƙungiyar Electronic Vision(s) ta Jami'ar Heidelberg ya nuna cewa tsarin analog na zamani, kamar dandalin neuromorphic na BrainScaleS, sun haɗa da duka haɓakar ci gaba da sadarwar tushen abubuwan da suka faru. Waɗannan tsare-tsaren suna cimma ingantaccen kuzari yayin yin hadaddun lissafi, suna goyan bayan da'awar Maley cewa ba za a iya rage lissafin analog zuwa ci gaba kawai ba.

Tasirin falsafar ya shimfiɗa zuwa muhawarar bayanin lissafi a kimiyyar fahimi. Idan Maley yana da gaskiya, to bayanan lissafi na fahimi ba sa buƙatar yin alkawari ko dai tsarin dijital kawai ko kuma tsarin ci gaba kawai. Wannan yana buɗe sarari don ƙarin lissafi masu ma'ana waɗanda suka fi dacewa da gauraye dabarun lissafi da ke bayyane a cikin tsarin halitta. Kamar yadda bincike daga Sashen Kwakwalwa da Fahimi na MIT ya nuna, kwakwalwa mai yiwuwa tana amfani da dabarun lissafi da yawa lokaci guda, tare da daban-daban da'irorin jijiyoyi waɗanda aka inganta don nau'ikan lissafi daban-daban.

7. Cikakkun Bayanai na Fasaha

Tushen lissafi na lissafin analog ana iya bayyana shi ta hanyar lissafin bambance-bambancen da ke ƙirar ci gaba mai ci gaba:

$$\frac{dx}{dt} = f(x, u, t)$$

inda $x$ ke wakiltar masu canjin yanayi, $u$ yana wakiltar siginonin shigarwa, kuma $t$ yana wakiltar lokaci. Don abubuwan analog daban-daban, ana iya ƙirar lissafin ta amfani da lissafin bambanci:

$$x[n+1] = g(x[n], u[n])$$

Babban alaƙar wakilci a cikin lissafin analog ya ƙunshi haɗin kai na tsari:

$$R(s_1, s_2) \leftrightarrow C(r_1, r_2)$$

inda $R$ ke wakiltar alaƙa tsakanin jihohin lissafi kuma $C$ yana wakiltar alaƙa tsakanin abubuwan da aka wakilta.

8. Sakamakon Gwaji

Gwaje-gwajen tarihi tare da kwamfutocin analog sun nuna iyawar lissafinsu:

9. Aiwar Code

Duk da yake ana aiwatar da lissafin analog a cikin kayan aiki, ga simintin Python na na'urar haɗin analog:

import numpy as np

class AnalogIntegrator:
    def __init__(self, initial_condition=0.0, time_step=0.01):
        self.state = initial_condition
        self.dt = time_step
    
    def update(self, input_signal):
        # Haɗin kai na Euler: x(t+dt) = x(t) + input*dt
        self.state += input_signal * self.dt
        return self.state
    
    def reset(self, new_state=0.0):
        self.state = new_state

# Misalin amfani
integrator = AnalogIntegrator()
input_signal = lambda t: np.sin(t)  # Siginar shigarwa

# Kwaikwayi haɗin kai
for t in np.arange(0, 10, integrator.dt):
    output = integrator.update(input_signal(t))
    print(f"Lokaci: {t:.2f}, Fitowa: {output:.4f}")

10. Aikace-aikacen Gaba

Lissafin analog yana fuskantar sabon sha'awa a yankuna da yawa:

• Lissafin Neuromorphic: Tsarin da aka yi wahayi da kwakwalwa ta amfani da abubuwan analog don aikace-aikacen AI masu ƙarancin wutar lantarki
• AI na gefe: Masu sarrafa analog don ingantaccen hujja a cikin na'urorin IoT
• Lissafin Kimiyya: Tsarin analog na musamman don warware wasu azuzuwan na musamman na lissafin bambance-bambance
• Kwaikwayon Quantum: Masu kwaikwayon quantum na analog don ƙirar hadaddun tsarin quantum

Hanyoyin bincike sun haɗa da haɓaka gine-ginen analog-dijital gauraye waɗanda ke amfani da ƙarfin duka hanyoyin biyu da ƙirar ƙirar ka'idodi masu zurfi don fahimtar dabarun lissafi gauraye.

11. Nassoshi

1. Maley, C. J. (mai zuwa). Lissafi na Analog da Wakilci. Jaridar Biritaniya don Kimiyyar Falsafa.
2. Goodman, N. (1968). Harsunan Fasaha: Hanya zuwa Ka'idar Alamomi. Bobbs-Merrill.
3. Piccinini, G. (2015). Lissafin Jiki: Lissafin Injiniya. Jami'ar Oxford Press.
4. Lewis, D. (1971). Analog da Dijital. Noûs, 5(3), 321-327.
5. Mead, C. (2020). Yadda Muka Ƙirƙira Aikin Injiniyan Neuromorphic. Lantarki na Yanayi, 3(7), 434-435.
6. Markram, H. (2006). Aikin Blue Brain. Nazarin Nazarin Kwakwalwa na Yanayi, 7(2), 153-160.
7. Davies, M. da saur. (2018). Loihi: Na'urar Lissafi ta Neuromorphic da yawa tare da Koyo akan Chip. IEEE Micro, 38(1), 82-99.